il 
 
 i. 
 
 

 of 
 
 
 JVo 
 
 Division 
 
 Range 
 
 Shelf 
 
 Received 
 

HISTORY 
 
 or 
 
 PHYSICAL ASTRONOMY, 
 
 FROM 
 
 THE EARLIEST AGES 
 
 TO 
 
 THE MIDDLE OF THE NINETEENTH CENTURY. 
 
 COMPREHENDING 
 A DETAILED ACCOUNT OF THE ESTABLISHMENT OF 
 
 THE THEORY OF GRAVITATION BY NEWTON, 
 
 AND ITS DEVELOPEMENT BY HIS SUCCESSORS; 
 
 WITH AN EXPOSITION OF THE 
 
 PROGRESS OF RESEARCH ON ALL THE OTHER SUBJECTS OF 
 
 CELESTIAL PHYSICS. 
 
 BY ROBERT GRANT, F.R.A.S. 
 
 LONDON : 
 HENRY G. BOHN, YORK STREET, COVENT GARDEN. 
 

 PREFACE. 
 
 THE main object of the work here submitted to the reader is to exhibit a 
 view of the labours of successive enquirers in establishing a knowledge 
 of the mechanical principles which regulate the movements of the celestial 
 bodies, and in explaining the various phenomena relative to their physical 
 constitution which observation with the telescope has disclosed. It may, 
 perhaps, be desirable to trace out briefly the plan I have pursued in 
 attempting to execute this undertaking. 
 
 The first part of the work, extending to the close of the thirteenth 
 chapter, is devoted to the history of the Theory of Gravitation. In 
 the first and third chapters I have endeavoured to give some account 
 of the immortal discoveries by which Newton established this theory 
 in its utmost generality. The researches of the learned Prof. Eigaud 
 have recently disclosed some interesting details respecting the original 
 publication of the Principia, of which I have not failed to avail myself in 
 the execution of this portion of the work. 
 
 The future history of Celestial Mechanics naturally admits of a division 
 into two distinct periods. The first comprehends the researches of 
 geometers from the time of Newton to the commencement of the nine- 
 teenth century. Towards the close of this period the analytical methods 
 devised for the developement of the Theory of Gravitation had attained a 
 high state of perfection, and the various phenomena which had seemed 
 irreconcilable with its principles, were all satisfactorily accounted for. 
 The second period embraces the further developement of the theory down 
 to the present time. 
 
 The third and following chapters to the ninth inclusive, are devoted to 
 the first of the above-mentioned periods. The third chapter contains an 
 account of the early researches of Euler, Clairaut, and D'Alembert on 
 the Problem of Three Bodies, and of the application of their respective 
 solutions to the lunar theory. The difficulty which for some time at- 
 tended the computation of the movement of the lunar apogee, was at 
 length effectually removed by Clairaut, and the triumph of the Newtonian 
 principles was practically exhibited in the construction of lunar tables by 
 Mayer, which possessed sufficient accuracy to be employed with confidence 
 in the solution of the great Problem of the Longitude. 
 
 It is a curious fact that, in the original edition of the Principia, Newton 
 gave the results of an investigation of the movement of the lunar apogee, 
 which seemed to imply that he had treated the subject by a method of a suf- 
 ficiently comprehensive character. These results were suppressed by him 
 in the second edition, doubtless in consequence of their not exhibiting so 
 
 a 2 
 
*1V PREFACE. 
 
 complete an accordance with observation as was manifest in his other 
 researches on the lunar theory *. That Newton really was in possession of 
 a method adequate to a complete investigation of the subject, is rendered 
 still further probable by the recent researches, of Mr. Adams, who, by the 
 aid of geometrical considerations, analogous to those expounded with so 
 much elegance in the Principia, has obtained results relative to the move- 
 ment of the lunar apogee, which present a complete accordance with 
 observation. 
 
 The fourth chapter is devoted to the early researches of geometers on 
 the perturbations of the planets and the stability of the planetary system. 
 While occupied with the former of these subjects, the illustrious Euler 
 devised a method of investigation which must be regarded as one of the 
 most remarkable in the annals of science. It consisted in regarding the 
 perturbations of a planet as arising from an incessant change in the 
 elements of its elliptic motion. This fertile idea was destined to acquire 
 an immense developement from the labours of succeeding geometers. 
 
 The sublime results which the analytical researches of Lagrange and 
 Laplace have disclosed, relative to the stability of the planetary system, 
 while they have served to invest astronomical science with additional 
 features of interest, are entitled to be classed among the noblest triumphs 
 which the human mind has achieved in the investigation of the laws of 
 the physical universe. The labours of these great geometers, which were 
 of a kindred nature throughout their whole career, are on this occasion 
 more especially interlaced. As some misapprehension appears to have 
 not unfrequently arisen from this circumstance, I have endeavoured, by a 
 careful reference to the volumes of the Academy of Sciences and other 
 original sources, to exhibit the results independently arrived at by each 
 geometer in the course of his researches on the subject, 
 
 The fifth chapter contains an account of the physical explanation of the 
 great inequality in the mean longitudes of Jupiter and Saturn, and of the 
 secular inequality in the mean motion of the Moon, as well as an allusion 
 to several points of minor importance in the Theory of Gravitation. The 
 irregularities in the mean longitudes of Jupiter and Saturn long continued 
 to form an inexplicable enigma to geometers. In vain did Euler employ 
 all the resources of his fertile genius in endeavouring to account for their 
 existence by the principles of the Theory of Gravitation. Equally fruitless 
 was the result of Lagrange's application of his commanding powers of 
 analytical research to the subject. It was reserved for Laplace to detect 
 the true origin of these anomalous phenomena in the mutual action of 
 the two planets. 
 
 Perhaps a still more remarkable result, due to the same geometer, was 
 the explanation of the secular inequality in the mean motion of the Moon. 
 The records of certain eclipses of the Moon observed at Babylon about 
 seven hundred years before the Christian era, when compared with obser- 
 vations of similar phenomena by the Arabian astronomers about the tenth 
 
 * See Appendix IV. 
 
PREFACE. *y 
 
 century, seemed to indicate that the Moon's angular velocity round the 
 Earth was subject to a slow acceleration. This fact was confirmed beyond 
 all doubt by the observations of modern astronomers ; but its existence 
 seemed absolutely irreconcilable with the results to which geometers were 
 conducted by their researches on the Theory of Gravitation. The physical 
 cause of this acceleration continued to escape the analytical scrutinies of 
 Euler, Lagrange, and Laplace, until at length the sagacity of the last- 
 mentioned geometer led to its detection. 
 
 The sixth chapter is devoted to an account of the labours of geometers 
 on the Figure of the Earth, the Precession of the Equinoxes, the 
 Libration of the Moon, and other kindred subjects. By an ingenious 
 application of his researches on the attraction of spheroids, Newton rigor- 
 ously determined the ellipticity of the Earth, upon the supposition of its 
 density being uniform, and of the figure of an oblate spheroid being com- 
 patible with the conditions of equilibrium of a fluid mass. The truth of 
 the last-mentioned supposition was afterwards demonstrated by Maclaurin 
 with all the elegance and rigour of the ancient geometry. With respect to 
 the internal structure of the Earth, the ellipticity deduced from the 
 measurement of arcs of the meridian was totally at variance with the 
 supposition of its homogeneity. It was reserved for Clairaut to determine 
 the ellipticity on the more probable hypothesis of the strata increasing in 
 density towards the centre of the Earth. 
 
 The Precession of the Equinoxes is beyond doubt the most remark- 
 able of all the perturbative effects by which the planetary system is cha- 
 racterised. Its original discovery as a sidereal phenomenon is due to the 
 great astronomer Hipparchus. The explanation of its true character 
 was first given by Copernicus, who shewed that it might arise from a 
 conical motion of the Earth's axis. The question relative to the physical 
 cause of this singular movement continued to be involved in impenetrable 
 mystery, until at length Newton discovered its origin in the disturbing 
 action of the Sun and Moon upon the redundant matter accumulated round 
 the terrestrial equator. The subsequent discovery of the Nutation of the 
 Earth's Axis by Bradley introduced a new cause of complication into 
 the subject. The complete solution of the problem of the Earth's motion 
 round its centre of gravity, by a rigorous application of the principles of 
 Mechanical Science, was reserved for D'Alembert. The subject of the 
 Libration of the Moon, which is noticed in the same chapter, exhibits 
 another striking illustration of the comprehensive character of the Theory 
 of Gravitation in assigning the physical explanation of the various phe- 
 nomena relative to the movements of the celestial bodies. The researches 
 of Newton on this subject were perfected by Lagrange, who succeeded in 
 obtaining results which accorded in a most satisfactory manner with those 
 deduced from observation. 
 
 The seventh and eighth chapters embrace a somewhat detailed history 
 of the theory of Jupiter's satellites. In the seventh chapter I have given 
 an account of the original discovery of these bodies by the illustrious 
 
*V1 PREFACE . 
 
 Galileo, and of the labours of subsequent astronomers in establishing 
 the laws of their complicated movements. The eighth chapter exhibits a 
 view of the researches of geometers, having for their object the explana- 
 tion of these laws by the Theory of Gravitation. Some of the most 
 curious effects of perturbation occur in this beautiful system. The results 
 are mainly due to Lagrange and Laplace. The powerful character of 
 the analysis which Laplace employed in these researches, is remarkably 
 exhibited in the determination of the ellipticity of Jupiter by means of 
 the derangements which the redundant matter accumulated round the 
 equator of the planet occasions in the motions of the satellites. The 
 illustrious geometer even boldly asserted, that the result thus derived 
 from theory was entitled to greater reliance than that obtained by direct 
 measurement with the micrometer ! 
 
 The ninth chapter commences with a brief notice of the labours of 
 geometers on some of the more hidden effects of perturbation. One of 
 the most interesting of these is the gradual diminution of the obliquity 
 of the ecliptic, occasioned by the disturbing action of the planets on 
 the earth. The sublime results arrived at by Lagrange and Laplace, 
 relative to the stability of the planetary system, assure us that such a 
 diminution will not continue indefinitely, but that after a certain limit of 
 obliquity has been attained, the angle contained between the planes of the 
 ecliptic and the equator will then commence to open out. This process 
 will continue until the obliquity attains a certain maximum value, when 
 the increase will be converted again into a diminution, and thus the 
 inclination of the two planes will continually oscillate between fixed 
 limits prescribed by the intensity of the disturbing forces. It follows as 
 a necessary consequence, that the climate of any particular country will 
 not undergo an essential change from this cause, such as would inevitably 
 ensue if the equator and ecliptic were ever to coincide, or to form with 
 each other an angle of ninety degrees. Thus the more profoundly does 
 analysis penetrate into the operations of nature, the more admirable is the 
 harmony which appears to pervade her various arrangements. 
 
 The subject of Comets was one of the severest tests to which the Theory 
 of Gravitation was submitted during the early period of its history. These 
 bodies seemed to be so destitute of any coherent structure, and at the 
 same time so capricious in their movements, that the attempt to make 
 them the groundwork of strict investigation was long considered to be 
 attended with insuperable difficulties. Newton, however, perceived, with 
 characteristic sagacity, that, however evanescent might be the physical 
 constitution of Comets, their material structure would subject them to the 
 influence of the principle of Gravitation ; and, in pursuance of this idea, 
 he framed a theory of their movements, according to which they all 
 revolved in orbits resembling one or other of the conic sections, having the 
 sun in the common focus. The apparition of the great comet of 1 680 fur- 
 nished him with the means of obtaining a complete verification of his theory. 
 By a rigorous discussion of its observed positions he demonstrated incon- 
 
PEEFACE. *yii 
 
 testably that the comet revolved in an orbit which sensibly coincided with 
 a parabola, and that the line joining it and the sun described equal areas 
 in equal times. Halley applied Newton's theory to a vast number of 
 recorded observations of comets, and among the results to which he was 
 led he arrived at the conclusion that the comet of 1682 would again pass- 
 through its perihelion in the year 1758 or 1759. The actual return of 
 this celebrated comet, agreeably to the prediction of Halley, is familiar 
 to every reader. The effects of planetary perturbation were calculated 
 beforehand by Clairaut, who succeeded in fixing the time of return with 
 remarkable precision. This was unquestionably one of the greatest tri- 
 umphs which had yet been achieved in the developement of the Theory of 
 Gravitation. The general theory of the Perturbations of Cometary Bodies 
 was a few years afterwards simplified and improved by Lagrange. 
 
 The ninth chapter closes with a brief allusion to the Mecanique Celeste. 
 The publication of that immortal work forms an important landmark in 
 the history of Physical Astronomy. The Theory of Gravitation, after 
 being subjected to a succession of severe ordeals, from each of which it 
 emerged in triumph, finally assumes an attitude of imposing mnjesty, 
 which repels all further question respecting the validity of its prin- 
 ciples. 
 
 The tenth chapter introduces the second period in the history of the 
 Theory of Gravitation. It commences with an account of the interesting 
 results obtained by geometers, about the beginning of the present century, 
 relative to the variations of the elements of the planetary orbits. The 
 highly-refined method of investigation due originally to the genius of 
 Euler, by which the perturbations of a planet are supposed to arise from 
 a continuous variation of the elements of elliptic motion, was now carried 
 to a state of unexampled perfection by Lagrange, and by the combined 
 labours of that illustrious geometer and Poisson, was rendered applicable 
 to all the great problems of the system of the world. 
 
 After a brief notice of some of the methods employed by modern 
 geometers in their researches on planetary perturbation, the chapter 
 closes with an account of the recent improvements in the lunar theory. 
 The irregularities in the Moon's longitude, which, throughout the greater 
 part of the nineteenth century, continued to occasion great embarrassment 
 to astronomers and mathematicians, finally assumed a definite character, 
 which rendered them a feasible subject of investigation with respect to 
 their physical origin, when the vast mass of the Greenwich observations, 
 extending from 1750 to 1830, were subjected to a comprehensive discus- 
 sion by the present Astronomer Royal, and new corrections of the 
 elements of the lunar orbit were deduced. Moreover, some hidden 
 inequalities, which hitherto had totally escaped the notice of astronomers, 
 and which seemed to be irreconcilable with theory, emerged from this 
 important discussion. The explanation of the origin of these various 
 anomalies by M. Hansen, forms an epoch of great importance in the 
 history of Physical Astronomy. The complicated movements of the 
 
*viii FEEFACE. 
 
 Moon, which had occupied the attention of mankind from the earliest 
 ages in the history of civilisation, upon which a long succession 
 of illustrious astronomers and mathematicians had exerted their utmost 
 powers of research, were at length completely analyzed, their laws clearly 
 traced out, and the various resulting inequalities accounted for in strict 
 accordance with the Theory of Gravitation. The consummation of this 
 great achievement constitutes a new laurel in the wreath of the Royal 
 Observatory of Greenwich, while it imperishably associates the already 
 illustrious names of Airy and Hansen with the history of one of the most 
 important departments of Astronomical Science. 
 
 The eleventh chapter is devoted to an account of the recent researches 
 of geometers on the particular cases of perturbation which occur in the 
 planetary system. Among the more important subjects which it embraces 
 may be mentioned the discovery of the long inequality in the mean lon- 
 gitudes of the Earth and Venus, by Airy ; the investigation of the per- 
 turbations of Halley's comet, on the occasion of its passage of the peri- 
 helion in 1835, by Rosenberger, Pontecoulant, and other geometers ; the 
 interesting researches of Le Verrier on various cases of conietary per- 
 turbation ; the completion of Lagrange's labours on the Libration of the 
 Moon, by Poisson; the determination of the ellipticity and mean density 
 of the Earth, by Bessel and other enquirers ; the final researches of Poisson 
 on the motion of the Earth about its centre of gravity, and the invariability 
 of the Sidereal Year ; and the definitive detection of periodical oscillations 
 in the Atmosphere depending on the perturbative influence of the Moon, 
 
 In the twelfth and thirteenth chapters I have endeavoured to give an 
 account of the theoretical discovery of the planet Neptune, as it resulted 
 from an investigation of the perturbations produced in the motion of 
 Uranus. This may perhaps be regarded as the most astonishing conquest 
 which the human mind has ever achieved in unfolding the arrangements 
 of the material world. Nor does it tend to diminish our admiration of 
 this great discovery, that it is due to the independent researches of two 
 contemporary geometers, who, by methods totally dissimilar in their 
 details, if not in their essential character, succeeded nearly about the 
 same time in determining the position of the disturbing body. The 
 brilliant researches of M. Le Verrier on this subject constitute the 
 strongest title which he has yet earned to the admiration of the scientific 
 world; while those of Mr. Adams, the other discoverer of the planet, 
 may be justly regarded as the noblest tribute which he could offer to the 
 memory of his illustrious countryman, the great founder of Physical 
 Astronomy. Some remarks suggested by this discovery, which it would 
 have been inconvenient to have inserted in the body of the work, will be 
 found in an Appendix at the end. 
 
 The thirteenth chapter closes the history of Celestial Mechanics. 
 Physical Astronomy, as usually understood, is confined to the researches 
 of geometers on this subject; but in its more comprehensive sense it 
 may be supposed to embrace the consideration of all the physical 
 
PREFACE. *ix 
 
 principles which are known to exercise an influence on celestial phe- 
 nomena, as well as the study of those facts respecting the structure 
 of the celestial bodies which admit of being explained by reference to 
 established principles of physics. In accordance with this more enlarged 
 signification, the subjects noticed in the greater portion of the remainder 
 of the work ought to be considered as forming an essential part of Phy- 
 sical Astronomy. 
 
 The invention of the telescope about the beginning of the seventeenth 
 century furnished the astronomer with an instrument of observation, the 
 mighty efficacy of which can only be compared with the aid which the 
 infinitesimal calculus affords to the geometer in his researches on the 
 effects produced by^the continuous agency of those forces which Nature 
 employs in her operations. Armed with such an instrument, the sagacious 
 Galileo was soon enabled to announce a multitude of discoveries in the 
 heavens, of startling novelty and of the highest importance. Myriads of 
 stars whose existence had eluded the scrutinies of the naked eye, were 
 now seen to illumine the unfathomable regions of space. The investiga- 
 tion of the cosmical arrangement of the celestial bodies, and the study 
 of their individual structure, were problems unexpectedly found to be 
 within the reach of the human faculties. This department of astronomical 
 science, no less remarkable for the sentiments which it is calculated to 
 inspire respecting the grandeur of the material universe, than for the 
 multitude of instructive and delightful views of the physics of the 
 celestial regions which it unfolds, has been prosecuted with ardour by a 
 succession of eminent astronomers from Galileo's time down to the pre- 
 sent day. 
 
 The fourteenth chapter exhibits a view of the progress of researches 
 on the physical constitution of the bodies of the solar system, and also 
 includes an account of the various discoveries by which it has been en- 
 riched in modern times. The observations of the solar spots have sug- 
 gested some highly interesting speculations respecting the great central 
 body which forms the source of the light and heat of the system. The 
 Moon, from her comparative proximity, has naturally given rise to much 
 physical enquiry. The observations of the planets have disclosed a mul- 
 titude of facts of a highly interesting character. Their rotatory move- 
 ments round fixed axes with corresponding elliptical figures, and the 
 diversified appearance of their surfaces, constitute striking points of 
 analogy between them and the Earth. The remarkable phenomena visible 
 in the polar regions of Mars, the belts of Jupiter and Saturn, and the 
 wondrous rings of the latter planet, have all furnished abundant materials 
 of observation and research. Nor are the satellites wanting in physical 
 features of an important character. The relation of equality between 
 their periods of rotation and revolution, which a variation of their bright- 
 ness, in several instances, has served to establish, constitutes a striking 
 point of analogy between them and the terrestrial satellite. The pheno- 
 
#X PEEFACE. 
 
 mena accompanying their transits and occultations are also suggestive of 
 some interesting speculations. 
 
 This chapter introduces a name which occupies a prominent place in the 
 remaining portion of the work it is the immprtal name of William Her- 
 schel. To the bulk of the intelligent class of readers this illustrious indi- 
 vidual appears in the character of an astronomer distinguished by his skil- 
 ful construction of huge telescopes, which he employed with marvellous 
 success in exploring the heavens. To the student who has advanced within 
 the precincts of astronomical science, he forms a more exalted object of ad- 
 miration, as an observer of almost unrivalled acuteness and sagacity, whose 
 exquisite faculty of discernment frequently enabled him to arrive at results 
 far beyond the scope of the mere instrumental resources available to him ; 
 and as a philosopher of the highest order, who, by his originality of thought 
 and capacity for comprehensive speculation, succeeded in establishing the 
 principles of Sidereal Astronomy upon a broad and indestructible basis. 
 
 The fifteenth chapter contains an account of the progress of enquiry 
 on the physical constitution of Comets. These mysterious bodies, beyond 
 doubt, perform some important function in the economy of nature, which 
 can only be ascertained by attentive observations of the phenomena which 
 accompany their various apparitions. 
 
 The sixteenth chapter is devoted to those physical principles whose 
 influence in disturbing the apparent positions of the celestial bodies, or 
 in modifying the features of celestial phenomena, must necessarily be 
 taken into account before astronomical observations can be rendered avail- 
 able as the groundwork of ulterior enquiry. It comprehends an account 
 of the progress of researches on Precession, Refraction, Aberration, Nuta- 
 tion, Diffraction, and Irradiation. In the history of Refraction the mighty 
 names of Newton and Laplace reappear with transcendant lustre. The 
 correspondence between Newton and Flamsteed, published by the late 
 Mr. Baily, has supplied some interesting materials connected with the 
 researches of Newton on this subject. The uncertainty which so long- 
 existed respecting the construction of Newton's table of refractions, which 
 Halley originally communicated to the Royal Society whether it was 
 based upon some physical theory of the subject, or whether it was cal- 
 culated merely by an empiric process has been effectually removed by the 
 correspondence above referred to. It appears that Newton studied pro- 
 foundly the theory of Astronomical Refraction, and succeeded in deter- 
 mining the results corresponding to various hypotheses respecting the 
 physical constitution of the atmosphere. His suggestion to Flamsteed, 
 recommending the practice of noting the indications of the barometer and 
 thermometer, as a desirable accompaniment to astronomical observations, 
 constitutes a striking illustration of the sagacity by which that great 
 philosopher was distinguished above ordinary enquirers. 
 
 The subjects of Aberration and Nutation are introduced, with an 
 account of the original discovery of these phenomena by the immortal 
 
PREFACE. * x i 
 
 Bradley. The chapter closes with an account of the most important 
 results which have been elicited by the labours of successive enquirers 
 on the subject of the Irradiation of Light. 
 
 The seventeenth chapter is devoted to the histoiy of the physical en- 
 quiries connected with eclipses of the Sun and Moon, the transits of the 
 inferior planets, and other occurrences of a similar character. These 
 phenomena are all influenced in so great a degree by Refraction, and the 
 other affections of light, that it would have been inconvenient to have 
 alluded to them at an earlier stage of the work. This chapter contains a 
 somewhat detailed exposition of the most important facts which have been 
 observed on the occasion of the various total eclipses of the Sun recorded 
 in history, including an investigation of the conclusions which they are cal- 
 culated to suggest respecting the physical constitution of the great central 
 body of the planetary system. The subject of the transits of Venus has 
 naturally suggested a brief notice of the life and labours of the lamented 
 Horrocks. There is a deep interest associated with the fate of this youthful 
 astronomer. Although dwelling in a remote district of Lancashire, in 
 almost entire seclusion from the rest of the scientific world, he unquestion- 
 ably arrived at a juster appreciation of Kepler's discoveries than any of the 
 successors of that great astronomer had hitherto done ; while the sagacity 
 and originality of his views on various points relating to astronomy, 
 his fertile and glowing imagination, and his ardent enthusiasm in the 
 pursuit of science all seemed to foreshadow a career of uncommon bril- 
 liancy, which a premature death unfortunately soon brought to a close. 
 Even his brief labours, however, have assured to him a reputation which 
 will live imperishably in the annals of science. By his own countrymen 
 he cannot fail to be regarded with peculiar interest, as the morning star 
 of a galaxy of men of genius, who continued for about a century to adorn 
 these isles by their successful cultivation of the physico-mathematical 
 sciences. The names of Horrocks, Gascoigne, Brouncker, Barrow, Wallis, 
 Wren, Gregory, Hooke, NEWTON, Taylor, Bradley, Simpson, and Maclaurin, 
 represent a constellation of scientific enquirers, which for splendour of 
 genius and high intellectual endowments has never been surpassed, and 
 rarely equalled, during a similar period in the history of any nation, whe- 
 ther of ancient or modern times. 
 
 As any work relating to astronomical science would be incomplete 
 without some allusion to the important subject of observation, the eight- 
 eenth chapter has been devoted to a condensed account of the pro- 
 gress of Practical Astronomy, from the earliest ages down to the present 
 time. The annals of physical science do not, perhaps, furnish a more 
 interesting picture of gradual advancement towards perfection than that 
 which exhibits the successive improvements effected in this department of 
 astronomy from the naked estimations of the Chaldean priests to the 
 refined and complicated methods of observation practised by modern astro- 
 nomers from the gnomon and the clepsydra, in their most rudimentary 
 forms, to the transit circle of the Greenwich Observatory, the pendulum 
 
*Xli PREFACE. 
 
 clock of the most improved construction, and the electro-magnetic record- 
 ing apparatus of the American astronomers. 
 
 In this chapter I have given a somewhat detailed account of the Royal 
 Observatory of Greenwich, from its origin down to the present time. The 
 observations which have emanated from that noble establishment have 
 proved of incalculable service to astronomical science. No other similar 
 institution, whether of ancient or modern times, can compare with it in 
 this respect. Its history affords an instructive lesson regarding the ad- 
 vantage to be derived from applying the resources of an observatory to 
 some definite object, and maintaining that object in view with unswerving 
 constancy of purpose. An uninterrupted succession of eminent astro- 
 nomers, who have directed the labours of this establishment, have con- 
 tributed to render it the storehouse from which the materials for deter- 
 mining the elements of Astronomical Science have been mainly derived 
 in modern times. With the triumphs of the Theory of Gravitation its 
 history is inseparably associated. During the early period of its exist- 
 ence, it had the glory of supplying Newton with a series of observations, 
 which served as a valuable guide to him while engaged in threading his 
 way through the intricacies of the lunar theory, and it has continued ever 
 since to furnish almost exclusively the astronomical facts, by an appeal to 
 which the successors of that illustrious geometer have been enabled to 
 establish the accuracy of their theoretical results. The recent reduction 
 of the entire mass of the Greenwich Observations of the Moon and Pla- 
 nets, extending -from 1750 to 1830, under the superintendence of the 
 present Astronomer Royal, is an achievement which, while in respect of 
 vastness it has few parallels in the annals of science, at the same time 
 forms one of the most valuable acquisitions which Astronomy has received 
 during the present century. 
 
 As a fitting sequel to the subject above-mentioned, the nineteenth chap- 
 ter contains a brief account of the labours of astronomers in the con- 
 struction of Catalogues of Stars. It is impossible to exaggerate the 
 importance of this department of Astronomical Science. The places of 
 the stars constitute so many fundamental facts, upon which depend all 
 exact conclusions relative to the movements of the planetary bodies. 
 The labours connected with their determination afford ample scope for 
 talents of the highest order ; but it must be acknowledged that they offer 
 little to captivate either the imagination or the intellect, while at the 
 same time they demand the most arduous exercise of the attention, and 
 the most unflinching perseverance. Despite these disadvantages, there 
 have not been wanting numerous examples of astronomers who, disre- 
 garding the eclat which usually attends discovery, have devoted the best 
 portion of their lives to the construction of a Catalogue of Stars. La- 
 caille, Piazzi, and Groombridge will be especially remembered in the 
 annals of astronomy, as individuals who sacrificed their days and nights 
 with unwearied assiduity to this object, cheered only by the consciousness 
 of the advantages which posterity would derive from their labours, and 
 
PREFACE. * x iii 
 
 by the secret charm which a constant intercourse with nature never fails 
 to yield. 
 
 The twentieth chapter contains the history of the Telescope. The re- 
 searches of Van Swinden have recently contributed to throw much inte- 
 resting light upon the original invention of that instrument. 
 
 The twenty-first chapter, which completes the work, is devoted to a 
 condensed account of the progress of researches in Stellar Astronomy. 
 The labours of modern enquirers in this department of Astronomical 
 Science have led to some conclusions of a highly interesting and important 
 nature. The existence of a sensible parallax in the fixed stars a question 
 which has occasioned much anxious investigation from the time of Coper- 
 nicus down to the present day has at length been definitively established 
 in several instances by the labours of Bessel, Henderson, Struve, Peters, 
 and Maclear. It is now ascertained beyond all doubt, that light, travelling 
 at the rate of 192,000 miles in a second, would require three years and 
 a half to traverse the space between one of the nearest of those lumina- 
 ries and the earth ! The motion of the solar system in space, is another 
 of those sublime conclusions which have been established by the re- 
 searches of modern astronomers. It appears from the labours of Sir 
 William Herschel and his successors on this subject, that not only do 
 the satellites move round the planets, and the planets round the Sun, but 
 that the Sun, with his whole cortege of planets and satellites, is being 
 constantly transported through space to a determinate point in the heavens, 
 revolving, in all probability, round the centre of gravity of some vast 
 system of suns, of which it forms one of the constituent members. Thus 
 the farther the human mind is allowed to penetrate into the mechanism 
 of the physical universe, the more overwhelming is the impression pro- 
 duced of the surpassing grandeur of its movements, and the more exalted 
 is the conception formed of the Omnipotent Being who constantly pre- 
 sides over its countless arrangements. 
 
 To the student of Celestial Physics, the researches of astronomers on 
 Double Stars offer a high degree of interest, inasmuch as they serve to 
 demonstrate that the law of Gravitation, as announced by Newton, actually 
 prevails in the mutual action of those remote bodies of the universe. The 
 phenomena of Nebula3 excited little interest among astronomers until they 
 attracted the attention of Sir William Herschel. The vast extent of 
 that astronomer's observations of those objects, and the originality of his 
 views on their physical constitution, had the effect of elevating them to 
 a high degree of importance in sidereal astronomy. The subsequent 
 labours of Sir John Herschel and Lord Rosse, in the same field of enquiry, 
 have materially contributed to the advancement of our knowledge respect- 
 ing those wonderful structures. 
 
 After a rapid view of the progress of research on the various subjects 
 above mentioned, allusion is made to the labours of astronomers on the 
 physical constitution of the Milky Way and the Distribution of the Stars 
 in space. The chapter concludes with a brief account of the interesting 
 
*xiv PBEFACE. 
 
 speculations of M. Struve on the Extinction of Light in its passage through 
 space. 
 
 In the prosecution of these labours I have generally endeavoured to 
 elucidate the various facts of history by reference to the fundamental 
 principles of astronomical science, adhering as closely as possible to the 
 ordinary phraseology of language. Occasionally, however, the subject con- 
 sidered, does not naturally admit of concise elucidation, so that an adherence 
 to this practice would have led to inconvenient I had almost said in- 
 terminable digressions. On the other hand, to have omitted all allusion 
 to such subjects would have been to sacrifice the principle of continuity 
 which forms so essential an attribute of history, and to present the reader 
 with an avowedly mutilated work. I have endeavoured to avoid these two 
 extremes, by noticing every fact which seemed to constitute an essential 
 link in the chain of historic exposition, but studiously aiming at con- 
 ciseness in all those instances wherein explanation would be necessarily so 
 prolix as to defeat its own object. This remark applies more particularly 
 to the subjects relating to the Theory of Gravitation. With respect to 
 the remaining portion of the work, it is to be hoped that no reader pos- 
 sessing an ordinary acquaintance with the elements of astronomical science 
 can experience any difficulty in pursuing it through its details. 
 
 In a work demanding extensive research, and embracing a great variety 
 of subjects, some of which are of a very abstruse nature, it is not pre- 
 tended that imperfections may not be discovered. I may be permitted, 
 however, to state, that it has not been without carefully consulting all the 
 original authorities accesssible to me, and bestowing an attentive con- 
 sideration upon each subject which it embraces, that I have ventured to 
 submit this production to the judgment of the public. It is to be hoped 
 that the accomplished reader will be enabled to discern in the following 
 pages sufficient evidence of the justness of this statement, to induce him 
 to regard with indulgence the shortcomings of the author in so far as his 
 personal abilities are concerned. 
 
 It affords me sincere pleasure to have this opportunity of gratefully 
 acknowledging my deep sense of obligation to Captain R. H. Manners, 
 R.N., Secretary of the Royal Astronomical Society, whose kind encourage- 
 ment and readiness in promoting my views I beneficially experienced on 
 numerous occasions while engaged in preparing these sheets for the 
 press. 
 
 R. GRANT. 
 
 London, March 2, 1852. 
 
CONTENTS. 
 
 PAGE 
 
 INTRODUCTION .... 
 
 CHAPTER I. 
 
 Early notions of Physical Astronomy. Newton. His first Researches on the sub- 
 ject of Gravitation. Cause of his failure Correspondence with Hooke. 
 
 Resumption of his previous Researches. Law of the Areas. Motion of a 
 Body in an Elliptic Orbit, the force tending to the Focus. Picard. His Measure- 
 ment^ of an Arc of the Meridian. Complete success of Newton's Investigation 
 relative to the Action of the Earth upon the Moon. His establishment of the 
 Principle of Gravitation in its widest generality. Consequences he derived from 
 it. The Principia Account of the circumstances connected with its publication. 
 Hallcy, Hooke, Wren Synopsis of the subjects treated of in the Principia. 
 Laplace's opinion of its merits . 15 
 
 CHAPTER II. 
 
 Newton's Intellectual Character considered in connection with his Scientific Re- 
 searches. His Inductive ascent to the Principle of Gravitation. Motion of a 
 Body in an Orbit of Variable Curvature. Attraction of a Spherical Mass of 
 Particles. Developement of the Theory of Gravitation. General Effects of 
 Perturbation. Inequalities of the Moon computed. Aid afforded by the Infini- 
 tesimal Calculus. Figure of the Earth. Attraction of Spheroids. Precession of 
 the Equinoxes. General accuracy of Newton's Results. Anecdotes illustrative 
 of his Natural Disposition. His Death and Interment 33 
 
 CHAPTER III. 
 
 Circumstances which impeded the early progress of the Newtonian Theory. Its 
 reception in England. Reception on the Continent. Huygens, Leibnitz. 
 Researches in Analysis and Mechanics. Their influence on Physical Astronomy. 
 Problem of Three Bodies. Motion of the Lunar Apogee. Clairaut. Lunar 
 Tables. Mayer "... 41 
 
 CHAPTER IV. 
 
 Perturbations of the Planets. Inequality of Long Period in the Mean Motions 
 of Jupiter and Saturn. Researches of Euler. Perturbations of the Earth. 
 Clairaut Perturbations of Venus. Lagrange. His investigation of the Problem 
 of Three Bodies. Secular Variations of the Planets. Laplace. His Researches 
 
#XVi CONTENTS. 
 
 PAGE 
 
 on the Theory of Jupiter and Saturn. Invariability of the Mean Distances of (he 
 
 Planets. Oscillations of the Eccentricities and Inclinations. Stability of the 
 
 Planetary System 47 
 
 CHAPTER V.' 
 
 Irregularities of Jupiter and Saturn. Researches of Lambert. Lagrange. Circum- 
 stances which determine the Secular Inequalities in the Mean Longitude. 
 Laplace's Investigation of the Theory of Jupiter and Saturn. His Discovery of 
 the physical cause of the Long Inequality in their Mean Motions. Acceleration 
 of the Moon's Mean Motion. Halley. Dunthorne. Failure of Euler and 
 Lagrange to account for the Phenomenon. Its explanation by Laplace Secular 
 Inequalities in the Moon's Perigee and Nodes. Inequalities depending on the 
 Spheroidal Figure of the-Earth. Parallactic Inequality 57 
 
 CHAPTER VI. 
 
 Theory of the Figure of the Earth. Newton. Huygens. Maclaurin. Clairaut. 
 Attraction of Spheroids. D'Alembert, Legendre. Theory of Laplace. 
 Motion of the Earth about its Centre of Gravity. Nutation. Bradley. Investi- 
 gation of Precession and Nutation, by D'Alembert. The Tides. Equilibrium 
 Theory. Researches of Laplace. Stability of the Ocean. Libration of the 
 Moon. Galileo. Hevelius. Newton. Cassini. Newton's Explanation of the 
 Moon's Physical Libration. Researches of Lagrange. Combination of the Prin- 
 ciple of Virtual Velocities with D'Alembert's Principle. Laplace investigates the 
 Effect of the Secular Inequalities of the Mean Motion upon the Libralion in 
 Longitude. His Theory of Saturn's Rings ....... 66 
 
 CHAPTER VII. 
 
 Jupiter's Satelites. Galileo. Simon Marius. Hodierna. Borelli. Cassini. His 
 first Tables. He is invited to France. He publishes his second Tables. His 
 Rejection of the Equation of Light. Researches of Maraldi I. He discovers 
 that the Inclination of the second Satellite is variable. Bradley's Discoveries. 
 Maraldi II. His Discoveries relative to the third and fourth Satellites. He adopts 
 the Equation of Light. Wargentin. He discovers the Inequalities in Longitude 
 of the first and second Satellites. He remarks that the third Satellite has two 
 Equations of the Centre. Motion of the Nodes of the fourth Satellite. Inclina- 
 tion of the third Satellite. Libratory Motion of the Nodes. Inclination of the 
 fourth Satellite 76 
 
 CHAPTER VIII. 
 
 Physical Theory of the Satellites. Newton. Euler. Walmsley. Bailly computes 
 the Perturbations of the Satellites. Researches of Lagrange. He obtains for 
 each Satellite four Equations of the Centre and four Equations of Latitude. 
 His mode of representing the Positions of the Orbits. Inutility of his Theory in 
 the Construction of Tables. Laplace. His Explanation of the constant Rela- 
 tions between the Epochs and Mean Motions of the three interior Satellites. He 
 completes the Physical Theory of the Satellites. Delambre. He calculates 
 Tables on the Basis of Laplace's Theory He determines the Maximum Value of 
 Aberration by means of the Eclipses of the first Satellite. Agreement of his 
 Result with Bradley's. Conclusions derivable from it . . . .87 
 
CONTENTS. *Xvii 
 
 i 
 
 CHAPTER IX. 
 
 PA OB 
 
 Secular Variations of the Planets. Elements of the Terrestrial Orbit. Variations of 
 the Eccentricity. Motion of the Aphelion. Obliquity of the Ecliptic. Its secu- 
 lar Variation computed by Theory. Euler Lagrange. Laplace. Influence of 
 the displacement of the Ecliptic on the length of the tropical Year. Indirect Action 
 
 of the Planets on the terrestrial Spheroid Its effect in restricting the Variations of 
 
 the Obliquity of the Ecliptic and the length of the tropical Year. Invariable Plane 
 
 of the Planetary System. Theory of Comets. Hevelius Borelli. Dorfel 
 
 Subjection of the Motions of Comets to the Theory of Gravitation by Newton. 
 Halley. Clairaut. Researches of Lagrange on Cometary Perturbation. Lexel's 
 Comet. Its perturbations investigated by Laplace. Publication of the Mecanique 
 Celeste. General Reflections on the Progress of Physical Astronomy . . 97 
 
 CHAPTER X. 
 
 Variation of the Mean Distances of the Planets Researches of Poisson. The 
 Theory of Planetary Perturbation resumed by Lagrange and Laplace. Uni- 
 formity of the results arrived at by these Geometers. The General Theory of 
 the Variation of Arbitrary Constants established by Lagrange. Researches of 
 Poisson on this subject. Death of Lagrange. Researches of Modern Geometers 
 on the Theory of Perturbation. Method of Hansen. Developement of the 
 Perturbing Function. Burchardt. Binet. New Methods devised for obtaining 
 the coefficients of the Perturbing Function. Secular Inequalities of the Planets. 
 Researches of Le Verrier. Theory of the Moon. Irregularities of the Epoch. 
 Equation of Long Period. Researches of Damoiseau, Plana, and Carlini. 
 Lunar Tables calculated by means of the Theory of Gravitation. Researches of 
 Lubbock and Poisson. Reduction of the Greenwich Observations. Discovery 
 of the True Cause of the Irregularities of the Moon's Epoch, by Hansen. Re- 
 searches for the purposes of determining the Value of the Moon's Mass . . 109 
 
 CHAPTER XI. 
 
 Theory of the Perturbations of the larger Planets. Theory of Mercury. Re- 
 searches of Le Verrier. Theory of Venus. Determination of its Mass. Theory 
 of the Earth. Solar Tables. Delambre. Long Inequality depending on the 
 Action of Venus discovered by Airy. Theory of Mars. Evaluation of its 
 Mass. Theory of Jupiter. Calculation of the Terms of the Long Inequality 
 involving the Fifth Powers of the Eccentricities. Researches of Plana. Cor- 
 rection of the value of Jupiter's Mass. Theory of Saturn. Researches relative to 
 the determination of its Mass. Theory of Uranus. Its anomalous Irregularities. 
 Discovery of an Exterior Planet by means of them. Theory of the Smaller 
 Planets. Hansen. Lubbock. Theory of Comets. Researches on the Motion of 
 Encke's Comet. Hypothesis of a Resisting Medium. Perturbations of Halley's 
 Comet calculated. Satellites of Jupiter, Saturn, and Uranus. Determination of 
 the Mass of Saturn's Ring, by Bessel. Libration of the Moon. Nicollet. Theory 
 of the Figure of the Earth. Researches of Ivory on the Attraction of Elliptic Sphe- 
 roids. Experiments with the Pendulum. Mean Density of the Earth. Motion 
 of the Earth about its Centre of Gravity. -Poisson. Researches on the Tides. 
 Oscillations of the Atmosphere. Experiments of Colonel Sabine . . . 123 
 
 CHAPTER XII. 
 
 Introductory Remarks. Ancient Observations of Uranus. Calculation of Tables 
 of the Planet by Delambre. Tables of Bouvard. Irregularities of the Planet 
 
 b 
 
*xviii CONTENTS. 
 
 PAGE 
 
 Speculations respecting their Origin. Errors of Radius Vector. Researches of 
 Geometers. Bessel. Adams. Inverse Problem of Perturbation. Account of 
 Adams' Researches relative to the existence of a Planet exterior to Uranus. Re- 
 sults obtained by him. Researches of the French Astronomers on the Theory of 
 Uranus. Eugene Bouvard. Le Verrier. Account of his Researches. Near 
 Agreement of his Results with those of Adams. Steps taken by Airy and Challis 
 for the purpose of discovering the Planet. New Results obtained by Adams. 
 Explanation of Errors of Radius Vector. Account of the second part of Le Ver- 
 rier's Researches on the Trans- Uranian Planet. Address of Sir John Herschel 
 at Southampton. The Planet discovered at Berlin by Galle. Admiration 
 excited by the Discovery. Account of Challis' Labours. Public Announce- 
 ment of Adams' Researches Impression produced by it. Historical Statement 
 
 of the Astronomer Royal. Publication of the Researches of Le Verrier and 
 Adams. Remarks suggested by the Discovery of the Planet . . . .164 
 
 CHAPTER XIII. 
 
 The Elements of the Planet Neptune deduced from Observation. They are found 
 to be discordant with the Results of Theory. The cause of Discordance as- 
 signed. The Planet observed by Lalande. Theory of its Perturbations. Re- 
 searches on the value of its Mass. Uncertainty respecting this Element. Re- 
 searches of M. Hansen on the Lunar Theory. Conclusion of the History of 
 Physical Astronomy 201 
 
 CHAPTER XIV. 
 
 Researches on the Solar Parallax. Modern Determinations of this Element. 
 Discovery of the Solar Spots. Consequences deduced from this Discovery. 
 Period of the Sun's Rotation. Theories of the Solar Spots. Wilson. Herschel. 
 Researches on the Lunar Parallax. Ellipticity of Mercury. Researches on 
 the Rotation of Venus. Discovery of the Ultra- Zodiacal Planets. Microme- 
 trical measures of Jupiter's Satellites. Micrometrical measures of Saturn, and of 
 his Ring. Discovery of the eighth Satellite of Saturn. Researches on the 
 Satellites of Uranus. Lassell's Discovery of the Satellite of Neptune Re- 
 searches on Comets. Halley's Comet Comet of 1843 211 
 
 CHAPTER XV. 
 
 General Aspect of Comets. Translucency of Cometic Matter. Structure and Di- 
 mensions of the Envelope. Description of the Tail. Its Direction and Curva- 
 ture. Peculiarities of Structure. Dimensions. Phenomena observed during 
 the Passage of Comets through their Perihelia. Comet of Halley. Comet of 
 1799. Variation of the Volume of Comets. Hevelius. Newton. Struve. 
 Herschel. Dissolution of Comets. Historical Statement of Ephorus. Comet 
 of Biela. Developement of the Tail. Comet of 1680. Comet of 1769. 
 Anomalous Appearances in the Tail. Instances of Remarkable Comets. Hypo- 
 theses respecting their Physical Constitution. Theories of the Variation of a 
 Comet's Volume. Newton. Valz. Herschel. Theories of the Tails of Comets. 
 Kepler. Newton. Electrical Theory. Light of Comets. Appearance of 
 Phases. Cassini. Cacciatore. Polarization of the Light of Comets. Re- 
 searches of Arago. Question respecting the Solidity of Comets. Newton. La- 
 place. Smallness of a Comet's Mass. Ultimate condition of Cometary Bodies. 
 Opinions of Newton, Laplace, and Herschel on this point .... 292 
 
CONTENTS. *xlx 
 
 CHAPTER XVI. 
 
 PAGE 
 
 Importance of Facts in the Cultivation of Physics. Astronomy a Science of Ob- 
 servation. Inequalities which affect the apparent Positions of the Celestial Bodies. 
 Precession. Its Discovery by Hipparchus. Researches of Modern Astro- 
 nomers on its Value. Bessel. Peters. Otto Struve. Refraction. Its Effect 
 upon the Place of a Celestial Body first remarked by Ptolemy. Opinion of 
 Tycho Brahe respecting its Nature. The first Theory of Refraction due to 
 Cassini. His Table of Refractions. Newton. His Correspondence with Flam- 
 steed on the subject of Refraction. Formula of Bradley. French Tables of 
 Refraction. Researches of Bessel. Aberration. Its Discovery by Bradley. 
 Modern Determinations of its Value. Nutation discovered by Bradley. Its most 
 approved Value. Researches on Parallax. Methods for facilitating the Reduction 
 of Observations. Method of Bessel. Physical Causes which more especially 
 affect the Aspect of the Celestial Bodies. Diffraction. Irradiation . . .316 
 
 CHAPTER XVII. 
 
 Eclipses of the Sun and Moon. Historical Statement of total Eclipses of the Sun. 
 Annular Eclipses observed in modern Times. Change of Colour which the 
 Sky undergoes during an Eclipse. Its Explanation by M. Arago. Corona of 
 Light observed around the Moon. Allusions made to it by Ancient Authors. 
 Explanations of its physical Cause by different Individuals. Protuberances on 
 the Moon's Limb. Their most probable Nature. Observations on the Surface 
 of the Moon during Eclipses. Undulations observed on the Occasion of the 
 Eclipse of 1842. Similar Phenomena observed during the Eclipse of 1733. 
 Explanation of their Origin. Optical Phenomena observed during Solar 
 Eclipses Threads, Beads, &c. Explanation of their Origin. Lunar Eclipses. 
 Transits of Venus. Physical Appearances observed during their Occurrence. 
 Transits of Mercury. Spot observed on the Planet's Disk. Its Explanation by 
 Professor Powell. Occultations of the Planets and Stars .... 358 
 
 CHAPTER XVIII. 
 
 Early Methods of observing the Celestial Bodies. Instruments of the Greek 
 Astronomers. Accurate Principles of Observation first employed by the Astro- 
 nomers of the Alexandrian School. Improvements effected by Hipparchus. 
 Ptolemy substitutes the Quadrant for the Complete Circle. Arabian Astronomers. 
 The Method by which they indicated the Time of an Observation. Revival of 
 Practical Astronomy in Europe. Labours of Waltherus. Tycho Brahe. Land- 
 grave of Hesse Hevelius. Close of the Tychonic School of Observation 
 Observatory of Copenhagen established. The Pendulum applied to Clocks by 
 Huyghens. The Royal Society of London, and the Academy of Sciences of 
 Paris, established Invention of the Micrometer. Application of the Telescope 
 to divided Instruments. Observatories of Paris and Greenwich established. 
 Labours of Roemer. Transit Instrument invented. The use of Circular Instru- 
 ments for taking Altitudes introduced. Labours of Flamsteed and Halley. 
 Royal Observatory of Paris. Commencement of the Era of accurate Observa- 
 tion Bradley. Lacaille Mayer. Maskelyne. Pond. Airy. Reduction 
 
 of Planetary and Lunar Observations. Present state of Practical Astronomy . 434 
 
 CHAPTER XIX. 
 
 Catalogues of the Fixed Stars. Their importance as forming the Groundwork of 
 Astronomical Science. Earlier Catalogues. Ptolemy. Ulugh Beigh. Tycho 
 
*XX CONTENTS. 
 
 FAGS 
 
 Brahe. Halley. Hevelius Flamsteed. Modern Catalogues. Bradley. La- 
 caille. Mayer. Maskelyne. Publication of the Histoire Celeste of Lalande. 
 Piazzi. Groombridge. Zone Catalogues of Stars. Bessel. Argelander. San- 
 tini. Catalogue of the Astronomical Society. Catalogues of Southern Stars. 
 Fallows. Brisbane. Johnson. Henderson. Standard Catalogues of Stars. 
 Catalogue of the British Association. Recent Standard Catalogues . . . 506 
 
 CHAPTER XX. 
 
 Early Notions of the Telescope. Invention of the Telescope in Holland. Galileo 
 constructs a Telescope. Kepler proposes the Telescope composed of Two 
 Convex Lenses. This Instrument first applied to Astronomical Purposes by 
 Gascoigne. Telescopic Observations of Huyghens and Cassini Reflecting 
 Telescope proposed by Gregory. Newton executes a Reflecting Telescope. 
 Efforts of his Successors to construct these Instruments. Invention of the Achro- 
 matic Telescope by Dollond. Reflecting Telescopes executed by Herschel. 
 Modern Improvements in the Refracting Telescope. Improvements in the Con- 
 struction of Reflecting Telescopes. Lassell. Lord Rosse .... 514 
 
 CHAPTER XXI. 
 
 Origin of Stellar Astronomy. Physical Changes observed in the Starry Regions. 
 Disappearance of Stars from the Heavens. New Stars. Stars of Variable 
 Lustre Photometric Researches on the Stars. Attempts to determine their 
 Apparent Diameters. Space-penetrating Power of Telescopes. Applied to 
 ascertain the relative Distances of the Stars. Absolute Distances of the Stars 
 determined by Photometric Principles. Parallax of the Fixed Stars. Early 
 
 Researches on the Subject. Modern Researches. Bessel Henderson. 
 
 Struve. Peters. Proper Motions of the Stars Motion of the Solar System in 
 Space Double Stars. Discovery of their Physical Connexion by Sir William 
 Herschel. Methods for determining the Elements of their Orbits. Nebulae. 
 Speculations of Sir William Herschel. Modern Researches on the Subject 
 Sir John Herschel. The Earl of Rosse. Early Speculations on the Milky Way. 
 
 Theory of Wright Observations of Sir William Herschel. Speculations of 
 
 that Astronomer on the breaking up of the Milky Way. Researches of Struve 
 on the Distribution of the Stars in Space. Gauges of Sir John Herschel in 
 the Southern Hemisphere. Speculations of M. Struve on the Extinction of 
 Light in its Passage through Space 537 
 
 APPENDIX. 
 
 I. Illustrations of Planetary Perturbation .... ... 583 
 
 II. Examination of some cases of actual Perturbation which occur in the Plane- 
 tary System 594 
 
 III. Reflections on certain circumstances connected with the Discovery of the 
 
 Planet Neptune 603 
 
 IV. Remarks on the Lunar Inequality termed the Evection . . . .618 
 
 V. Note respecting Horrocks 621 
 
 VI. Account of some recent Results of Astronomical Observation . . . 622 
 VII. Copy of the Observation of y Draconis which originally suggested to Bradley 
 
 his Discovery of the Aberration of Light . 624 
 
HISTORY 
 
 PHYSICAL ASTRONOMY 
 
 INTRODUCTION. 
 
 ASTRONOMY is not only one of the most ancient of the physical sciences, 
 but also one of those which present the most alluring invitations to the 
 contemplative mind. The starry heavens, spangling with countless lumi- 
 naries of every shade of brilliancy, and revolving in eternal harmony 
 round the earth, constitute one of the most imposing spectacles which 
 nature offers to our observation. The waning of the placid moon, the 
 variety and splendour of the constellations, and the dazzling lustre of the 
 morning and evening star, must in all ages have excited emotions of ad- 
 miration and delight. Sometimes the occurrence of an eclipse, or the 
 sudden appearance of a comet, would create universal astonishment and 
 terror; for these unusual phenomena have been generally regarded in 
 early times as manifestations of divine displeasure, and the precursors of 
 some impending calamity. But the wants of mankind rendered indis- 
 pensable some degree of attention to the appearance of the heavens, even 
 in the rudest state of society. The sun and moon minister so obviously 
 to our subsistence and comfort, that their motions could not fail to be 
 watched with interest in all ages. The stars, too, would soon be found 
 to subserve some useful purposes. The mariner would find in them an 
 unerring guide, while pursuing his way through the ocean ; and the hus- 
 bandman, by observing the times of their rising and setting throughout 
 the year, would obtain indications of the change of the seasons, and would 
 thereby be enabled to regulate the labours of the field. 
 
 But a powerful incentive to study Astronomy in early ages originated 
 in a delusive opinion, that the destinies of human life were affected by 
 the aspects and positions of the stars. Nor is it to be wondered at that 
 these unapproachable objects should have been invested with a mysterious 
 influence before science had disclosed their real nature. If the sun, by 
 advancing with majestic regularity in his annual course, exercised so be- 
 nign an influence on the animal and vegetable world, the planets, on the 
 other hand, by their wayward evolutions and ever varying configurations, 
 appeared, naturally enough to minds imbued with imperfect notions of the 
 purposes of creation, meetly to foreshadow the countless vicissitudes of 
 human life. Hence the phenomena of the planetary movements were 
 watched with feelings of superstitious awe ; and all the particulars relat- 
 ing to them were carefully recorded for future guidance. 
 
 It is in Asia, the seat of all the early inventions of mankind, that we 
 discern the dawn of this sublime science. The annals of the Chinese con- 
 tain the earliest records of celestial phenomena; but the Chaldean observ- 
 
 B 
 
11 INTRODUCTION. 
 
 ations are more interesting to Europeans on account of their connexion 
 with modern astronomy. The serene skies and mild climate of central 
 Asia were eminently favourable for contemplating the heavens. Accord- 
 ingly we find that at Babylon eclipses and other phenomena were assidu- 
 ously observed from a very remote antiquity. 
 
 But mere observation cannot constitute science. Facts, however care- 
 fully recorded, must be subsequently scrutinized, compared, and classified, 
 before any general conclusions can be derived from them, relative to the 
 arrangements of the material universe. The astronomers of Asia, al- 
 though patient observers, do not appear to have in any age aspired to this 
 more exalted occupation of the mind. The Greeks first reduced the 
 knowledge relative to the celestial motions into a systematic form. This 
 object was not, however, effected during the early period of Grecian his- 
 tory. The Chaldeans, by confining their attention to the mere occurrence 
 of phenomena, were unable to arrive at general views of the celestial 
 motions ; the philosophers of the Grecian schools, on the other hand, long 
 wasted their transcendent talents in groundless speculations, which were 
 equally ineffectual in producing any permanent influence on the progress 
 of Astronomy. 
 
 Amid the numberless ideas which perpetually occurred to the specula- 
 tive minds of the Greek philosophers, it is perhaps not surprising that 
 the true system of the world should have suggested itself to them. Py- 
 thagoras is said to have taught his followers that the sun is placed im- 
 moveable in the centre of the universe ; and that the earth moves round 
 him in an annual orbit. This system was first taught publicly by Phi- 
 lolaus, and was adopted by several ancient philosophers. Nicetas of Syra- 
 cuse, on the other hand, is said to have explained the diurnal appearance 
 of the heavens by the motion of the earth round a fixed axis. The ulti- 
 mate abandonment of these sublime doctrines by the Greek philosophers, 
 has been attributed to the hostility of the Aristotelians, who had placed 
 the earth immoveable in the centre of the universe. It is doubtful, how- 
 ever, whether they were at any time supported by sound arguments drawn 
 from observation. We know at least that the Pythagoreans, like the 
 other sects of the Greek philosophers, were more prone to indulge in 
 speculation than to examine facts. 
 
 It was not until the reign of the Ptolemies commenced at Alexandria, 
 that Astronomy, under the munificent patronage of those princes, was 
 cultivated as a science of observation and theory. HIPPARCHUS, who 
 flourished about the year 160 A.C., is the most illustrious astronomer of 
 antiquity. The island of Rhodes is known to have been the principal 
 scene of his labours. He is also alleged to have made observations at 
 Alexandria; but this is a point which cannot be easily decided. This 
 great man was at once a mathematician, an observer, and a theorist ; and 
 in all these capacities he exhibited powers of genius of the highest order : 
 only two or three individuals can rank with him in the history of physical 
 science. We owe to .him the earliest catalogue of the stars, and the 
 first theories of the sun and moon, in which their motions were submitted 
 to strict calculation. He also executed the greater portion of the observ- 
 ations for a similar theory of the planets ; discovered the precession of 
 the equinoxes, and invented the sciences of plane and spherical trigono- 
 metry. He represented the motions of the sun and moon by means of 
 epicycles revolving on circular orbits. This ingenious hypothesis had 
 been already imagined by the Greek philosophers ; but it proved of little 
 
INTRODUCTION. u *j 
 
 value so long as it was unaccompanied by a calculus. Hipparchus sup- 
 plied this desideratum by his invention of trigonometry, and computed 
 tables of the sun and moon. The epicyclical theory did not indeed 
 accord with the real state of the heavens ; but it served the valuable pur- 
 pose of enabling the astronomer to group together the facts derived from 
 observation, and to predict the places of the celestial bodies with all the 
 accuracy demanded by the existing condition of practical science. Nor 
 should it be forgotten, in estimating the merits of this theory, that it was 
 by a comparison of its results with those derived from actual observation 
 that the real nature of the planetary motions was finally discovered. 
 
 The most eminent astronomer of ancient times after Hipparchus is 
 PTOLEMY, who flourished about the year 140 A.D. He devoted his atten- 
 tion chiefly to the task of extending and improving the theories of Hip- 
 parchus. He established the theory of the planets in accordance with 
 the principles of that astronomer. He also discovered the inequality in 
 the moon's longitude, termed the evection, and was the first who pointed 
 out the effect of refraction in altering the place of a heavenly body. He 
 is the author of a treatise on Astronomy called in Greek the Syntaxis, 
 but which has been more frequently designated by the Arabian name of the 
 Almagest. This work, which has come down to us entire, is remarkable 
 for containing nearly all the knowledge we possess of the ancient Astro- 
 nomy. Ptolemy adopted as the basis of his work, the system of the world 
 which places the earth immoveable in the centre of the universe, the sun, 
 moon, and planets revolving severally in orbits of different magnitudes, 
 and the whole heavens turning round it every twenty-four hours. This 
 system has been termed the Ptolemaic, because it was defended by the 
 author of the Syntaxis ; but, if we are to look for its origin, we must as- 
 cend to a much higher antiquity. 
 
 With the irruption of the followers of Mahomet into Egypt, and the 
 destruction of the famous library of Alexandria, about the middle of the 
 seventh century, the science of Astronomy, which had long been declining 
 among the Greeks, finally ceased altogether to be cultivated by that 
 people. The Arabians, who now succeeded to the empire of the civilized 
 world, devoted themselves with laudable assiduity to the study of the 
 Greek authors, and Bagdad henceforth assumed the place of Alexandria, 
 as the centre of literature and philosophy. Astronomy was cultivated by 
 them with great ardour ; but, like all other oriental nations, they exhibited 
 an incapacity for speculation, and consequently the science did not acquire 
 any extension from their labours. They generally adhered with super- 
 stitious reverence to the theories of the Greek astronomers, which they 
 sought to amend only by means of more accurate observations. In the 
 practical department of the science they indeed displayed a marked 
 superiority to their masters, whose natural genius was averse to the 
 monotonous task of observation. The Arabian astronomers may be said 
 to have acted merely as the faithful guardians of science until the progress 
 of events transferred it to a race of greater intellectual vigour. 
 
 After ages of profound slumber, Western Europe finally awoke to 
 pursue her glorious career. In the ninth and tenth centuries, several 
 enlightened persons travelled from France and England into Spain, to 
 study mathematics and astronomy at the Moorish universities, and upon 
 their return home diffused a knowledge of those sciences among their 
 countrymen. In the thirteenth century the Almagest was translated 
 from Arabic into Latin, under the auspices of the emperor Frederick the 
 
 +- B 2 
 
IV INTRODUCTION. 
 
 Second. This step was attended with the most beneficial consequences to 
 the study of Astronomy, which was now rendered generally accessible to 
 persons of learning throughout all those countries where the Latin 
 language prevailed. In the thirteenth century, Alphonso X., King of 
 Castile, conferred a great benefit on science "by causing the publication of 
 new tables of Astronomy. They were executed at an immense expense, 
 under the superintendence of the most eminent astronomers who could be 
 found at the Moorish universities. Alphonso is reported to have said of 
 the prevailing system of Astronomy, teeming with 
 
 " Cycle upon epicycle, orb on orb," 
 
 that if the Deity had consulted him at the creation of the world he would 
 have given him good advice. This remark, though irreverent in the 
 highest degree, was doubtless meant to convey a censure upon the cumbrous 
 mechanism by which the system of the world was represented, rather than 
 upon the actual arrangements of the system itself. 
 
 About the close of the fifteenth century the study of Astronomy received 
 a great impulse from the labours of Purbach and Regiomontanus, two 
 Germans of very original genius. They introduced some modification of 
 the ancient theories, and improved the methods of calculation. Nearly 
 about the same time the art of observation was revived by Waltherus, an 
 astronomer of considerable merit, and a native also of Germany. 
 
 NICHOLAS COPERNICUS, the restorer of the true system of Astronomy, 
 was born at Thorn, a town in Polish Prussia, on the 12th of February, 
 1473*. This illustrious man was gifted with a profound sagacity, which 
 enabled him to distinguish the genuine principles of nature from the 
 contrivances of the human imagination. He had long meditated on the 
 system of the world, and was struck with the complication of the theory 
 representing it, when contrasted with the harmony which everywhere 
 pervaded the arrangements of creation. The earth was placed immoveable 
 in the centre of the universe, while the sun, moon, and planets, and even 
 the starry heavens, revolved round it with inconceivable velocities. He, 
 however, considered it impossible to reconcile this hypothesis with the 
 variable appearance presented by the superior planets in different parts of 
 their orbits relative to the sun. He remarked especially that when Mars was 
 in opposition, he almost rivalled Jupiter in brilliancy, while towards conjunc- 
 tion he dwindled to a star of the second magnitude. This fact appeared to 
 him to offer irresistibly conclusive evidence that the earth could not be the 
 centre of the planet's motion. He now began to ponder upon the opinions oi 
 some ancient philosophers on this subject. He found in the writings oi 
 Martianus Capella an opinion ascribed to the Egyptians, which supposed 
 Mercury and Venus to revolve in orbits round the sun, while they 
 accompanied him in his annual motion round the earth. He perceived 
 that this theory would offer a most satisfactory account of the alternate 
 appearance of the planets on each side of the sun, and would also deter- 
 mine the limit of their digressions. The increasing magnitude of the 
 
 * Copernicus died in the year 1543. He was of Sclavonic extraction. His grand- 
 father, Nicholas Copernicus, was a native of Bohemia ; but about the close of theT four- 
 teenth century he removed to Poland, and established himself in Cracow. His name 
 appears inscribed in the records of that city for the year 1396. His Bohemian origin was 
 duly attested on the occasion of his enrolment. 
 
INTKODUCTION. V 
 
 superior planets as they approached towards opposition, when contemplated 
 in connexion with this doctrine, naturally led him to conceive that they 
 also might probably revolve round the sun as the centre of their motions. 
 This conclusion was strengthened by the opinion of Pythagoras, who had 
 placed the sun immoveable in the centre of the universe, and assigned to 
 the earth an annual motion in the ecliptic. Finally it occurred to him, that 
 Nicetas, of Syracuse, and some other ancient philosophers, had supposed 
 the heavens to be at rest, and sought to explain their diurnal changes by 
 ascribing to the earth a motion round a fixed axis. Having reflected 
 profoundly upon these various principles, he found that, by combining 
 them together, the resulting system accounted with the most scrupulous 
 fidelity for all the phenomena of the celestial motions, while it was 
 distinguished by a union of harmony and simplicity which admirably 
 accorded with the general economy of nature. The alternate vicissitudes 
 of night and day, the varied circle of the seasons, the stations and retro- 
 gradations of the planets, and their variable appearance at different times 
 of the year, all offered themselves as immediate consequences of this 
 beautiful system. 
 
 According to Copernicus, then, the sun is placed immoveable in the 
 centre of the universe, and all the planets, including the earth, revolve 
 round him in the order of the signs in concentric orbits, Mercury and 
 Venus revolving within the earth's orbit, and all the other planets without 
 it. While the earth is traversing her annual orbit, she is also constantly 
 revolving from west to east round a fixed axis passing through the celestial 
 poles, accomplishing a complete revolution every twenty-four hours. 
 Copernicus explained the motion of the moon by supposing her to revolve 
 in a monthly orbit round the earth, while at the same time she accompanied 
 her in her annual motion round the sun. He also very ingeniously accounted 
 for the precession of the equinoxes, by attributing to the earth's axis a slow 
 conical motion in a direction opposite to the apparent motion of the stars. 
 This great man has given to the world a full exposition of his principles 
 in his famous work, " De Revolutionibus Orbium Celestium." It is said, 
 that he received the first copy of this work, upon the contents of which 
 he had meditated thirty-six years, only a few hours before his death. 
 
 Although Copernicus greatly simplified the system of the world, he 
 still retained the machinery of epicycles to represent the motions of the 
 planets, and therefore left an ample field of research to his successors. 
 But before the investigation of the actual form of the planetary orbits 
 could be prosecuted with any hopes of success, it was necessary that a 
 great improvement should be effected in practical astronomy. The art of 
 observation still continued in the same condition in which it existed 
 among the Greeks and Arabians. Copernicus was less conspicuous for 
 the qualities of an observer than for his sagacity in unfolding the prin- 
 ciples of nature. The various tables of astronomy had all fallen con- 
 siderably into error, and the necessity of reconstructing them upon a more 
 accurate basis appeared indispensable to the future progress of the science. 
 It is clear, then, that the present crisis required less a theorist of the first 
 order, than an astronomer who might possess sufficient genius and practical 
 skill to perfect the methods of observation, to imagine new instruments, 
 and by these means to establish a number of accurate facts relative to the 
 motions of the planets. These qualities were eminently fulfilled in TYCHO 
 BRAKE, whose labours introduce a new era in the art of_ observation. 
 This illustrious astronomer was born in the year 1546 at Knudsthorp, a 
 
VI INTRODUCTION. 
 
 province of Sweden, then attached to the Danish monarchy. His great 
 celebrity induced Ferdinand, king of Denmark, to build for him in the 
 island of Huena, at the mouth of the Baltic, a magnificent observatory, 
 which he designated by the appellation of "Qraniburg, or the City of the 
 Heavens. Herein he deposited a magnificent collection of instruments, and 
 under the munificent patronage of his sovereign he continued to prosecute 
 researches in astronomy during a period of nearly twenty years. Several 
 important discoveries relative to different branches of the science, and a 
 vast mass of observations, infinitely superior in point of accuracy to any 
 that had ever before been executed, were the happy result of his labours. 
 Strange to say, he rejected the Copernican system of the world, adopting 
 in its stead a system of his own, called, in consequence, the Tychonic. 
 According to this system the earth is placed immoveable in the centre of 
 the universe, while the sun revolves in an annual orbit in the ecliptic, 
 accompanied by all the planets circulating round him as the centre of their 
 motions. The inferiority of this system to the Copeniican is so obvious 
 that it found only a very small number of followers, and it soon fell into 
 total oblivion. 
 
 This eminent astronomer, who had contributed so much towards the 
 glory of Denmark, had the misfortune, in the latter part of his life, to 
 incur the hostility of the ministers of his sovereign, Christian VII., who 
 succeeded Frederick on the throne. They were mortified to find them- 
 selves completely eclipsed by their illustrious countryman, who had won 
 his laurels in a field which they had been always accustomed to regard 
 with contempt. They were especially chagrined on account of the number 
 of distinguished individuals who annually resorted from all parts of 
 Europe to the island of Huena, to pay their respects to its renowned 
 inhabitant. Under the pretence that the finances of the kingdom could 
 no longer admit of maintaining the establishment of Uraniburg, they 
 totally withdrew from him the revenues which Frederick had assigned to 
 him for that purpose ; and he was compelled, in consequence, to look out 
 for an asylum in a foreign land. He finally selected Germany as his 
 future place of residence. Embarking, therefore, in a small vessel with 
 his family, after putting on board his books, his instruments, and all his 
 effects, he set sail from the beloved scene of his labours, and bade a final 
 farewell to his ungrateful country. He was kindly received by the Em- 
 peror Rodolph, who bestowed on him the appointment of imperial 
 astronomer, and assigned to him a splendid mansion near the city of 
 Prague. He was not destined, however, to enjoy long the favours of his 
 new patron ; for, only two or three years after his arrival in Germany, he 
 was seized with a severe illness, of which he expired on the 14th of Oc- 
 tober, 1601, in the fifty-fifth year of his age. 
 
 While the study of Astronomy continues to delight the human mind, 
 the name of Tycho Brahe will be held in grateful remembrance. The vast 
 extent of this astronomer's observations, the ingenuity of his methods, 
 and the patience and skill which he exhibited in carrying them into 
 effect, have deservedly earned for him an immortal reputation. He 
 did not indeed scan the heavens with the philosophic eye of a Kepler 
 or a Newton, but his labours were no less essential to the progress of 
 astronomy, than the more captivating discoveries of these illustrious 
 geniuses. His catalogue of the stars, his researches on comets and on 
 refraction, and his beautiful discoveries in the motion of the moon, will 
 remain enduring monuments of his glory. Nor can it be accounted the 
 
INTKODUCTION. vii 
 
 least of the obligations which posterity owes to him, that his accurate 
 observations on the planets were the means of conducting Kepler to the 
 discovery of those famous laws which form the groundwork of modern 
 Astronomy. 
 
 Few of those philosophers who have extended the boundaries of science 
 have accomplished results of equal importance with those due to the illus- 
 trious KEPLER. This eminent astronomer was born at Wiel, in the 
 Duchy of Wirtemberg, in the year 1571. Gifted with a genius of the 
 highest order, and a strong tendency towards speculation, he seemed des- 
 tined by Providence to effect a complete revolution in the theories of As- 
 tronomy. Tycho's observations on the planets were eagerly seized by 
 him ; and, after seventeen years of incessant application, during which he 
 continued to submit them to a searching scrutiny, he finally arrived at 
 those famous theorems which embody the true principles of the system 
 of the world. Copernicus, as we have already remarked, did not attack the 
 principle of the epicyclical theory: he merely sought to make it more 
 simple by placing the centre of the earth's orbit in the centre of the uni- 
 verse. This was the point to which the motions of the planets were re- 
 ferred, for the planes of their orbits were made to pass through it, and 
 their points of least and greatest velocities were also determined with re- 
 ference to it. By this arrangement the sun was situate mathematically 
 near the centre of the planetary system, but he did not appear to have 
 any physical connexion with the planets as the centre of their motions. 
 The Copernican theory continued in this incomplete state until Kepler, 
 in the course of his consummate researches, demonstrated the important 
 fact that the planes of the orbits of all the planets, and the lines joining 
 their apsids, passed through the sun. This discovery alone, by assigning 
 to the sun his just relation to the planets, contributed in a vast degree 
 towards a more accurate knowledge of the true state of the solar system. 
 
 Kepler's famous laws of the planetary motions are known to every 
 reader. The first is, that all the planets move in ellipses, having the sun 
 in one of the foci ; the second, that a line joining the planet and the sun 
 sweeps over equal areas in equal times; the third, that the squares of the 
 periodic times are proportional to the cubes of the mean distances from 
 the sun. Kepler was conducted to the first and second of these laws by 
 researches on the motion of the planet Mars, the orbit of which, being 
 more eccentric than that of any of the other superior planets, exhibited in 
 stronger relief the errors of the ancient theories. They were first an- 
 nounced by him in the year 1609, in his famous work, " De Motibus Stellre 
 Martis." * The third law, although apparently more easy to arrive at, did 
 not yield to his researches until nine years afterwards. The delight he 
 felt upon finding he had discovered this law may be imagined from the 
 following passage of his work on " Harmonics," in which he first mentioned 
 it. " What I prophesied twenty- two years ago, as soon as I discovered 
 the five solids among the heavenly orbits what I firmly believed long be 
 fore I had seen Ptolemy's harmonics what I had promised my friends in 
 the title of this book, which I named before I was sure of my discovery 
 what sixteen years ago I urged as a thing to be sought that for which 
 I joined Tycho Brahe, for which I settled in Prague, for which I have 
 devoted the best part of my life to astronomical contemplations at length 
 I have brought to light, and have recognised its truth beyond my most 
 
 * Astronomia Nova, seu Physica Coelestis tradita Commentariis de Motibus Stellse 
 Martis. Pragae, 1C09. 
 
Vlll INTRODUCTION. 
 
 sanguine expectations It is now eighteen months since I got the 
 
 first glimpse of light, three months since the dawn ; very few days since 
 the unveiled sun, most admirable to gaze on, burst out upon me. No- 
 thing holds me ; I will indulge in my sacred fury ; I will triumph over 
 mankind by the honest confession that I have stolen the golden vases of 
 the Egyptians* to build up a tabernacle for my God far away from the 
 confines of Egypt. If you forgive me, I rejoice : if you are angry, I can 
 bear it : the die is cast, the book is written ; to be read either now or by 
 posterity, I care not which : it may well wait a century for a reader, as 
 God has waited six thousand years for an interpreter of his works. " f 
 
 This great man was harassed with poverty throughout his whole career. 
 He filled the office of imperial astronomer, to which a munificent salary 
 was attached ; but he found by sad experience that the remuneration was 
 rather nominal than real ; for only a miserable pittance of his claims was 
 doled out to him at distant intervals ; and, in order to prevent his family 
 from starving, he was compelled to publish a low prophesying almanack, 
 for which he entertained the utmost contempt. In hopes of recovering 
 the arrears due to him, he resolved to proceed to Ratisboii and represent 
 his claims to the Diet. Pursuant to this design, he set out upon his jour- 
 ney in the month of November, 1630, and arrived in Ratisbon worn out 
 with ill health and anxiety. In this last appeal to his country he was un- 
 happily unsuccessful ; and the disappointment he felt in consequence, 
 reacting upon his debilitated frame, threw him into a violent fever, which 
 carried him off a few days afterwards, in the sixtieth year of his age. 
 
 Kepler was one of those exalted geniuses who appear from time to time 
 on the theatre of the world to give an impulse to the progress of physical 
 science. In acuteness arid sagacity he is equalled among modern philoso- 
 phers only by Galileo and Newton. He did not indeed exhibit the 
 wariness of these illustrious sages in his researches, but he compensated by 
 his daring adventure for his want of stratagetic skill. Gifted with an ar- 
 dent imagination, which revelled in the formation of theories, and possess- 
 ing indomitable powers of application, he threw the whole strength of 
 his intellectual faculties into his researches, and continued to prosecute 
 them with unceasing energy, until he assured himself of the truth or 
 falsehood of the principles on which they were founded. He was no doubt 
 frequently induced, by the specious illusions which conjured themselves 
 up before his mind, to waste his powers on a mere phantom ; but, even in 
 his wildest aberrations, we discern flashes of genius which threw a bright 
 gleam upon many obscure points of nature, and served like so many guid- 
 ing stars to succeeding philosophers. His candour in dismissing hy- 
 potheses as soon as he found them untenable, was no less remarkable than 
 the aptitude he evinced in their formation ; and to these valuable qualities, 
 combined with the fertility of his inventive powers and his unconquer- 
 able perseverance, may be ascribed the brilliant success with which his 
 labours were rewarded. 
 
 The advantages which accrued to the science of Astronomy from Kep- 
 
 * Kepler alludes in this allegory to Ptolemy, who had fixed with remarkable accuracy 
 the ratio of the orbit of each planet to the earth's orbit, or, in the language of the Ancient 
 Astronomy, the ratio of the deferent to the epicycle. These ratios, slightly corrected by 
 Tycho Brahe, formed the data by means of which Kepler was conducted to his great 
 discovery. 
 
 f Harmonices Mundi, p. 178. See also Life of Kepler, Library of Useful Know- 
 ledge. 
 
INTRODUCTION. IX 
 
 ler's labours are obvious to every reader. By his discovery of those re- 
 markable laws with which his name has been immortally associated, he 
 razed the existing theories to their very foundation, sweeping away the 
 whole machinery of cycles and epicycles, with which the human mind in 
 the weakness of its earlier investigations had defaced the fair arrangements 
 of the heavens, and introducing in its stead the sublime spectacle of the 
 planets revolving with majestic simplicity and harmony in elliptic orbits 
 round the sun in the foci. In all his investigations he sought to shape 
 his theories so as to accord with the physical principles which he con- 
 ceived to govern the celestial motions ; and, although he has nowhere 
 succeeded in demonstrating by legitimate reasoning the reality of those 
 principles, still the practice which he pursued in this respect had the ad- 
 vantage of continually leading him to concentrate his ideas on the main 
 object of his researches, and thereby of finally assuring a triumphant issue 
 to his labours. 
 
 Our own island was about this time adorned by a discovery that was 
 destined to prove of incalculable advantage to the astronomer in his fu- 
 ture labours. It is manifest that, as the observations on the celestial 
 bodies continued to acquire greater precision, it became necessary to intro- 
 duce a corresponding degree of refinement into the calculations to which 
 they gave rise. The sines and tangents of arcs, which form the basis of 
 such calculations, cannot be expressed in finite numerical terms, and 
 therefore admit only of approximate values, which are more accurate in 
 proportion to the number of terms they contain. The arithmetical opera- 
 tions performed on such functions become in consequence exceedingly la- 
 borious ; and this is very apparent when we consider that the questions 
 of plane and spherical trigonometry generally consist in finding a fourth 
 proportional to three given numbers. The illustrious NAPIER*, by his 
 invention of logarithms, supplied astronomers with an easy and universal 
 method of abbreviating all such calculations, its effect being to replace 
 all operations of multiplication, division, and evolution, by the more com- 
 modious and agreeable processes of addition and subtraction. " This ad- 
 mirable artifice/' says Laplace, " engrafted on the ingenious algorithm of 
 the Indians, by reducing to a few days the work of several months, doubles, 
 if we may so speak, the life of the astronomer, and spares him the errors 
 and the disgust inseparable from long calculations ; an invention which is 
 the more gratifying to the human mind, in so far as it has derived it en- 
 tirely from its own resources. In the arts man avails himself of the ma- 
 terials and forces of nature to increase his power ; but here everything is 
 his own work."f 
 
 While Napier was pondering in remote seclusion over his immortal 
 invention, and Kepler, amid continual struggles with poverty and mis- 
 fortune, was engaged in those toilsome researches which resulted in placing 
 the science of Astronomy on its present basis, universal Europe was ring- 
 ing with the fame of a philosopher whose labours produced no less im- 
 portant effects on the progress of science than those of his illustrious con- 
 temporaries, and ushered in with fitting splendour the train of magnificent 
 discoveries by which the seventeenth century was so eminently dis- 
 tinguished. 
 
 GALILEO GALILEI was born at Pisa, a city in the Grand Duchy of 
 Tuscany in Italy, in the year 1564. While a student at the university, 
 
 * Born in 1550, at Merchistoun, near Edinburgh; died in 1C17. 
 f Exposition du Systeme du Monde, Liv. v., chap. iv. 
 
X INTRODUCTION. 
 
 he distinguished himself by his powers of discussion, and by the freedom 
 with which he questioned some of the leading doctrines of the Aristote- 
 lian philosophy. At this period of his life, also, the idea of employing the 
 pendulum for the purpose of measuring time rst suggested itself to him, 
 on seeing a lamp suspended from the roof of the cathedral of Pisa con- 
 tinuing for some time to swing to and fro. In 1C09, having heard that a 
 Dutch spectacle maker had succeeded in combining lenses so as to make dis- 
 tant objects appear larger and nearer, he very soon succeeded in tracing 
 this effect to the refraction of the visual rays in passing through the glass ; 
 and upon this principle he constructed the first telescope used for scientific 
 purposes. Turning his instrument towards the heavens, his ingenuity soon 
 found its reward, in the discovery of a multitude of beautiful phenomena. 
 To him we are indebted for the first announcement, that the sun is 
 covered with dark irregular spots that the moon is diversified with hills 
 and valleys like the earth that the planets have a round appearance like 
 the sun or moon that Venus exhibits phases depending on her position 
 relative to the earth and sun that Jupiter is accompanied by four satellites 
 that the appearance of Saturn is totally unlike that of the other planets 
 and that the milky way consists of a countless multitude of stars. He also 
 discovered the diurnal libration of the moon ; and, from the solar spots, 
 he drew the important inference that the sun has a rotatory motion round 
 a fixed axis. Galileo is still more famous for his researches in mechanical 
 science. He was the first who announced, in distinct terms, the principle 
 of virtual velocities, and its utility in determining the relation between 
 the power and the weight in all combinations of machines. He also dis- 
 covered the law of acceleration of falling bodies, whether descending verti- 
 cally or along inclined planes, and he determined the path of a projectile 
 by considering the horizontal motion to be uninfluenced by the vertical 
 action of gravity. 
 
 The brilliant success which rewarded the physical researches of Galileo, 
 and the withering influence which his discoveries exercised on the doctrines 
 of the Aristotelian philosophy, excited against him the implacable animosity 
 of his opponents, who saw with dismay the boasted citadel of learning, 
 within which the human mind had for ages reposed in complacency, now 
 exposed to the powerful and reiterated assaults of a daring innovator. 
 Unable to vanquish him in the field of argument, they sought to recover 
 their sinking position by enlisting the church under their banners ; and, 
 with this view, they proceeded to represent the Copernican theory as 
 dangerous to religion, by contending that it was at variance with the re- 
 ceived interpretation of the Holy Scriptures. Galileo became, in con- 
 sequence, involved in a quarrel with the Church, which finally resulted in 
 his being summoned before the Inquisition, and compelled to abjure on 
 his knees the doctrines which taught that the sun is placed immoveable 
 in the centre of the universe, and that the earth revolves in an annual 
 orbit round him. It is said that the venerable philosopher had no sooner 
 finished this humiliating recantation than he stamped the ground with his 
 foot, and whispered to one of his friends " E pur si muove."* He was 
 condemned to strict seclusion during the remaining few years of his life, 
 and died in 1642, at the age of seventy-eight years. 
 
 Galileo's merits as a philosopher are at once great and varied. He 
 broke down the barrier which had so long interposed between the human 
 
 * " It moves howevei\" 
 
INTRODUCTION. xi 
 
 understanding and the beautiful system of the material world, denouncing 
 with unrivalled force the pernicious subtleties of the schools, and con- 
 tending for the necessity of constant observation and experiment, as the 
 only reliable guides in conducting the mind to general principles in phy- 
 sical science. He may, therefore, be considered, in conjunction with our 
 illustrious countryman, Bacon, to have founded the inductive method of 
 investigation, by the aid of which man has achieved so many brilliant 
 conquests over nature during the last two centuries. Nor is it his sole 
 merit that he overthrew the idols of the ancient philosophy, and recom- 
 mended by his powerful reasoning the necessity of a careful examination of 
 facts in all physical researches. He supplied the most conclusive argu- 
 ments in favour of his principles, in the multitude of splendid discoveries 
 which he had the glory of first announcing to the world. His example 
 also stimulated a band of ardent minds to embark in the same hopeful 
 career ; and an impulse was thus given to the study of experimental phi- 
 losophy which has continued to be maintained with unabated vigour until 
 the present day. 
 
 The astronomical discoveries of Galileo, although remarkable for their 
 brilliancy, derived their chief value from the support they lent to the 
 Copernican theory, and the influence they exerted in overthrowing the 
 false system of philosophy which then prevailed. But it is in his important 
 researches relative to mechanical science, that the genius of this great 
 philosopher is most apparent. The science of motion could not indeed be 
 said to have existed before his time, for the sole knowledge on this sub- 
 ject consisted of a few unintelligible maxims scattered through the works 
 of Aristotle. It required no common degree of penetration to expose the 
 errors which lurked amid the sophisms of the illustrious Stagyrite ; but a 
 genius of a higher order was necessary to establish the clear and immutable 
 laws of nature, in the room of the unmeaning subtleties of the schools. 
 The sagacity and skill which Galileo displays in resolving the phenomena 
 of motion into their constituent elements, and hence deriving the original 
 principles involved in them, will ever assure to him a distinguished place 
 among those who have extended the domains of science. It is, perhaps, 
 impossible, in the present advanced state of mechanical philosophy, to form 
 a just estimate of the difficulties which then interposed towards a precise 
 and luminous view of the fundamental principles of motion. It is uni- 
 versally admitted that those phenomena which come under the daily ob- 
 servation of mankind, and which on that account do not possess any salient 
 features on which the imagination can repose, are generally those which 
 are most liable to elude the inquiries of ordinary minds. The principles 
 which Galileo established by his sagacious researches had the effect of 
 elevating mechanical science to the dignity of one of the most important 
 subjects which can concern the attention of mankind. They were essential 
 elements in the train of investigation which conducted Newton to the sub- 
 lime discovery of Universal Gravitation ; and, in fact, they constitute the 
 basis upon which the vast superstructure of the physico-mathematieal 
 sciences has been reared. 
 
 DESCARTES was undoubtedly one of the greatest geniuses of the 
 seventeenth century ; but it can hardly be said that his labours 
 had a direct tendency to promote the progress of Astronomy. In 
 order to account for the motions of the various bodies of the solar 
 system, he imagined the famous system of ethereal vortices. The 
 planets were all supposed to revolve in a vortex, of which the sun 
 
Xli JNTKODUCTION. 
 
 was the centre, and the satellites revolved in smaller vortices round 
 their respective primaries. This system offered a plausible explana- 
 tion of the motions of the planets and satellites in one common 
 direction ; but it was inconsistent with the motions of comets, and a 
 multitude of other phenomena, and, besides, was nothing else than a 
 mere gratuitous assumption. Some writers commend the Cartesian sys- 
 tem of vortices, as the earliest attempt to explain the motions of the 
 planets by mechanical principles ; but Delambre has justly remarked, that, 
 by misleading men's minds from nature, this fiction of the imagination 
 retarded rather than promoted the progress of true science. Descartes, 
 however, deserves honourable mention in the history of Astronomy on 
 account of the vigorous efforts he made to overthrow the Aristotelian phi- 
 losophy, and especially for his important discoveries in the pure mathe- 
 matics. By his happy innovation of expressing the fundamental property 
 of a curve by means of an equation between two variable co-ordinates, he 
 extended incalculably the powers of analysis, besides thereby preparing 
 the way for the discovery of the infinitesimal calculus, and its application 
 to the vast domain of Celestial Dynamics. 
 
 Nearly about the same time with Descartes flourished HUYGENS, a phi- 
 losopher endued with equal genius, but exhibiting greater caution in his 
 researches. Posterity is indebted to him for one of the most admirable 
 inventions of modern times the application of the pendulum to clocks. 
 Mechanical constructions moved by weights had been employed to measure 
 time as early as the thirteenth century, and Galileo had already conceived 
 the idea of using the pendulum for a similar purpose. The Italian phi- 
 losopher failed, however, in all his attempts to construct an accurate time- 
 keeper, because he constantly sought to apply the pendulum as the prime 
 mover. Huygens accomplished this object with the most complete suc- 
 cess, by simply making the pendulum to regulate the descent of the weight 
 in the ancient clocks. It would be difficult to say whether the ordinary 
 concerns of life, or the more refined purposes of science, have gained 
 most by this valuable improvement. Huygens is distinguished by his 
 telescopic discoveries in the heavens. He it was who first established the 
 real character of the appendage with which Saturn is furnished, having 
 found it to consist of a luminous ring, encompassing the body of the 
 planet, at an appreciable distance from his surface. He also discovered 
 the most conspicuous of the satellites of that planet ; but he forgot his 
 habitual caution when he asserted that as his discovery made the number 
 of satellites equal to that of the planets, no others of a similar kind would 
 be made in the solar system. Huygens discovered the principal theorems 
 relative to the motion of a body compelled to revolve in a circular orbit, 
 under the influence of a force acting constantly at the centre. These 
 theorems were announced at the end of his treatise, " De Horologio Oscil- 
 latorio," published in the year 1671 ; but no demonstration was given of 
 them. By his elegant speculations on the e volutes of curves he also faci- 
 litated the application of the same principles to orbits of variable curva- 
 ture. This philosopher is indeed universally admitted to be one of the 
 most original geniuses who flourished in the seventeenth century. In his 
 intellectual character there appears the rare union of all those qualities 
 which form the mathematician and the experimental philosopher. In this 
 respect he approaches more nearly to the illustrious Newton than any 
 other individual of modern times. 
 
 CASSINI, the contemporary of Huygens, was one of the greatest astro- 
 
INTRODUCTION. xiiL 
 
 nomers of the age in which he lived. We owe to him a multitude of dis- 
 coveries, which have secured for him an imperishable reputation. He 
 constructed the first tables of Jupiter's satellites which could lay any 
 claim to accuracy. He discovered four of Saturn's satellites ; determined 
 the rotations of Jupiter and Mars, and arrived at a very approximate value 
 of the solar parallax. He also discovered the belts of Jupiter and the 
 zodiacal light ; established the singular coincidence of the nodes of 
 the lunar equator and orbit ; and, lastly, constructed an excellent table 
 of refractions. 
 
 While astronomical science was thus flourishing on the Continent, it 
 had already dawned upon England. 
 
 HARRIOT, the celebrated mathematician, was an assiduous observer of 
 celestial phenomena. We owe to him some valuable observations of the 
 comet of 1607, which have since been found to refer to one of the 
 periodical apparitions of the famous comet of Halley. He was one of the 
 first individuals who employed the telescope in exploring the heavens. 
 His observations of Jupiter's satellites date from the 17th of October, 
 J610. He also observed the solar spots very soon after their discovery 
 on the Continent. 
 
 JEREMIAH HORROCKS, a native of the north of England, displayed a 
 capacity of the highest order for the cultivation of astronomy ; but un- 
 fortunately his career was soon brought to a close by a premature death. 
 We owe to him the earliest observation of the transit of Venus. He and 
 his friend Crabtree were the only two individuals who witnessed this rare 
 phenomenon on the 24th of November, 1639. He effected an important 
 improvement in the lunar theory, and made many sagacious remarks on 
 other subjects relating to astronomy. He died suddenly on the 3rd of 
 January, 1641, at the age of about twenty-two years. 
 
 WILLIAM GASCOIGNE, the contemporary of Horrocks, had the merit of 
 originating some remarkable improvements in practical astronomy. He 
 was one of the first who employed the Keplerian telescope in astronomical 
 observations. He introduced the use of telescopic sights. He was the 
 original inventor of the micrometer, and was also the first who applied it 
 to divided instruments. Like Horrocks, this highly-gifted individual 
 perished in the flower of his age. He fell at the battle of Marston Moor, 
 on the 2nd of July, 1 644, when he had only attained the age of twenty- 
 four years. 
 
 HEVELIUS was one of the most eminent observers of the seventeenth 
 century. His labours extended over a period of about fifty years ; but as 
 he continued throughout his whole career to adhere to the ancient methods 
 of practical astronomy, the results achieved by him do not possess a value 
 commensurate with his merits as an observer. 
 
 During the seventeenth century, a great revolution was effected in prac- 
 tical astronomy. The application of the pendulum to clocks by Huyghens 
 had the effect of introducing a method of observation which had been 
 devised in the preceding century, but which was found to be impracticable 
 in consequence of the difficulty attending the measurement of time. It 
 consisted in observing the altitude of a celestial body on the meridian, 
 and noting the instant of its passage. By this means the declination and 
 right ascension were obtained without any trigonometrical calculation. In 
 consequence of this improvement, the observations of the celestial bodies 
 were henceforward made chiefly with instruments fixed in the meridian. 
 The micrometer, the invention of which is due originally to Gascoigne, 
 
XIV INTEODUCTION. 
 
 was reinvented on the Continent, and was brought to great perfection by 
 AUZOUT. About the same time, the use of telescopic sights was introduced 
 both in England and on the Continent. 
 
 The establishment of public observatories . was another circumstance 
 which imparted a strong impulse to the cultivation of astronomy. The 
 earliest of these institutions is the Observatory of Copenhagen, which dates 
 from the year 1656. The Royal Observatory of Paris was founded in 
 1667, and the Royal Observatory of Greenwich in 1675. 
 
 One of the most eminent astronomers of this period was PICARD. We 
 owe to him the first careful measurement of an arc of the meridian upon 
 strictly scientific principles. He was also one of the first astronomers who 
 employed telescopic sights in astronomical observations. His remarks on 
 various subjects relating to astronomical science are characterised by great 
 sagacity; He died in the year 1682. 
 
 ROEMER, the Danish astronomer, has immortalized himself by his dis- 
 covery of the gradual propagation of light. This important fact was sug- 
 gested to him by observations of the eclipses of Jupiter's satellites, which 
 he found to take place earlier or later than the computed time according 
 as the distance between the earth and planet was less or greater than the 
 mean distance. Its truth was established beyond all doubt in the follow- 
 ing century by Bradley 's discovery of Aberration. Roemer effected many 
 important improvements in practical astronomy, one of the most valuable 
 of which was the invention of the transit instrument. 
 
 During the latter part of the seventeenth century, astronomy was cul- 
 tivated in England by various eminent individuals. WREN and HOOKE 
 applied their attention to the advancement of the practical department of 
 the science. They also contributed by their splendid talents to throw 
 light on various interesting points relating to theoretical astronomy. 
 JAMES GREGORY is known to most readers by the invention of the re- 
 flecting telescope which bears his name. We owe also to this celebrated 
 mathematician the original suggestion of the utility of the transits of the 
 inferior planets for determining the value of the solar parallax. FLAM- 
 STEED had commenced his long series of valuable observations at the Royal 
 Observatory of Greenwich. HALLEY had returned from St. Helena, and 
 was ardently engaged in promoting the objects of astronomical science. 
 
 We are now arrived at the epoch of the immortal discoveries of NEWTON. 
 Before attempting to give an account of them, it will be desirable to 
 notice briefly the ideas of celestial physics which prevailed before his 
 time. 
 
CHAPTER I. 
 
 Early notions of Physical Astronomy Newton. His first Researches on the subject of 
 Gravitation. Cause of his failure. Correspondence with Hooke. Resumption of his 
 previous Researches Law of the Areas Motion of a Body in an Elliptic Orbit, the 
 
 force tending to the focus. Picard His Measurement of an Arc of the Meridian 
 
 Complete success of Newton's Investigation relative to the Action of the Earth upon the 
 Moon. His establishment of the principle of Gravitation in its widest generality. 
 Consequences he derived from it The Principia. Account of the circumstances 
 
 connected with its publication. Halley, Hooke, Wren Synopsis of the subjects 
 
 treated of in the Principia. Laplace's opinion of its merits. 
 
 ATTEMPTS were made at an early period in the history of astronomy to 
 account for the motions of the celestial bodies by means of some common 
 principle. The Greeks, as might be expected, were the first people who 
 invented a physical theory of the heavens ; but the result of their spe- 
 culations in this instance was totally unworthy of their high intellectual 
 character. Conceiving that the constant succession of phenomena in the 
 same order could only be effected by means of some material agency, they 
 supposed each of the planets to be inclosed in a solid sphere of trans- 
 parent structure, having the earth situate in the centre. The motion of 
 the planet was then supposed to be accomplished by the revolution of the 
 entire sphere in the direction of the planet's real motion, and with a 
 velocity corresponding to its periodic time. In order to account for the 
 various irregularities of its motion, each of the planets was provided with 
 several spheres, which modified each other's effects ; and at an immense 
 distance beyond the planetary apparatus was situated the primum mobile, 
 or sphere of the starry heavens, which revolved from east to west ifi 
 twenty-four hours, carrying along with it all the fixed stars, lit cer- 
 tainly affords a remarkable illustration of the proneness of the human 
 mind to ascend from the phenomena of nature to some ulterior cause, 
 that this monstrous theory should have commanded the assent of the 
 learned world until the close of the sixteenth century. Aristotle intro- 
 duced it into his system of philosophy, and by this means it came to be 
 generally adopted as part of the ancient astronomy. We must not, how- 
 ever, confound this offspring of the imagination with the epicyclical theory 
 of Hipparchus, which, although involving certain gratuitous principles, 
 was notwithstanding framed in accordance with observation. The latter, 
 in fact, was a pure mathematical theory, devised for the purpose of repre- 
 senting the motions of the planets, without reference to the physical cause 
 of those motions ; and, although incomplete in its structure, in so far as it 
 took no cognizance of the distances of the planets, still, as it could be sub- 
 mitted to a rigorous calculus, it held out to astronomers the prospect of 
 arriving at the true system of nature by means of a comparison of its 
 results with those of observation. The history of the two theories pre- 
 sents us, indeed, with an instructive lesson of the value of an hypothesis 
 which contains some elements of truth as contrasted with the inanity of a 
 mere fiction of the mind. The mathematical theory, besides affording 
 admirable scope for the inventive powers, had the advantage of enabling 
 astronomers throughout a long course of ages to predict the places of tho 
 planets with tolerable accuracy; and, finally, was instrumental in conduct- 
 
16 HISTORY OF PHYSICAL ASTRONOMY. 
 
 ing Kepler to a knowledge of their real motions : the physical theory, on 
 the other hand, continued during an equal period to mislead men's minds, 
 without possessing the redeeming merit of forming a subject of intellectual 
 exercise ; and, when it was at length overthrown by the invincible force 
 of reasoning based upon facts, it disappeared without leaving a single 
 trace of its existence behind. 
 
 It is difficult to ascertain what were the real opinions of Copernicus 
 relative to the physical constitution of the heavens. While engaged, 
 however, in establishing the Pythagorean system of the world, he was 
 led to use a remark which may be said to contain the earliest notion of 
 the principle of gravitation. The Aristotelians had asserted that heavy 
 bodies, to use their own phraseology, naturally tend towards the centre of 
 the universe, and as observation showed that a similar tendency existed 
 towards the centre of the earth, they hence concluded that the earth 
 must be placed immoveable in the centre of the universe. Copernicus, 
 however, remarked that the parts of matter had a natural appetency to 
 congregate together and unite in the form of spheres, and that the 
 constant tendency of bodies towards the centre of the earth was merely a 
 sensible manifestation of this inherent quality of matter. 
 
 Tycho Brahe was not endowed with qualities favourable to speculation, 
 but he deserves to be mentioned in the history of physical astronomy, on 
 account of the effect of his researches in leading to the overthrow of the 
 ancient theory of solid orbs. By means of a series of careful observations 
 on the comet of 1577, he discovered that it was at least three times more 
 remote from the earth than the moon is ; whence it followed, since comets 
 traverse the celestial regions in all directions, that the heavens could 
 not be composed of a solid mechanism such as the Aristotelians had 
 imagined. 
 
 Gilbert, an English philosopher of great merit, who flourished towards 
 the close of the sixteenth century, was one of the first persons who arrived 
 at general notions on the subject of gravitation. His researches on mag- 
 netism, pursued in strict accordance with the principles of the inductive 
 philosophy, were much esteemed by Kepler and Galileo, both of whom 
 profess to have been greatly indebted to him for their views on that 
 subject. In his treatise on the magnet, published in 1600, he explains 
 the influence of the earth upon the moon by comparing the former to a 
 great loadstone. He announces his opinions, however, much more 
 explicitly in his posthumous work on the " New Philosophy," * which 
 first appeared about the middle of the seventeenth century. In this 
 treatise, he asserts that the earth and moon act upon each other like two 
 magnets ; but he considers the influence of the earth to be greater than 
 that of the moon, on account of its superior mass. It is important to note 
 his explanation of the mode in which the two bodies affect each other. 
 " It is not," says he, " so as to make the bodies unite like two magnets, 
 but that they may go on in a continuous course." In another part of the 
 same work, he ascribes the tides partly to the influence of the moon. 
 " The moon," says he, " does not act on the seas by its rays or its light. 
 How then ? Certainly by the common effort of the bodies, and (to explain 
 it by something similar) by their magnetic attraction." He seems to 
 have been more perplexed in accounting for the ebb of the tide than for 
 its flow. In order to explain this part of the phenomenon, he assumes 
 
 * De Mundo Nostro Sublunari, Philosophia Nova, Amstelodami, 1651. 
 
HISTORY OF PHYSICAL ASTRONOMY. 17 
 
 that, besides the waters of the ocean, the earth contains subterranean 
 humours and spirits, which are drawn out by the attraction of the moon ; 
 and, when that body has retired, are then absorbed again into the bowels 
 of the earth. " The moon," says he, " attracts not so much the sea as 
 the subterranean spirits and humours, and the interposed earth has no 
 more power of resistance than a table or any other dense body has to 
 resist the force of a magnet." 
 
 The preceding remarks of Gilbert contain unquestionably one of the 
 earliest traces which is to be found among the writings of modern authors, 
 of the notion of an attractive force acting between the bodies of the solar 
 system. The moon's attractive influence upon the earth is naturally 
 enough suggested by the phenomenon of the tides ; but the influence of 
 the earth upon the moon is mixed up with a great deal of error and con- 
 fusion. It appears to him to be indicated not by the revolution of the 
 moon in a curvilinear orbit round the earth, but by her accompanying that 
 body in a continuous course round the sun. In fact the principle of 
 terrestrial attraction is suggested by the notion of the earth dragging the 
 moon, along with her in her annual orbit. Finding himself utterly unable 
 to account for the mutual attraction of the earth and moon, without the 
 continual approach and ultimate union of the two bodies, he attempts to 
 get rid of the difficulty by shifting his hypothesis, or, in other words, by 
 asserting that the effects resulting from the mutual influence of the two 
 bodies is not similar to the effects of magnetic attraction. Although 
 Gilbert, therefore, deserves much credit for the sagacity with which he 
 recognised, to a certain extent, the principle of gravitation, his ideas of it 
 are so vague and inconsistent, that his speculations cannot be said to rise 
 above the merit of mere conjectures. 
 
 Kepler, in the introduction to his " Astronomia Nova," published in 1609, 
 announces the mutual gravitation of matter in very remarkable terms. 
 He asserts, as Copernicus had already done, that bodies do not tend 
 towards the centre of the earth, because it is the centre of the universe, 
 but because it is the centre of a round body of the same nature with 
 themselves. If two stones were situated in space beyond the influence of 
 a third body, they would approach towards each other like two magnetic 
 needles, and would meet in an intermediate point, each passing through a 
 space proportional to the comparative mass of the other. If the moon 
 and earth were not retained by their animal force, or some other equiva- 
 lent, the earth would mount to the moon by a fifty-fourth part of their 
 distance, and the moon would fall to the earth through the other fifty- 
 three parts, and they would there meet. If the earth should cease to 
 attract the waters to itself, all the waters of the sea would be raised, and 
 would flow to the body of the moon. 
 
 These remarks are indeed very striking, and show how profoundly their 
 illustrious author could penetrate into the secrets of nature ; but we should 
 not be justified in attaching to them all the importance due to a distinct 
 recognition of the principle of gravitation. In his ideas and reasoning he 
 coincides with Gilbert, except that he extends the principle of gravitation 
 to the whole material universe. The difficulty which Gilbert experienced 
 in accounting for the constant separation of the moon and earth, notwith- 
 standing their mutual attraction, occurs with its full force to Kepler. ^ The 
 latter, however, gets over it not as Gilbert had done, by assuming a 
 principle inconsistent with his previous ideas on the subject, but by 
 supposing the terrestrial attraction to be neutralized by the animal force 
 
 c 
 
18 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 of the moon or some other equivalent. It is clearly possible to establish 
 any principles whatever, if we are at liberty to have recourse to such 
 assumptions in support of our reasoning. It will be remarked that 
 Kepler does not seek to explain how the motion of the moon in her orbit 
 is continually kept up ; he doubtless assigned this task to the animal force 
 which regulated the distance between the two bodies. The difficulty of 
 accounting for the motion of a body in its orbit, by means of a centripetral 
 force, occurs to him perpetually throughout the Astronomia Nova in course 
 of his speculations on the physical cause of the planetary motions. In- 
 attempting to explain the phenomena of these motions by means of a 
 force emanating from the sun, he is now compelled, like Gilbert, to intro- 
 duce a principle totally at variance with his previous notions of gravitation ; 
 for he imagines that the planet requires to be continually impelled in its 
 orbit by the solar force. To meet this view of the case, he supposes the 
 sun to revolve from west to east, upon an axis perpendicular to the plane 
 of the ecliptic, and to send forth continually magnetic rays, which attract 
 the planet in a direction transverse to the line joining it and the sun. 
 
 It is hardly necessary to state that this opinion of the planets being 
 kept revolving by a force continually whirling them round in their orbits 
 is not only at direct variance with the character of a gravitating force, but 
 is also inconsistent with the fundamental principles of motion. It must be 
 admitted that there was more of truth in Ross's words than he could perhaps 
 justly take credit for, when he asserted tbat " Kepler's opinion, that the 
 planets are moved round by the sunne, and that this is done by sending 
 forth a magnetic virtue, and that the sunbeames are like the teethe of a 
 wheele taking hold of the planets, are senselesse crotchets fitter for a 
 wheeler or a miller than a philosopher." * 
 
 Kepler might have formed more accurate ideas on the physical cause of 
 the planetary motions, if the science of mechanics had been more advanced 
 in his time ; but it is surprising that, although he constantly strove 
 throughout his researches on the planet Mars, as detailed by him in the 
 Astronomia Nova, to connect the varying motion of the planet with a 
 force emanating from the sun, he nowhere speculates so judiciously on 
 that force as in the introduction to his work ; and at the conclusion of his 
 labours he inspires no more confidence in his reader respecting the reality 
 of the force than he did at the commencement of them. In fact, it is to 
 the extraordinary tenacity with which he clung to the idea of a solar force 
 acting somehow on the planets, and his strong conviction that their 
 motions were regulated by fixed laws, that we must ascribe the brilliant 
 result of his researches, rather than to any clear perception either of the 
 nature of the force or of its mode of operation. 
 
 It is difficult to say whether Gilbert or Kepler was first led to speculate 
 on the physical theory of the celestial motions. Kepler's earliest notions 
 on the subject are to be found in his " Mysterium Cosmographicum," which 
 was published in 1596. Gilbert's " Treatise on the Magnet " appeared in 
 1600, and he died in 1603, leaving behind him his posthumous work, 
 which was published only in 1651. It is clear from the nature of 
 Gilbert's ideas, which turn entirely upon the magnet, that they could not 
 have been suggested to him by Kepler's speculations. It is equally 
 certain that the latter was not indebted to any person for his opinion 
 
 * The New Planet no Planet, or the Earth no Wandering Star, 4to., London. 1646. 
 See also Life of Kepler L.U.K. 
 
HISTORY OF PHYSICAL ASTRONOMY. 10 
 
 relative to the existence of some physical principle directing the motions 
 of the planets. When, however, he attempted at a subsequent period of 
 his researches to devise a consistent theory of the solar force, he adopted 
 the views of Gilbert by assuming it to be a modified form of magnetism. 
 This appears from his great work, the " Astronomia Nova,"* wherein he 
 cites the opinion of Gilbert while proceeding to frame his theory of a 
 whirling force. 
 
 Galileo, by means of his admirable researches on mechanics, contributed 
 in a high degree towards the formation of more distinct ideas on the 
 subject of curvilinear motion. The principle of mutual gravitation does 
 not seem, however, to have found any favour with him, for he censures 
 Kepler on account of his opinion relative to the attraction of the earth by 
 the moon. He admitted the attraction of the moon by the earth, but he 
 by no means formed a distinct conception of the mode in which the force 
 of gravity in this case operates. " The parts of the earth," f says he, 
 " have such a propensity to its centre, that when it changes its place, 
 although they may be very distant from the globe at the time of the 
 change, yet must they follow. An example similar to this is the perpetual 
 sequence of the Medicean stars, although always separated from Jupiter. 
 The same may be said of the moon obliged to follow the earth." 
 
 The earth's attraction is here evidently inferred from the moon con- 
 stantly attending her in her annual orbit round the sun. It might, how- 
 ever, be concluded from the same phenomenon, with equal shew of 
 reason, that the moon attracts the earth ; for the moon cannot be said to 
 follow the earth any more than the earth can be said to follow the moon, 
 since, in fact, both bodies, while revolving round the sun, revolve also 
 continually round their common centre of gravity. The grand fact which 
 leads to the establishment of the action of the earth upon the moon, 
 consists in the revolution of the latter in a curvilinear orbit which is 
 concave with respect to the earth. It has been sometimes said that Kepler 
 only required a more complete knowledge of the laws of motion in order 
 to have demonstrated the existence of the principle of gravitation. Here, 
 however, we have a philosopher equal in sagacity to Kepler who had 
 successfully analyzed the phenomenon of curvilinear motion in one of its 
 manifestations at least, and who moreover had access to the opinions of 
 Kepler on the subject of gravitation; still, notwithstanding all these ad- 
 vantages, he failed to recognise the existence of an attractive force, either 
 in the motion of the moon round the earth, or in the motions of the 
 planets round the sun. This circumstance ought to render us cautious in 
 attaching an undue value to mere sagacious surmises unsupported by 
 legitimate proof, and in ascribing to individuals any credit for discoveries 
 which 'are not the actual result of their own labours. 
 
 We do not propose to make any further allusion to Descartes' theory of 
 vortices, beyond the few words we have already said respecting it in the 
 introduction to this work. No doubt, we think, can exist that this 
 celebrated fiction exercised a most pernicious influence in retarding the 
 progress of sound mechanical ideas relative to celestial physics. Like 
 the theory of solid orbs, it at length utterly disappeared before the ad- 
 vancing light of true science, after continuing for nearly a century to 
 
 * Astronomia Nova, cap. xxxv., p. 176. 
 
 J r Dialago sopra i due Massimi Sistemi del Mondo Firenze, 1632. See also 
 Life of Galileo L. U. K. 
 
20 HISTORY OF PHYSICAL ASTRONOMY. 
 
 indulge its adherents with the miserable delusion that it revealed to them 
 the whole secret of the mechanism of the universe. 
 
 Borelli, in his theory of the Medicean stars, published in 1666, appears 
 to have speculated more judiciously on the physical theory of the planets 
 than any of his predecessors. He remarks that the motions of the planets 
 round the sun, and those of the satellites round their respective primaries, 
 must doubtless depend in each case on some virtue residing in the central 
 body. He seems to have arrived at pretty accurate notions of the motion 
 of a body in a circular orbit. He remarks that bodies so revolving have a 
 tendency to recede from their centre of revolution, as in the case of a 
 wheel revolving 011 its axle, or a stone whirled by a sling. When this 
 force is equal to the tendency of the body to the centre, a compensa- 
 tion of effects takes place, and the body will neither approach nor recede 
 from the centre of force, but will continually revolve round it. 
 
 Here, for the first time, an attempt is made to account for the motion of a 
 body in a circular orbit, by means of a force directed continually to the centre 
 of the circle. It must be admitted, however, that Borelli's explanation is 
 at once imperfect and indistinct. He does not analyze the phenomenon 
 of curvilinear motion into its constituent elements, but merely seeks to 
 establish the necessity of a constant central force by an appeal to expe- 
 riment. He rightly asserts that the body tends continually to recede 
 from the centre, but he gives no account of the origin of this centrifugal 
 force : nor does he explain by what means the motion of the body in its 
 orbit is continually kept up. His account of the last-mentioned part of the 
 phenomenon is so obscure, that it is quite evident he had obtained only a 
 very weak hold of the problem. After remarking that the compensatory 
 effects of the two constant forces will maintain the body at a determinate 
 distance from the centre, he then says, " therefore the planet will appear 
 balanced and floating on the surface."* 
 
 Although Borelli's speculations possessed much merit, still they 
 were not sufficiently clear to lead to any measurable results, and 
 until a complete dynamical view of the problem of centripetal forces 
 could be obtained, it was obviously hopeless to attempt its mathema- 
 tical solution. Without stopping here to notice the partial researches 
 of Hooke, Huygeus, Wren, and Halleyf, we shall at once proceed to give 
 some account of the immortal discoveries of NEWTON. This illustrious 
 philosopher was born in the year 1642, at Woolsthorpe, in the county of 
 Lincoln. Before attaining the years of maturity he made a multitude of 
 beautiful discoveries in Analysis, and was even in possession of the method 
 of Fluxions when he was only twenty-four years of age. He was now 
 about to enter upon a field of speculation which was destined to offer a 
 magnificent theatre for displaying the resources of that powerful instrument 
 of investigation. Pemberton states that Newton, having quitted Cam- 
 bridge, for Woolsthorpe, in 1665, to avoid the plague, was sitting one day 
 in his garden, when he was led to reflect on the principle which causes all 
 bodies to tend towards the centre of the earth. As this tendency did not 
 appear to suffer any sensible diminution on the tops of the highest build- 
 
 * " Ideoque planeta libratus apparebit et supernatans." Theories Mediceorum Plane- 
 tarum in causis physicis deductse. Florentise, 16G6. 
 
 f We shall have occasion to notice incidentally in the following pages the labours of 
 these philosophers on the subject of centripetal forces. Newton commenced his re- 
 searches at least as early as any of his contemporaries ; nor does it appear, throughout all 
 this career, that he was indebted to one or other of them for any of his ideas. 
 
HISTORY OF PHYSICAL ASTRONOMY. 21 
 
 ings, or even on ascending the loftiest mountains, it occurred to him that 
 it might possibly extend to the moon ; and, if it did, might be the cause 
 which retained that body in her orbit. Pursuing his meditations, he was 
 led to imagine that a similar force directed continually towards the sun 
 might retain the planets in their orbits. But a question naturally 
 suggested by this generalization of his ideas was this Did the solar force 
 act with the same intensity on all the planets, or did it diminish with the 
 distance from the centre, as the slower motion of the more remote planets 
 seemed to indicate? His next step, therefore, was to determine, by a 
 mathematical investigation, the magnitude of the force which retains a 
 body in a circular orbit, the force being continually directed to 
 the centre of the circle. The solution of this problem gave him an 
 expression for the centripetal force in terms of the velocity of the body 
 in its orbit and its distance from the centre, or, which amounts to the 
 same thing, in terms of the periodic time and the distance. Hence, 
 when the relation between these two elements was known, it was easy to 
 express the force in terms of the distance alone, and by this means to 
 ascertain the law according to which it varied. Now, Kepler had shown 
 that the squares of the periodic times of the planets are proportional to 
 the cubes of their distances from the sun ; Newton hence inferred that 
 the planets are retained in tneir orbits by a force directed towards the 
 sun and varying inversely as the square of the distance from his centre. 
 
 The result of Newton's investigation relative to the law of attraction 
 was strengthened by the analogy which other natural emanations 
 from centres offered : but it would manifestly have received a vast 
 accession of support if it were found that the attraction exerted by 
 the earth upon the moon, when compared with her attraction of ob- 
 jects at the surface, diminished also according to the same law of the 
 distance. The solution of this question might, therefore, now be con- 
 sidered as the experimentum crucis which was to decide whether Newton 
 had penetrated into the secret of the celestial motions, or whether he had 
 been occupying his mind with speculations of a purely mathematical 
 nature. Now, the force which determines the descent of a body at the 
 surface of the earth is measured by the space through which it falls into a 
 given small portion of time ; and the force which retains the moon 
 in her orbit is measured by the versed sine of the small arc de- 
 scribed by her in the same time ; for, if no force had acted, the moon 
 would have proceeded in the direction of a tangent to her orbit, and the 
 versed sine being the measure of deflection from the tangent, indicates, 
 therefore, the intensity of the deflecting force. It is obvious that, in 
 order to compare these two small spaces, they must both be expressed iii 
 terms of the same unit, as a foot for example. Now, the versed sine of 
 the lunar arc is readily expressed in terms of the radius of the orbit, and 
 again the latter is derivable from the earth's radius by means of the lunar 
 parallax. The question relative to the comparison of the two forces is, 
 therefore, finally reduced to the determination of the distance in feet, 
 between the centre of the earth and the surface. This object may be 
 very readily effected when once the length of a given arc of the meridian 
 is known ; but, at the time we are considering, this point was by no means 
 accurately ascertained. Newton employed in his calculation the rough 
 estimate of GO miles to a degree, which was in use among geographers 
 and navigators ; whereas the real length of a degree is about 69|- miles. 
 It may hence be readily inferred that the result obtained by him did not 
 
32 HISTORY OF PHYSICAL ASTRONOMY. 
 
 satisfy his expectations. Having determined the earth's force upon the 
 moon by diminishing the gravity of bodies at the surface in the ratio of 
 the square of the distance from the centre, and then compared the result 
 with the force indicated by the motion of the moon in her orbit, he found 
 that, instead of the two quantities being .exactly equal, the former ex- 
 ceeded the latter by about one-sixth. Deeming this discordance too great 
 to justify his bold surmise, he laid the investigation aside, doubtless with 
 the intention of reconsidering it at some future time. 
 
 Newton's attention was again called to the subject of centripetal forces, 
 by a letter he received from Hooke, in 1679, relative to the path described by 
 a projectile, taking into account the effect of the earth's diurnal motion. 
 Hooke was unquestionably endowed with a genius of a very high order ; but, 
 partly from the desultory character of his researches, and partly from his 
 deficiency in mathematical skill, he has not achieved results by any means 
 commensurate with his great acuteness and originality. As early as the year 
 1666 he had illustrated, by means of a beautiful experiment, the motion 
 of a body revolving in an ellipse under the influence of a force directed 
 continually to the centre ; and, in his letter to Newton on the occasion 
 above referred to, he declared that, if gravity decreased according to the 
 reciprocal of the square of the distance, the path of a projectile would be 
 an ellipse, having the centre of the earth in the focus. Although this 
 assertion was unaccompanied by any proof, and consequently did not 
 possess any merit beyond that of a sagacious conjecture, still it excited a 
 strong interest in the mind of Newton, who had already devoted much 
 attention to the subject of central forces. His researches had hitherto 
 been confined to bodies revolving in circular orbits : he now proposed to 
 investigate the vastly more difficult question of a body revolving in an 
 orbit of variable curvature. 
 
 Considering generally the motion of a body projected in free space, 
 and exposed to the incessant action of a force tending towards a fixed 
 centre, he arrived at the remarkable conclusion, that an imaginary line 
 joining the centre of force and the body would constantly sweep over 
 equal areas in equal times. Now Kepler had found that the planets 
 revolve round the sun precisely according to this law ; it followed, then, 
 that all these bodies were retained in their orbits by a force directed con- 
 tinually to the centre of the sun. 
 
 It still remained for Newton to investigate the law of the force correspond- 
 ing to the variation of the distance in the same orbit. According to Kepler's 
 first law, the planets move in ellipses, having the sun in one of the foci. The 
 question, therefore, was to determine the law of the force by which a body is 
 compelled to revolve in an elliptic orbit, the force being continually directed 
 to one of the foci of the ellipse. This problem is of a much more complex 
 character than the similar one relative to a circular orbit. In order to form 
 some idea of the difference between the two cases, we may remark generally, 
 that when a body has once received an impulse in any direction, it would 
 persevere with a uniform motion in the direction of the impulse, if it were 
 not exposed to the influence of any extraneous force. Now, when a body 
 revolves in a curvilinear orbit, it is continually changing the direction of 
 its motion ; this is, therefore, a clear proof that it is acted upon by some 
 force which continually deflects it from the tangent to the orbit in the 
 direction of which it is every instant naturally endeavouring to move. 
 Now, the force required to retain a body in a curvilinear orbit at any given 
 point depends partly on the curvature of the orbit and partly on the 
 
iriSTOBY OF PHYSICAL ASTRONOMY, 23 
 
 velocity with which the body is moving ; for, with the same velocity, but a 
 greater amount of curvature, the body will require to be deflected in a 
 given time through a greater space, and therefore the deflecting force must 
 be more intense ; and again, for the same amount of curvature, but a 
 greater velocity, the body will be deflected in a less time through the same 
 space, and therefore in this case also the force will be more intense. In 
 order that the centripetal force may retain the body in its orbit without 
 producing any other effect, it is necessary that it should constantly act at 
 right angles to the tangent ; for, if it act in an oblique direction, it will 
 be partly expended in increasing or diminishing the tangential motion, 
 according as the body is approaching to, or receding from, the centre of 
 force. Now, when a body is compelled to revolve in a circular orbit by a 
 force tending continually to the centre of the circle, the direction of the 
 force is constantly perpendicular to the tangent ; and therefore the force 
 neither accelerates nor retards the body, but simply retains it in its orbit. 
 The velocity of the body will, therefore, continue uniform, and, since the 
 curvature of a circle is also uniform, it follows, from what we have already 
 stated, that the centripetal force will have the same intensity for every 
 point of the orbit. 
 
 But the question is much more complicated when we consider 
 the motion of a body in an elliptic orbit. In this case, the force acts 
 in an oblique direction with respect to the tangent at every point of 
 the orbit except the two extremities of the major axis, and hence it is 
 constantly expended, partly in deflecting the body into its orbit, and partly 
 in accelerating or retarding the tangential motion. The velocity being 
 therefore variable, and the same being true with respect to the curvature 
 of the ellipse, it follows that the deflecting force which depends upon these 
 two elements is also subject to continual variation. This force, however, 
 which constantly acts at right angles to the tangent, can only be increased 
 or diminished by means of a corresponding change in the intensity of the 
 centripetal force, of which it forms one of the resolved parts. It follows, 
 therefore, that the centripetal force varies not only from being more or 
 less effectual in retaining the body in its orbit, but also because the 
 elements upon which the effective part depends are also in a state of 
 continual variation *. 
 
 The preceding remarks may serve in some degree to show the peculiar 
 difficulties of the problem which now suggested itself to Newton. En- 
 veloped as it was in complications and obscurities, his inventive genius 
 devised the means of its solution, and he found that the centripetal force varied 
 inversely as the square of the distance from the focus of the ellipse. This 
 result accorded in a most satisfactory manner with the conclusion to 
 which he was conducted by his previous researches, founded on the sup- 
 position of the planets revolving in circular orbits. Assuming the solar 
 
 * The resistance offered by a body to move in a curvilinear orbit has been termed its 
 centrifugal force ; it is therefore equal, and opposite to, the resolved part of the centri- 
 petal force, which acts perpendicularly to the tangent. Hence, when a body revolves in a 
 circular orbit by means of a force directed to the centre of the circle, the centripetal and 
 centrifugal forces will be equal ; but, in every other case, the latter of these forces will ex- 
 ceed the former, and will tend not to the centre of force, but to the centre of the circle 
 of curvature, corresponding to the infinitely small arc of the orbit in which the body is 
 moving at the given instant. It is obvious that the centrifugal force has no positive ex- 
 istence ; it merely arises from the resistance offered by the inertia of the body, in virtue 
 of which the latter tends constantly to persevere in a straight line. 
 
24 HISTORY OF PHYSICAL ASTRONOMY. 
 
 force to extend to the remotest pl^ets, and to vary everywhere according 
 to the inverse square of the di^Blpfrom the sun, he demonstrated that 
 the squares of the periodic time^oi the planets would he proportional to 
 the cubes of their mean distances. This was the third of Kepler's famous 
 laws of the planetary motions. It followed,, therefore, that the law of the 
 inverse square of the distance was true, not only when the distances re- 
 lated to the same orbit, but even when they were compared in different 
 orbits. He had already arrived at this conclusion, by assuming the orbits 
 to be circular, and now he found it to hft demonstrable for the more 
 rigorous case of elliptic orbits. 
 
 Notwithstanding the satisfactory nature of Newton's researches relative 
 to the planets, the law of gravitation appeared to his cautious mind to be 
 imperfectly established, so long as the serious discordance offered by the 
 moon remained unexplained. A circumstance, however, had recently oc- 
 curred, which induced him to suspect that the cause of this discordance 
 lay in assuming an erroneous value for a degree of the meridian. We have 
 mentioned that, in computing the earth's semi-diameter, he used the com- 
 monly received estimate of 60 miles to a degree. Picard. the French as- 
 tronomer, however, having in the intermediate period measured an arc of 
 the meridian with great care, and obtained a result considerably different, 
 he resolved to repeat his previous calculation by means of it. To his un- 
 speakable delight he now obtained a result which completely harmonized 
 with his researches on the planets. Assuming that the semi-diameter of 
 the lunar orbit was equal to 60 semi-diameters of the earth, he found that 
 the space by which the moon is deflected from the tangent to her orbit in 
 one minute is exactly equal to the space through which bodies at the 
 earth's surface fall in one second. In order to appreciate the conclusive- 
 ness of this result, we may remark that, when a body is acted upon by a 
 continuous force during a small portion of time, the space described by 
 it in consequence varies in the direct ratio of the force and the square 
 of the time. Hence if the force be supposed to vary in the inverse 
 ratio of the square of the distance, the space will vary as the square of 
 the time directly and the square of the distance inversely. It is clear, 
 then, that when two bodies are placed at unequal distances from the centre 
 of force, the minute spaces through which they are drawn by the force can 
 only be equal, when the time, during which the more remote body is under 
 the influence of the force, exceeds the corresponding time of the nearer 
 body, in the same ratio in which its distance from the centre exceeds the 
 corresponding distance of the other. Conversely, if two bodies fall through 
 equal spaces in times which are to each other in the direct ratio of the 
 distances from the centre of force, we may conclude that the force varies 
 in the inverse ratio of the square of the distance *. Now, Newton assumed 
 in his calculation that the moon is 60 times more distant from the centre 
 of the earth than objects at the surface ; and he found that the time occu- 
 
 * Let/ f be the force of gravity at the earth's surface and at the moon, d d' the cor- 
 responding distances from the earth's centre, s s' the minute spaces through which bodies 
 would fall at those distances in the*, times t t' ; then, as mentioned in the text, we have 
 s = aft-,fj / =aft'' 2 a being a constant quantity. Now, if we assume with Newton, 
 
 that s = s', we have ft~=f t'- ; hence f \ f ::7' : 7' 2 . But Newton found that t : t' :. 
 1 1 1 1 II 
 
 d : d'; therefore?' : p :: d 1 : d", and consequently,/;/' :: d- : d' 2 . 
 
HISTORY OF PHYSICAL ASTRONOMY. 5 
 
 pied by her in falling through a given^ice * was exactly 60 times greater 
 than that occupied by a body at th JHp^'s surface in falling through an 
 equal space. It thus appeared that tr^force which retained the moon in 
 her orbit, as deduced from her actual motion, was less than the force of 
 gravity at the earth's surface, in the exact ratio of the inverse square of 
 the distance from the centre of the earth f. 
 
 When Newton had thus satisfied himself by indisputable evidence that 
 he had discovered the true law of gravitation, he proceeded to investigate 
 more profoundly its real chapter. He had found that the planets gravi- 
 tate towards the centre of the sun, and the satellites towards the centres 
 of their respective primaries, but it did not escape his sagacity that these 
 points could not of themselves exert any physical influence ; and that the 
 attractive force was directed towards them solely in consequence of the 
 mass of material particles which in each case surround them. He was 
 thus led to regard the principle of attraction as residing in the constituent 
 particles of the attracting body, and to conclude that the tendency of the 
 force to the centre was no other than the resultant of all the molecular 
 forces acting with unequal intensities and in different directions. In or- 
 der to establish this important fact, it was necessary for him to investigate 
 the nature of the attraction exercised by a mass of particles agglo- 
 merated in the form of a sphere ; for observation shewed that all the 
 heavenly bodies were spherical, or very nearly so. In the course of these 
 researches he was conducted to the remarkable conclusion that, if the 
 sphere were of uniform density, or even if it consisted of concentric strata 
 of uniform density throughout each stratum, but differing in density from 
 one stratum to another, the combined effect of the attraction of all the 
 molecules would be the same, both in intensity and direction, as if the 
 whole mass had been collected at the centre. This result afforded a most 
 satisfactory explanation of the fact that, in accounting for the motion of the 
 planets by a solar force, varying according to the inverse square of the dis- 
 tance, it was in all cases found necessary to measure the distance from the 
 centre of the sun ; and the same explanation applied to the motions of 
 the satellites round their respective primaries. 
 
 Having thus assured himself that the tendency towards the central body 
 was due to a quality inherent in the constituent particles, and not to any 
 virtue residing in the centre, he naturally was led to suppose that this 
 tendency must be mutual for all the parts of matter, and that as the sun 
 attracts the planets, and the planets the satellites, so, in like manner, the 
 planets attract the sun, and the satellites the planets, and even objects at 
 the surface of the earth attract the earth. The equality of action and re- 
 action, which was strikingly illustrated in all the other relations of the 
 material world, rendered this proposition self-evident; nor did his sagacity 
 fail to discover sensible manifestations of this principle in the irregular 
 movements of the celestial bodies, especially in those of the moon J. He 
 
 i: ~ The force which retains the moon in her orbit is here supposed to act in the same 
 direction during a very short space of time. This supposition is not strictly true, but for 
 a very small arc of the lunar orbit it cannot sensibly affect the final result. 
 
 f It is said that Newton became so much agitated as soon as he began to suspect the 
 probable result of his calculation, that he was compelled to assign to a friend the task of 
 bringing it to a conclusion. 
 
 % Cotes, in his admirable preface to the second edition of the Principia, demonstrates 
 in the following simple and convincing manner that the action of gravity is equal on both 
 sides : " Let the mass of the earth be divided into any two parts whatever, cilher equal or 
 anyhow unequal ; now, if the weights of the parts towards each other were not mutually 
 
26 HISTORY OF PHYSICAL ASTKOXOMY. 
 
 therefore finally arrived at the conclusion, that every particle of matter in 
 the universe attracts every other particle, with a force varying inversely as 
 the square of their mutual distances, and directly as the mass of the 
 attracting particle. 
 
 When Newton had thus ascended to the principle of gravitation in its 
 most comprehensive form, he devoted the whole energies of his vast 
 intellect to the unfolding of its consequences ; and, with a sagacity and 
 power of investigation unexampled in ancient or modern times, he suc- 
 ceeded in tracing all the grand phenomena of the universe to its agency. 
 Considering generally a body projected in free space, and exposed to the 
 action of a central force, varying according to the inverse square, of 
 the distance, he demonstrated, by means of a beautiful geometry which 
 he had specially invented for such researches, that the body would re- 
 volve in a curvilinear orbit which would be some one of the conic sec- 
 tions. It might be a circle, an ellipse, a parabola, or an hyperbola, but 
 it must necessarily be one of them the question as to the particular 
 species of curve depending entirely on the primitive position of the body, 
 and the velocity of the impulse. He showed that, when once the initial 
 distance and the velocity and direction of the impulse were given, not 
 only the conic section in which the body would move was readily 
 assignable, but also the magnitude, position, and form of the orbit. 
 Applying these principles to the motions of comets, he discovered that 
 these bodies, like the planets, are retained in their orbits by the at- 
 traction of the sun ; and he invented a method for determining the ele- 
 ments of a comet's orbit, by means of three distinct observations. 
 
 He perceived that, while the planets and satellites are mainly 
 influenced by the attraction of the central bodies round which they 
 revolve, they are also liable to be disturbed in their motions by their 
 mutual attraction. Considering the moon as disturbed by the sun in her 
 orbit round the earth, he found that the action of that body would ac- 
 count for the numerous inequalities which astronomers had from time to 
 time detected in her motion. He demonstrated that the mean effect of 
 such a disturbing force would be to cause the apsides to advance in the 
 direction of the moon's motion, and the nodes to regress in the opposite 
 direction, both of which results are conformable to observation : nor did 
 he stop here, but actually computed the exact quantity of many of the 
 most important of the lunar inequalities. He discovered that the mutual 
 gravitation of the molecules composing the earth's mass, combined \vith 
 the centrifugal force generated by her motion round her axis, would cause 
 her to be flattened at the poles. Assuming the actual figure to be an oblate 
 spheroid, he assigned the ratio between the polar and equatorial axes, and de- 
 termined the law of gravity at the surface. With a sagacity almost divine, he 
 perceived that the action of the sun and moon upon the redundant matter 
 accumulated at the equator, would produce the slow conical motion of the 
 earth's axis which occasions the Precession of the Equinoxes, and he indi- 
 cated the quantity of the motion due to each of the two disturbing bodies. 
 He shewed, also, that the attraction of the sun and moon, by elevating the 
 waters of the ocean, would continually disturb their equilibrium, and would 
 thereby give rise to the phenomenon of the Tides. Finally, what is 
 
 equal, the lesser weight would give way to the greater, and the two parts joined together 
 would continue moving in a right line ad infinitum, towards the part to which the greater 
 weight tends ; a result which is entirely contrary to experience." 
 
HISTORY OF PHYSICAL ASTRONOMY. 27 
 
 perhaps the most astonishing of all the results to which he was conducted 
 by his theory, he found that the quantities of matter contained in the 
 heavenly bodies might be ascertained by observing the effects of their 
 mutual attraction. By means of this principle, he was enabled to com- 
 pare the mass of the sun with the masses of those planets that are accom- 
 panied by satellites, and also to compare the mass of the moon with that of 
 the earth*. 
 
 Newton has given a full exposition of these sublime discoveries in his 
 immortal work, the Principia. As the appearance of this work was 
 destined to introduce a new era in science, it may not be uninteresting to 
 mention briefly the circumstances connected with its publication. Newton 
 does not appear to have contemplated communicating to the world his 
 researches on the subject of gravitation until the occasion of a visit paid 
 him by Dr. Halley in 1684. About the beginning of that year, Halley 
 had discovered, by means of Kepler's third law, that the centripetal force 
 for circular orbits varied according to the inverse square of the distance. 
 This result gave him the law of the solar force from one orbit to another, 
 on the supposition that the planets move in circles, with the sun in the 
 centre ; but, as in reality, they move in elliptic orbits, with the sun in the 
 focus, the distance, in the same orbit, was subject to continual variation ; 
 and hence it became necessary to ascertain the corresponding variation of 
 the force. Finding his mathematical powers inadequate to the task of 
 successfully grappling with this more difficult problem of dynamics, he 
 applied to Wren and Hooke, in hopes of receiving from either of them 
 a solution of it. Wren, according to Newton's statement, had deduced the 
 law of the inverse square of the distance (for circular orbits) several years 
 previous to Halley 's present communication with him. When Halley pro- 
 posed to him the problem of the law of the force in an elliptic orbit, he 
 replied, that he had bestowed much thought on it, but was compelled to 
 give it up from inability to make any impression on it. Hooke asserted 
 that he had solved it, and had found that the force varied according to 
 the inverse square of the distance. When pressed to produce his solution, 
 he refused to do so, declaring that he would conceal it, until others trying 
 and failing, might know how to value it when he should make it public. 
 It is quite clear, however, that he was unable to support his assertion by 
 any mathematical proof, for if such had been the case he would have given 
 it forth to the world as the surest means of vindicating his claims, when 
 he attempted, a year or two afterwards, to appropriate to himself the credit 
 of Newton's discoveries. 
 
 Unable to obtain a solution of this interesting problem from any of his 
 acquaintance in London, Halley proceeded to Cambridge, in the month of 
 August, 1684, for the express purpose of conferring with Newton on the 
 subject. To his inexpressible delight, he learned the good news that his 
 friend had already brought the demonstration to perfection. So little was 
 Newton's mind occupied at this time with such researches, that he was 
 unable to lay his hand on the papers relating to them when Halley visited 
 him, but he promised to send them to him soon after his return to 
 London. It appears that Newton subsequently worked out the propo- 
 sitions afresh, and transmitted them to Halley, in the month of November 
 of the same year. Halley immediately set out upon a second visit to 
 
 ' * For a concise but very luminous exposition of the mode by which Newton established 
 the principle of gravitation, see the " History of Astronomy," Library of Useful Know- 
 ledge, p. 83, et seq. 
 
28 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Cambridge, to procure more information, and to encourage Newton to 
 pursue his researches. In December, of the same year, we learn the 
 progress of Newton's labours, from Halley 's announcement to the Society, 
 on the 10th of that month, " that he had lately seen Mr. Newton, at Cam- 
 bridge, and that he had shown him a curious treatise ' cle Motu,' which, 
 upon his desire, he said was promised to be sent to the Society, to be 
 entered upon their register."* In fulfilment of his promise, Newton 
 transmitted to the Society, about the middle of February, 1685, a paper 
 containing his early researches on centripetal forces. This communication 
 consisted of eleven propositions, the greater number of which were similar 
 to those which subsequently formed the second and third sections of the 
 Principia. Newton, in acknowledging the registration of his paper by the 
 Society, thus writes to Mr. Aston, the secretary, on the 33rd of February. 
 " I thank you for entering in your register my notions about motion. I 
 designed them for you before now ; but the examining several things has 
 taken greater part of my time than I expected, and a great deal of it to 
 no purpose. And now I am to go into Lincolnshire for a month or six 
 weeks. Afterwards I intend to finish it as soon as I can conveniently."! 
 It is quite clear from the above letter that, although Newton was already 
 in possession of the groundwork of all his discoveries in Physical 
 Astronomy, he had not at this time developed his thoughts beyond the 
 substance of the brief essay transmitted to the Society. Indeed, he can 
 hardly be said to have entered seriously upon the composition of the 
 Principia until his return to Cambridge, in April, 1685. Mr. Kigaud 
 has justly remarked, in reference to this fact, that the Principia was not 
 a protracted compilation from memoranda which might have been written 
 down under the impression of different trains of thought. It had the 
 incalculable advantage of being composed by one continued effort, during 
 which the mutual bearing of all the several parts was vividly presented to 
 the author's mind J. 
 
 On the 21st of April, 1686, Halley read before the Ptoyal Society a 
 paper on gravity ; in -which, after alluding to the labours of Galileo, 
 Toricelli, and Huygens, he mentions the truths " now lately discovered 
 by our worthy countryman, Mr. Isaac Newton, who has an incomparable 
 ' Treatise of Motion ' almost ready for the press." The prospect held out 
 by Halley was very soon realised ; for, on the k ^5th of the same month, 
 Dr. Vincent presented to the Society a manuscript treatise of Mr. Isaac 
 Newton's, entitled, " Philosophic Naturalis Principia Mathematica." 
 This was the first book of the Principia. The Society directed that a 
 letter of thanks should be addressed to the author : they also referred the 
 question of printing it to the consideration of the Council, and the drawing 
 up of a report 011 it to Dr. Halley. On the 19th of May, the Society 
 ordered that the book should be printed forthwith : whence an impression 
 has been generally formed that the Principia was printed at the expense 
 of that body. This conclusion, however, is not borne out by the words on 
 the title page of the work, which are, " Jussu Societatis Regiae," not 
 " Jussu et Sumptibus," as was usual in those cases where the expense of 
 printing was defrayed out of the funds of the Society. But a decisive 
 
 * Journal Book of the Royal Society ; see also Rigaud's Historical Essay on the first 
 publication of the Principia. Oxford, 1838. 
 
 f Letter Book of the Royal Society, vol. x. p. 28. See also Rignud's Essay. Ap- 
 pendix, page 24. The original letter has not been discovered. 
 
 % Rigaud'd Essay, page 25. Phil. Trans., vol. xvi. p. 6. 
 
JIISTORY OF PHYSICAL ASTRONOMY. 29 
 
 refutation of the current opinion is furnished by a resolution passed at the 
 meeting of the Council on the 2nd of June, to the effect that Mr. Newton's 
 book be printed, and " that E. Halley shall undertake the business of 
 looking after it and printing it at his own charge, which he engaged to 
 do." The fact is, that when the Council, which took cognizance of all the 
 pecuniary affairs of this Society, came to consider the resolution adopted 
 at the general meeting of May the 19th, they found that the state of their 
 finances could not admit of their carrying it into effect. A work, "De 
 Historia Pisciurn," by Fr. Willughby, had been published in 1686, " Jussu 
 et Sumptibus," and the outlay incurred by this publication appears to have 
 completely exhausted the funds of the Society. To such extremities, 
 indeed, were they reduced by this act of imprudent liberality, that they 
 were compelled to pay their officers in copies of this work on fishes, in 
 consequence of their inability to procure purchasers for it. 
 
 Meanwhile a violent reclamation was raised by Hooke relative to the 
 discovery of the law of gravitation. This individual, who would be well 
 entitled by his genius to occupy a high place in the history of physical 
 science, if he had displayed more uprightness and moderation in his rela- 
 tions with contemporary philosophers, had no sooner heard of the manu- 
 script which Dr. Vincent had presented to the society in Newton's name, 
 than he asserted that it was he who first communicated to the author the 
 law of the inverse square of the distance, as well as various other dis- 
 coveries announced in the manuscript. We have mentioned that, as early 
 as 1666, Hooke had arrived at very accurate notions 011 the subject of 
 centripetal forces. In 1 674 he published a work, entitled " An Attempt to 
 prove the Motion of the Earth from Observations," in which he describes 
 the general nature of gravitation with remarkable clearness and accuracy. 
 Although, however, he remarked that the attractive forces acting between 
 bodies tf are more powerful as the distances from the centres are less," it is 
 quite clear that the idea of computing by a mathematical investigation the 
 intensity of the force in any case at different distances from the centre, 
 and thereby ascertaining the law of its variation, did not at all occur to 
 him ; for, after referring to the varying intensity of the force, he then 
 goes on to say : " now what these several degrees are I have not yet ex- 
 perimentally verified." It would appear, however, that, guided by the 
 analogy of other emanations from centres, he had subsequently adopted 
 the inverse square of the distance as the law of the force which retains 
 the planets in their orbits ; and then, extending the same law to the 
 earth, he concluded, by an inversion of the question, that the path of a 
 projectile was an ellipse, with the centre of the earth in the focus. We 
 have mentioned already that Hooke was unable to produce a demonstra- 
 tion of the law of the inverse square of the distance, although he boasted 
 repeatedly that he had arrived by legitimate reasoning at that result. 
 The fact is that, although a man of extraordinary acuteuess in physical 
 matters, he had no talents for mathematical science ; and this defect con- 
 stituted an effectual bar towards his establishing, upon a satisfactory basis, 
 any of the great truths relating to the theory of gravitation. 
 
 But although Hooke 's powers were inadequate to the complete investi- 
 gation of the problem of centripetal forces, there was much merit in the 
 clearness with which he pointed out the mode in which a body is retained 
 in a curvilinear orbit by a force continually directed towards a fixed cen- 
 tre. His views on this subject were in strict accordance with mechanical 
 
oO HISTORY OF PHYSICAL ASTRONOMY. 
 
 principles, and it must be admitted that they formed an important step 
 towards a rigorous solution of the problem. 
 
 When Halley learned the extreme pretensions of Hooke, he deemed it 
 his duty to acquaint Newton with the charge preferred against him. This 
 called forth a long and interesting letter from Newton, dated June 26th, 
 1686, in which he mentions a variety of particulars connected with the 
 progress of his researches. He asserts that he had discovered the law of 
 the inverse square of the distance (for circular orbits) even previous to the 
 publication of Huygen's treatise " De Horologio Oscillatorio."* He 
 admits that he was led to consider the law of the force in an elliptic or- 
 bit by Hooke's letter to him in 1679, but he positively denies being in- 
 debted to him in any other way for the results at which he arrived. This 
 letter contains some interesting information relative to the progress of his 
 labours in composing his great work. " I designed," says he, " the whole 
 to consist of three books; the second was finished last summer, being 
 short, and only wants transcribing, and drawing the cuts fairly. Some 
 new propositions I have since thought of, which I can as well let alone. 
 The third wants the theory of comets." Thus it appears that, about fif- 
 teen months after he returned from Lincolnshire to Cambridge, he had 
 almost completed the three books of the Principia. This fully corrobo- 
 rates the statement of Pemberton, that Newton was engaged only about 
 eighteen months in the composition of his immortal work. When we 
 contemplate, in connexion with this fact, the prodigious mass of original 
 discoveries announced in the Principia, the mind is lost in amazement at the 
 power of thought which could have reared into existence so stupendous a 
 monument in such a brief space of time. 
 
 Newton seems to have been so much disgusted with Hooke's violent conduct, 
 that, in the letter above referred to, he intimated his resolution to suppress 
 the third book altogether, containing the application of his dynamical dis- 
 coveries to the system of the world. On the occasion of announcing his 
 splendid discoveries in Optics at an earlier period, he had experienced much 
 annoyance from the ignorance and jealousy of rival claimants, arid he now feared 
 that his peace of mind might be disturbed again by a similar cause. " Philo- 
 sophy," says he, " is such an impertinently litigious lady, that a man had as 
 good be engaged in lawsuits, as have to do with her. I found it so formerly, 
 and now I am no sooner come near her again but she gives me warning. 
 The two first books without the third will not bear so well the title of ' Phi- 
 losophise Naturalis Principia Mathematica ;' and therefore I had altered it 
 to this, ' De Motu Corpomm libri duo;' but upon second thoughts I retain 
 the former title, 'twill help the sale of the book, which I ought not to di- 
 minish now 'tis yours." Halley wrote a soothing reply to Newton, declar- 
 ing his belief in the groundlessness of Hooke's charges, and imploring him 
 not to persevere in his resolution of suppressing the third book of his 
 work. Newton seems to have listened favourably to the advice of his 
 friend, and he gave a proof of his conciliatory disposition by adding a 
 scholium to the fourth proposition of the first book, in which he mentions 
 that Wren, Hooke, and Halley, had all found, by means of the relation 
 between the periodic times and the distances, that the force which retains 
 
 * In a subsequent letter to Halley, dated July 14th, 1686, he mentions having arrived 
 at the law of the inverse square of the distance, by means of Kepler's theorem, about 
 twenty years previously. This would carry back his original speculations to about the 
 time assigned to them by Pemberton. The original of this letter is in the guard-book of 
 the Royal Society. 
 
HISTORY OF PHYSICAL ASTRONOMY, 31 
 
 the celestial bodies in their orbits (supposed circular) varies according to 
 the inverse square of the distance. 
 
 It is impossible too much to admire the conduct of Halley in regard to 
 the part he took in the publication of the Principia. Indeed we may 
 reasonably doubt whether that immortal work would ever have been 
 written at all, if it had not been for his enlightened zeal in the cause of 
 science; for Newton himself appears to have been imbued much more 
 strongly with the love of pondering in secret over his discoveries, than he 
 was urged by the equally natural feeling of communicating them to others. 
 This disposition of mind was fostered by a lively recollection of the an- 
 noyance he had suffered from the publication of his researches in Optics, 
 and the consequent dread he entertained of having his tranquillity again 
 disturbed by a controversy with envious rivals. Halley, therefore, besides 
 discovering the only individual living who could unfold the physical 
 theory of the celestial motions, is entitled to the credit of having per- 
 suaded him to communicate his discoveries to the world. Nor was this 
 all ; for, as has been already hinted, he defrayed the expense of publish- 
 ing* the Principia, at a time too when his finances could ill afford such 
 an outlay f ; and also undertook the revision of it in its progress through 
 the press. Posterity has retained a grateful recollection of those princes 
 who at different periods of history have distinguished their reign by a 
 munificent patronage of learning and science ; but, among all those who 
 have thus contributed indirectly to the progress of knowledge, there is 
 none who exhibits such a bright example of disinterestedness and self- 
 sacrificing zeal as the illustrious superintendent of the first edition of the 
 Principia. It is pleasing to reflect that Halley received such a noble re- 
 ward for his exertions in the splendid discovery with which his name is 
 immortally associated, and to which he was mainly conducted by Xew- 
 ton's researches on comets. 
 
 The Principia was published in 1687, and was dedicated to the 
 Royal Society. At the beginning of it was inserted a Latin poem in 
 hexameter verse by Halley, in honour of Newton's discoveries. The con- 
 cluding line runs thus : 
 
 " Nee fas est propius mortal! attingere divos ; " J 
 
 " an eulogium," says the severe Delambre, " which no one has charged with 
 exaggeration. " 
 
 The whole work is divided into three books. The first book treats of 
 motion in free space ; the second is occupied chiefly with questions re- 
 lating to resisted motion ; the third is upon the system of the world. 
 
 The first book is divided into fourteen sections, and contains ninety- 
 eight propositions, besides a number of corollaries, lemmas, and scholia. 
 In the first section, Newton explains the geometry which he employs in 
 his subsequent investigations. It is termed by him the method of prime 
 and ultimate ratios, and is essentially the same as the differential calculus. 
 In the second section he enters upon the subject of centripetal forces, 
 demonstrating Kepler's theorem of areas, and investigating tlie law of the 
 
 * It must be understood that Halley was subsequently reimbursed for the expenses 
 connected with the publication of the Principia by the sale of the copies of the work. 
 
 + He was brought up in affluent circumstances, but in 1684 his father died, after com- 
 pletely wasting his fortune. 
 
 | Nor is it lawful for mortals to approach nearer the Deity. 
 
 Histoire de 1'Astronomie de Dixhuitieme Siecle, p. 2, 
 
33 HISTORY OF PHYSICAL ASTRONOMY. 
 
 force in various curves. In the third section, lie considers the motion of 
 a body compelled to revolve in any of the conic sections by a force 
 directed continually to the focus. The fourth and fifth sections are 
 purely geometrical, relating to methods of drawing conic sections through 
 given points and touching given straight lines. The sixth section treats 
 of the motion of a body in a given orbit. The seventh treats of the 
 motion of a body ascending or descending in a straight line relative to the 
 centre of force. The eighth contains the investigation of the orbit 
 described by a body when the law of the centripetal force is given. The 
 ninth relates to the motion of bodies in moveable orbits. This section 
 contains the famous investigation of the motion of the apsides. The 
 tenth treats of bodies moving on given surfaces, and of the motion of 
 pendulums. 
 
 Hitherto Newton has been considering only the motion of material 
 points. In the eleventh section he investigates the motion of bodies 
 exposed to their mutual attraction. The twelfth treats of the attraction 
 of spheres. The thirteenth of the attraction of bodies not spherical. 
 The fourteenth relates to the motion of small particles passing from one 
 medium into another. 
 
 The second book is divided into nine sections, and contains fifty-three 
 propositions. It treats of bodies moving in resisting media upon different 
 hypotheses of the resistance ; and, whether moving in straight lines, or 
 curves, or vibrating like pendulums. It also takes cognizance of the 
 more recondite parts of several other branches of the Physico-mathematical 
 sciences. The second lemma to the eighth proposition contains an 
 exposition of the method of Fluxions, which is rendered necessary in most 
 of the investigations of this and the following book. 
 
 The third book contains forty-two propositions. From the first to the 
 eighteenth inclusive, Newton demonstrates various general theorems 
 relative to the attraction of the sun, moon, and planets. In the nineteenth 
 and twentieth he investigates the ratio of the earth's axes, and compares 
 the weights of bodies at the surface in different latitudes. In the four 
 following propositions, he shows that the precession of the equinoxes, the 
 irregularities of the moon and the other satellites, and the phenomena of 
 the tides, are all explicable by the principle of gravitation. From the 
 twenty-fifth to the thirty-fifth inclusive, he computes the various in- 
 equalities of the moon's motion. The thirty-sixth and thirty-seventh 
 treat of the tides. The thirty-eighth, of the figure of the moon. The 
 thirty-ninth, of the precession of the equinoxes. The remaining three 
 propositions are devoted to the theory of comets. At the conclusion is a 
 scholium to the whole work, containing general reflections on the con- 
 stitution of the material universe, and on the eternal and omnipotent 
 Being who presides over it *. 
 
 The publication of the Principia marks by far the most important 
 epoch in the history of physical science. Previous to its appearance the 
 researches of philosophers may be said to have resembled the voyages of 
 the early navigators, who continued creeping timidly along the coasts, 
 without daring to launch their barks into the boundless ocean. Newton, 
 like another Columbus, disdained to confine himself within the common- 
 
 * Besides the original edition of the Principia, two others were published during 
 the life of the author. The second edition was published at Cambridge in 1713, under 
 the superintendence of Cotes. The third edition was published at London in 1726, by 
 Pemberton. 
 
HISTORY OF PHYSICAL ASTRONOMY. 33 
 
 place conventionalities of ordinary minds ; and, guided by the eagle eye 
 of genius, explored the secret springs which animate a whole system of 
 worlds. We cannot convey to the general reader a more adequate idea of 
 the merits of the incomparable work just mentioned, than by 
 citing the judgment pronounced upon it by the most illustrious of 
 Newton's followers. Laplace, after enumerating the various astronomical 
 discoveries first announced in the Principia, concludes in the following 
 terms : " The imperfection of the Infinitesimal Calculus, when first dis- 
 covered, did not allow Newton to resolve completely the difficult problems 
 which the system of the world offers, and he was often compelled to give 
 mere hints, which are always uncertain until they are confirmed by a 
 rigorous analysis. Notwithstanding these unavoidable defects, the number 
 and generality of his discoveries relative to this system, and many of the 
 most interesting points of the Physico-mathematical sciences, the multi- 
 tude of original and profound views, which have been the germ of the 
 most brilliant theories of the geometers of the last century, all of which 
 were presented with much elegance, will assure to the Principia a pre- 
 eminence above all the other productions of the human intellect." * 
 
 CHAPTER II. 
 
 Newton's Intellectual Character considered in connexion with his Scientific Researches. 
 His Inductive Ascent to the Principle of Gravitation. Motion of a Body in an 
 Orbit of Variable Curvature. Attraction of a Spherical Mass of Particles. Develope- 
 
 ment of the Theory of Gravitation General Effects of Perturbation. Inequalities of 
 
 the Moon computed Aid afforded by the Infinitesimal Calculus. Figure of the 
 
 Earth Attraction of Spheroids Precession of the Equinoxes General accuracy of 
 
 Newton's Results. Anecdotes illustrative of his Natural Disposition.- His Death and 
 Interment. 
 
 NEWTON was singularly endowed with all those qualities which enable the 
 mind to unfold the laws of the material world. He could detect with a 
 glance the distinctive features of natural phenomena, and with mar- 
 vellous sagacity divine the principles on which they depended. With 
 these valuable qualities he combined a proneness to generalization, which 
 constantly led him to connect together the facts he was contemplating, 
 and advance from them to more comprehensive views of the operations of 
 nature. He possessed also powers of mathematical invention adequate on 
 all occasions to surmount the difficulties he might encounter, either in 
 ascending by induction to general laws, or in subsequently redesceuding 
 from them to the explanation of their various consequences. When we 
 consider, moreover, that he was imbued with an extreme love of truth, 
 which induced him to reject all speculations, however ingenious and 
 beautiful, that were not reconcileable with facts that his whole soul was 
 wrapped up in the study of nature and her works, and that he possessed 
 in an extraordinary degree the power of concentrating the whole energies 
 of his intellect upon the object of his researches, we may form some 
 conception of the advantages under which he approached the examination 
 of physical questions. It is, in fact, in consequence of his possession of 
 
 * Exposition du Systeme du Monde, liv. v. chap. v. 
 
 D 
 
34 HISTORY OF PHYSICAL ASTRONOMY. 
 
 all these qualities in so high a degree, that he stands without a rival 
 among ancient or modern philosophers. His discovery of Universal 
 Gravitation, heyond all comparison the greatest achievement that the 
 human mind can boast of, affords abundant illustration of the truth of 
 this remark. Throughout the magnificent Jrain of investigations which 
 that discovery suggested to his mind, we see him constantly uniting the 
 sagacious and comprehensive views of the genuine interrogator of nature 
 with the fertility of invention, the skilful research, the profundity and 
 elegance, of the consummate mathematician. We have, in fact, presented 
 to us the unexampled combination in one individual of all those attributes 
 of genius which ennoble the human intellect, and which have thrown the 
 halo of immortality around the names of Kepler and Leibnitz of Galileo 
 and Descartes of Bradley and Laplace. 
 
 The transcendent powers of Newton's intellect are equally discernible 
 in his inductive ascent to the principle of gravitation, and in his sub- 
 sequent developement of its numberless consequences. Notwithstanding 
 the sagacity he exhibited in connecting the fall of a stone at the 
 surface of the earth with the motion of the moon in her orbit, and 
 both of these phenomena with the motions of the planets round the sun, 
 he would inevitably have failed in establishing this sublime conception as 
 a physical truth, if he had not also possessed sufficient mathematical 
 genius to solve the problem of central forces for an orbit of variable cur- 
 vature. To those who are acquainted with the state of mechanical sci- 
 ence in Newton's time it would be superfluous to mention that the highest 
 powers of invention were indispensable for this purpose. When we reflect 
 on the fact that Kepler spent a considerable part of his life in vain efforts 
 to establish a connexion between the motions of the planets and the con- 
 tinual agency of some physical principle, that the question entirely escaped 
 the sagacity of Galileo, and that Huygens, although in complete posses- 
 sion of the laws of motion, was unable to advance in its solution beyond 
 the case of a circular orbit, we may well imagine the obscurity in which 
 it was enveloped, and the mathematical difficulties which the investigation 
 must have offered. Even when Newton had succeeded in this research, 
 he merely established the mutual gravitation of the planets, accord- 
 ing to the law of the inverse square of the distance, but he was not 
 also enabled to extend the same principle to the ultimate particles 
 of which the masses of the planets are composed. In order to effect 
 this object, and thereby to establish the law of gravitation in its 
 widest generality, he was compelled to determine the effect of the 
 attraction of a spherical agglomeration of particles. This problem is 
 of a totally opposite nature to the one already referred to ; for here we 
 have an infinite number of particles in juxtaposition, all attracting the 
 body with unequal intensities and in different directions. Its intricacy is 
 manifest at first sight ; nor was this circumstance compensated by any 
 preliminary hints calculated to facilitate its solution, for the mere con- 
 ception of such a problem had not yet occurred to any mathematician. 
 Newton, however, again triumphed over opposing difficulties, and thus 
 succeeded in riveting, with the bonds of demonstrative reasoning, all the 
 links of his magnificent generalization. 
 
 In redescending from the principle of universal gravitation, and pur- 
 suing it into its remoter consequences, he displays even more astonishing 
 force of genius than he does in the course of his inductive ascent. It 
 might be supposed that when once the highest step of generalization was 
 
HISTORY OF PHYSICAL ASTKONOMY. 35 
 
 attained, the functions of the natural philosopher would cease, and the 
 task of tracing the derivative truths of a principle so essentially con- 
 versant with the abstractions of space and time as that of gravitation, 
 would devolve entirely on the mathematician. This is indeed true to a 
 great extent in our own day, when, from a few differential equations, in- 
 volving the general law of gravitation, all the phenomena of the planetary 
 motions may be derived by a process of pure symbolical reasoning. But 
 in Newton's time such a method of investigation was utterly impracticable, 
 for the groundwork of it could not be said to exist. The science of me- 
 chanics was not sufficiently advanced to admit of the immediate transla- 
 tion of the conditions of a problem into an analytical form * ; and even 
 if such a step had been already possible, no further progress could have 
 been made in the same direction without a more powerful calculus than 
 Newton was in possession of. The theory of differential equations was 
 yet a mere germ, and the arithmetic of angular functions f, which tends 
 so much to condense and simplify the processes of analysis, and thereby 
 to increase its efficiency, was utterly unknown. It was therefore solely 
 upon the innate resources of his genius as a philosopher and a mathe- 
 matician that Newton had to rely in pursuing the consequences of the 
 theory of gravitation. By a profound study of the mode in which forces 
 operate, aided by his admirable sagacity in referring phenomena to their 
 true physical causes, he was enabled to trace with astonishing accuracy 
 the various consequences resulting from the mutual gravitation of the 
 bodies of the solar system. It would be difficult for any mathematician 
 of the present day, armed with all the resources of mechanical science, to 
 expound more fully and more clearly the general effects of perturbation 
 than Newton has done in the sixty-sixth proposition, and its corollaries, 
 of the first book of the Principia. When he proceeded to investigate the 
 actual values of these effects, with the view of submitting his theory to 
 a rigorous comparison with observation, he found his path beset with 
 mathematical difficulties infinitely more formidable than any he had 
 hitherto encountered, in consequence of the excessive complication occa- 
 sioned by the perturbing forces. Nor was the geometry he employed in 
 
 * We allude here more especially to the investigations connected with the figures of 
 the heavenly bodies, their motions around their centres of gravity, and the oscillations of 
 the fluids on their surfaces. 
 
 f Although the use of trigonometrical formulae in analytical processes was not intro- 
 duced among mathematicians until half a century after the publication of the Principia, 
 it would perhaps be unsafe to pronounce a positive opinion on this point with respect 
 to Newton himself, for his investigations show him to have been at least in complete pos- 
 session of the algebraic character of angular functions. Thus, in tracing the horary 
 motion of the nodes (Prin., book iii. prop, xxx.) by means of the triple product 
 sin T P I. sin P T N. sin S T N, or the moon's distance from quadratures, her dis- 
 tance from the nodes, and the distance of the nodes from the sun, he describes the effect 
 upon the formula of the varying magnitudes of the several angles with as much apparent 
 ease as the most expert analyst of the present day could do. The illustrious Euler may, 
 however, be considered as the real originator of this valuable extension of analysis, since 
 it was he who first introduced it generally to the knowledge of mathematicians. This 
 he did in his memoir on the inequalities of Jupiter and Saturn, which obtained for him 
 the prize of the Academy of Sciences of Paris for the year 1748. After deriving the 
 analytical expressions for the perturbing forces, he then proceeds in the following terms : 
 " La plupart du calcul roulera done sur les angles, quej'introduirai eux-memes dans le 
 calcul, en marquant leur sinus, cosinus, tangentes, cotangentes par les caracteres sin cos. 
 tang, et cot. mises devant les lettres qui expriment les angles. Cela abregera tres con- 
 siderablement le calcul surtout dans les integrations et differentiations." Recherches des 
 Inegalites de Jupiter et de Saturne, p. 15. 
 
 D 2 
 
36 HISTORY OF PHYSICAL ASTEONOMY. 
 
 these researches calculated to facilitate his labours. He loved, on all pos- 
 sible occasions, to adhere to the synthetic method of the ancient geo- 
 meters ; but this course entailed upon him a vast expenditure of thought, 
 for not only was it with the utmost difficulty that the ancient geometry 
 could be wielded in such delicate inquiries, 'but as it could not furnish 
 any general method of investigation, he was compelled to devise a fresh 
 mode of attack for each successive problem, and thus his inventive powers 
 were constantly called into severe exercise. Notwithstanding the rude 
 and unmanageable character of the instruments he had to deal with, he 
 applied them with amazing dexterity to the computation of some of the 
 most complex effects of perturbation, such as the irregularities of the 
 moon's motion, the figure of the earth, and the precession of the equi- 
 noxes. The difficulty of treating such subjects by the ancient geometry 
 may be imagined from the fact, that no one of his successors has been 
 enabled by its aid to advance a single step beyond the point at which he 
 arrived * ; and, in order to proceed with the further developement of the 
 theory of gravitation, it has been found necessary to have recourse to the 
 more easy and comprehensive methods of analysis. 
 
 Nor are the results to which he was conducted such rude approximations 
 as one would be apt to suppose from the unsuitableness of synthesis for such 
 intricate subjects. His researches on the lunar theory are especially re- 
 markable for their ingenuity and elegance, and for the general accordance 
 of the results with observation. He computed the inequality termed the 
 variation, and fixed its mean value at 36' 10"f ; Mayer, in his celebrated 
 tables of the moon, made it 35' 47". Laplace considers the method pur- 
 sued by Newton in investigating this inequality as forming one of the most 
 remarkable portions of the Principia, and he has shewn that, by viewing it 
 through the medium of analysis, it conducts to the usual differential equa- 
 tions of the moon's motion {. He computed the mean motion of the nodes 
 with still greater accuracy. He obtained 19 18' 1".23 for the regres- 
 sion in a sidereal year ; the astronomical tables assigned 19 21' 22".50 
 as the real value. The difference was therefore less than y-Joth 'part of 
 the whole motion. He obtained equally satisfactory results for the horary 
 motion of the nodes, and for the variation of the inclination correspond- 
 ing to different positions of the moon and her nodes. He also computed 
 several other inequalities of a more hidden nature, but contented himself 
 with merely announcing their greatest values ||. Among these were in- 
 cluded the annual equation, which he fixed at 11' 51", assuming the 
 eccentricity of the earth's orbit to be .016916. Mayer's tables give 
 11' 14" for the coefficient of this equation. He also assigned the values 
 of the inequalities in the mean motions of the apogee and nodes, de- 
 pending on the motion of the earth in her orbit. The inequality of the 
 apogee was fixed by him at 19' 43", and that of the nodes at 9' 24". Ac- 
 cording to the modern tables these" inequalities are equal to 22' 17" and 9' 0"; 
 they had entirely escaped the notice of astronomers until Newton derived 
 them from his theory. It was while engaged in these profound researches, 
 that the infinitesimal calculus, the brilliant discovery of his earlier years, 
 
 * Maclaurin's beautiful speculations on the attraction of elliptic spheroids may be 
 considered as forming the only exception to this remark, 
 f Principia, b. iii. prop. 29. 
 | Mecanique Celeste, liv. xvi. chap. ii. 
 Principia, book iii. prop. 32. 
 1| Ibid., book iii. prop. 35. Scholium. 
 
HISTOKY OF PHYSICAL ASTKONOMY. 37 
 
 came so opportunely to his aid, by enabling him to sum up the effects of 
 minute forces, varying every instant in intensity and direction. It is true, 
 that the infant powers of this noble calculus were yet comparatively feeble ; 
 but still, without its aid, the problems relating to the perturbing action 
 of the heavenly bodies would have been utterly unassailable. The success 
 with which Newton investigated the lunar theory is astonishing, when the 
 intricacy of the subject is considered. We may form some idea of the 
 complicated character of the moon's motion from the fact that it is only 
 in our own day that all her irregularities have finally yielded to the scru- 
 tinies of a most refined analysis *. 
 
 In one remarkable instance Newton failed to derive from his theory a 
 result agreeing with observation. He had shown, by a method of uncom- 
 mon ingenuity and^subtlety, that a small disturbing force of the same 
 nature with that exerted by the sun upon the moon would not sensibly 
 alter the elliptic form of the disturbed body's orbit, but would, on the 
 whole, cause the line of apsids to advance continually in the direction in 
 which the body was moving -(-. When he applied this result to the theory 
 of the moon, by calculating the mean motion of the lunar apogee, he 
 obtained 1 31' 88" for the monthly progression. The value, however, 
 assigned by observation, amounted to 3 4', a quantity nearly double the 
 result obtained by Newton. We shall have occasion in the next chapter 
 to mention the origin of this discordance. 
 
 The same commanding powers of investigation marked his pro- 
 gress as he penetrated into still more recondite parts of his theory. His 
 solution of the problem of the figure of the earth is a remarkable in- 
 stance of his success in accomplishing a great result by very small means. 
 He perceived that the mutual gravitation of the particles, combined with 
 the effect of their diurnal rotation, would occasion a flattening of the earth 
 at the poles ; but the question was to ascertain its real form, and the 
 ratio between the equatorial and polar axes. Proceeding upon the sup- 
 position that the earth was originally in a fluid state, and that its density 
 was homogeneous, he concluded that the forces acting upon the particles 
 would cause it to assume the form of an oblate spheroid. This solution 
 of a difficult question of hydrostatics was nothing more than a sagacious 
 conjecture ; yet, strange to say, it was afterwards confirmed by a rigorous 
 investigation, founded on the conditions of equilibrium of a homogeneous 
 mass. In order to determine the ratio of the axes, he conceived two 
 columns of the fluid to extend from the centre of the earth to the sur- 
 face ; one to the equator, and the other to one of the poles. Since 
 these two columns were in equilibrium, they would press each other with 
 equal intensities, and hence the ratio of their lengths would be found by 
 equating their weights. Now the weight of the equatorial column depends 
 partly on the gravitation of the particles, and partly on their centrifugal 
 force ; but as the polar column is not affected by the diurnal rotation, its 
 weight will depend simply on the gravitation of the particles. The cen- 
 trifugal force of a particle is very easily ascertained by means of its 
 angular motion and its distance from the centre, but its gravitation, result- 
 ing from the combined attraction of the surrounding particles, can be 
 
 * We allude to the result of M. Hansen's recent researches relative to the irregularities in 
 the moon's epoch. We shall endeavour to give some account of this important discovery 
 in its proper place. 
 
 f Frincipia, book i. sec. ix. prop. xlv. cor. 2. 
 
38 HJSTOKY OF PHYSICAL ASTEONOMY. 
 
 determined only by a profound mathematical investigation. Newton, by 
 a method of great elegance, had previously found the gravitation of a 
 particle within a spherical mass ; but the result he obtained on that occa- 
 sion was useless in the present case, since the question now referred to a 
 spheroid and not a sphere. He was thus led to consider a series of pro- 
 blems relating to the attraction of spheroids, all of which he solved with 
 great elegance by means of the ancient geometry*. Applying these results 
 to the investigation in question, he then found, by an indirect but most 
 ingenious process, that the polar axis of the earth was to the equatorial 
 axis as 229 to 230 f. The ellipticity of the earth is considerably greater, 
 whence it may be inferred that the density is not homogeneous. It is 
 remarkable, however, that Newton's solution of the problem on the sup- 
 position of homogeneity is quite correct ; for when geometers subsequently 
 applied to it all the resources of analysis and mechanics, they were con- 
 ducted to exactly the same result. 
 
 He also shewed that the spheroidal figure of the earth, combined 
 with its diurnal motion, would cause the weights of bodies at the surface 
 to vary in different latitudes ; and this result of pure theory explained 
 the singular fact first noticed by Richer, the French astronomer, who 
 found that a clock regulated to mean time of Paris lost 2'. 28" daily at 
 Cayenne in Africa {. 
 
 His explanation of the precession of the equinoxes is one of the 
 most beautiful illustrations of his genius. Conceiving a satellite to 
 revolve round the earth in the plane of the equator, he had already 
 found that the effect of a disturbing body exterior to it would be to 
 cause the nodes of the satellite to regress on the orbit of the disturbing 
 body. Imagining, then, a ring of such satellites to encompass the earth, 
 the instantaneous effect produced on the ring by the disturbing body 
 would manifestly be similar to that produced on any one satellite in course 
 of a complete revolution. The nodes of the ring would therefore con- 
 stantly regress on the plane of the disturbing body's orbit, and if the 
 ring actually adhered to the earth the nodes would still regress, but with 
 a much smaller velocity, in consequence of the enormous mass of the 
 earth participating in the regression while the moving force retained the 
 same value. This is precisely the real case of nature, the equatorial 
 matter forming the circumambient ring, and the sun or moon representing 
 the disturbing body. Thus, after the lapse of nearly two thousand years 
 since its discovery by Hipparchus, the precession of the equinoxes was 
 finally traced to its physical origin. This grand phenomenon had in all 
 ages appeared utterly inexplicable to astronomers ; even Kepler, notwith- 
 standing his unrivalled aptitude in the formation of hypotheses, was 
 unable to account for it by any physical principle. Newton's explanation 
 was so natural that it could not fail to carry with it instant conviction. 
 Mr. Airy has well remarked that, "if at this time we might presume to 
 select the part of the Principia which probably astonished and delighted 
 and satisfied its readers more than any other, we should fix, without 
 hesitation, on the explanation of the precession of the equinoxes." 
 
 The sagacity ^ which Newton displayed in the discovery of the true 
 
 * Principia, book i. prop. 91, and book iii. prop. 19. 
 
 + Ibid., book iii. prop. 19. 
 
 i Ibid, book iii. prop. 20. 
 
 Encyc. Metrop., art. Figure of the Earth. 
 
HISTORY OP PHYSICAL ASTRONOMY. 39 
 
 cause of the conical motion of the earth, can only be equalled by his 
 boldness in making it the subject of a mathematical investigation ; for the 
 theory of the motion of a rigid body around its centre of gravity was yet 
 totally undeveloped. By means of several ingenious suppositions he suc- 
 ceeded in bringing the problem within the reach of his geometry, and 
 computed the quantity of precession due to each of the two disturbing 
 bodies *. The imperfect state of mechanical science, combined with the 
 intricacy of the subject, happened indeed in this instance to betray him 
 into a mistake ; but his solution of this great problem was on the whole 
 sound, and Laplace, who has critically examined it, has not failed to point 
 out its excellent merits f . 
 
 In pursuing his way through these abstruse researches, Newton seems 
 to have compensated by the innate resources of his genius for the defective 
 state of his methods. The accuracy of his results, in many cases in which 
 a rigorous course of investigation was impracticable, is one of the most 
 inexplicable facts in the annals of science. His clear insight into the 
 operation of physical principles and his fine discriminating judgment, 
 qualities which contributed so effectually to enhance the value of his delicate 
 researches in Optics, appear to have been equally favourable to him while 
 engaged in considering the less tangible and less familiar relations of the 
 system of the world. It is this wonderful facility of seizing truth as it 
 were with a single bound, without pursuing the long avenue of sequences 
 by which ordinary inquirers are conducted to it, which has led Delambre 
 to remark that the words of Fontenelle, in relation to Cassini, might be 
 much more appropriately applied to the English philosopher " Un 
 Astronome si subtil est presque uii devin ; on dirait qu'il pretend a la 
 gloire d'un astrologue." J 
 
 It is much to be regretted that Newton should have persevered so 
 generally in expounding his discoveries by the synthetic methods of the 
 ancient geometers, for it can hardly be doubted that he was in most cases 
 conducted to them by analysis. He probably feared that the infinitesi- 
 mal calculus would not be considered as imparting to his researches that 
 character of severe reasoning by which the synthetic mode of demonstration 
 is peculiarly distinguished. His apprehension will appear by no means 
 unreasonable, when we consider that the analytical instrument of inves- 
 tigation was then in its infancy, and that very few persons were acquainted 
 with its true principles. By his practice, however, of presenting his re- 
 searches in a synthetic form, he deprived himself of the honour attached 
 to many important discoveries in analysis, which his results indicate him 
 to have been in possession of. The famous problem of the solid of least 
 resistance affords a striking illustration of this remark. In the scho- 
 lium to the 34th proposition of the second book of the Principia, he gives 
 the construction of this solid, but does not accompany it with any demon- 
 stration. This is the first of a peculiar class of problems that was ever 
 solved, and it is clear, from Newton's construction, that he must have been 
 acquainted with those principles of the infinitesimal analysis which form 
 the basis of the Calculus of Variations . 
 
 * Book iii. prop. 39. t Mec. Cel., liv. xiv. chap. 1. 
 
 \ Histoire de 1'Astronomie Moderne, tome ii. p. 739, and Histoire au Dixhuitieme 
 Siecle, p. 630. 
 
 It is quite conceivable, when we consider Newton's powers of generalization, that, if 
 he had devoted much attention to problems of this nature, he might have been conducted 
 to the Calculus of Variations. We have no reason however to conclude, from his solution 
 of the problem cited in the text, that he was in possession of the general method of Lagrange 
 
40 HISTOKY OF PHYSICAL ASTBONOMY. 
 
 This illustrious philosopher, who contributed more than any other mortal 
 ever did towards enlarging the domain of human knowledge, appears to 
 have been quite unconscious of any difference between himself and or- 
 dinary inquirers of nature. Alluding to his discoveries in a letter to Dr. 
 Bentley, he says, " If I have done the puMic any service this way, it is 
 due to nothing but industry and patient thought." In fact, it was only 
 by the most strenuous contention of mind, and the sternest subjection of 
 the will, that even Newton was enabled to penetrate into the more recondite 
 parts of the system of the world. One of his biographers has remarked * 
 that, during the two years he was engaged in preparing the Principia, he 
 lived only to calculate and think. Oftentimes lost in the contemplation of 
 those grand objects to which it relates, he acted unconsciously, his thoughts 
 appearing to take no cognizance of the ordinary concerns of life. Fre- 
 quently, when rising in the morning, he would be arrested by some new 
 conception, and would remain for hours seated on his bedside in a state of 
 complete abstraction. He would even have neglected to take sufficient 
 nourishment if he had not been reminded by others of the time of his 
 meals. Speaking of the mode by which he arrived at his discoveries, he 
 said, " I keep the subject constantly before me, and wait till the first 
 dawnings open slowly by little and little into a full and clear light." On 
 another occasion, when some of his friends were complimenting him on 
 the great results he had achieved, he replied : " I know not what the 
 world will think of my labours, but to myself it seems to me that I have 
 been but as a child playing on the sea-shore ; now finding some pebble 
 rather more polished, and now some shell rather more agreeably variegated 
 than another, while the immense ocean of truth extended itself unexplored 
 before me." What a lesson of humility is here conveyed to those ex- 
 plorers of nature who cannot congratulate themselves on the discovery 
 even of such shells and pebbles as those which adorn the cabinet of the 
 Principia. 
 
 Newton died on the 20th March, 1727, at the advanced age of 
 eighty-five years. Unlike some of his illustrious predecessors, he con- 
 tinued throughout his long career to receive the honours due to his 
 exalted genius, and his death was deplored as a national calamity. His 
 funeral obsequies were performed with the ceremonies usually confined 
 to persons of royal birth. His body lay in state in the Jerusalem 
 Chamber, and was subsequently interred in Westminster Abbey, his pall 
 having been borne by six peers. A monument was erected over his re- 
 mains, the inscription upon which concludes with the following suitable 
 words : " Sibi gratulentur mortales, tale tantumque extitisse humani 
 generis decus."f 
 
 for this purpose, any more than we should be warranted in inferring from Fermat's theory 
 of Maxima and Minima, or Barrow's Method of Tangents, that either of these mathema- 
 ticians had discovered the Differential Calculus. The probability is, that in this, as in many 
 other instances, Newton solved the problem merely en passant, attending less to the means 
 than the end to be obtained by them. 
 
 * Biot. Biographic Universelle. See also Life of Newton, L. U.K. 
 
 f Let mortals congratulate themselves that so great an ornament of the human race has 
 existed. 
 
HISTORY OF PHYSICAL ASTRONOMY. 41 
 
 CHAPTER III. 
 
 Circumstances which impeded the early progress of the Newtonian Theory. Its reception 
 in England. Reception on the Continent. Huygens, Leibnitz. Researches in Ana- 
 lysis and Mechanics. Their influence on Physical Astronomy. Problem of Three 
 Bodies. Motion of the Lunar Apogee. Clairaut. Lunar Tables. Mayer. 
 
 NOTWITHSTANDING the multitude of sublime discoveries by which the 
 theory of gravitation was first announced to the world, no attempt was 
 made to develope the views of its immortal founder, during the first half 
 century that elapsed after the publication of the Principia. The seductive 
 speculations of Descartes had already taken a firm hold of men's minds, 
 and had been introduced as a branch of scientific study into the principal 
 universities of Europe. Independently of this circumstance, the profound 
 and intricate reasoning, which Newton was compelled to adopt in the 
 Principia, formed a serious impediment to the early dissemination of his 
 doctrines. As the questions considered in that immortal work were ge- 
 nerally of the kind which required the aid of the higher geometry for their 
 complete investigation, only a very small number of mathematicians were 
 qualified to appreciate the evidence upon which the conclusions of the au- 
 thor were founded. The methods also which he employed in expounding 
 his discoveries were almost wholly the creation of his own genius, and it 
 was necessary to study them with deep attention in order to become fa- 
 miliar with their real character. Hence it is easy to understand why the 
 severe doctrines of the Principia continued long to be neglected, while 
 the more accommodating principles of the Cartesian theory met with 
 universal favour. 
 
 The country which gave birth to Newton may in some degree be con- 
 sidered an exception to these remarks. The Principia, upon its first ap- 
 pearance, was read with admiration by the most eminent mathematicians 
 of the day ; and the sublime truths announced in it were enthusiastically 
 embraced by the more intelligent classes of the community. The uni- 
 versity of St. Andrews, in Scotland, has the honour of being the first Aca- 
 demic Institution which admitted the Newtonian theory as a subject of 
 study. In 1690, James Gregory, the celebrated mathematician who was 
 then professor of philosophy in that university, published a thesis con- 
 taining twenty-five positions, twenty-two of which are said to have formed a 
 compendium of the Principia. The same principles were introduced into 
 the university of Cambridge under the auspices of Dr. Samuel Clarke, 
 the personal friend of Newton. Whiston first expounded them from the 
 chair, in the year 1699. They were also taught at Oxford by Keil, as 
 early as the year 1704. 
 
 On the continent, all the great mathematicians were unanimous in 
 their hostility to the Newtonian theory. Huygens, although he generally 
 speaks of Newton in terms of profound admiration, was so strongly im- 
 pressed with his own peculiar notions of gravity, that he failed to appre- 
 ciate the force of the reasoning by which the doctrines of his contemporary 
 were supported. He admitted the mutual gravitation of the planets and 
 satellites according to the law of the inverse square of the distance ; but 
 he could not be persuaded to extend the same principle to the material 
 molecules of which the several bodies are composed. He had adopted 
 
S HISTOEY OF PHYSICAL ASTRONOMY. 
 
 Descartes' notion of a vortex, to explain the descent of bodies at the 
 earth's surface ; but in order to account for their invariable tendency to 
 the centre of the earth, and not to the axis, he supposed the ethereal me- 
 dium composing the vortex to circulate rounjl the earth in all directions. 
 In accordance with these views, he considered the force of gravity to be 
 equally intense at all equal distances from the centre of the earth ; and his 
 investigation of the figure of the latter was founded simply on the statical 
 relation connecting the absolute value of gravity with the centrifugal force 
 generated by the diurnal motion. Alluding in one of his works to New- 
 ton's researches relative to the figure of the earth, he says that they are 
 based upon a principle which appears to him inadmissible, inasmuch as it 
 supposes that all the particles of matter attract each other ; but this he 
 contends to be an unfounded assumption, which cannot be reconciled with 
 the established laws of mechanics. On another occasion his language, 
 though more cautious, is decidedly hostile to the doctrines of the English 
 philosopher. " Newton," says he, " believes that the space between the 
 celestial bodies is void ; or at least that the fluid pervading it is so rare 
 as not to affect the motions of the planets ; but, if this were true, my ex- 
 planation of light and gravity would be entirely overthrown." It is inte- 
 resting to remark the sound views by which this distinguished philosopher 
 was guided when his mind was not wholly under the influence of his own 
 favourite notions. In course of some allusions to the Cartesian theory, 
 he thus expresses his deliberate opinion respecting the merits of that cele- 
 brated fiction. "The entire system of Descartes, concerning comets, 
 planets, and the origin of the world, rests upon so weak a foundation, that 
 I wonder how the author of it took the trouble of arranging so many re- 
 veries. We should have achieved a great step if we succeeded in forming 
 a clear idea of what really exists in nature, but we are still very far from 
 having attained that end."* 
 
 Leibnitz and John Bernouilli were equally conspicuous in their opposi- 
 tion to the Newtonian theory. In 1689 Leibnitz published a physical 
 dissertation in the Leipsic acts, in which he explained the motions of the 
 planets by means of an ethereal fluid, somewhat after the manner of Des- 
 cartes. By the aid of several arbitrary assumptions, he succeeded in shew- 
 ing the possibility of an elliptic motion in a vortex, and hence deduced the 
 law of the inverse square of the distance ; but it is remarkable that, al- 
 though he was indebted to Newton for the suggestion of this law, he merely 
 incidentally mentions the name of the English philosopher in connexion 
 with it; and appears to be totally ignorant of the Principia, although two 
 years had passed since it was published. " I see," says he " that this law 
 has been already deduced by the celebrated geometer, Isaac Newton, as 
 appears from an account of it given in the Leipsic acts, but I am unac- 
 quainted with the mode by which he arrived at it." 
 
 In France, the Cartesian philosophy, as may naturally be supposed, was 
 for a long time even more popular than in any other country. Cassini, 
 and Maraldi, persisted till their deaths in rejecting the theory of gravita- 
 tion ; and their example was generally followed by contemporary astro- 
 nomers. The earliest historical recognition of Newton's principles in 
 France, is contained in a memoir by Louville, which appeared in the vo- 
 lume of the Academy of Sciences for the year 1730. The motion of a 
 
 * Kosmotheoros sive de Terris Celestibus earuraque natura conjecturoe. 4to, Hagre, 
 1698. 
 
HISTORY OF PHYSICAL ASTEONOMY. 43 
 
 body in an elliptic orbit is there explained by means of two forces the 
 one a momentary impulse directed along the tangent ; the other a con- 
 tinuous force tending towards the focus of the ellipse. Maupertius was 
 the first astronomer of France who undertook a critical defence of the 
 theory of gravitation. In his treatise on the figures of the celestial bodies, 
 which appeared in the year 1732, he compared together the theories of 
 Descartes and Newton, and concluded by expressing a strong opinion in 
 favour of that of the latter philosopher. The person, however, who con- 
 tributed most to the general diffusion of the doctrines of gravitation in 
 France, was unquestionably Voltaire. In 1738 that celebrated writer 
 published a brief but very luminous exposition of Newton's most import- 
 ant discoveries in optics and astronomy. Being written in a popular 
 style, this little work soon found its way into all ranks of society ; and 
 from the time of its first appearance we may date the triumph of New- 
 ton's principles over those of his once redoubtable rival. 
 
 Although Physical Astronomy may be considered as almost stationary 
 during the period we have been considering, there were causes in silent 
 operation which contributed powerfully to its future developement. Since 
 the time of its invention, by Newton and Leibnitz, the infinitesimal ana- 
 lysis continued to be assiduously cultivated by the most eminent mathemati- 
 cians of Europe, and was rapidly advancing to a high state of perfection. 
 Without the aid of this powerful instrument of research, it would have been 
 impossible to determine with precision the minute irregularities which 
 take place in the motions of the planets in virtue of their mutual attrac- 
 tion. Newton, in his investigations, had applied the ancient geometry 
 with almost superhuman address ; but he appeared to have utterly ex- 
 hausted its resources, and no other course remained for his successors 
 than to devise other methods of greater fertility and more easy applica- 
 tion. Leibnitz, and the two Bernouillis, by means of their brilliant re- 
 searches in the new calculus, were unconsciously promoting this desirable 
 end. These eminent analysts little imagined, while sneering at the 
 theory of gravitation, that their own labours were destined to become 
 subservient in reconciling its most minute consequences with the observed 
 motions of the celestial bodies, and thereby in placing it for ever beyond 
 the reach of cavil. The researches in mechanics, which engaged the at- 
 tention of geometers during this period, also exercised a favourable in- 
 fluence in preparing men's minds for the consideration of the great ques- 
 tions relating to the system of the world. This branch of science ap- 
 peared to offer an unlimited field of original speculation, until D'Alern- 
 bert*, in 1740, discovered a general principle by means of which every 
 question of motion was immediately reducible to a corresponding one of 
 equilibrium. The statical equations being easily formed, the difficulties 
 attending all such researches henceforth assumed a purely analytical cha- 
 racter. It is not improbable that this important generalization had the ef- 
 fect of directing the attention of geometers to physical astronomy, which 
 now presented the most inviting field of study. 
 
 The success which attended Newton's efforts to explain the phenomena of 
 the system of the world, by the principle of universal gravitation, was well 
 calculated to encourage his followers to engage in similar researches. 
 Not only did he give a complete theory of the motion of two bodies 
 revolving under the influence of their mutual attraction, but, with un- 
 
 * Born at Paris, 1717; died in 1783. 
 
44 HISTOEY OF PHYSICAL ASTEONOMY. 
 
 rivalled sagacity, he also traced the various disturbing effects produced by 
 the action of a third body upon either of them, and even actually com- 
 puted several of the more important inequalities in the moon's motion; 
 He did not attempt to investigate the effects of the mutual attraction of 
 the planets, but he clearly perceived that* the elliptic motion of each 
 would in consequence be more or less deranged ; and he especially re- 
 marked that the action of Jupiter on Saturn, when these two planets 
 were in conjunction, attained such a magnitude that it could not be over- 
 looked *. In one important instance Newton signally failed in recon- 
 ciling his theory with observation. "We allude to his attempt to deter- 
 mine the motion of the lunar apogee, on which occasion he obtained a 
 result equal only to half the quantity which observation assigned. This 
 discordance was naturally considered as offering a serious objection to the 
 Newtonian theory ; for the evection, which is the largest inequality in the 
 moon's longitude, after the elliptic inequality, depends, to a certain extent, 
 on the motion of the apogee, and therefore it still remained inexplicable 
 by the principle of gravitation. 
 
 Euler appears to have been the first geometer who attempted the 
 developement of physical astronomy beyond the point at which the founder 
 of it had left it. In 1745 he investigated the perturbations of the moon, 
 and in the following year he constructed new lunar tables based upon his 
 researches; but, as he employed few observations in determining the 
 maximum values of the inequalities, his tables did not present a marked 
 superiority over those in actual use. About the same time Clairaut f and 
 DAlembert, two of the fii'st geometers of France, undertook the investi- 
 gation of the lunar perturbations without any knowledge of each other's 
 intentions. 
 
 The Academy of Sciences of Paris having offered their prize of 1748, 
 for an investigation of the irregularities of Jupiter and Saturn, Euler J 
 composed a memoir on the subject, which he transmitted to the Academy 
 in the month of July, 1747. The two geometers above mentioned, 
 naturally imagining that their eminent contemporary might anticipate 
 them in their researches, took the precaution of communicating the result of 
 their labours to the Academy before the time appointed for the award of 
 the prize. Clairaut lodged his memoir in the hands of the Secretary on 
 the 9th of November, 1747, and DAlembert on the 15th of the same 
 month. In all the three memoirs, the perturbing action of the celestial 
 bodies was investigated by an analytical process. Clairaut mentions that 
 he first endeavoured to calculate the lunar inequaHtes after the manner of 
 Newton ; but, having been soon stopped by insuperable difficulties, he 
 decided upon having recourse to analysis alone in all his researches. 
 
 The subject, even when so treated, is one of astonishing intricacy ; but, 
 
 * Newton remarked that when Jupiter and Saturn are in conjunction, the action of 
 Jupiter upon Saturn is to the action of the sun upon the same planet, as I to 211 : 
 " whence," says he, " there arises, in each conjunction with Jupiter, a derangement of 
 Saturn's orbit, which is so sensible, as to be the cause of embarrassment to astronomers." 
 Princip. , b. iii. prop 13. Euler, however, discovered by analysis that the corresponding 
 derangement of Jupiter is about six times greater, although the action of Saturn upon 
 that planet is to the action of the sun only as 1 to 500. " This remark of Euler's," says 
 Laplace, " shows us that we ought not to adopt, but with exfreme reserve, the most 
 plausible appearances so long as they are not verified by decisive proofs." Mec. Cel., 
 tome v. p. 302. 
 
 f Born at Paris, 1713; died, 1765. 
 
 Born at Basle, 1707 ; died at St. Petersburg, 1783. 
 
HISTORY OF PHYSICAL ASTBONOMY. 45 
 
 fortunately, the planetary system is so constituted as to favour the re- 
 searches of the mathematician. The problem of a planet's motion, when 
 considered in its most general sense, requires that we should include in 
 one common investigation the attractive forces exerted upon the planet by 
 the various bodies composing the solar system. The sun, however, exer- 
 cises such a preponderating influence, on account of his enormous mass, 
 that we may regard each of the planets as revolving round him in an orbit, 
 approaching very closely to an ellipse ; while the other planets may be 
 considered as so many perturbing bodies, producing continual irregularities 
 in the elliptic motion. These perturbations being very minute, the action 
 of each planet may be investigated in succession, without taking into 
 account the simultaneous action of the others ; and the aggregate of the 
 results so obtained, when applied to the elliptic motion, will determine the 
 true place of the planet in its orbit. The whole question is, therefore, 
 reduced to the investigation of the motion of one body revolving round 
 another, and continually disturbed by the attraction of a third body. 
 Thus originated the famous Problem of Three Bodies, which has formed 
 the basis of so much profound research in physical astronomy. The 
 rigorous solution of this problem has been found to surpass the powers of 
 the understanding, notwithstanding the many improvements which have 
 been effected in the infinitesimal analysis ; but the same considerations, 
 which limit the investigation to the mutual attraction of three bodies, 
 conduct also to other important simplifications. The masses of the 
 planets being in fact very small, compared with the sun's mass, and the 
 eccentricities as well as the inclinations of the planetary orbits being also 
 very inconsiderable, a number of terms involving these elements in the 
 general solution of the problem become, in consequence, so small as to 
 admit of being rejected ; and the geometer is thereby enabled to bring the 
 subject within the reach of his analysis. Notwithstanding these obvious 
 advantages, the utmost resources of a profound calculus, combined with 
 the most consummate analytical skill, are indispensably required, in order 
 to effect a solution of this difficult problem ; and even then the object can 
 only be attained by a process of successive approximation. In the lunar 
 theory, the principal disturbing body is the sun ; for the planets are either 
 too small or too remote to exercise much influence. It might naturally 
 be supposed that the sun, on account of his enormous mass, would veiy 
 much derange the moon's motion ; but in reality the effect of his attractive 
 power is greatly diminished by the immense distance at which he is placed 
 compared with the earth, which is in this case the central body. Still the 
 inequalities of the moon's motion are much more considerable than the 
 perturbations which take place in the motions of the planets ; and, on this 
 account, they were justly considered to afford the most favourable means 
 of testing the theory of gravitation. We have already alluded to the 
 failure which attended Newton's attempt to determine the motion of the 
 lunar apogee. Singular enough, when Clairaut and the other two 
 geometers above mentioned deduced the motion of the apogee from their 
 respective analytical solutions of the problem of the lunar perturbations, 
 they found, like Newton, that the result was equal only to half the 
 observed motion. This anomalous fact excited great surprise in the 
 scientific world, and many persons began to entertain a strong suspicion 
 that the law of gravitation, as announced by Newton, was erroneous. 
 Clairaut, despairing of being able to reconcile the ordinary law with the 
 results of observation, proposed that, instead of representing the force by 
 
46 HISTORY OP PHYSICAL ASTRONOMY. 
 
 a term depending on the inverse square of the distance, it should be 
 expressed by two terms, one composed of the inverse square, and the 
 other of the inverse of the fourth power of the distance. Buffoii adduced 
 metaphysical arguments against this law ; and the question continued to 
 excite a deep interest among men of science. At length Clairaut dis- 
 covered that, when the lunar perturbations were rightly computed, accord- 
 ing to the Newtonian law, the motion of the apogee, when so computed, 
 was exactly conformable to the observed motion. 
 
 He found, in fact, by repeating the approximation and taking into 
 account certain small terms which he had previously neglected, that the 
 value obtained by him in the first instance was now exactly doubled. 
 D'Alembert and Euler, upon a revisal of their labours, arrived at the same 
 conclusion ; and thus a circumstance, which at one time threatened to 
 subvert the whole structure of the Newtonian theory, resulted in becoming 
 one of its strongest confirmations. 
 
 It is right, also, to mention that Thomas Simpson arrived at the correct 
 motion of the apogee before he learned the successful result of Clairaut's 
 labours. This eminent analyst might have done much ta sustain the 
 reputation of his country in the researches of physical astronomy if he had 
 lived under more auspicious circumstances. 
 
 The method of lunar distances, which offers such advantages in finding 
 the longitude at sea, rendered an accurate knowledge of the moon's motion 
 peculiarly desirable. In 1754, Clairaut and D'Alembert published lunar 
 tables based upon their respective theories. Those of Clairaut obtained 
 considerable credit for accuracy ; but D'Alembert's efforts were less for- 
 tunate, chiefly in consequence of having paid too little attention to observ- 
 ation in the evaluation of his coefficients. In 1755 Euler published his 
 researches in the lunar theory, accompanied with new tables, greatly 
 superior in accuracy to those of 1746. In his analysis he resolved the 
 forces acting upon the moon along three rectangular co-ordinates, after the 
 example of Maclaurin, who, a few years previously, had first employed 
 this method in his elegant geometrical investigations connected with the 
 question of the Tides. In 1772 he published a third set of tables, based 
 upon a most elaborate analysis of the moon's motion ; but, notwithstanding 
 the amount of thought expended on them, they proved inferior in point of 
 accuracy to those of Mayer, chiefly in consequence of his having placed too 
 much reliance on theory in fixing the maximum values of the equations. 
 Mayer, to whom allusion has been already made, was the first person who 
 constructed lunar tables of sufficient accuracy for the great practical pur- 
 pose of finding the longitude at sea. This he did in 1755, by means of 
 Euler's theory and a skilful discussion of observations. These tables 
 were found to come within the limit of accuracy fixed by the Board of 
 Longitude of this country ; and a recompense of 3000 was in consequence 
 awarded to the widow of Mayer, the astronomer himself having died some 
 years before this decision was come to. Bradley, who was appointed to 
 compare the tables with observation, states, in his report of them, that in 
 no case did the error exceed l. They were first printed in the year 
 1770. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 47 
 
 CHAPTER IV. 
 
 Perturbations of the Planets. Inequality of Long Period in the Mean Motions of Jupiter and 
 Saturn. Researches of Euler. Perturbations of the Earth. Clairaut. Perturbations 
 of Venus. Lagrange. His Investigation of the Problem of Three Bodies. Secular 
 Variations of the Planets. Laplace. His Researches on the Theory of Jupiter and 
 Saturn. Invariability of the Mean Distances of the Planets. Oscillations of the Ec- 
 centricities and Inclinations. Stability of the Planetary System. 
 
 THE planets, while revolving round the sun, continually disturb each other 
 by their mutual attraction, and hence arise numerous inequalities in their 
 motions, similar to those which take place in the motion of the moon 
 round the earth. Although these disturbing forces form a class of rela- 
 tions as complicated as the mind can perhaps imagine, the study of their 
 effects is on many accounts peculiarly attractive to the thoughtful enquirer. 
 The fundamental ideas are clear and well defined ; the principles are 
 firmly established, the methods of research are derivable wholly from 
 the resources of the intellect, and the subject is both vast in extent and 
 varied in character. The magnificent prizes which the theory of gra- 
 vitation offers prospectively to the mathematician, as the rewards of 
 his labours, are also calculated to allure his researches, while its ex- 
 treme intricacy serves only to redouble his energies, and stimulate his 
 inventive powers. Hence Physical Astronomy is characterized by a 
 multitude of conceptions at once ingenious, subtle, and profound, while its 
 investigations are pursued, throughout their long and intricate windings, 
 with a coherence and beauty of ratiocination unequalled in any other 
 branch of Natural Philosophy. 
 
 Apart from those more obvious questions which impart an interest to 
 the study of Celestial Mechanics, others of the highest moment, with re- 
 spect to the stability of the system of the world, are also involved in the 
 subject. These questions naturally offered themselves to mathematicians, 
 while engaged in researches connected with the actual motions of the 
 planets, and continued for some time to form the subject of profound 
 study. Their complete solution will ever be ranked among the most 
 brilliant triumphs recorded in the annals of science, while it has shed an 
 imperishable lustre on the names of those eminent individuals by whose la- 
 bours it has been achieved. 
 
 The masses of the planets being small compared with the mass of the 
 central body, the derangements occasioned by their mutual attraction do 
 not in any case attain a magnitude comparable to that of the lunar ine- 
 qualities. Indeed their existence has generally been established only by 
 a comparison of distant observations, conducted with all the refinements of 
 practical astronomy. In many instances theory has preceded observation, 
 and has pointed out inequalities which, on account of their extreme mi- 
 nuteness, might otherwise have for ever escaped detection. The planets 
 Jupiter and Saturn, being favourably placed in the system for the exer- 
 tion of their mutual attraction, and their masses being also considerable, 
 it might be expected that the inequalities of their motions would be more 
 readily appreciable than those of the other planets. In fact, as early as 
 1625, Kepler remarked that the observed places of these planets could 
 not be reconciled with the usually admitted values of their mean motions. 
 
48 HISTORY OF PHYSICAL ASTKONOMY. 
 
 The errors of both planets were found to increase continually in the same 
 direction, with this difference, that the tables made the mean motion of 
 Jupiter too slow, and that of Saturn too quick. Lemomiier found that, by 
 adopting the mean motion of Saturn, as determined by a comparison of 
 ancient with modern observations, the planet, had fallen behind its com- 
 puted place to the extent of 2' in 1598, 20|' in 1657, and 36^' in 1716. 
 
 Halley first suspected that the anomalous irregularities of the two pla- 
 nets were due to their mutual attraction. He also attempted to determine 
 the magnitude of the inequality for each planet. He concluded from his 
 researches that in 2000 years the acceleration of Jupiter amounted to 
 3 49', and the retardation of Saturn to 9 16'. In his tables of the pla- 
 nets he represented the errors by two secular equations increasing as the 
 square of the time, the one being additive to the mean motion of Jupiter, 
 and the other subtractive from the mean motion of Saturn. 
 
 The Academy of Sciences of Paris, desirous of obtaining an explana- 
 tion of these inequalities, in accordance with the theory of gravitation, of- 
 fered its prize of 1748 for their complete investigation. Euler was in- 
 duced to compose a memoir on the subject, which was crowned by the 
 Academy ; but, although his researches contain a valuable exposition of the 
 analytical theory of planetary perturbation, he was unable to throw any 
 light on the main object of the inquiry. He found a series of inequalities 
 in the mean motions of both planets, but they were all such as completed 
 the cycles of their values every time that the planets returned to the 
 same configurations. He concluded, therefore, that the observed irregula- 
 rities must be attributed to some extraneous cause, and not to the mutual 
 attraction of the two planets. 
 
 Euler in this memoir resolved the differential equation, relative to the 
 latitude of the disturbed planet, into two differential equations of the first 
 order, one of them expressing the differential of the inclination, and the 
 other that of the planet's distance from the node. This may be con- 
 sidered as the germ of the famous method of the variation of arbitrary con- 
 stants. 
 
 The theory of Jupiter and Saturn offers some difficulties of a peculiar 
 kind, which did not occur in the investigation of the lunar inequalities. 
 The disturbing action of one body upon another may be expressed by a 
 series of terms involving the ratio of the mean distances of both from the 
 central body. In the lunar theory this fraction is very small, on account 
 of the great distance of the sun, which is the disturbing body ; hence the 
 terms converge with great rapidity, and an approximate value of the se- 
 ries is readily obtained. When the question, however, refers to the mu- 
 tual action of Jupiter a,nd Saturn, the same fraction rises to a considerable 
 magnitude, and the terms of the series converge in consequence with 
 such extreme slowness, as to render impracticable the usual method of 
 computation. Euler's genius was eminently conspicuous in devising the 
 means of vanquishing this difficulty, which would effectually have ob- 
 structed a mind gifted wjth less fertile powers of invention. 
 
 The explanation of the motion of the lunar apogee by Clairaut in 1749, 
 having inspired renewed confidence in the principle of gravitation, as ade- 
 quate to account for all the phenomena of the planetary motions, the 
 Academy of Sciences was again induced to propose the theory of Jupiter and 
 Saturn as the subject of their prize for 1752. Euler was on this occasion 
 also the successful competitor, but he now actually discovered secular equa- 
 tions in the mean motions of both planets, depending on the angular distance 
 
HISTORY OF PHYSICAL ASTRONOMY. 49 
 
 between the aphelia of their orbits. Contrary to observation, however, he 
 found that the two equations were equal in magnitude, and were in both 
 cases additive to the mean motion. He fixed the inequality at %' 24" for 
 the first century, counting from 1700. Notwithstanding the analytical 
 skill which this geometer displayed in his researches, he signally failed in 
 his efforts to account for the irregularities of the two planets by the New- 
 tonian theory ; and their physical origin, therefore, still continued to be 
 involved in profound mystery. 
 
 The attention of geometers was now directed to the perturbations in 
 the earth's motion occasioned by the other planets. Euler investigated 
 this subject in an elaborate memoir, which was crowned by the Academy 
 of Sciences in the year 1756. It was on this occasion that he explained 
 and partially developed the theory of the variation of arbitrary constants. 
 In considering the motion of a planet in an elliptic orbit, there are six 
 constants or elements, which by their independent variations would se- 
 verally modify the motion. These are 1, the major axis of the orbit, or 
 the mean distance ; 2 the eccentricity ; 3, the position of the line of 
 apsides ; 4, the inclination of the orbit with respect to a fixed plane ; 5, 
 the position of the line of nodes ; 6, the longitude of the planet at any 
 assigned instant, or the longitude of the epoch, as it is called. Now if the 
 planet were exposed only to the action of the sun these elements would 
 remain invariable, and the planet would continually revolve in the same 
 ellipse. Its place, corresponding to any given time, might therefore be 
 readily computed, by means of Kepler's law of the areas, when once these 
 six elements were known. As, however, it is continually disturbed in its 
 motion by the action of the other planets, the theory of a constant ellipse 
 will no longer be applicable to the question. Still, as its aberrations from 
 an elliptic orbit are very small, its place may be computed by assuming it 
 to move in a mean ellipse, and then ascertaining the minute irregularities 
 occasioned by the perturbing forces. This is the course which geometers 
 had hitherto pursued in all researches connected with the problem of 
 three bodies. Euler, however, proposed to compute the motion wholly by 
 the elliptic theory, upon the supposition that the planet continually re- 
 volved in an ellipse, the elements of which varied every instant from the 
 action of the other planets. By these means the whole effect of perturba- 
 tion was thrown upon the elements of the orbit, and when these were as- 
 certained for any given instant, it was easy to calculate the corresponding 
 place of the planet by the elliptic theory alone. As this refined concep- 
 tion has not unfrequently been ascribed to Lagrange, it may be proper to 
 cite Euler's own words in reference to it. After obtaining the differential 
 expressions of the elements, he then proceeds in the following terms to 
 point out their advantages : " These formulae appear to be peculiarly com- 
 modious in computing the deviations of the motion from Kepler's laws ; 
 since they have reference to motion in an ellipse, which varies continually, 
 as well in respect to the parameter as to the eccentricity and the po- 
 sition of the apsides. For, during an indefinitely small portion of time, 
 the motion of the planet may be conceived as taking place in an ellipse, 
 according to the laws of Kepler ; and, if the elements of this ellipse be 
 computed for any given time, by means of the formal just found, the true 
 place of the planet, relative to an assumed plane, may be also assigned."* 
 This investigation of Euler's, like the two previous ones, displays abun- 
 
 * Prix de P Academic, tome viii. Investigatio Motuum Planotanim. ]>. '2V. 
 
50 HISTORY OP PHYSICAL ASTRONOMY. 
 
 dant proofs of the amazing fertility of his inventive powers, and his great 
 command of analysis ; but in regard to the final results obtained by him 
 he was not equally fortunate. Grave errors of calculation prevented him, 
 on this as well as on several other occasions, from duly appreciating the 
 importance of his own methods. 
 
 Clairaut, about the same time, investigated the Earth's perturbations in 
 a memoir distinguished by great perspicuity and skill *. By a comparison 
 of his theory with the observations of Lacaille, he fixed the lunar equation 
 at 8".7. This result gives for the moon's mass J T of the earth's, a 
 quantity which differs considerably from the value assigned to it by 
 Newton. In order to compute the actual perturbations occasioned by the 
 other planets, it was necessary to possess a knowledge of their masses. 
 He skilfully determined the mass of Venus by means of observations 
 made on the sun when the moon was in that part of her orbit wherein she 
 produced no effect on the earth's motion. The mass of Jupiter, the only 
 other planet that he conceived would occasion a sensible derangement of 
 the Earth, was easily derivable from the elongations of his satellites, and 
 had already been determined by Newton. Combining together the pertur- 
 bations of Jupiter, Venus, and the Moon, he found that when they con- 
 spired in the same direction the error of the Earth in longitude might rise 
 to 1'. 
 
 D'Alembert also investigated the subject of the planetary perturbations 
 in the year 1754 f ; but his researches did not add anything new to the 
 subject. Lalande applied Clairaut 's theory to the perturbations of Mars, 
 by Jupiter and the Earth, and found that the derangement might rise 
 to 2'. Mayer, about the same time, arrived at a similar conclusion by 
 means of Euler's theory. Lalande also computed the perturbations of 
 Venus, and obtained 15" for the maximum value; a result which was 
 confirmed by similar researches of Father Walmsley in England. 
 
 Meanwhile another geometer, gifted with powers of the highest order, 
 was about to commence his brilliant career. In the volume of the Turin 
 Memoirs for 1763, Lagrange J gave a new solution of the Problem of Three 
 Bodies, which he applied to the theory of Jupiter and Saturn. He ob- 
 tained for Saturn a secular equation equal to 14".221, and subtractive 
 from the mean motion ; and for Jupiter a similar equation equal to ".740, 
 and additive to the mean motion. This result agreed better with observa- 
 tion than that of Euler, who made the equations both additive and equal 
 in magnitude ; but it by no means assigned a complete explanation of the 
 irregularities in the mean motions of the two bodies. 
 
 Attention was now directed to the secular inequalities of the pla- 
 nets. A comparison of distant observations had shown that the elliptic 
 elements of each planet were subject to a slow variation, which proceeded 
 continually in the same direction, and apparently to an indefinite extent. 
 These variations have been denominated secular because they require an 
 immense number of ages for their complete developement ; while, on the 
 other hand, those that are termed periodic complete the cycles of their 
 values with all similar configurations of the planets. It is obvious that 
 this shifting of the elements, however slow, would ultimately render 
 useless the tables of the planets, constructed for any given epoch, unless 
 due account were constantly taken of the altered value of each element. 
 
 * Mem. Acad. des Sciences, 1754. 
 
 + Recherches sur difterens points du Systeme du Monde, tome 1 and 2. 
 
 | Born in 1736 at Turin ; died at Paris in 1813. 
 
HISTORY OP PHYSICAL ASTRONOMY. 51 
 
 It is indispensable then to investigate these variations, and to compute 
 their numerical values, with the view of applying them as corrections to 
 the fundamental elements of the tables. But, apart from all consider- 
 ations connected with the requirements of practical astronomy, the study 
 of the secular variations is pregnant with the deepest interest to the 
 physical inquirer ; for it is manifest that their indefinite continuance in 
 the same direction would result in the complete destruction of the sta- 
 bility of the planetary system. 
 
 The illustrious Euler led the way in these sublime researches. In his 
 memoirs of 1748 and 1752, he determined the secular variations of the 
 elements of Jupiter and Saturn ; but he was prevented by the intricate 
 nature of the subject, and the immense calculations which it entailed upon 
 him, from arriving at very accurate conclusions. He found that the 
 aphelia of both planets had a progressive motion, as in the case of the 
 lunar apogee. He fixed the annual progression of Jupiter's aphelion at 
 9". 5, and that of Saturn's at 13". 
 
 But the most important element was the mean motion. We have 
 already mentioned that Euler found a secular inequality in that element, 
 equal and additive for both planets, and that Lagrange was conducted to a 
 result which accorded better with the observed irregularities, but still was 
 inadequate to their complete explanation. It was at this stage of the 
 planetary researches that Laplace*, for the first time, appeared as the rival 
 of Lagrange. Struck with the discordant conclusions to which geometers 
 had been conducted, he resolved to institute a searching investigation into 
 the subject. Euler and Lagrange had neglected all terms which exceeded 
 the second powers of the eccentricities and inclinations ; Laplace, 
 besides carefully repeating the calculations of these geometers, carried 
 his approximation to the terms of the third order. When he 
 came to apply his formula to the mean motion of Saturn, he was sur- 
 prised to find that all the terms affecting that element destroyed each 
 other. He obtained a similar result, when, by means of the same for- 
 mula, he computed the effect of Saturn's disturbing action upon the mean 
 motion of Jupiter. Justly suspecting that these results had no connexion 
 with the particular values of the elements of Jupiter and Saturn, he inves- 
 tigated the subject by a general analysis, applicable to any two planets 
 of the system, and he now again found that the .sum of the terms affecting 
 the mean motion was identically equal to zero. He remarked, that if any 
 such terms were contained among those involving the fourth or higher 
 powers of the eccentricities and inclinations, they would be so small that 
 their effects would not become sensible until an immense number of ages 
 had elapsed. He therefore arrived at the important conclusion that, 
 from the time of the earliest astronomical observations which history 
 records down to the existing epoch, the mean motions of the planets has 
 not been sensibly altered by their mutual attraction, and hence he inferred 
 that the irregularities of Jupiter and Saturn must be attributed to some 
 disturbing cause independent of that principle f. 
 
 Although the result to which Laplace was conducted by his researches 
 was decisive in so far as the question relative to the irregularities of 
 Jupiter and Saturn was concerned, it still remained uncertain whether an 
 inequality of this kind might not exist among the terms involving the 
 higher powers of the eccentricities and inclinations. Such an inequality, 
 
 * Born in 1749, at Beaumont, in Lower Normandy ; died at Paris in 1827. 
 f Mem. des Savans Strangers, tome vii. 
 
 E 2 
 
52 HISTORY OF PHYSICAL ASTRONOMY. 
 
 however minute, would ultimately become considerable by continual accu- 
 mulation, and might affect the mean motions and the mean distances of the 
 planets to so great an extent as to occasion the total derangement of the 
 planetary system. In 1776 Lagrange investigated this important ques- 
 tion * on the supposition that the planets move in ellipses ; the elements 
 of which continually vary in consequence of their mutual perturbations. 
 The conclusion at which he arrived is one of a very remarkable character. 
 He discovered, by a very simple analysis, that the mean distances are 
 not subject to any secular variations whatever ; but are merely affected 
 by a series of inequalities, which compensate themselves in short periods 
 depending on the mutual configurations of the different planets. Thus, 
 amid all the changes that are incessantly taking place in the other 
 elements of the celestial orbits, the conservation of the mean distances 
 stands out in striking contrast to this law of mutation. The eccentricities 
 and inclinations will perpetually vary in magnitude ; the apsides and nodes 
 will similarly vary in position ; but, throughout an indefinite lapse of 
 ages, the mean motions of the planets will remain unaltered by their 
 mutual attraction. This result offers to our contemplation a sublime 
 example of the order which reigns among the vast bodies of the universe, 
 and of the unerring character of the laws by which they are controlled in 
 their courses. When viewed in relation to its effects upon the invariability 
 of the solar year, and the stability of the planetary system, it is justly 
 regarded as one of the most valuable truths in the whole range of physical 
 science. 
 
 Lagrange and Laplace were now zealously engaged in investigating 
 generally the secular variations of the planets. A knowledge of the 
 variations of all the elements is indispensable for the purposes of prac- 
 tical astronomy ; but, in so far as the stability of the system is concerned, 
 it is manifest that the variations of the apsides and nodes cannot produce any 
 effect. In the researches of physical astronomy the eccentricities and the 
 apsides are generally considered together by a common analysis, and the 
 same remark holds good in regard to the nodes and inclinations. In 
 1774 Lagrange investigated the secular variations of the nodes and 
 inclinations of the planets in an elaborate memoir, which appeared in the 
 volume of the Academy of Sciences for the same year. Having obtained 
 the differential expressions of these elements, he computed their annual 
 variations by assuming each element to vary at a uniform rate during a 
 limited number of years. This supposition is rendered allowable by the 
 excessive slowness with which the elements vary, and the method of 
 computation founded on it is sufficient for all purposes connected with the 
 actual state of astronomy. But in order to ascertain the real nature of 
 these variations, so as to be enabled to predict the condition of the ele- 
 ments throughout an indefinite number of ages, it is absolutely necessary 
 to integrate the differential equations relative to them. These appeared at 
 first to offer insuperable difficulties ; but Lagrange, by a happy transform- 
 ation of the variables, reduced them to linear differential equations of the 
 first order ; whence, by integration, he obtained finite expressions for both 
 elements. Examining, then, the mutual action of two planets, he found 
 that the inclinations would perpetually oscillate about mean values from 
 which they would deviate only by very small quantities. Applying this 
 principle to the planets Jupiter and Saturn, which he considered as form- 
 
 * Mem. Acad. des Sciences de Berlin, 1776. 
 
HISTORY OF PHYSICAL ASTRONOMY. 53 
 
 ing with the sun a system apart in the heavens, he found that the 
 greatest inclination of Jupiter's orbit to the ecliptic would be 2 % 18", 
 and his least 1 17 " 15"; and that the greatest inclination of Saturn's 
 orbit would be 2 32' 41" and his least 46' 49". Thus the whole varia- 
 tion of Jupiter's inclination amounted to 45' 3", and that of Saturn's to 
 1 45' 51". When the number of planets whose mutual action is con- 
 sidered exceeds two, the question offers greater difficulties ; and Lagrange, 
 in consequence, did not at this period of his researches attempt to inquire 
 whether the inclinations of the four planets nearest the sun oscillated 
 round mean values, like those of Jupiter and Saturn, or whether they 
 increased continually in the same direction, attaining in succession all 
 degrees of magnitude with respect to a fixed plane. 
 
 From the analytical expressions of the inclinations, he derived an 
 elegant method of determining geometrically the positions of the orbits at 
 the end of any given time, and of representing their several motions 
 relatively to each other. 
 
 Laplace successfully applied Lagrange's method of integration to his 
 own differential expressions of the nodes and inclinations. He also ex- 
 tended the same method to the equations of the eccentricities and the 
 aphelia, and obtained finite expressions for those elements similar in form 
 to those which Lagrange had already found for the nodes and inclina- 
 tions*. 
 
 The method of successive approximation which Clairaut and his con- 
 temporaries employed in the problem of the Perturbations was attended 
 with the inconvenience of introducing into the expression of the radius 
 vector a series of terms depending on arcs of circles wiiich increased 
 continually with the time. Such terms, it is clear, would have the effect 
 of causing the planet's distance from the central body to increase to an 
 indefinite extent ; but, as this conclusion was at variance with observation, 
 it necessarily followed that the method of approximation was defective. 
 The same inconvenience, indeed, is found to arise when the method 
 is employed in less complicated researches than those relating to the 
 planetary perturbations ; and wherein it is demonstrable that the rigorous 
 integrals do not contain any terms susceptible of indefinite increase f. 
 When this difficulty first presented itself to the geometers engaged with 
 the lunar theory, they very soon discovered that it arose from the motion 
 of the apogee, and they found the means of getting rid of the embarrassing 
 terms by assuming the motion of that element in the outset ; and after- 
 wards computing its value by the method of indeterminate coefficients. 
 
 In the theory of the planets, the inconvenience of such terms is simi- 
 larly found to arise from the motion of the aphelia ; but the mode of 
 obviating it is much more difficult in this case, on account of the irregu- 
 larity of the motion, and the mutual dependence of the aphelia of both 
 planets. Lagrange vanquished this difficulty by the invention of a new 
 method of integration, which he first employed in an investigation of the 
 motions of Jupiter's satellites \. In an elaborate memoir which Laplace 
 communicated a few years afterwards to the Academy, he shewed that the 
 
 * Mem. Acad. des Sciences, 1772, part i. This memoir was not written until 1776, 
 although it was inserted in the volume of the Academy for 1772. 
 
 f Lagrange has given an example of this kind in a memoir which appears in the volume 
 of the Berlin Academy for 1783. 
 
 t The memoir which contained this investigation was crowned by the Academy of 
 Sciences in the year 1766. See Prix de 1' Academic, tome ix. 
 
54 HISTORY OF PHYSICAL ASTRONOMY. 
 
 ordinary method of integration might be freed from the inconvenience 
 of circular arcs by means of the variation of the arbitrary constants in the 
 approximate integrals*. Proceeding upon this supposition, he obtained 
 very simple differential expressions of the secular variations ; and by 
 transforming them into linear equations, after the manner of Lagrange, he 
 was enabled to integrate them without any difficulty. He then considered 
 the mutual action of two planets, and arrived at the same conclusion rela- 
 tive to their eccentricities, as that to which Lagrange had been conducted 
 relative to their inclinations. In other words, he established the im- 
 portant fact that the eccentricities of the two planets would not increase to 
 an indefinite extent in virtue of their mutual attraction, but would be 
 confined within certain fixed limits between which they would perpetually 
 oscillate. Applying his formula to the theory of Jupiter and Saturn, he 
 found that the eccentricity of Jupiter's orbit would vary between 0.061776 
 and 0.024006, and that of Saturn's between 0.083094 and 0.011478. The 
 period of these variations he found to be the same for both planets, and 
 equal to about 35, 000 years. 
 
 In 1782 Lagrauge investigated the perturbations of the planets by a 
 method which embraced both the secular and periodic inequalities in one 
 common analysis f . This method consists in supposing all the derange- 
 ments of each planet to be occasioned by a continual variation of the elliptic 
 elements. We have seen that Euler originally employed this refined 
 method of investigation, which offers peculiar advantages in computing the 
 effects of perturbing forces of small value. Lagrange having obtained the 
 differential expressions of the elements, decomposed them into two parts, 
 one depending on the configuration of the planets, the other on the masses 
 and the elements themselves. The former class of terms gave him the 
 periodic variations ; the latter gave him the secular. Applying himself 
 first to the secular variations, he considered the mutual action of Jupiter 
 and Saturn, and obtained results similar to those which Laplace and him- 
 self had already derived from their researches. He next considered the 
 system formed by Mars, the Earth, Venus, and Mercury, taking into account 
 the action of Jupiter and Saturn upon each of those bodies. We have remarked 
 on a previous occasion that this case is much more difficult than that in 
 which only two planets are concerned. The genius of Lagrange, however, 
 was triumphant in these researches, and he succeeded in demonstrating, as 
 in the case of the larger planets, that the eccentricities and inclinations 
 would always be confined within very narrow limits. He found that the 
 ecliptic would not be displaced to a greater extent than 5 23' by the 
 action of the planets upon the earth, and that all the planetary orbits w : ould 
 be perpetually comprised within a zone of the heavens whose breadth was 
 7 58'. He therefore announced, as the final result of his researches, 
 that the secular variations of the elements were in all cases such as would 
 for ever assure the stability of the planetary system. 
 
 The same illustrious geometer extended his researches to the periodic 
 inequalities, which he investigated in two elaborate memoirs communicated 
 
 * Mem. Acad. des Sciences, 1772, part ii. Laplace had given a brief outline of this 
 method in a note at the end of the preceding volume. He continued to improve it 
 in two successive memoirs, which appeared in the volumes of the Academy for 1777 and 
 1789. In the last memoir the method assumed the same form as in the Mecanique 
 Celeste. Lagrange has very much simplified this mode of obtaining the secular varia- 
 tions in a memoir which appears in the volume of the Berlin Academy for the year 
 1783. 
 
 t Mem, Acad. Berlin, 1781, 82, 83. 
 
HISTORY OF PHYSICAL ASTRONOMY. 55 
 
 by him to the Academy of Sciences of Berlin *. He derived the ana- 
 lytical expressions of these inequalities from the periodic variations of 
 the elements, and then computed their numerical values for each planet. 
 
 The interesting results obtained by Lagrange relative to the stability of 
 the system were founded upon a knowledge of the masses of the several 
 planets. The computation of the masses of those planets that are accom- 
 panied by satellites is not a difficult problem, but it is quite different when 
 the question refers to the other planets of the system. Theoretically 
 speaking, the masses of all the planets may be ascertained by observing 
 the effects of their mutual perturbations, but these effects are generally so 
 very minute that they are almost entirely lost in the errors of observation. 
 Lagrange determined the masses of the planets that have no satellites by 
 combining their volumes with their densities, assuming the latter to vary 
 in the inverse ratio of the planet's distance from the sun. This principle, 
 although naturally suggested by the relative densities of the Earth, Jupiter, 
 and Saturn, was, notwithstanding, gratuitously assumed, and therefore the 
 consequences derived from it could not be altogether free of uncertainty. 
 Lagrange, indeed, shewed the improbability of any minute alteration in 
 the values of the masses affecting essentially the conclusions at which he 
 arrived ; but still it was desirable that such valuable truths should be 
 established by an analysis divested of all considerations of a hypothetic 
 character. This important step was made by Laplace f. In 1784 he 
 demonstrated that, no matter what might be the relative masses of the 
 planets, the eccentricities and inclinations if once inconsiderable would 
 always continue so, provided the planets were subject to this one condition 
 that they all revolved round the sun in the same direction. This remarkable 
 truth is embodied in two elegant theorems, which the great geometer just 
 mentioned was the first to announce to the world. The theorem relative 
 to the oscillations in the form of the orbits may be thus stated : If the 
 mass of each planet be multiplied by the square of the eccentricity, and this 
 product by the square root of the mean distance, the sum of these 
 quantities will always retain the same magnitude. Now when this sum 
 is determined for any given epoch, it is found to be small ; by the 
 preceding theorem, then, it will always continue so; it follows, there- 
 fore, a fortiori, that each quantity will continue small, and, consequently, 
 the eccentricity cannot in any case become considerable. The theorem 
 relative to the positions of the orbits is equally elegant. It may be expressed 
 in the following terms : If the mass of each planet be multiplied by the 
 square of the tangent of the orbit's inclination to a fixed plane, and this 
 product by the square root of the mean distance, the sum of such quantities 
 will continue invariable. Considerations similar to those we employed in 
 the previous instance enable us to conclude from this theorem that the 
 orbits of the planets will suffer only a very inconsiderable displacement 
 from their mutual attraction J. 
 
 * Mem. Acad. Berlin, 1783-4. 
 
 f Mem. Acad. des Sciences, 1784. This memoir of Laplace's is remarkable for con- 
 taining the first announcement of three of the most important discoveries in Physical 
 Astronomy. These were 1st, the explanation of the long inequality of Jupiter and Saturn ; 
 2nd, the investigation of the origin of the curious relations which connect the epochs and 
 mean motions of the three interior satellites of Jupiter ; 3rd, the results mentioned in 
 the text. 
 
 The value of Laplace's researches on the present occasion does not rest merely on the 
 discovery of the two theorems announced in the text. The fact is, that the investigation 
 of the ultimate condition of the eccentricities and the inclinations depends in each case on 
 
50 HISTORY OF PHYSICAL ASTRONOMY. 
 
 The laws which thus regulate the eccentricities and inclinations of the 
 planetary orbits, combined with the invariability of the mean distances, 
 secure the permanence of the solar system throughout an indefinite lapse 
 of ages, and offer to us an impressive indication of the Supreme Intelli- 
 gence which presides over nature, and perpetuates her beneficent arrange- 
 ments. When contemplated merely as speculative truths, they are un- 
 questionably the most important which the transcendental analysis has 
 disclosed to the researches of the geometer, and their complete establish- 
 ment would suffice to immortalize the names of Lagrange and Laplace, even 
 although these great geniuses possessed no other claims to the recollection 
 of posterity. 
 
 It cannot fail to have occurred to the reader that in these sublime re- 
 searches the two mighty rivals pressed forward always at an equal pace, 
 insomuch that it would be hardly possible for the most discerning judg- 
 ment to assign the palm of superiority to either of them. Their investi- 
 gations of the secular variations were in both cases equally original, and 
 equally entitled to admiration. Laplace's method might be more simple ; 
 Lagrange 's was more luminous, and had the advantage of being direct. In 
 his researches connected with the mean motion, Laplace displayed a 
 practical sagacity which rarely characterized the speculations of Euler or 
 Lagrange, and, perhaps, this quality was more valuable to him throughout 
 his career than an unexampled command of analysis was to his great 
 rival. In the integration of the differential equations relative to the 
 secular variations of the planets, the genius of Lagrange was eminently 
 conspicuous. Laplace admits that he was compelled to abandon the 
 design of integrating his own equations on account of the difficulties they 
 offered, and was only induced to resume the subject on becoming acquainted 
 with the ingenious method devised for that purpose by his illustrious 
 contemporary *. 
 
 the resolution of an algebraic equation, equal in degree to the number of planets whose mutual 
 action is considered, and involving their masses in indeterminate forms. Lagrange shewed 
 that if any of the roots of this equation should be equal or imaginary, the corresponding 
 element (whether the eccentricity or the inclination) would increase to an indefinite ex- 
 tent, but, if the roots should be all real and unequal, the same elements would perpetually 
 oscillate between fixed limits. Having ascertained the masses of the planets by the 
 methods mentioned in the text, he substituted them in each equation, and then, by the method 
 of successive approximation, he obtained the values of the several roots. These he found 
 to be all real and unequal, whether the equation referred to the eccentricities or the incli- 
 nations, whence he concluded that these elements would perpetually oscillate. The 
 peculiar merit of Laplace's researches consisted in shewing that the roots were all real 
 and unequal, without having recourse to the actual solution of the equations, and, conse- 
 quently, without the necessity of employing any determinate values of the masses. 
 
 * " Je m'etais propose depuis long temps de les integrer mais le peu d'utilite de ce calcul 
 pour les besoins de P Astronomic joints aux difficultes qu'il presentait m'avait fait abandonner 
 cette idee et j'avoue que je ne 1'aurais pas reprise sans la lecture d'un excellent memoire, 
 sur les inegalites seculaires du mouvement des nceuds et de 1'inclinaison des orbites des 
 Planetes que M. De Lagrange vient d'envoyera 1' Academic." Mem. Acad. des Sciences, 
 Annee 1772, part i. p. 371. 
 
HISTORY OF PHYSICAL ASTRONOMY. 5? 
 
 CHAPTER V. 
 
 Irregularities of Jupiter and Saturn Researches of Lambert. Lagrange Circum- 
 stances which determine the Secular Inequalities in the Mean Longitude. Laplace's 
 Investigation of the Theory of Jupiter and Saturn. His Discovery of the physical cause 
 of the Long Inequality in their Mean Motions. Acceleration of the Moon's Mean 
 Motion. Halley Dunthorne. Failure of Euler and Lagrange to account for the 
 Phenomenon. Its explanation by Laplace. Secular Inequalities in the Moon's Pe- 
 rigee and Nodes. Inequalities depending on the Spheriodal Figure of the Earth. 
 Parallactic Inequality. 
 
 ALTHOUGH the principle of gravitation was shewn to be admirably cal- 
 culated for maintaining the stability of the solar system, the strange irre- 
 gularities in the mean motions of Jupiter and Saturn still continued to 
 perplex astronomers, and in some degree to tarnish the lustre of the 
 Newtonian theory. In 1773 Lambert published an interesting essay on 
 this subject, in which he attempted to represent the inequalities of the 
 planets by means of empiric equations. The researches of this astro- 
 nomer contributed to throw some light upon the real character of the 
 phenomenon. It had been hitherto supposed that the mean motion of 
 Jupiter was continually accelerated, and that of Saturn similarly retarded. 
 These results were derived from a comparison of the observations cited 
 by Ptolemy in the Syn taxis, and those of the earlier astronomers of Eu- 
 rope, with the observations of modern times. Lambert, however, found, 
 on comparing the observations of Hevelius with those of the following 
 century, that the mean motion of Jupiter was retarded, while that of 
 Saturn was accelerated. This important fact indicated that the inequa- 
 lities did not increase indefinitely in the same direction, but were merely 
 periodic, like those depending on the configurations of the planets. The 
 researches of Lagrange, in 1776, tended to strengthen this conclusion ; 
 but it is important to remark, that the result he obtained relative to the 
 invariability of the mean distance does not necessarily exclude the exist- 
 ence of secular inequalities in the mean motion. When, indeed, we con- 
 sider a single planet revolving round the sun in an undisturbed orbit, the 
 mean motion will depend solely on the mean distance, and will not in any 
 manner be affected by the elements which prescribe the form and po- 
 sition of the orbit. Thus we may make the eccentricity and the other 
 elements vary in any manner we please, but so long as the mean distance 
 retains the same magnitude the mean motion will continue unalterable. 
 The relation which connects these two elements forms the third of Kepler's 
 famous laws, and when one of them is known the other is readily de- 
 ducible from it by means of that relation. But the case will be quite 
 different when we suppose the planet to be perpetually disturbed in its 
 orbit by the action of another planet. The two elements will no longer 
 be connected together by Kepler's law, for the perturbing forces will now 
 introduce into the expression of the mean motion a class of terms depend- 
 ing upon the eccentricities and the other elements of both planets. These 
 elements, in virtue of their secular variations, might produce an effect on 
 the planet's longitude which would ultimately become sensible, and hence 
 might arise a secular inequality in the mean motion, notwithstanding the 
 invariability of the mean distance. It became, therefore, an object of 
 
58 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the highest importance to ascertain whether the mean motions of the 
 planets were affected in this manner, and if so, to determine, in the case 
 of Jupiter and Saturn, whether the effects were of such a magnitude as 
 to account for the observed irregularities of the two planets. 
 
 In 1783 Lagrange investigated this interesting question. He had pre- 
 viously found that if all the terms exceeding the first powers of the ec- 
 centricities and inclinations were neglected, the perturbing forces would 
 not in any manner whatever affect the mean motion. On the present 
 occasion he extended his inquiries to the terms involving the squares of 
 the eccentricities, and he now actually discovered among them a secular 
 equation affecting the mean motion. Applying his formula to the theory 
 of Jupiter and Saturn, he found that the equation was utterly insensible 
 in both planets ; for in neither case did it exceed the thousandth part of 
 a second, even when it reached its maximum value *. " This result," says 
 Lagrange, " will allow us to dispense with a similar examination of the 
 secular inequalities in the mean motions of the other planets, as we ori- 
 ginally proposed to do, for it is easy to predict that the values of the 
 equations will be even less than those we have just found. We may, then, 
 henceforth consider it as a truth rigorously demonstrated, that the mutual 
 attraction of the principal planets cannot produce any sensible alteration 
 in their mean motions, "f 
 
 This result is one of the most interesting in physical astronomy, and 
 we have seen that the merit of establishing it is almost wholly due to 
 Lagrange. At this stage of the planetary researches it had the effect of 
 narrowing the question relative to the irregularities of Jupiter and Saturn ; 
 for it shewed that if these irregularities resulted from the mutual action 
 of the two planets, their explanation must be sought for among the pe- 
 riodic terms, and not among those depending on the secular variations of 
 the elements. It is clear, then, that, apart from its intrinsic value, this 
 result must be considered as forming a most important step in the 
 developement of the theory of gravitation. 
 
 It appears from Lagrange 's words, as quoted above, that he did not 
 consider himself warranted in concluding from his researches that the 
 mean motions of the secondary planets might not be affected with secular 
 inequalities of sensible magnitudes. Unfortunately for his fame, it did 
 not occur to him to apply his formulae to the moon, although the secular 
 inequality which astronomers had actually detected in the mean motion of 
 that satellite might have suggested such a step to a mind of much less 
 sagacity than his. By this inadvertence he missed one of the noblest 
 discoveries in physical astronomy, and it happened to him, as on several 
 other occasions, that, while he allowed his brilliant researches to remain 
 comparatively fruitless in his hands, he had the mortification of seeing 
 the prize carried off by his more persevering and ambitious rival. 
 
 Geometers being now assured that the mutual attraction of Jupiter and 
 Saturn could not produce an inequality of a secular character in their 
 
 * The mean longitude of a planet depends upon two elements : 1st, the mean mo- 
 tion ; 2nd, the mean longitude corresponding to any given epoch, or, more simply, the 
 longitude of the epoch. As the mean motion is supposed to be derivable from the mean 
 distance by Kepler's law, it cannot affect the mean longitude with a secular inequality, in 
 consequence of the invariability of the element upon which it depends. Hence, in the 
 theory of the variation of arbitrary constants, the secular inequality in the planet's motion 
 is ascribed solely to the variation of the longitude of the epoch, the constant forming the 
 sixth element of elliptic motion. 
 
 *h Mem. Acad, Berlin, 1783, p. 223. 
 
HISTORY OF PHYSICAL ASTRONOMY. 59 
 
 mean motions, it only remained for them to inquire whether the anoma- 
 lous irregularities of the two planets might not be explicable by some 
 periodic inequality of long duration. This was the form which the ques- 
 tion assumed when Laplace applied the energies of his powerful mind to 
 a rigorous examination of all the circumstances calculated to affect it. 
 He first proceeded to inquire whether the inequalities were connected 
 together by relations similar to those which would ensue on the suppo- 
 sition that they were produced by the mutual action of the two planets. 
 By a very simple analysis he found that the mean motion of Jupiter 
 would be accelerated, while that of Saturn was retarded, and vice versa. 
 He also discovered that, if we only regard inequalities the periods of which 
 are very long, the corresponding derangements of the two planets would 
 always be to each other as the products formed by multiplying the mass 
 of each planet into the square root of its mean distance. He hence 
 easily concluded that the derangement of Jupiter at any time would be 
 to the simultaneous derangement of Saturn very nearly as 3 to 7. Now, 
 by assuming, according to Halley, that the retardation of Saturn in 
 2000 years amounted to 9 16', this relation gave him 3 58' for the cor- 
 responding acceleration of Jupiter, a quantity which differs only by 9' 
 from the result obtained by Halley. 
 
 Being thus furnished with a strong indication that the irregularities of 
 the two planets were due to their mutual attraction, he entered upon a 
 searching inquiry into their real source. This he finally discovered in 
 the near commeusurability of the mean motions of the two planets. Five 
 times the mean motion of Saturn is very nearly equal to twice the mean 
 motion of Jupiter. In fact, if n, n' represent the mean motions of the 
 two planets, 5rc 2?i' is equal only to about T \th of the mean motion of 
 Jupiter. Now, Laplace found that certain terms, involving this quantity 
 in the differential equations of the longitude, would receive, by double 
 integration, the square of the same quantity as divisors, and in conse- 
 quence would rise very much in value. Terms of this class are, indeed, 
 generally very minute, being only of the order of the cubes of the eccen- 
 tricities and inclinations ; but Laplace, with characteristic sagacity, sus- 
 pected that the small divisors they acquired might render them sensible, 
 and that they might possibly explain the irregularities of the two planets. 
 The result of actual calculation entirely confirmed his suspicion. He 
 found that the terms assigned to Saturn an inequality equal to 48' 44", 
 and to Jupiter a contrary inequality equal to 20' 49". The periods of the 
 two inequalities were equal, and amounted to 929 years. They reached 
 their maximum values in the year 1560. The apparent mean motions of 
 the two planets henceforth continually approximated towards their true 
 mean motions, and finally coincided with them in the year 1 790. This is 
 the reason why Halley, on comparing ancient with modern observations, 
 found the mean motion of Jupiter to be quicker, and that of Saturn 
 slower, while Lambert, on the other hand, from a comparison of modern 
 observations with each other, arrived at a diametrically opposite conclu- 
 sion. 
 
 Laplace found that his equations accounted in a most satisfactory 
 manner for the irregularities of the two planets. Among forty-three oppo- 
 sitions of Saturn which he compared with theory, the error in no case 
 exceeded 2', and generally it fell very far short of that quantity. At a sub- 
 sequent period of his researches he diminished the errors of both planets 
 to 12", although only a small number of years before the errors in the 
 
60 HISTORY OF PHYSICAL ASTRONOMY. 
 
 best tables of Saturn exceeded 20' *. By tbis capital discovery Laplace 
 banisbed empiricism from tbe tables of Jupiter and Saturn, and extricated 
 the Newtonian theory from one of its gravest perils. " The irregularities 
 of the two planets," says that illustrious geometer, " appeared formerly to 
 be inexplicable by the law of universal gravitation they now form one of 
 its most striking proofs. Such has been the fate of this brilliant disco- 
 very, that each difficulty which has arisen has become for it a new subject 
 of triumph, a circumstance which is the surest characteristic of the true 
 system of nature."! 
 
 We shall now give a brief account of the circumstances connected with 
 a remarkable inequality in the moon's motion, which continued to form 
 the subject of toilsome research until its true physical cause was at length 
 discovered. From an extensive comparison of ancient with modern ob- 
 servations, it was established beyond doubt by the astronomers of the last 
 century, that the mean motion of the moon has been becoming continually 
 more rapid ever since the epoch of the earliest recorded observations. 
 Halley was the first person who suspected this important fact. We may 
 remark that, if the moon's mean motion be more rapid now than it was 
 in ancient times, the place of that satellite, when computed for any re- 
 mote epoch by means of the modern tables, will be less advanced than 
 her actual place, and hence the time of an eclipse, when calculated in 
 this manner, will appear to happen earlier than the recorded time. It is 
 also obvious that, if we make a similar computation for any intermediate 
 epoch, the moon in this case too will be thrown back in her orbit, though 
 not to such an extent as in the previous case, and it is manifest that the 
 error will diminish continually as we descend towards the epoch of the 
 tables. Now this was the character of the results which Halley obtained 
 from an examination of some ancient eclipses recorded by Ptolemy and 
 the Arabian astronomers, and which in consequence induced him to sup- 
 pose that the moon's mean motion was subject to a continual acceleration. 
 He first alluded to this phenomenon in 1693, but no attempt was made to 
 confirm his suspicion until the year 1749, when Dunthorne communicated a 
 memoir to the Royal Society, in which he discussed all the observations 
 calculated to throw light upon the subject. He computed by the modern 
 tables an eclipse of the moon observed at Babylon in the year 721 A.C. ; 
 another, observed at Alexandria in the year 201 A.C. ; a solar eclipse, 
 observed by Theon in the year 364 A.D., and two similar phenomena, ob- 
 served by Ibyn Jounis, at Cairo, in Egypt, towards the close of the tenth 
 century. In all these cases the computed time of the phenomenon was 
 earlier than the observed time ; and the error generally was greater as 
 the eclipse was more ancient. He therefore concluded that the several 
 observations could only be reconciled with the tables by assuming that 
 the mean motion was continually accelerated agreeably to the remark of 
 Halley, and, from a comparison between the observed and computed times 
 
 * Laplace first explained these inequalities in the volume of the Academy of Sciences 
 for the year 1784. In the volumes for the two following years he gave a complete ana- 
 lysis of the theory of Jupiter and Saturn, and shewed its accordance with the ancient and 
 modern observations. An admirable exposition of the origin of the famous inequality men- 
 tioned in the text is contained in Airy's Treatise on Gravitation ; a little work which 
 should be in the hands of every person (whether a mathematician or not) who desires to 
 obtain clear ideas of the various modes in which the planets disturb each other by their 
 mutual attraction. 
 
 f Mem. Cel., tome v. p. 324. 
 
HISTORY OF PHYSICAL ASTRONOMY. 01 
 
 of a number of eclipses, he was induced to fix the amount of the acce- 
 leration at 10" in a century, counting from the year 1700. 
 
 A similar discussion conducted the celebrated astronomer Mayer to a 
 secular acceleration of the mean motion. In his lunar tables, published 
 in 1753, he fixed it at 1" in a century ; but in those published at London, 
 in 1770, it was raised to 9". Lalande also investigated the question in 
 the year 1757, and deduced from his researches a secular equation of 
 9".886, which he ultimately fixed at 10". 
 
 Astronomers having thus demonstrated by incontestable evidence that 
 the moon's mean motion was becoming continually more rapid, it hence- 
 forth became an interesting question to discover the physical cause of this 
 phenomenon. The Academy of Sciences at Paris, always actuated by a 
 zealous desire to promote the cause of science, offered their prize of 1770 
 for an investigation, which should have for its object to ascertain whether 
 the theory of gravitation could render a satisfactory account of this secu- 
 lar inequality in the moon's motion. The prize was carried off by Euler ; 
 but that illustrious geometer was unable to discover any equations in the 
 mean motion of a secular character. Towards the conclusion of his me- 
 moir, he uses the following remarkable words : " There is not one of the 
 equations about which any uncertainty prevails, and now it appears to be 
 established by indisputable evidence, that the secular inequality in the 
 moon's mean motion cannot be produced by the forces of gravitation."* 
 The future history of this inequality should teach us to accept with the 
 utmost caution the dictum of any authority, however high, when it tends 
 to impugn the generality of a principle supported, as in the present in- 
 stance, by a multitude of phenomena of the most unequivocal character. 
 
 Anxious to obtain a solution of this difficult question, the Academy of 
 Sciences again proposed it for their prize of 1772. Euler and Lagrange 
 were declared the successful competitors and shared the prize between 
 them. Euler concluded his memoir by repeating the assertion he had 
 made on the previous occasion, adding that no doubt henceforth could 
 exist that the inequality arose from the resistance of an ethereal fluid 
 pervading the celestial regions f. Lagrange, in his memoir, gave a new 
 solution of the Problem of Three Bodies, which he applied to the moon J, 
 but he reserved for a future occasion a rigorous inquiry into the cause of 
 the acceleration. Meanwhile, some persons began to entertain a suspicion 
 that the spheroidal figures of the earth and moon, by disturbing the law 
 of their mutual attraction, might occasion the inequality. This induced 
 the Academy again to propose their prize of 1774 for an investigation of 
 the subject. Lagrange was declared the successful competitor. He 
 examined the effects of the moon's figure upon her motion, by a very 
 skilful analysis, but he could find no equation of a secular character. By 
 a simple process of reasoning, he extended the same conclusion to the 
 earth, and he assured himself with equal confidence that the attraction of 
 the planets and satellites could not be the cause of the phenomenon. He 
 then entered upon a critical discussion of the observations upon which the 
 alleged acceleration of the mean motion was founded, and his final con- 
 clusion was, that in general the data were of a doubtful character, and 
 that perhaps the best course would be to reject the inequality altogether . 
 
 * Prix de 1' Academic, tome ix. 
 f Ibid., tome ix. 
 Ibid., tome ix. 
 g Mcmoires des Savans fttranjrers, tome vii. 
 
62 HISTOEY OP PHYSICAL ASTRONOMY. 
 
 Laplace, about the same time, investigated this interesting' subject. 
 Having carefully examined the ancient observations, he was induced to 
 consider it as fully established, that the moon's mean motion was be- 
 coming more rapid in modern times. Some persons had endeavoured to 
 explain the phenomenon by means of a contiftual retardation of the earth's 
 diurnal motion. If this supposition were true, an acceleration ought to 
 have manifested itself in the mean motions of the planets, as well as in 
 that of the moon, but this was not borne out by observation. But, besides, 
 no sufficient cause could be assigned why the rotatory motion of the earth 
 should be continually retarded. It was indeed alleged, that this effect 
 might be produced by the continual blowing of the easterly winds, 
 generated by the heats of the torrid zone, against the great mountain 
 chains which run from north to south in both hemispheres. Laplace, 
 however, mentions that he examined this point with attention, and arrived 
 at the conclusion that no retardation of the diurnal motion could possibly 
 arise from such a cause. He considered another solution of the problem, 
 founded on the supposition that the regions of space are occupied by an 
 ethereal fluid, which continually resists the motions of the celestial 
 bodies. He admits that such an hypothesis suffices to explain the phe- 
 nomenon, but he contends that we have no independent proof of the 
 existence of an ethereal fluid, and until we are assured beyond all 
 possibility of doubt that the theory of gravitation cannot account for the 
 moon's acceleration, we ought not to have recourse to any extraneous 
 source of explanation *. His views on this subject are unquestionably more 
 sagacious and philosophical than those of Euler or Lagrange 
 
 Unable to discover a secular inequality in the disturbing action of the 
 sun, and yet reluctant to derive this result from any foreign principle, he 
 was led to consider what effect might be produced by adopting a different 
 conception of gravity. It had been always assumed that the effects of 
 this principle were propagated instantaneously from bodies. Laplace, 
 however, considered, that some time might be required for this purpose, 
 and he readily perceived that such a supposition would have the effect of 
 modifying the intensity of the force exerted on the moving body. He 
 therefore computed what ought to be the velocity of gravity, in order that 
 the gradual transmission of that principle should occasion the observed 
 acceleration of the moon's mean motion, and he arrived at the remarkable 
 conclusion that it must exceed the velocity of light eight millions of 
 times. He remarked that if a satisfactory account of the origin of the 
 phenomenon be adduced, without having recourse to this hypothesis, it 
 would follow that the effects of the successive transmission of gravity 
 would be insensible, and therefore the velocity must be at least fifty 
 millions of tim.es greater than the velocity of light ! 
 
 No further progress was made in this question until the close of the 
 year 1787, when Laplace finally announced that he had discovered the 
 cause of the phenomenon in the gradual diminution of the mean action 
 of the sun, arising in consequence of the secular variation of the ec- 
 centricity of the terrestrial orbit f. The mean action of the sun upon the 
 moon tends to diminish the moon's gravity to the earth, and thereby 
 causes a diminution of her angular velocity. This diminution being once 
 supposed to occur, the angular velocity would afterwards remain constant, 
 provided the mean solar action always retained the same value. This, 
 
 * Mem. des Savans Strangers, tome vii. 
 t Mem. Acad. des Sciences, 1786. 
 
HISTORY OF PHYSICAL ASTRONOMY. 63 
 
 however, is not the case, for it depends to a certain extent on the 
 eccentricity of the terrestrial orbit, an element which we know to be 
 in a state of continual though inconceivably slow variation, from the 
 action of the planets on the earth. This variation of the earth's 
 eccentricity will, therefore, produce a corresponding variation in the 
 mean action of the sun ; and the earth, in consequence, having more 
 or less power over the moon, will either quicken or retard her angular 
 velocity, whence will ensue a secular inequality in the mean motion 
 conformably to observation. Now, the eccentricity of the earth's orbit 
 has been continually diminishing from the date of the earliest recorded 
 observations down to the present time; hence the sun's mean action 
 must also have been diminishing, and consequently the moon's mean 
 motion must have been continually increasing. This acceleration will 
 continue as long as the earth's orbit is approaching towards a circular 
 form, but as soon as this process ceases, and the orbit again begins to 
 open out, the sun's mean action will increase, and the acceleration of the 
 moon's mean motion will be converted into a continual retardation *. 
 
 Laplace computed the acceleration, and found it to amount to 
 10".1816213', t denoting the number of centuries before or after the 
 year 1801. This result agrees as nearly as possible with that which 
 astronomers have derived from a comparison of ancient with modern 
 observations. 
 
 If the inequality were rigorously determinable by the preceding for- 
 mula, it would obviously continue for ever to increase in the same 
 direction, a conclusion which would be totally at variance with the expla- 
 nation we have just given of its physical cause. The fact is, however, 
 that the complete analytical expression of it is a periodic function of the 
 time, and the quantity 10".1816213 2 is merely the second term in the de- 
 velopement of it f, the others being so small as to admit of being rejected, 
 when the computation does not extend to more than about 2000 years. 
 Laplace, indeed, found that when the moon's place was calculated for the 
 time of the Chaldean observations, it would be necessary to take into 
 account the term depending on the cube of t. The inequality would then 
 be expressed thus: 10".1816213 2 -1-0".01853844 :J . 
 
 The variation of the earth's eccentricity, upon which the inequality in 
 the moon's mean motion depends, cannot be calculated from theory 
 without a knowledge of the masses of the planets. When it is considered 
 what uncertainty prevails respecting the masses of Mars and Venus, it is 
 surprising how close the agreement is between theory and observation. 
 Fortunately, the planet which exercises by far the greatest influence on 
 the eccentricity is Jupiter, whose mass is easily derived from the elonga- 
 tions of his satellites. It is remarkable that the action of the planets on 
 the moon, when transmitted to her indirectly through the medium of the 
 sun, should be more considerable than their direct action upon her. 
 
 The moon, in the present day, is about two hours later in coming to the 
 
 * It does not necessarily follow that because an inequality is secular it should increase 
 continually in the same direction. Lagrange found that the secular inequalities in the 
 mean motions of Jupiter and Saturn were of a recurring character, although their du- 
 ration extended to the immense period of 70414 years ! The secular inequality in the 
 moon's mean motion, being a more complicated phenomenon, has a much longer period 
 than this. 
 
 f The first term, being proportional to the time, is absorbed in the mean motion, and 
 therefore cannot form part of the inequality as determined by observation. 
 
64 HISTORY OF PHYSICAL ASTEONOMY. 
 
 meridian than she would have been if she had retained the same mean 
 motion as in the time of the earliest Chaldean observations. It is a 
 wonderful fact in the history of science, that those rude notes of the 
 priests of Babylon should escape the ruin of successive empires, and, 
 finally, after the lapse of nearly three thousand years, should become 
 subservient in establishing a phenomenon of so refined and complicated a 
 character as the inequality we have just been considering. 
 
 Laplace also discovered that the lunar perigee and nodes were subject to 
 secular inequalities from the same cause. He found that the inequality in 
 the perigee was to the corresponding inequality in the mean motion as 33 
 to 10, and was sub tractive from the mean longitude. He also discovered 
 that the secular inequality of the nodes amounted to seven-tenths of that 
 of the mean motion, and was additive to the mean longitude. Thus it 
 appeared that, while the mean motion was continually accelerated, the 
 perigee and nodes were continually retarded, the three inequalities being 
 as the numbers 1, 3, .7 *. It hence also followed that the moon's 
 motions, with respect to the sun, her perigee, and her nodes, continually 
 increased in the ratios of 1,4, 0.265. The existence and magnitude of 
 these inequalities were confirmed in a most satisfactory manner by 
 Bouvard, who for this purpose instituted an extensive comparison between 
 the ancient and modern observations. 
 
 These great inequalities all depend on the secular variation of the 
 earth's eccentricity. They will continually become more perceptible as 
 ages roll on, but a vast number of years will elapse before they will have 
 passed through all their values f . They will one day affect the secular 
 motion of the moon to the extent of at least the fortieth part of the 
 circumference, and that of the perigee to the extent of the thirteenth 
 part*. 
 
 It might be imagined that the secular variation in the position of the 
 ecliptic would have the effect of modifying the sun's action on the moon, 
 and would in consequence disturb the mean inclination of the lunar orbit. 
 Laplace, however, found that the moon was constantly maintained by the 
 sun at the same inclination towards the moveable plane of the ecliptic, so 
 that her declinations were subject to the same secular changes as those 
 of the sun, and were due solely to the continued diminution of the 
 obliquity of the ecliptic. 
 
 It was not until Laplace announced his discovery of the cause of the 
 moon's acceleration, that Lagrange became aware of the oversight he had 
 committed, while engaged in similar researches in 1783, by neglecting to 
 apply his analysis to the moon. He now made the inquired substitutions, 
 and, computing the numerical value of the inequality, he obtained a result 
 which almost coincided with that of Laplace . 
 
 We shall conclude this historical notice of the secular inequalities of 
 
 * Since the mean motion of the lunar perigee is direct, the effect of an inequality, 
 which is subtractive from the mean longitude, will manifestly be to retard the perigee 
 behind its true place. On the other hand, since the motion of the nodes is retrograde, 
 a retardation can only take place when the inequality is additive to the mean longitude. 
 
 f Leverrier has found that the eccentricity of the terrestrial orbit will continue to di- 
 minish during the period of 23,980 years. It will then attain a minimum value equal to 
 0.003314. Memoire sur les variations seculaires des elemens des orbites pour les 
 sept planetes principales. See also Connaissance des Temps, 1843. 
 
 Exposition du Systeme du Monde, tome ii., liv. iv. chap. v. 
 
 Mem. Acad. Berlin, 1792-3. 
 
HISTORY OF PHYSICAL ASTRONOMY. 65 
 
 the moon, with a brief account of two other remarkable results, which 
 Laplace derived from his researches in the lunar theory. The spheroidal 
 figure of the earth occasions a sensible perturbation of the moon's motion 
 both in longitude and latitude. The inequality in longitude was dis- 
 covered by Mayer, who was ignorant of the physical cause of it, but re- 
 presented it in his tables by an empiric equation. Laplace derived the 
 equation from theory, and found it to depend on the longitude of the 
 moon's node. Burg, by a comparison of numerous observations, was led 
 to estimate the greatest value of the coefficient at 6". 7. This result 
 gives 3-0-^3- f r tne eai 'th' s ellipticity. The inequality in latitude was 
 discovered by Laplace to vary with the sine of the moon's true longitude. 
 Its value was derived by Burg and Burckhardt, from the combined ob- 
 servations of Bradley and Maskelyne, and was fixed by them at 8", a 
 quantity which implies an ellipticity equal to -JOT-S* 
 
 The agreement between the results derivable from these two distinct 
 equations is very interesting. If the earth were homogeneous, it is de- 
 monstrable that the ellipticity would be equal to -g^', it follows, then, that 
 the density must increase towards the centre a fact which we know to 
 be true from other sources. 
 
 A comparison of arcs of the meridian, measured in different parts of 
 the world, presents a series of anomalous results, which lead us to con- 
 clude that the figure of the earth is not that of an exact spheroid. It is 
 remarkable, however, that when two arcs are compared, the distance 
 between which is so great as to obviate the effects of any minute in- 
 equalities in the spheroidal figure, they indicate an ellipticity almost equal 
 to that derived from the lunar inequalities. Thus, the result of a com- 
 parison between a meridional arc at the equator and one measured in 
 France, gives ^-g for the earth's ellipticity. 
 
 Another striking result which Laplace derived from his researches 
 was the value of the solar parallax. Among the equations in longitude, 
 he found one involving that element, and varying with the angular 
 distance between the sun and moon. The coefficient of this equation, 
 when compared with observation, was found to give 8". 6 for the mean 
 value of the solar parallax. This result agrees with the mean of those 
 obtained by astronomers from observations on the transit of Venus in 
 1769. " It is very remarkable," says Laplace, " that an astronomer, 
 without leaving his observatory, by merely comparing his observations 
 with analysis, has been enabled to determine with accuracy the magnitude 
 and figure of the earth, and its distance from the sun and moon, elements, 
 the knowledge of which has been the fruit of long and troublesome voy- 
 ages in both hemispheres." * 
 
 * Exposition du Systeme du Monde, tome ii. p. 91. 
 
66 HISTORY OF PHYSICAL ASTRONOMY. 
 
 CHAPTER VI. 
 
 Theory of the Figure of the Earth. Newton. Huygens. Maclaurin. Clairaut. At- 
 traction of Spheroids. D'Alembert. Legendre. Theory of Laplace. Motion of the 
 Earth about its Centre of Gravity. Nutation Bradley Investigation of Precession 
 and Nutation, by D'Alembert The Tides. Equilibrium Theory. Researches of 
 Laplace. Stability of the Ocean. Libration of the Moon. Galileo. Hevelius. 
 Newton. Cassini Newton's Explanation of the Moon's Physical Libration. Re- 
 searches of Lagrange. Combination of the Principle of virtual Velocities with 
 D' Alfimbert's Principle. Laplace investigates the Effect of the secular Inequalities of 
 the mean Motion upon the Libration in Longitude. His Theory of Saturn's Rings. 
 
 THE Figure of the Earth was the first of the subjects treated of in the 
 Principia, which engaged the attention of geometers. In 1690 Huygens 
 published his treatise " De Causa Gravitatis," in which he investigated 
 the ratio of the earth's axis in accordance with his own views of gravity. 
 Assuming the density to be homogeneous, he imagined, like Newton, two 
 fluid columns, reaching from the centre of the earth to the surface ; one in 
 the plane of the equator and the other along the polar axis. The particles 
 of the equatorial column were acted upon by gravity and by the centrifugal 
 force arising from their rotation ; those of the polar column were acted 
 upon by gravity alone. The equatorial particles being, therefore, severally 
 lighter than the polar, and the two columns being also in equilibrium, it 
 was necessary that the equatorial column should compensate, by its supe- 
 rior length, for the diminished pressure of its particles. Huygens as- 
 sumed that gravity urged the particles to the centre of the earth with 
 a force varying according to the inverse square of the distance. This 
 supposition was inconsistent with the theory of gravitation, for Newton 
 had found that, in consequence of the attraction of the surrounding 
 particles, the tendency of each particle to the centre would vary in the 
 direct ratio of the distance. We have already remarked, however, that 
 Huygens rejected the mutual attraction of the particles of matter, and 
 admitted only their gravity towards a central point. Having computed 
 the lengths of the two columns on the supposition that they were in 
 equilibrium, he found that the equatorial column would exceed the polar, 
 assumed equal to unity, by half the ratio of the equatorial centrifugal force, 
 to the equatorial gravity, or by x J-g = ^4^- Hence the ratio of the 
 two axes would be as 579 to 578. ~He also found that the increase of 
 gravity at the surface, from the equator to the pole, would vary in the 
 proportion of the square of the sine of the latitude, and that the total 
 increase, supposing the equatorial gravity equal to unity, would be equal 
 to twice the ratio of the equatorial centrifugal force to the equatorial 
 gravity, or 2 x -^-J-g. Thus the fraction expressing the ellipticity* was to 
 that expressing the total increase of gravity as J to 2. Newton's theory, 
 on the other hand, gave the same fraction in the one case as in the other ; 
 both being measured by ^fths the ratio of the equatorial centrifugal force 
 to the equatorial gravity. It is remarkable, however, that the sum of the 
 fractions is the same in both theories for the same values of the last- 
 
 * The ratio of the excess of the equatorial over the polar axis to the latter axis is 
 termed the ellipticity of the spheroid. Hence, if the polar axis be assumed equal to unity, 
 the ellipticity will be represented simply by the excess of the equatorial axis over it. 
 
HISTORY OF PHYSICAL ASTRONOMY. 67 
 
 mentioned ratio. Thus, in Newton's theory, the two fractions being both 
 equal to -J x -j-J-g, their sum is equal to f x -^ ; in Huygens' theory, 
 the same sum is equal to Jx ^ + Sx-^ = |X T ^. These are 
 only particular cases of a general theorem discovered by Clairaut, connect- 
 ing the ellipticity of spheroids with the variation of gravity at their sur- 
 faces. This theorem, indeed, supposes the mutual gravitation of the 
 particles of matter, which Huygens refused to admit ; but the investigation 
 of that philosopher may be considered as founded on the same principle, 
 by imagining the spheroid to be composed of strata of different densities ; 
 the exterior stratum being infinitely rare, and the density thence increas- 
 ing to the centre, where it is infinite. 
 
 The theories of Newton and Huygens involve the two extreme cases of 
 density, and therefore assign the limits of ellipticity for a heterogeneous 
 spheroid revolving round a fixed axis. Hence, since there is strong 
 reason to believe that the density of the earth increases towards the centre, 
 it might naturally be expected that the ellipticity would be comprised 
 between these limits. This conclusion has been verified in the most 
 satisfactory manner by the researches of astronomers, who have found 
 that the ellipticity, whether as determined by the measurement of me- 
 ridional arcs, by experiments with the pendulum, or by observations on the 
 motion of the moon, lies between -^-J-^ and 5 -^g, the values assigned by the 
 two extreme cases of the problem. 
 
 Neither Newton nor Huygens demonstrated a priori that the earth 
 might possibly assume the form of an oblate spheroid. This important 
 step was reserved for Maclaurin*. In his prize memoir on the Tides, 
 which appeared in 1740, this distinguished mathematician proved, by a 
 beautiful application of the ancient geometry, that an oblate spheroid 
 would satisfy the conditions of equilibrium of a homogeneous fluid mass, 
 differing little from a sphere, and endued with a rotatory motion round 
 a fixed axis. He also demonstrated that the increase of gravity from the 
 equator to the pole would vary as the square of the sine of the latitude, 
 and that the ratio of the total increase to the gravity at the equator would 
 be expressed by the fraction representing the ellipticity, or, in other words, 
 by -fths the ratio of the equatorial centrifugal force to the equatorial 
 gravity. These results confirmed the assumptions of Newton ; but, as they 
 were founded on the supposition of a homogeneous fluid, they were not 
 applicable to the earth, which evidently increased in density towards the 
 centre. They formed, however, an important advance towards a more 
 correct theory of the earth's figure, and on this account deserve to be 
 considered as a valuable contribution to Physical Astronomy. The in- 
 vestigations by means of which Maclaurin arrived at these results have 
 been universally admired for their ingenuity and elegance, and are justly 
 considered as rivalling, in these respects, the most finished models of the 
 ancient geometry. 
 
 In 1743 Clairaut published his valuable treatise on the Figure of the 
 Earth. In this work the general equations of the equilibrium of fluids, 
 independently of any hypothesis with respect to the density or the law of 
 the attraction, are for the first time given. By means of these equations 
 Clairaut investigated the figure of the earth on the supposition of the den- 
 sity being heterogeneous ; and he found, that in this case also an elliptic 
 spheroid would satisfy the conditions of equilibrium, provided the mass was 
 
 * Born in 169&; at Kilmoddan, in Argyllshire; died at Edinburgh, in 1746. 
 
 F Q 
 
68 HISTORY OF. PHYSICAL ASTRONOMY. 
 
 disposed in concentric strata of similar forms and homogeneous density. 
 The ellipticities of the successive strata will obviously depend on the law 
 of the density, and the other- conditions of the problem ; but Clairaut 
 discovered that the following theorem is generally true : the sum of the 
 fractions expressing the ellipticity and the increase of gravity at the pole is 
 equal to two and a half times the fraction expressing the centrifugal force at 
 the equator*. This theorem, combined with that relating to the variation of 
 gravity at the surface, enables us to determine the ellipticity of the earth, 
 by means of observations on the force of gravity, in two different latitudes. 
 Its peculiar value consists in being independent of any hypothesis with 
 respect to the internal constitution of the earth. We have seen that the 
 results obtained by Newton and Huygens offer particular illustrations of 
 this important theorem, which is generally designated by the name of its 
 inventor. Little real progress has been made in the theory of the Figure 
 of the Earth beyond the results to which Clairaut was conducted by his 
 admirable researches on this occasion. 
 
 The actual ellipticity of the earth may be determined by three distinct 
 methods. The simplest of these in principle depends on the measure- 
 ment of two arcs of the meridian lying in different latitudes. The other 
 two methods are derived from the theory of gravitation. One of these is 
 suggested by Clairaut's theorem, and requires a knowledge of the force of 
 gravity in two different latitudes. These data may be found by means of 
 experiments with the pendulum. The other method, assigned by theory, 
 depends on the effect of the earth's ellipticity in disturbing the moon's 
 motion. It may not be uninteresting to compare the results obtained by 
 these three methods ; and for this purpose we shall select the examples 
 given by Mr. Airy in his treatise on the Figure of the Earth f. 
 
 With respect to the first method, Lambton measured an arc of the 
 meridian in India, comprised between lat. 8 9' 38" .4, and lat. 10 59' 
 48" .9, and found its length to be 1029100.5 feet, Swanberg, on the 
 other hand, measured a similar arc in Sweden from lat. 65 31' 32" .2, 
 to lat. 07 8' 49" .8, and found its length 593277.5 feet. These measures 
 assign -j^^-.-j as the earth's ellipticity. 
 
 Again, ait Madras, in latitude 13 4' 9", the length of the seconds 
 pendulum has been found to be equal to 39.0234 inches; at Melville 
 Island, in latitude 74 47' 12", the corresponding length is 39.2070 
 inches. These results give ^^ for the ellipticity. 
 
 Lastly, the coefficient of the inequality in the moon's latitude, depend- 
 ing on the spheroidal figure of the earth, is found by observation to be 
 equal to 8". This result indicates an ellipticity equal to -j^,*. 
 
 The near agreement of these values of the ellipticity, determined by 
 methods so very dissimilar, constitutes a powerful argument in favour of 
 the theory of gravitation. 
 
 It is obvious that the question relative to the figure of the earth, and 
 the variation of gravity at the surface, is intimately connected with the 
 theory of the attraction of spheroids. In 1773 Lagrange demonstrated 
 by analysis the results to which Maclaurin was conducted by his re- 
 searches on this subject, and extended them to the general form of the 
 
 * In this enunciation of Clairaut's theorem, the unit of force is represented by the 
 equatorial gravity. 
 
 f Mathemalical Tracts on the Lunar and Planetary Perturbations. 
 
 \ This result does not exactly coincide with Laplace'*, on account of a slight difference 
 in the data. 
 
HISTORY OF PHYSICAL ASTRONOMY. 69 
 
 ellipsoid. Maclaurin had limited his investigation to the attraction of 
 particles either contiguous to the surface of the spheroid, or situated in 
 its interior. It was desirable, however, to complete the theory of the 
 subject, by determining the attraction of a point situated anywhere with- 
 out the spheroid. D'Alembert first gave a theorem, by means of which 
 the attraction in this case might be found, when the particle was situated 
 in the prolongation of one of the axes, and Legendre afterwards discovered 
 a similar theorem applicable to an exterior point, situated anywhere 
 whatever when the attracting body was an ellipsoid of revolution. The 
 problem for the general case of the ellipsoid presented analytical diffi- 
 culties, which continued for some time to elude the researches of the 
 most profound analysts. In 1784 Laplace finally succeeded in effecting 
 its solution, but his method was embarrassed with series, and did not by 
 any means possess the elegance and perfection which distinguished the 
 other parts of the theory. 
 
 In 1782 Laplace explained a general theory of the attraction of 
 ellipsoids. His researches were based wholly upon a partial differential 
 equation of the second order of a very remarkable character, which has 
 been subsequently employed with great success in many important in- 
 vestigations connected with the Physico-mathematical sciences. By 
 simple differentiation, he determined the figure assumed by a hetero- 
 geneous mass of fluid, differing only in a small degree from a sphere, 
 and by a similar process he also obtained the law of attraction at the 
 external stratum. His results coincided with those to which Clairaut 
 had been already conducted by a less direct analysis. The investigation 
 of this great geometer is indeed more remarkable, for the method by 
 which he derives the theorems of his predecessors, than for any new light 
 he throws on the difficult subject to which it relates. The calculus he 
 employs in it is described by one of the most eminent mathematicians of 
 the present age, as the most singular in its character, and the most 
 powerful in its application, which has ever been devised *. 
 
 The motion of the earth about its centre of gravity was one of those 
 great problems of the system of the world, which demanded for its solu- 
 tion the most advanced principles of mechanical science. Newton's re- 
 searches on this subject have been admired as one of the most remark- 
 able triumphs of his genius, but a more complete and systematic investi- 
 gation was rendered desirable by the improved state of analytical me- 
 chanics. Further researches were also called for by Bradley 's discovery 
 of Nutation. It did not escape the sagacity of Newton, that besides the 
 motion which occasions the Precession of the Equinoxes, the earth's axis 
 would be affected by an oscillatory motion, arising from the variable 
 position of the plane of the equator with respect to the direction of the 
 sun's disturbing force f. In fact, if we suppose the earth to be situated 
 in the vernal equinox, the sun's disturbing force will pass through the 
 plane of the ring formed by the redundant matter at the equator, and, 
 therefore, it can produce no effect on the position of that plane. As the 
 earth proceeds in her course, the sun's force becoming inclined to the 
 ring, will tend to disturb its position, and this disturbance will coatinoalty 
 increase to the solstice, where the inclination reaches its maximum. 
 From this point the tendency of the sun to disturb the ring continually 
 
 Airy, Encycl. Metrop. Art. Figure of the Earth, 
 t Principle, book i. prop. 66, cor. 20. 
 
70 HISTORY OF PHYSICAL ASTRONOMY. 
 
 diminishes, until it finally vanishes once more upon the earth's arrival in 
 the autumnal equinox, when the disturbing force passes through the 
 plane of the ring. The same succession of changes will manifestly take 
 place from the autumnal to the vernal equinox. This constant variation 
 of the influence of the sun's disturbing foree upon the position, of the equa- 
 tor will give rise to an oscillatory movement of the latter plane, which 
 will pass through its values in the course of half a year, and it will be ac- 
 companied by a corresponding nutation of the earth's axis with respect to 
 the plane of the ecliptic. Newton announced the period of this inequality, 
 but did not compute its value, deeming it too inconsiderable to be de- 
 tected by observation *. In fact, it does not amount to half a second at 
 its maximum. A similar nutation arises from the action of the moon on 
 the terrestrial spheroid. It completes its period in half a month, but, 
 like the solar nutation, it is quite insensible. 
 
 But, if the plane in which either of the disturbing bodies moves should 
 vary in position with respect to the plane of the equator, it is clear that a 
 nutation of the earth's axis will arise, independent of that which we have 
 just been considering. In this case the effect of the disturbing force will 
 increase or diminish with the increase or diminution of the inclination 
 between the two planes, and it will give rise to an inequality, the period 
 of which will be equal to that comprised between the least and greatest 
 angles of inclination. Since the plane of the ecliptic constantly preserves 
 the same inclination with respect to the equator, at least, if we neglect 
 its secular displacement, no nutation of this kind can arise from the action 
 of the sun. But the case is quite different when the disturbing force of 
 the moon is considered. The lunar orbit is inclined to the ecliptic at an 
 invariable angle, but, as its nodes have a retrograde motion upon that 
 plane, its inclination to the equator will continually vary. The incli- 
 nation of the lunar orbit to the ecliptic is about 5 8', and the nodes 
 perform a complete revolution in somewhat more than 18 years. The in- 
 clination to the equator will therefore pass from its maximum to its mini- 
 mum value in about 9 years, varying to the extent of 10 16', and in the 
 succeeding 9 years it will return to its original state. Hence arises an 
 inequality in the motion of the earth's axis, which completes its period in 
 a little more than 18 years. This inequality had escaped the notice of 
 geometers, until Bradley detected it by observation. That great as- 
 tronomer discovered irregularities in the places of the stars, which could 
 not be reconciled either with the phenomenon of aberration, or with the 
 annual motion of precession. Having prosecuted his observations during 
 a number of years, he found that the irregularity of each star passed 
 through all its values' in course of a complete revolution of the moon's 
 nodes. Thus, for example, he found that, during the nine years com- 
 prised between 1727 and 1736, the star y Draconis moved 10" to the 
 north, while during the nine following years it continued to move south- 
 wards, until it finally arrived in its original position. He explained 
 these irregularities by an oscillatory movement of the earth's axis, the 
 period of which extended to a revolution of the moon's nodes. In virtue 
 of this nutation, the earth's axis alternately approaches to, and recedes 
 from, the plane of the ecliptic, and the equinoctial points alternately 
 advance and recede upon the same plane. Both of these effects may be 
 accounted for by imagining the pole of the equator to describe a small 
 
 * Principia, book iii. prop. 21. 
 
HISTOKY OF PHYSICAL ASTRONOMY. 71 
 
 ellipse in the heavens round its mean place, the major and minor axes of 
 the ellipse being 18" and 13", and the former of these coinciding with 
 the circle of latitude passing through the mean pole of the equator. 
 
 Bradley, besides determining the period and maximum value of Nuta- 
 tion, had the sagacity also to discover its true physical cause. It now 
 remained for geometers to compute the inequality by theory. In 1749 
 D'Alembert published his important work on the Precession of the Equi- 
 noxes, which contained a rigorous investigation of the motion of the earth 
 about its centre of gravity. The quantities of precession and nutation, 
 when computed by theory, were found to accord in the most satisfactory 
 manner with observation. Solutions of the same great problem, differing 
 more or less from each other, were soon afterwards given by Euler, Frisi, 
 Thomas Simpson, and several other geometers. Laplace at a later period 
 examined the effect which might be produced on the motion of the earth's 
 axis by the fluid state of the ocean, and he was conducted to the following 
 remarkable conclusion : the motion of the earth's axis is the same as if 
 the whole sea formed a solid mass adhering to its surface. 
 
 About the time that geometers resumed the consideration of the figure of 
 the earth, their attention was also directed to the theory of the Tides. The 
 Academy of Sciences of Paris having proposed it as the subject of their prize 
 of 1 740, four individuals were considered to possess just claims to distinction, 
 and the prize was shared among them. Three of these, Euler, Maclaurin, 
 and Daniel Bernouilli, adopted the principle of gravitation as the basis of 
 their respective investigations ; the fourth, Father Cavalleri, endeavoured 
 to explain the phenomena by the system of vortices. This was the last 
 honour paid to the Cartesian theory, which soon afterwards sank into total 
 oblivion. The three geometers first mentioned supposed that the action 
 of the sun or moon upon the ocean drew the earth every instant into the 
 form of an aqueous spheroid, which would be maintained in equilibrium 
 if the forces continued to operate with the same intensity and in the same 
 direction. This w r as termed the equilibrium theory, and it is manifest 
 from its fundamental principle that the researches suggested by it essen- 
 tially coincided with those relating to the figure of the earth. In reality, 
 however, the continual change in the positions of the sun and moon with 
 respect to the earth does not allow the waters of the ocean to attain a 
 state of equilibrium, and it is by the mutual blending of the oscillations 
 hence arising that the different phenomena of the tides are occasioned 
 The question is therefore one of dynamics, and not of statics. Laplace 
 first considered the subject in its proper light, its investigation having 
 been recently very much facilitated by the researches of D'Alemberf 011 
 the motion of fluids, and by his invention of the calculus of partial dif- 
 ferences. The theory of Laplace., although generally allowed to be a 
 signal effort of mathematical genius, is based upon two suppositions, which 
 cannot be reconciled with the real condition of the earth. These are 1st, 
 that the whole exterior stratum of the earth is covered with an aqueous 
 fluid ; 2nd, that the depth of the ocean is uniform under the same paral- 
 lel of latitude. Discovering the impossibility of adapting his results to 
 the actual state of the Tides, on account of the influence of a multitude of 
 circumstances which could not be ascertained with precision, and even if 
 they were so ascertained could not be introduced into his theory, he was 
 compelled to assume as a general principle that the oscillations of the 
 waters of the ocean are periodical, like the forces which produce them, but 
 that they are not necessarily proportional to the magnitudes of those forces, 
 
72 HISTORY OF PHYSICAL ASTEONOMY. 
 
 nor are the times of their maxima and minima necessarily coincident with 
 the times of the maxima and minima of the forces. In other words, he as- 
 sumed that, if the disturbing forces of the sun or moon be expressed by a 
 series of cosines of angles, the oscillations of the sea will be expressed by 
 a corresponding series of cosines, the arguments being the same in both 
 cases, but the epochs and coefficients being different. This assumption has 
 been justly regarded as tantamount to an evasion of the difficulties of the 
 problem, rather than a real conquest of them. Indeed, it is now generally 
 admitted, that a long course of observations, conducted with great skill, 
 and under a variety of different circumstances, can alone lead to a theory 
 of this subject which shall be of any service in the construction of accu- 
 rate Tide tables. 
 
 An interesting question which Laplace considered in connexion with 
 that of the Tides was the stability of the Ocean. It is important to know 
 whether the condition of the ocean is such that any disturbance which it 
 might suffer would produce only temporary oscillations, in course of which 
 the waters would gradually relapse into their former position, or whether 
 the condition is so unstable that the communication of a small quantity 
 of motion would cause the waters to leave their ordinary bed and over- 
 whelm the whole surface of the earth. Laplace found that the equilibrium 
 would be stable provided the density of the sea was less than the mean 
 density of the earth. Now, the various experiments made on the attrac- 
 tion of mountains, and those executed for a similar purpose with the tor- 
 sion balance of Cavendish, all concur in showing that the mean density of 
 the earth is about five times the density of the sea. We are therefore 
 assured that, under the present constitution of the material universe, the 
 face of the earth will not be liable to any overwhelming inundation of the 
 waters of the ocean, a conclusion which beautifully illustrates the lan- 
 guage of Scripture " hitherto shalt thou come, and no further."* 
 
 Another important subject which soon afterwards engaged the atten- 
 tion of geometers was the libration of the moon. It had been remarked, 
 from the most ancient times, that the moon turns the same side towards 
 the earth throughout the entire course of every revolution. A curious 
 consequence of this fact is, that the motion of that body round the earth 
 is equal to her motion round her axis. It is singular, however, that this 
 conclusion does not appear to have suggested itself to astronomers until 
 the revival of science in modern times. Galileo first discovered that the 
 appearance of the moon's surface is subject to a slight variation, depend- 
 ing on her altitude above the horizon. This fact he rightly explained by 
 the" variable position of a spectator at the earth's surface on account of the 
 diurnal motion. In fact, unless the moon be in the zenith, a spectator always 
 views her in a direction different more or less from that in which he would 
 view her if he were placed at the centre of the earth. This phenomenon, in 
 consequence of passing through all its phases in twenty-four hours, has been 
 designated the diurnal libration of the moon. Hevelius discovered a similar 
 libration in longitude, which he ascribed to the displacement of the centre 
 of the orbit from the centre of motion ; but Newton first gave a clear expla- 
 nation of this phenomenon in a letter addressed to Mercator, which appeared 
 in a work on astronomy, published by that individual in the year 1676. 
 He showed that it arose from the inequalities of the moon in longitude 
 causing the angle described by her round the earth sometimes to exceed 
 
 * Job xxxviii. 2. 
 
HISTOKY OF PHYSICAL ASTBONOMY. 73 
 
 in magnitude the angle described by her round her axis, and other times 
 to fall short of the same angle ; whence it happened, that the great circle 
 formed by the intersection of the lunar surface \vith a plane passing 
 through the moon's centre, and perpendicular to the line joining the earth 
 and moon (which great circle determines the lunar hemisphere visible to 
 the spectator), does not maintain a fixed position, but oscillates continually 
 round a mean state. Hence the moon will appear to librate continually 
 to and fro in the plane of her motion. In the same letter Newton ex- 
 plained the libration in latitude, which arises in consequence of the moon's 
 axis of rotation being inclined to her orbit. This phenomenon, like the 
 two already mentioned, is purely optical. 
 
 Cassini is the next person whose researches contributed to throw light * 
 upon this interesting subject. This astronomer discovered the remark- 
 able fact, that the nodes of the moon's equator always coincide with the 
 nodes of her orbit. He also found that a plane drawn through the moon's 
 centre, parallel to the plane of the ecliptic, is always contained between the 
 planes of her equator and orbit, so that the poles of the latter are con- 
 stantly situated in the same great circle with the pole of the ecliptic, but 
 on opposite sides of it. He fixed the inclination of the lunar equator to 
 the ecliptic at 2 30'. 
 
 Mayer, about the middle of the last century, undertook an extensive 
 series of observations for the purpose of verifying the conclusions of Cas- 
 sini. He measured the distance between the nodes of the equator and 
 orbit, and found it to amount to 3 30'. He remarked, however, that the 
 displacement might be considered as absolutely insensible, since its de- 
 termination depended on the inclination of the lunar equator, an error in 
 which of only 5' would produce a corresponding error of 20 or 25 in the 
 distance between the nodes. He fixed the inclination of the lunar equator 
 at 1 45', a quantity considerably less than the corresponding estimate 
 of Cassini. Lalande, a short time afterwards, made observations on the 
 moon, and arrived at conclusions which mainly agreed with those of 
 Mayer, but he obtained 2 9' for the inclination of the lunar equator. 
 Recent observations have, however, completely confirmed the value as- 
 signed to that element by the illustrious astronomer of Gottingen. 
 
 The librations we have hitherto mentioned are apparent, not real ; for they 
 do not depend upon any actual inequality in the motion of the moon round 
 her axis. Newton, however, did not fail to perceive that the action of the 
 earth would, under certain conditions, affect the figure of the moon, and 
 would thereby occasion a real variation of her rotatory motion. Proceed- 
 ing upon the supposition that she was originally in a fluid state, he con- 
 cluded that the terrestrial attraction would draw her into the form of a 
 spheroid, the longer axis of which, when produced, would pass through 
 the earth's centre. Comparing this phenomenon with the tidal spheroid, 
 occasioned by the action of the moon upon the earth, he found that the 
 diameter of the lunar spheroid, which is directed towards the earth, would 
 exceed the diameter at right angles to it by 186 feet. He discovered in 
 this elongation of the moon the cause why she always turns the same side 
 towards the earth, for he remarked that in any other position the action 
 of the earth would not maintain her in equilibrium, but would constantly 
 draw her back, until the elongated axis coincided in direction with the line 
 joining the earth and moon. Now, in consequence of the inequalities of 
 the moon in longitude, the elongated axis will not always be directed 
 exactly to the earth. Newton therefore concluded that a real libration of 
 
74 HISTOBY OF PHYSICAL ASTKONOMY. 
 
 the moon would ensue, in virtue of which the elongated axis would oscil- 
 late perpetually on each side of its mean place. 
 
 D'Alembert was the first of Newton's successors who undertook to in- 
 vestigate the subject of the moon's physical libration. In 1754 this 
 great geometer, encouraged by his researches on the Precession of the 
 Equinoxes,- applied the same method of investigation to the problem of 
 the moon's motion about her centre of gravity. He did not, however, 
 pay sufficient attention to the modification rendered necessary by the 
 slow rotatory motion of the moon, and the near commensurability of 
 the motions of revolution and rotation. For these reasons the results 
 obtained by him did not accord so well with observation as those to which 
 he was conducted by his previous researches of a similar kind relative to 
 the motion of the earth. The Academy of Sciences of Paris having 
 offered their prize of 1764 for a complete theory of the moon's libration, 
 Lagrange composed an admirable memoir on the subject, which obtained 
 for him the prize. It was in this investigation that he first employed the 
 principle of virtual velocities in combination with the dynamical principle 
 recently discovered by D'Alembert. By this step he reduced every ques- 
 tion relating to the motion of a system of bodies to the integration of a 
 series of differential equations of the second order, whence the only dif- 
 ficulties that remained to be overcome were those of a purely analytical 
 nature. This refined conception forms the basis of his celebrated work, 
 the Mecanique Analytiquc, which he published at a subsequent period of his 
 life, and in which all the great problems of mechanical science are inves- 
 tigated by a process divested of every trace of geometrical reasoning. 
 
 Lagrange, in the rgemoir above mentioned, proceeded first to consider 
 the figure which the moon would assume in consequence of the various 
 forces exerted upon the particles composing her mass, which he supposed, 
 with Newton, to have been originally in a fluid state. It does not appear 
 to have occurred to the latter, that the centrifugal force generated by the 
 rotatory motion of the moon would affect her figure to an extent com- 
 parable with the effect occasioned by the action of the earth. Lagrange, 
 however, found that both effects were of the same order, and that the moon 
 would in reality acquire the form of an ellipsoid, the greatest axis being 
 directed towards the earth, and the least being perpendicular to the plane 
 of the equator. The greatest axis, and the mean axis, will both lie in the 
 last-mentioned plane ; the mean position of which, as we have already stated, 
 is parallel to the plane of the ecliptic. Lagrange also found that the excess 
 of the axis turned towards the earth over the least axis was four times 
 greater than the excess of the axis at right angles to it over the same axis. 
 
 Considering next the effect of the earth's attraction upon the rotatory 
 motion of the moon, Lagrange found that the mean motion would be 
 affected by a series of inequalities corresponding to those of the mean 
 motion in longitude. The velocity of rotation is on this account some- 
 times accelerated beyond its mean state, and at other times retarded behind 
 it, whence there ensues a real libration similar to that remarked by New- 
 ton. Lagrange shewed that it was not necessary to suppose that at the 
 origin the motions of rotation and revolution were exactly equal. If they 
 differed by an arbitrary quantity confined within certain narrow limits, 
 the effect of this difference would be merely to occasion a slight inequality, 
 in the motion of rotation, in virtue of which the axis directed towards the 
 earth would librate continually on each side of the line joining the earth 
 and moon. The most careful observations of the moon's surface have not 
 
HISTORY OF PHYSICAL ASTRONOMY. 75 
 
 disclosed to astronomers any traces of a libratory motion of this character ; 
 whence we may conclude that the motions of rotation and revolution did 
 not originally differ by a sensible quantity *. 
 
 Lagrange next considered the lib ration of the moon in latitude. In 
 this memoir he did not succeed in explaining the singular fact discovered 
 by Cassini relative to the coincidence of the nodes of the lunar orbit and 
 equator. When he assumed this coincidence in the outset of his re- 
 searches, he found that the lunar equator, instead of being fixed with 
 respect to the ecliptic, continually approached towards that plane, while 
 observation on the other hand went to prove that it was inclined to it at 
 nearly an invariable angle. This portion of his researches being imper- 
 fect, he resumed the subject fifteen years afterwards, and in the volume 
 of the Berlin Academy for 1780, he published an admirable memoir, in 
 which he completed the theory of the moon's motion about her centre of 
 gravity. On this occasion he was conducted to the remarkable conclusion, 
 that if the mean nodes of the lunar equator and orbit be supposed to 
 have originally coincided, the action of the earth upon the lunar ellipsoid 
 would constantly maintain this coincidence. He also determined the laws 
 of the small oscillations, by which the true node of the lunar equator 
 deviates from the mean node. 
 
 The only question connected with this subject which still remained to 
 be examined was the effect which the secular inequalities in the mean 
 motion of the moon might produce upon the appearance of the lunar 
 surface. These inequalities will one day derange the mean place of the 
 moon to the extent of several circumferences of the circle, and if the 
 rotatory motion of the moon remained constant during the whole period 
 of their developement, the inevitable consequence would be, that the moon 
 would present the whole of her surface in gradual succession towards the 
 
 * Several writers on astronomy, when describing the various librations of the moon, 
 affirm that the fourth, or physical libration, was discovered by Lagrange. If this refers 
 to the libratory motion mentioned in the text, it cannot be called a discovery, since its 
 aclual existence has not yet been established by astronomers. The only real libration 
 which observation has detected is that depending on the lunar inequalities in longitude 
 (chiefly the annual equation ; see Chapter XI.), and this phenomenon was first remarked 
 as a theoretical truth by the great founder of Physical Astronomy, who unfolded the whole 
 mechanism of the planetary system, and by his unrivalled sagacity anticipated those results 
 which his successors, by the aid of a refined analysis, have been enabled only to confirm 
 and extend. Laplace is surprised that Newton should have failed to notice thai, in order 
 to assure the constant equality of the motions of rotation and revolution, it was not abso- 
 lutely necessary that at the origin they should have been exactly equal. This, however, 
 might be considered as a natural corollary to the remark of Newton, that any disturbance 
 of the elongated axis of the moon would merely result in an oscillatory motion on each 
 side of its mean place ; for the possibility of allowing the arbitrary constants of any 
 system to vary a little on each side of a mean state, without occasioning any permanent 
 derangement of the system, is a manifest attribute of the condition of stable equilibrium, 
 and such a condition is clearly implied in Newton's words: " Unde ad hunc situm 
 semper oscillando redibit." Princip., lib. iii. prop, xxxviii. If the motions of rotation 
 and revolution had differed a little at the origin, as Laplace conceived they might, it is 
 clear that the elongated axis would not have coincided exactly with the line joining the 
 earth and moon ; and hence, according to Newton's statement, it would oscillate con- 
 tinually on each side of that, line. Newton, however, evidently refers to the difference in 
 the two motions occasioned by the inequalities in the moon's longitude. It is natural 
 enough, indeed, to suppose that the illustrious author of the Principia did not feel any 
 anxiety to repudiate the original equality of the motions of rotation and revolution a 
 relation which, although perhaps difficult to explain by the doctrine of chances, becomes 
 very interesting and suggestive when it is considered as the result of Supreme Intel- 
 ligence. 
 
76 HISTOKT OF PHYSICAL ASTRONOMY. 
 
 earth. Laplace investigated this interesting question, and arrived at the 
 conclusion that such a condition was inconsistent with the theory of gra- 
 vitation. He found, in fact, that the terrestrial attraction would always 
 draw the moon's axis into coincidence with the line joining the earth 
 and moon, so that the rotatory motion will participate in the secular acce- 
 leration of the motion in longitude, and consequently the lunar hemi- 
 sphere, which is turned away from us, will remain for ever concealed from 
 view, with the exception of the small portion disclosed by the periodic 
 inequalities. 
 
 Laplace has considered the circumstances which determine the sta- 
 bility of the singular mechanism with which the planet Saturn is 
 furnished. He considers that the rotatory motion of the rings may be 
 accounted for by supposing the particles composing them to be homoge- 
 neous, and to move freely among each other like the particles of a 
 fluid. Under such conditions, he shews that they would be maintained in 
 equilibrium by the action of the planet and the centrifugal force generated 
 by their own rotatory motion, the exterior surfaces assumed by both rings 
 being such, that all sections perpendicular to them, and passing through 
 the centre of the planet, would be ellipses, whose major axes when produced 
 would pass through that point. Laplace hence concluded that the period of 
 the rotation of the rings is equal to that of a satellite revolving at the 
 distance of the centre of the generating ellipse. This period he found to 
 be equal to lOh. SS'.Sd". It is remarkable that Herschel inferred, from 
 certain periodic changes in the appearance of the rings, that they accom- 
 plished a revolution round the planet in lOh. 32M5"*. 
 
 If the rings were uniform and circular, and were not exposed to the 
 action of any extraneous force, it would still be possible for them to re- 
 volve constantly round the planet ; but it is clear that the least disturb- 
 ance, as the action of a satellite or comet, would affect their stability, and 
 ultimately precipitate them upon the body of the planet. In order, there- 
 fore, to assure the permanence of the rings, Laplace conceived that it was 
 necessary to suppose their figures to be irregular, so that any disturbance 
 either of them might suffer would be rapidly checked in course of rota- 
 tion by the unequal distribution of the mass. 
 
 CHAPTER VII. 
 
 Jupiter's Satellites. Galileo. Simon Marius. Hodierna Borelli. Cassini. His first 
 
 Tables. He is invited to France. He publishes his Second Tables. His Rejection of 
 the Equation of Light. Researches of Maraldi I. He discovers that the Inclination 
 of the second Satellite is variable. Bradley's Discoveries. Maraldi II His Dis- 
 coveries relative to the third and fourth Satellites. He adopts the Equation of Light. 
 Wargentin. He discovers the Inequalities in Longitude of the first and second 
 Satellites. He remarks that the third Satellite has two Equations of the Centre. 
 Motion of the Nodes of the fourth Satellite. Inclination of the third Satellite. 
 Libratory Motion of the Nodes. Inclination of the fourth Satellite. 
 
 THE discovery of Jupiter's satellites is one of the most interesting events 
 in the history of astronomy. Even in any age it would have been deemed 
 
 * Phil. Trans. 1790. 
 
HISTORY OF PHYSICAL ASTRONOMY. 77 
 
 an important contribution to science ; but in the beginning of the seven- 
 teenth century, when men's minds were wavering between the ancient 
 and modern ideas of the system of the world, it exercised an influence of 
 which it is impossible to form an adequate conception in the present day. 
 The existence of four bodies revolving round one of the principal planets 
 of the solar system, exhibited a beautiful illustration of the moon's motion 
 round the earth, and furnished an argument of overwhelming force in 
 favour of the Copernican theory. The announcement of this fact pointed 
 out also the long vista of similar discoveries which have continued from 
 time to time down to the present day to enrich the solar system, and to 
 shed a lustre on the science of astronomy. Jn more recent times the 
 physical theory of Jupiter and his attendants has supplied evidence of the 
 most varied and satisfactory character in favour of the principle of Uni- 
 versal Gravitation. All the irregularities which arise from the mutual 
 action of the larger bodies of the system are here exhibited in miniature. 
 Their study also offers peculiar advantages to the mathematician, for, as 
 they generally pass through all their values in short periods, their real 
 character is readily appreciable, and on this account they are eminently 
 favourable for testing the conclusions of his theory. Nor is it merely in 
 its relation to speculative science that the discovery of Jupiter's satellites 
 is to be regarded as of capital importance. The eclipses of these bodies 
 soon suggested a new solution of the great problem of the longitude. 
 Their theory thus came to be associated with one of those questions 
 which most deeply affect the progress of civilization the promotion of 
 mutual intercourse between the various nations of mankind, and a more 
 earnest and more generally diffused interest was naturally felt in the re- 
 searches connected with its improvement. 
 
 When Galileo first turned his telescope to the planets, he was delighted 
 to perceive that they exhibited a round appearance like the sun or moon. 
 Jupiter presented a disc of considerable magnitude, but in no other re- 
 spect was he distinguishable from the rest of the superior planets. 
 Having, however, examined him with a new telescope of superior power on 
 the 7th January, 1610, his attention was soon drawn to three small but 
 very bright stars that appeared in his vicinity, two on the east side and 
 one on the west side of him. He imagined them to be three fixed stars, 
 and still there was something in their appearance which excited his ad- 
 miration. They were all disposed in a right line parallel to the plane of 
 the ecliptic, and were brighter than other stars of the same magnitude. 
 
 This did not, however, induce him to alter his opinion that they were 
 fixed stars, and therefore he paid no attention to their distances from 
 each other, or from the planet. Happening, by mere accident, to examine 
 Jupiter again on the 8th January *, he was surprised to find that the 
 stars were now arranged quite differently from what they were when he 
 
 * " Cum autem die octava, ncscio quo fato ductus, ad inspectionom eandem reversus 
 essem." Sidereus Nuncius, p. 20. 
 
78 HISTORY OF PHYSICAL ASTRONOMY. 
 
 first saw them. They were all now on the west side of the planet, and 
 
 * * * 
 
 were nearer to each other than they had been on the previous evening ; 
 they were also disposed at equal distances from each other. The strange 
 fact of the mutual approach of the stars did not yet strike his attention, 
 but it excited his astonishment, that Jupiter should be seen to the east of 
 them all, when only the preceding night he had been seen to the west of 
 two of them. He was induced, on this account, to suspect that the 
 motion of the planet might be direct, contrary to the calculations of 
 astronomers, and that he had got in advance of the stars by means of his 
 proper motion. He therefore waited for the following night with great 
 anxiety, but his hopes were disappointed, for the heavens were on all 
 sides enveloped in clouds. On the 10th he saw only two stars, and they 
 were both on the east side of Jupiter. He suspected that the third 
 
 might be concealed behind the disc of the planet. They appeared as 
 before in the same right line with him, and lay in the direction of the 
 zodiac. Unable to account for such changes by the motion of the planet, 
 and being at the same time fully assured that he always observed the 
 same stars, his doubts now resolved themselves into admiration, and he 
 found that the apparent motions should be referred to the stars them- 
 selves and not to the planet. He therefore deemed it an object of 
 paramount importance to watch them with increased attention. 
 
 On the llth he again saw only two stars, and they were also both on 
 the east 
 
 side of Jupiter. The more eastern one appeared nearly twice as large as 
 the other, although on the previous evening he had found them almost 
 equal. This fact, when considered in connexion with the constant change 
 of the relative positions of the stars and the total disappearance of one 
 of them, left no doubt on his mind of their real character. He therefore 
 came to the conclusion, that there are in the heavens three stars revolving 
 round Jupiter in the same manner as Venus and Mercury revolve round 
 the sun. On the 12th he saw three stars; two on the east side of 
 
 Jupiter, and one on the west side. The third began to appear about 
 three o'clock in the morning, emerging from the eastern limb of the 
 
HISTORY OF PHYSICAL ASTRONOMY. 79 
 
 planet ; it was then exceedingly small, and was discernible only with 
 great difficulty. On the 13th he finally saw four stars; Three of them 
 
 were on the west side of the planet, and the remaining one on the east 
 side. They were all arranged in a line parallel to the ecliptic, with the 
 exception of the central star of the three western ones, which declined a 
 little towards the north. They appeared of the same magnitude, and, 
 though small, were very brilliant, shining with a much greater lustre than 
 fixed stars of the same magnitude *. 
 
 The future observations of Galileo established beyond all doubt that 
 Jupiter was attended by four satellites. He continued to examine them 
 until the latter end of March, noting their configurations, arid recording 
 the stars which appeared in the same field of view with them. 
 
 Soon after Galileo's famous discovery, he perceived the utility of 
 the satellites for finding the longitude, and he continued for many 
 years to make observations on them, with the view of constructing a 
 theory of their motions. Much has been said about his tables of the 
 satellites, which were to have been published by his friend and pupil Ri- 
 mieri, but which, by some unaccountable accident, disappeared at the death of 
 that person, and could nowhere be found, until they were finally discovered 
 a few years ago in a private library at Rome. We know that Galileo him- 
 self was very sanguine of their practical utility, but his opinion of their 
 merits does not seem to be borne out by the actual examination of them 
 consequent on their rediscovery. Indeed, when we reflect on the many 
 painful efforts which it cost his successors to arrive at even a tolerable 
 knowledge of the elements of the satellites, we might very reasonably 
 conclude, ci priori, that his tables can only be regarded in the present day 
 as an object of scientific curiosity. An interesting fragment of his early 
 researches on the satellites is to be found in one of his letters to Welser, 
 the person through whom he carried on the controversy with Schener the 
 Jesuit, relative to the discovery of the solar spots. At the end of a letter 
 dated December 1st, 1612, he gives a sketch in rough drawings of the 
 configurations of the satellites from 1st March till 7th May of the follow 
 ing year. 
 
 Simon Mayer, the German astronomer, who contended for the inde- 
 pendent discovery of the satellites, resolved to strengthen his claims by 
 the construction of tables of their motions. The crude labours of this im- 
 pudent pretender were, however, no sooner given to the world than they 
 fell into deserved oblivion. Hodierna, a Sicilian astronomer, is the next 
 person who is mentioned as having devoted his attention to this subject. 
 In 1G56 he published his observations on the satellites, accompanied 
 with remarks on the theory of their motions. He is the first astronomer 
 who pointed out the superior importance of eclipses of the satellites as 
 compared with other phenomena. He also calculated tables of their 
 motions, but they are said to have been so very inaccurate, that in a few 
 years they even ceased to represent the configurations of the different 
 bodies. In 1666 Borelli attempted to establish a theory of the satellites, 
 
 * The preceding configurations are derived from those given by the illustrious dis- 
 coverer in the Sidereus Nuncius. 
 
80 HISTORY OF PHYSICAL ASTBONOMY. 
 
 by means of his own observations and those of Hodierna, but his labours 
 were attended with very imperfect success. 
 
 The earliest tables which enjoyed any confidence among astronomers were 
 those of Cassini, which first appeared in 1 668 at Bologna. Picard, the cele- 
 brated French astronomer, having comparedthem with a number of observed 
 eclipses, found them to be even more accurate than their author anticipated. 
 He, in consequence, recommended him to Colbert as an astronomer, whose 
 talents would be an ornament to France, and, at the suggestion of that 
 minister, Louis the Fourteenth invited him to his capital. Cassini, upon 
 his arrival in Paris, resolved to perfect his previous researches on the 
 motions of the satellites, and during many years he continued to make 
 observations on their eclipses. In .1693 he published his second tables, 
 which far exceeded in accuracy any previous efforts of the kind. Those 
 of the first satellite especially were found to represent the times of the 
 eclipses with remarkable fidelity, and by means of them the longitude 
 was determined with a precision hitherto unknown. In these tables the 
 orbits of the four satellites were considered to be circular ; they were in- 
 clined to Jupiter's orbit at equal angles, and their nodes had all a common 
 rition. Cassini estimated the inclination of the orbits at 2 55', and 
 fixed the nodes in 10 s 14 30' of longitude ; both of these elements 
 were supposed invariable. He did not employ the equation of light in 
 his tables, although at one time he was favourably disposed towards the 
 hypothesis of Roemer. He perceived that the successive propagation of 
 light explained the irregularities in the eclipses of the first satellite when 
 the earth was in different positions of her orbit ; but, finding that it did 
 not account in an equally satisfactory manner for the irregularities of the 
 other satellites, he rejected it altogether, and instead of it he used in the 
 tables of the first satellite an empiric equation depending on the relative 
 positions of the Earth and Jupiter. Although the error in an eclipse of 
 the first satellite seldom exceeded I' of time, yet it happened occasionally 
 that it rose to 5' or 6'. The inequality which principally occasioned this 
 error was certainly not easy to discover ; but it is surprising that a similar 
 inequality in the second satellite, which rises to a much greater magni- 
 tude, should have escaped the sagacity of Cassini. He also failed to 
 notice the principal inequality in the fourth satellite, although it causes 
 the times of eclipses to vary to the extent of an hour. Notwithstanding 
 these defects, the tables of Cassini mark an important epoch in the 
 history of the satellites, and their construction will ever remain a monument 
 of the ingenuity and patience of their illustrious author. 
 
 Maraldi I., the nephew of Cassini, also devoted much attention to the 
 subject of Jupiter's satellites. He admitted, in common with his relative, 
 that the equation of light gave a very satisfactory account of the errors in 
 the first satellite, when the earth was in different parts of her orbit, but 
 he maintained that, if this equation was founded upon true physical 
 principles, it should vary from the perihelion to the aphelion of Jupiter's 
 orbit, a conclusion which the observations 011 eclipses did not seem to him 
 to warrant. He also remarked, that if the errors in the times of the 
 eclipses depended upon the successive propagation of light, they should 
 be equal for all the satellites when the earth was in the same parts of her 
 orbit. It did not occur to him that other irregularities might exist in the 
 motions of the satellites, and might cause the errors of eclipses to be very 
 different for each satellite. It is true that the orbits were supposed 
 circular, and as* long as astronomers entertained this belief there could 
 
HISTOEY OF PHYSICAL ASTRONOMY. 81 
 
 be no equation of the centre ; but, as Delambre justly remarks, there 
 might exist the inequality of the variation even in a circular orbit, and, as 
 long as it was neglected, it would occasion an apparent discordance 
 between the several equations of light. The arguments of Maraldi were, 
 however, considered by some of his most eminent contemporaries to be 
 fatal to the theory of Roemer. " It appears then," says Fontenelle, " that 
 we must renounce, though perhaps with regret, the ingenious and se- 
 ductive hypothesis of the successive propagation of light How 
 
 little prevents us from falling into great errors ! If Jupiter had but one 
 satellite, or if the eccentricity had been less, and these two things are 
 very possible, we should have concluded with the utmost confidence that 
 light traversed the annual orbit of the earth in 14 minutes."* 
 
 Maraldi first established the important fact, that the inclination of the 
 second satellite is variable. He was led to this discovery by observing 
 that the duration of eclipses was not always the same when the satellite 
 was at the same distance from the nodes, a fact of which he assured him- 
 self by a careful comparison of a great number of eclipses. For example, 
 on the 21st January, 1668, when Jupiter was in that part of his orbit 
 wherein the eclipses are shortest, he found that the semi-duration of 
 the eclipse was l h 19 m ; on the 17th September, 1715, when all the 
 circumstances were the same, the semi-duration was only l h 7 m 14 s . 
 The difference amounted to ll m 46 s , and, as this quantity was too great 
 to be ascribed to the errors of observation, he concluded that it must 
 have proceeded from a change in some of the elements upon which 
 the phenomenon depended. He remarked that the duration of the 
 eclipse might be modified by three distinct causes ; 1st, a variation in 
 the eccentricity of the satellite ; 2nd, a variation in the inclination ; 
 3rd, a variation in the place of the nodes. With respect to the first 
 of these causes, the variation would require to be enormous, in order 
 that it might occasion so great a' difference between the eclipses; 
 with respect to the second, he remarked that the duration of the eclipse 
 varied even when the satellite was at the same distance from the node. 
 He concluded, therefore, that the phenomenon must be ascribed to a 
 change in the inclination of the orbit. In 1707 he found the inclination 
 to be equal to 3 33' ; whence it appeared to have increased nearly a 
 degree since the publication of Cassini's tables. 
 
 Bradley is the next astronomer whose researches contributed to throw 
 light upon this interesting subject. In 1719 he constructed tables of the 
 satellites; but they were not given to the world until 1749, when they 
 were published along with Halley's tables of the planets. In these tables 
 the places of the satellites were given by Bradley, in degrees and minutes of 
 space ; but there were appended to them ecliptic tables of the first satellite 
 calculated in time by Pond, his uncle. He determined the mean motions 
 with great accuracy, by means of a comparison between the observations of 
 preceding astronomers and those made by himself at Waustead, after 
 Jupiter had completed four revolutions. We have seen that Cassini and 
 Maraldi refused to admit the equation of light; Halley, in 1694, argued 
 more philosophically on the subject; for he maintained the necessity of 
 applying it to all the satellites. Bradley was the first who introduced this 
 equation into the tables of their motions. He fixed it at the usually 
 received value of 14, adding a smaller equation of 3| m to account for the 
 
 
 * Mem. Acad. des Sciences, Hist. p. 80. 
 
82 HISTORY OF PHYSICAL ASTRONOMY. 
 
 effect of Jupiter's eccentricity. The maximum value which he assigned to 
 the aberration of light would have given him 16 m 26 s * for the greater 
 equation a result which would have been much more conformable to 
 observation than the quantity he actually employed. It is surprising that 
 he should have overlooked the importance pf his great discovery in furnish- 
 ing an independent means of calculating this equation. 
 
 The irregularities in the motions of the satellites were the cause of 
 much perplexity to Bradley. The second satellite, especially, presented 
 anomalies which could not be accounted for either by a circular or an 
 elliptic orbit. Sometimes it deviated from its mean place to so great an ex- 
 tent, and in so short a time, as to be incompatible with a small eccentricity ; 
 while, on the contrary, other observations rendered it impossible that the 
 orbit should differ much from a circle. He discovered that the three 
 interior satellites passed through the irregularities of their motions in 437 
 days ; the errors returning at the close of this period in the same order 
 and magnitude as before. He considered that about the middle of this 
 period the inequality of the second satellite might amount to 30 or 40 
 minutes. He remarked that the period of the inequalities corresponded 
 to that which brought back the satellites to the same position relatively 
 to each other, and to the axis of Jupiter's shadow; and he hence 
 inferred, with his usual sagacity, that the inequalities resulted from the 
 mutual attraction of the satellites. " While we carefully attend," says he, 
 " to future observations, by means of which the theory of the satellites may 
 be established, a posteriori, let us hope that some rival of the great Newton, 
 relying upon the sure and tried principle of gravitation, will achieve the 
 noble task of investigating a priori the effects of their mutual attraction." 
 Bradley retained the inclinations of the three interior satellites at 2 55', 
 as fixed by Cassini ; but he reduced that of the fourth to 2 40'. This 
 was a happy alteration ; Delambre's tables make it 2 40' 42" for the same 
 epoch. He also discovered that the 'orbit of the fourth satellite is eccentric ; 
 and he fixed the maximum value of the equation of the centre at 48 m . 
 
 Maraldi II. devoted much of his time to researches on the satellites, and 
 effected some very important improvements in the theory of their motions. 
 In a memoir, which appeared in the volume of the Academy of Sciences 
 for 1732, he proved that the inclination of the third satellite is variable ; 
 and he also established the eccentricity of the fourth satellite. With 
 respect to the first of these points, he found that the durations of the 
 eclipses of the satellites had been continually diminishing ever since the 
 year 1693. It was impossible to explain this constant diminution by an 
 eccentricity in the orbit, since the effect of such a supposition would be to 
 produce sometimes a diminution ; and at other times an increase in the 
 duration of the eclipse. Nor would a motion of the nodes suffice for this 
 purpose ; for he shewed that the utmost change in their position which 
 could possibly occur would not exceed 3, and this would occasion a change 
 of only 10 s in the duration of eclipses at the limits; whereas observa- 
 tion shewed it to amount to 16 m 44 s . Besides, upon this suppo- 
 sition, the same variation ought to iiave manifested itself at the nodes as 
 at the limits ; but the duration of eclipses varied only to a very small 
 extent when they happened in the former of these positions. The observ- 
 ations, therefore, could only be reconciled together by admitting that the 
 
 * Strictly speaking, the equation is equal only to half this quantity ; but in the tables 
 of the satellites the coefficients are doubled in order to render the results always additive. 
 
HISTOEY OF PHYSICAL ASTKONOMY. 83 
 
 inclination of the orbit was continually increasing. He calculated the 
 inclination for 1691 and 1727, and found it to be at the former of these 
 epochs 3 0' 30", at the latter, 3 12' 5". Thus it appeared to have 
 increased to the extent of 11' 35" in the space of 36 years. 
 
 Maraldi established, in an equally satisfactory manner, the eccentricity 
 of the fourth satellite, and fixed the greatest equation of the centre at 55 m . 
 This was a much more accurate determination than Bradley 's ; Delambre's 
 tables make it 55 m 28 s . At the conclusion of his memoir he intimates 
 a suspicion that the orbit of the first satellite was equally eccentric. The 
 inequality in time would be eight or nine times less on account of the 
 more rapid motion of the satellite ; but, in fact, the suggestion of Maraldi 
 is altogether erroneous. Delambre, notwithstanding the vast extent of his 
 researches, was unable to discover the slightest trace of ellipticity in the 
 orbit of the first satellite ; which may therefore be considered as offering, 
 in this respect, a feature quite singular in the system of the world. 
 
 The astronomers of France, influenced by an undue admiration of 
 Cassini, were long reluctant to introduce any change into the elements of 
 the satellites as assigned by him in his tables. The elder Maraldi finally 
 mustered sufficient courage to emancipate his judgment from this thraldom, 
 by announcing that the inclination of the second satellite is variable. 
 Bradley advanced much further in his researches ; but, by a very absurd in- 
 stance of negligence, his discoveries were not communicated to the world until 
 thirty years after he was in possession of them. Meanwhile, Maraldi II. 
 contributed, by his labours, to widen the breach his father had already made 
 in the theory of Cassini ; for he had just shewn that one of the orbits was 
 eccentric, and that the inclination of another was variable. Fontenelle 
 makes some very judicious reflections in connexion with these salutary 
 innovations. "All this," says he, " begins to verify what we announced, 
 and in some sort predicted, in 1727, that the doctrine of concentric orbits, 
 immoveable nodes, and constant inclinations, possibly might not exist in 
 the theory of the satellites; they were not physical enough in their 
 character, nor did they present that kind of regularity which nature loves 
 to follow. Already we see the constancy of the inclinations destroyed in 
 the three first satellites, and the concentricity in the fourth. The immo- 
 bility of the nodes still holds out ; but it is very probable that in the end 
 all will share the same fate." * 
 
 The same feeling of excessive veneration of Cassini to which we have 
 just alluded, as having, in some degree, retarded the theory of the 
 satellites, also induced the successors, and especially the more immediate 
 relatives of that astronomer, to refuse introducing into the tables of the 
 satellites the equation depending on the successive propagation of light. 
 Maraldi II., in the outset of his career, imitated the example of all the 
 members of his family, by strenuously opposing the ingenious theory of 
 Roemer. Bradley, however, having dispelled all doubts upon this ques- 
 tion by his discovery of aberration, Maraldi no longer persevered in 
 rejecting the equation of light ; and, in a memoir published by him in 
 1741, he shewed that it explained much of the irregularity observable in 
 the motion of the third satellite. 
 
 In 1746 Wargentin, a Swedish astronomer, published tables of Jupiter's 
 satellites, which far exceeded in accuracy any that had yet appeared. 
 This meritorious individual devoted his whole life to researches on the 
 
 * Mem. Acad. des Sciences, 1732, Hist. p. 85. 
 
 G 2 
 
84 HISTORY OF PHYSICAL ASTRONOMY. 
 
 motions of these interesting bodies ; and the success which attended his 
 labours affords an encouraging illustration of the valuable results which 
 may be achieved by a mind, even although gifted with no extraordinary 
 powers, when its whole energies are perseveringly directed to any specific 
 object. Having collected together all the observations which could be con- 
 sidered as worthy of any confidence, he instituted a careful comparison be- 
 tween them ; and in this manner he was led to form a number of empiric 
 equations, which enabled him to represent the motions of the satellites with 
 wonderful accuracy. He applied the equation of light to all the satellites ; 
 but he judiciously profited by Bradley 's discovery in fixing its maximum 
 value at 16 m 25 s instead of 14 m , the quantity that had been originally 
 suggested by the errors in the eclipses of the first satellite. The tables of 
 the first satellite, constructed severally by Cassini and Pond, although they 
 generally represented the times of eclipses with great precision, yet 
 happened occasionally to be 6 or 7 minutes in error. Wargentin applied 
 an equation of 3 ra 40 s with a period of 437 d 19 h 41 m , and by this means 
 he reduced the error to 1. The irregularities of the second satellite were 
 much more considerable than those of the first, and had very much 
 perplexed astronomers. Wargentin almost entirely removed these anoma- 
 lies by applying an equation of 16| m with a period equal to that of the 
 equation of the first satellite. We have seen that Bradley had already 
 detected these inequalities ; but, as his remarks were not published until 
 1749, the merit of independent discovery cannot be withheld from the 
 Swedish astronomer. 
 
 In 1759 there appeared, in Lalande's astronomy, an improved edition of 
 Wargen tin's tables of the satellites. The most important change was 
 made in the tables of the third satellite. Maraldi had already suspected 
 that the orbit was eccentric ; but he did not attempt to estimate the 
 equation of the centre. Wargentin, whose views were directed solely 
 towards the perfection of the tables, attempted to satisfy the observed 
 irregularities of the satellite by means of an empiric equation of 8 m , the 
 period of which he estimated at 12 years. In 1771 he published in the 
 Nautical Almanack a new edition of the tables of this satellite. Instead 
 of the equation of 8 m , which his tables of 1759 contained, he now employed 
 three different equations. One of these was equal to 2 m 30 s , and had 
 a period of 437 d 19 h 41 m , similarly to the equations of the first and second 
 satellites. The others amounted to 4 30 s and 2 m 30 s ; the period of the 
 greater equation being somewhat more than 12J years, and that of the 
 smaller one being nearly 14 years. Speaking of the inequalities which 
 formed the basis of these two equations, he says that, towards the close of 
 the preceding century and the beginning of the current one, they both con- 
 spired in the same direction, and formed one large inequality of 15 or 16 
 minutes. Subsequently, in consequence of the difference of their periods, 
 the one had been accelerating, while the other was retarding, the satellite ; 
 until at length they almost destroyed each other, and it became possible to 
 omit them altogether by merely adding 7 m to the epoch. He confesses 
 that his hypothesis does not posesss the character of probability ; but he 
 considers that it may be admitted until experience should put astronomers 
 in possession of a more accurate mode of reconciling all the observations * 
 He concludes with the remark, that, perhaps, the orbit might somehow 
 have a variable eccentricity, and, in that case, that the two inequalities 
 
 * Tabulae Novae Tertii Satellitis Jovis, Lond., 1779, p. 12. 
 
HISTORY OF PHYSICAL ASTRONOMY. 85 
 
 might in reality be only one. He subsequently adopted this hypothesis as 
 offering the best explanation of the phenomenon. 
 
 In 1781 he wrote to Lalande, stating that recent observations induced him 
 to suppose there was only one inequality, with a period of about thirteen 
 years. This inequality amounted to 7| m between 1670 and 1720. From 
 1 720 to 1 760 it had diminished to 2 m , and it had remained constant during 
 the succeeding twenty years *. This was not a happy modification of the 
 original idea of two independent equations. Lagrange and Laplace have 
 demonstrated, a priori, the existence of two distinct equations of the 
 centre, in the motion of this satellite, and this remarkable result of pure 
 theory has been confirmed in the most satisfactory manner by the 
 laborious researches of Delambre. 
 
 Very little progress had been made by astronomers in the researches 
 relative to the nodes of the satellites. In 1758 Maraldi invested this 
 subject with a lively interest by the communication of a memoir to the 
 Academy of Sciences, in which he announced that the nodes of the fourth 
 satellite had a direct motion upon the plane of Jupiter's orbit. Newton, 
 by considering the action of the sun upon the satellite, had found the 
 motion to be retrograde, as in the case of the moon's nodes relative to 
 the earth's orbit. Wargentin concurred with Maraldi in supposing that 
 the motion was direct, and he fixed its annual value at A? 15". This 
 unexpected fact seemed to be at variance with the theory of gravitation, 
 for Newton and his followers had shewn that the mean effect of a 
 disturbing force was to occasion a retrograde motion of the nodes on the 
 plane of the disturbing body. Lalande, however, shewed that the motion 
 of the nodes might be direct upon one plane and retrograde upon another, 
 and upon this ground he contended that, unless the principal disturbing force 
 passed through the plane of Jupiter's orbit, the motion would not be neces- 
 sarily retrograde. Now, in the present case, the third satellite exercises a 
 much more powerful influence on the motion of the nodes than the sun does, 
 and the same is true of the ellipticity of Jupiter. However, as neither 
 the plane in which the satellite revolves, nor the plane of the planet's 
 equator, coincides with the plane of the planet's orbit, it followed that the 
 direct motion of the nodes on the latter plane could not be considered as 
 invalidating the theory of gravitation. 
 
 The inclinations of the orbits presented great difficulties to astronomers, 
 and formed the subject of much laborious research. We have seen that 
 the elder Maraldi first discovered that the inclination of the second 
 satellite is variable. Wargentin afterwards found that during fifteen 
 years and a half the inclination continually increased, and that it then 
 diminished by like degrees during other fifteen years and a halff. The 
 whole period of variation was therefore equal to about thirty-one years. 
 He fixed the extreme limits of the inclination at 3 47' and 1 IS'. Sub- 
 sequently he made the greatest inclination 3 46', and the least 2 46'. 
 In 1765 Maraldi published a memoir, in which he shewed that the 
 inequalities in the duration of eclipses could not be explained by the 
 periodic change of the inclination. Proceeding on the supposition that 
 the nodes were fixed, he calculated the inclination for two eclipses, ob 
 served in 1714 and 1715, and he found that, during the eleven months 
 embraced between them, it had increased to the extent of 20', or more 
 than a fourth of the whole periodic variation. By a similar process he 
 
 * Lalande, Traite d' Astronomic, tome iii. p. 145. 
 t Mem. Acad. Upsal, 1743. 
 
86 HISTORY OF PHYSICAL ASTRONOMY. 
 
 found that, during thirteen months which elapsed between two eclipses, 
 observed in 1750 and 1751, the inclination presented a diminution of 
 18' 20". These great changes occurred in such brief intervals, that it 
 was impossible they could have proceeded from the periodic variation of 
 the inclination. Maraldi finally discovered that the observations might 
 be reconciled with the generally received theory of the inclination, by 
 supposing the nodes to librate continually on each side of their mean place 
 to the extent of 10 13' 48", the period of libration being equal to that 
 which restored the same values of the inclination. Having compared this 
 hypothesis with observation, he was gratified to find that a remarkable 
 accordance generally prevailed between the results derived from both 
 sources. Among 127 eclipses which he calculated, the difference between 
 the observed and computed durations did not exceed 2 m , except in one 
 instance ; and only 8 were found in which the difference exceeded l m *. 
 
 Bailly shewed that the libration of the nodes proceeded from their 
 retrograde motion on the orbit of the first satellite, which was in this case 
 the principal disturbing body. He also remarked that the inclination was 
 constant with respect to the orbit of this satellite, and that it was variable 
 with respect to Jupiter's orbit, in consequence of the retrograde motion of 
 the nodes upon the former orbit. This explained the coincidence of the pe- 
 riod of libration with that which restored the inclination to the same value. 
 
 When we consider the complicated character of the phenomenon in- 
 vestigated by Maraldi, his explanation of it must be regarded as one of the 
 most ingenious conceptions which mere observation has ever suggested to 
 the astronomer. Laplace has employed this libration of the nodes as one 
 of the data from which he derived the masses of the satellites. Wargentiii 
 published tables of the second satellite for the Nautical Almanack for 
 1779 ; the most remarkable peculiarity of which was the libratory motion 
 of the nodes, which he admits to have been first suggested by Maraldi. 
 
 The period in which the inclination of the third satellite passed through 
 all its values was much longer than the corresponding period of the second 
 satellite. Maraldi had found that during the current century it had been 
 continually increasing. In 1763 he fixed it at 3 25' 41". This indi- 
 cated an increase of 22' since the publication of Cassini's tables. In 1769 
 he discovered that the inclination was only 3 23' 33". Pursuing his 
 researches, he found that the inclination reached its maximum in the years 
 1633 and 1765, and its minimum in 1699. Hence it followed that the incli- 
 nation increased during 66 years, and then diminished during an equal 
 space of time ; the whole variation being consequently comprised within a 
 period of 132 years. Maraldi also fixed the mean place of the nodes in 
 10 s 13 52', and estimated the extent of libration at 1 32' 24" f. 
 
 The inclination of the fourth satellite had long been considered in- 
 variable. We have seen that Bradley estimated it at 2 42'. Wargentin, 
 in 1750, made it 2 39', and Maraldi, in 1758, made it 2 36'. In 1781 
 Wargentin concluded from his researches that during a few preceding 
 years the inclination had been slowly increasing. This opinion has been 
 confirmed by the observations of subsequent astronomers, who have found 
 that the increase of inclination has been going on down to the present day. 
 
 Bailly, before becoming acquainted with the researches of Wargentin, 
 made the following sagacious remark upon this subject in his History of 
 Astronomy " The inclination of the fourth satellite has not hitherto 
 
 * Mem. Acad. des Sciences, 1768. f Ibid. 1769. 
 
HISTORY OF PHYSICAL ASTRONOMY. 87 
 
 appeared to vary sensibly ; but it will vary, for everything in the universe 
 is subject to fixed laws ; and the same circumstances always reproduce the 
 same phenomena. We perceive merely that the period of the inclination 
 must be very long and must extend to several centuries."* 
 
 This prediction has been verified by the physical researches of Laplace, 
 who has found that the nodes have an annual retrograde motion of 
 4' 32" upon a fixed plane, accomplishing a complete revolution in 532 
 years. It is this revolution of the nodes which occasions a variation of an 
 equal period in the inclination of the satellite. 
 
 CHAPTER VIII. 
 
 Physical Theory of the Satellites Newton. Euler. Walmsley. Bailly computes the 
 
 Perturbations of the Satellites. Researches of Lagrange. He obtains for each Satellite 
 four Equations of the Centre and four Equations of Latitude. His mode of repre- 
 senting the Positions of the Orbits. Inutility of his Theory in the Construction of 
 Tables. Laplace. His Explanation of the constant Relations between the Epochs 
 and Mean Motions of the three interior Satellites. He completes the Physical Theory 
 of the Satellites. Delambre. He calculates Tables on the Basis of Laplace's Theory. 
 He determines the Maximum Value of Aberration by means of the Eclipses of the 
 first Satellite. Agreement of his Result with Bradley's Conclusions derivable from it. 
 
 AFTER much laborious observation and research, the theory of the 
 satellites was now sufficiently matured to form the basis of an explanation 
 of their motions by the principle of universal gravitation. It is worthy of 
 remark, that this is the order in which the various branches of astronomy 
 have advanced towards their present high state of perfection. The 
 phenomena were first observed, and all the details relating to them 
 carefully recorded. They were then submitted to a critical discussion, 
 and, by a sagacious discrimination of their several peculiarities, they were 
 grouped together under general laws. Finally these laws, although at first 
 merely empiric, served the valuable purpose of suggesting the physical 
 principles on which they depended ; and when once this dependauce was 
 fully established, they henceforward assumed the more elevated character 
 of laws of nature. This order of inquiry is especially manifest in the 
 history of the lunar theory. A similar course has also been strongly 
 recommended in our own day for the purpose of extending our knowledge 
 of the Tides ; and, indeed, it may be considered as offering the only means 
 of ever conducting philosophers to a complete theory of that subject 
 founded upon rigorous principles of geometry and physics. 
 
 If we only considered the disturbing action of the sun upon the satellites, 
 the derangements in their motions would be in all respects analogous to 
 those in the motion of the moon; and the analysis employed in the lunar 
 theory would suffice for their complete investigation. In the present case, 
 however, the problem is much more complicated. Each satellite is 
 disturbed, not only by the sun, but by the other three satellites in course 
 of every synodic revolution round the central body. Nor are these the 
 only sources of complication. If Jupiter were a perfect sphere, his attraction 
 would be the same, both in quantity and direction, as if his whole mass were 
 collected at his centre ; and the question relative to his action upon each 
 
 * Bailly, Hist. Ast. Mod., tome iii. p. 183. 
 
88 HISTORY OF PHYSICAL ASTRONOMY. 
 
 satellite would be reduced to the simple consideration of a material particle 
 attracting the body at that point. This, however, is not the real case of 
 nature ; for observation shews that the figure of the planet is that of an 
 oblate spheroid, whose axes are to each other nearly as 13 to 14. This 
 circumstance causes the law of his attraction to deviate from the inverse 
 square of the distance, and hence originates a disturbing force which 
 powerfully deranges the motions of the satellites. 
 
 Newton, in the third book of the Principia, considers the disturbing 
 action of the sun upon Jupiter's satellites, and attempts to determine the 
 inequalities of their motions by the principles of the lunar theory. In this 
 manner he found that the nodes of the fourth satellite had a retrograde 
 motion upon the plane of Jupiter's orbit, the annual quantity of which 
 amounted to 5'*. We have seen that this result was subsequently contra- 
 dicted by observation ; the actual motion having been discovered by 
 astronomers to be direct. The phenomenon in question does not, in fact, 
 depend so much upon the sun as upon the third satellite and the ellipticity 
 of Jupiter ; causes of disturbance which were not taken into account by 
 Newton. 
 
 Euler, in 1748, first remarked that the spheroidal figure of Jupiter 
 would occasion an irregularity in the law of his attraction f. Walmsley, in 
 1758J, shewed that the disturbance hence arising would produce a motion 
 of the nodes and apsides of each satellite. In 1763 Euler communicated a 
 memoir to the Academy of Berlin, in which he examined the perturbations 
 of a satellite revolving round a planet of a spheroidal figure. He shewed 
 that when the satellite revolved in the plane of the planet's equator the 
 action of the protuberant matter generally occasioned a progressive motion 
 of the apsides. As the orbit of the satellite became more inclined to this 
 plane, the motion of the apsides continually diminished, and it ceased 
 altogether when the angle of inclination was equal to 54 44'. From this 
 position the motion of the apsides was regressive, and it continued to 
 increase until the orbit of the satellite was perpendicular to the plane of 
 the equator. 
 
 Bailly, about the same time, employed Clairaut's theory of the moon 
 in researches on the perturbations of the satellites. He discovered, by a 
 simple analysis, that the mutual attraction of the three interior satellites 
 occasioned those inequalities in their motions which produced a regular 
 return of their eclipses at the end of 437 days. We have seen that 
 Bradley was the first astronomer who threw out a suspicion of this fact. 
 These inequalities are precisely analogous to the lunar variation, the only 
 difference being, that the disturbing body is in each case one of the satel- 
 lites themselves, and not the sun. In the theory of the first satellite 
 the principal disturbing body is the second, for the exterior satellites are 
 too remote to exercise any sensible influence, and the effect of Jupiter's 
 ellipticity is equally inappreciable, because the orbit of the satellite is 
 situated in the plane of his equator, and at the same time does not pos- 
 sess any eccentricity. It is clear, then, that by comparing the coefficient 
 of the equation furnished by theory with the magnitude of the inequality, 
 
 * Principia, lib. iii. prop. 23. Newton, in the same proposition, makes the in- 
 equality of the fourth satellite depending on the disturbing action of the sun, and, similar 
 to the lunar variations, equal to 5" 12'". 
 
 f Recherches des Inegalites de Jupiter et de Saturne. Prix de 1' Academic, tome vii. 
 
 j Phil. Trans., 1758. 
 
 Born at Paris in 1736 ; perished by the guillotine in 1793. 
 
HISTORY OF PHYSICAL ASTRONOMY. 89 
 
 as assigned by observation, the mass of the second satellite may be readily 
 determined. In this manner Bailly found it to be equal to 0.0000211 
 Jupiter's mass being supposed equal to unity. This was a tolerable ap- 
 proximation to the true value.- Laplace makes the mass equal to 0.0000232. 
 
 The inequality of the second satellite is essentially a more complex 
 phenomenon than that of the first, for it depends on the combined action 
 of the first and third satellites. In form, however, the two inequalities 
 are precisely similar, the effects of the disturbing bodies in the theory of 
 the second satellite being blended together so as to form one great inequa- 
 lity, governed by the same law, and extending over the same period as 
 the inequality of the first satellite. This singular coincidence derives its 
 origin from two remarkable relations, connecting together the mean lon- 
 gitudes and mean motions of the three interior satellites. Bailly found 
 that the equation of sensible magnitude, depending on the action of the 
 first satellite, is expressed by the sine of the difference between the mean 
 longitudes of the first and second, and that the equation of a similar 
 nature, depending on the action of the third satellite, is expressed by the 
 sine of twice the difference between the mean longitudes of the third 
 and second*. Now, observation shewed that these two arcs differed 
 from 180 by only a very small quantity. Wargentin's tables, in fact, 
 suppose the difference to be equal only to 30' at the commencement 
 of the year 1760. The arcs being therefore nearly supplementary to 
 each other, it followed that their sines were equal, and hence Bailly 
 was enabled to combine the two equations together, by merely adding 
 their coefficients and retaining either of the arguments. It is in con- 
 sequence of this union of the effects of the two disturbing satellites that 
 the inequality of the second satellite exceeds so much the analogous in- 
 equalities in longitude of the first and third. 
 
 The derangements produced by the two disturbing satellites being thus 
 confounded together, it was impossible to pronounce how much of the 
 resulting inequality was due to each satellite ; and hence, in order to de- 
 termine the masses of those bodies, another independent datum, derived 
 from observation, was indispensable. Bailly selected for this purpose the 
 motion of the nodes of the second satellite. This phenomenon depends 
 on the action of the first and third satellites, and also upon the disturb- 
 ance occasioned by the oblate figure of Jupiter. Having formed an inge- 
 nious supposition respecting the density of the planet, Bailly computed 
 the effect of his oblateness in disturbing the place of the nodes, and then, 
 subducting the result from the observed motion, he obtained the quantity 
 due to the action of the two satellites. Combining this datum ^vith the 
 one assigned by the inequality in longitude, he determined the masses of 
 
 * In both cases there are terras depending on the two arguments mentioned in the 
 text, but, when the first satellite is the disturbing body, the term having for its argument 
 the difference between the mean longitudes greatly exceeds all the others ; and, on the 
 other hand, when the third satellite is the disturbing body, the most considerable term is 
 that depending on twice the difference between the mean longitudes. The predominance 
 of these terms arises from the fact, that twice the mean motion of the second satellite is 
 very nearly equal to the mean motion of the first, and twice the mean motion of the 
 third satellite is very nearly equal to the mean motion of the second. The circumstance 
 is, indeed, exactly similar to that which gives rise to the long inequality in the theory of 
 Jupiter and Saturn, or to the analogous inequality in the theory of the Earth and Venus. 
 The inequalities of the satellites differ, however, from those just cited, in being inde- 
 pendent of the eccentricities. Their investigation will be found in Woodhouse's Physical 
 Astronomy, chapter xx. For the more intricate parts of the theory of the satellites, see the 
 Mecanique Ctleste, liv. viii. ; also Mrs. Somerville's Mechanism of the Heavens, book iv. 
 
90 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the disturbing satellites ; but the results he obtained in this instance 
 were by no means so accurate as his estimation of the mass of the second 
 satellite. 
 
 While Bailly was engaged in these researches, the Academy of Sci- 
 ences offered their prize of 1766 for an investigation of the inequalities 
 of the satellites. The successful competitor was Lagrange, who trans- 
 mitted to the Academy a magnificent memoir on the subject. This illus- 
 trious geometer grappled with the real difficulties of the problem, which 
 it must be acknowledged that Bailly left untouched. When the orbits of 
 the satellites are supposed to be circular, and their planes to be all coin- 
 cident, the effects of their mutual attraction may be computed in any in- 
 stance by considering in succession the action of each body upon the dis- 
 turbed satellite. For this purpose the method of approximation employed 
 in the lunar theory is amply sufficient, and by means of it the inequalities, 
 independent of the eccentricities and inclinations, may be easily calcu- 
 lated. But when the actual conditions of the orbits are taken into ac- 
 count, the mutual perturbations of the satellites become so entangled 
 together as to render the ordinary method of integration totally inappli- 
 cable, and it becomes absolutely necessary to devise some adequate means 
 of surmounting the difficulties of the problem. This important step was 
 accomplished by Lagrange, who investigated the inequalities of each 
 satellite by a method which embraced the simultaneous actions of the 
 sun and the other three satellites, as well as the disturbance arising from 
 the oblate figure of Jupiter. This comprehensive mode of treating the sub- 
 ject entailed upon him an extent of analytical research which, to use 
 Delambre's words*, it is somewhat frightful to contemplate. Neglecting 
 first the eccentricities and inclinations, he found for each of the three 
 interior satellites an inequality in longitude of 437 days, corresponding 
 to the inequality which Bradley and Wargentin originally derived from 
 observation. We have already mentioned that Bailly succeeded in com- 
 puting these inequalities by the aid of Clairaut's theory. Lagrange also 
 calculated the value of the analogous inequality of the fourth satellite, but 
 he found it to be insensible. Delambre's tables, in fact, make it only 11 s . 
 
 Considering next the inequalities dependent on the eccentricities, he 
 obtained four equations of the centre for each satellite. One of these 
 depended on the satellite's own eccentricity, the other three were the 
 reflected effects of the eccentricities of the disturbing satellites. He did not 
 determine the maximum values of these equations, nor did he perceive the 
 analogy between those of the third satellite and the two equations of the 
 centre, which Wargentin deduced from observation. This is only one of 
 a number of instances in which this great genius failed to derive any 
 substantial results from his brilliant researches. 
 
 Finally, he investigated the effects of the disturbing forces perpendicu- 
 lar to the planes of the orbits, and obtained for each satellite four equations 
 of latitude similar to the four equations of the centre, to which his re- 
 searches on the motion in longitude conducted him. He represented the 
 position of the orbit of each satellite by means of four planes passing 
 through the centre of Jupiter. The first of these revolved upon the orbit 
 of the planet with a constant inclination ; the second revolved in a similar 
 manner upon the first ; the third upon the second ; and finally the fourth, 
 
 * " Une analyse nouvelle, puissante, et dont les developpemens ont quelque chose 
 d'effrayant." Astronomic Theorique et Pratique, tome iii. p. 498. 
 
HISTORY OF PHYSICAL ASTRONOMY. 91 
 
 which was the orhit of the satellite, revolved with a constant inclination 
 upon the third. 
 
 Lagrange did not prosecute his researches to the full extent of his de- 
 sign : he concluded by announcing his intention of resuming the subject 
 on some future occasion. He did not, however, at any period of his life, 
 realize this promise ; it was reserved for Laplace to establish a complete 
 theory of the satellites by developing the views of his great rival, and en- 
 riching them with several valuable discoveries of his own. An important 
 mistake was committed by Lagrange, in assuming that the plane of Jupi- 
 ter's equator coincided with the plane of his orbit. He was aware that 
 the two planes did not exactly coincide, but he conceived that the angle 
 of inclination was so small that the disturbing effect would be insensible. 
 Laplace, however, has shewn that some of the most remarkable pheno- 
 mena connected with the motions of the satellites derive their existence 
 from this circumstance. 
 
 The researches of Lagrange did not in any degree contribute to the 
 perfection of the tables of the satellites ; but, as we have already men- 
 tioned, they afforded some valuable hints to his illustrious contemporary. 
 Just before he communicated his memoir to the Academy, Bailly published 
 his researches in a treatise entitled " Essai sur la Theorie des Satellites 
 de Jupiter.'" He, with good reason, suspected that Lagrange might an- 
 ticipate him in his discoveries, and he took the precaution of securing his 
 own rights by a timely publication of his labours. 
 
 In 1784 Laplace communicated a memoir to the Academy of Sciences, 
 in which he explained the physical origin of two remarkable relations 
 which connect the three interior satellites. Astronomers had discovered 
 from observation that the mean motion of the first satellite was nearly 
 double that of the second, and that the mean motion of the second satel- 
 lite was nearly double that of the third. It hence followed that the mean 
 motion of the first satellite, plus twice that of the third, was nearly equal 
 to three times that of the second. Another relation no less interesting 
 was the following : the mean longitude of the first satellite, plus twice 
 the mean longitude of the third, minus three times the mean longitude of 
 the second, was always nearly equal to 180. This is a direct conse- 
 quence of the relation between the mean longitudes to which we have 
 already referred, when speaking of the inequality in longitude of the 
 second satellite. 
 
 If the preceding relations between the mean motions and mean lon- 
 gitudes were rigorous, it would follow as a necessary consequence that the 
 three satellites could never be eclipsed at once. Now, it was found that 
 the tabular values of the elements in question very nearly satisfied this 
 condition. Thus, by employing the longitudes and mean motions of War- 
 gentin, and setting out from the epoch of his tables, it has been calcu- 
 lated that simultaneous eclipses of the three satellites cannot take place 
 before the lapse of 1,317,900 years*, and a difference of only a third of 
 1" in the annual motion of the second satellite would suffice to render 
 this phenomenon for ever impossible. 
 
 Laplace suspected that both relations were rigorous, and that the small 
 differences which appeared to exist were really attributable to errors of 
 observation. He therefore instituted a searching examination into the 
 theory of the satellites, in hopes of discovering the source of these singular 
 
 * Acta. Soc. Upsal. 1743, p. 41. 
 
92 HISTOKY OF PHYSICAL ASTEONOMY. 
 
 relations, in the mutual attraction of the bodies. In this scrutiny he 
 was not disappointed, having found their physical origin among the 
 terms involving the squares of the disturbing forces. It appeared, then, 
 from his researches, 1, that the mean motion of the first satellite, plus 
 twice the mean motion of the third, minus three times the mean motion 
 of the second, is rigorously equal to zero ; 2, that the mean longitude 
 of the first satellite, plus twice the mean longitude of the third, minus 
 three times the mean longitude of the second, is equal to 180. 
 Delambre's researches afforded a most satisfactory confirmation of these 
 results. By comparing together a vast number of eclipses, that astronomer 
 found that the relation between the mean motions differed from zero 
 by only 9". 007, and that at midnight, on January 1st, 1750, the relation 
 between the mean longitudes differed from 180 by only V 3". It is not 
 necessary to suppose that, at the origin of their movements, the satellites 
 were so disposed as to satisfy accurately the above-mentioned relations 
 between the epochs and mean motions. Laplace shewed that, provided 
 the relations were true within certain limits, the mutual attraction of the 
 satellites would subsequently render them rigorous *. In this case, the 
 mean longitude of the first satellite, plus twice the mean longitude of the 
 third, minus three times the mean longitude of the second, would oscillate 
 round 180 as a mean value. The three satellites participate in this 
 oscillation ; each satellite being affected to an extent depending on its 
 mass, and its distance from Jupiter's centre. This phenomenon, in virtue 
 of which the three bodies appear to balance each other by their move- 
 ments, has been denominated by Laplace the libration of the satellites. 
 The period of libration is the same for each satellite, and is equal to 2270 d 
 18 h or a little more than six years. Its extent, and the time when 
 it is equal to zero, are two elements which can only be determined by 
 observation. Delambre was unable to discover any traces of a Kbratory 
 motion of this kind, notwithstanding the vast number of eclipses which 
 he examined in the course of his researches for the purpose of determining 
 the elements of Laplace's theory. It is clear, then, that if such a pheno- 
 menon does actually exist, it must be altogether insignificant ; and 
 therefore we may conclude that the above relation between the mean 
 longitudes does not at any time differ sensibly from 180. 
 
 As far then as observation indicates, the above-mentioned relations are 
 rigorously true. In this case Laplace's researches tend to shew that they 
 are also in a state of stable equilibrium, any disturbing force, which does 
 not exceed a certain limit, merely occasioning oscillations of the mean 
 motions and epochs on each side of a mean state. This condition of 
 stability will for ever prevent the inequality of the second satellite from 
 being resolved into its constituent inequalities depending on the action of 
 the first and third satellites, as is evident from our explanation of the 
 
 * It has been frequently asserted in favour of the actual existence of these librations, 
 that it is extremely improbable the relations between the epochs and mean motions should 
 have been, at the origin, rigorously true. This argument might be admitted, if the 
 arrangements of the planetary system were the result of a fortuitous combination of 
 circumstances ; but since there exist so unequivocal manifestations of a Supreme Intelli- 
 gence presiding over them, it savours much less of sound philosophy than of impious 
 presumption. The mathematician, in his chamber, may modify, ad libitum, the arbitrary 
 constants of his problems so long as he confines his speculations to ideal existences ; but 
 when he proceeds to apply his principles to the material universe, he must accept the 
 constants which nature offers to him, without hazarding any opinion respecting their 
 original condition. 
 
HISTORY OF PHYSICAL ASTRONOMY. 93 
 
 circumstances which determine the complete union of those inequalities. 
 If the disturbing force should exceed the prescribed limits of stability, a li- 
 bratory motion would cease to take place, and the two inequalities of the 
 second satellite would then separate, and would henceforward continue 
 quite distinct. 
 
 The permanent character of the relations discovered by Laplace is one 
 of their most striking peculiarities. They are not altered by any secular 
 inequalities in the mean motions, for these will be so determined by the 
 mutual attraction of the satellites, that the secular inequality of the first 
 satellite, plus twice that of the third, minus three times that of the 
 second, shall be always equal to zero. They are equally independent of 
 the effects of a resisting medium, for the accelerations of the satellites, 
 while descending towards the planet, will always maintain the same 
 relation as that which connects the mean motions. Laplace shewed that 
 the libration extended to the rotatory motions of the satellites*. The 
 attraction of Jupiter, in fact, causes these movements to participate in the 
 secular inequalities of the mean motions, and consequently maintains 
 them always, so that the rotatory motion of the first satellite, plus twice 
 that of the third, minus three times that of the second, is equal to zero. 
 
 We have already mentioned it to be a necessary consequence of the 
 relations between the epochs and mean motions, that the three interior 
 satellites of Jupiter can never be eclipsed at once. In simultaneous 
 eclipses of the second and third the first is always in conjunction with 
 Jupiter ; it is always in opposition in simultaneous transits of the other two. 
 
 Although no libration is perceptible in the satellites, their stability is 
 liable to be disturbed by an extraneous cause acting unequally upon them ; 
 as, for example, by the passage of a comet in their neighbourhood. If the 
 disturbing force was small, it would merely occasion a libratory motion 
 similar to that already described ; on the other hand, if it exceeded the 
 prescribed limit of stability, it would permanently alter the mean motions 
 and mean longitudes of the satellites. In either case, then, the presence of 
 the force would be discoverable by means of its observed effects. It is re- 
 markable, however, that, although the comet of 1767 and 1779 passed 
 through the middle of Jupiter's system, no derangement was observed to 
 ensue in consequence ; and this fact affords conclusive proof that the 
 masses of comets are very small. 
 
 In 1788 and 1789 Laplace published an elaborate theory of the 
 satellites in the volumes of the Academy of Sciences for those years. 
 By means of a comprehensive analysis, which embraced all the causes 
 of perturbation, he computed the inequalities of the satellites, both 
 in longitude and latitude*; 'and obtained results which proved of in- 
 calculable service to the practical astronomer. From the perturbations 
 in longitude he derived four equations of the centre, after the example of 
 Lagrange, who had been conducted to a similar conclusion by his researches 
 in 1766. The orbit of the first satellite being, according to all appearance, 
 perfectly circular, and the orbits of the second and third being nearly so, 
 the three equations of the centre depending upon the disturbing satellites 
 are generally insensible, with the exception of the one in the third satellite 
 
 * In 1713 Maraldi I. concluded, from the periodic appearance of certain spots on the 
 fourth satellite, that it had a rotatory motion round a fixed axis, which \vas equal to its 
 motion round its primary, as in the case of the moon. This curious fact has been 
 confirmed hy the observations of succeeding astronomers, and has been found to be 
 true for all the satellites. 
 
94 HISTORY OF PHYSICAL ASTRONOMY. 
 
 depending upon the action of the fourth, the orbit of which is considerably 
 eccentric. The combination of this equation with the satellite's own equation 
 of the centre gives rise to a single equation of variable magnitude, which im- 
 parts a somewhat complicated character to the motion of the satellite, and 
 renders it difficult to trace the respective sonrces of each inequality by the 
 aid of mere observation. Laplace found from theory that the lower apsides 
 of the two satellites coincided in the year 1 682 ; and, in consequence, the two 
 equations combined together into one equation equal to their sum, and 
 amounting to 796".411 of space. In 1777 the lower apsis of the third 
 satellite had advanced 180 before that of the fourth, and the resulting equa- 
 tion was equal only to the difference of the two elementary equations. In this 
 position it therefore only amounted to 307". 651. These results are exactly 
 conformable to those which we have seen that Wargentin and other 
 astronomers had previously derived from observation. In his researches on 
 the perturbations in latitude, Laplace gave a strong proof of his sagacity by 
 taking into account the effect of the inclination of Jupiter's equator to his 
 orbit. We have already remarked that this important element of disturb- 
 ance was entirely omitted by Lagrange. 
 
 The general tendency of Jupiter's ellipticity is to draw the satellites into 
 the plane of his equator. This is clearly seen in the actual positions of 
 the orbits, which in each case deviate to a greater extent from the plane of 
 the equator, according as the satellite is more remote from its primary. 
 The inclinations of the orbits had occasioned much trouble to astronomers, 
 chiefly in consequence of the difficulty of finding a plane of reference with 
 which they might be connected by fixed relations. Laplace discovered that 
 the orbit of each satellite revolved with a constant inclination upon a fixed 
 plane contained between the planes of Jupiter's equator and orbit, and passing 
 through their common intersection. If there had been no other disturbing 
 body than the sun, the fixed plane of each satellite would have been the plane 
 of Jupiter's orbit ; also, if the protuberant matter around Jupiter's equator 
 alone disturbed the satellite, the fixed plane would have coincided with the 
 plane of his equator ; and a similar result would follow if any of the other 
 three satellites were the sole disturbing body. It is clear, then, that the 
 actual position of the fixed plane will in each case be determined by a 
 reference to the opposing tendencies of the five disturbing forces, and it 
 will manifestly hold an intermediate place between the planes of Jupiter's 
 orbit and equator, which are the two extreme planes in which these 
 disturbing forces act. This conclusion agrees with what we have mentioned 
 above, relative to Laplace's determination of these planes. The fixed 
 plane of each satellite might, therefore, be considered as the resultant 
 plane of the disturbing forces ; and the motion of the nodes upon it was 
 accordingly found by Laplace to be retrograde, conformably with the 
 general effect of a disturbing force acting continually in the plane. This 
 result offered a satisfactory explanation of the curious movements of the 
 nodes on the plane of Jupiter's orbit; phenomena which, when first recog- 
 nised by astronomers, appeared to be irreconcileable with the principles of 
 the Newtonian theory, in consequence of the plane of Jupiter's orbit 
 having been erroneously assumed to be the plane of the disturbing force. 
 
 The disturbing force which exercises most influence in determining the 
 positions of the fixed planes, is that arising from the ellipticity <of Jupiter ; 
 and this force is obviously more effective relatively to the sun's action, 
 according as the satellite is more remote from its primary. The inclina- 
 tion of Jupiter's equator to his orbit is 3 5' ; but the inclinations of the 
 
HISTOEY OF PHYSICAL ASTEONOMY. 05 
 
 fixed planes of the satellites towards Jupiter's equator, counting from the 
 first satellite, are only 1", V 3", 6' 2", 24' 33". 
 
 As the nodes of the satellites all regress upon their fixed planes, the 
 mutual positions of the orbits will be continually varying ; and this cir- 
 cumstance, by occasioning a continual alteration of the mutual action of 
 the satellites, will disturb the absolute positions of the orbits. Laplace 
 expressed -the latitude of each satellite, relative to the plane of Jupiter's 
 orbit, by means of five terms. The first of these depended on the position 
 of the fixed plane, with respect to the planet's orbit ; the second, on the 
 inclination of the satellite towards its fixed plane ; the other three were 
 determined by the positions of the nodes of the disturbing satellites on 
 their fixed planes *. 
 
 The analytical expression which Laplace obtained for the latitude 
 enabled him to explain the singular changes which astronomers had 
 remarked in the inclination of the fourth satellite. From 1680 till 1760, 
 the inclination appeared to have been stationary and equal to about 2.4 ; 
 since 1760 it had been sensibly increasing. Now, Laplace found from 
 theory, that in 1680 the inclination was equal to 2.476 ; in 1620 it 
 amounted to 2.448, and in 1760 to 2.441. It reached its minimum 
 in 1756. Since that epoch it had been constantly increasing; when 
 computed for 1800, by Laplace's formula, it is found to amount to 2.5791. 
 " It is curious," says Laplace, " to see thus emanating from analysis those 
 singular phenomena which observation has partially disclosed ; but which, 
 resulting from the combination of many simple inequalities, are too com- 
 plicated to allow the discovery of their laws by astronomers."! 
 
 Since the motion of each satellite is determined by three differential 
 equations of the second order, the motions of the four satellites will be 
 determined by twelve such differential equations. The integration of these 
 equations will, therefore, involve twenty-four arbitrary constants ; the 
 values of which must be derived from observation. Besides these twenty- 
 four constants, there are seven others which it is necessary to determine 
 before tables of the satellites can be constructed upon the basis of their 
 physical theory. These are the masses of the four satellites ; the 
 ellipticity of Jupiter ; the inclination of his equator to his orbit ; and the 
 position of the nodes of his equator. Five phenomena were selected by 
 Laplace as best adapted for assigning the masses of the satellites and the 
 ellipticity of their primary. The first of these was the inequality in 
 longitude of the first satellite, extending over the period of 437.659 d , 
 which restores the eclipses of the three interior satellites in the same 
 order. As this inequality depends on the action of the second satellite, it 
 gave him the mass of that body with great accuracy. The similar ine- 
 quality of the second satellite depends upon the combined actions of the 
 first and third satellites ; it was the second datum employed by Laplace in 
 these researches. The third datum was the motion of the nodes of the 
 same satellite ; a phenomenon which depends upon the action of the first 
 and third satellites, and upon the disturbing influence of Jupiter's ellip- 
 
 * The fixed planes of the satellites are not absolutely immoveable, since their positions 
 are determined by those of Jupiter's orbit and equator, both of which are continually 
 varying ; the former from the action of the planets upon Jupiter, the latter from the 
 action of the sun and the satellites upon the redundant matter accumulated round his 
 equator. Laplace took into account the effects of both these changes in computing the 
 latitudes of the satellites. 
 
 An interesting account of the perturbations of Jupiter's satellites will be found in Airy's 
 Treatise on Gravitation. 
 
 f Mec, Cel., tome iv., Pref. p. xiv. 
 
96 HISTORY OF PHYSICAL ASTRONOMY. 
 
 ticity. The fourth datum was the equation of the centre of the third 
 satellite, depending on the position of the perijove of the fourth. The 
 fifth was the motion of the apsides of the fourth satellite. 
 
 By comparing these data with his analytical formulae, Laplace determined 
 the masses of the satellites and the ratio between the equatorial and polar 
 axes of their primary. It appeared from his results that the third satellite 
 contained the greatest quantity of matter, and the first satellite the least *. 
 The mass of the third satellite was found to be about double the moon's 
 mass, and that of the fourth satellite was equal to it. By assuming the 
 equatorial axis of Jupiter to be equal to unity, he found that the polar axis 
 was equal to .9286. It hence followed that the lengths of the polar and 
 equatorial axes were very nearly as 13 to 14 ; a result which almost 
 coincides with that derived from micrometric measurements of the two 
 axes. Laplace, indeed, considers that in this case theory conducts to a 
 more accurate result than direct observation. It is assuredly one of the 
 greatest triumphs that the human mind can boast of, to have been enabled 
 to determine the precise shape of the planet, by merely observing the 
 eclipses of the small bodies which circulate round him. 
 
 Delambre determined the thirty-one elements of Laplace's theory by 
 comparing together a vast number of eclipses observed by astronomers at 
 different periods. Having executed this important task, he then com- 
 puted the numerical values of all the equations, and employed them in the 
 construction of ecliptic tables of the satellites. These tables were in- 
 serted in the third edition of Lalande's Astronomy, which was published 
 in the year 1792, and were found to surpass greatly in accuracy the tables 
 of Wargentin, and those of all preceding astronomers. 
 
 The eclipses of the first satellite originally led to the discovery of the 
 successive propagation of light, and this important doctrine was afterwards 
 established upon an indisputable basis by Bradley 's discovery of aberra- 
 tion. Laplace, however, conceived that the order of the inquiry might be 
 inverted, by deriving the maximum value of aberration from the velocity 
 of light, as indicated by the eclipses of the satellite. Having suggested 
 this view of the question to Delambre, that indefatigable astronomer 
 undertook the laborious task of computing the velocity of light by the 
 discussion of a great number of eclipses ; and from the result obtained by 
 him, he concluded that the maximum value of aberration is equal .to 
 20". 25. This value agrees precisely with that which Bradley derived 
 from direct observations on a great number of stars. It is interesting to 
 trace so close an agreement between two methods so widely different. This 
 coincidence shews that the motion of light is uniform within the earth's 
 orbit, for the aberration is derived, in the one case from the velocity of 
 light in the earth's orbit, and, in the other case, from the time which it 
 takes in traversing the diameter of the orbit. Its motion is also uniform 
 within the orbit of Jupiter, for the variations of the radius vector of the 
 planet are very sensible, and the differences in the times of eclipses which 
 these occasion are found to correspond exactly with the supposition of the 
 uniform motion of light. 
 
 * The following are the values of the masses of the satellites as given by Laplace in the 
 Mecanique Celeste, liv. viii. chap, viii., Jupiter's mass being supposed equal to unity. 
 
 Mass. 
 
 1st satellite 0.0000173281 
 2nd 0.0000232355 
 3rd 0.0000884972 
 4th 0.0000426591 
 
HISTORY OF PHYSICAL ASTRONOMY, 97 
 
 CHAPTER IX. 
 
 Secular Variations of the Planets Elements of the Terrestrial Orbit. Variations of the 
 Eccentricity. Motion of the Aphelion. Obliquity of the Ecliptic. Its secular Varia- 
 tion computed by Theory Euler. Lagrange. Laplace. Influence of the displace- 
 ment of the Ecliptic on the length of the tropical Year. Indirect Action of the Planets 
 on the terrestrial Spheroid. Its effect in restricting the Variations of the Obliquity of the 
 Ecliptic and the length of the tropical Year Invariable Plane of the Planetary Sys- 
 tem. Theory of Comets. Hevelius. Borelli. Dorfel. Subjection of the Motions 
 of Comets to the theory of Gravitation by Newton. Halley. Clairaut Researches 
 of Lagrange on Cometary Perturbation. Lexell's Comet. Its Perturbations investi- 
 gated by Laplace. Publication of the Mecanique Celeste. General Reflections on 
 the Progress of Physical Astronomy. 
 
 THE theory of the secular variations of the elements of the planetary 
 orbits forms one of the most interesting subjects of physical astronomy. 
 The actual existence of some of these variations was long a disputed point 
 with astronomers; but they have been established beyond all doubt in 
 recent times by the accuracy of modern observations. The secular varia- 
 tions of the terrestrial orbit have naturally excited a more lively interest 
 than the others of the same class, on account of their connexion with the 
 physical condition of the earth. The investigation relative to the eccen- 
 tricity is manifestly an object of the highest importance, since the indefinite 
 increase of that element, at however slow a rate, would ultimately occasion 
 such violent alternations of heat and cold at the earth's surface, in the course 
 of every year, as utterly to destroy the existing economy of animal and 
 vegetable life. The sublime researches of Lagrange have shewn, however, 
 that such a condition cannot possibly ensue ; for the terrestrial eccentricity 
 will always be maintained by the action of the planets within certain 
 narrow limits between which it will perpetually oscillate. At present it is 
 diminishing at the rate of 18" in a century. An immense number of ages 
 will elapse before it reach its minimum state ; but, when this takes place, 
 it will then pursue a contrary order of variation, increasing at the same 
 slow rate as that at which it had previously diminished. We have seen 
 that the variation of this element forms the medium through which the 
 action of the planets is propagated to the moon ; occasioning thereby the 
 secular inequality in the mean motion of that body, which was so long the 
 cause of embarrassment to mathematicians and astronomers, until its 
 physical origin was at length discovered by Laplace. 
 
 The motion of the earth's aphelion was first discovered by the celebrated 
 Arabian astronomer, Al Batani. As in the case of the lunar apogee, it 
 advances in the order of the signs, though at a much slower rate. Its 
 annual motion is estimated at 11" or 12". The variation of this element 
 is interesting on account of the clear evidence it affords of the disturbing 
 action of the planets on the earth ; but it obviously cannot exercise any 
 influence on the physical condition of the latter. 
 
 But the question is very different when we consider the position of the 
 earth's orbit. A variation of this kind, by altering the obliquity of the 
 ecliptic, would manifestly affect the temperature and climate of the earth 
 in an equal degree with the variation of the eccentricity. The true state 
 of the obliquity of the ecliptic was long a subject of controversy ; some 
 astronomers asserting that it was invariable, while others maintained that 
 
98 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 it was constantly diminishing. The earliest measurement of it, if we 
 exclude the records of Eastern nations, is due to Eratosthenes, who 
 flourished about the year 370 A.C. This astronomer found the angle 
 between the tropics to amount to 47 42' 27", whence the obliquity of the 
 ecliptic was equal to 23 51' 13". Al Batafii, in the ninth century, fixed it 
 at 23 35'. Waltherus, the German astronomer, made it 23 29' 47" about 
 the close of the fifteenth century ; and Tycho Brahe made it 23 29' 
 about the year 1581. Riccioli, Gassendi, and Flamstead maintained that 
 the obliquity was invariable, ascribing the discordances of astronomers 
 wholly to errors of observation. On the other hand, Bouillaud and 
 Wendelin contended that it was continually diminishing ; and this opinion 
 was urged with great ability by Louville, in the Memoirs of the Academy 
 of Sciences for 1716. About the middle of the last century, Bradley, 
 Lacaille, and Mayer found the obliquity to be 23 28' 18", and in 1800, 
 Delambre, Mechain, and Lefrancius made it 23 28'. Thus it appears 
 that, although the earlier observations are not entitled to much confidence 
 when considered by themselves, the aggregate of the results indicates 
 beyond all question a constant diminution of the obliquity. 
 
 Euler first explained the variation of the obliquity of the ecliptic by the 
 theory of gravitation. In his memoir of 1748, he showed that the action 
 of Jupiter on the earth would occasion a displacement in the plane of the 
 ecliptic ; tending to bring it nearer to the equator. He investigated the 
 same subject more completely in the Berlin Memoirs for 1754, and also in 
 his memoir on the perturbations of the Planets, which was crowned by 
 the Academy of Sciences of Paris in 1756. On the last-mentioned 
 occasion he made the secular diminution equal to 48", a quantity which 
 differs only about 2" from the most recent determinations of astronomers*. 
 
 Lagrange computed the diminution of th obliquity in the Berlin 
 Memoirs for 1782, and obtained 61".5 for the amount of the secular 
 variation. This result is universally allowed to be too great. The source 
 of Lagrange 's error doubtless lay in the erroneous value which he assumed 
 for the mass of Venus, the planet which exercises the greatest influence on 
 the position of the ecliptic. 
 
 An interesting question arises ; will the obliquity continually diminish 
 until the equator and ecliptic coincide ? If this should happen, the sun 
 will daily attain the same meridional altitude as at the equinoxes, and an 
 eternal spring will reign over the whole earth. Lagrange first shewed 
 that such a condition cannot possibly exist ; the mutual action of the 
 planets occasioning only small oscillations in the positions of their orbits. 
 The ecliptic will, therefore, continue to approach the equator until it 
 reach the limit assigned by the action of the perturbing forces, after which 
 it will gradually recede from that plane according to the same law as 
 that which determined its previous approach. The diminution of the 
 obliquity is not uniform ; but the law of variation can only be ascertained 
 by theory. The formula for computing the obliquity corresponding to any 
 assigned time may be thus expressed : 6 = 23 27' 54".8 0". 4885 66f 
 0". 000005 2 , t denoting the number of years before or after 1800. This 
 formula will be accurate enough for all the purposes of astronomy, when 
 the value of t does not exceed ten or twelve centuries ; it will even serve 
 for all the ancient observations, when we take into account the uncertainty 
 that hangs over them. In the lapse of ages the law of variation will be 
 
 * Bessel in his Tabulso Regiomontanse, 1830, makes it 45". 7. 
 
HISTORY OF PHYSICAL ASTRONOMY. 99 
 
 more completely developed ; and it will be necessary to include in the 
 formula the cubes and higher powers of t, if the same epoch should be 
 always retained. 
 
 Laplace compared the preceding formula with an ancient observation 
 recorded in the annals of the Chinese. It appears that Tcheou Kong, the 
 regent of China, measured the summer solstice about the year 1100, before 
 the Christian era, and from the result obtained by him, combined with 
 another recorded measurement of the winter solstice, astronomers have 
 deduced 23 54' 2". 5 as the obliquity of the ecliptic in his time. Now, if 
 we substitute 2900 for t in the preceding formula, applying to it the 
 negative sign, because it represents the number of years by which the 
 recorded observation has preceded the epoch of the formula, we get 23 
 51' 30" for the value of the obliquity. The near agreement of this 
 result with that derived from the Chinese records is very remarkable, 
 especially when we consider that the instrument with which Tcheou Kong 
 made his observation was a vertical gnomon only eight feet high. The 
 accordance between theory and observation is still more striking when we 
 institute a comparison between the results of the former and the accurate 
 determinations of modern astronomers. Thus Arago and Mathieu, from 
 observations on the solstices made in the years 1812, 1813, 1814, con- 
 cluded that the obliquity for the year 18 13" was 23 27' 49".28. If we 
 compute its value for the same epoch by the above formula, Ave obtain 
 23 27' 4S".69 as our result. The difference between the observed and 
 computed values is, therefore, only 0".59. 
 
 The displacement of the ecliptic, caused by the action of the planets on 
 the earth, affects the precession of the equinoxes, and the length of the 
 tropical year. This displacement is found to produce a very slow motion 
 of the equinoctial points upon the plane of the ecliptic in the direction of 
 the earth's motion. Its effect is, therefore, contrary to that produced by 
 the action of the sun and moon upon the terrestrial spheroid ; but, as it is 
 very minute compared with the latter, it merely occasions a small diminu- 
 tion of the annual quantity of precession. The mean value of precession, 
 as determined by observation for the epoch of 1800, is 50".22350. The 
 lunisolar precession computed for the same epoch by the theory of gravita- 
 tion is 50". 373 15 ; hence the effect due to the displacement of the 
 ecliptic amounts to 0". 14965. 
 
 The progression of the equinoxes, caused by the action of the planets on 
 the earth, will manifestly affect the length of the tropical year. The 
 action of the sun and moon upon the terrestrial spheroid accelerates the 
 arrival of the earth in the equinoxes, and, therefore, shortens the year; 
 the action of the planets on the other hand retards its arrival, and 
 consequently lengthens the year. The acceleration being, however, greater 
 than the retardation, the tropical year will, on the whole, be shortened by 
 the motion of the equinoctial points. If this motion was uniform, the 
 length of the tropical year would be invariable ; but such, in fact, is not 
 the case. At present it is slowly increasing, and on this account the 
 tropical year is gradually becoming shorter. The rate of diminution is 
 about half a second in a century ; and consequently the tropical year is 
 now shorter by about ten seconds than it was in the time of Hipparchus. 
 
 If the position of the equator was fixed, the variation of the obliquity 
 of the ecliptic would depend entirely on the displacement of the latter 
 plane, occasioned by the action of the planets on the earth. Laplace, 
 however, has shewn that this displacement gives rise to a corresponding 
 
 H 2 
 
100 HISTORY OF PHYSICAL ASTRONOMY. 
 
 oscillation of the equator, which considerably modifies the variation that 
 would otherwise ensue. It is clear, from our remarks on the inequality 
 of nutation in a preceding chapter, that, as the ecliptic approaches the 
 equator, the mean action of the sun upon the terrestrial spheroid will 
 continually vary. This variation of the "solar force will give rise to a 
 nutation of the earth's axis, exactly similar to that depending on the 
 variable inclination of the lunar orbit to the equator. In the present 
 instance, however, the period of the inequality will be vastly greater, in 
 consequence of the extreme slowness with which the displacement of the 
 earth's orbit proceeds. The mean disturbing action of the moon upon the 
 terrestrial spheroid will also be subject to a corresponding variation ; for 
 the lunar orbit constantly maintains the same angle with respect to the 
 plane of the ecliptic, and, therefore, participates in the displacement of 
 that plane relative to the equator. Hence will arise an oscillatory move- 
 ment of the earth's axis of the same period with that depending on the 
 action of the sun. Laplace has found that, in virtue of the combined 
 effect of these oscillations, the variation of the obliquity is reduced to about 
 one-fourth of that which would have resulted from the displacement of the 
 ecliptic alone. He has shewn, in fact, that if we only take into account 
 the last-mentioned cause of variation, the obliquity will oscillate to the 
 extent of 4 53' 33" on each side of a mean state ; whereas, on the other 
 hand, if the action of the sun and moon on the terrestrial spheroid, arising 
 from the displacement of the ecliptic, be considered, the extent of 
 oscillation will be reduced to 1 33' 45"*. 
 
 The movements of the equator and the ecliptic being periodical, the 
 phenomena which depend on their relative positions must necessarily be 
 periodical also. Hence the tropical year, although at present in a state of 
 slow diminution, will not always continue so. When the obliquity of the 
 ecliptic has reached the limit prescribed by the action of the planets on 
 the earth, it will then vary in the opposite direction, increasing according 
 to the same law as that which determined its previous diminution. 
 Laplace found that the utmost alteration in the length of the tropical year 
 would not exceed 38.8 seconds. If it were not for the modified action of 
 the sun and moon upon the terrestrial spheroid depending on the displace- 
 ment of the ecliptic, the extent of variation would be 162 seconds f. 
 
 We have already remarked that the earth's aphelion has a progressive 
 motion relative to the stars amounting to 11" or 12" annually. If we 
 consider its motion with respect to the equinoxes, we must add the value 
 of precession to the above quantity, which gives about 62" for the tropical 
 motion. Hence, in little more than twenty thousand years, the major 
 axis of the earth's orbit will have accomplished a complete revolution with 
 respect to the intersection of the equator and ecliptic. Laplace has 
 considered two remarkable epochs in connexion with this circumstance. 
 One of these is that at which the major axis of the terrestrial orbit 
 coincided with the line of the equinoxes ; the other is that at which it was 
 perpendicular to the same line. The first of these epochs, when com- 
 puted by theory, is found to correspond to the year 4107 before the 
 Christian era. This was about a century previous to the creation of man ; 
 the solar perigee then coincided with the autumnal equinox. The epoch, 
 at which the major axis of the orbit was perpendicular to the line of the 
 
 * Connaissance des Temps, 1827, p. 237. 
 f Mec. Cel., liv. xiv. chap. i. 
 
HISTORY OF PHYSICAL ASTRONOMY. 101 
 
 equinoxes, is of much more recent date. Laplace found by computation 
 that it fell in the year 1250 A.D. The solar perigee then coincided with 
 the winter solstice. He therefore proposed that the year 1250 A.D. should 
 be used as a universal epoch, and that the first day of the year should 
 begin with the passage of the sun through the vernal equinox*. 
 
 An interesting discovery to which Laplace was conducted by his re- 
 searches on the planets was the existence of an invariable plane in the 
 solar system. It is well known that astronomers generally fix the posi- 
 tion of a celestial body by determining its distances with respect to two 
 great circles of the celestial sphere at right angles to each other. If the 
 planes of these circles be immoveable, it is clear that observations, however 
 numerous or distant from each other, may be referred to them, and any 
 changes of position which may have occurred will be discovered by a com- 
 parison of the recorded distances from each circle. On the other hand, 
 if the position of the correlative planes be variable, it is equally undeni- 
 able that any conclusions drawn from such a comparison will be totally 
 vitiated, at least unless due account be taken .of the altered position of 
 the planes at the time of each observation. Now as the orbits of all the 
 planets are continually shifting their positions, in consequence of the 
 mutual attraction of the several bodies, it is impossible to use any of 
 their planes as the plane of one of the great circles of reference ; and the 
 same may be said of the plane of the equator, the position of which is 
 continually varying from the action of the sun and moon upon the terres- 
 trial spheroid. It becomes, therefore, highly desirable to discover some 
 plane, the position of which shall be independent of the mutual perturba- 
 tions of the planets, and which may, therefore, be used as a common ground 
 for comparing distant observations f. This important object was effected by 
 Laplace, who ascertained that, amid the disturbances to which the planets 
 are continually exposed by their mutual attraction, there exists an invari- 
 able plane, about which the orbits perpetually oscillate, deviating from it 
 only to a very small extent on either side. This plane passes through the 
 centre of gravity of the solar system, and it is so situated, that if all the 
 planets be projected on it, and if the mass of each planet be multiplied into 
 the area, corresponding to any given time which is described by the pro- 
 jected radius vector, the sum of such products will be a maximum. By 
 means of this property, which is independent of any particular epoch, it 
 will be easy for astronomers in future ages to determine the exact position 
 of the plane, and to compare observations together by means of it J. 
 
 This plane is not peculiar to the solar system. It exists in all those 
 systems wherein the bodies are not exposed to any other forces than those 
 arising from their mutual attraction. Its position in the solar system has 
 been calculated, by referring it to the plane of the ecliptic, corresponding 
 to the year 1750. In this manner it is found that the inclination of the 
 plane is 1 35' 31", and the longitude of the ascending node 102 57' 
 30". If a similar calculation be made for the year 1950, the inclination 
 will be 1 35' 31", and the longitude of the node 102 57' 15". The 
 agreement of these results is very surprising when we take into account the 
 uncertainty that prevails respecting the masses of several of the planets . 
 
 * Mec. Cel., liv. vi. chap. x. 
 
 f Of course the relation between the two planes determines the position of the other 
 plane. 
 
 $ Journal de 1' Ecole Polytechnique, Annce, 1798; see also Mec. Cel., liv. ii. chap.vii 
 
 Mec. Cel., liv. vi. chap. xvii. See also Pontecoulant's Theorie Analytique du 
 Systeme du Monde , liv. vi. chap. xxii. 
 
102 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 We shall now proceed to give some account of the researches of astro- 
 nomers on the motions of comets. These bodies were generally considered 
 to be meteoric substances, generated in the upper regions of the atmo- 
 sphere, until Tycho Brahe demonstrated that they were situated beyond 
 the moon's orbit. That astronomer erred, however, in supposing them to 
 revolve in circular orbits, nor did Kepler approach nearer the truth when 
 he affirmed that they moved in straight lines. Hevelius first remarked 
 that the paths of comets are curved near the perihelion, the concave side 
 being turned towards the sun*. He even threw out the suggestion that 
 the form of the curve might be a parabola ; but he did not assert that the 
 sun would occupy the focus. Borelli also about the same time hinted 
 that the orbits of comets might be either parabolic or elliptic. Dorfel, 
 a native of Upper Saxony, was the first person who proved that comets 
 move in parabolas, having the sun in the focus. This he did, in 1081, by 
 means of a careful discussion of the observations on the great comet which 
 appeared in the preceding year. It is right, however, to state that he 
 arrived at this conclusion, merely by a graphic process, and that he makes 
 no mention of any fixed law regulating the motions of comets. 
 
 Newton, having been already assured by the researches of astrono- 
 mers that comets traverse the regions of the planets, was led, by his 
 discovery of the principle of gravitation, to suppose that they move in 
 conic sections round the sun in the focus. He was of opinion that the 
 orbits are really elliptic, like those of the planets ; but he remarked that 
 on account of their great eccentricity they might be assumed, without any 
 appreciable error, to be parabolas near the perihelia. He demonstrated, 
 by a comparison of his theory with the observations of astronomers, that 
 the comet of 1680, and several other bodies of the same class, revolved in 
 orbits which were sensibly parabolic, and that the radii vectores drawn to 
 them from the sun, supposed in the focus, described in each case equal 
 areas in equal times. He also invented a method for determining the 
 elements of a comet's orbit by means of three distinct observations. This 
 method, being founded on the supposition of the body moving in a parabola, 
 did not extend to the determination of the major axis when the comet re- 
 volved in an elliptic orbit. Newton, however, remarked that this element 
 and the time of revolution might be derived from a comparison of those 
 comets which returned in the same orbits after very long periods f. 
 
 The researches of Newton were soon enriched by a brilliant corollary. 
 Halley, having collected all the recorded observations on comets which 
 could be entitled to any credit for accuracy, proceeded to calculate the 
 elements of their orbits, in hopes of thereby detecting the reappearance of 
 some of the bodies. This illustrious astronomer, having devised an arith- 
 metical calculus for Newton's method of investigation, succeeded, after in- 
 credible labour, in computing the elements of twenty-four comets. Among 
 these there were three which, on account of the close resemblance of their 
 orbits and the uniformity of their appearances, afforded strong grounds for 
 suspicion that they were the same comet. The first was observed by Ap- 
 pian in 1531; the second by Kepler in 1607; and the third by Halley 
 himself in 1682. His suspicion of their identity was further confirmed 
 by historical records of the appearance of a comet in 1305, of another in 
 1380, and of a third in 1456. In all these cases the periods seemed to 
 vary alternately from 75 to 76 years, every two successive revolutions oc- 
 
 * Cometographia, fol. Gedani. 1668. 
 f Principia, lib. iii. prop. i. 
 
HISTORY OF PHYSICAL ASTRONOMY. 103 
 
 cupying about 151 years. The only objection which offered itself to the 
 opinion of their being the same comet arose from the irregularities of the 
 periods, and the difference in the inclinations of the orbits. The interval 
 comprised between the comets o 1531 and 1607 amounted to 76 years, 
 62 days ; that comprised between the comets of 1607 and 1682 was 
 equal only to 75 years, less 42 days. The difference between the two in- 
 tervals was therefore more than fifteen months. The inclination of the 
 orbit was also found to vary nearly to the extent of a degree on the occa- 
 sion of each successive appearance of the comet. These discordances 
 would have offered an insuperable difficulty to many inquirers in attempt- 
 ing to establish the identity of the comets ; but Halley was too well ac- 
 quainted with the principles of the Newtonian theory not to perceive that 
 they might be occasioned by the disturbing action of the planets. He 
 remarked that the period of the planet Saturn sometimes varied to the 
 extent of 1 3 days from the action of Jupiter, and that, under certain cir- 
 cumstances, the alteration of the time of revolution might even amount to 
 a month. " How much more liable to derangement then," says he, " is a 
 comet whose excursion into space is four times greater than that of Saturn, 
 and whose orbit is so eccentric, that, if the velocity were increased by T -J ^th 
 part of its value, the ellipse described by the comet would be changed into 
 a parabola." 
 
 He remarked, that in the summer of 1681, when the comet was ap 
 proaching its perihelion, it passed so close to Jupiter that the force exerted 
 by that planet on it amounted to T \jth of the sun's force ; and, as it con- 
 tinued for several months exposed in this manner to the powerful in- 
 fluence of the planet, he inferred that the periodic time must have been in 
 consequence affected to a very considerable extent. The question therefore 
 which now suggested itself to him was to ascertain the precise time when 
 the comet should again return. The period of revolution, as determined 
 by the appearances of 1531 and 1607, would assign the month of November, 
 1758, for its next return; on the other hand, if the period derived from 
 the appearances of 1607 and 1682 were adopted, the^ comet ought to re- 
 turn in the month of August, 1757. No means existed in Halley 's time 
 of computing the derangement of the comet's motion caused by the pla- 
 nets ; but he very sagaciously concluded that the action of Jupiter would 
 have the effect of retarding its arrival, and that in consequence it would 
 not be visible before the end of 1758, or the beginning of 1759. " Where- 
 fore," says this illustrious astronomer, " if it should return according to our 
 prediction about the year 1758, impartial posterity will not refuse to ac 
 knowledge that this was first discovered by an Englishman."* 
 
 As the time fixed by Halley for the return of the comet drew nigh, an 
 intense interest was awakened in the minds of astronomers by the expected 
 event, but no one had the courage to calculate the precise time when the 
 comet should be visible by taking into account the perturbing action of the 
 planets. At length, in 1757, Clairaut, who had already distinguished him- 
 self by his researches in physical astronomy, undertook the examination of 
 this difficult question. By applying his solution of the problem of three 
 
 * " Quoclrca si secumlum predicta nostra redierit iterum circa annum 1758, hoc primum 
 ab homine Anglo inventum fuisse non inficiabitur aequa posteritas." Synopsis Astronomise 
 Cometicae. This important little treatise was first published in the volume of the Philo- 
 sophical Transactions for the year 1705. It was afterwards considerably enlarged by the 
 author, but it was not published in this form until 1749, when it appeared along with his 
 tables of the planets. The words above cited are not contained in the earlier edition. 
 
104 HISTORY OF PHYSICAL ASTKOXOMY. 
 
 bodies, he computed the derangements caused by the planets Jupiter and 
 Saturn throughout three successive revolutions. In the immense calcula- 
 tions to which these researches gave rise, he received efficient aid from 
 Lalande, who was then just entering upon his long career. He finally ar- 
 rived at the conclusion that the comet would be retarded 100 days by the 
 action of Saturn, and 518 days by the action of Jupiter. Hence the whole 
 period of revolution would extend to 76 years, 211 days, and as the comet 
 had passed its perihelion on the 14th of September, 1682, it ought to return 
 to it again on the 13th of April, 1759. Clairaut announced the result of 
 his labours to the Academy of Sciences on the 14th of November. 1758. 
 He took the precaution, however, of stating that the omission of many 
 small quantities, which was rendered necessary by the method of approxi- 
 mation he employed, might cause the actual time of the comet's arrival in 
 perihelion to differ as much as a month from the computed time. He also 
 added " that a body which passes into regions so remote, and which is 
 hidden from our view during such long periods, might be exposed to the 
 influences of forces totally unknown, such as the action of other comets, or 
 even of some planet too far removed from the sun to le ever perceived." 
 
 All the astronomers of Europe were now looking forward with anxious 
 expectation to an event which was destined to exercise so important an 
 influence on the fate of the Newtonian theory. At length the comet was 
 seen for the first time on the 25th of December, 1758, by George Palitsch, 
 a native of Saxony, and an amateur astronomer. It reached its perihelion 
 on the 13th of March, just one month earlier than the time fixed by Clair- 
 aut, but still within the limit assigned by that illustrious geometer. 
 
 Having revised his labours, Clairaut reduced the error in the computed 
 time of the comet to 22 days, and at a subsequent period he reduced it to 
 19 days. He would have approached still nearer the truth if he had been 
 in possession of more accurate values of the masses of Jupiter and Saturn. 
 The return of this comet so near the predicted time was one of the 
 most brilliant triumphs which the Newtonian theory had yet achieved. It 
 established beyond all doubt that comets, while mainly controlled by the 
 preponderating influence of the sun, were also liable to be deranged in 
 their motions by the other bodies of the system, and the theory of their per- 
 turbations henceforth formed a subject of deep importance to geometers. 
 Clairaut employed in his researches the method of approximation he had 
 previously devised for the lunar theory, but he introduced into it several 
 ingenious modifications, in order to adapt it to the peculiar difficulties of 
 cometary perturbation. It will readily be perceived that the same facilities 
 do not exist in this case for calculating the influence of a disturbing body 
 as when the question relates to a planet. In the latter case the eccen- 
 tricity and inclination of the disturbed body being small fractions, it is al- 
 ways possible to expand the perturbing function into a rapidly converging 
 series, arranged according to ascending powers of these quantities; but, as 
 the orbits of comets are very eccentric, and inclined at all angles to the 
 elliptic, the series into which the perturbing function is developed con- 
 verges with such slowness as to render the usual method of integration quite 
 impracticable. Little progress was made in these researches until the year 
 1780, when the Academy of Sciences of Paris having proposed to geometers 
 the theory of cometary perturbation, Lagrange composed an admirable 
 memoir on the subject, which obtained for him the prize of the Academy. 
 The method which that illustrious geometer invented for the purpose of 
 obviating the peculiar difficulties of the problem is at once ingenious and 
 
HISTORY OF PHYSICAL ASTRONOMY. 105 
 
 effective, and has formed the basis of all subsequent researches relative to 
 the same object. It is founded on the theory of the variation of 
 arbitrary constants ; but in integrating the differential expressions of the 
 comet's elements the usual mode of procedure is not adhered to. In 
 the lunar and planetary theories the integrations are so effected, that they 
 conduct to formula by means of which the place of the disturbed body may 
 be readily calculated for any assignable instant whether past or future. A 
 similar course not being practicable in the theory of comets, on account of 
 the peculiarities to which we have already referred, Lagrange proposed 
 to substitute instead of it what has been termed the method of quadratures. 
 This consists in dividing the orbit of the comet into a number of distinct 
 arcs, and then summing up tjie effect of perturbation for each arc. By this 
 process a fresh set of elements is obtained at the end of each summation, 
 and these form the basis of computation for the following arc. The appli- 
 cation of this process to the whole of the orbit would demand an enormous 
 amount of calculation, but Lagrange shewed that such a course was not ne- 
 cessary. When the comet is near the perihelion, the method of quadratures 
 is indispensable ; but, when it is traversing the superior part of its orbit, 
 the ordinary method of integration may be practised on account of the great 
 distance of the comet compared with the distance of the disturbing body. 
 
 In 1770 a comet appeared, the circumstances connected with which led to 
 very interesting results. The observations on it seemed inexplicable by 
 any parabolic orbit that could be devised, until Lexell finally shewed that 
 they might be all reconciled with the supposition of the comet revolving 
 in an ellipse in a period of nearly six years. The opinion of Lexell was 
 confirmed in the most satisfactory manner by Burchardt, who for this pur- 
 pose undertook a careful discussion of all the observations. Strange to 
 say, the comet never afterwards appeared, notwithstanding the shortness of 
 its period. In order to account for this fact, Lexell remarked that it had 
 been always invisible until the year 1770, but that in 1767 it passed so 
 near Jupiter that it was thrown by the powerful disturbance of that planet 
 into a new orbit and thereby rendered visible; and that in 1779 it again 
 passed so near the planet as to be thrown into another orbit and rendered 
 invisible. Laplace undertook an analytical investigation of this interesting 
 question, and he found that the disturbing action of Jupiter would be 
 capable of producing the singular effects ascribed to it by Lexell *. No 
 doubt, therefore, can exist on the cause either of the appearance or the 
 subsequent disappearance of the comet. 
 
 As this comet approached very near the earth, it offered a favourable 
 example for ascertaining to what extent comets in general affect the other 
 bodies of the system. The result of its action on the earth would be to 
 diminish the force of that body towards the sun, and thereby to lengthen 
 the sidereal year. No such change has been detected by astronomers, 
 whence we may conclude that the masses of comets are very small. 
 Laplace found that, if the sidereal year had increased 1 s since the year 
 1770, the mass of the comet would not have exceeded 3-0*0 o^ 1 P art f the 
 earth's mass. It is evident, however, that the mass is much less than 
 this, for, although the comet passed through the system of Jupiter's satel- 
 lites both in 1767 and in 1779, it did not produce the slightest perceptible 
 derangements in the motions of any of those bodies. 
 
 Laplace, after having investigated with the most brilliant success every 
 subject connected with the system of the world, finally conceived the design 
 * Mec. Gel. liv. ix. chap. ii. 
 
106 HISTOEY OF PHYSICAL .ASTRONOMY. 
 
 of uniting in one great work all the discoveries that had been effected in 
 Physical Astronomy. This design appears realised in the Mecanique 
 Celeste, one of the most stupendous monuments of the human intellect 
 which modern civilization can boast of. It consists of five quarto volumes, 
 which were published at different times in the course of the author's life. The 
 first and second volumes appeared in 1799 ; the third in 1803 ; the fourth 
 in .1 805 ; and the fifth in 1825. The whole work is divided into sixteen 
 books. Ten of these occupy the first four volumes ; the remaining six 
 contained in the last volume may be considered as supplementary to the 
 others. The first book of this immortal production treats of the laws of 
 equilibrium and motion ; the second, of the law of universal gravitation and 
 of the centres of gravity of bodies ; the third, of the figures of the celestial 
 bodies ; the fourth, of the oscillations of the sea and the atmosphere ; the 
 fifth, of the motions of the celestial bodies about their centres of gravity ; 
 the sixth, of the theory of the planets ; the seventh, of the lunar theory ; the 
 eighth, of the theory of the satellites of Jupiter, Saturn, and Uranus ; the 
 ninth, of the theory of comets ; the tenth, of the theory of refraction and 
 other points relative to the system of the world. In the first book of the 
 fifth volume or the eleventh of the whole work, Laplace considers the 
 figure and rotation of the earth. The twelfth book treats of the attraction 
 and repulsion of spheres and of the laws of the equilibrium and motion of 
 elastic fluids ; the thirteenth, of the oscillations of the fluids which cover 
 the surfaces of the planets ; the fourteenth, of the motions of the celestial 
 bodies about their centres of gravity ; the fifteenth, of the motions of the 
 planets and comets ; the sixteenth, of the motions of the satellites. Besides 
 the five volumes above mentioned, Laplace composed at different times 
 supplements to several of the books. 
 
 The physical theory of the planetary system is exhibited in the Mecanique 
 Celeste in a state of almost complete developernent. No material progress 
 has in consequence been effected in this branch of astronomy since the 
 publication of that immortal work. One discovery of a very remarkable 
 character has indeed been recently added to the long list of triumphs 
 which adorn its history ; but during the present century geometers have 
 been mainly occupied in correcting and extending previous results, in im- 
 proving the methods of investigation, and in illustrating the more obscure 
 points of the theory. 
 
 In reviewing the progress of Physical Astronomy since the close of 
 Newton's career, it is impossible not to be struck with the truth of the re- 
 mark, that great occasions always call forth from the bosom of society 
 suitable minds to cope with the emergencies of the times, and to triumph 
 over opposing difficulties. It has been said that Newton appeared on 
 the theatre of the world when the materials of the magnificent structure 
 erected by him had been already amassed by the persevering industry of 
 preceding ages. The true state of the planetary system had been un- 
 folded by the successive labours of Hipparchus, Copernicus, and Kepler ; 
 the laws of motion had been fully established by Galileo, and his suc- 
 cessors Huygens, Wallis, and Wren ; nay, the all-pervading principle 
 which animates and controls the bodies of the universe had been dimly 
 surmised by more than one philosopher. There was still, however, 
 wanting some master-spirit to detect the mutual dependence of these 
 disjointed principles, and by a mighty effort of generalization to reduce 
 all the phenomena of the heavens under one dominant law of nature. The 
 prospect of achieving this grand result was the alluring motive by which 
 
HISTORY OF PHYSICAL ASTRONOMY. 107 
 
 genius was invited to the study of celestial physics in the seventeenth cen- 
 tury ; and to the English philosopher was assigned the immortal honour of 
 its realisation. We may discern a similar adaptation of intellectual power 
 to existing exigencies in the period which elapsed between the publication 
 of the Principia and the appearance of the Mecanique Celeste. Newton 
 had fully established the principle of gravitation by his own unaided efforts; 
 but he bequeathed a vast heritage of profound research to his successors. 
 With a sagacity unexampled in the history of the human mind, he detected 
 the agency of this principle in all the grand phenomena of the planetary 
 system, and by the aid of a sublime geometry of his own invention he 
 succeeded in reducing to calculation a number of its most hidden results. 
 It still remained, however, for geometers to ascertain the effects of the minute 
 perturbations which ensue from the mutual action of the planets, to invent 
 formula enabling the astronomer to determine their positions throughout 
 all ages, both pastand future; and, finally, to solve the momentous question 
 whether the planets are gradually being absorbed into the sun, or whether 
 the system is so constituted that they will revolve in permanent orbits 
 round the central body. Such were the magnificent problems which New- 
 ton's discoveries suggested to his successors. We have seen what mighty 
 energies were awakened by these problems and with what brilliant success 
 their solution was effected. Perhaps no period of history can exhibit an 
 array of mathematical genius, equal to that which adorned the eighteenth 
 century. The labours of Euler, D'Alembert, Clairaut, Lagrange, and 
 Laplace will fill many a bright page in the annals of science, and their 
 names will be for ever associated with that of the illustrious founder of 
 Physical Astronomy, whose reputation they have so much enhanced by 
 their sublime discoveries. 
 
 Among the various circumstances which are calculated to excite our 
 admiration, while reviewing this portion of the history of Physical Astro- 
 nomy, not the least remarkable are the resources of the transcendental 
 analysis ; by means of which the geometer has been enabled to unravel the 
 most complicated relations of the system of the world, and to decipher in 
 the anomalous movements of the celestial bodies the constant operation of 
 one all-pervading principle. In vain would the human mind have ever 
 attempted to penetrate into the more recondite parts of the theory of 
 gravitation without the aid of this powerful instrument of research. Its 
 assiduous cultivation was, therefore, essentially necessary for the develope- 
 ment of that theory ; and, on this account, the pure analysts, such as 
 Leibnitz and the two eldest Bernoullis, deserve to be associated with 
 those who have more directly contributed to the progress of the science. 
 " The discovery of the system of the world by Newton," says Delambre, 
 " was a fortunate event for geometers. Never could the transcendental 
 analysis find a worthier or a more sublime theme. Whatever progress 
 is made in it, the original discoverer will always maintain his rank. 
 Lagrange, who often asserted Newton to be the greatest genius that 
 ever existed, used to remark also ' and the most fortunate ; we do 
 not find more than once a system of the world to establish.' It has 
 required a hundred years of labours and discoveries to construct the 
 edifice of which Newton laid the foundation ; but all is ascribed to him, 
 and he is supposed to have pursued the whole extent of the career on 
 which he entered with an eclat so well calculated to encourage his 
 successors."* 
 * Memoires de Hnstitut, 1812, p. xlv. (Notice sur la vie et les outrages de Lagrange.) 
 
108 HISTORY OF PHYSICAL ASTBOXOMI*. 
 
 An illustrious living philosopher of France*, when alluding to the 
 discovery of universal gravitation, has said, that no Frenchman can reflect 
 without an aching heart on the small participation of his own country in 
 that memorable achievement. If an Englishman could be supposed to be 
 equally sensitive, he has ample reason to iregret the inglorious part his 
 country played during the long period which marked the developement of 
 the Newtonian theory. With the exception of Maclaurin and Thomas 
 Simpson (the former of whom certainly contributed towards the solution of 
 one of the great problems of the system of the world, and the latter at least 
 gave ample proofs of his capacity for such researches), hardly any individual 
 of these islands deserves even to be mentioned in connexion with the 
 history of physical astronomy during that period. This deplorable fact 
 has been generally attributed to the pertinacity with which the English 
 mathematicians adhered to the synthetic method of investigation, the 
 resources of which had been already completely exhausted by Newton ; 
 and also to their perseverance in employing the fluxional calculus of that 
 great geometer; which, besides being less commodious in point of nota- 
 tion, did not at any time attain the high state of perfection which, at a 
 comparatively early stage of its history, distinguished the rival invention 
 of Leibnitz. The feeling of veneration which they naturally cherished 
 towards their illustrious countryman was doubtless the main cause of their 
 injudicious attachment to his peculiar methods of research ; but it was also 
 fostered in a strong degree by the unhappy quarrel which arose between 
 them and the continental mathematicians relative to the original invention 
 of the infinitesimal calculus. Were it not for the mutual estrangement 
 which then ensued between both parties, it would have been an easy task 
 to transfer the improvements of the differential calculus to the fluxional 
 calculus of Newton, which, in point of fact, was identical with it ; and by 
 this means the analysts of England might have advanced at an equal pace 
 with those on the continent. When the unpleasant feeling, just referred 
 to, finally died away, the intellectual energies of England were already 
 directed towards objects diametrically opposed to contemplative science; 
 and the few persons who still cultivated mathematics, perceiving how far 
 the analysts on the continent had advanced beyond them in the improve- 
 ments of the infinitesimal calculus, appear to have abandoned in despair all 
 intentions of original research in physical astronomy, contenting themselves 
 merely with timid dissertations on the Principia. At the beginning of 
 the present century there was hardly an individual in this country who 
 possessed an intimate acquaintance with the methods of investigation which 
 had conducted the foreign mathematicians to so many sublime results. 
 It is gratifying to reflect that a vigorous attempt has been made since that 
 time to recover for England her due position in the physico-mathematical 
 world. Notwithstanding the disadvantages under which they laboured, 
 the geometers of this country have already given ample proof that it was 
 not from any natural defect of intellectual ability that their fathers were 
 compelled so long to remain silent spectators of the triumphs of their 
 neighbours. The most recondite parts of analysis are now studied with 
 ardour and success by a number of talented persons ; and England, in 
 the present day, can boast of some of the most distinguished mathe- 
 maticians of Europe. The late Professor Woodhouse, of Cambridge, 
 deserves to be mentioned as the person who laboured most zealously in 
 
 * M. Arago. 
 
HISTORY OF PHYSICAL ASTRONOMY. 1Q9 
 
 removing from the minds of his countrymen the prejudices they had so 
 long cherished against the analytical methods that were in universal use 
 on the continent. In the sequel we shall have the pleasure of noticing 
 occasionally some of the results which may be considered as the first fruits 
 of this salutary innovation. 
 
 CHAPTER X. 
 
 Variation of the Mean Distances of the Planets Researches of Poisson The Theory 
 
 of Planetary Perturbation resumed by Lagrange and Laplace. Uniformity of the re. 
 suits arrived at by these Geometers The General Theory of the Variation of Arbi- 
 trary Constants established by Lagrange. Researches of Poisson on this subject. 
 Death of Lagrange. Researches of Modern Geometers on the Theory of Perturba- 
 tion. Method of Hansen Developement of the Perturbing Function. Burchardt 
 
 Binet New Methods devised for obtaining the coefficients of the Perturbing Func- 
 tion. Secular Inequalities of the Planets Researches of Le Verrier. Theory of 
 the Moon Irregularities of the Epoch. Equation of Long Period. Researches of 
 Damoiseau, Plana, and Carlini. Lunar Tables calculated by means of the Theory of 
 Gravitation. Researches of Lubbock and Poisson. Reduction of the Greenwich Ob- 
 servations Discovery of the True Cause of the Irregularities of the Moon's Epoch, 
 
 by Hansen. Researches for the purposes of determining the Value of the Moon's Mass. 
 
 THE first important discovery which distinguished the progress of phy- 
 sical astronomy in the nineteenth century related to the variation of the 
 mean distances of the planets from the sun. We have already given an 
 account of the researches of Lagrange on this point of the planetary 
 theory, and have mentioned the remarkable conclusion at which he arrived. 
 It appeared that the mean distance of a planet, when disturbed in its 
 elliptic orbit by the other bodies of the system, was not subject to any 
 variations which increased constantly with the time, but was merely affected 
 by a series of periodic inequalities depending on the relative places of the 
 planets in their orbits. Lagrange shewed that this theorem was true for 
 all powers of the eccentricities and inclinations ; but his investigation did 
 not extend beyond a first approximation, and, therefore, was limited to 
 terms of the first order with respect to the disturbing forces*. The inte- 
 resting question, therefore, still remained to be examined, whether a repe- 
 tition of the approximation would introduce into the expression of the 
 mean distance any terms increasing with the time, and thereby occasioning 
 a secular inequality in the mean motion. This problem was first attacked 
 by a young geometer, who was destined to pursue a brilliant career in the 
 physico-mathematical sciences. In the year 1808, Poisson, who was then 
 only twenty-five years of age, communicated a memoir to the Institute, in 
 which he investigated the variation of the mean distance, carrying the 
 approximation to the square of the perturbing forces. By means of a most 
 elaborate analysis, he succeeded in shewing that the repetition of the ap- 
 proximation would introduce into the formula for the variation of that 
 element, only a class of terms depending on sines and cosines of angles, 
 increasing proportionally with the time. It followed, then, that so far as 
 
 * Memoire sur les Inegalites Seculaires des Mot/ens Mouvemens des Planetcs. This 
 memoir was read at the Institute, in June 1808, and was subsequently published in the 
 eighth volume of the Journal de lEcole Pali/technique. 
 
110 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the mean distances were concerned, the mean motions of the planets were 
 invariable by the second as well as by the first approximation. 
 
 The interesting result to which Poisson was conducted by his i'esearches, 
 had the effect of again inducing Lagrange and Laplace to direct their at- 
 tention to the theory of planetary perturbation. Poisson, after the ex- 
 ample of these geometers, had assumed, as the basis of his investigation, 
 the elliptic equations of the undisturbed orbit, and obtained the variations 
 of the elements, by supposing the constants in these equations to be every 
 instant changing their values by infinitely small quantities. Lagrange, 
 however, was led, by reflecting on Poisson's researches, to consider the sub- 
 ject under a more general aspect. He assumed as the basis of his inves- 
 tigation the three differential equations of the planet's motion, derived 
 from the supposition that it was exposed only to the central action of the 
 sun. Each of these equations being of the second order, its complete in- 
 tegral would contain two arbitrary constants, and, therefore, the three equa- 
 tions which determine the place of the planet in its orbit would contain 
 six arbitrary constants*. When the action of the planets is taken into ac- 
 count, another quantity is introduced into the differential equations, termed 
 the perturbing function. Conceiving, then, this function to arise from a 
 continuous variation of the six constants in the primitive equations, La- 
 grange succeeded in obtaining the expressions for the variation of each 
 constant, without assuming the ellipticity of these equations. The varia- 
 tions, when investigated by this uniform process, exhibited a very remark- 
 able form, being all expressed by partial differentials of the perturbing 
 function, taken with respect to the constants, and multiplied into quan- 
 tities, which were functions only of the constants . This form presented a 
 great advantage in practice, for, as it was possible to expand the perturbing 
 function into a series of sines and cosines of angles, increasing propor- 
 tionally with the time, the secular variations of the elements were at once 
 obtained by means of the terms that were explicitly independent of the 
 time, while the remaining terms being integrated, and then substituted in 
 the formula for finding the place of a planet in an elliptic orbit, gave the 
 longitude and latitude of the planet in the disturbed orbit corresponding 
 to any assignable time. Lagrange then applied his analysis to the ques- 
 tion of the invariability of the mean distance. Poisson had not considered 
 the effect of the variations of the elements of the disturbing planets, on 
 account of the analytical difficulties offered by the perturbing function, 
 which did not preserve the same form throughout the investigation when 
 that supposition was introduced. Lagrange got rid of this inconvenience 
 by transferring the origin of co-ordinates from the centre of the sun to 
 the centre of gravity of the sun and planets. The perturbing function 
 being then symmetrical with respect to all the planets, the same analysis 
 was applicable, whatever might be the planet whose elements were sup- 
 posed to vary. Lagrange by this means succeeded in shewing that the 
 second approximation would not introduce into the expression for the 
 mean distance any term which increased constantly with the time, even 
 when the variations of the elements of the disturbing planets were in- 
 cluded in the investigation. 
 
 It is right to mention that the variations of most of the elements 
 had already appeared in the form under which Lagrange just presented 
 them. That great geometer had so expressed the variation of the mean 
 
 * Memoircs de 1'Institut, 1808. 
 
HISTORY OF PHYSICAL ASTRONOMY. Ill 
 
 distance as early as 1776, and Laplace subsequently obtained similar ex- 
 pressions relative to the eccentricity, the inclination, and the longitude 
 of the node #. The importance of Lagrange's researches on the present 
 occasion was, however, of a twofold character, for, besides exhibiting the 
 variations of all the elements under the same form, the direct analysis 
 by which he obtained his results, and the general aspect under which he 
 viewed the elements (considering them merely as the six arbitrary con- 
 stants involved in the complete integrals of the differential equations, 
 without reference to their individual functions in an elliptic orbit), seemed 
 to indicate a general theory, of which the variations of the elements of the 
 planetary orbits served only as a particular illustration. 
 
 On the very day that Lagrange communicated to Laplace the interest 
 ing result of his researches on the variations of the elements, the latter 
 exhibited to him analogous expressions, to which he had just been con- 
 ducted by an investigation of the same subject. Such was the remark- 
 able parity of inventive power which distinguished the rival efforts of 
 these illustrious geometers, and which so long held the judgment of Eu- 
 rope in suspense upon the question of their relative merits ! 
 
 Notwithstanding the identity of the results obtained by Lagrange and 
 Laplace on the present occasion, it was not difficult to discern in the re- 
 searches of each geometer the peculiar bent of his genius. Lagrange, 
 who wielded the powers of the transcendental analysis with unrivalled 
 effect, considered the subject in its most abstract form, and by this means 
 imparted a generality to his researches, which could not fail to lead to 
 important results. Laplace, always less enamoured with the beauty of 
 mathematical speculation than he was anxious to unfold the system of the 
 world, contented himself with reducing the expressions for the variations 
 of the epoch and perihelion to the same form with those relating to the 
 other elements, not considering them in connexion with any general prin- 
 ciple, but simply deriving them from established formula?. In effecting 
 this object, he was considerably aided by a relation between the two ele- 
 ments which Poisson had recently discovered. These results appeared in 
 a supplement to the third volume of the Mecanique Celeste \. Laplace ex- 
 hibited a beautiful illustration of their practical utility, by employing them 
 in the investigation of the lunar inequalities occasioned by the spheroidal 
 figure of the earth. The expressions which he obtained by this process 
 for the inequalities both in longitude and latitude coincided exactly, in 
 all respects, with those he had already arrived at by the usual method of 
 approximation. It is exceedingly interesting to trace the final agreement 
 of two methods differing so essentially in their original conception. 
 
 Soon after Lagrange and Laplace arrived at the above-mentioned results, 
 the former of these geometers communicated a memoir to the Institute, in 
 which he exhibited the application of the theory of the variation of arbi- 
 trary constants to all questions of mechanical science \. Assuming as 
 the basis of his researches the three differential equations of the second 
 order to which he had already shewn, in the Mecanique Analytique, that 
 the motion of every system of bodies might be reduced, he supposed the 
 six arbitrary constants of the complete integrals to vary from the effect of 
 a small disturbing force and to be represented in the differential equations 
 
 * Mec. Cel., Hv. ii. chap. viii. 
 
 + Laplace first announced them at the sitting of the Bureau des Longitudes, 17th of 
 August, 1808. 
 
 \ Memoires de I'lnstitut, P. 257, et seq. 
 
112 . HTSTOEY OF PHYSICAL ASTRONOMY. 
 
 by a small quantity termed the perturbing function. He tben demon- 
 strated, by a process similar to that which he employed in the less gene- 
 ral case of a planet revolving round the sun, that the expression for the 
 instantaneous variation of each constant contained only terms involving 
 partial differentials of the perturbing function relative to the constants, 
 each differential being multiplied by a function only of the constants. 
 
 In this memoir Lagrange remarked that the same principles were 
 applicable to the determination of the motions of the planets around 
 their centres of gravity, taking into account the action of the disturbing 
 planets upon the equatorial matter of the disturbed planet. Having 
 exhibited a statement of the general conditions of the problem and pointed 
 out its connexion with the theory of the variation of elements, he con- 
 cluded by announcing his intention of making it the subject of a future 
 memoir. At no subsequent period of his life did he carry into effect this 
 resolution ; but, indeed, Poisson a few months afterwards rendered such a 
 step unnecessary, by communicating to the Institute an excellent memoir 
 on the subject. Euler first gave the differential equations relative to the 
 motion of a body about its centre of gravity when it has received an initial 
 impulse and is not afterwards exposed to the action of any forces. These 
 equations being three in number, and of the second order, their complete 
 integrals will contain six arbitrary constants. Their integration would 
 therefore lead to the equations of a planet's motion about its centre of 
 gravity if it were not continually disturbed by the action of the sun and 
 the other planets of the system. By considering the latter, however, as 
 so many perturbing bodies which tend to produce a continual change in 
 the elements of rotation, the variations of these elements may be investi- 
 gated by a process similar to that employed in determining the variations 
 of the elements of the orbit. The formulae for these variations being then 
 integrated and substituted in the primitive equations depending solely on 
 the initial impulse will conduct to three complete equations, by means of 
 which the positions of the planet's axis and the velocity of rotation cor- 
 responding to any assignable time may be readily ascertained. By a 
 judicious selection of constants, Poisson obtained formulae for the variations 
 of the elements of rotation exactly analogous to those which Lagrange and 
 Laplace had already arrived at relative to the orbit of the planet. This 
 remarkable result constituted the crowning triumph of the theory of the 
 variation of elements, for by means of it the two great problems of the 
 system of the world, although differing essentially in conception, were most 
 unexpectedly exhibited in a relation of close affinity, and the geometer 
 was thus enabled to contemplate all the effects of planetary perturbation 
 through the medium of the same analysis *. 
 
 * Memoire sur la variation des constantes arbitrages dans les questions de Mecanique, 
 Journal de I' Ecole Poly technique, tome viii. p. 266, et seq. In this memoir Poisson in- 
 vestigates the expressions for the variations of the arbitrary constants in the general 
 problem of Mechanics by a more direct analysis than that which Lagrange had employed 
 in his original demonstration of the same results. It is right, however, to state that the 
 last-mentioned geometer was conducted about the same time to a similar improvement of 
 his own method, (Memoires de 1'Institut, 1809, p. 343, et seq). A complete account of 
 the theory of the variation of arbitrary constants by means of Poisson's analysis will be 
 found in Pontecoulant's Theorie Analytique du Systeme du Monde, tome i. liv. ii. 
 chap. iii. See also on this subject the seventeenth chapter of Mr. De Morgan's 
 Treatise on the Differential and Integral Calculus, Library of Useful Knowledge. 
 This chapter contains a concise, but singularly able exposition of the most comprehensive 
 theories of mechanical science. The reader is conducted by means of them to the very 
 threshold of the great problems of the system of the world. 
 
HISTORY OF PHYSICAL ASTEONOMY. 113 
 
 The complete establishment of this sublime theory was the last great 
 effort of Lagrange 's genius. We have already remarked that Euler's 
 researches contain the earliest traces of the use of the variation of 
 elements in computing the perturbations of . the planetary motions. Al- 
 though that geometer, however, has the undoubted merit of first employing 
 this fertile method of investigation, the magnificent expansion which it 
 subsequently received, and to which it owes all its practical value, is wholly 
 due to the illustrious mathematician above mentioned-:'. In Physical 
 Astronomy, it is indeed very naturally suggested by observation ; for the 
 elements of the planetary orbits had been already found by astronomers 
 to be in a state of slow variation, although their elliptic forms did not 
 appear to be undergoing any change. It is in questions of this kind, where 
 the perturbing forces are small compared with the principal forces which 
 animate the system, that the variation of elements can be most advan- 
 tageously employed. Lagrange resolved to embody his final researches on 
 this subject in a new edition of the Mecanique Analytique ; and with this 
 view he undertook a complete revisal of that immortal work ; but the 
 fatigue he incurred in consequence brought on a fever which carried him 
 off before the termination of his labours, on the 10th April, 1813. 
 
 Lagrange deserves to be ranked among the greatest mathematical 
 geniuses of ancient or modern times. In this respect he is worthy of a 
 place with Archimedes or Newton, although he was far from possessing the 
 sagacity in physical enquiries which distinguished these illustrious sages. 
 From the very outset of his career he assumed a commanding position 
 among the mathematicians of the age, and during the course of nearly half 
 a century previous to his death, he continued to divide with Laplace the 
 homage due to pre-eminence in the empire of the exact sciences. His 
 great rival survived him fourteen years, during which he reigned alone 
 as the prince of mathematicians and theoretical astronomers. 
 
 In recent times the general theory of planetary perturbation has derived 
 much improvement from the profound researches of Poisson, Plana, Ivory, 
 Lubbock, and other geometers. The most remarkable innovation is due, 
 however, to M. Hansen. That distinguished geometer conceives the 
 elliptic elements of the planet to be invariable, and assumes the time alone 
 to be subject to perturbation f. The method of investigation founded on this 
 refined notion possesses some important advantages over the ordinary 
 methods employed for the same purpose. M. Hansen has applied it with 
 success to the theory of Jupiter and Saturn, and also in researches on the 
 lunar perturbations. 
 
 The derangements in the elliptic motion of a planet, occasioned by the 
 action of another planet on it, depend upon an algebraic expression, in- 
 volving the mutual distance of the two planets, and termed the perturbing 
 
 * Euler explained the method of the variation of elements in his memoir on the 
 perturbations of the planets, which he transmitted to the Academy of Sciences in 1756; 
 but his investigation was imperfect, because he omitted to take into account the variation 
 of the epoch. The same defect characterized the researches of Lagrange, which appeared 
 in the volume of the Turin Academy for 1763. It was not until he published his famous 
 memoirs on the planetary perturbations in the volumes of .the Berlin Academy for 
 1782-3-4, that the last-mentioned geometer gave a complete theory of the subject by 
 investigating the expressions for the variations of the six elements of the undisturbed 
 orbit. 
 
 f Pontecoulant has expounded this method in the Connaissance des Temps for 1837. 
 
 I 
 
114 HISTORY OF PHYSICAL ASTRONOMY. 
 
 function. Before any progress can be made in computing these pertur- 
 bations, it is necessary that the algebraic expression on which they depend 
 should be decomposed into individual terms. -This object is generally 
 effected by expanding the function into a series of sines and cosines of 
 angles increasing proportionally with the time, and arranged according 
 to ascending powers of the eccentricities and inclinations. If no other 
 operation was necessary, and the inequalities were represented by the terms, 
 simply as they appear in the expanded function, the computation of those that 
 are of sensible magnitudes would not be very troublesome ; for, as the eccen- 
 tricities and inclinations of the planets are generally very inconsiderable, 
 at least if we except the smaller planets, the series converges with great 
 rapidity ; and for all purposes of comparison between theory and observation, 
 it would not be necessary to take into account any terms beyond those of 
 the second order with respect to these quantities. But this is by no means 
 the real state of the question. After the perturbing function has been 
 expanded in the form just mentioned, it undergoes two successive inte- 
 grations before the terms composing it can be made subservient in 
 representing the planet's inequalities in longitude. By this process 
 the circumstances of the problem are totally altered, and its difficulties 
 in a vast degree augmented, for it may happen that a term which is 
 quite insignificant in the original expansion will acquire by double 
 integration a divisor which will render it very considerable *. This 
 divisor is a multiplier of the time in the original terms of the expanded 
 function, and it is generally formed by combining together in endless ways, 
 by addition and subtraction, the mean motions of the disturbing and dis- 
 turbed planets. The geometer, therefore, cannot safely reject any terms 
 in the expanded function from a mere regard to their order in the series, 
 unless he has assured himself at the same time that they cannot be affected 
 to a sensible extent by any of the divisors depending 011 the various com- 
 binations of the mean motions. It is this circumstance which occasions 
 the necessity of calculating the terms of the third and even the fifth orders 
 in the theory of Jupiter and Saturn; and indeed a similar course is in- 
 dispensable when the question refers to any of those inequalities of long 
 duration which extend over several revolutions of the disturbing and dis- 
 
 * The expression for the longitude contains a term of the form k j j ^ in which 
 
 R denotes the perturbing function, i the epoch of the disturbed planet, and It a constant 
 quantity. Now R, when expanded, is found to contain a series of terms of the form 
 
 P cos ((in V n') t -f n / j + Q j , in which n n' denote the mean motions of the 
 
 disturbed and disturbing planets, & i the epochs, i V any integers whatever, P a function 
 of the eccentricities ?,nd inclinations of the two planets, and Q a function of the 
 
 perihelia and the nodes. Hence k f C d ^ w m contain a series of terms of the form 
 
 J t J i di 
 
 k i f \ 
 
 :r-7^ P sin f (i n i'n') t -\- n / + Q )> and it is clear that if in any case i n 
 
 (in I'n y v ) 
 
 be very nearly equal to i' n', the corresponding term of the longitude may be considerable, 
 even although P be of a high order relative to the eccentricities and inclinations. For 
 example, in the theory of Jupiter and Saturn, 5 n is very nearly equal to 2 n', and hence 
 arises the famous inequality in the longitudes of those planets which Laplace was the first 
 to trace to its true physical source. 
 
HISTOEY OF PHYSICAL ASTEONOMY. 115 
 
 turbed planets *. As the terms to be taken into account rise in degree 
 the labour of computing the coefficients increases with frightful rapidity. 
 With the view of facilitating the researches of geometers, Burchardt 
 calculated all the terms of the perturbing function to the sixth powers 
 of the eccentricities!. It still remained to execute a similar calcula- 
 tion with respect to the inclinations. This laborious task was per- 
 formed by Binet, who carried the developement to the seventh powers 
 of the eccentricities and inclinations. This has been found to be amply 
 sufficient for computing the perturbations of the older planets, but 
 it is by no means so, when the question refers to the small planets lying 
 between the orbits of Mars and Jupiter, or when the perturbations of 
 comets are considered. In both these cases the eccentricities and incli- 
 nations are so considerable that the terms of the disturbing function con- 
 verge with extreme slowness ; and on this account, it is necessary to cal- 
 culate a much greater number of them than in the theory of the older 
 planets, in order to attain an equal degree of accuracy. Geometers appear 
 to have abandoned all hopes of determining the coefficients of the higher 
 terms by the ordinary process of algebraic developement, the operation 
 rapidly assuming so complicated a form as to become totally unmanageable. 
 Other methods have accordingly been devised for effecting this object. 
 One of these is founded on the principle of mechanical quadratures J. 
 M. Hansen has determined the coefficients of the disturbing function by 
 this method in a memoir on the theory of Jupiter and Saturn which ob- 
 tained for him the prize of the Academy of Sciences of Berlin. 
 
 Another method consists in giving particular values to the disturbing 
 function, and then, by means of the equations formed between them and 
 the corresponding values of the series, eliminating as many coefficients as 
 may be deemed desirable. This method has been practised with complete 
 success by M. Le Verrier in computing the perturbations of Uranus by 
 Saturn . 
 
 * We have mentioned in the preceding note that R contains a series of terms of the 
 form Pcos ( (in tV) t + i - ' + Q Y Now the lowest terms which involve any 
 
 given values of i i' are of the order i i 1 relative to the eccentricities and inclinations. 
 The next lowest terms having the same arguments would be of the order i i' -\- 2 ; and 
 the order of the succeeding term swould increase by 2 at each step. For example, if 
 i = 5 and i f = 2, then the lowest terms of the form 
 
 P cos ( (on - 2n') t+ 5 - 2 { + 
 
 ( (on - 2n') 
 
 would be of the third order ; the next lowest of the fifth order, and so on. Hence we 
 perceive the reason why the terms upon which the long inequality of Jupiter and Saturn 
 depends, are at least of the third order. Similarly in the long inequality of the Earth 
 and Venus, which arises from the smallness of 13 n 8 n 1 , the terms are at least of the 
 fifth order. 
 
 f Memoires de I'lnstitut, 1808. 
 
 I This method, the germ of which may be traced to D'Alembert, forms the subject of 
 two papers by Poisson, which appear in the volumes of the Connaissance des Temps for 
 1825 and 1836. Pontecoulant has explained it in his TMorie Analytique du Systeme dn 
 Monde, and has also given an example of its application in computing the great inequality 
 of Jupiter and Saturn. See the work just cited, tome iii. liv. vi. chap. vi. vii. xxi. 
 
 Recherches sur le Mouvement de la Planete Herschel, Connaissance des Temps, 
 1849. Le Verrier does not give the details of his investigation of the perturbations of 
 Uranus by this method, his object being merely to shew the accordance of its results with 
 those he obtained by the ordinary method of algebraic developement. In a memoir already 
 published by him (I)eveloppeme?is sur diffcrents points de la ThCorie des Perturbations 
 
 i 2 
 
116 HISTORY OF PHYSICAL ASTKONOMY. 
 
 We have given some account in a previous chapter of the researches of 
 Lagrange and Laplace on the secular inequalities of the planetary motions, 
 and have also mentioned the results to which they were conducted 
 relative to the stability of the system of the world. Laplace de- 
 monstrated that neither the eccentricities nor the inclinations would in- 
 crease indefinitely with the time, but he did not assign any means of 
 determining the exact limits between which they would perpetually oscil- 
 late. It is conceivable, indeed, that both elements might vary to a con- 
 siderable extent, without invalidating the famous theorems of that geometer 
 relative to their limits. Le Verrier found that a small planet revolving 
 round the sun at twice the mean distance of the earth would be so 
 disturbed by Jupiter and Saturn that the inclinations of its orbit relative 
 to the orbits of those planets would attain considerable magnitudes, 
 even although they were originally very small *. Now it is remarkable 
 that the small planets discovered between the orbits of Mars and 
 Jupiter, whose inclinations we know to be greater than those of the 
 other planets, have all been found to revolve in the neighbourhood of 
 this region. Le Verrier also found a similar region between Mercury 
 and Venus, in which, if a small planet revolved, its inclinations relative 
 to the orbits of the Earth and Venus would experience considerable 
 variations from the disturbing action of those planets. 
 
 The only definite conclusion which could be drawn from Laplace's re- 
 searches, was that the expressions for the eccentricities and inclinations 
 would consist of a series of sines and cosines of angles, increasing with 
 the time, but would not contain any term involving the time, ivithout the 
 functional symbols. It still remained to compute the numerical values 
 of the constants entering into these terms, in order to ascertain the values 
 of the elements corresponding to any time, past or future, and to assign 
 the exact limits within which they would perpetually oscillate. This 
 operation, however, was one of extreme difficulty, for it involved the resolu- 
 tion of an algebraic equation, equal in degree to the number of planets 
 whose mutual action was considered, and demanded also a most laborious 
 process of elimination. Lagrange made the first successful attack on this 
 problem, by the aid of an ingenious simplification, which consisted in 
 grouping the planets into two systems, one composed of Jupiter and 
 Saturn, to which he subsequently added Uranus ; and the other composed 
 of Mercury, Verms, the Earth, and Mars, taking also into account the 
 action of the larger planets upon each of these bodies. By this process 
 he found that the eccentricities and inclinations would continually oscil- 
 late between very narrow limits, and he assigned the numerical values of 
 the limits for each planet. This investigation of Lagrange 's, although 
 valuable as a first attempt to establish an important point in the system 
 of the world, was considerably vitiated by the erroneous values he assigned 
 to the masses of the smaller planets, especially Venus, the mass of which 
 he estimated at a half more than its true value. In more recent times, 
 when the masses of the planets and the elements of their motions came 
 to be ascertained with greater accuracy, a strong desire was felt that the 
 
 des Planetes, No. 1) he explained the ingenious process by which he eliminated the co- 
 efficients of the disturbing function. A translation of this memoir is given in Taylor's 
 Scientific Memoirs, part xviii. See also on this subject a paper by Sir John Lubbock, in 
 the Philosophical Magazine for August, 1848. 
 
 * Mcmoire sur les Mouvements des Inclinaisons et des Nceuds des trois Plundtes Ju- 
 piter, Saturn et Uranus. 
 
HISTORY OF PHYSICAL ASTRONOMY. 117 
 
 question should be submitted to a fresh investigation. This task was 
 undertaken by Le Vender, who took into account the simultaneous action 
 of the seven planets *. This excellent geometer was conducted by his 
 researches to some very interesting conclusions. He found that after the 
 lapse of a few hundred years, Lagrange 's formulae for the elements would 
 become inaccurate ; but it is remarkable that the superior limits of the 
 eccentricities as assigned by that geometer did not differ materially from 
 those obtained by Le Verrier. This circumstance depends upon a 
 curious relation which Le Verrier found to connect the variation of the 
 limit, with supposed errors in the masses of the disturbing planets. He 
 discovered, in fact, that the limit would vary only to a very slight extent, 
 even although considerable errors were committed in the estimation of 
 the masses. This theorem is true with respect to all the planets,, 
 except the Earth and Venus. The coincidence in these two instances, 
 depends upon the particular value which Lagrange assigned to the mass 
 of Venus. By employing any other value of the mass, he would have 
 obtained very different values for the limits of the eccentricities of the 
 two planets f. 
 
 A remarkable period which Le Verrier has considered in connexion 
 with his researches on the secular variations, is that which would restore 
 the eccentricities and perihelia of the three superior planets, Jupiter r 
 Saturn, and Uranus, to the same mutual relations. When the slowness 
 with which these elements vary, is taken into account, one might reason- 
 ably suppose that many millions of years would elapse before such a re- 
 storation could take place. Le Verrier found, however, that a period of 
 nine hundred thousand years would suffice for this purpose, although 
 the elements of the planets will have passed through all their values only 
 a small number of times in that interval, and the elements of Uranus will 
 have completed only one cycle of their values. He considers that the 
 error of this period does not exceed four thousand years, or ^l^th of its 
 computed value. 
 
 The researches on the secular variations of the planets had hitherto 
 been confined to the first powers of the eccentricities and inclinations. 
 As these elements vary with extreme slowness, it was supposed that the 
 effects of the superior powers would be very insignificant, and that their 
 
 * Pentecoulant had calculated the expressions for the elements of the seven planets, 
 and published his researches in the third volume of his Theorie Analytique du Systime 
 du Monde, but Le Verrier, upon comparing them with his own results, found them to be 
 totally erroneous. For further particulars in connexion with this circumstance, see the 
 Comptes Rendus, tome ix. p. 550, tome x. pp. 539, 739, tome xi. pp. 872, 881 ; see 
 also the Connaissance des Temps for 1843, Additions, p. 24. 
 
 f The following are the superior limits of the eccentricities of the six older planets, as 
 assigned respectively by Lagrange and Le Verrier. 
 
 Lagrange. Le Verrier. 
 
 Mercury 0.22208 .. 0.22565 
 
 Venus 0.08271 0.08672 
 
 The Earth 0.07641 0.07775 
 
 Mars 0.14726 0.14224 
 
 Jupiter 0.06036 0.06155 
 
 Saturn 0.08408 0.08492 
 
 It would be difficult to account for the near agreement of these results, except by the 
 theorem alluded to in the text, relative to the errors in the values of the masses. Le 
 Verrier has fixed the minimum value of the Earth's eccentricity at 0.003314; whence 
 it appears that her orbit will never attain a circular form, as some persons have imagined. 
 
118 HISTOEY OF PHYSICAL ASTEONOMY. 
 
 computation would not alter any of the conclusions at which geometers 
 had arrived relative to the stability of the planetary system. Le Verrier, 
 in a second memoir on the secular variations of the planets, investigated 
 this subject by carrying the approximation to the third powers of the 
 eccentricities and inclinations *. The result, of his researches was in some 
 respects contrary to what had been anticipated. He discovered that the terms 
 of the third order produced effects which very soon became sensible, and 
 therefore could not be neglected. With respect to the stability of the 
 system, he found that when the planets Jupiter, Saturn, and Uranus 
 were considered, the introduction of the terms of the third order had the 
 effect of confirming the results of previous researches 011 the subject; but 
 when the question referred to the four smaller planets, it was impossible to 
 arrive at any definite conclusion, on account of the uncertainty that ex- 
 isted respecting the masses of those bodies. 
 
 The theory of the moon has in all ages occasioned much trouble to 
 astronomers. Some of the irregularities in the motion of that body are of 
 such magnitude as to force themselves upon the notice of the observer, 
 even in a very rude state of astronomy, and a strong desire has in conse- 
 quence been always felt to ascertain their real character. In more recent 
 times the advantage of a knowledge of the moon's motion in promoting 
 the purposes of geography and navigation, and in affording a ready means 
 of testing the theory of gravitation, has imparted an unusual degree of 
 interest to the study of her various inequalities. Towards the close of 
 the eighteenth century the most esteemed tables of the moon were those 
 of Mayer, revised in 1780 by Mason. In 1798 the French Institute, 
 desirous of obtaining corrections of the elements of her motion, proposed 
 as the subject of a prize, the determination of the mean places of the 
 apogee and ascending node of the lunar orbit, by means of at least 500 
 observations. This prize was awarded to Burg, an astronomer of Vienna, 
 who employed in his calculations as many as 3232 observations. Tables 
 were then constructed by him upon the basis of the corrected elements. 
 The arguments of the equations were derived from Laplace's theory, but 
 the coefficients were determined by observation. In one instance only 
 were so few as 668 equations of condition employed in determining the 
 value of a coefficient. Having compared his tables with the observations of 
 Bradley and Maskelyne, Burg discovered a general discordance in the 
 epochs which he was unable to account for. Similar errors presented them- 
 selves when he instituted a comparison between the computed longitudes, 
 and the observations of Lahire and Flamstead, towards the close of the 
 seventeenth century. Laplace suspected that the errors were produced 
 by some periodic inequality of long duration in the moon's mean longitude, 
 and he pointed out two equations, either of which might possibly be 
 the cause of them. One of these depended on the disturbing action of 
 the sun, and had for its argument twice the longitude of the moon's node, 
 plus the longitude of her perigee, minus three times the longitude of the 
 sun's perigee. Its period amounted to 184 years. The other equation 
 depended on the fact that the figure of the earth is not symmetrical on 
 each side of the equator. It had a period of 179 years. The equation, 
 depending on the action of the sun, being of the tenth order of magnitude, 
 
 * It is easy to see from the form of the expressions for the variations of the elements, 
 that the next step in the approximation will introduce the third powers of the eccen- 
 tricities. 
 
HISTORY OF PHYSICAL ASTRONOMY. 119 
 
 Laplace did not undertake the excessive labour of calculating its maximum 
 value. Burg, however, selected it for the purpose of representing the 
 errors of the tables, applying to it an empiric coefficient equal to 15" 
 In 1812 Burchardt obtained corrections of Burg's elements, which he em- 
 ployed in the calculation of new tables. He rejected the equation of 
 long period depending on the action of the sun, and substituted instead of 
 it, the equation which Laplace attributed to the difference between the 
 two hemispheres of the earth. This equation was not calculated any 
 more than the other ; Burchardt merely endeavoured to satisfy the ob- 
 servations by applying to it an empiric coefficient equal to 12".5. 
 
 The lunar tables were hitherto principally indebted to observation for 
 the details as well as the groundwork of their construction, since the ar- 
 guments alone of the equations were derived from theory. As this cir- 
 cumstance was considered derogatory to the dignity of Physical Astro- 
 nomy, the French Institute in 1824 proposed as the subject of a prize, 
 a theory of the moon's motion which should only exact from observation 
 the data required to determine the six fundamental elements. Two me- 
 moirs were deemed worthy of being crowned; one by Damoiseau, the 
 other by Plana and Carlini. The former of these has been published in 
 the third volume of the "Memoires des Savans Strangers;" the latter 
 has not been given to the world, but an elaborate work on the same sub- 
 ject, and avowedly executed upon the same plan, was published by Plana, 
 in 1832*. Damoiseau has used Laplace's method of investigation ; but he 
 has carried the approximation to a much greater extent than that illus- 
 trious geometer has done. His memoir has been much admired for the 
 clearness which pervades its vast expansion, and the beautiful symmetry 
 which distinguishes the arrangement of the terms. He calculated tables 
 of the moon solely by the aid of his theory, which have been regarded as 
 at least equal to any of those in previous use. The method of Plana 
 agrees essentially with that pursued by Clairaut and his successors ; but 
 he has introduced into it several ingenious modifications. The entire 
 researches of this distinguished geometer exhibit the most commanding 
 mastery of his subject. It is impossible to repress a feeling of sympathy 
 for the author, when he informs us that throughout all the immense calcu- 
 lations of this work, he had not the benefit of a single assistant f. 
 
 Damoiseau. as well as Plana and Carlini, found reason to believe that the 
 equations of long period, suggested by Laplace, did not possess sensible 
 values. Laplace, who always had strong misgivings respecting the mag- 
 nitude of these equations, concurred in this opinion, and it was now ge- 
 nerally admitted that the errors in the moon's epoch could not be ac- 
 counted for by an equation of any known form. Carlini in 1824 sug- 
 gested four equations for the purpose of reconciling the tables with ob- 
 servation. Some of these he considered to be preferable to Laplace's, but 
 he maintained that the errors were best represented by a term depending 
 on the square of the time. The admission of this explanation would have 
 been tantamount to an abandonment of the question ; but such a course 
 would have been a reproach to the advanced state of Physical Astronomy, 
 and could not on any account be sanctioned. 
 
 * Theorie du Mouvement de la Lune, 3 tomes 4to, Turin, 1832. 
 
 t " Je n'ai pu me faire aider par personne; j'ai du traverser seul, cette longue chaine 
 de calculs, et il n'est pas Dormant si par inadvertence, j'ai omis quelques termes qu'il fail- 
 lait considerer pour me conformer a la rigueur de mes propres principes." Discours 
 Preliminaire, p. xii. 
 
120 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Sir John Lubbock has investigated the lunar perturbations in some 
 valuable papers which have appeared in the volumes of the Royal Society, 
 and also in a special treatise on the subject. The most remarkable inno 
 vation which he has introduced into his researches is that of employing 
 the mean longitude of the moon as the independent variable. This is 
 the practice which had always been pursued in the planetary theory, but 
 in the lunar, it had been hitherto deemed more convenient to derive the 
 mean longitude in terms of the true, considered as the independent 
 variable, and then by the reversion of series to obtain the expression for 
 the true longitude in terms of the mean. The eminent geometer just 
 mentioned conceives, however, that the use of the mean longitude as the 
 independent variable conduces to greater simplicity in practice, even when 
 the question relates to the lunar perturbations. His example was soon 
 afterwards followed by Poisson, who introduced another important innova- 
 tion into the lunar theory, by employing in his researches the method of 
 the variation of elements *. 
 
 The only difficulty which still continued to attach to the lunar theory 
 arose from the errors in the mean longitude, which had occasioned so 
 much fruitless discussion since the commencement of the nineteenth 
 century. Although the inequality of long period, depending on the action 
 of the sun, which Laplace suggested as the probable explanation of 
 these anomalies, was generally believed to be insensible, still, as no 
 attempt had been made to calculate its real value, the question as to its 
 adequacy to account for the errors of the tables continued to be involved in 
 doubt. Poisson, having examined this point with great attention, dis- 
 covered the important fact that the disturbing action of the sun could not 
 produce an inequality in the moon's mean longitude of the form indicated 
 by Laplace. He then considered the inequality depending on the 
 difference in the compression of the two hemispheres, and he found, as 
 Laplace had already done, that it was quite insensible. Sir John Lubbock, 
 about the same time, very simply arrived at a similar conclusion by the 
 aid of his own formula}. 
 
 Doubts now began to be entertained respecting the accuracy with which 
 the observations were reduced, for the theory of gravitation was found to 
 be so satisfactory in all other respects that it seemed impossible to ques- 
 tion its adequacy to account for all the real irregularities in the motions of 
 the heavenly bodies. A step, however, was at length taken which esta- 
 blished in the clearest light the actual existence of the phenomenon, and 
 terminated in the triumphant vindication of Newton's principles. For 
 some years past all the observations on the sun, moon, and planets, which 
 have been made at Greenwich since the middle of the last century, have 
 been undergoing a course of reduction conformably to a uniform plan, 
 under the able superintendence of the present Astronomer Pioyal. In 
 the summer of ] 846, the lunar observations were so far completed as to 
 enable Mr. Airy to obtain fresh corrections for the elements, and with 
 these the epochs were calculated for different times and compared with 
 corresponding observations. This comparison had the effect of confirming 
 by the most decisive evidence the researches of Burg and other astrono- 
 mers. It appeared evident that the epoch was affected by some inequality 
 of very long period, and probably of a very complicated form. Mr. Airy, 
 aware that M. Hansen was then engaged with the lunar theory, transmitted 
 
 * Mem. Acad. des Sciences, 1835. 
 
HISTORY OF PHYSICAL ASTRONOMY. 121 
 
 to him the data he had just obtained, under the full assurance of that 
 illustrious mathematician's competency to investigate the intricacies of 
 the moon's perturbations. As Poisson and Liibbock had already shewn 
 that the errors of mean longitude could not be traced to the direct action 
 of the sun, or the disturbing influence of the earth's figure, the question 
 was narrowed to the investigation of the effects produced by tbe action of 
 the planets, which had been hitherto supposed to be almost insensible. 
 Hansen, guided by his profound knowledge of the theory of perturbation, 
 undertook a rigorous scrutiny of all the inequalities of long period which 
 appeared likely to afford an explanation of the errors of the tables. He 
 calculated many equations of this nature that were found to be insensible ; 
 but he finally discovered two depending on the action of Venus, the 
 magnitudes of which were totally unexpected. One of these arises from 
 the fact that sixteen times the mean motion of the earth, plus the mean 
 motion of the moon, minus eighteen times the mean motion of Venus, is 
 a very small quantity. Indeed, when its numerical value is computed, it 
 is found to amount only to about ^-^^ th of the moon's mean motion. 
 Now the terms of the perturbing function which have this quantity for a 
 multiplier of the time under the symbols sine or cosine, although of the 
 third order with respect to the eccentricities and inclinations, will acquire 
 by double integration its square as a divisor, and will on this account 
 form an equation of considerable magnitude in the expression for the 
 longitude. Hansen found the maximum value of this equation to amount 
 to 27".4, and its period to 273 years. The other equation depends on 
 this that the difference between thirteen times the mean motion of the 
 earth, and eight times the mean motion of Venus, is a very small fraction. 
 Its maximum value amounts to 23".2, and its period to 239 years. The 
 inequality represented by this equation is manifestly analogous to the long 
 inequality in the earth's epoch discovered by Mr. Airy. Indeed, it is not 
 difficult to see that the latter inequality will occasion a variation in the 
 mean value of the disturbing action of the sun, and will thereby give rise 
 to an inequality of a similar nature in the moon's longitude. 
 
 These two inequalities discovered by M. Hansen, when applied to the 
 moon's computed longitude, completely account for the errors in the tables, 
 which had so long perplexed the astronomers and mathematicians of 
 Europe. The lunar theory may, therefore, now be considered as divested 
 of all serious embarrassment; and in its present state it undoubtedly 
 constitutes one of the noblest monuments of intellectual research which 
 the annals of science offer to our contemplation. From the age of 
 Hipparchus down to the present day, the complicated movements of the 
 moon have formed the subject of anxious enquiry. One by one have her 
 numerous inequalities been detected, and their laws ascertained, until the 
 astronomer is finally enabled to predict her place with all the accuracy 
 called for by the most refined appliances of modern observation. Perhaps 
 no other part of astronomy exhibits so many unequivocal triumphs of the 
 theory of gravitation as the researches connected with the moon's motion. 
 The coincidence between the deductions of the geometer and the results 
 of actual observation is truly astonishing, when one considers the intricacy 
 of the subject. Newton furnished incontestable evidence of the truth of 
 his principles when he calculated the motion of the moon's nodes to within 
 3-^th part of the actual motion. In the present day, however, the theories 
 of Plana and Damoiseau assign the motions of the apsides and nodes to 
 
HISTORY OF PHYSICAL ASTRONOMY. 
 
 \vithin -jo.Vo^h P art ^ t ^ ie ^ r observed values *. Euler conceived that 
 the disturbing action of the planets would offer unsurmountable difficulties 
 towards arriving at a complete theory of the moon's motion, and he 
 asserted that this circumstance would for ever prevent astronomers from 
 reducing the error in the computed place of* that body below SO' 7 -]-. This 
 statement is well calculated to suggest the important character of the 
 results to which M. Hansen has been conducted by his researches in the 
 present instance J. 
 
 The moon's mass has been variously estimated by astronomers. Newton, 
 by a comparison of his theory of the tides with observation, concluded that 
 it amounted to iTy-Tirs"' tne ear th's mass being supposed equal to unity . 
 Laplace similarly inferred from the height of the tides at Brest that the 
 moon's mass was equal to -^.^H- This result is considerably less than 
 that assigned by Newton ; out Laplace conceives that on account of the 
 influence of local circumstances on the height of the tides at Brest, the 
 real value of the moon's mass is even still less. He, therefore, determined 
 the mass by other methods, and estimated its most probable value by 
 taking a mean of all the results. Three distinct methods offer themselves 
 for this purpose, besides that suggested by the theory of the tides. One 
 of these depends upon the fact that the force which retains the moon in 
 her orbit, as indicated by her periodic time and observed distance, is due 
 not merely to the action of the earth, but to the united actions of the 
 earth and moon. Hence, by computing the force in this manner, we 
 get the sum of the masses of the two bodies, and if the earth's mass 
 is already known, the moon's mass becomes known also. Adopting 57' 
 12".03 as the mean parallax of the moon, Laplace obtained by this 
 method T ^ t for the value of her mass. 
 
 Another method for determining the moon's mass is suggested by the 
 inequality in the sun's longitude, depending on the displacement of the 
 earth from the common centre of gravity of the earth and moon. Since 
 this is the point to which astronomers refer the computed place of the 
 earth, it is clear that the motion of that body round it will generally cause 
 the computed and observed places of the sun to differ. When the moon 
 is in syzigees the inequality vanishes ; for then the sun appears in the 
 same position, whether observed from the earth, or from the centre of 
 gravity of the earth and moon. It manifestly attains its maximum value 
 at the quadratures, where the lines drawn from the sun to the earth and 
 
 * See Poisson's Memoirs du Mouvement de la Lune autour de la Terre, Mem. Acad. 
 des Sciences, tome xiii. 1835. 
 
 *i* " Au reste je ne doute pas, qu'en corrigeant les lieux moyens de 1'apogee et du noeud 
 dans les tables ordinaires, on ne puisse par ce moyen parvenir a determiner le lieu de la 
 lune a 30" pres. Or pour un plus haut degre" de 'precision on ne saurait jamais 1'esperer 
 a cause de 1'action des autres planetes a laquelle la Lune est assujetie." Theorie de la 
 Lune, Prix de 1' Academic, tome ix. 
 
 J Since the preceding lines were written, we have ascertained that at the meeting of 
 the Astronomical Society for September 1848, Mr. Airy communicated the corrections 
 of the elements of the lunar orbit, deduced from the Greenwich observations from 1750 
 to 1830. When we consider the extent and accuracy of these observations, embracing 
 the united labours of Bradley, Maskelyne, and Pond; and the eminent talents of the 
 astronomer who has superintended their reduction and discussion, we may confidently expect 
 that the results which have been obtained by means of them, will impart greater precision 
 to the lunar tables than any others of a similar character that have yet been arrived at. 
 
 Princip. lib. iii. prop. 37, cor. 4. 
 
 || Mec. Cel. liv. vi. chap. xvi. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 123 
 
 to the centre of gravity of the earth and moon, diverge most from each 
 other. Now the amount of this divergence depends on the relative 
 distances of the earth and moon from their common centre of gravity, 
 and these again depend on the relative masses of the two bodies. Hence, 
 when the maximum value of the inequality is determined by observation 
 and the mass of the earth is at the same time known, the mass of the 
 moon becomes known also. Now Delambre inferred, from a great number 
 of observations on the sun, that the maximum value of the lunar equation 
 was 7". 5. This result gave Laplace ^ >T for the value of the moon's 
 mass. 
 
 The third method which Laplace employed for determining the moon's 
 mass is suggested by the inequality of nutation. This inequality being 
 due to the action of the moon on the terrestrial spheroid, it is clear that a 
 comparison of its observed value with the formula for it, furnished by 
 theory, will lead to a knowledge of the moon's mass. Laplace assumed 
 the maximum value of nutation to be 9". 6, as estimated by Maskelyne, 
 and hence inferred that the moon's mass was equal to -^. 
 
 Comparing together these different results he finally fixed upon ^-JU- as 
 the most probable value of the mass. 
 
 The researches of succeeding astronomers generally lead to the con- 
 clusion that the real value of the moon's mass is somewhat less than 
 the estimate of Laplace. It is fortunate that this is a point, in which 
 great precision is not called for by the existing state of science. 
 
 CHAPTER XI. 
 
 Theory of the Perturbations of the larger Planets. Theory of Mercury. Researches 
 of Le Verrier. Theory of Venus. Determination of its Mass. Theory of the 
 
 Earth Solar Tables. Delambre. Long Inequality depending on the Action of 
 
 Venus discovered by Mr. Airy. Theory of Mars. Evaluation of its Mass. Theory 
 of Jupiter. Calculation of the Terms of the Long Inequality involving the Fifth 
 Powers of the Eccentricities. Researches of Plana. Correction of the value of Ju- 
 piter's Mass. Theory of Saturn. Researches relative to the determination of its 
 Mass. Theory of Uranus. Its anomalous Irregularities. Discovery of an Exterior 
 Planet by means of them. Theory of the Smaller Planets. Hansen. Lubbock. 
 
 Theory of Comets Researches on the Motion of Encke's Comet Hypothesis of a 
 
 Resisting Medium. Perturbations of Halley's Comet calculated. Satellites of Jupiter, 
 Saturn, and Uranus. Determination of the Mass of Saturn's Ring, by Bessel. 
 Libration of the Moon. Nicollet. Theory of the Figure of the Earth. Researches 
 of Ivory on the Attraction of Elliptic Spheroids. Experiments with the Pendulum. 
 Mean Density of the Earth. Motion of the Earth about its Centre of Gravity. 
 Poisson Researches on the Tides. Oscillations of the Atmosphere. Experiments 
 of Colonel Sabine. 
 
 ALTHOUGH the methods devised by the mathematicians of the last century 
 for the purpose of computing the effects of planetary perturbation were com- 
 plete in so far as the more important bodies of the system were concerned, 
 there still remained, even in this part of the theory, various points which 
 called for further investigation. The masses of the planets in some cases 
 required to be determined upon more satisfactory principles, or by means 
 
124 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of more precise data ; while, in other cases, there appeared discordances 
 in the results ohtained by different methods, the origin of which it was 
 desirable to ascertain. Perplexing errors also began to creep into the 
 tables of several of the planets, and once more threatened to tarnish the 
 fair fame of the Newtonian theory. It isgratifying to reflect that these 
 anomalies, one by one, have yielded to the researches of the geometer, and 
 the law of gravitation still retains the character of simple grandeur by which 
 it was distinguished, when first announced by its immortal discoverer. 
 
 The planet Mercury, notwithstanding its insignificance, has in all ages 
 given more trouble to astronomers than any other of the older planets 
 of the system. This has mainly arisen from the imperfect character of 
 the observations, by means of which the elements of its motion have 
 been determined; for, previous to the invention of the telescope, it could 
 only be seen a little before or after sunset, when the vapours of the 
 horizon rendered it difficult to ascertain its precise place. It is clear, 
 also, that the magnitude of the eccentricity would tend to aggravate the 
 effect of any error in the position of the orbit. The transits of the 
 planet across the sun's disk afford a favourable means of testing the theory 
 of its motion, and serve as valuable data for the correction of the ele- 
 ments. The earliest transit which history records took place in 1 631, 
 A.D. Kepler had predicted the phenomenon by means of the Ro- 
 dolphine tables, and Gassendi had the good fortune to witness its occur- 
 rence. The accordance between theory and observation was found to be 
 pretty satisfactory, but it may be considered as the effect of a fortuitous 
 combination of circumstances, rather than the result of well established 
 principles ; for, at a subsequent period, Hevelius and his assistants were 
 compelled to remain four days at their telescopes, waiting for a similar 
 phenomenon. Halley's tables of the planets were found to give the 
 times of the transits with greater precision than those of any preceding 
 astronomer, but still the errors frequently amounted to several hours. 
 Lalande, after a long course of persevering efforts, published tables of 
 the planet, which he conceived to possess all desirable accuracy. In the year 
 1786, a transit, calculated by means of them, having been announced to take 
 place, the day appointed for the occurrence of the phenomenon was looked 
 forward to with great interest by the Parisian Savaiis. " At sunrise," says 
 Delambre, " it rained ; all the astronomers of Paris were at their tele- 
 scopes, but, fatigued with waiting, and no longer retaining any hope, they 
 quitted their places half an hour after the time announced for the planet's 
 egress from the sun's disk. I resolved to wait till the moment indi- 
 cated by Halley's tables ; but such a degree of perseverance was unne- 
 cessary, for the phenomenon took place three quarters of an hour later than 
 the time fixed for it by Lalande, and three quarters of an hour earlier than 
 that assigned by the tables of the English astronomer." Lalande was ex- 
 ceedingly annoyed by this circumstance, more especially as he had previously 
 denounced a transit recorded by Wing, merely on the ground that it did 
 not conform to his theory. Nowise daunted, however, he resumed his 
 researches on the planet, and finally calculated tables, which, if not as satis- 
 factory as could be wished, were certainly far superior in accuracy to any 
 that had hitherto appeared. The first improvement which they received 
 is due to Lindenau, who published new tables of the planet in 1813. His 
 researches were founded principally on 17 recorded transits. He con- 
 cluded from his results that the motion of the planet could not be suffi- 
 ciently accounted for, without assigning a considerable increase to the 
 
HISTORY OF PHYSICAL ASTRONOMY. 125 
 
 mass of Venus. In 3844, Le Verrier instituted a profound examination 
 into the theory of Mercury. He calculated all the terms of perturbation 
 which could sensibly affect the motion of the planet, and then employed 
 them in the formation of preliminary tables, for the purpose of obtaining 
 corrections of the elements. His researches were based on about 400 
 meridional observations of the planet, made at the Koyal Observatory of 
 Paris during the present century, and also on a considerable number of 
 transits, all of which he submitted to a careful discussion before intro- 
 ducing them into the equations of condition. Having in this manner ob- 
 tained new elements of the planet, and also a correction for the mass of 
 Venus, he constructed tables, which were found to represent the observa- 
 tions with wonderful precision. The following interesting Account of a 
 transit which had been previously calculated by means of them is given 
 by Mr. Mitchell, of the Observatory of Cincinnati, in the United States : 
 " Five minutes before the computed time of the contact, I took my 
 place at the instrument ; the beautiful machinery that carries the telescope 
 with the sun was set in motion, and the instrument directed to that part 
 of the sun's disk at which it was anticipated the contact would take place. 
 And there I sat, with feelings which no one in this audience can rea 
 lise. It w r as my first effort; all had been done by myself. After remain- 
 ing there for what seemed to be long hours, I inquired of my assistant 
 how much longer I would have to wait ; I was answered four minutes. I 
 kept my place for what seemed an age, and again inquired as before ; he 
 told me that but one minute had rolled by. It seemed as if time had folded 
 his wings, so slowly did the moments crawl on. I watched on until I 
 was told that but one minute remained, and within sixteen seconds of the 
 time I had the almost bewildering gratification of seeing the planet break 
 the contact, and slowly move on till it buried itself, round, and deep, and 
 sharp in the sun." 
 
 The foregoing account may serve to give the general reader an idea of 
 the accordance existing in the science of astronomy, between theory and 
 observation, even under circumstances of the most disadvantageous cha- 
 racter. In the present case, this accordance reflected the highest honour 
 on the accuracy of Le Verrier's researches, and augured favourably for 
 the future efforts of that illustrious geometer. 
 
 As Mercury disturbs the motions of the other planets only in a very 
 small degree, and as it is moreover unaccompanied by one or more satel- 
 lites, it has been found very difficult to ascertain the precise value of its 
 mass. In the absence of more satisfactory methods, this element has 
 been determined by assuming the densities of the planets to vary in the 
 inverse ratio of their mean distances from the sun, and then combining 
 the density of the planet found in this manner with its volume, as indi- 
 cated by its apparent diameter. By this means astronomers have ob- 
 tained T) T> oV.To (T f r tne va l ue of the mass of the planet, the sun's mass 
 being represented by unity. Encke, however, has concluded from his re- 
 searches on the perturbations of the comet which bears his name, that the 
 mass of Mercury does not exceed -^,-^^,-^f *. Le Verrier, on the other 
 hand, assigns ^,ooo l ,ooo tn as tne most probable value of the mass. Mr. 
 Ilothman, again, by comparing the theory of the planet with the ob- 
 served motion of Venus 's perihelion, estimates the mass at 3VT8?,Trr7 1 
 This result agrees very nearly with Le Verrier's, but it must be admitted 
 
 * Pro. Astr. Soc., February, 1842. f Mem. Astr. Soc., vol. xii. 
 
126 HISTOKY OF PHYSICAL ASTRONOMY. 
 
 that considerable uncertainty still rests upon this point. It is fortunate 
 that the very circumstance which renders it so difficult to ascertain the 
 mass of this planet with precision, should also in a great measure relieve 
 the astronomer from the embarrassment of an erroneous evaluation. 
 
 The perturbations of Venus, though very minute, are more considerable 
 than those of Mercury, on account of her greater proximity to the other 
 planets. The principal disturbing body is the earth, but even in this 
 case the greatest inequality in longitude does not exceed 10". Laplace 
 computed the terms of perturbation as far as the third powers of the 
 eccentricities and inclinations, but he neglected those of higher orders, 
 under the impression that they were too minute to be appreciable by 
 observation. Mr. Airy, however, has discovered among the terms of the 
 fifth order a sensible inequality, depending on the action of the Earth. 
 It takes 240 years to pass through all its values, although its greatest 
 magnitude does not exceed 2. "9. We shall presently have occasion to 
 mention the circumstance which gave rise to the detection of this interest- 
 ing inequality. 
 
 Halley's tables of Venus were those which were held in most esteem by 
 astronomers throughout the last century, until they were supplanted by 
 those of Lalande towards its close. In 1810, Lindenau published tables 
 founded on the Greenwich observations, and on those made on the 
 continent during the present centuiy. They are the tables now generally 
 used by astronomers. 
 
 The mass of Venus is an element of physical astronomy, which has oc- 
 casioned much research. As the planet is unaccompanied by a satellite, 
 its mass can only be determined by means of the perturbations it pro- 
 duces in the motions of the other bodies of the system. These, how- 
 ever, are so very small, that until recent times no dependence could be 
 placed on the results derivable from them. Lagrange, in his famous 
 researches on the planets which appeared in the Berlin Memoirs for 
 1781-82-83, determined the mass of Venus, by assuming the densities of 
 the planets to vary in the inverse ratio of their mean distances from the 
 sun. In this manner he found a value for the mass of the planet, which 
 exceeded the value of the earth's mass, nearly in the proportion of three 
 to two. This will manifestly result from his hypothesis, when we con- 
 sider that the volumes of Venus and the Earth are nearly equal, and that 
 the mean distance of the latter from the sun, exceeds that of the former 
 nearly in the proportion of three to two. That this estimate, however, 
 greatly exceeded the real value, was evident from the result which La- 
 grange arrived at, relative to the displacement of the Earth's orbit by the 
 action of the other planets. In this case, the principal disturbing bodies 
 are Jupiter and Venus, and as the mass of the former of these planets 
 was sufficiently well known, it was clear that any discordance between 
 theory and observation ought to be referred to an error in the mass of the 
 latter. Lagrange computed by theory, the displacement of the terrestrial 
 orbit, and obtained 61". 5 for the secular diminution of the obliquity of 
 the ecliptic ; but as the observations of astronomers generally gave less 
 than 50" as the real value, it hence followed that the mass of Venus was 
 too great, and that the hypothesis on which its determination was founded 
 was erroneous. Delambre, while engaged in the construction of his solar 
 tables, determined the mass of Venus by means of the periodic inequa- 
 lities which she occasions in the Earth's longitude. Clairaut had pre- 
 viously sought to determine the mass of the planet by this method, but 
 
HISTORY OF PHYSICAL ASTRONOMY. 127 
 
 he had not for his data the accurate observations of Bradley and Maske- 
 lyne, nor was the knowledge relative to the reduction of observations, and 
 the mode of combining them together, sufficiently advanced in his day. It 
 is not to be wondered at, then, that he erred in his estimation of the 
 planet's mass, nearly as much as Lagrange did by a less legitimate process, 
 having made it, in fact, equal only to two-thirds of the Earth's mass. De- 
 lambre, under superior advantages, obtained irs ^ t ^ TS for the mass of the 
 planet. By a curious coincidence this result agrees almost exactly with 
 the most approved evaluation of the Earth's mass *. Lindenau concluded, 
 from his researches on the motion of Mercury, that the mass of Venus 
 considerably exceeds the value assigned to it by Delambre. Burchardt, 
 on the other hand, by a comparison of the solar tables with Maskelyne's 
 observations, was induced to fix the mass of the planet at TTJT ij TT |. Mr. 
 Airy, by means of later observations at Greenwich, obtained -^jy^T f r 
 the mass of the planet J. M. Le Verrier was conducted to a mass equal 
 to -g-^oliyfro' by his researches on the motion of Mercury . These values 
 agree very nearly with each other, and also with the value assigned by the 
 diminution of the obliquity of the ecliptic. Mr. Rothman, however, has 
 concluded from the motion of Mercury's nodes, that the mass of Venus is 
 at least equal to -3-^,^-0^ II- The more complete developement of the se- 
 cular variations of the planetary orbits, can alone lead to desirable pre- 
 cision on this point. 
 
 A knowledge of the perturbations occasioned in the motion of the Earth 
 by the action of the other planets, forms an indispensable preliminary to 
 the construction of accurate solar tables. We have seen that Clairaut 
 first investigated these perturbations by the application of his solution of 
 the problem of three bodies. His results were introduced into Lacaille's 
 solar tables, which continued in use among astronomers until the close of 
 the last century. 
 
 One of the first steps taken by the French Board of Longitude, after 
 its establishment in 1795, was to procure the construction of new tables 
 of the sun, moon, and planets. In pursuance of this object Delambre in- 
 vestigated the elements of the solar orbit by means of the observations of 
 Bradley and Maskelyne, and calculated tables which were first published 
 in 1806. The arguments of the equations depending on perturbation were 
 derived from Laplace's theory, but the coefficients were determined by 
 observation. Delambre by this means obtained values of the masses of 
 Venus, Mars, and the Moon. In 1812, Burchardt, with the view of ob- 
 taining corrections of the solar elements, compared Delambre 's tables with 
 about 4000 Greenwich observations. He concluded from his researches 
 that the epoch, the perigee, and the eccentricity required slight correc- 
 tions. He also found that the mass of Mars should be diminished by 
 o\,th, and the mass of Venus by -JthlT. In 1827, Mr. Airy compared the 
 solar tables with 86 observations of Sir James South 's, and concluded that 
 the epoch and the perigee, especially the latter, ought to be sensibly 
 altered**. In 1828 he discussed 1200 right ascensions of the sun, ob- 
 
 * Pontecoulant, in the third volume of his Theorie Analogue du Systeme du Monde> 
 gives 337 jL 3 as the value of the earth's mass, 
 f Connaissance des Temps, 1816. 
 \ Phil. Trans., 1828. 
 Connaissance des Temps, 1847. 
 || Mem. Astr. Soc., vol. xii. 
 
 ^ Connaissance des Temps, 1816; see also Mcmoires de flnstituf, 1812. 
 ** Phil. Trans., 1827. 
 
128 HISTORY OF PHYSICAL ASTRONOMY. 
 
 served at Greenwich with the new transit instrument between the years 
 181.6 and 1826*. The corrections he obtained for the elements agreed 
 very nearly with those to which Burchardt was conducted. He also found 
 for the mass of Venus a value equal to Burchardt's, but he concluded that 
 the mass of Mars should be diminished* in the proportion of 22 to 15. 
 Delambre, in his tables, had fixed the coefficient of the lunar equation at 
 7 ".5 ; Mr. Airy, by a method of great elegance and simplicity, obtained 
 a correction which reduced it to 6".4. Having discovered a series of 
 anomalies in the mean longitude, he was led to suspect that they pro- 
 ceeded from an inequality of long duration, depending on the disturbing 
 action of some of the planets. It finally occurred to him that an in- 
 equality of this nature is occasioned by the action of Venus, and that it 
 might possibly be of such magnitude as to account for the errors of the 
 tables. Among the terms of the disturbing function there is a certain 
 class in which the time (under the symbols, sine, and cosine) is multiplied 
 by the difference between thirteen times the mean motion of the Earth, and 
 eight times the mean motion of Venus. This quantity being a very small 
 fraction, Mr. Airy perceived that the operation of two successive integrations 
 would introduce very minute divisors into the corresponding terms of the 
 longitude. The terms in other respects are very small, for their arguments 
 indicate them to be only of the fifth order, relative to the eccentricities and 
 inclinations. It became then a matter of calculation to ascertain whether 
 the increase which they acquired by double integration would so far com- 
 pensate for their extreme minuteness, as to give rise to an inequality of 
 sensible magnitude. This arduous task was performed by the eminent 
 geometer above mentioned, and the results obtained by him entirely justi- 
 fied his previous suspicion. He found that the terms represented an in- 
 equality in the Earth's longitude equal to 2 // .05 ; he also obtained a similar 
 inequality for Venus, depending upon the reciprocal action of the Earth, 
 and amounting to 2".9. The period in each case extends to 240 years. 
 These inequalities vanished in 1742, and attained their maximum values 
 in 1802. Mr. Airy remarks, that if the mean motions of the two planets 
 had been derived from a comparison of Bradley 's observations, with those 
 of recent years, the longitude of the Earth at the time of the next transit 
 of Venus in 1874 would be too small by 4", and that of Venus too great 
 by 6" ; and these errors would occasion a derangement in the geocentric 
 longitude of the latter planet, amounting to between 20" and 30" f . This 
 inequality is exactly similar to the long inequality of Jupiter and Saturn, 
 but the labour of computing it is vastly greater. We must admit that 
 its detection reflects the highest honour on the sagacity of Mr. Airy, 
 especially when we consider the very minute form under which it appeared 
 among the observations, and the slowness with which it is developed. 
 
 The comparative magnitude of this inequality shews how unsafe it is to 
 estimate the perturbations of a planet by the mere order of the terms re- 
 lative to the eccentricities and inclinations. In the theory of Venus the 
 greatest inequality among the terms of the second and third orders does 
 not amount to 1".4 ; and all the inequalities depending on the terms of 
 the fourth order fall below 0".l. In the theory of the Earth the contrast 
 is still more striking. The greatest inequality among the terms of the 
 
 * Phil. Trans., 1828. 
 f Ibid., 1832. 
 
HISTORY OP PHYSICAL ASTRONOMY. 129 
 
 second order is equal only to 1".07 ; and all those depending on the terms 
 of the third and fourth orders are less than 0".l *. 
 
 The researches of geometers on the perturbations of Mars have not led 
 to any interesting results ; they form a striking contrast in this respect 
 with those memorable researches in connexion with the same planet by 
 means of which Kepler was conducted to his great discoveries relative to 
 the fundamental laws of the motions of the planets and the forms of their 
 orbits. The perturbations produced by this planet in the motions of the 
 other bodies of the system are so small as to render the determination of 
 its mass exceedingly difficult. Laplace effected this object by the aid of 
 the hypothetic principle that the densities of the planets vary in the in- 
 verse ratio of their mean distances from the sun. In this manner he ob- 
 tained T ,-8T<5,o~8T f r tne mass f tne planet*. Delambre, by comparing 
 Laplace's formula of the Earth's perturbations with the solar observations 
 of Bradley ancl Maskelyne, was induced to fix the mass at -g- ,3rlr,T2TT t- 
 Burchardt by a similar process obtained Y/sTra^a'T f r ^ s true va l ue t- 
 The accordance between these results is sufficiently satisfactory ; but Mr. 
 Airy has inferred from his researches on the solar theory that Delambre 's 
 estimate should be diminished in the proportion of 22 to 15. It is for- 
 tunate, as in the case of Mercury, that the disturbing effects of this 
 planet are so insignificant as to dispense with the necessity of extreme 
 accuracy. 
 
 In the theory of Jupiter the most important point is the long ine- 
 quality depending on the action of Saturn. This inequality is mainly 
 contained among the terms of the third order relative to the eccen- 
 tricities and inclinations; but Laplace suspected that the terms in- 
 volving the fifth powers of the eccentricities might also be sensible. 
 Burchardt performed the laborious operation of calculating these terms, 
 but unfortunately he applied them with the wrong sign. Laplace soon 
 afterwards noticed this circumstance in a supplement to the third volume 
 of the Mecanique Celeste, and he shewed that, when it was duly taken into 
 account, the theory would present a most satisfactory accordance with a 
 conjunction of Jupiter and Saturn observed by Ibyn Jounis, at Cairo, 
 towards the close of the eleventh century. That astronomer has assigned 
 1439" as the excess of Saturn's geocentric longitude over that of Jupiter 
 on the 31st October, 1087, at 16 h mean time of Paris. Now, when the 
 places of the two planets were calculated by theory for the same epoch 
 previous to the detection of Burchardt's error, the excess of longitude was 
 found to amount only to 72 9". When the effect of that error, however, 
 was subsequently taken into account by Laplace, the same quantity rose to 
 11 17". The difference between this result of theory and the recorded 
 excess of longitude amounts to 322" or 5' 22'V a quantity which falls 
 considerably within the errors of the observations of the Arabian 
 astronomers. 
 
 * Mec. Cel., liv. vi. chap. ix. et x. ; Theorie Analytique du Systeme du Monde, liv. 
 chap. xiv. et xv. The largest inequalities in Venus and the Earth depending on the 
 terms of the third order are due to the disturbing action of Mercury. The reciprocal 
 action of these planets occasions analogous inequalities in the motion of Mercury, the 
 maximum effect of Venus amounting to 8", but that of the Earth only to 0".5. 
 
 f Mec. Cel., liv. vi. chap. vi. J Tables du Soleil, 1806. 
 
 Connaissance des Temps, 1816. Pontecoulant attributes this value to Bessel 
 (Theorie Analytique du Systeme du Monde, tome iii. p. 346); but as it is less than 
 Delambre's exactly by *th, which was the correction obtained by Burchardt, it is clear that 
 we ought to read for Bessel's name that of the last-mentioned astronomer. 
 
 K 
 
180 HISTORY OP PHYSICAL ASTRONOMY. 
 
 In 1824, Plana having raised an objection against Laplace's researches 
 on the part of the long inequality of Jupiter and Saturn depending on the 
 square of the disturbing force, a controversy arose, in which these two 
 geometers, as well as Poisson and Pontecoulant, took part, and which finally 
 terminated in establishing the point at issue in a more satisfactory state*. 
 
 The most important improvement which the theory of Jupiter has 
 received in recent times consists in a correction of the value of his mass. 
 This element may be determined by means of the perturbations which the 
 planet occasions in the motions of the other bodies of the system. It may 
 also be found by comparing the periodic time and mean distance of one of 
 the satellites round its primary with the periodic time and mean distance 
 of the- planet round the sun. This was the method which Newton em- 
 ployed in the Principia. Having assumed that the period of the fourth 
 satellite amounted to 16 d .6888, and its greatest heliocentric elongation 
 to 8' 15".85, he hence concluded that the mass of the planet was equal to 
 ToV"7> ^ ne sun's mass being represented by unityf. This value was found 
 by Laplace to agree very nearly with that derived from the perturbations 
 of Saturn, and was introduced by him into the calculations of the Mecanique 
 Celeste. Astronomers, however, subsequently discovered that it was irre- 
 concileable with the perturbations occasioned by the planets in the motions 
 of the other bodies of the system. In 1836 Nicolai concluded from the 
 perturbations of Juno that the mass of Jupiter was equal to TO-^-.TJYT- 
 About the same time Encke obtained -pyVo f r the value of the mass by 
 means of the perturbations of Vesta ; while his researches on the motion of 
 the comet which bears his name assigned -^4- as the true value. These 
 results, agreeing all so nearly with each other, derived additional confirm- 
 ation from the researches of Gauss on the perturbations of Pallas. It 
 now became exceedingly desirable to verify the original determination of 
 the planet's mass which presented so considerable a discordance with these 
 results. The observations on the fourth satellite which formed the data of 
 Newton's investigation were made by his contemporary, Pond ; but these 
 could hardly be expected to possess the accuracy attainable by astronomers 
 in the present day. Mr. Airy, suspecting that the discordance might be 
 traced to an error in Pond's observations, undertook a series of measure- 
 ments of the elongations of the fourth satellite, and arrived at a result 
 which accorded very satisfactorily with that derived from the perturbations 
 of the smaller planets. The mean distance of the satellite from its 
 primary as indicated by these elongations assigned -r^V^TT as ^ ne mass f 
 the planet. Mr. Airy subsequently undertook a more extensive course of 
 observations on the satellites, and derived from them a similar result. 
 Bessel also about the same time measured the elongations of the satel- 
 lites, and obtained -IO^T.-STT ^ or tne mass f tne planet, a result differing 
 only about a thousandth part from Mr. Airy's. Thus a serious source of 
 perplexity has been in a great measure removed from Physical Astronomy 
 by these researches, for the mass of Jupiter is so considerable that a small 
 error in its value might occasion a very sensible discordance between the 
 observed and calculated perturbations of some of the planets. The only 
 difficulty which still remains in connexion with this question arises from 
 the anomalous result derived from the perturbations of Saturn, Bouvard 
 having by this means obtained T ^ TT j- for the value of the mass. It is to 
 
 * Mem. Astr. Soc., vol. ii. In the same paper Plana points out several other in- 
 accuracies into which Laplace had fallen in the Mecanique Celeste. 
 f Princip., liv. iii, prop. viii. cor. i. 
 
HISTORY, OF PHYSICAL ASTRONOMY, 181 
 
 be Loped that the planet Neptune will be found to derange the motion of 
 Saturn to such an extent as to account for the errors of perturbation 
 which arise from the assumption of the more probable value of Jupiter's 
 mass. 
 
 The theory of Saturn is so closely linked with that of Jupiter, that any 
 remarks relative to the perturbations of one of the planets are generally 
 applicable to those of the other. The masses of the two planets have also been 
 determined by similar methods. Newton obtained ^VT f r tne mass of 
 Saturn, by assuming that the period of the sixth satellite amounted to 
 15 d .9453, and its greatest elongation to 3'. 4"*. The latter quantity, 
 however, considerably exceeds the real value, and therefore the results 
 derived from it were erroneous. Laplace supposed the elongation to be 
 equal only to 2' 59", and hence inferred that the mass of the planet is 
 equal to ^nrrgt- Bouvard obtained -^-f-j-g f r the value of the mass by 
 means of the perturbations of Jupiter. This result is confirmed by the 
 researches of Bessel, who has been conducted to a mass equal to 
 by a careful measurement of the elongations of the sixth satellite. 
 
 In 1808, Bouvard published tables of Jupiter and Saturn, but they were 
 soon found to be vitiated by the errors in the theory of both planets, to 
 which allusion has already been made. This defect was remedied by the 
 astronomer just cited, who in 1821 published tables of the planets 
 adapted to the corrected theory. Mr. Adams has recently discovered an 
 important error in the tables of Saturn. While engaged in researches 
 on the motion of that planet, he found that the calculated values of one of 
 the terms of the perturbation in latitude were totally irreconcileable with 
 the formula from which they were professedly derived. He has explained 
 the probable origin of this discordance, which is somewhat curious J. 
 
 Until very recently the theory of Uranus has occasioned much trouble 
 to astronomers. Tables of the planet were published by Delambre in 
 1790, and by Bouvard in 1821 ; but, notwithstanding the care and 
 skill which had been employed in their construction on each of these 
 occasions, it was found that they failed to represent the actual motion. 
 Irregularities were indicated by the observations, which could not be 
 accounted for either by the principles of elliptic motion, or by the disturb- 
 ing action of the other bodies of the system. Without pursuing this 
 interesting subject further at present, we shall merely state that these 
 anomalous errors in the motion of Uranus have led to the discovery a priori 
 of a new planet exterior to it. In the ensuing chapter we shall give a 
 detailed account of the circumstances connected with this remarkable 
 result of the theory of gravitation. 
 
 Astronomers have not yet arrived at a sufficiently satisfactory result 
 relative to the mass of Uranus. Sir William Herschel having announced 
 that the fourth satellite revolved round the planet in 13 d .4559, and that 
 its greatest heliocentric elongation was equal to 44".23, Laplace hence 
 concluded that the mass of the planet was equal to T^OT!!- Bouvard, on 
 
 * Princip., liv. iii. prop. viii. cor. i. f Mec. Cel., liv. vi. chap. vi. 
 
 $ The principal terms of the perturbation in latitude are 
 
 9'/.67 sin. (p_2 <p'-60.29) + 28".i9 sin. (2 0-4<p' + 66. 12) 
 
 where <p <f>' denote the mean anomalies of Saturn and Jupiter. In tabulating the last term, 
 Bouvard appears to have employed <p- 2 <p' instead of 2 <p 4 <p', so that the two terms 
 may be united in a single term, represented by 25".85 sin (<p 2 <p' + 43 :> .88). The 
 calculated values of this term were found by Mr. Adams to agree very closely with the table. 
 Phil. Trans., 1788. II Mec. Cel., liv. vi. chap. vi. 
 
 K 2 
 
13 HISTOKY OF PHYSICAL ASTKONOMY. 
 
 the other hand, has obtained jpfirff for the value of the mass by means of 
 the perturbations produced by the planet in the motion of Saturn. It is 
 to be hoped that the researches on the satellites, in which M. Otto Struve 
 is known to be engaged at present, will lead to more satisfactory results 
 relative to this important point *. 
 
 The theory of the smaller planets still continues in a very imperfect 
 state. This circumstance is attributable to the magnitude of the eccen- 
 tricities and inclinations, in consequence of which the disturbing function 
 converges with such slowness as to render the usual methods of approxima- 
 tion generally inapplicable. The only one of the ancient planets which 
 bears any analogy in this respect to those more recently discovered is 
 Mercury; but in this case the disturbed body is so near the sun, and at 
 the same time so remote from the larger planets of the system, that its 
 perturbations are very insignificant, and a small number of the terms of 
 the disturbing function suffice for the calculation of all the inequalities 
 that are of sensible magnitude. The smaller planets, on the other hand, 
 all revolve in the region comprised between the orbits of Mars and Jupiter, 
 and on this account their elliptic motions are very much deranged by 
 the powerful action of the latter planet. Attempts have frequently been 
 made to investigate the perturbations of these bodies by the usual methods 
 of approximation, but their places when thus determined have been found 
 very soon to present a marked discordance with those indicated by actual 
 observation. The perturbations of Vesta, Juno, and Ceres, have been com- 
 puted with more or less success by Daussy, Santini, Damoiseau, and other 
 geometers ; but those of Pallas, which revolves in an orbit, inclined at an 
 angle of 34 to the ecliptic, have deterred even the most persevering analysts 
 from undertaking their complete investigation. In recent times, attention 
 has been principally directed towards the algebraic form of the disturbing 
 function, with the view of devising modes of development, which shall be 
 practicable whatever be the magnitude of the eccentricities and inclina- 
 tions. The researches of Cauchy, Liouville, Le Verrier, Hansen, and 
 Lubbock, in connexion with this subject, have resulted in various ingenious 
 processes by means of which it is to be hoped that this part of the planetary 
 theory will soon attain a degree of perfection, equal to that which is so 
 conspicuous, when the question relates to the perturbations of the larger 
 bodies of the system. Le Verrier has applied his method to the com- 
 putation of a remarkable inequality in the mean motion of Pallas, occa- 
 sioned by the disturbing action of Jupiter. This inequality depends upon 
 the near commensurability of the mean motions of Jupiter and Pallas. 
 Eighteen times the mean motion of Jupiter, minus seven times the mean 
 motion of Pallas, forms a quantity which amounts to only T ^oth of the 
 mean motion of the latter planet. Now, as this quantity appears in the 
 disturbing function under the symbols sine and cosine, the operation of 
 two successive integrations will introduce its square into the denominators 
 of the corresponding terms of the longitude. This circumstance may cause 
 the term sto acquire a sensible magnitude, although in other respects 
 they are very inconsiderable, being, according to the theory of planetary 
 perturbation, only of the eleventh order with respect to the eccentricities 
 and inclinations. Le Verrier shewed it to be one of the advantages of his 
 method, that the great inclination of the disturbed planet, so far from 
 
 * Dr. Lament, of Munich, by observing the elongations of the satellites, has obtained a 
 value for the mass of the planet considerably less than either of those mentioned in the 
 text. See Mem. Ast. Soc., vol. xi. 
 
HISTOBY OF PHYSICAL ASTRONOMY. 133 
 
 forming a barrier to his researches, on the contrary, conduced to their 
 simplification. He found the greatest value of the inequality to amount 
 to 896", or 14' 56," and its period to upwards of 675 years. This in- 
 equality is manifestly similar to several others of long duration, to which 
 we have already had occasion to allude, but it differs from them in so far as 
 the particulars relative to it are not susceptible of being tested by observa- 
 tion, on account of the short time that has elapsed since the discovery of 
 the planet. As it was desirable to verify the calculations of Le Verrier, 
 M. Cauchy determined the value of the inequality by a method of his own, 
 and obtained a result which completely accorded with that of the original 
 discoverer. 
 
 The researches on the perturbations of the smaller planets gave rise to 
 an interesting discusssion among astronomers respecting the essential 
 nature of the principle of gravitation. In 1826, Nicolai having com- 
 pared the analytical expressions for the perturbations of Juno by Jupiter, 
 with fifteen observed oppositions of the planet, met with such discordances 
 as induced him to suppose that the absolute attraction of Jupiter on the 
 sun and on the planet were unequal, or, in other words, that the total 
 amount of attraction exerted by one body upon another depended on the 
 quality of the matter contained in the attracted body, as well as upon its 
 quantity. This doctrine, being at variance with the fundamental principle 
 of gravitation, attracted a considerable degree of attention on the occasion 
 of its first announcement ; but the subsequent researches of astronomers 
 have served to shew that it is untenable. Bessel, for this purpose, made a 
 great number of experiments with pendulums, composed of different sub- 
 stances, such as ivory, glass, marble, meteoric stones, &c. ; but he was 
 unable to discover in the times of oscillation any indication that the in- 
 tensity of the terrestrial attraction depended 011 the quality of the 
 pendulous body. 
 
 The theory of Comets depends on the solution of two problems of capital 
 importance. The one relates to the investigation of the species of conic 
 section, in which the comet moves, and the determination of the elements 
 of the orbit ; the other relates to the calculation of the effects produced by 
 the disturbing action of the planets. Both of these problems have largely 
 occupied the attention of geometers, from the establishment of the theory 
 of gravitation by Newton, down to the present day. The first solution of 
 the problem for determining the orbit of a comet, by means of observa- 
 tions on its motion, was given by Newton in the Principia. It was 
 founded on the supposition, that the species of conic section, described by 
 the comet, is a parabola. This assumption conduced much to the simplifi- 
 cation of the problem, nor did it entail any sensible error on the ultimate 
 results, when the eccentricity of the orbit is very great. On the other 
 hand, the solution was defective, inasmuch as it assigned no means of 
 ascertaining the value of the mean distance in the case of the orbit being 
 really elliptic. This element could only be determined by means of the 
 relation between it and the periodic time, the latter being deduced from 
 the interval comprised between two successive appearances of the comet. 
 Various solutions of the same problems have been given by geometers 
 since Newton's time, some of which are independent of any assumption 
 with respect to the form of the orbit. The most celebrated of the latter 
 class are those of Laplace and Gauss. 
 
 The researches on the perturbations of comets offer difficulties pre- 
 cisely analogous to those which occur in the theory of the smaller planets. 
 
134 HISTORY OF PHYSICAL ASTEONOMY. 
 
 As the usual solutions of the Problem of Three Bodies completely fail in 
 this case, the effects of planetary disturbance are computed by the method 
 of mechanical quadratures. We have already mentioned that Lagrange 
 first presented this method in a systematic form. In 1810, Bessel 
 published his famous researches on the 'comet of 1807. He. concluded, 
 from the observations, that the comet moved in an ellipse of great 
 eccentricity. In computing the action .of the planets on it, he resolved 
 the disturbing force in the directions of the radius vector, of a perpen- 
 dicular to it, and a perpendicular to the plane of the orbit. He then 
 determined, by the method of quadratures, the values of the elements 
 for every thirty days during which the comet was within the sphere of 
 planetary influence. He assigns 1543 years as the most probable value 
 of the periodic time. A comet which appeared in 1815 was found by 
 Olbers to revolve in an elliptic orbit with a period of about 72 years. 
 The perturbations were computed by Bessel, whose researches on the 
 subject appeared in the Berlin Memoirs for 1813*. Fresh elements 
 were computed for every 25 days during which the comet was visible ; 
 for every year from 1815 to 1833, and for every two years throughout the 
 remaining part of the orbit. He has fixed the 9th February, 1887, as 
 the time of the next return to perihelion. In 1818, a comet was dis- 
 covered by Pons, the observed motion of which could not be reconciled 
 with the supposition of a parabolic orbit. M. Arago remarked that 
 its elements bore a strong resemblance to those of a comet which 
 appeared in 1805, and Olbers about the same time was led in a similar 
 manner to suspect its identity with a comet which appeared in 1795. 
 Encke found that the observations might all be satisfied by supposing 
 the comet to move in an elliptic orbit, with a period of about three years 
 and a half. He also computed the perturbations, taking into account the 
 action of all the planets, with the exception of Uranus and the small 
 bodies revolving between the orbits of Mars and Jupiter. The perturba- 
 tions of Mercury were computed for every 4 days ; those of Venus and 
 the Earth for every 12 days; and those of Mars, Jupiter, and Saturn for 
 every 36 days. This process was continued until the action of the 
 planets ceased to be sensible, after which the motion of the comet was 
 referred to the centre of gravity of the sun and planetsf. The comet, on 
 the occasion of its perihelion passage in 1822, was not favourable for 
 observation in the northern hemisphere, but it was seen by Rumker at 
 Paramatta in New South Wales. A comparison of the earlier with the 
 more recent observations seemed to indicate that the period of revolution 
 was continually diminishing, and Encke was hence led to suspect the 
 existence of a resisting medium. The perihelion passage of 1825 was 
 not favourable for deciding so delicate a question, but that of 1829 offered 
 peculiar advantages for this purpose. In order to understand this, it is 
 necessary to remark that the axis of the comet lies almost in the 
 plane of Jupiter's motion, and that the aphelion extends very nearly 
 to the orbit of that planet. Hence it is clear that, when Jupiter is in that 
 part of his orbit which is in the neighbourhood of the comet's aphelion, 
 he will very much disturb the motion of the latter; and, if an erroneous 
 value be assumed for his mass, the difference between the computed and 
 observed places of the comet may be very considerable, even inde- 
 
 * Airy's account of the progress of Astronomy, British Association Report for 1832. 
 f Ibid. 
 
HISTORY OF PHYSICAL ASTRONOMY. 136 
 
 pendently of the effects which might be produced by a resisting medium. 
 This condition was nearly fulfilled during the comet's revolution of 1819 
 22, on which occasion Encke, having computed the action of Jupiter by 
 means of the ancient value of his mass, found that the error in the time 
 of the comet's arrival in perihelion could not be wholly accounted for by 
 the supposition of a resisting medium. He now investigated the pertur- 
 bations of the comet, assuming the existence of a resisting medium, and 
 ascribing an indeterminate error to Jupiter's mass. Equating then the 
 effects produced by these causes to the observed errors of the comet's 
 motion, he obtained a number of equations of condition, the subsequent 
 discussion of which conducted him to a most satisfactory conclusion. He 
 now found for the mass of the planet a value which almost coincided with 
 that derived from the perturbations of the smaller planets; and this 
 improved value, combined with the hypothesis of a resisting medium, 
 afforded a complete explanation of the errors in the various revolutions of 
 the comet. Comparing together the observed and computed places 
 throughout three revolutions, he found that the mean error of a single 
 place was only 13".3, whereas, by rejecting the hypothesis of a resisting 
 medium, the error rose to 2 17". 6. The effect of the resistance is to 
 shorten the time of each revolution by about half a day. 
 
 The doctrine of a resisting medium has always been a favourite subject 
 of speculation with astronomers ; but on no occasion has it been supported 
 by evidence of such a plausible character as in the example above cited. 
 It is manifest, however, that more extensive indications of such a medium 
 must be discovered before the problem of its existence can be con- 
 sidered as having received a definitive solution. It has not yet affected 
 to a sensible extent any of the other celestial bodies, and, until such 
 is found to take place, the question relative to it must remain in 
 abeyance. 
 
 On the 27th February, 1826, M. Biela, an Austrian officer residing at 
 Josephstadt, in Bohemia, discovered in the constellation of Aries a round 
 nebulous body, which appeared to him to be a comet. His suspicion was 
 confirmed by a re-examination of the same object on the following evening, 
 when he found that, during the period that had elapsed since his first ob- 
 servation it had advanced about a degree to the east of its original place. 
 The comet was seen on the 9th March, by M. Gambart, at Marseilles ; 
 and, on the 10th, by M. Clausen, at Altona. Its elements, when calculated 
 on the supposition of the orbit being a parabola, were found to resemble 
 those of other two comets which appeared in 1805 and 1772. Gambart 
 and Clausen, therefore, simultaneously undertook the calculation of elliptic 
 elements, and obtained results which not only agreed with each other, but 
 also satisfied the observations much better than the original elements. 
 The mean period of a revolution was found to be about 6f years. 
 
 M. Damoiseau computed the perturbations which the elements of this 
 comet would experience during the revolution of 1826-82', and he found 
 that it would again return to its perihelion on the 27th November, 1832*. 
 The planets whose disturbing influence he took into account were Saturn, 
 Jupiter, and the Earth. He found that the combined action of these 
 bodies would have the effect of retarding the comet's arrival in perihelion 
 to the extent of 9.6642 days. Some degree of alarm was excited by the 
 
 * Memoires de t Academic des Sciences, tome viii. ; see also the Connaissance des 
 Temps for 1 830. 
 
136 HISTORY OF PHYSICAL ASTRONOMY. 
 
 announcement that the comet, a little before its perihelion passage, would 
 cross the plane of the ecliptic at a distance of only 20,000 miles from the 
 Earth's orbit, and near the place where the latter would then be moving. 
 The results of exact calculation were sufficient, however, to dissipate all 
 fears on this point, for it was found that the comet would cross the ecliptic 
 on the 29th October, 1832; but that the Earth would not arrive at the 
 same place until the 30th November. This comet returned agreeably to 
 prediction, and has subsequently reappeared in 1839 and 184(3. On the 
 last-mentioned occasion it underwent a singular transformation, having 
 separated into two distinct comets, which continued to travel together at 
 a mutual distance of 3' or 4' during the whole period of their visibility. 
 One of these objects was a little fainter than the other, but each of them 
 exhibited the distinctive features of a comet. The tails were parallel to 
 each other, and extended in a direction perpendicular to the line joining 
 the centres of the nuclei. This extraordinary change in the constitution 
 of the comet appears to have taken place very suddenly. It was first ob- 
 served in Europe on the 15th of January, 1846, by Mr. Challis of Cam- 
 bridge, and M. Wichmann of Koenigsberg; but it was afterwards found 
 that it had been seen on the 12th of the same month by Lieutenant 
 Maury, at the Observatory of Washington, in the United States. M. 
 Plantamour of Geneva determined the elements of each comet by obser- 
 vation, and then computed the perturbations occasioned by the Earth, 
 Jupiter, and Mars. The motions of both comets, when calculated by this 
 process, agreed very closely with their observed motions for the whole 
 period during which they were visible. M. Plantamour found that the 
 absolute distance between each nucleus was constantly the same, and was 
 equal to about two-thirds of the radius of the lunar orbit. 
 
 The approaching return of Halley's comet in 1835 excited a lively in- 
 terest in the scientific world, and a strong desire was felt that the pertur- 
 bations of its elements should be computed. The data necessary for this 
 purpose are the elements of the comet corresponding to the time of its 
 perihelion passage in 1759. These are readily deducible from the obser- 
 vations of that year with the exception of the major axis. This element 
 may be determined by assuming as the major axis corresponding to the 
 perihelion of 1682 the value indicated by the time of revolution between 
 1682 and 1.759, supposing the comet to move in an ellipse, and then 
 applying to it the perturbations it would suffer from the action of the 
 planets during the same period. But these perturbations cannot be 
 computed without a knowledge of the fundamental values of the other 
 elements. It is clear, then, that in order to obtain a complete set of 
 data for calculating the perturbations of the comet relative to its perihelion 
 passage in 1835, the geometer must possess a knowledge of the perihelion 
 elements for 1682. In the Connaissance des Temps for 1819, Burchardt 
 has given the elements for 1682 and 1759. His results relative to 1682 
 are founded on the observations of Flamstead, and those relative to 1759 
 on the observations of Messier. 
 
 A comparison of the three revolutions of this comet comprised between 
 the years 1531, 1607, 1682, and 1759, affords a striking indication of the 
 powerful perturbations which it experiences from the action of the planets. 
 The first of these periods includes 27,811 days; the second 27,352 days; 
 and the third 27,937 days: thus the first exceeds the second by 469 days, 
 and falls short of the third by 126 days. It was clearly impossible, there- 
 fore, to arrive at any accurate conclusion relative to the next return of the 
 
HISTORY OF PHYSICAL ASTBONOMY. 137 
 
 comet by means of these data alone, or even to affirm that the revolution 
 subsequent to 1759 would be longer or shorter than the preceding revolu- 
 tion. In 1812 the Academy of Turin proposed as the subject of a prize, 
 the perturbations of Halley's comet. The prize was awarded to Damoi- 
 seau, whose investigation was subsequently published in the Turin Me- 
 moirs for 1817. He determined the value of the major axis, at the time 
 of its perihelion passage in 1759, by computing the action of the planets 
 on it throughout the preceding revolution. Setting out, then, from the 
 complete elements of 1759, he computed the alterations they would suffer 
 throughout the time which would elapse until the comet would again 
 arrive in perihelion. The method he employed in his researches is 
 founded on the variation of elements, and coincides essentially with that 
 explained by Lagrange in 1780. He did not, however, adopt the mode 
 of proceeding suggested by that geometer for the superior part of the 
 orbit, preferring to execute the whole of the calculations by the safer 
 though more laborious process of mechanical quadratures. In computing 
 the perturbations of the major axis from 1682 to 1759, he changed the 
 elements only once, but, in performing a similar operation upon all the 
 elements throughout the revolution subsequent to 1759, he used the cor- 
 rected elements at every 30 of eccentric anomaly. The planets whose 
 action he took into account in his original memoir were Jupiter, Saturn, 
 and Uranus ; and his final result relative to the time of return was, that 
 the comet would pass its perihelion on the 16th November, 1835. Dis- 
 covering on a subsequent occasion that the Earth would exercise a sensible 
 disturbance on the comet after it had passed its perihelion in 1759, he 
 computed the derangement arising from this cause, and found that it 
 would have the effect of shortening the next revolution to the extent of 
 12 days. Hence, according to his previous conclusion, the passage of the 
 perihelion would take place on the 4th November. 
 
 The researches of Encke having rendered probable the existence of a 
 resisting medium, the return of Halley's comet was anxiously looked 
 forward to by astronomers, under the impression that it would throw some 
 light upon this interesting question. It was principally with this object 
 in view that the Academy of Sciences of Paris proposed the perturbations 
 of Halley's comet as the subject of a prize. After twice offering the 
 prize without obtaining any competitors, the Academy finally awarded it, 
 in 1829, to M. Pontecoulant. The details of this geometer's researches 
 were published in the sixth volume of the Mcmoires des Savans Strangers. 
 He assumed, as the basis of his calculations, the elements of Burchardt 
 for 1682 and 1759, and computed the perturbations by a process similar 
 to that employed by Damoiseau. He found that the comet would pass its 
 perihelion on the 7th of November, 1835. In the Connaissance des Temps 
 for 1837 * he corrected this result by taking into account the action of 
 the Earth before the perihelion passage of 1759, and by employing, instead 
 of Bouvard's value of Jupiter's mass, that which Nicolai had recently 
 deduced from the perturbations of Juno. His final conclusion was that 
 the comet would pass its perihelion on the morning of the 14th of No- 
 vember, 1835. 
 
 The perturbations of Halley's comet formed also the subject of pro- 
 found investigations by Lehmann and Rosenberger, two German mathe- 
 
 * Published in 1834. 
 
138 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 maticians of great eminence. The researches of Rosenberger were more 
 complete than those of any of his contemporaries. He determined the 
 elements of 1682 and 1759 by an able discussion of all the observations 
 that were in each case available to him. He also computed the perturba- 
 tions occasioned by Mercury, Venus and Mars, as well as those due to the 
 larger planets of the system. 
 
 It was announced by astronomers that the comet, if visible at all to the 
 naked eye, would be so about the middle of October, when it attained its 
 nearest distance to the Earth. The event fully justified this prediction/ On 
 the evening of the 5th of August the comet was seen for the first time, at 
 the Observatory of Rome. It gradually increased in brilliancy until it 
 finally was visible to the naked eye in the beginning of October. 
 By the 12th "of that month it appeared like a star of the second 
 magnitude, and was accompanied by a tail seven or eight degrees 
 long. \ It soon afterwards plunged into the rays of the sun, and 
 ceased 'to be visible; but it was again discovered by astronomers early 
 in the following year, after passing its perihelion. On account of its 
 southern declination, its reappearance was not favourable for observation 
 in Europe, but it was seen to great advantage at the Cape of Good Hope 
 by Mr. Maclear, the Astronomer Royal for that station, and also by Sir 
 John Herschel, who was then engaged in prosecuting his sidereal observa- 
 tions in the southern hemisphere. These astronomers continued to 
 observe it until the 5th of May, 1836, when it finally ceased to be visible *. 
 
 The various calculations which have been undertaken, for the purpose of 
 determining the elements of this famous comet by means of the observa- 
 tions made on the occasion of its last appearance, generally concur in 
 assigning noon of the ] 7th of November as the instant of the perihelion 
 passage. This result presents a very satisfactory agreement with that 
 which we have seen that Pontecoulant arrived at by the aid of theory. 
 Having subsequently revised his calculations, this geometer rendered the 
 accordance still more complete. By employing improved values of the 
 masses of the perturbing planets, he found that the passage of the perihe- 
 lion would take place at noon on the 16th of November t. 
 
 It must be ackowledged that Rosenberger's result did not coincide so 
 closely with that derived from observation, notwithstanding the elaborate 
 character of his researches. In consequence of the errors which in- 
 evitably affect all observations in a greater or less degree, and the uncer- 
 tainty which exists respecting the real values of the masses of the planets, 
 it is not to be expected that an error of a few days may not occur in the 
 calculated time of the comet's return. The fidelity with which it responded 
 to the deductions of the geometer on the occasion of its last appearance 
 forms one of the many magnificent triumphs which adorn the history of the 
 Theory of Gravitation J. 
 
 * Some interesting particulars relative to the physical changes which this comet under- 
 went, during the period of its visibility, are contained in Sir John Herschel's Account of 
 Astronomical Observations at the Cape of Good Hope. 
 
 t See the Connaissance des Temps for 1838. In this final revisal of his researches 
 Pontecoulant employed the masses of Saturn, Jupiter, and the Earth, as assigned severally 
 by Airy, Bessel, and Encke. 
 
 J The following statement of the elements of the comet, derived from the observations 
 of 1 759 and 1835, and the elements for 1835 as assigned by the theory of gravitation, 
 will at once indicate the magnitude of the perturbations which the motion of the comet 
 experiences, and the accuracy with which they have been computed : 
 
HISTORY OF PHYSICAL ASTRONOMY. 
 
 139 
 
 On the 22nd of November, 1843, M. Faye, of the Royal Observatory of 
 Paris, discovered a comet, the motion of which could not be reconciled 
 with parabolic elements. Dr. Goldsmicht, a German astronomer, shortly 
 afterwards found that the observations might be satisfied by supposing the 
 comet to move in an ellipse with a period of about 7^ years. Le Verrier 
 has calculated the perturbations of this comet, and has fixed the 4th of 
 April, 1851, as the time when it will return to its perihelion. He found 
 that the action of the planets would retard its arrival 7.67 days. 
 
 We have alluded on a former occasion to the comet of 1770, generally 
 known as Lexell's comet, which was rendered visible by the action of 
 Jupiter in 1767, and was subsequently thrown into an orbit of larger 
 dimensions, and rendered invisible by the action of the same planet in 
 1779. The discovery of a new comet revolving in an elliptic orbit nearly 
 equal in magnitude to the orbit of Lexell's comet, and occupying the 
 same region of the heavens with it, induced some astronomers to suspect 
 that the two bodies were identical. M. Valz of Marseilles appears to 
 have first advanced this hypothesis. He remarked that, by supposing a 
 slight increase in the period of Faye's comet, it would have approached 
 yery near to Jupiter in the year 1815, and would have been so powerfully 
 disturbed by that planet, that if it had been previously revolving in 
 an orbit of wider dimensions it would have been thrown by the action of 
 the planet into the small ellipse in which it is now moving. Considering 
 next the effect produced on Lexell's comet by the action of Jupiter in 
 1779, he found by means of Burchardt's data that the new ellipse into 
 which the comet was then thrown would have a period of rather more than 
 sixteen years. Hence, when the comet had made a little more than two 
 revolutions, it would have again arrived in a position favourable for the 
 action of Jupiter, and would be thrown into the smaller orbit in which it 
 was moving previous to 1779. Comparing the elements of this orbit with 
 those of the orbit in which Faye's comet moved, he conceived that the 
 resemblance was so strong as to justify the conclusion that the two orbits 
 referred to the same comet, the one being periodically convertible into 
 the other by the disturbing action of Jupiter. This idea was no less 
 novel and ingenious than it was interesting and plausible ; but, as it rested 
 merely on a rough estimate of Jupiter's influence during the period com- 
 prised between the actual appearances of the two comets, it could not be 
 
 
 Elements derived 
 by Burchardt from 
 the Observations 
 of 1759. 
 
 Elements derived 
 by Lieutenant Strat- 
 tord from the Ob- 
 servations of 1835. 
 
 Pont^coulant's 
 Elements for 1835, 
 obtained by com- 
 puting the Pertur- 
 bations of the 
 Planets. 
 
 Passage of the Perihelion, M.T. 1 
 Greenwich. / 
 
 1759, Mar. 12.58 
 1801861 
 
 1835, Nov. 15.93 
 18 0779386 
 
 1835, Nov. 15.01 
 18.00008 
 
 Ratio of the eccentricity to the \ 
 Semi Axis Major. J 
 Longitude of the Perihelion on 1 
 the Orbit. / 
 Longitude of the Ascending 1 
 Node. J 
 
 0.9675571 
 303 D 10' V, 
 
 53 50' 11" 
 17 37' 12" 
 
 0.9675509 
 304 32' 9".2 
 
 55 8' 21 ".2 
 17 45' 56".7 
 
 0.9672807 
 304 31' 42" 
 
 55 10' 15" 
 17 44' 53" 
 
 
 
 
 
140 HISTOKY OF PHYSICAL ASTRONOMY. 
 
 recognised as an established truth in physical astronomy. The subject 
 was one well adapted to the searching powers of a Laplace or a Poisson, 
 and in their countryman, M . Le Verrier, astronomy found on the present 
 occasion a worthy representative of these illustrious geometers. The 
 mode of proceeding which Le -Verrier proposed to adopt in this inquiry 
 was first to determine the effect produced by Jupiter on Lexell's comet, 
 from its discovery in 1770 until the action of the planet ceased to be 
 sensible, and then to trace back the elements of Faye's comet through the 
 various revolutions comprised between the appearance of that body in 1843, 
 and the epoch down to which he had conducted his researches on Lexell's 
 comet. If the ultimate elements of Faye's comet, when thus determined, 
 were found to coincide with those of Lexell's for the same epoch, it might 
 then be concluded that the two comets were identical ; but on the other 
 hand, if they exhibited discordances which could not be accounted for by 
 any admissible supposition of errors, whether of observation or calculation, 
 it must necessarily follow that the comets were two distinct bodies. Le 
 Verrier found that the ultimate results would be very much affected by 
 the errors in the original elements of both comets, for the effects of these 
 errors continually increased with the lapse of time, insomuch that in some 
 instances a very small variation of the fundamental elements would be 
 sufficient to alter entirely the character of Jupiter's influence. The in- 
 vestigation was therefore much more complicated and the conclusions less 
 definite than might have been expected if the data had been more precise. 
 Le Verrier having submitted to a careful discussion the observations of 
 1770 on Lexell's comet, determined by means of them the elements of 
 the orbit, and then investigated the action of Jupiter on the comet. He 
 found that, when the latter arrived within the sphere of the planet's in- 
 fluence, it was compelled to deviate from its elliptic orbit, and described 
 an hyperbola round the planet. The errors of the elements might even 
 be such that, after the action of the planet ceased to be sensible, the comet 
 would still continue to move in an hyberbola, and in that case would never 
 again return to the solar system. Le Verrier computed the elements of 
 the comet for the time when it quitted the sphere of Jupiter's influence, 
 and then compared the results with the elements of Faye's comet, the 
 latter being traced up to the same epoch through the various revolutions 
 anterior to its appearance in 1843. He found that, upon any possible 
 supposition of the errors of observation, the elements of Faye's comet could 
 not be reconciled with those of Lexell's, and he therefore came to the 
 conclusion that they were two distinct bodies. 
 
 It is possible that Faye's comet may have originally emerged from the 
 boundless regions of space describing a parabola or hyperbola having the 
 sun in the focus, but that on its arrival within the sphere of Jupiter's in- 
 fluence it was thrown into a new orbit by the powerful action of that 
 planet, and was permanently fixed in the solar system. If the funda- 
 mental elements of the comet were mathematically accurate, this question 
 might be decided, at least for any determinate period, by tracing back the 
 comet through the various revolutions anterior to 1843. The errors, 
 however, with which the elements are affected by the inevitable errors of 
 observation, impart so indeterminate a character to the results, that, even 
 if the comet had been so introduced into the solar system, it would have 
 been impossible to ascertain the exact time when this event happened. 
 But although the question does not admit of a definitive solution, on 
 account of the circumstance to which we have just alluded, still it is pos- 
 
HISTORY OP PHYSICAL ASTBONOMY. 141 
 
 sible to assign the minimum time during which the comet has been re- 
 volving within the limits of the solar system. Le Verrier found that it 
 must have been introduced into the system at least as early as the year 
 1747; whence it followed that it had made at least thirteen revolutions 
 in an elliptic orbit previous to its discovery. 
 
 The interest excited by the periodic comet of 1843 had only abated in a 
 small degree when the solar system was enriched by another discovery 
 of the same class. On the 29th of August, 1844, De Vico, the director 
 of the Observatory at Rome, discovered a comet, which was soon after- 
 wards found by M. Faye to revolve in an ellipse with a period of about five 
 years and a half. MM. Laugier and Mauvais, of the Royal Observatory of 
 Paris, instituted a comparison between the elements of this comet and those 
 of one observed in 1585 by Tycho Brahe and Rothmann. Halley had cal- 
 culated the elements of the last-mentioned comet on the supposition that 
 it revolved in a parabola, but the French astronomers shewed that the 
 motion might be satisfied better by an elliptic orbit with a period of five 
 years and two months. From the close resemblance which the elements 
 of- this comet bore to those of the comet of 1844, MM. Laugier and 
 Mauvais concluded that the two bodies were identical, the actual dis- 
 cordances of the elements being ascribed by them to the effects of planetary 
 perturbation. The grounds upon which this conclusion rested were indeed 
 very plausible, for the eccentricities of both orbits were almost the same, 
 the places of the perihelia did not differ more than 30, and the distance 
 between the nodes was only 22. It is manifest, however, that the 
 identity could only be established beyond all doubt by a comparison of 
 the elements of both comets when rigorously determined for some 
 common epoch. Le Verrier investigated the subject by tracing back 
 the comet of 1844 through the anterior revolutions up to 1585, and 
 then comparing the elements for that epoch with those of the recorded 
 comet. The results at which he arrived shew how unsafe it is in researches 
 of this nature to adopt any conclusion which is not verified by rigorous 
 calculation. As we have mentioned already, the distance between the 
 perihelia of the comets observed in 1844 and 1585 was only 30, and it 
 was reasonably enough supposed that this displacement might have been 
 produced by the action of the planets. Le Verrier, however, found that, 
 when the orbit of the comet of 1844 was traced back, the perihelion, 
 instead of approaching towards that of the comet of 1585, on the contrary 
 receded further and further from it, insomuch that, at the epoch of 1585, 
 the perihelia of the two comets were diametrically opposite to each other. 
 The nodes also of the comet of 1 844 continually receded from those of the 
 comet of 1585, so that, in order to coincide with the latter at the epoch of 
 comparison, they would require to move through 338, and not 22 during 
 the period comprised between 1844 and 1585. The elements of both 
 comets, when thus determined for the common epoch of 1585, offered dis- 
 cordances of such magnitude as appeared to Le Verrier to be incompatible 
 with identity, and he therefore came to the conclusion that the two comets 
 were totally distinct bodies. He also ascertained in the course of the 
 same researches that the comet of 1844 was not identical with Lexell's 
 comet. He discovered, however, such a strong resemblance between 
 the elements of the new comet and those of a comet observed in 
 1078 by La Hire, that he considered himself fully justified in concluding 
 that they were identical. Thus, although the comet of 1844 has doubtless 
 formed a part of the solar system for many ages, and has frequently ap- 
 proached very near the earth, history records only one instance of its 
 
142 HISTORY OF PHYSICAL ASTRONOMY. 
 
 appearance previous to the year 1844. The planet Jupiter, which in all 
 probability chained it down orginally to the system, will one day act upon 
 it with equal intensity, but in an opposite direction, and we may reasonably 
 presume that, when it has escaped from his influence,' it will again fly off 
 into infinite space, describing a parabola or Jiyperbola. 
 
 The theory of Jupiter's satellites has not received any material improve- 
 ment since the publication of the Mecanique Celeste. In 1817 Delambre 
 published new tables of the satellites founded on all the eclipses that had 
 been observed from 1660 down to the commencement of the present century. 
 These were succeeded by Darnoiseau's tables which appeared in 1836. 
 
 The satellites of Saturn have hitherto occupied the attention of geometers 
 only in a very small degree. This has chiefly arisen from the small pro- 
 gress made by astronomers in determining by observation the elements of 
 their motions, and am tracing, a posteriori, the more considerable in- 
 equalities resulting from their mutual perturbation. We have seen a 
 striking proof of the utility of observation for both these purposes, in the 
 history of Jupiter's satellites. The influence of the spheroidal figure of 
 Saturn is clearly indicated by the positions of the ring and the orbits of 
 the interior satellites, which coincide almost with the plane of his equator. 
 As the satellites recede from their primary, the disturbing action of the 
 sun increases relatively to that occasioned by the spheroidal figure of the 
 planet, and the orbits commence to deviate sensibly from the plane of his 
 equator, and to incline towards that of the ecliptic. The sixth, or Huy- 
 genian satellite, which is the brightest of all, and therefore the most 
 favourable for observation, has formed the subject of an elaborate investi- 
 gation by Bessel. From the motion of the apsides of this satellite, he 
 concluded that the mass of the ring amounted to T j-g of the planet's mass. 
 He also obtained for the latter a value agreeing very nearly with -that 
 deduced by Bouvard from the equations of condition employed in the con- 
 struction of Jupiter's tables. Some valuable observations of the satellites 
 were made by Sir John Herschel in the course of his residence at the 
 Cape of Good Hope. From those of the sixth satellite he derived elements 
 which agreed very, nearly with the values assigned by Bessel for the epoch 
 of 1830, taking into account the variation of each element during the inter- 
 mediate period. He also computed the epochs and mean motions of the 
 other satellites, and obtained results which accorded very w r ell with those 
 deducible from the earlier observations of Sir William Herschel. 
 
 If the theory of Saturn's satellites is still in its infancy, the remark 
 applies with still greater force to the satellites of Uranus. These bodies 
 can only be rendered visible by means of the most powerful telescopes, and 
 therefore it may naturally be presumed that a considerable time will elapse 
 before a correct theory of their motions be formed. W T hen their elements 
 are once determined by observation, they will offer peculiar interest to the 
 geometer in consequence of their motions being retrograde and the planes 
 of their orbits being nearly perpendicular to the plane of the ecliptic. 
 
 The consummate researches of Lagrange left little to be accomplished 
 in the theory of the Libration of the Moon. Poisson applied his powers of 
 analysis to this interesting subject, but the results at which he arrived had 
 only the effect of confirming those obtained by the illustrious geometer 
 just mentioned *. Although the mean motions of the moon with respect to 
 rotation and revolution be both equal to each other, still the inequalities 
 
 * Connaissance des Temps, 1821-22. The researches of Poisson are principally, 
 directed to the inequalities in the inclination and node of the lunar equator. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 148 
 
 in longitude will cause them to differ generally for any assignable time. 
 The longest axis of the lunar ellipsoid will therefore deviate always a little 
 from the direction of the earth's action, and hence will arise a series of 
 inequalities in the moon's rotation corresponding to her various inequalities 
 in longitude, and causing a real libration in her motion. The magnitude 
 of these inequalities manifestly depends on the figure of the moon, or in other 
 words on the ratios of the three axes of the lunar ellipsoid. Hence, if the 
 ratios of these axes be known, we shall be enabled to compute the maxi- 
 mum values of the inequalities, and, vice versa, if the latter be determined 
 by observation, we can readily derive from them the ratios of the axes, and 
 consequently the exact elongation of the moon's figure. Bouvard and 
 Nicollet undertook for this purpose a series of careful observations of the 
 moon's libration in longitude at tke Royal Observatory of Paris. The 
 Connaissance des Temps for 1S22 contains a beautiful paper by Nicollet, 
 in which he submitted these observations (amounting in number to 174) 
 to a searching discussion. The only sensible inequality was that cor- 
 responding to the annual equation in longitude : it appeared by observa- 
 tion to have a maximum value equal to 4' 45". The results at which he 
 arrived relative to the ratios of the axes do not accord with the generally 
 admitted opinion respecting the primitive condition of the moon. He 
 found, in fact, that the difference between the least and greatest axes was 
 greater than what it would be on the supposition that the moon was 
 originally a fluid mass. 
 
 It has been well remarked by the illustrious Humboldt, that no inquiry 
 in physical science can compare with that relating to the Figure of the 
 Earth in the disproportion which exists between the ultimate object of 
 attainment and the number of ingenious and refined processes both in 
 mathematical and astronomical science, which the long and arduous pursuit 
 of it has given birth to. The theory of this subject remains nearly in the 
 condition in which Clairaut left it, for the researches of Laplace, notwith- 
 standing the remarkable character of the analysis employed in their expo- 
 sition, contributed only in a small degree to its advancement. We have 
 mentioned in one of the foregoing chapters that the attraction of elliptic 
 spheroids is intimately associated with the question of the figures of the 
 celestial bodies. The most important improvement which this part of the 
 theory of gravitation has received in recent times is due to the late Mr. 
 Ivory*. The problem for determining the attraction of a spheroid upon a 
 particle situated in its interior had yielded at an early period to the 
 resources of the ancient geometry, and was afterwards found to admit of an 
 easy solution by analysis. The analogous problem for an exterior particle, 
 on the other hand, offered difficulties which long seemed to be insuperable, 
 and, although Laplace finally succeeded in devising its solution, his method 
 was so incomplete as to leave ample scope for further research. The sub- 
 ject continued to engage the attention of the ablest analysts until Mr. 
 Ivory finally discovered the well-known beautiful theorem, by means of 
 which the attraction of a spheroid upon a point without it is immediately 
 derived from its attraction on a point within itf. This theorem is remark- 
 able for being the most important contribution to mechanical science which 
 
 * Born at Dundee in 1765 ; died at Hampstead, near London, in 1841. During the 
 early period of his career he was in all probability the only person in Britain who possessed 
 an intimate acquaintance with the methods of analysis employed in the higher investiga- 
 tions of Physical Astronomy. 
 
 f Phil. Trans., 1809. 
 
144 HISTOEY OP PHYSICAL ASTRONOMY. 
 
 had been made by a native of the British Isles since the days of Mac- 
 laurin. The memoir which contains its original announcement deserves 
 also to be mentioned, on account of the intimate acquaintance which the 
 author of it exhibits with methods of analytical investigation, the use of 
 which had been hitherto confined exclusively to the mathematicians of the 
 continent. Mr. Ivory soon afterwards gave another striking proof of his 
 talents by a critical examination of Laplace's researches relative to the 
 attraction of spheroids of small eccentricity. Having pointed out what he 
 conceived to be certain defects in Laplace's reasoning, he expounded the 
 peculiar calculus of that great geometer by a method of his own, remarkable 
 for its clearness and elegance. The objections urged against Laplace's 
 demonstration are now admitted to have originated mainly in a miscon- 
 ception of the author's meaning ; but the memoir of Mr. Ivory has been 
 universally admired as a fine exhibition of analytical skill *. The important 
 subject of the attraction of spheroids has more recently engaged the atten- 
 tion of Plana, Gauss, Poisson, Airy, and other eminent geometers, but no 
 striking results have been elicited by their researches. 
 
 Before proceeding to notice the applications which have been made of 
 Clairaut's theorem to the determination of the Earth's ellipticity, it may 
 not perhaps be uninteresting to give a brief account of the geodetic 
 operations which have been carried on in recent times with the view of 
 attaining the same object by the actual measurement of arcs on the 
 Earth's surface. 
 
 An arc of the meridian has been measured in the present century by 
 Gauss, extending from Gottingen to Altona, and embracing an amplitude 
 of 2 0' 57". The latitudes at the two extremities of the arc were deter- 
 mined by means of Ramsden's famous zenith sector. An arc of still 
 greater extent has been measured in Russia by M. Struve. Its northern 
 extremity is situated in Hochland, an island in the Gulf of Finland ; and 
 from this point to Jacobstadt, its southern extremity, it embraces an 
 amplitude of 3 35' 5". One of the peculiarities connected with the 
 measurement of this arc consisted in the determination of the latitudes 
 by means of the transits of stars across the prime vertical f. We 
 may remark that this mode of observation is extensively practised by the 
 German astronomers of the present day, for the purpose of ascertaining 
 the 'declinations of the stars. The operations of M. Struve were subse- 
 quently connected with those of Von Tenner in the south of the Russian 
 empire, and the whole arc now extends to 8 2' 2S"-91. The geodetic 
 operations by means of which Bessel J connected the arc of M. Struve, in 
 Russia, with the extensive triangulations of the west and south of Europe, 
 exhibited in a remarkable degree the power of that illustrious astronomer 
 to sytematize and perfect every subject which bore any relation to his 
 favourite science. It may be remarked that in all geodetic operations 
 more angles are generally observed, than those which the principles of 
 geometry render indispensably necessary to be known for the purposes of 
 computation. This circumstance will manifestly give rise to a number of 
 relations between the observed angles, which would be rigorously satisfied 
 by the latter if they were mathematically accurate. This condition, how- 
 
 * Phil. Trans., 1812-22. 
 
 + Born at Minden 1784 ; died at Konigsberg 1846. He is generally allowed to be 
 the greatest astronomer which the present century has hitherto produced. 
 
 f The latitudes were also found with the zenith sector, and a mean of both results was 
 in each case taken for the final determination. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 145 
 
 ever, being practically unattainable, it remains for the computer to inves- 
 tigate the true correction which should be applied to the values of the 
 several angles. For this purpose each angle is assumed to be affected 
 with an unknown error, and then, by means of the relations above men- 
 tioned, a number of equations of condition are formed between the unknown 
 quantities. Now Bessel determined the values of these quantities, not 
 according to the practice hitherto pursued, of grouping the equations of 
 condition into a number of isolated systems, but by combining them all 
 together, and submitting them to one uniform and systematic mode of treat 
 ment. The superior advantage of thus making the totality of the observa- 
 tions subservient to the determination of their individual errors is too 
 obvious to require any further notice. 
 
 The numerous arcs of the Earth's surface which have been measured in 
 recent times, with the most scrupulous attention and skill in all their 
 details, have enabled astronomers in the present day to arrive at more 
 definite conclusions relative to the magnitude and figure of the earth than 
 it was possible to have deduced at an earlier period. In 1832, Mr. Airy 
 discussed all the arcs of any value that had been measured either in the 
 direction of the meridian, or perpendicular to it. Kejecting the arcs of 
 parallel as unworthy of confidence in so delicate an inquiry, and also all 
 those arcs of the meridian which, being situated in mountainous countries, 
 might ' be vitiated by the effects of local disturbance, he derived the 
 elements of the earth's figure from the remaining data by a very simple 
 process, in which he was mainly guided by a sagacious appreciation of the 
 relative merits of the ancient and modern measurements. His final con- 
 clusion was that the exterior surface of the earth may be represented by 
 an ellipsoid of revolution, the polar semidiameter of which is 20,853,810 
 feet, or 3949.585 miles; and the equatorial semidiameter 20,923,713 feet, 
 or 3962.824 miles *. This gives 69,903 feet, or 13.239 miles for the excess 
 of the equatorial over the polar semidiameter, and ^-g-g-.-j-g- for the value 
 of the ellipticity. These results have received a most satisfactory 
 confirmation from the researches of Bessel, who in 1841 was con- 
 ducted to an ellipticity equal to -j-g-g.-nr by an elaborate discussion of 
 all the most reliable arcs of the meridian. We may mention that the 
 elements of Mr Airy are those which have been employed in all the 
 more recent calculations connected with the Ordnance Survey. We 
 shall have occasion presently to notice a very satisfactory confirmation of 
 their accuracy which has been afforded by the measurement of an exten- 
 sive arc of parallel. 
 
 The great meridional arc of India has recently received a considerable 
 extension. The operations connected with this arc were commenced by 
 Colonel Lambton about the beginning of the present century, and the first 
 section, extending from Punnce in lat. 8 9' 35" to Damargida, in lat. 18 
 3' 15", was completed by that officer in 1815. Another section extending 
 from Damargida to Kalianpur, in lat. 1 4 7' 1 1", was executed by Colonel 
 Everest, who succeeded Colonel Lambton in the superintendence of the 
 operations, upon the death of the latter in 1823. The whole arc from 
 Pumice to Kalianpur embraced, therefore, an amplitude of 15 57' 40", and 
 was consequently the most considerable which had yet been measured. The 
 methods employed were similar to those practised in the measurement of 
 
 * Encycl. Metrop., Art. Figure of the Earth. 
 
146 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the English arc, and the result was generally considered by competent 
 judges to be equal in point of accuracy to the very best modern deter- 
 minations of a similar character. The recent extension to which we have 
 alluded is due to Colonel Everest, who has now prolonged the arc to 
 Kaliana, in latitude 29 30' 48". He effected this object not by continuing 
 the triangulation from Kalianpur, the northern extremity of the great arc, 
 but by proceeding in the opposite direction from Kaliana to Kalianpur. 
 For this purpose a base was measured in the Valley of Dhera Dhun, near 
 the inferior range of the Himalayan Mountains. The extreme station 
 of the arc was situated at a distance of seventy miles to the south of the base, 
 Colonel Everest justly fearing that, if a less remote locality were selected, 
 the attraction of the Himalayan Mountains might exercise a disturbing 
 influence on the celestial observations. In 1837, Colonel Everest com- 
 pleted the triangulation as far as Kalianpur; and, as he had some doubts 
 respecting the accuracy of his previous operations beyond this point, he 
 continued to advance southwards, until he reached Damargida, the northern 
 extremity of Colonel Lambton's arc. The celestial amplitude was deter- 
 mined by dividing the terrestrial arc into two sections at Kalianpur, and 
 then making simultaneous observations on the stars at the two extremities 
 of each section. Thirty-six stars were observed in determining the ampli- 
 tude of the northern section, and thirty-two in determining that of the 
 southern section. In each instance half of the stars were situated to the 
 south and the other half to the north of the zenith points of both ex- 
 tremities of the arc ; but the greatest distance of any star from the nearest 
 zenith did not exceed 5. The amplitude of the northern section was 
 found to be 5 23' 37".051, and that of the southern section, 6 3' 55".973. 
 This gives 11 27' S3".024 for the amplitude of the whole arc measured 
 by Colonel Everest. The terrestrial length of the northern arc was 
 found to be 1961157.117 feet, and that of the southern arc 2202926.196 
 feet. Comparing these results with the amplitudes, it appears that 
 the length of a degree of the meridian in mean latitude 26 49' is 
 363,606 feet, and that the length of a degree in mean latitude, 21 5', 
 is 363,187 feet. The whole of Colonel Everest's arc, when compared 
 with the English arc between Dunnose and Clifton, gives -g-L^ for 
 the ellipticity of the earth. A similar comparison with the French arc 
 gives 3^; with the Russian arc 3-^-9-; and with the Swedish arc g-i^. Be- 
 sides the base measured in the valley of Dhera Dhun, two bases of veri- 
 fication were measured by Colonel Everest, one at the southern extremity 
 of the whole arc, and the other near Kalianpur, the middle station. The 
 verification was effected by computing the bases at the two extremities of 
 the arc from the base in the middle, and then comparing the results with 
 those derived from actual measurement. In this manner the length of the 
 base at the northern extremity was found to be 39183.273 feet by com- 
 putation, and 39183.873 feet by actual measurement. The difference, 
 therefore, amounted only to T 6 oths of a foot, or about seven inches. Again, 
 the length of the base at the southern extremity was found to be 41578.178 
 feet by computation, and 41578.536 feet by measurement. This gives a 
 difference of T ^^ths of a foot, or a little more than four inches. The near 
 agreement of these results affords a strong guarantee for the accuracy of 
 the whole operation. The bases were measured with an apparatus devised 
 by General Colby while engaged in the operations of the Irish Survey. It 
 consisted essentially of two metallic bars, each ten feet long, so connected 
 
HISTORY OF PHYSICAL ASTRONOMY. 147 
 
 together as by their unequal expansion to obviate the necessity of apply- 
 ing a correction for temperature *. 
 
 The great Indian arc from Punnce to Kaliana now embraces an ampli- 
 tude equal to 21 21' 13". The southern portion may not perhaps be so 
 unexceptionable in its execution as it was at one time generally supposed 
 to be ; but still, when taken in its full extension, this arc is unquestionably 
 one of the most valuable data we possess for determining the figure of the 
 earth, and is destined in all ages to shed a brilliant lustre on the history 
 of British rule in India. 
 
 The arc of the meridian measured by Lacaille, at the Cape of Good 
 Hope, presented an unaccountable anomaly when compared with similar 
 measurements executed on the opposite side of the equator. It would 
 appear, from the result at which he arrived, that the earth's surface is less 
 curved in the southern than it is in the northern hemisphere. This con- 
 clusion excited the surprise of astronomers, being totally at variance with 
 the theory of gravitation, which assigns the same ellipticity to both hemi- 
 spheres. On the other hand, the high celebrity of the astronomer upon 
 whose authority it rested, served only to render the question still more 
 perplexing. When Colonel Everest visited the Cape of Good Hope, in 
 1821, he carefully inspected the tract of country in which the arc was 
 measured, and drew up the result of his observations in a letter addressed 
 to Colonel Lambton, which appears in the first volume of the " Memoirs of 
 the Astronomical Society." The southern extremity of the arc was si- 
 tuated at Lacaille's Observatory in Cape Town, and the northern extre- 
 mity at Kleip Fonteyn. The celestial amplitude was 1 12' 1".55, and 
 the latitude of the middle point was 83 18' 30". Lacaille found the ter- 
 restrial length of the arc to be 68469 toises, whence 1 was equal in 
 length to 57037 toises. Now, if we assume the earth to be an oblate 
 spheroid, having an ellipticity equal to -g-J^, a supposition which agrees 
 very well with the result of a comparison of meridional arcs in the north- 
 ern hemisphere, the amplitude of an arc whose terrestrial length and 
 mean latitude is the same as that of Lacaille's will be found to be 
 1 12' 10". 54. This result exceeds, by 8". 9 9, the amplitude of the arc 
 as determined by Lacaille. Colonel Everest strongly suspected that the 
 discordance arose from the disturbing influence occasioned by the attrac- 
 tion of the mountains in the neighbourhood of the two terminal stations. 
 He remarked that the mountains at Cape Town would so affect the plumb 
 line as to make the zenith appear a little to the south of its true place, 
 while, on the other hand, those at Kleip Fonteyn would cause the zenith 
 of that station to deviate a little to the north of its true place. Hence 
 the apparent amplitude of the arc as derived from the zenith distances of 
 the stars at its two extremities would be less than the true amplitude by 
 the sum of both zenith errors. Colonel Everest therefore concluded, that 
 Lacaille's measurement might be reconciled with the usual value of the 
 
 * The accuracy of the results obtainable by the use of this apparatus was put to a severe 
 test by the remeasurement of the bases. The base of Dhera Dhun was remeasured in an 
 opposite direction, and, although the whole length exceeded seven miles, the two results 
 did not differ by so much as 2^ inches. Another mode of verification consisted in 
 dividing the base into three sections, and, having remeasured the middle section, denying 
 the other two from it by triangulation. The whole length of the base when determined 
 by this process did not differ more than a quarter of an inch from the original measure- 
 ment. An equally satisfactory result was obtained by a similar remeasurement of the base 
 at Damargida. the southern extremity of the arc. 
 
 L 2 
 
148 HISTORY OF PHYSICAL ASTRONOMY- 
 
 ellipticity, by assuming that the zeniths of the two extreme stations were 
 disturbed by local attraction to the extent of 8".99. After alluding to 
 the inexpediency of remeasuring the arc, in consequence of the practical 
 difficulty of observing the angles from Lacaille's stations, this distin- 
 guished officer then proceeds in the following terms : " It might be in- 
 teresting, no doubt, to ascertain the exact latitudes of both extremes of 
 the arc, by a series of triangles connecting them with the observatory now 
 about to be erected in this neighbourhood, and this, which will doubtless 
 be hereafter done, may in able hands furnish a new datum respecting the 
 attraction of mountains ; but, as to the arc itself, it seems to me to be too 
 small to be of any weight, even were all other objections removed, and 
 the labour of correcting the old result, except for the mere curiosity of 
 the matter, would therefore be much better expended upon a new series 
 of triangles. Such a series, instead of terminating at Kleip Fonteyn, 
 might veiy easily be carried through the country of the Narnaquas to the 
 northern boundary of the colony, which would furnish a very pretty arc 
 of nearly 4 in amplitude, and, I doubt not, set for ever at rest the ano- 
 malous hypothesis of the different form of the two opposite hemispheres of 
 the globe." 
 
 We have cited these remarks, not only because they reflect the 
 highest credit on the sagacity of Colonel Everest, but also on account 
 of the interesting confirmation which they have recently derived from the 
 labours of Mr. Maclear, the Astronomer Royal at the Cape of Good Hope. 
 In the year 1837 the latter determined the latitude of Lacaille's Obser- 
 vatory by means of a triangulation connecting it with the Royal Obser- 
 vatory. The result, when compared with that derived by Lacaille from 
 direct observation, seemed to indicate the existence of local attraction, 
 but the discordance was not sufficiently great to account for the whole 
 anomaly of Lacaille's arc. Mr. Maclear resolved, therefore, to verify the 
 entire operations of that astronomer by a careful remeasurement of the 
 arc. The latitudes at the extreme stations, as determined by means of 
 the zenith sector, were found to agree with the values assigned by La- 
 caille, but the computation of the triangles had the effect of shortening 
 the arc by 200 feet, and thereby reducing the anomaly in its length to 
 about half its previous magnitude. Suspecting that the remaining part 
 of the error arose from the ill-conditioned character of Lacaille's tri- 
 angles, he chose another set of stations, and then repeated the whole 
 operation ; but to his great disappointment he obtained a result which 
 agreed almost exactly with that at which he had previously arrived. He 
 now resolved to measure an arc of three or four degrees, and to select 
 the two extreme stations, so as to be beyond the reach of local disturb- 
 ance. This object he successfully effected notwithstanding many hard- 
 ships he had to encounter in consequence of the inclemency of the weather, 
 and the impassable nature of the country in which his operations were 
 conducted. The triangulation was carried southwards to Cape Point, and 
 northwards as far as Kamies Berg. The distance between these two ex- 
 tremes comprehended an arc of nearly 4 2' ; but, as Mr. Maclear sus- 
 pected that the station at Cape Point was subject to local disturbance, he 
 fixed the southern limit of the arc at the Royal Observatory. The dis- 
 tance between this station and Kamies Berg included an arc of 3 34'. 
 Two intermediate stations were selected, one at Kleip Fonteyn, and the 
 other to the north of that station. The final result at which he arrived 
 was of the most gratifying character. He found that the length of a 
 
HISTORY OF PHYSICAL ASTRONOMY. 149 
 
 degree was now almost exactly reconcilable with the ellipticity derived 
 from a comparison of meridional arcs in the northern hemisphere. He 
 also completely succeeded in tracing the various circumstances which 
 conspired to vitiate Lacaille's arc. We have already mentioned that the 
 error was reduced to half its original magnitude by the remeasurement of 
 the terrestrial arc. The remaining half was found by Mr. Maclear to 
 arise from errors in the latitudes of the two extreme stations, occasioned 
 by the attraction of the mountains in their neighbourhood. When the 
 latitudes were determined at stations removed from the influence of local 
 attraction, and then connected trigonometrically with the arc, they were 
 found to be very nearly reconcilable with the usually received value of 
 the ellipticity. A slight deviation of the plumb-line took place- at the 
 southern station, but a much greater deviation was occasioned by the at- 
 traction of the mountains at Kleip Fonteyn. The errors at both stations, 
 however, conspired together in reducing the amplitude of the arc, agree- 
 ably to the remark of Colonel Everest. Mr. Maclear has earned for him- 
 self a high place among living astronomers by the ability with which he 
 has executed this important geodetic operation. It is gratifying to reflect 
 that his labours have removed a serious difficulty from the science of 
 astronomy, since we are now assured that the actual measurement of 
 meridional arcs on each side of the equator concurs with the theory of 
 gravitation, and the experiments with the pendulum, in assigning the same 
 ellipticity to both hemispheres. 
 
 The arc of the meridian connected with the trigonometrical survey of 
 Great Britain now extends from Dunnose, in the Isle of Wight, to Balta, 
 one of the Shetland Isles, and embraces an amplitude of 10" 7' 55".28. 
 The latitudes were determined with Ramsden's zenith sector at ten dif- 
 ferent places, including the two extreme stations. When the whole course 
 of triangulation was executed, the latitudes at the various stations were 
 then computed by means of an assumed value of the ellipticity, and the 
 relative bearings and distances, setting out from Greenwich, with which 
 the operations were trigonometrically connected. The latitudes found in 
 this manner for the two extreme stations, on being compared with those 
 determined with the zenith sector, presented a discordance which seemed 
 to imply an error either in the observations, or in the assumed value of the 
 ellipticity. The latitude of Dunnose was again determined with the new 
 Ordnance zenith sector*, but no error was discovered in the previous mea- 
 surement. Another station was then selected about a mile distant, and 
 the latitude, 011 being determined with the same instrument, was found to 
 differ as much as 3". 2 from the result obtained at the original station. 
 This circumstance is the more remarkable, as the surrounding country 
 does not seem to indicate the existence of any disturbing influence. The 
 latitude as thus determined at the new station coincided exactly with that 
 previously found by a geodetic process, and thereby afforded an important 
 confirmation of the value of the ellipticity upon which the latter result 
 depended. The computed and observed latitudes of the northern extre- 
 mity of the arc at Balta presented also a similar discordance, and were 
 similarly reconciled together by repeating the observations with the zenith 
 sector at a place in the neighbourhood of the original station. The me- 
 thod of determining the latitude of a place by connecting it trigonome- 
 
 * The superb instrument of Ramsden, having been deposited for safety in the ar- 
 moury of the Tower, was unfortunately destroyed by the fire which consumed that part 
 of the building in 1841. 
 
150 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 trically with a distant station, is probably destined to throw much valuable 
 light on the subject of local disturbance, especially since the true figure 
 of the earth is now pretty well ascertained. 
 
 It will readily appear on the inspection of a map that the position of 
 the British Isles is well adapted for -the measurement of an extensive arc 
 of parallel. An important illustration of the truth of this remark has 
 been recently afforded by Mr. Airy's determination of the arc of longitude 
 comprised between Greenwich and Valentia, a small island on the south- 
 west coast of Ireland #. This island is situated about 11 west of 
 Greenwich, and lies nearly in the same latitude with it. Mr. Airy 
 proposed in the first instance to determine the exact difference of the 
 longitudes of the two places by the transportation of chronometers, and 
 then to effect the same object by means of the bearings and distances 
 assigned by the Ordnance Survey, combined with certain assumed elements 
 of the earth's figure. If the two results were found to agree within 
 sufficiently narrow limits, it might then be fairly presumed that the 
 elements of the earth's figure were well determined. On the other hand, 
 if they differed to a sensible extent, the amount of the difference would 
 serve to indicate the correction which it would be necessary to apply to 
 the assumed elements. Feagh Main, in the island of Valentia, was 
 selected as the extreme western point of operations, while Kingston, near 
 Dublin, and Liverpool, were used as intermediate stations. The elements 
 of the earth's figure, assumed as the basis of the geodetic calculations, 
 were those which Mr. Airy had arrived at, by a discussion of arcs of the 
 meridian, and have been already mentioned in this chapter. The com- 
 parison of the chronometrical and geodetic arcs exhibited a most gratifying 
 accordance, and thereby afforded a valuable confirmation of the assumed 
 elements of the earth's figure f. This is assuredly not the least valuable 
 of the many results for which astronomy is indebted to Mr. Airy. 
 
 We now proceed to give some account of the researches that have been 
 prosecuted for the purpose of deducing the ellipticity of the earth from the 
 variation of gravity at its surface. We have already mentioned that 
 
 * Mem. Ast. Soc., vol. xvi. 
 
 'f The following are the results obtained by a comparison of the various geodetic and 
 chronometrical arcs. 
 
 Geodetic arc of longitude from Greenwich to Liverpool . . 12 m s .35 
 Chronometrical arc 12 .05 
 
 Chronometrical arc smaller .30 
 
 Geodetic arc from Greenwich to Kingston 24 m 31 s .48 
 
 Chronometrical arc ...... 24 31 .20 
 
 Chronometrical arc smaller .28 
 
 Geodetic arc from Greenwich to Feagh Main 41 m . 23 s .07 
 
 Chronometrical arc 41. 23 .23 
 
 Chronometrical arc larger 0.16 
 
 Geodetic from Liverpool to Kingston 12 m . 31 s . 13 
 
 Chronometrical arc .... ..... 12 31 .15 
 
 Chronometrical arc larger .02 
 
 Geodetic arc from Kingston to Feagh Main 16 m 51 s .59 
 
 Chronometrical arc ..... 16 62 .03 
 
 Chronometrical arc larger ." . _ .44 
 
HISTORY OF PHYSICAL ASTRONOMY. 151 
 
 Clairaut's theorem enables us to ascertain the value of this element when 
 once we know the relative intensities of gravity in two different latitudes. 
 The pendulum which Huygens had already applied so admirably to the 
 measurement of time derived from this circumstance a vast accession of 
 importance in the estimation of astronomers. In order to understand how 
 the oscillations of a pendulum lead to a knowledge of the figure of the 
 earth, it is necessary to obtain a clear view of the various circumstances 
 which affect the rate of oscillation. A brief notice of them here may 
 not perhaps be unacceptable to the reader, as they are inseparably 
 associated with the history of the application of the pendulum to scientific 
 purposes. 
 
 When a pendulum oscillates in vacuo through very small arcs, the rate 
 of oscillation will depend on the length of the pendulum and the intensity 
 of the moving force. If the oscillations be supposed indefinitely small, a 
 simple relation connects these three elements together, so that by means 
 of it we can ascertain the value of any one of them when the other two are 
 already known. Hence the intensity of the moving force may be readily 
 derived from the length of the pendulum and the rate of oscillation ; and 
 if the latter element remain constant, or, in other words, if the pendulum 
 continue to perform the same number of oscillations in the same time, the 
 variation of the moving force will be indicated by the different lengths 
 which it will be found necessary to assign to the pendulum. On the other 
 hand, if the length of the pendulum be assumed to be constant, the 
 variation of the moving force will be indicated by the greater or less 
 quickness with which the oscillations are performed. Hence arise two 
 distinct methods of comparing the different intensities of a force by means 
 of experiments with the pendulum. In the one case, the variation of force 
 is thrown upon the length of the pendulum ; in the other, it is thrown 
 upon the rate of oscillation. Both these methods have been employed in 
 determining the variation of gravity at the earth's surface. 
 
 The preceding remarks have reference to the purely mfthematical 
 theory of the pendulum, and therefore do not take cognizance of those 
 disturbing causes which in all [cases complicate physical inquiries. It is 
 necessary then to investigate the effects produced by these disturbing 
 causes, so that by subducting them from the phenomenon we may arrive 
 at the abstract conditions which form the basis of our reasoning. Hence 
 arise various corrections which it is necessary to take into account before 
 the experiments with the pendulum can be made available for the purpose 
 of determining the ellipticity of the earth. 
 
 In the first place, the theory of oscillation above stated supposes that, in 
 all experiments with the same pendulum, its length remains constant. 
 This, however, is a condition which cannot obtain in nature, for the 
 fluctuations of temperature will cause the pendulum continually to vary in 
 length, and the effect of this variation will manifestly be to disturb the 
 rate of oscillation. In order then to render the theory applicable to the 
 actual results of experiment, a certain standard of temperature is assumed, 
 and the effect due to the deviation from this standard as indicated by the 
 thermometer is then computed and applied to the actual rate of oscillation. 
 This is termed the correction for temperature. 
 
 Again, the oscillations of the pendulum are supposed to be indefinitely 
 small. In reality, however, they all possess a finite magnitude, and also 
 vary continually from one oscillation to another. Both these circumstances 
 will cause the number of oscillations actually performed in a given time to 
 
152 HISTORY OF PHYSICAL ASTRONOMY. 
 
 differ in all cases from the number of indefinitely small oscillations which 
 would be performed in the same time. In every case of actual experiment 
 the time of a single oscillation will exceed a certain finite quantity 
 depending on the length of the pendulum and the intensity of the moving 
 force; but, the smaller the arc is, the more nearly will the time of 
 oscillation approach this quantity ; which may, therefore, be considered as 
 the time corresponding to indefinitely small oscillations. Hence, in order 
 to reduce the experiments to an accordance with theory, the effect due to 
 the magnitude of the arc is computed, and then applied to the actual rate 
 of oscillation. This is termed the correction for the amplitude of the arc. 
 
 The third correction which it is necessary to take into account, in 
 conducting experiments with the pendulum, depends on the fact that the 
 force of gravity varies at different distances from the centre of the earth. 
 Clairaut's theorem has reference to the variation of gravity at the surface 
 only of the terrestrial spheroid. It is necessary, therefore, to make 
 allowance for the altitude of the place where the experiments are made, by 
 diminishing the force indicated by the oscillations, in the ratio of the 
 square of the distance from the earth's centre. 
 
 Lastly the oscillations are supposed to take place in a vacuum. In 
 reality, however, they are performed in a medium of air. Newton first 
 considered, in accordance with mathematical principles, the effect produced 
 on the motion of a pendulum by the resistance of the air. He has 
 demonstrated, on the two hypotheses of the resistance being proportional 
 to the first and second powers of the velocity, that, when a pendulum 
 makes very small oscillations in a cycloid, it does not experience any 
 sensible retardation from this cause*. Poisson subsequently showed that 
 this was also true for a pendulum oscillating in a circle when the arcs are 
 supposed very small f ; in fact, although the resistance of the air opposes the 
 action of gravity when the pendulum is descending to a vertical position, 
 and in consequence tends to prolong the time of oscillation, yet, when the 
 pendulum is ascending on the opposite side, the same cause conspires with 
 gravity in destroying the velocity, and on this account tends to shorten 
 the time of oscillation. A compensation thus takes place between every two 
 half oscillations, which restores the times of the whole oscillations to nearly 
 a uniform state, rendering necessary only the correction due to the 
 amplitude of the arc. It must be remarked, however, that this conclusion 
 is founded 011 an imperfect conception of the nature of the resistance 
 offered by the air ; for it is assumed that the particles of the latter, as soon 
 as impinged on, immediately afterwards cease to exercise any influence 
 upon the motion of the pendulum, either directly or by means of the 
 agitation they excite among the surrounding particles of the medium. 
 Newton, indeed, did not fail to perceive that this view of the question did 
 not accord with the real condition of nature, for he remarked that the pen- 
 dulum while descending with accelerated velocity would continue to operate 
 upon the particles of the medium after the first impact, and that the time 
 of oscillation would in consequence be prolonged, while, on the other hand, 
 when the pendulum was ascending on the opposite side, the continual 
 diminution of the velocity would allow the particles to escape from a similar 
 succession of impacts ; and hence the effect of the resistance in the one 
 half of the arc of oscillation would not be exactly compensated by the 
 
 * Princip. , lib. ii. prop. 26 et 27. 
 
 f Journal de 1'Ecole Polytechnique, tome vii. 
 
HISTORY OF PHYSICAL ASTRONOMY. 153 
 
 corresponding effect in the other half. It was generally considered, how- 
 ever, that, when the oscillations are very small, the disturbance arising 
 from the resistance of the air was altogether insensible. We shall have 
 occasion presently to mention a series of experiments which clearly esta- 
 blished the fallacy of this opinion. 
 
 But the circumambient air exercises on bodies a statical effect, which is 
 totally independent of the resistance it offers to their motion. Since a 
 body immersed in a fluid suffers a diminution of weight equal to that of 
 the fluid displaced by it, a pendulum will manifestly oscillate more quickly 
 in a vacuum than it will do in air. It is necessary, therefore, in all experi- 
 ments to reduce the oscillations to those which would take place in a 
 vacuum, by computing the effect due to the weight of the atmosphere as 
 indicated by the barometer. This has been termed the correction for the 
 buoyancy of the atmosphere. 
 
 Numerous experiments were made with the pendulum in the course of 
 the last century, for the purpose of ascertaining by means of them the 
 ellipticity of the earth ; but, as they were not conducted with due attention 
 to all those minute circumstances which affect such delicate operations, 
 they cannot be considered as worthy of any reliance. We have already 
 mentioned that experiments of this kind may be conducted by two distinct 
 methods. The length of a pendulum which performs a certain number of 
 oscillations in a given time (for example, the seconds' pendulum) may be 
 determined in different latitudes, and the results on being compared 
 together will indicate the variation of gravity, and hence, also, the ellipticity 
 of the earth. The same object may also be effected by transporting an 
 invariable pendulum to different latitudes, and noting the number of 
 oscillations which it makes in a given time at each place. This is generally 
 considered to be the safest mode of experimenting, as it is independent of 
 the absolute length of the pendulum, the ascertainment of which at any 
 time is an operation of extreme delicacy. 
 
 Borda, a French philosopher of great merit, was the first who deter- 
 mined the length of the seconds' pendulum with sufficient accuracy for 
 scientific purposes. This step was suggested by the measurement of the 
 great arc of the meridian of France, which took place towards the close 
 of the last century, and the operation was conducted by him with consum- 
 mate skill in all its details. In 1807, Biot determined, by this method, 
 the lengths of the seconds' pendulum at various stations of the arc between 
 Dunkirk and Formentera, and the results obtained by him may be con- 
 sidered as the earliest data of this kind which fully deserved the confidence 
 of astronomers. This distinguished philosopher afterwards made similar 
 experiments at various other places in the south of Europe, and also at 
 Leith and Unst in the British Isles. Comparing together the lengths of 
 the seconds' pendulum at Unst and Formentera, he obtained -3-^-5- for the 
 value of the earth's ellipticity. This result agrees very well with that 
 derived from the comparison of geodetic measurements, and is doubtless a 
 very near approximation to the truth. With respect to other stations, 
 however, it must be acknowledged that the results were not in all cases 
 equally satisfactory. 
 
 In 1818, fresh interest was awakened in experiments of this kind by 
 Captain Kater's invention of a new method of great ingenuity for deter- 
 mining the length of the seconds' pendulum. Huygeus had already shewn 
 that, whatever be the form of an oscillating body, the centres of suspension 
 and oscillation are convertible. Availing himself of this beautiful property, 
 Captain Kater attached two points of suspension to a pendulum, and then 
 
154 HISTORY OF PHYSICAL ASTRONOMY. 
 
 by means of a simple adjustment he brought it to make the same number 
 of oscillations in a given time from whatever point it was suspended. 
 When this took place, it clearly followed that the length of a simple pen- 
 dulum oscillating at the same rate was measured by the distance between 
 the two points of suspension *. Captain Jvater shortly afterwards made 
 experiments with the pendulum at various stations of the British arc. 
 He employed a pendulum of a constant length in all his operations, and 
 determined the variation of gravity by counting the number of oscillations 
 which it made at each station in a mean solar day. A comparison of the 
 results obtained by him at Unst, in the Shetland Isles, and Dunnose, in 
 the Isle of Wight, the two extreme stations, gave -j-$ T for the ellipticity 
 of the earth f. One peculiarity of these experiments consisted in the cor- 
 rection for the altitude of the station being different from that hitherto 
 employed. Dr. Young had previously remarked that this correction was 
 in all cases too great, as no account was taken of the attraction of the 
 elevated mass on which the experiments in each instance were madej. 
 If we were raised on a sphere a mile in diameter, and having a density 
 equal to the mean density of the earth, its attraction would be about -^^th 
 of the attraction of the whole earth, and the correction for the elevation of 
 the station, which would be -3-^-5 ^ ^e attraction varied merely according 
 to the inverse square of the distance, would be thereby reduced to -^oVo' or 
 only about three-fourths of the usual correction. Dr. Young's researches 
 induced him to conclude, that if the mean density of the earth be assumed 
 equal to 5.5, and that of an elevated tract of table land to be 2.5, the true 
 correction will be less than that hitherto employed in the ratio of 66 to 
 100. The necessity for a change in the usual correction, on the grounds 
 assigned by the philosopher just cited, cannot admit of any doubt; but the 
 true correction, which it will be necessary to apply in each case, will always 
 be liable to great uncertainty on account of our ignorance of the density of 
 the elevated mass, and the exact conformation of its materials. For these 
 reasons it will generally be the safest mode of proceeding to perform all ex- 
 periments of this kind at inconsiderable altitudes above the level of the sea. 
 In the year 1817, Captain Freycinet, of the French Navy, was sent out 
 by his government on a voyage round the world, one of the principal objects 
 of which was to swing the pendulum in different latitudes. Experiments 
 were made by him at various stations on each side of the equator, and a 
 comparison of his results gave ^V-^<r ^ or the ellipticity of the earth . 
 His countryman, Captain Duperrey, made a number of similar experiments 
 in the course of an expedition of discovery which he commanded in the 
 years 1822-25. The ellipticity assigned by a comparison of his results 
 was -jf 7$-J.-|y \\. A great number of valuable experiments with invariable 
 pendulums were made by Captain SabineU in different parts of the world. 
 He obtained -?$%.-$ for the ellipticity, as the final result deducible from 
 them. Experiments with invariable pendulums have also been made by 
 Goldingham *#, at Madras, and, by his directions, at a small island in the 
 
 * Phil. Trans. 1818. f Ibid. 1819. J Ibid. 1819. 
 
 This is the value of the ellipticity which Mr. Baily deduced from Freycinet's obser- 
 vations after applying to them the true correction for the reduction to a vacuum. See 
 Mem. Ast. Soc., vol. vii. For an account of Freycinet's experiments, see Voyage autour 
 du Monde. Paris, 1825. 
 
 || This result is also that of Mr. Baily. For an account of Duperrey's experiments, 
 see the Connaissance des Temps for 1830. 
 
 1 Account of experiments for the purpose of determining the Figure of the Earth, 
 London, 1823. 
 
 ** Phil. Trans. 1822. 
 
HISTORY OF PHYSICAL ASTRONOMY. 155 
 
 Indian Ocean, almost under the equator ; by Hall*, at various places in the 
 Pacific Ocean; by Sir Thomas Brisbane f, at New South Wales ; by Foster J, 
 at Port Bowen, in the North Seas ; by Fallows , at the Cape of Good Hope ; 
 and by Leutke||, an officer in the Kussian navy, at several places in both 
 hemispheres. In 1826, Bessel determined the length of the seconds' pendu- 
 lum with great accuracy by a new method. Having fixed two points of sus- 
 pension in a vertical position with respect to each other, he suspended from 
 each of them a spherical ball by a fine wire. The distance between the two 
 points of suspension was entirely arbitrary. Bessel made it exactly equal to 
 the Peruvian toise. The two pendulums when in a vertical position were 
 equally depressed, and therefore the difference of their lengths was 
 measured by the distance between the points of suspension. The depres- 
 sion of the lowest parts of the surfaces of the balls to the same level was 
 effected by means of a delicate apparatus, termed the lever of contact. 
 From an approximate knowledge of the lengths of the pendulums, it was 
 easy to derive the correction due in each case to the spherical form of the 
 ball. Hence, the difference of the lengths and the difference of the cor- 
 rections being given, the difference of the lengths of the simple pendulums 
 corresponding to the two points of suspension was readily assignable. 
 Again, by counting the number of oscillations performed in a given time 
 by each pendulum, the ratio of the lengths of the simple pendulums was 
 also ascertained. By means of these two data, Bessel was enabled to com- 
 pute the absolute length of each of the simple pendulums. This method 
 of determining the length of the seconds' pendulum is generally considered 
 to be susceptible of greater precision than any other which has been 
 devised for the same purpose. 
 
 While Bessel was engaged in the experiments just referred to, he dis- 
 covered that the usual correction for reducing the oscillations of a pendulum 
 to a vacuum were erroneous to a considerable extent. This important fact 
 was first announced by him in a memoir which appeared in the volume of 
 the Berlin Academy of Sciences for 1826. He established its reality 
 beyond dispute ; first, by swinging two pendulums in air, one of brass and 
 the other of ivoiy, and then by swinging the same brass pendulum in air 
 and in water. It appeared from both experiments that the retardation of 
 a pendulum oscillating in a fluid medium was greater than had been 
 hitherto imagined. In the one case he found that the true correction for 
 reducing the oscillations to a vacuum exceeded the correction usually em- 
 ployed in the proportion of 1.956 to 1 ; and in the other case, in the pro- 
 portion of 1.625 to I. He attempted to account for this increase in the 
 amount of retardation by ascribing it to the influence of a coating of air, 
 which, according to him, adheres to the pendulum, and is dragged along 
 with it during its motion. The mass of the pendulum being enlarged by 
 this addition, while the moving power remains the same, it is clear that 
 the accelerative force of each particle will be less intense than it would be 
 in a vacuum, and that a diminution of motion will ensue as a necessary 
 consequence. It is singular that, as early as the year 1786, Du Buat, a 
 French experimentalist, recognised the existence of this retardation, and 
 even endeavoured to give an explanation of its physical origin; but it 
 appears to have entirely escaped the notice of all philosophers until the 
 period of its rediscovery by Bessel. 
 
 * Phil. Trans. 1823. -] Ibid. 1823. J Ibid. 1826. Ibid. 1830. 
 
 || Mem. Acad. des Sciences de St. Petersburg; see also Phil. Mag. 1832. 
 
156 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 The researches of the astronomer just mentioned, being mixed up with 
 theoretical views which were not clearly established, the Board of Longi- 
 tude of this country resolved to submit the question to the issue of direct 
 experiment, by swinging the same pendulum both in air and in a vacuum. 
 The operations for this purpose were executed with great care by Colonel 
 Sabine, at the Royal Observatory of Greenwich, in the year 1828. The 
 mean of his results gave 10.36 as the excess of the number of oscillations 
 in a mean solar day, made by a pendulum swinging in vacuo over the 
 corresponding number of oscillations made by the same pendulum swinging 
 in air. The old correction for the buoyancy of the atmosphere gave only 
 6.26 oscillations. It followed then that the coefficient for the reduc- 
 tion to a vacuum should be increased in the proportion of 1.655 to 1*. 
 Mr. Baily shortly afterwards repeated these experiments with a great 
 variety of pendulums and arrived at results of a similar character f. The 
 amount of retardation differed with the pendulum employed in the 
 experiment, and was found to depend mainly on its form and extent of 
 surface. It appeared also that the air was dragged chiefly by the parts of 
 the surface which were perpendicular to the plane of motion, and that only 
 a small quantity adhered to the sides. Mr. Baily clearly shewed that the 
 true correction can only be determined with precision by means of direct 
 experiments with each particular pendulum J. 
 
 The usual correction for reducing the oscillations of a pendulum to a 
 vacuum having thus been demonstrated, by evidence of the most indis- 
 putable character, to be too small, it followed that all the results which had 
 been derived from experiments hitherto performed were more or less 
 erroneous. When the question relates to the determination of the figure 
 of the earth, the error depending on the imperfect reduction is indeed 
 small ; since in this case the variation of gravity at the surface of the 
 terrestrial spheroid, and not its absolute intensity, forms the subject of 
 research; but, as in delicate inquiries of this nature the most minute 
 circumstance must be taken into account, the true correction has been 
 employed in all subsequent reductions. 
 
 The most extensive series of experiments with the pendulum which 
 have been made by any individual are due to the late Captain Foster, who 
 commanded a scientific expedition which was sent out to the South Seas 
 by the Government of this country in the year 1829. This talented 
 officer having unfortunately been drowned a little before the time appointed 
 for the return of the expedition, his papers, upon being brought to 
 England, were put into the hands of the late Mr. Baily, who drew up a 
 detailed account of them, which is contained in the seventh volume of the 
 Memoirs of the Astronomical Society. The experiments were made at four- 
 
 * Phil. Trans. 1829. + Phil. Trans. 1832. 
 
 J Poisson has adopted a different opinion respecting the physical origin of this 
 correction. He considers that the successive impulses of the pendulum would give rise 
 to alternate contractions and expansions of the surrounding medium, whence the particles 
 of the latter, by their reaction, could not fail to produce a sensible effect on the rate of 
 oscillation. The correction is thus made to depend on the resistance offered to the pendu- 
 lum by the aerial medium, the mode of action being considered in its most absolute 
 character, and independently of any assumed relation between the resistance and the 
 velocity. Proceeding upon this principle, Poisson has investigated the correction by a 
 profound analysis, and has arrived at results which, in some instances, are confirmed by 
 direct experiment. See Mem. de tlnstitut, tome xi., or the Connaissance des Temps for 
 1834. This view of the subject has also been adopted by Plana, Sir John Herschel, and 
 several other eminent philosophers. 
 
HISTORY OF PHYSICAL ASTRONOMY. 157 
 
 teen different stations included between 10.38 / north latitude and 62. 56' 
 south latitude. All the details of these experiments appear to have been 
 conducted with the most scrupulous regard to accuracy, and the results 
 deserve to be classed among the most valuable data we possess for 
 determining the ellipticity of the earth by means of the pendulum. Mr. 
 Baily obtained ^J-Ts ^ or tne va l ue of the ellipticity as the final result 
 deducible from Captain Foster's experiments. He also arrived at an 
 ellipticity equal to ^-g^fp V combining together the results of all the 
 experiments hitherto made with invariable pendulums. These evaluations 
 agree very nearly with each other, and also with that due to Colonel 
 Sabine, whose experiments were more extensive than those of any other 
 voyager, previous to Captain Foster. 
 
 The experiments with the pendulum generally agree in assigning to the 
 earth an ellipticity somewhat greater than that derived from the com- 
 parison of arcs of the meridian. In the one case the ellipticity may be 
 said to be ^^ ; in the other case only -^-^. The perturbations of the 
 moon again "indicate an ellipticity equal to T ^. The agreement of the 
 second and third of these values is sufficiently satisfactory. It is difficult, 
 however, to account for the discordance of the first and second ; and also 
 for the anomalies which present themselves in some instances when only 
 two arcs of the meridian or two experiments with the pendulum form the 
 grounds of comparison. The results of recent geodetic operations concur 
 in shewing that the meridional anomalies are mainly attributable to the 
 effects of local disturbance, and that, when the amount of this disturbance 
 can be in any case independently ascertained, and then eliminated from 
 the measurements, the comparison of the latter may be satisfied by an 
 ellipticity a little greater than -g-^*. With reference to the anomalies 
 which occur in pendulum experiments, it appears that the results generally 
 indicate the intensity of gravity to be greater on islands than on con- 
 tinents. This is partly explained by the greater density of islands which 
 are frequently of volcanic origin ; but, on the other hand, it is not to be 
 denied that the density of the surrounding ocean is considerably less than 
 the mean density of the earth, and therefore ought to produce an effect of an 
 opposite kind. Much doubtless will depend on the depth of the ocean at 
 the place where the experiments are made, and the nature of the stratum 
 on which it rests ; for it must be borne in mind that, although Clairaut's 
 theorem allows the density of the terrestrial spheroid to vary from one 
 stratum to another, according to any law whatever, it supposes the 
 density to be uniform throughout each stratum. The influence exercised 
 on experiments with the pendulum by "the geological character of the 
 substratum was first remarked by Colonel Sabine. 
 
 When we consider how difficult it is to form a just estimate of the 
 irregularities of the earth's surface, and the variations in the density of 
 the exterior stratum, we have ample reason to be surprised that the 
 anomalies we have been referring to are not greater than they really are. 
 "If the form of the earth's meridian," says Mr. Airy, "were traced on 
 paper, the nicest eye would be unable to distinguish it from a circle. The 
 
 * Some idea of the effect of local disturbance may be formed when we state that, at the 
 station of Banog, within fifty miles of the Himalayah Mountains, Colonel Everest found 
 the difference between the computed and observed azimuths to amount to as much as 
 20".156. It is true that the measurement of azimuth angles is the most delicate part of 
 geodetic operations ; but, in the present instance, the discrepancy manifestly exceeds 
 the probable error of observation. 
 
158 HISTORY OF PHYSICAL ASTRONOMY. 
 
 ellipticity is so small that the closest inspection without measure could not 
 judge which was intended for the greater and which for the smaller axis. 
 The whole quantity in dispute is less than one-sixteenth of this ellipticity. 
 Instead of being surprised that such a difference exists, we may well be 
 astonished at the accuracy of modern measures of all kinds, which make 
 so small a quantity a subject of controversy."* 
 
 As soon as astronomers were persuaded that the principle of gravitation 
 extended to the constituent parts of the celestial bodies, it became an 
 interesting question to ascertain whether the attraction of masses at the 
 earth's surface exerted any appreciable influence. The first attempt to 
 establish this fact was made by Bouguer and his associates, while 
 engaged in measuring an arc of the meridian in South America. Astro- 
 nomical observations having been made in the neighbourhood of the lofty 
 mountain Chimborazo, it was found that the attraction of the latter caused 
 the plumb line to deviate towards it to the extent of 7". 5. This result 
 was so far confirmatory of the Newtonian theory ; but it was generally 
 admitted that the experiment had not been made with sufficient care to 
 merit the confidence of astronomers. The question was not mooted again 
 until 1772, when, Dr. Maskelyne having suggested the repetition of the 
 experiment to the Royal Society, it was resolved by that body that 
 immediate steps should be taken to carry it into effect. The mountain of 
 Schehallien, in Perthshire, was selected as offering peculiar advantages 
 for this purpose. It is a narrow ridge running nearly east and west, and 
 rising to an elevation of about 2000 feet above the level of the surround- 
 ing country. The mode of proceeding employed in the experiment was 
 this: two stations were selected, one on the north side and the other on 
 the south side of the mountain ; and the difference of their latitudes \vas 
 determined, first by means of astronomical observations at each station, 
 and then by means of the meridional distance between the two stations, 
 and certain assumed elements of the earth's figure. Now it is clear that 
 the attraction of the mountain would compel the plumb line to deviate 
 from its vertical position, and would thereby occasion a displacement of 
 the zenith point opposite in direction at each station. Hence the 
 difference of latitudes as determined by astronomical observation ought to 
 exceed the difference resulting from geodetic computation by the sum of 
 the displacements of the zenith points ; and this latter quantity is mani- 
 festly the measure of the sum of the attractions exerted by the mountain 
 at the two stations. Now the zenith distances of a certain number of stars, 
 having been determined at both stations, were found to indicate a difference 
 of latitude amounting to 54".6. The meridional distance between the 
 stations, as computed by a process of triangulation, was 4364.4 feet, and 
 the difference of latitude hence deduced was 42". 9. The resulting 
 difference, II". 7, was, therefore, the quantity due to the attraction of the 
 mountain at the two stations. Thus it was established by actual ex- 
 periment that the principle of gravitation operates not only between the 
 bodies of the solar system, but also between the smaller masses of matter 
 of which they are composed. 
 
 An interesting question suggested by the experiment just alluded to is 
 that relative to the mean density of the earth. It is clear that, if we knew 
 the quantity of matter contained in the mountain, this datum, combined 
 with the ratio of the attraction of the mountain to that of the earth, as 
 
 * Encycl. Metrop., Art. Figure of the Earth. 
 
HISTORY OF PHYSICAL ASTRONOMY. 159 
 
 assigned by the preceding experiment, would enable us to ascertain the 
 absolute mass of the earth ; and, the volume of the latter being already 
 known, we might hence determine its mean density. The mass of 
 Schehallien was determined by computing its volume trigonometrically, 
 and assuming its mean density to be two and a half times the density of 
 pure water. The final result was that the mean density of the earth 
 might be considered equal to four and a half times the density of pure 
 water*. The astronomical observations connected with this famous 
 experiment were made by Dr. Maskelyne, and the laborious calculations 
 to which it gave rise were executed by Dr. Hutton. . Playfair, having 
 subsequently ascertained by experiment the densities of the different 
 materials composing the mountain, and also their positions relative to the 
 two places of observation, arrived at the conclusion that the mean density 
 of the earth is contained between 4.867 and 4.559, the mean density of 
 pure water being supposed equal to unity. This gave 4.713 for the mean 
 result f. 
 
 Soon afterwards an attempt was made upon a much smaller scale to 
 accomplish the object sought for in the Schehallien experiment, by means 
 of an apparatus termed the torsion balance. It consisted essentially of a 
 deal rod suspended by a fine wire and having two leaden balls about two 
 inches in diameter attached to its extremities. Two leaden spheres 
 about eight inches in diameter were then brought near the smaller ones on 
 opposite sides of the rod, and their attraction, combined with the torsion of 
 the wire, produced an oscillatory horizontal motion of the rod on each side of 
 a position of equilibrium. Now the extent and the time of oscillation 
 depend, cateris paribus, on the relative intensities of the acting forces, or, 
 in other words, on the torsion of the wire and the attraction of the spheres. 
 Hence, if these two elements be determined by observation, we shall be 
 enabled to ascertain the intensities of the two forces, and to compare the 
 attraction of the spheres with the earth's attraction, as indicated by the oscil- 
 lations of a vertical pendulum. Finally, since we know the quantity of 
 matter contained in the spheres, we can arrive at the quantity of matter 
 contained in the earth; and. knowing its volume, we may hence derive its 
 mean density. This delicate apparatus was originally devised by Michell, 
 but we owe to Cavendish the first application of it to the determination 
 of the mean density of the earth. From seventeen experiments made 
 with it, that philosopher concluded that the mean density of the earth is 
 5.48, that of water being unity J. 
 
 In 1836, M. Reich, of Freiburg, repeated Cavendish's experiments; 
 the only difference being that he used one ball instead of two. The 
 average of all his results gave him 5.438 for the mean density of the 
 earth. By far the most valuable experiments that have been made with 
 the torsion balance are due to the late Mr. Baily . They were conducted 
 at the public expense upon a recommendation to that effect having been 
 made to the Government by the Astronomical Society ; and they extended 
 over the whole period comprised between October, 1838, and May, 1842. 
 The final result deduced by Mr. Baily was that the mean density of the 
 earth is equal to 5.660 ||. This may be considered as the nearest 
 
 * Phil. Trans., 1776. f Phil. Trans. 1811. 
 
 { Phil. Trans. 1798. $ Born at Newbury, 1774; died in London, 1844. 
 
 || Mem. Ast. Soc., vol. xiv. 
 
160 HISTORY OF PHYSICAL ASTRONOMY. 
 
 approximation to the truth which has yet been arrived at by philosophers *. 
 It is remarkable that Newton conjectured that the mean density of the 
 earth is about five or six times the density of water f. 
 
 The Schehallien experiment for determining the mean density of the 
 earth is purely statical ; on the other hand, the experiment with the 
 torsion balance is founded on dynamical principles, being in fact a case of 
 the horizontal pendulum. The vertical pendulmn has also been em- 
 ployed for a similar purpose. The attraction on the top of a high 
 mountain may be decomposed into two parts ; one of which is the 
 attraction at the level of the sea diminished in the inverse ratio of the 
 square of the distance, and the other is the attraction of the mountain 
 itself. Hence, if the intensities of gravity on the mountain and at the level 
 of the sea be determined by observation, the difference of the two forces 
 will indicate the attraction due to the mountain, and, by a process similar 
 to that employed in the Schehallien experiment, we shall be enabled to 
 ascertain the mean density of the earth. Experiments for this purpose 
 were made by Carlini at the hospice of Mount Cenis, which has an 
 elevation of 6375 feet above the level of the sea ; and the conclusion at 
 which he arrived was that the mean density of the earth is 4.39, that of 
 water being unity. 
 
 We have mentioned already that D'Alembert succeeded in accounting 
 completely for the motion of the earth's axis in space, arising from the action 
 of the sun and moon upon the redundant matter accumulated round the equa- 
 tor. It still remained, however, for geometers to ascertain whether the dis- 
 turbing forces affected the position of the axis relative to the surface of the 
 terrestrial spheroid, or whether they occasioned any change in the velocity 
 of rotation. Observation, indeed, gave a negative answer to both of these 
 questions; for neither the latitudes of places on the earth's surface nor 
 the length of the day appeared to have undergone any variation from the 
 earliest period of history. It was desirable, however, to establish these 
 facts by demonstrative reasoning founded on the theory of gravitation ; 
 for, in the absence of such conclusive evidence, there existed no grounds 
 for supposing that the position of the axis and the velocity of rotation 
 might not be affected by secular inequalities, which, though slow in their 
 developement, would in the lapse of ages become sensible by continual 
 accumulation. If the axis experienced any such displacement, the 
 position of the equator would be constantly shifting with inconceivable 
 slowness, and the sea, by always flowing towards the new position to 
 restore the equilibrium of the particles, would eventually occasion a total 
 change in the relation of land and water on the earth's surface. It is 
 clear also that the latitudes of places would be ultimately affected by the 
 displacement, and hence would ensue a corresponding alteration of the 
 seasons. Poisson first examined this point with all the attention due to 
 its importance. In an admirable paper, which was published in the 
 
 * Notwithstanding all the precautions used by Mr. Baily, he found that the resting 
 points of the balls and the times of oscillation were subject to disturbances, the cause of 
 which he was unable to explain. In the Philosophical Transactions for 1847, there is a 
 paper by Mr. Herne, of the Royal Military College of Sandhurst, in which he attempts 
 to account for these anomalies by the supposition of a magnetic state of the masses and 
 balls. 
 
 t Verisimile est quod copia materia3 totius in Terra quasi quintuple vel sextuple major sit 
 quam sit tota ex aqua constaret. Princip., lib. iii. prop. 10. 
 
HISTORY OF PHYSICAL ASTRONOMY. 16 J 
 
 Memoirs of the Academy of Sciences for 1824, he has shewn that the 
 disturbing forces of the sun and moon cannot produce, in the variables 
 which determine the relative position of the earth's axis, any secular 
 inequalities which might ultimately become sensible. He also found that 
 the velocity of rotation could not be sensibly affected hy the same cause ; 
 whence it followed that the length of the sidereal day is not subject to 
 any variation depending on the action of the sun or moon. 
 
 The conclusion at which Poisson arrived is fully borne out by an examina- 
 tion of ancient eclipses. It is clear that, if the diurnal motion of the earth 
 be variable, the period comprised between two successive returns of a star to 
 the same position relative to the horizon cannot constitute a fixed standard 
 of time ; and consequently the interval between the present time and any 
 remote epoch, when expressed in terms of the sidereal day as determined 
 by modern observation, will not correspond to the number of revolutions 
 which the earth has actually accomplished, as indicated by historical 
 records. It will follow also that if the diurnal motion constantly vary in 
 the same direction, the difference between the computed and the historic 
 epochs will increase with the lapse of time. We may therefore conclude 
 that the places of the planets, when computed for any remote epoch by 
 means of the modern value of the sidereal day, 'will differ from their actual 
 places as assigned by the recorded observations of astronomers ; and this 
 difference will be more considerable for the moon than for any other body, 
 on account of her rapid motion. Now, if the rotation of the earth is 
 really invariable, the longitudes of the sun and moon, when computed for 
 any ancient lunar eclipse, ought not to differ from 180 by a quantity 
 greater than the sum of their semi-diameters, and the difference may 
 naturally be expected to be in many cases much less. In the Con- 
 tiaissance des Temps for 1800, there is a paper by Laplace, containing 
 calculations of this nature for 27 eclipses recorded by the Chaldeans, 
 Greeks, and Arabians, and the results in all instances go to prove the 
 invariability of the sidereal day. The greatest quantity by which the 
 distance between the centres of the sun and moon differs from 180, 
 amounts to 27' 41", and relates to an eclipse which happened in the year 
 382 A.C. Even this difference, however, falls short of the sum of the solar 
 and lunar semi-diameters, and, therefore, does not preclude the possibility 
 of an eclipse having taken place. It is clear, then, that the length of the 
 sidereal day is not subject to any sensible inequalities, since the conclusions 
 deducible from the supposition of its being constant accord so well with 
 observation. In order to illustrate this interesting fact more fully, Poisson 
 assumed that the length of the day had diminished by a ten-millionth part 
 since the most ancient of the Chaldean eclipses, which happened in the year 
 720 A.C. ; and then, calculating the longitudes of the sun and moon for that 
 epoch, he found them to differ from 180 by 34'. This quantity being 
 greater than the sum of the semi-diameters of the two bodies, is incom- 
 patible with the occurrence of an eclipse, whence it follows that, during 
 the lapse of 2500 years, the length of the sidereal day has not altered by 
 so much as the ten-millionth part. 
 
 An interesting question which Laplace first considered in connexion 
 with the length of the sidereal day, is that relating to the mean temperature 
 of the earth. Various facts concur to strengthen the opinion that the 
 earth was originally a fluid mass, which subsequently became solid by a pro- 
 cess of cooling, which is even still going on. This gradual diminution of 
 temperature being necessarily accompanied by a corresponding diminution 
 
 -*- M 
 
162 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of the earth's mass, the particles composing the latter will all in con- 
 sequence approach nearer to the axis. Now, it follows immediately from 
 a well-known principle in Mechanical Science, that when a body is endued 
 with a rotatory motion, and is not exposed to the action of any extraneous 
 forces, the principal moment of inertia, or, in other words, the sum of the 
 products formed by multiplying each particle into its angular velocity and 
 the square of its distance from the axis of rotation, is a constant quantity. 
 The number of particles then remaining the same, if their distances from 
 the axis be diminished, their angular velocities must be increased, and 
 vice versa. Hence, if the dimensions of the earth be in a state of con- 
 traction from cooling, the velocity of rotation must be increasing, and the 
 length of the sidereal day must be diminishing. It is not difficult, how- 
 ever, to show that if the earth is really becoming cooler, the diminution 
 of temperature must be proceeding at a very slow rate. We have seen 
 that, during a period of 2500 years, the sidereal day has not been shortened 
 by so much as the ten-millionth part. Now, the principles of Mechanics 
 teach us that this result would ensue if the earth's radius experienced a 
 diminution of only one twenty-millionth part of its length. It follows, 
 then, that during the period which has elapsed since the earliest Chaldean 
 observations, the mean temperature of the earth has not varied to ^uch an 
 extent as to cause the terrestrial radius to contract by one twenty-millionth 
 part of its length. 
 
 The important question of the Tides has recently attracted consider- 
 able attention in this country. The Encyclop&dia Metropolitana con- 
 tains a valuable essay on the mathematical part of the subject, by Mr. 
 Airy, founded on the theory of undulations. Sir John Lubbock and Dr. 
 Whewell have been engaged during many years in determining the laws 
 of the tides by observation, and in tracing their connexion with the places 
 of the sun and moon. The results to which they have been conducted 
 by their researches are contained in a series of admirable papers, which 
 continue to be published from time to time, in the volumes of the Royal 
 Society. These distinguished philosophers are now endeavouring to do 
 for the theory of the tides what astronomers had done for the lunar 
 theory previous to the establishment of the theory of Gravitation. Let us 
 hope that their efforts will be attended with similar success, and that the 
 day is not very remote when this important branch of Physical Astronomy 
 will be in a condition to invite the researches of the geometer, and to 
 reward him with a rich harvest of results. 
 
 It is clear that if the sun and moon by their action on the earth occa- 
 sion oscillations in the waters of the ocean, they ought to produce a 
 similar movement in the atmospheric fluid. Laplace investigated the 
 theory of this subject upon a somewhat restricted hypothesis*, and Bouvard 
 undertook an extensive series of observations of the height of the baro- 
 meter, with the view of detecting periodical oscillations depending on the 
 places of the disturbing bodies. The effects, however, were so very minute 
 as to be almost entirely masked by irregularities arising from other causes, 
 and no satisfactory conclusion could be deduced from the observations. 
 
 The oscillations of the atmospheric tide will manifestly be greatest 
 near the equator, and the most favourable station for detecting them would 
 
 * Mec. Cel. liv. iv. chap, iv., liv. xiii. chap. vii. The temperature of the atmosphere 
 was assumed to be uniform, and the density at each point proportional to the compressing 
 force. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 163 
 
 be some small island in the middle of the ocean, because the barometer 
 would in that case be least liable to be affected by the fluctuations arising 
 from the irregularities of the earth's surface. With the view of throwing 
 some light on this delicate subject Captain Lefroy, of the Royal Artillery, 
 undertook a series of barometrical observations at the island of St. Helena. 
 These observations were conducted solely with reference to the place of 
 the moon, as the effect of the sun's influence was naturally expected to be 
 insensible. They extended from August, 1840, to December, 1841, and 
 therefore comprised a period of seventeen months. The mean result of 
 these observations clearly indicated the existence of a lunar atmospheric 
 tide. It gave 28.2714 inches for the height of the barometer when the 
 moon was on the meridian, and 28.2675 when she was on the horizon. The 
 difference was therefore .0039 inches*. The observations were subse- 
 quently resumed by Captain Smythe in October, 1842, and were continued 
 till September, 1843. The average of all the results obtained during this 
 period gave .00255 inches for the excess of the- altitude of the barometer, 
 when the moon was on the meridian, over the altitude when she was six 
 hours distant from it. The observations for the following two years were 
 compared together by Lieutenant Colonel Sabine at Woolwich, and the 
 results he derived from them presented a satisfactory accordance with 
 those previously obtained by Lefroy and Smythe. The average excess of 
 barometrical pressure during this period amounted to .00365 inches, or in 
 round numbers to .004 inches. It is manifest that the effect of the moon's 
 action ought to be greatest when she is in perigee, and least when she is 
 in apogee. This is unequivocally indicated by the observations, as appears 
 from the following results of the mean barometrical excess, obtained by 
 a comparison of observations made when the moon was on the medidian, 
 and when she was six hours distant from it : - 
 
 Mean excess of pressure derived 
 
 from 13 epochs of perigee, between ] OQ4()7 . } 
 
 Oct. 1843 and Sept. 1844. J 
 
 from 13 epochs of perigee, between 1 
 Oct. 1844 and Sept. 1845. f 
 
 from 13 epochs of apogee, between ) nnu 
 
 Oct. 1843 and Sept. 1844. j 
 
 from 14 epochs of apogee, between ) 
 Oct. 1844 and Sept. 1845. j 
 
 These quantities are small, but still they are sufficiently sensible to 
 establish beyond doubt the existence of oscillations in the atmosphere, 
 similar to those which affect the waters of the ocean. This is not the 
 least interesting of the many facts in physical science which would have 
 for ever escaped detection, if their existence had not been suggested by 
 the theory of gravitation. 
 
 * Phil. Trans., 1847. 
 
104 HISTOKY OF PHYSICAL ASTRONOMY. 
 
 CHAPTER XII. 
 
 Introductory Remarks. Ancient Observations of Uranus. Calculation of Tables of the 
 Planet by Delambre. Tables of Bouvard. Irregularities of the Planet. Speculations 
 respecting their Origin. Errors of Radius Vector. Researches of Geometers. Bessel. 
 Adams. Inverse Problem of Perturbation. Account of Adams' Researches relative 
 to the existence of a Planet exterior to Uranus. Results obtained by him. Researches 
 of the French Astronomers on the Theory of Uranus. Eugene Bouvard Le Verrier. 
 
 Account of his Researches Near agreement of his Results with those of Adams. 
 
 Steps taken by Airy and Challis for the purpose of discovering the Planet New 
 Results obtained by Adams Explanation of errors of Radius Vector. Account of 
 the second part of Le Verrier's Researches on the Trans- Uranian Planet. Address of 
 Sir John Herschel at Southampton. The Planet discovered at Berlin by Galle. 
 Admiration excited by the Discovery. Account of Challis' Labours. Public An- 
 nouncement of Adams' Researches. Impression produced by it. Historical Statement 
 of the Astronomer Royal. Publication of the Researches of Le Verrier and Adams. 
 Remarks suggested by the Discovery of the Planet. 
 
 THE Theory of Gravitation is not more remarkable for tlie sublimity of its 
 results than for its varied and effective character, when considered as an 
 instrument applicable to the discovery of truth. By unfolding its prin- 
 ciples, the astronomer, without leaving his observatory, has been enabled 
 to determine the distances of the sun and moon from the earth, to weigh 
 the planets as in a balance, and to educe order and stability from the 
 countless irregularities of their motions. It has conducted him to a know- 
 ledge of the figure of the earth by merely watching the motion of the moon 
 or the swinging of a pendulum, and it supplies the means of ascertaining 
 the figures of the celestial orbs without measuring their apparent dimen- 
 sions. The eccentric aberrations of comets, the ebbing and flowing 
 of the tides, and the oscillations of the atmosphere, all equally attest the 
 value of its guidance in exploring the hidden operations of nature. But a 
 still more striking triumph of this magnificent theory was reserved for our 
 own day, when the mathematician, by meditating in his chamber upon its 
 principles, has succeeded in revealing the existence of a new planetary 
 world, vastly exceeding the earth in magnitude, which had hitherto escaped 
 the scrutinies of astronomers, aided by all the powerful appliances of optical 
 science. 
 
 Soon after the discovery of Uranus by Sir William Herschel in 1781, it 
 was ascertained that astronomers had observed it on many previous occa- 
 sions without recognising it to be a planet. Even as early as 1690, Flam- 
 stead had designated it as a star of the sixth magnitude ; and from that year, 
 down to 1781, astronomers had determined its position no fewer than 
 nineteen different times, under an erroneous impression of its real nature *. 
 
 * Bode first discovered two ancient observations of Uranus; one in the Historia Celestis 
 of Flamstead (the observation of 1690), and the other in one of Mayer's Catalogues. Soon 
 afterwards Lemonnier detected three positions of the planet among his own observations. 
 Bessel, while engaged in reducing Bradley's observations, found that the position of Uranus 
 
HISTORY OF PHYSICAL ASTRONOMY. 165 
 
 These observations have proved eminently serviceable in conducting astro- 
 nomers to the true theory of the planet's motion ; for, as it takes eighty-four 
 years to effect a complete revolution round the sun, it is manifestly impos- 
 sible to arrive at definite ideas respecting the irregularities of its motion 
 except by means of observations which are considerably distant from each 
 other. In 1790, the observations of the planet had become sufficiently 
 numerous to induce the Academy of Sciences of Paris to propose the theory 
 of its motion as the subject of a prize. Delambre was on this occasion the 
 successful competitor. The elliptic elements were determined by a skilful 
 combination of the observations subsequent to the discovery of the planet, 
 and the perturbations occasioned by Jupiter and Saturn were computed by 
 means of the formulae of the Mecanique Celeste. The theory of the planet 
 established upon these principles was found to agree very well with three 
 ancient positions which had been already detected among the observations 
 of Flamstead, Lemonnier, and Mayer. Delambre employed it in cal- 
 culating tables of the planet, which continued for a few years to represent 
 the actual motion with tolerable accuracy. As time, however, wore on, 
 the discordance between theory and observation constantly increased, and 
 a growing desire was felt by astronomers that the theory should be revised 
 and employed in the calculation of new tables. This task was. undertaken 
 by Bouvard, whose tables of the planet appeared in 1821. While engaged 
 in correcting the elements for this purpose, he experienced a singular 
 cause of perplexity. He found that the earlier observations of Flamstead, 
 Mayer, Lemonnier, and Bradley, might all be satisfied by an ellipse of a 
 determinate form and position ; but he attempted in vain to include in the 
 same orbit the observations of the planet made subsequently to its discovery, 
 although these, on the other hand, might also be satisfied by an ellipse, the 
 elements of which were different from those of the other. " The construc- 
 tion of the tables, then," says Bouvard, " involves this alternative : if 
 we combine the ancient observations with the modern, the former will 
 be sufficiently well represented, but the latter will not be so, with all the 
 precision which their superior accuracy demands; on the other hand, if 
 we reject the ancient observations altogether, and retain only the modern, 
 the resulting tables will faithfully conform to the modern observations, but 
 will very inadequately represent the more ancient. As it was necessary 
 to decide between these two courses, I have adopted the latter, on the 
 ground that it unites the greatest number of probabilities in favour of 
 truth, and I leave to the future the task of discovering whether the 
 difficulty of reconciling the two systems is connected with the ancient 
 observations, or whether it depends on some foreign and unperceived cause 
 which may have been acting upon the planet." 
 
 Bouvard accordingly rejected the ancient observations, and constructed 
 his tables exclusively on the basis of those comprehended between the dis- 
 
 had been on one occasion determined by that astronomer. Burchardt, having made new 
 researches into Flamstead's Historia Celestis, discovered four additional observations of 
 the planet, one on the 2nd April, 1712, and the other three on the 4th, 5th, and 10th of 
 March, 1715. Bouvard having carefully inspected all Lemonnier's observations found 
 ten more positions of the planet. It is remarkable, that of six observations by that 
 astronomer, two were made by him on two consecutive days, and the other four on four 
 consecutive days. If it had only occurred to him to compare together his observations 
 on either of these occasions, he could not fail to have anticipated Herschel in the discovery 
 of the planet. Le Verrier, in his investigation of the theory of Uranus, rejects Flam- 
 stead's observation of the 5th March, 1712, and adopts another by the same astronomer 
 dated the 29th April, 1712, without, however, mentioning the person who first detected it. 
 
166 HISTORY OF PHYSICAL ASTRONOMY. 
 
 covery of the planet in 1781 and the year 1820. These tables, like 
 Delambre's, presented at first a very satisfactory accordance with obser- 
 vation, but after only a few years had elapsed they began to be sensibly 
 erroneous, and they continued henceforward to deviate more and more 
 from observation. The difficulty connected with the theory of the planet 
 now assumed a more definite character, for it clearly did not depend on the 
 ancient observations, since those of a more recent date were becoming 
 equally irreconcileable with the tables. 
 
 Bouvard was in all probability the first person who was led to ascribe 
 the irregularities of Uranus to the perturbations produced by an unknown 
 planet. The passage from his tables already cited contains an obscure 
 allusion to this hypothesis; but we should not be warranted on such 
 grounds in awarding to him the merit of its original conception, if we did 
 not possess abundant evidence from other sources that he had a strong 
 persuasion of its truth. In fact, the venerable astronomer appears to have 
 clung with tenacity to this explanation of the anomalies of the planet, 
 down to the latest years of his life. Nor, indeed, was the idea of a planet 
 exterior to the acknowledged boundaries of the solar system altogether 
 new. Even as early as the year 1759, we find Clairaut speculating upon 
 the probability of Halley's comet being exposed to the disturbing action of 
 a planet too remote to be visible*. 
 
 Dr. Hussey was unquestionably one of the first astronomers who had 
 the sagacity to divine the true cause of the irregularities in the motion of 
 Uranus. Writing to Mr. Airy, in 1834, he mentioned, that having care- 
 fully determined the position of Uranus on several occasions during the 
 preceding year, he was led to examine closely Bouvard 's tables of the 
 planet, and he remarked that the strange inconsistency- of the ancient and 
 modern observations had suggested to him the possible existence of some 
 disturbing body beyond Uranus f. He intimated, also, a design of sweep- 
 ing for the planet with his large reflector, provided one or more positions 
 of it were determined empirically. He added, in the same letter, that he 
 had some conversation on the subject with Bouvard, who, in reply, asserted 
 that he entertained a similar opinion with respect to the cause of the 
 planet's irregularities, and had been corresponding with Hansen respecting 
 it. Hansen replied, that one exterior planet would not account for the 
 errors of the tables, and that two planets were necessary for this purpose. 
 
 As the errors of the tables continued to increase, the conviction of 
 their real origin was constantly gaining ground among astronomers. M. 
 Valz, of Marseilles, writing to M. Arago in 1835, on the subject of 
 Halley's comet, made the following interesting remarks relative to the 
 probable existence of a Trans-Uranian planet. "I would rather have 
 recourse to an invisible planet situated beyond Uranus. Its period, 
 according to the order of the distances, would be at least triple that of the 
 comet, so that the perturbations of the latter would nearly recur at the 
 close of every three revolutions, and the calculations made for four or five 
 well-established cycles would enable us to trace them. Would it not be 
 
 * See page 104 of this work. 
 
 f Account of some Circumstances historically connected with the Discovery of the 
 Planet exterior to Uranus, by G. J3. Airy, Esq., Astronomer Royal. This important 
 collection of correspondence relating to the theoretical discovery of the planet Neptune 
 was read before the Astronomical Society on the 13th November, 1846, and was pub- 
 lished both in the Monthly Proceedings, and also in vol. xvi. of the Memoirs of the same 
 Society. The letter of Dr. Hussey, cited in the text, forms the commencement of the 
 correspondence, and is marked No. 1. 
 
HISTORY OF PHYSICAL ASTRONOMY. 167 
 
 admirable to arrive thus at a knowledge of the existence of a body which 
 cannot be perceived."* 
 
 Guided by the same sagacious and philosophical views, but reasoning upon 
 more legitimate grounds, Mrs. Somerville alludes in the following terms to 
 the probable existence of an unknown planet in the third edition of her 
 interesting little work on "The Connexion of the Physical Sciences ."f " The 
 tables of Jupiter agree almost perfectly with modern observations ; those 
 of Uranus, however, are already defective, probably because the discovery 
 of the planet in 1781 is too recent to admit of much precision in the 
 determination of its motions, or that possibly it may be subject to disturb- 
 ances from some unseen planet revolving about the sun beyond the present 
 boundaries of our system. If, after the lapse of years, the tables formed 
 from a combination of numerous observations should still be inadequate to 
 represent the motions of Uranus, the discrepancies may reveal the exist- 
 ence, nay, even the mass and orbit of a body placed for ever beyond the 
 sphere of vision." One more of such extracts will shew how strong the 
 persuasion now was respecting the existence of a Trans-Urariian planet. 
 Professor Madler, in his " Treatise on Popular Astronomy" after remarking 
 that Uranus might have been discovered by means of the perturbations it 
 produces in the motion of Saturn, alludes in the following prophetic terms 
 to the probability of discovering a planet exterior to Uranus : " Applying 
 this conclusion to a body beyond Uranus, we approach a planet acting 
 upon and disturbing it. We may, indeed, express the hope that analysis 
 will one day or other solemnize this, her highest triumph, making dis- 
 coveries with the mind's eye in regions where, in our actual state, we are 
 unable to penetrate." 
 
 The steadiness with which the errors of the tables continued to increase 
 rendered the necessity of their explanation more and more indispensable. 
 In 1835, the computed geocentric longitudes of the planet exhibited a 
 discordance with observation amounting to 30"; in 1838 the discordance 
 amounted to 50", and in 1841 to 70". Nor were these errors simply the 
 effects of errors in the heliocentric longitude of the planet. On the con- 
 trary, Mr. Airy clearly shewed, by means of his observations of the planet 
 made at Cambridge in the years 1833-34-35, and at Greenwich in 1836, 
 that the radius vector of the tables was also considerably in error. 
 
 The time had now arrived for the geometer to apply the powers of 
 analysis to the investigation of these anomalies. The illustrious Bessel 
 appears to have entertained the idea of attacking this important problem. 
 On the occasion of his visit to England in 1842, he expressed to Sir John 
 Herschel his conviction that the irregularities in the motion of Uranus 
 were occasioned by the action of some unknown planet, and he added, that 
 as soon as he should obtain leisure from other researches in which he was 
 engaged he would undertake the determination of its actual position}. It 
 appears that, as a preliminary step to the inquiry, he had instructed M. 
 Flemming, a young German astronomer, to reduce with great care all the 
 observations of the planet. Flemming executed the task assigned to him ; 
 but, unfortunately, soon afterwards, Bessel was seized with the illness 
 which proved fatal to him, and the inquiry was not prosecuted further . 
 
 * See the Comptes Rendus, tome xxiv. p. 35. 
 
 + Published in 1836. \ Athenceum, October 3rd, 1846. 
 
 M. Flemming died soon after he completed the calculations. The reduced observa- 
 tions are now in the possession of M. Schumacher of Altona. See Sir John Herschel's 
 Notice of the life of Bessel, in the sixteenth volume of the Memoirs of the Astronomical 
 Society. 
 
168 HISTORY OF PHYSICAL ASTRONOMY. 
 
 The theory of Uranus was now about to be submitted to a severe 
 examination by a young mathematician of England. Mr. J. C. Adams, 
 while still pursuing his studies at St. John's College, Cambridge, had pur- 
 posed investigating the cause of the strange irregularities in the motion of 
 the planet. His attention was first drawn to the subject by Mr. Airy's 
 allusion to those anomalies in his valuable account of the progress of 
 astronomy in the nineteenth century, contained in the Report of the 
 British Association for 1832. Mr. Adams, on referring to his note-book 
 at a subsequent period, found the following memorandum inserted in it 
 under the date of the 3rd July, 1841 : " Formed a design, in the begin- 
 ning of this week, of investigating, as soon as possible after taking my 
 degree, the irregularities in the motion of Uranus which are yet unac- 
 counted for ; in order to find whether they may be attributed to the action 
 of an undiscovered planet beyond it, and if possible, thence to determine 
 approximately the elements of its orbit, &c., which would probably lead 
 to its discovery."* 
 
 Mr. Adams having taken his degree in January, 1843, proceeded to 
 consider the subject of his future researches. The problem which offered 
 itself to him for solution may be stated in the following terms : Assuming 
 that Uranus was disturbed by some unknown body, to determine the posi- 
 tion of the latter, its mass, and the elements of its orbit, by means of the 
 irregularities it produces in the motion of the disturbed planet. This 
 problem being the inverse case of the ordinary problem of planetary per- 
 turbation, is manifestly of a very intricate character, and demands the 
 resources of a very refined analysis for its successful treatment. Nay, it is 
 even more complicated than at first it appears to be, for the elements of 
 Uranus, which form the basis of the geometer's researches, are vitiated 
 by the action of the unknown planet, and their rectification, however 
 desirable, can only be effected by the actual solution of the problem. In 
 order to acquire clear ideas upon this point, the reader must bear in mind 
 that the fundamental or mean orbit of Uranus is an ellipse, in which it 
 would constantly revolve if it was exposed solely to the attractive influence 
 of the sun, and that the action of the other bodies of the system tends 
 merely to occasion minute excursions of the planet now on one side and 
 now on the other side of this orbit. It is manifest, then, that in deter- 
 mining the elliptic elements of a planet's motion by means of its positions 
 as assigned by observation, the effects of perturbation must be subducted 
 from the co-ordinates of each position, in order that the planet maybe reduced 
 to the place which it would occupy in the mean elliptic orbit. Now when 
 Delambre and Bouvard were severally engaged in determining the elements 
 of Uranus, they applied the perturbations due to Jupiter and Saturn as cor- 
 rections to the positions derived from observation ; but, as they did not take 
 into account the action of the unknown planet, it is manifest that, if the 
 latter really existed, the final values of the heliocentric co-ordinates, as de- 
 termined by each of these astronomers, must have failed to represent the 
 elliptic positions of the planet. Hence, the elements deduced from these 
 erroneous data were necessarily inaccurate, and it is manifest that this 
 circumstance alone would have the effect of distorting the orbit of the 
 planet, and thereby occasioning discordances between the observed and 
 computed values of the longitude, latitude, and radius vector. The errors 
 of the tables of Uranus were, therefore, attributable to two distinct causes, 
 being due partly to the errors in the elements of the planet's own orbit, 
 
 * Mem Ast. Soc., vol. xvi.; see also the Nautical Almanac for 1851 (Appendix). 
 
HISTORY OF PHYSICAL ASTRONOMY. 169 
 
 and partly to the disturbing action of the unknown planet. These 
 two causes of error, although totally opposite in their natures, had both a 
 common origin, and their effects on this account were so thoroughly en- 
 tangled in each other, that it was impossible to investigate either inde- 
 pendently. This circumstance, as may well be supposed, vastly increased 
 the difficulty of the problem. If it had been possible to ascertain what 
 portion of the irregularities of the planet was in each case due to the 
 errors of the elements, the values of these errors might have been deter- 
 mined by the ordinary methods of astronomy; and when once the elements 
 were thus corrected, it would have been undoubtedly a less arduous task to 
 ascend from them to the elements of the unknown planet. But it clearly 
 follows, from the remarks we have already made, that the elements of Uranus 
 cannot be determined without taking into account the whole effects of plane- 
 tary perturbation, and this again implies a knowledge of what is the very 
 object of inquiry, namely, the elements and mass of the unknown planet. 
 The problem, then, admits of being completely treated only by a method 
 which shall embrace in one simultaneous investigation the corrections to the 
 elements of Uranus and the elements and mass of the unknown planet. Now, 
 the elements of a planet are six in number. The problem, when considered 
 in all its generality, will therefore involve thirteen unknown quantities. 
 As, however, it appeared from observation that the perturbations of Uranus 
 in latitude were very small, the two planets might be supposed, for all the 
 purposes of a first approximation, to revolve in the same plane, and by this 
 simplification the number of unknown quantities was reduced to nine. 
 These were: the corrections to the mean distance, the eccentricity, the 
 longitude of the perihelion, and the epoch or mean longitude of Uranus; 
 and the absolute values of the same elements relative to the unknown 
 planet together with its mass. Now, in the case of one planet acting upon 
 another and disturbing its motion, the theory of perturbation enables the 
 geometer to express the corrections to the co-ordinates of the disturbed 
 planet in terms of these nine unknown quantities; and, if the hypothesis 
 of an unknown planet was true in the present case, these corrections ought 
 to account for the differences between the observed and computed positions 
 of the planet Uranus. Hence, by comparing the analytical formulae for 
 the corrections to the co-ordinates of Uranus with the numerical errors 
 of the tables, a number of equations of condition are formed, and the 
 problem is finally reduced to the elimination of the unknown quantities 
 from these equations. It may readily be imagined that this operation is 
 attended with difficulties of no ordinary kind. In fact, only a thorough 
 acquaintance with the nature of planetary perturbation, and a complete 
 command of analysis, combined with consummate skill in its application, 
 will suggest to the mathematician such artifices as may lead to the dis- 
 engagement of the unknown quantities from the complicated expressions 
 in which they are involved. 
 
 Nor does the mere elimination of the unknown quantities constitute the 
 only difficulty attending the solution of the problem. Unless the equa- 
 tions of condition be skilfully combined together, it may happen that the 
 values of the unknown quantities, although deduced by a strictly legiti- 
 mate process of reasoning, will prove totally erroneous when considered 
 as physical results. This will be readily understood by the reader when he 
 takes into account the mode in which the equations of condition are formed. 
 In each case the error of the planet's place is expressed algebraically in 
 terms of the nine unknown quantities of the problem, and the equation of 
 
170 HISTORY OF PHYSICAL ASTEONOMY. 
 
 condition is formed by putting this expression equal to the actual error as 
 determined by a comparison of the observed and computed places of the 
 planet. Every tabular error furnishes a corresponding equation, and thus 
 the number of equations of condition is limited only by the number of in- 
 dependent observations. Now, if the latter ^fere mathematically accurate, 
 the equations of condition would all be consistent with each other, so that 
 any nine of them would suffice for the determination of the nine unknown 
 quantities of the problem, and the values hence deduced would rigorously 
 satisfy all the other equations. But, as all observations are necessarily 
 more or less erroneous, the errors resulting from a comparison of the ob- 
 served and calculated places of the planet will not be wholly dependent 
 on the unknown quantities of the problem; and the equations of condition 
 being vitiated in consequence, will prove to a certain extent incom- 
 patible with each other, so that every nine equations selected for the de- 
 termination of the unknown quantities will conduct to different results. 
 With a view to elude this source of error, the number of equations of 
 condition is generally made to exceed in a great degree the number of 
 unknown quantities, and the grand object, then, is to combine them to- 
 gether, so that the errors of observation may destroy each other, and a 
 system of equations may finally be arrived at which will assign the true 
 values of the unknown quantities. 
 
 Mr. Adams first proceeded to examine the perturbations produced 
 in the motion of Uranus by the other planets, in order to assure himself 
 beyond doubt that the errors of Bouvard's tables did not proceed from 
 an erroneous application of the existing theory*. For this purpose he 
 recomputed the principal perturbations due to Jupiter and Saturn, 
 and introduced some new inequalities which had been first pointed 
 out by Hansenf. He also took into account the correction to Jupiter's 
 mass, to which recent researches had conducted Astronomers. Not- 
 withstanding these improvements, the theory still failed to represent 
 the motion of the planet. Two important advantages were, however, 
 gained by these preliminary labours. In the first place, it was clearly 
 established that the cause of the irregularities must be sought elsewhere 
 than in the development of the actual theory. In the second place, the 
 application of the improvements had the effect of exhibiting the errors of 
 the tables as residual facts wholly dependent on some extraneous influence, 
 and consequently they now assumed a more precise and definite character 
 than they had previously done. The first point to be decided in this 
 inquiry was, the most suitable mode of exhibiting the irregularities in 
 the motion of the planet. We have mentioned already, that both the 
 heliocentric longitude and radius vector had been discovered to be 
 sensibly in error. Now it may be remarked, that the problem admits 
 of solution by employing as the basis of investigation an adequate number 
 of the errors of either of these co-ordinates, independently of those of the 
 other. In point of fact, however, the errors of the radius vector were 
 too inconsiderable to be employed with safety in such an inquiry, although 
 they might be subsequently used with advantage in verifying results 
 otherwise derived. Mr. Adams, therefore, had recourse to the errors of 
 heliocentric longitude, which in some instances amounted to %' or 3', and 
 extended over a period embracing more than a revolution and a half of 
 
 * Mem. Ast. Soc., vol. xvi. ; Naut. Aim., 1851. 
 
 f These inequalities are of the order of the squares of the disturbing forces, and are by 
 far the most considerable of the class to which they belong. 
 
HISTORY OF PHYSICAL ASTRONOMY. 17J 
 
 the planet round the sun. But here a difficulty occurs, the nature of 
 \vhich it is necessary briefly to explain. The earth being the place from 
 which all observations are made, the position of a planet in the zodiac is 
 determined by its geocentric longitude, or its angular distance from the 
 vernal equinox relative to the centre of the earth. But, as the sun is the 
 natural centre of the planet's motion, the theory of the latter assigns only 
 the heliocentric longitude, or the distance from the vernal equinox relative 
 to the centre of the sun. In order, then, to compare the observations 
 of the planet with the results of theory, it is necessary to pass from the 
 geocentric longitude, derived immediately from observation, to the cor- 
 responding value of the heliocentric longitude. This object may be ef- 
 fected by a simple process of trigonometry, if we know the length of the 
 radius vector of the planet, and the position of the earth in her orbit, 
 corresponding to the time of observation. The former of these data may 
 be obtained from the tables of the planet, and the latter from the solar 
 tables. It is manifest, however, that if the tabular radius vector of the 
 planet be erroneous, the computation will be vitiated, and a false value 
 will be assigned to the heliocentric longitude. The question then arises, 
 how are we to pass from the geocentric longitude of the planet to the 
 heliocentric longitude without complicating the result with the effect of 
 the error of the radius vector. This object is accomplished per se for all 
 observations made when the planet is in opposition, for the sun, the earth, 
 and the planet being then in the same straight line, the geocentric and 
 heliocentric longitudes will necessarily coincide, and they will both retain 
 the same common value, whatever be the length of the planet's radius vector. 
 Even if the observations should not be made when the planet is actually 
 in opposition, the heliocentric longitudes may be obtained free from the 
 errors of radius vector by skilfully combining together the observations 
 made before and after opposition*. Mr. Adams in this manner deduced 
 from the observations of Uranus twenty equidistant values of heliocentric 
 longitude, for the period included between 1780 and 1840. Comparing 
 these with the tabular values he obtained a corresponding series of 
 errors in heliocentric longitude, which, with those derived from the 
 ancient observations of the planet, formed the data of his final investi- 
 gation of the problem. 
 
 Mr. Adams commenced his researches by supposing the orbit of the 
 planet to be circular, and its mean distance from the sun double the mean 
 distance of Uranus. It was probable from analogy that both these sup 
 
 * If we suppose the radius vector of the tables to be too small, then, before the earth 
 arrives in opposition, the planet will appear behind its computed place ; and, on the other 
 hand, when the earth has passed opposition, it will appear in advance of its computed place. 
 Hence it is not difficult to perceive that these opposite effects may be destroyed by a suit- 
 able combination of observations made before and after opposition. The same remark 
 will manifestly apply, if the tabular radius vector be too large ; the only difference being, 
 that in this case the planet before opposition will appear in advance of its computed place, 
 and after opposition will appear behind it. After Kepler made the memorable discovery 
 that the orbit of Mars was not a circle, but retired within that curve towards the mean 
 distance, his active imagination soon devised a theory in which the planet was supposed 
 to move in an oval, the distance of which varied according to a certain law. This hypo- 
 thetic orbit was, however, too much compressed in the sides to represent the true ellipse of 
 the planet ; and, accordingly, Kepler mentions that David Fabricius, to whom he com- 
 municated his theory, remarked to him that the observations of the planet before and after 
 opposition indicated that the distances of the oval were all too short. " So nearly," says 
 he, " did that astronomer anticipate me in the discovery of the true orbit of the planet." 
 De Motibus Stellce Martis, cap. Iv. p. 266. 
 
HISTORY OF PHYSICAL ASTRONOMY. 
 
 positions did not differ widely from the truth*. Without some assumed 
 value of the mean distance, the operation of eliminating the unknown 
 quantities would have been totally impracticable ; but, when this object 
 was once accomplished, a more accurate value might be afterwards arrived 
 at, either by varying the hypothesis and comparing the results with those 
 derived in the first instance, or by introducing into the second solution 
 a correction to the assumed mean distance in the shape of a new un- 
 known quantity. The results which Mr. Adams obtained by means of 
 his first essay were sufficiently satisfactory to encourage him to pursue 
 his researches. The observations which he employed were most defective 
 throughout the period included between the years 1818 and 1826, and it 
 was precisely in that period also that the errors of his theory were greatest. 
 This circumstance induced him to apply to the Astronomer Royal, through 
 his friend Professor Challis, for the Greenwich Observations of the planet 
 then in process of reduction. Professor Challis' letter to the Astronomer 
 Royal on this occasion is dated the 13th February, 1844 f. He mentions 
 in it that Mr. Adams, a young friend of his, was engaged in researches 
 on the theory of Uranus. He then specifies the nature of his request, 
 expressing also a desire to know whether, in comparing the observations of 
 the planet with the theory, any alteration had been made in the tables of 
 Bouvard, except that depending on the correction to the value of Jupiter's 
 mass. The Astronomer Royal a day or two afterwards returned a suitable 
 reply to Professor Challis' letter, and kindly transmitted, for the use of 
 Mr. Adams, all the Greenwich Observations of the planet from 1750 to 
 1830 completely reduced J. 
 
 Furnished with these valuable data, Mr. Adams was now in a con- 
 dition to pursue his researches with the prospect of ultimate success. 
 He accordingly undertook a more comprehensive investigation of the pro- 
 blem by considering the orbit of the disturbing planet to be elliptic. By 
 repeating the approximation several times, introducing on each occasion 
 more and more terms of the perturbation, he succeeded in gradually reduc- 
 ing the errors of Uranus, until its computed places finally exhibited a very 
 general and satisfactory accordance with those derived from observation. 
 In the autumn of 1846, he considered his researches were so far matured 
 as to warrant the presumption that his results might be employed with a 
 strong probability of success in searching for the new planet. Accordingly 
 in the month of September, before leaving Cambridge, he placed in the 
 hands of Professor Challis a paper containing numerical values of the 
 
 * The following curious law regulating the mean distances of the planets from the sun 
 was first announced by Bode, the German astronomer. It is said, however, that he was 
 indebted for the original notion of it to Titian, a professor of Wurtemberg. 
 
 Mercury =4 =4 
 
 Venus = 4 + 3.2 = 7 
 
 The Earth = 4 + 3.2 1 = 10 
 
 Mars = 4 + 3.2 2 = 16 
 
 Ceres (as the mean of the smaller planets) = 4 + 3.2 3 = 28 
 Jupiter . . . . . . = 4 -f 3.2* = 52 
 
 Saturn = 4 + 3.2 5 = 100 
 
 Uranus . . . . . . = 4 + 3.2" = 196 
 
 If we compare these numbers with the actual distances (supposing the earth's distance 
 to be in both cases represented by 10), we shall find a very remarkable agreement. It is 
 easy to perceive that as the planets recede from the sun, their successive distances become 
 more nearly double each other. 
 
 f Airy's Historical Statement of circumstances connected with the discovery of the planet 
 beyond Uranus, No. 6. 
 
 f Airy's Historical Statement, No. 7. 
 
HISTORY OF PHYSICAL ASTRONOMY. 173 
 
 mass, the epoch, the eccentricity, and the longitude of the perihelion 
 of the disturbing planet, together with its geocentric longitude for tho 
 30th of September, 1845*. Mr. Adams was also anxious to communicate 
 his results to the Astronomer Royal, and for this purpose the kind offices of 
 Professor Challis were again tendered. The letter of Professor Challis to 
 the Astronomer Royal on this occasion is dated the 22nd September, 1845 f. 
 He mentions in it that Mr. Adams had completed his investigation re- 
 lative to the supposed existence of a planet exterior to Uranus ; that his 
 researches were founded on the observations which Mr. Airy was kind 
 enough to send him some time previously, and that he was desirous of 
 communicating his results personally to him. He added, also, that from 
 Mr. Adams' character as a mathematician, and his practice in calculation, 
 he considered that his conclusions had been accurately deduced from his 
 premises. Mr. Airy happened to be from home when Mr. Adams called at 
 Greenwich, but a few days afterwards he wrote a letter to Professor Challis J, 
 expressing the strong interest he felt in the subject of Mr. Adams' re- 
 searches, and mentioning that he would be happy to hear by letter from 
 him respecting them. 
 
 On one of the last days of October, 1845, Mr. Adams called at the 
 Royal Observatory, and left a paper containing the elements of the 
 new planet, and the errors resulting from a comparison of the improved 
 theory of Uranus with a great number of observations of the planet from 
 1690 to 1840 . These errors, which, by Bouvard's tables, amounted fre- 
 quently to 3', were now for the most part little more than 1". The fol- 
 lowing are the elements of the planet, as given by Mr. Adams in this 
 important paper: 
 
 Mean distance from the sun, the earth's 
 
 distance being represented by unity . 38.4 
 
 Mean sidereal motion in 365.25 days . 1 30'. 9 
 
 Mean longitude, 1st October, 1845 . . 323.34' 
 Longitude of perihelion . . . . 315.55 
 
 Eccentricity . . . . . . .1610 
 
 Mass (that of the sun being unity) . . .0001656 
 These elements give 7 39' for the mean anomaly of the planet on the 1st 
 October, 1845, and 3 3' for the equation of the centre. Hence, by adding 
 the latter to the mean longitude, we get 326 37' for the true heliocentric 
 longitude of the planet. Now, if we compute the place of the planet for 
 the same instant by means of the elements derived from observation, we 
 shall obtain 324 48' for the ^true longitude ||. The difference, therefore, 
 between the actual and theoretical places was only 1 49' ; and it is clear 
 that if we had employed, as the epoch of comparison, the 23rd September, 
 1846 (the epoch of the actual discovery of the planet), the result would 
 not have been materially different. 
 
 Thus it appears that, as early as the month of October, 1845, seven 
 months before any other person had arrived at a similar conclusion, 
 Mr. Adams had solved the inverse problem of planetary perturbation; 
 that, by means of his solution, he had discovered, theoretically, the 
 existence of a planet exterior to Uranus; and that he had assigned to 
 
 * Challis' Report to the Syndicate of the University of Cambridge ; see also Phil. 
 Mag., 1847. 
 
 f Airy's Hist. Statement, No. 9. Airy's Hist. Statement, No. 10. 
 
 Ibid, No. 11. 
 
 || The elements here employed are those deduced from observation by Professor 
 Walker of Washington. 
 
174 HISTORY OP PHYSICAL ASTRONOMY. 
 
 the unknown body a place in the heavens which was subsequently found 
 to differ little more than one degree from its actual place. All that was 
 now wanting, therefore, to assure both to Mr. Adams and to his country 
 the undivided honour of one of the noblest ^discoveries recorded in the 
 annals of science, was some zealous observer to give effect to his 
 results, by carefully searching the heavens in the vicinity of the place 
 indicated by his theory as that occupied by the planet. If such a scru- 
 tiny had been undertaken, and prosecuted for some time, it would beyond 
 all doubt have resulted in the actual discovery of the planet, and the name 
 of Adams would have been alone associated with that remarkable triumph 
 of science. Such a consummation was not destined to be the reward of 
 Mr. Adams ; but this circumstance does not detract in the slightest de- 
 gree from the merit of his researches ; for it is now universally admitted 
 that he was the first theoretical discoverer of the planet, and that, as far 
 as the task of the mathematician was concerned, he left no part of the 
 problem relative to the determination of its actual position to be com- 
 pleted by others. 
 
 A few days after the Astronomer Royal received Mr. Adams' paper con- 
 taining the elements of the new planet, he wrote a letter to that gentleman, 
 thanking him for his communication, and stating that the results appeared 
 to him very satisfactory*. He mentioned, however, that he was desirous 
 of knowing whether the theory gave an equally satisfactory account of the 
 errors of radius vector, directing Mr. Adams' attention to the fact of these 
 errors having recently become very considerable. 
 
 Mr. Airy deemed the explanation of the errors of radius vector to be an 
 experimentum crucis, which would decide, in his mind, the question of the 
 legitimacy of Mr. Adams' researches, and he naturally enough waited for 
 the reply of that gentleman before taking any active steps for the purpose 
 of discovering the planet. Unfortunately, Mr. Adams did not consider it 
 a matter of importance to transmit prompt information to Mr. Airy on 
 this point ; and it was not until nine months afterwards, when his results 
 were confirmed by similar researches, prosecuted in another quarter, that 
 any attempt was made to obtain their verification. It must not, however, 
 be inferred, from the fact of Mr. Adams not having returned an immediate 
 answer to Mr. Airy's letter, that he was prevented from doing so by any 
 imperfection in his solution of the inverse problem of perturbation. When 
 once the elements of the unknown planet, and the corrections to the elements 
 of Uranus, have been deduced from the errors of longitude, the errors of 
 radius vector may then be calculated by a direct process which does not 
 involve any analytical difficulties beyond those already vanquished in the 
 Mecanique Celeste. We shall again have occasion to advert to this point. 
 
 It is necessary to state, before proceeding further, that Mr. Adams' re- 
 searches on the theory of Uranus were not hitherto made known to the 
 public. The two astronomers whom we have had frequently occasion to 
 allude to in connexion with him, and a few of his friends at Cambridge, 
 appeared to have been the only individuals who were acquainted with the 
 nature of his labours. We shall now give an account of the researches of 
 the French astronomers in connexion with the same subject. 
 
 In the month of September, 1845, Eugene Bouvard, nephew of the astro- 
 nomer Alexis Bouvard, presented to the Institute new tables of Uranus f. 
 They were founded on the observations of the planet made subsequently 
 
 * Airy's Hist. Statement, No. 12. This letter is dated the 5th November, 1845. 
 f Comptes Rendu.3 de 1' Academic, tome xxi, p. 524. 
 
HISTORY OF PHYSICAL ASTRONOMY. 175 
 
 to its discovery in 1781, and on the anterior observations of Bradley, 
 Lemonnier, and Mayer. The actual motion of the planet was represented 
 better by them than by the tables constructed in 1821, but the residual 
 errors were still, in many instances, too great to be accounted for by any 
 probable errors of observation. This was candidly admitted by the author 
 of the tables, who intimated also his belief that the errors were of such a 
 nature as to give countenance to the opinion entertained by his uncle that 
 they were due to the perturbations produced by another planet*. 
 
 The failure of this laborious attempt to correct the tables of Uranus 
 without the introduction of any new hypothesis, beyond doubt produced a 
 strong impression on the minds of the French astronomers ; and it was 
 probably this circumstance which induced M. Arago to propose to his 
 friend, M. Le Verrier, the theory of Uranus as a subject eminently 
 worthy of attention. We have already had frequent occasions to allude 
 to the labours of this talented mathematician. He had recently been 
 occupied with the theory of comets ; but, at the suggestion of the illustrious 
 philosopher just mentioned, he temporarily laid aside his researches on 
 that subject, and resolved to institute a searching scrutiny into all the 
 circumstances affecting the motion of Uranus. An account of the first 
 part of his researches appeared in the Comptes Rendus of the Academy 
 of Sciences, for the 10th of November, 1845. It contained the result of a 
 rigorous examination of the motion of the planet according to the princi- 
 ples of the actual theory. The only interior planets which produce sen- 
 sible perturbations in the motion of Uranus are Jupiter and Saturn, and 
 of these the latter exercises the more powerful influence, on account of 
 his comparative proximity to the disturbed planet. Le Verrier deter- 
 mined the value of every inequality depending on the action of Saturn, 
 that exceeded the twentieth part of a second, employing two distinct 
 methods of calculation, in order to assure greater accuracy to his results f. 
 He also computed all the perturbations occasioned by the action of Jupiter. 
 Nor did he confine his researches to the inequalities of the first order of 
 magnitude. All the principal inequalities depending on the squares of 
 the disturbing forces were also taken into account by himj. A great 
 number of small terms were thus introduced, for the first time, into the 
 
 * In a letter from Eugene Bouvard to Mr. Airy, dated the 6th October, 1837, we 
 find also an allusion to the opinion entertained by his uncle, Alexis Bouvard, that the ir- 
 regularities of Uranus were occasioned by a disturbing planet. After adverting to the 
 inconsistency of the tables with observation, he then proceeds thus : " Cela tient-il a une 
 perturbation inconnue apportee dans le mouvement de cet astre par un corps situe au- 
 dela ? Je ne sais, raais c'est du moins'l'idee de mon oncle." Airy's Hist. Statement, No. 3. 
 
 t One of these methods is that to "which allusion has been made in page 1 15 of this work. 
 
 J When the mutual action of two planets is considered, their perturbations are first 
 computed by supposing them to move in ellipses, and the resulting inequalities are of the 
 first order with respect to the disturbing forces. In a second approximation the perturba- 
 tions consequent upon the derangements of the motions of the two planets, as assigned by 
 the first approximation, are taken into account, and the inequalities hence derived are of the 
 second order with respect to the disturbing forces. It is important to remark that the 
 inequalities of the second order may be materially modified by the derangements of both 
 planets depending upon the action of a third planet. This happens when the theory of 
 Uranus and Saturn is considered, the action of Jupiter exercising a very sensible influ- 
 ence on the mutual perturbations of those bodies. On account of his great mass and his 
 comparative proximity to Saturn, Jupiter produces very extensive perturbations in the 
 motion of that planet. Le Verrier, who resolved to verify everything by actual calcula- 
 tion, was induced by this circumstance to investigate a great part of the theory of Saturn, 
 even although, in the present case, it was only with the ulterior view of computing the 
 action of that planet upon Uranus. 
 
176 HISTOKY OF PHYSICAL ASTHONOMY. 
 
 heliocentric co-ordinates of the planet, the previous omission of which, 
 he shewed, was alone sufficient to occasion sensible errors in the tables. 
 
 An account of the second part of Le Verrier's researches appeared in 
 the Comptes Rendus, for the 1st of June, 1&46. After having corrected 
 the theory of the planet, he next proceeded *to compare it with the obser- 
 vations, in order to ascertain whether the latter might be satisfied by 
 applying suitable corrections to the elements, or whether it was impossible 
 to account for them by any ellipse whatever and the perturbations of 
 the known planets. He selected, for this purpose, nineteen ancient ob- 
 servations of the planet, and 260 observations made at the Observatories of 
 Greenwich and Paris, during the period comprised between the discovery of 
 the planet in 1781 and the month of September, 1845. In order ef- 
 fectually to guard against every contingency of error, he undertook the 
 laborious task of reducing anew all these observations. "Having employed 
 the results in computing the geocentric co-ordinates of the planet for each 
 observation, he then proceeded to deduce from theory the corresponding 
 values of the co-ordinates. It was necessary for this purpose to determine, 
 in the first instance, the heliocentric co-ordinates of the planet. When these 
 are known, and also the place of the earth in her orbit, a simple calculation, 
 the converse, in fact, of that to which we have already alluded*, will suffice 
 for passing from the heliocentric to the geocentric co-ordinates. Le Verrier 
 therefore calculated the heliocentric longitude, latitude, and radius vector 
 of the planet ; and then, by means of these data and the places of the earth 
 in her orbit, derived from the solar tables, he determined the values of the 
 geocentric co-ordinates. Finally, subtracting the value of each co-ordinate 
 from the corresponding value assigned by observation, he obtained the 
 errors of his theory. The question which now offered itself was this : Can 
 these errors be destroyed by applying suitable corrections to the elliptic 
 elements of the planet ? Now, it is easy to obtain the analytical expression 
 for the error in geocentric longitude, in terms of the errors of the elements 
 of the planet, these errors being exhibited in indeterminate forms. In 
 the present case, the only elements which it is necessary to take into 
 account are the mean distance, the epoch, the eccentricity, and the 
 longitude of the perihelion ; for the effects due to errors in the other two 
 elements are of an inferior order of magnitude, and, in consequence, may 
 be neglected. By putting the algebraic expression for the error of the 
 theory equal to each of the numerical values which he had previously 
 obtained by a comparison of the observed and calculated geocentric longi- 
 tudes, Le Verrier formed a series of equations of condition, which ought 
 to be satisfied if the discordances between theory and observation 
 were really due to errors in the elements. Every observation gave 
 him a corresponding equation of condition; so that the total number 
 of equations thus formed by him amounted to two hundred and 
 seventy-nine. Setting aside the equations of condition depending on 
 the ancient observations, he formed four final equations, by a suit- 
 able combination of all the others, and from them deduced the cor- 
 rections to the four elements. The motion of the planet, when 
 calculated for a great number of places by means of the new ellipse, 
 resulting from the application of these corrections to the tabular elements, 
 still exhibited discordances with the actual motion, which were generally 
 by far too great to be accounted for by any probable errors of observation. 
 
 * See page 171. 
 
HISTORY OF PHYSICAL ASTRONOMY. 177 
 
 It appeared, therefore, impossible to avoid the conclusion that some 
 extraneous cause must be constantly acting upon the planet, the influence 
 of which had not hitherto been taken into account in calculating its motion. 
 In order, however, to establish, beyond all doubt, that the discordances 
 were not due to the particular values of the elements employed by him, 
 he had recourse to a general method by which he formally demon- 
 strated the incompatibility of the existing theory of the planet with the re- 
 sults of observation. Pursuing a process which it would be out of place to 
 explain here, he obtained a final equation, one part of which was a 
 numerical quantity amounting to 35 6", while the other part was an 
 analytical expression involving eleven mean errors of observation in 
 indeterminate forms, these mean errors being in each case generally the 
 resultant of a great number of individual errors of observation. Now, if 
 the discordances between the computed and the actual motion of the planet 
 were really due to errors of observation, this equation ought to be 
 rigorously true. The question, therefore, which now presented itself to 
 M. Le Verrier was this: is it possible, by ascribing to the errors of 
 observation any admissible values, to render the indeterminate part of the 
 equation equal to the numerical part ? With the view of arriving at a 
 definite solution of this question, he gave to each error a value considerably 
 greater than was probably due to it ; he further supposed that the errors 
 all took place in the same direction, and also that they had in all cases 
 attained their maximum values. These assumptions, although very 
 improbable, were all favourable towards rendering the equation identically 
 true ; still, notwithstanding this circumstance, the resulting value of the 
 indeterminate part of the equation amounted only to 92", and consequently 
 of the 356", which formed the constant part, there still remained 264" 
 unaccounted for. Le Verrier, therefore, finally concluded that the theory 
 of Uranus in its existing state was absolutely incapable of representing the 
 actual motion of the planet; and that the 264" which formed the 
 residual part of the equation must be attributed to some extraneous 
 cause acting upon the planet, and hitherto unknown to astronomers. 
 
 Le Verrier next examined the various hypotheses which had been 
 advanced with the view of accounting for the irregularities in the motion 
 of Uranus. Some persons imagined that the solar force did not diminish 
 in intensity according to the exact ratio of the inverse square of the 
 distance ; and they suspected that, for a body so remote as Uranus, the 
 deviation from the Newtonian law might become sensible. Le Verrier 
 justly considered all such hypotheses to be inadmissible, until it was found 
 that the anomalies of the planet could not be accounted for in accordance 
 with the recognised principles of the theory of gravitation. Again, others 
 were disposed to ascribe the irregularities to the influence of a resisting 
 medium pervading the regions of space. This explanation he considered 
 to be equally unworthy of credit ; since the effects of a resisting medium 
 had not been found to be sensible, even in cases much more favourable for 
 the manifestation of its presence. 
 
 Were the errors, then, due to a large satellite which accompanied 
 Uranus in its orbit, and constantly disturbed its motion ? This explana- 
 tion was likewise untenable ; for the perturbations produced by a satellite 
 would pass through their values in short periods, whereas the actual 
 irregularities of the planet appeared to develope themselves with extreme 
 slowness. Besides, the satellite would require to be very large, and in 
 that case could not fail to have been discovered by astronomers. 
 
 N 
 
178 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 In the next place, were the irregularities due to a comet which came 
 into collision with the planet, and suddenly changed the direction and 
 quantity of its motion ? The effect of such a collision would be to throw 
 the planet out of the ellipse in which it was moving, into another ellipse 
 having different elements. Its motion, therefore, previous to the epoch 
 of collision, and during an indefinite lapse of time afterwards, would be satis- 
 fied by two distinct systems of elliptic elements, and consequently in neither 
 case ought there to appear any outstanding irregularities, when once the 
 elements were duly corrected by means of observations relating exclusively 
 to the ellipse under consideration. This hypothesis acquired some degree 
 of plausibility from the fact, that Bouvard succeeded in representing with 
 tolerable accuracy, by means of an elliptic orbit, all the observations of 
 the planet comprised between the years 1781 and 1820. In order, 
 however, to justify its adoption, it would be necessary that this ellipse 
 should tally either with the observations anterior to 1781, or with those 
 subsequent to 1830, conditions both of which had been found by astrono- 
 mers to be incompatible with the actual motion of the planet. 
 
 It was manifest, then, that the irregularities must be occasioned by 
 some cause acting continuously upon the planet, and varying slowly in the 
 intensity of its influence. This can be no other than a planet, and the 
 question then arises : is it possible to assign the place in the heavens 
 which it ought to occupy ? In the first place, it could not be situated within 
 Saturn, for, if so, it would disturb that planet to a greater extent than it 
 disturbs Uranus ; but this was contrary to fact, the perturbations which 
 it produces in the motion of Saturn being insensible. Secondly, was it 
 situated between Saturn and Uranus '? In that case, it would require to 
 be nearer Uranus than Saturn, and as its mass, in consequence, must 
 necessarily be very inconsiderable, the perturbations produced by it 
 would be sensible only in conjunction. But the periodic times of the two 
 planets would be very nearly equal. It followed, therefore, that the 
 perturbations would be sensible only once during the period including all 
 the existing observations of Uranus. This conclusion, however, was at 
 variance with the actual character of the irregularities of the planet. 
 The disturbing body must, therefore, be situated beyond Uranus. It 
 must not be very near that planet, for its mass would then be incon- 
 siderable, and its perturbations, as in the preceding case, would exhibit 
 a character inconsistent with observation. Nor must it be situated very 
 far beyond Uranus ; for, if it were so, its respective distances from Saturn 
 and Uranus would be comparable with each other, and it would be im- 
 possible to account for the irregularities of Uranus without developing 
 similar irregularities of the same order of magnitude in Saturn ; but of 
 these there did not exist any sensible traces. It manifestly followed, 
 therefore, that the planet must be situated at some moderate distance 
 beyond Uranus. Now, according to Bode's law, the successive distances of 
 the more remote planets are nearly double each other. Le Verrier, there- 
 fore, assumed as the basis of a first approximation, that the disturbing 
 planet was twice as distant from the sun as Uranus, and, arguing similarly 
 from analogy, he concluded that it revolved very nearly in the plane of 
 the ecliptic. He was thus led to propound the subject of his researches 
 in the following form: "Is it possible that the irregularities of 
 Uranus may arise from the action of a planet situated in the ecliptic at a 
 mean distance double that of Uranus ? If such be the case, what is the 
 actual position of this planet ? What is its mass ? and what are the ele- 
 
HISTOKY OF PHYSICAL ASTRONOMY. 179 
 
 merits of the orbit which it describes ? " The problem being thus enun* 
 elated, Le Verrier next proceeded to explain his method of solution. It 
 was impossible to consider the disturbing planet without also taking into 
 account the errors in the elements of Uranus; for the irregularities of the 
 latter planet, which formed the data of the problem, depended on both 
 these causes ; nor was it possible to eliminate the effects due to either cause 
 without a knowledge of those due to the other. The problem, therefore, 
 admitted of solution only by a method which would embrace in one 
 simultaneous investigation the elements of the disturbing planet, and 
 the corrections due to the elements of Uranus. It was necessary for this 
 purpose to compute the heliocentric co-ordinates of the latter planet by 
 means of the actual ellipse, and the perturbations of the known planets, 
 and then to apply to the results 1, the expression for the perturbations of 
 the unknown planet, in terms of its mass and the elements of its orbit, 
 2, the expression for the correction due to the false ellipse of Uranus, 
 in terms of the errors of the elements. Each of the two last-mentioned 
 expressions contained four unknown quantities, and therefore the com- 
 plete value of any of the heliocentric co-ordinates would contain eight un- 
 known quantities. Equating this result to the corresponding value of 
 the co-ordinate derived from observation, an equation of condition was 
 formed between the eight unknown quantities, and the solution of the prob- 
 lem was reduced to the elimination of these quantities from a system of 
 such equations. 
 
 Le Verrier employed as the basis of his researches eighteen errors of 
 heliocentric longitude*. Three of these errors depended on observations 
 of the planet made by Flamstead, in 1690, 1712, and 1715. The other 
 fifteen extended over the period embraced between 1747 and 1845, and 
 were separated by equal intervals of seven years. By means of these 
 eighteen errors he formed an equal number of equations of condition. 
 He remarked that the corrections to the elements of Uranus might be 
 readily eliminated from the equations of condition ; and hence the re- 
 sulting equations would contain only four unknown quantities, namely, the 
 mass, the epoch, the eccentricity, and the longitude of the perihelion of the 
 disturbing planet. Now, it was easy to obtain expressions for the mass, 
 the eccentricity, and the longitude of the perihelion, in terms of the 
 epoch. The reader who possesses a knowledge of the elements of mathe- 
 matics will hence perceive that by means of these expressions an equation 
 might finally be formed involving the epoch alone ; and upon its elimi- 
 nation the solution of the problem would manifestly depend. This element, 
 however, presented itself in such a complicated form, that Le Verrier 
 did not consider it advisable to attempt the solution of the problem by 
 means of such an equation. He proposed to attain the same end by 
 
 * He bad previously employed these errors in demonstrating the incompatibility of the 
 actual theory of Uranus with the results of observation ; but, in order to avoid unneces- 
 sary complication, we did not make any allusion to them on that occasion. As the errors 
 were all subject to the condition of being equidistant, it was impossible to determine them 
 generally except by a process of interpolation ; and, as the ancient observations were sepa- 
 rated from each other by considerable intervals, it is manifest that in some instances the 
 numerical values of the errors could not be relied upon for extreme accuracy. Besides, 
 the probable effect of the error of radius vector was not taken into account. Le Verrier 
 clearly saw that the errors arising from both these causes were too insignificant to de- 
 serve notice when the object merely was to obtain an approximate value of the mean longi- 
 tude of the disturbing planet. In his final solution he completely eluded both sources of 
 error by employing as the basis of his investigation the geocentric longitudes of Uranus. 
 
 N 2 
 
180 HISTORY OF PHYSICAL ASTRONOMY. 
 
 assigning to the epoch a succession of numerical values, and, having de- 
 termined by means of it the corresponding values of the other elements, 
 then ascertaining which system of values agreed best with the obser- 
 vations. 
 
 Le Verrier eliminated the corrections to the elements of Uranus from the 
 equations of 1715, 1775, 1810, and 1845 ; and, setting aside those of 1690 
 and 1715, he grouped the remaining twelve into three mean equations cor- 
 responding to the years 1758, 1793, and 1828. Each of these equations 
 contained the mass, the eccentricity, the longitude of the perihelion, and the 
 epoch of the disturbing planet. Now, by assigning any particular value 
 to the epoch, it was easy to determine the values of the other three un- 
 known quantities. These values might then be employed in computing 
 the place of Uranus corresponding to any given observation ; and, by a 
 comparison of the observed and computed places, the error of the theory 
 depending on the assumed value of the epoch might be ascertained. Le 
 Verrier proposed, by this means, to compare his theory with the observa- 
 tions of 1690 and 1747 for a great number of values of the epoch, with 
 the view of discovering whether the errors in any case were so small that 
 it might be fairly presumed they were due to errors of observation. This 
 was the criterion by which he resolved to test the legitimacy of his 
 theory ; and its suitableness for this purpose may be readily understood, 
 for it is manifest that any errors committed in the calculation of the ele- 
 ments of the disturbing planet by means of the equations of condition, 
 founded mainly on the modern observations, could not fail to produce 
 sensible effects when the theory was compared with the more remote ob- 
 servations of 1690 and 1747*. In order to confine his labours within as 
 narrow a sphere as possible, he proceeded to inquire what values of the 
 epoch were really admissible, for it was useless to employ any values that 
 did not tally with the conditions of the problem. Now, it was clear that 
 those values of the epoch which assigned negative values to the mass ought 
 to be rejected, for all such values implied that the disturbing planet exerted 
 on Uranus a pushing force, and not an attractive force, conformably to the 
 theory of gravitation. Le Verrier found by an elaborate and skilful scrutiny 
 of the form of the algebraic expression for the mass that it had a positive signi- 
 fication for all those values of the epoch comprised between 96 40' and 
 189 55', and also for those between 263 8' and 358 41' ; and that it was 
 negative for all the remaining values comprised within the circuit of the 
 ecliptic. Again, it was evident that those values of the epoch which made the 
 mass immoderately large were inadmissible ; for, in all such cases, the planet 
 would produce sensible perturbations in the motion of Saturn ; but this con- 
 clusion was at variance with observation. Rejecting all such values, Le 
 Verrier succeeded in bringing still nearer to each other the limits he had 
 previously found. The arc which had 96 40' and 189 55' for its limits 
 now extended only between 108 and 162; while the arc which was 
 
 * Some of our readers may be disposed to conclude, by similar reasoning, that it 
 would be more advantageous to test the theory by the equations of 1712 and 1690 than 
 by those of 1747 and 1690. This is, no doubt, "true in an absolute sense; but it must 
 be borne in mind that the equation of 1715 was employed for the purpose of eliminating 
 the corrections to the elements of Uranus, and was on this account invariably equal to 
 zero. It is easy, then, to perceive, when we take into account the close proximity of the 
 observations of 1712 and 1715, that the equation of 1712 would, in all cases, be exceed- 
 ingly small, and consequently it could be of little value in testing the accuracy of the 
 theory in any particular case. 
 
HISTORY OF PHYSICAL ASTRONOMY. 181 
 
 bounded by 263 8' and 358 41' was now wholly included between 297 
 and 333. 
 
 It only now remained for him to compute the values of the mass, the 
 eccentricity, and the longitude of the perihelion of the disturbing planet, 
 for a number of particular values of the epoch contained between those 
 limits which he had found to include all the admissible values, and then 
 to determine the corresponding errors of the theory in 1690 and 1747. 
 This calculation he executed for a great number of equidistant values of 
 the epoch, but he was mortified to find that the errors were in all cases 
 so considerable that they could not be accounted for by any probable 
 errors of observation, and the conclusion seemed to be inevitable, that it 
 was absolutely impossible to represent the irregularities of Uranus by the 
 hypothesis of a disturbing planet. Thus it appeared to him that he was 
 all the while engaged in pursuing a phantom, or, to use the words of the 
 illustrious Kepler on a similar occasion, "all his labours vanished in 
 smoke."* 
 
 Notwithstanding this unexpected conclusion, Le Verrier was still reluc 
 tant to abandon the hypothesis of an exterior planet ; for, in such abstruse 
 and complicated inquiries, there may exist just reasons for supposing that 
 the final results have been influenced in an inordinate degree by some 
 hidden cause, depending either on the method of solution or on the na- 
 ture of the problem itself. He did not therefore despair of rendering his 
 theory consistent with observation by the detection of some peculiarity of 
 this kind ; nor did his genius fail to come eventually to his aid in this 
 perplexing emergency. He discovered, in fact, that the form of the ana- 
 lytical expression for the mass was such, that a very small error committed 
 in the observations of Uranus would affect, to an enormous extent, its nu- 
 merical value corresponding to any given value of the epoch ; whence it 
 followed that the errors of the theory in 1690 and 1747, which had been 
 computed by means of the values of the mass, and the other elements of 
 the disturbing planet obtained by supposing the observations to be abso- 
 lutely correct, had not been fairly represented by the results relative to 
 those quantities at which he had finally arrived. It appeared to him, 
 therefore, that no legitimate conclusion could be deduced from the equa- 
 tions of condition until the supposition of possible errors in the observa- 
 tions was introduced into them. He now resumed the consideration 
 of the three mean equations of 1758, 1793, and 1828, assuming that all 
 the observations which entered into their composition were affected with 
 indeterminate errors. By a simple inspection of their forms he discovered 
 that these equations could only be affected to a sensible extent by the errors 
 of the observations of 1715 and 1775f. In addition, therefore, to the four 
 unknown quantities, relative to the disturbing planet, each equation con- 
 tained these two errors represented by appropriate symbols. He now re- 
 solved to assign a succession of values to the epoch in the two equations of 
 
 * Itaque causse physicae, cap. xlv. in fumos abeunt, De Motibus Stella Mortis, cap. Iv. 
 Such are the terms in which Kepler announces the failure of his oval theory to account 
 for the motions of Mars, a theory to which he long continued to cling with the most abso- 
 lute conviction of its truth, and upon which he expended an almost incredible amount of 
 ingenious reasoning and toilsome calculation. While pondering in great perplexity on 
 the cause of the failure, a happy inspiration of his genius revealed to him the grand truth 
 that the orbit of the planet is an ellipse. 
 
 t The errors of observation for 1810 and 1845 were also similarly calculated to 
 affect the equations ; but, as they were in all probability very small, Le Verrier considered 
 that he might safely dispense with taking them into account. 
 
182 HISTORY OF PHYSICAL ASTRONOMY. 
 
 1793 and 1828, and then to eliminate from them the eccentricity and the 
 longitude of the perihelion of the disturbing planet. From what \ve have 
 already said, relative to the composition of these equations, it is manifest 
 that each of the eliminated elements would be expressed in terms of three 
 unknown quantities, namely, the mass, and tne two indeterminate errors 
 of observation. He now proposed, by means of them, to determine the 
 errors of the theory in 1690, 1747, and 1758, in order to ascertain whether 
 they might be made sufficiently small for any value of the epoch. These 
 errors no longer appeared in the form of simple numerical results, as they 
 did by his first method. They now contained the mass, and the two 
 errors of observation in indeterminate forms ; and it was only by a discus- 
 sion founded on the limits, within which each of these three quantities 
 might possibly vary, that the numerical value of the error of the theory 
 could be in any case arrived at. 
 
 Le Verrier proceeded to apply this method of investigation, purposing 
 to extend it to the whole of the ecliptic. For this purpose he made 
 the epoch of the disturbing planet vary for every 9 from zero to 360, 
 and computed the corresponding errors of the theory in 1690, 1747, and 
 1758. Examining the expressions for these errors, he found that, for all 
 values of the epoch from zero to 189, no admissible values of the mass 
 and the other two indeterminate quantities could render the results in all 
 the three cases so small that they might reasonably be attributed to errors 
 of observation. As the epoch increased from 189, the errors in each of 
 the three cases began to diminish, and they all became very small, when 
 it attained a value equal to 243 or 252, or any of the intermediate 
 values. From 252 the errors began to increase and soon became 
 inadmissible ; nor did they present any diminution throughout the remain- 
 ing part of the circumference of the ecliptic. Le Verrier therefore came 
 to the conclusion that there is only one region of the ecliptic in which it is 
 possible to place the disturbing planet so as to account for the movements of 
 Uranus, and that the mean longitude of this planet, on the 1st of January, 
 1800, must be included between 243 and 252". 
 
 The next point to ascertain was, whether a planet actually situated in 
 the region indicated by his researches would account generally for the 
 irregularities of Uranus ; for, although he had found that a planet whose 
 mean longitude was somewhere about 252, and whose eccentricity and 
 longitude of perihelion were determined by the equations of 1793 and 
 1828, would also satisfy the equations of 1690, 1747, and 1758, it did not 
 follow as a necessary consequence that all the equations of condition depend- 
 ing severally upon the individual observations of the planet would also be 
 satisfied by the same supposition. In order to establish this point, he 
 resolved to compute the errors of the theory corresponding to the eighteen 
 individual observations which formed the basis of his researches. There 
 was this advantage, however, gained by his previous labours, that it was no 
 longer necessary to extend his investigation to the whole circuit of the 
 ecliptic, it being merely sufficient to examine the region in which he had 
 already found that the planet, if really existing, must be situated, at the 
 commencement of the year 1800. With this view he formed eighteen 
 expressions for the errors of the theory for five equidistant values of the 
 epoch comprised between 234 and 270, the corresponding values of 
 the eccentricity and the longitude of the perihelion being derived, as 
 before, from the two mean equations of 1793 and 1828. The result of 
 this investigation afforded a complete confirmation of his previous re- 
 
HISTORY OF PHYSICAL ASTRONOMY. 183 
 
 searches. He now found that, when the epoch was made equal to 52, 
 the eighteen errors of the theory could be so diminished by assigning to 
 the mass, and the two indeterminate errors of observation, values within 
 their prescribed limits, that the residual quantities might reasonably be 
 supposed to arise from errors of observation. As the epoch diverged on 
 each side of 252, the errors continued small for the first 9; but after- 
 wards they began to increase, and became inadmissible before it reached 
 234 or 270. He therefore concluded that the observations of Uranus 
 might generally be satisfied by the hypothesis of a disturbing planet, whose 
 mean longitude at the commencement of the year 1800 was nearly equal to 
 252. 
 
 It still remained for him to determine the approximate value of the true 
 longitude, a knowledge of which was indispensable to the discovery of the 
 planet? For this purpose, it was necessary for him to investigate the 
 values of the eccentricity and the perihelion corresponding to the value of 
 the epoch adopted by him as the most probable approximation to the truth. 
 Now the expressions for these elements were obtained by eliminating them 
 from the mean equations of 1793 and 1828, after substituting for the epoch 
 the numerical value 252, and consequently each of them contained three 
 unknown quantities ; namely, the mass and the two indeterminate errors 
 of observation. By a skilful discussion of the errors of the theory corre- 
 sponding to the eighteen fundamental equations of conditions, Le Verrier 
 had already arrived at approximate values of these three quantities * 
 He therefore readily determined the numerical values of the eccentricity 
 and the longitude of the perihelion f ; by means of which, and the other two 
 elements already known, he computed the approximate value of the true 
 longitude. He finally concluded that the true longitude of the disturbing 
 planet for the 1st of January, 1847, was 325, and that the probable error 
 did not exceed 10. 
 
 Le Verrier's paper contained the earliest account of researches respect- 
 ing the hypothetical planet that was given to the world, and^ as may well 
 be conceived, it was read with delight by all the astronomers of Europe. 
 Mr. Airy received the Comptes Rendus for the 1st June, on the 23rd of 
 the same month. Finding that the place assigned by Le Verrier to the 
 disturbing planet did not differ more than a degree from that which Mr. 
 Adams had assigned to it eight months previously, he felt a strong per- 
 suasion of the accuracy of the labours of both mathematicians. He was 
 still, however, anxious to ascertain whether the action of the hypothetic 
 planet would account for the errors in the radius vector of Uranus as satis- 
 factorily as it accounted for the errors in longitude, and he now applied to 
 M. Le Verrier for information on this point, as on a similar occasion he 
 
 * Le Verrier, indeed, does not give any account of* the method by which he 
 assigned to the errors of observation their most probable values ; but it is probable that 
 he effected this object by a careful comparison of the residual errors of the theory, which 
 in all cases were expressed in terms of the mass, and the two indeterminate quantities de- 
 noting the errors of observation. It is not impossible also, that, in order to assure 
 greater accuracy to his results in the present instance, he took into account the effect 
 of the errors of observation for 1810 and 1845 ; for, although the presumed insignifi- 
 cance of these errors allowed their rejection when the object was merely to ascertain the 
 region of the ecliptic in which the planet was to be found, still, when the question referred 
 to the determination of its actual position, it is not difficult to perceive the desirableness 
 of taking them into account. In fact, Le Verrier shews, at page 202 of his Memoir, that 
 they exercise a very sensible influence on the ultimate values of the errors of the theory. 
 
 f The paper in the Comptes Rendus for the 1st June does not contain any numerical 
 values of these elements. 
 
184 HISTORY OF PHYSICAL ASTRONOMY. 
 
 had applied to Mr. Adams. In his letter to the French mathematician, 
 he remarks, that the tabular radii vectores of Uranus were too small in 
 recent years ; and he asks whether this would result from the disturbance 
 of an exterior planet occupying the position indicated by the theory. " I 
 imagine," says Mr. Airy, " that it would not be so, because the principal 
 term of the inequality would probably be analogous to the moon's varia- 
 tion, or would depend on sine 2 (v ?/); and in that case the perturba- 
 bation in radius vector would have the sign for the present relative 
 position of the planet and Uranus. But this analogy is worth little until 
 it is supported by proper symbolical computations." 
 
 The reply of Le Verrier to the Astronomer Royal was at once prompt 
 and satisfactory. He stated that his theory accounted for the errors of 
 radius vector as well as those of longitude ; and he explained the circum- 
 stances which caused them to disappear. We have already mentioned 
 that the irregularities of Uranus, if due to a disturbing planet, must have 
 proceeded partly from the errors in the elements of the planet's own orbit, 
 and partly from the perturbations occasioned by the undiscovered planet. 
 Now, Le Verrier found that the errors of radius vector almost wholly 
 vanished when he applied to the elements the corrections derived from 
 the errors of longitude. It was clear, then, that the errors directly de- 
 pendent on perturbation were quite insignificant, compared with those 
 arising from the distortion of the orbit, and this circumstance afforded a 
 satisfactory explanation of the apparent inconsistency between theory and 
 observation, alluded to by the Astronomer Royal in his letter to Le 
 Verrier. The latter, in fact, found that both the eccentricity and the 
 longitude of the perihelion ought to be increased ; and it happened, in con- 
 sequence of the actual position of the planet, that the application of these 
 corrections had the effect of increasing the tabular value of the radius vector 
 almost to the whole extent required by the observations *. 
 
 The results of Mr. Adams, which received so remarkable a confirmation 
 from those of M. Le Verrier, appeared now to the Astronomer Royal to 
 be established beyond all doubt by the satisfactory communication he re- 
 ceived from the latter of these mathematicians. At a meeting of the 
 Board of Visitors of the Observatory of Greenwich, held on the 29th 
 June, 1846, Mr. Airy mentioned the near agreement of the results ob- 
 tained by Le Verrier and Adams relative to the supposed existence of a 
 planet exterior to Uranus ; and he suggested in strong terms the desir- 
 ableness of some Observatory devoting its resources to a systematic 
 search for the undiscovered body. In pursuance of this view he wrote a 
 letter to Mr. Challis, dated the 9th July, recommending an examination 
 of the heavens with the Northumberland refractor, and offering to supply 
 him with an assistant if he should not have leisure to superintend the 
 operation personally f. On the 13th of the same month he wrote a second 
 letter to Mr. Challis on the same subject, inclosing in it a paper headed, 
 " Suggestions for the Examination of a portion of the Heavens in search 
 
 * Airy's Hist. Statement, No. 14. 
 
 f Airy's Hist. Statement, No. 15. It is perhaps right to mention, for the use of some 
 of our readers, that at Greenwich the object of the observations is to determine with the 
 utmost possible precision the apparent positions of the celestial bodies, rather than to 
 acquire a knowledge of the physical structure of the heavens. Telescopes of great power 
 are not, therefore, required at the Royal Observatory. In the present instance it was 
 necessary to observe all the stars, in the part of the heavens appointed for examination, 
 down to the tenth magnitude, but at Greenwich there were no telescopes sufficiently power- 
 ful for this purpose. The instrument alluded to by Mr. Airy is a magnificent refractor pre- 
 sented to the University of Cambridge by the late Duke of Northumberland. 
 
HISTORY OF PHYSICAL ASTRONOMY. 185 
 
 of the New Planet." He proposed taking a sweep of the heavens in the 
 direction of the ecliptic 30 long, and 10 broad, the centre being the 
 place indicated by the theory as the locus of the planet. The paper con- 
 tained the details of a plan for conducting the examination. In his letter 
 he says, " I only add at present that in my opinion the importance of 
 this inquiry exceeds that of any current work which is of such a nature 
 as not to be totally lost by delay." * Professor Challis declined Mr. Airy's 
 offer of an assistant, having himself formed the resolution (as he had pre- 
 viously intimated to Mr. Adams f ) of searching for the planet on the oc- 
 casion of the approaching opposition. Having received a paper from Mr. 
 Adams, containing instructions relative to the theoretical place of the 
 planet, he commenced his observations for this purpose on the 29th July J. 
 The plan contemplated was to sweep over the region of tlje zodiac selected 
 for examination at least three times, completing each sweep before the 
 commencement of the following one. It was concluded that to accomplish 
 this object three hundred hours of observing would be required. The 
 discovery of the planet would be effected by finding that one of the stars 
 in the examined region had not the same position in each sweep. Mr. 
 Challis continued to prosecute his search till the end of September. 
 We shall find that his observations contained more than one place of the 
 planet, and that their subsequent comparison, which was included in the 
 plan of operations, would have infallibly led to its discovery. 
 
 We now return to Mr. Adams. On the 2nd September, 1846, he trans- 
 mitted a second paper to the Astronomer Royal, containing an account of 
 his further researches on the Trans- (Iranian planet. A comparison of his 
 original results with the observations of Uranus had induced him to 
 suspect that the mean distance was somewhat too great. He therefore dimi- 
 nished it to the extent of ^th, assuming it to be equal to 37.5, and then 
 repeated his previous solution. He hoped that by this means the theory 
 would be brought to agree better with the observations of recent years, 
 and that a smaller value would be obtained for the eccentricity, which ap- 
 peared to him too large, as it resulted from his first hypothesis. In his 
 communication to the Astronomer Royal, he gave the elements of the 
 planet by the two hypotheses of the mean distance, and appended a list of 
 residual errors of longitude formed by a comparison of his theory with a 
 great number of observations of the planet included between the years 
 1712 and 1840. These errors were smaller by the second hypothesis 
 than by the first, and the eccentricity was also considerably diminished. 
 Mr. Adams was of opinion that by continuing to diminish the mean dis- 
 tance the theory might be rendered still more accordant with observation, 
 and he was induced to conclude, from an examination of the residual errors 
 of recent years, that, by assigning to the mean distance a value equal to 
 33.6, a very near approximation to the truth would be obtained. This 
 
 * Airy's Hist. Statement, No. 16. 
 
 f Challis' Report to the Syndicate of the University of Cambridge. 
 
 + Ibid. It must be borne in mind that at this time Le Verrier had obtained an ap- 
 proximate value of the position of the planet, but had not assigned determinate values to 
 the mass or the elements of the orbit. A knowledge of the mass was necessary for the 
 purpose of ascertaining the class of stars among which it might be expected that the 
 planet would be found. Mr. Adams, guided by his theoretical results, had mentioned to 
 Professor Challis that the planet would be equal to a star of the ninth magnitude. This 
 circumstance induced Mr. Challis to note the positions of all stars down to the tenth mag- 
 nitude. The actual discovery of the planet has shewn that the range of search adopted 
 was at once necessary and sufficient. 
 
186 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 surmise has been fully borne out by the results derived from actual obser- 
 vations of the planet ; and, while it is highly creditable to Mr. Adams' 
 sagacity, it also shews the thorough insight he had obtained into the 
 mutual bearings of the various parts of the intricate problem with which 
 he was engaged. The following are the elements he deduced from his 
 second hypothesis of the mean distance : - 
 
 Mean longitude, October 1, 1846 . . . 323 2' 
 Longitude of the perihelion .... 299 11' 
 
 Eccentricity . . 12062 
 
 Mass ........ .00015003 
 
 Mr. Adams gave examples of the correction to the tabular value of the 
 radius vector. The correction for 1834 almost coincided with that which 
 Mr. Airy had deduced from observation. The corrections for later years 
 were not quite so satisfactory ; but in this respect also the second hypo- 
 thesis presented a better agreement with observation than the first did. 
 Mr. Adams mentioned that he was then engaged in determining the in- 
 clination and place of the node, and that he hoped to complete his investi- 
 gation in a few days. 
 
 The corrections to the tabular radius vector transmitted, on this occa- 
 sion by Mr. Adams to the Astronomer Royal, naturally suggest a few 
 remarks. We have already mentioned that the latter attached much 
 value to this part of the theory, as affording a criterion for testing the 
 accuracy of the results derived from the researches on the motion in 
 longitude. We can easily imagine that some of our readers will be slow 
 to concur with the views of the Astronomer Royal on this point. If indeed 
 the cause of the irregularities of Uranus was doubtful, it is not difficult to 
 perceive that the explanation of the errors of radius vector by the pertur- 
 bations of an assumed planet would possess much weight in establishing 
 the legitimacy of such an hypothesis ; for, granting that the irregularities 
 were due to some other cause, although it is conceivable that the theory of 
 gravitation might be made to represent the errors in longitude by a suit- 
 able evaluation of the constants of the problem, it is utterly im- 
 probable that the same constants and the same values of them would also 
 account for the errors of radius vector, with which they had no physical 
 connexion. But the necessity of computing the errors of radius vector in 
 addition to those of longitude does not appear so obvious, if it be admitted 
 that the irregularities of Uranus are really due to a disturbing planet, and 
 that the sole point to be decided was the accuracy of the results. In this 
 case it was known a priori that the constants which entered into the ex- 
 pressions of the errors, both of longitude and radius vector, were the bond 
 fide representatives of the physical elements of the problem. It was 
 also known that these expressions were legitimately deduced from esta- 
 blished principles, and consequently were not mere empyrical formula. 
 Hence it might be presumed that results which accounted so satisfactorily 
 for the errors in longitude throughout a period embracing more than a 
 revolution and a half of the planet could hardly fail to account with equal 
 fidelity for the errors of radius vector. This reasoning involves the tacit 
 assumption that, if certain values of the unknown quantities of the problem 
 satisfy the errors of one of the co-ordinates of the planet, they must 
 either be absolutely correct, or must constitute very near approxima- 
 tions to the truth. This principle, however, is at variance with the 
 result of researches in physical astronomy* for it has been found, in 
 
HISTOBY OF PHYSICAL ASTRONOMY. 187 
 
 the case which we are actually considering, that the equations of con- 
 dition involving the errors of longitude may assign to the elements of the 
 disturbing planet, and to the corrections of the elements of Uranus, values 
 which shall account for these errors with sufficient accuracy, but still may 
 differ widely from the true values. Now, if any such system of erroneous 
 values was employed in computing the errors of radius vector, it manifestly 
 does not follow as a necessary consequence that, because the motion in 
 longitude had been satisfied by a mutual compensation of errors, the results 
 in this case also would accord equally well with observation. We are 
 therefore led to conclude that, even if the existence of an exterior planet 
 had been already placed beyond all doubt, the explanation of the errors of 
 radius vector would prove extremely valuable in testing the accuracy of 
 results derived from the errors of longitude. It may be remarked, how 
 ever, that the Astronomer Royal, in his letter to M. Le Verrier, expressed 
 in very explicit terms his doubts respecting the accuracy of the final results 
 of that geometer, without indeed going so far as to reject in toto the hy- 
 pothesis of a disturbing planet. In his letter to Mr. Adams, on the 
 contrary, he does not suggest any such doubts, but simply inquires whether 
 the errors of radius vector were accounted for by his theory as faithfully 
 as those of longitude. We may suppose, then, that Mr. Adams, who had 
 for many years been strongly impressed with the existence of a Trans- 
 Uranian planet, and who had already been conducted to such satisfactory 
 results by his researches on the motion in longitude, may not have duly 
 appreciated the importance attached by the Astronomer Royal to the 
 explanation of the errors of radius vector. It is to be regretted, however, 
 that he -was so tardy in replying to Mr. Airy, especially as he could not 
 have experienced any analytical difficulty in complying at once with his 
 request *. 
 
 An account of the third part of Le Verrier 's labours on the theory of 
 Uranus appeared in the Comptes Rendus for the 31st August, 1846. The 
 main object of the second part of his researches, as announced in the 
 Comptes Rendus for the 1st June, was to obtain an approximate value of 
 the epoch or mean longitude of the hypothetic planet at a given instant. 
 When this was once accomplished, the true value might be investigated by 
 applying to the approximate value an indeterminate correction, and then 
 deducing it from the conditions of the problem simultaneously with the 
 other unknown quantities* There was this advantage gained by a first 
 approximation to the epoch, that, as the correction to the true value might 
 be presumed to be small, it was possible so to conduct the investigation 
 that it would not be necessary to take into account any terms beyond those 
 involving the first and second powers of the correction. For a similar 
 reason a more accurate value of the mean distance might be obtained by 
 supposing the approximate mean distance to be affected with an indeter- 
 
 * We have maintained that it does not necessarily follow, because the errors of longi- 
 tude are satisfied, that the errors of radius vector are satisfied also. In the present in- 
 stance, however, it happens that such is really the case. Mr. Adams^ in his Memoir on 
 the Perturbations of Uranus, has given an expression for the correction to the radius vec- 
 tor involving the correction to the mean longitude and its differential, together with the 
 eight unknown quantities of the problem ; and he has shown that by far the most consider- 
 able part of the expression is due to the term involving the differential of the correction to 
 the mean longitude. Hence it manifestly follows that, if the tabular errors of longitude be 
 satisfied, the errors of radius vector will be satisfied also. This result, however, depends 
 upon the particular values obtained for the unknown quantities, and could not be pre- 
 dicated by any a priori reasoning. 
 
188 HISTORY OF PHYSICAL ASTRONOMY. 
 
 minate error, and then treating the latter as one of the unknown quantities 
 of the problem. There were, therefore, five quantities to be determined 
 relative to the disturbing planet ; namely, the corrections to the mean dis- 
 tance and the epoch, and the absolute values of the mass, the eccentricity, 
 and the longitude of the perihelion. The^e five quantities, together with 
 the corrections to the mean distance, the epoch, the eccentricity, and the 
 longitude. of the perihelion of Uranus, formed nine unknown quantities, 
 upon the determination of which the solution of the problem depended. 
 
 In the investigation of an approximate value of the epoch, Le Verrier 
 employed as the basis of his reasoning a select number of errors of helio- 
 centric longitude. These were obtained by a comparison of the theory 
 with observations made when the planet was in opposition. It would have 
 been impossible to deduce accurately the errors of heliocentric longitude 
 from all the observations, because many of the latter were made when the 
 planet was near the quadratures, and in that case the process of passing 
 from the geocentric to the heliocentric longitude could not be rigorously 
 effected without a knowledge of the error of radius vector ; but this was 
 al together uncertain. He now had recourse to the errors in geocentric lon- 
 gitude, which could be readily computed without a knowledge of the errors 
 of either of the heliocentric co-ordinates, and were, therefore, deducible with 
 equal accuracy from all the observations. In the first part of his researches 
 he had carefully computed the errors in geocentric longitude correspond- 
 ing to two hundred and seventy-nine observations of the planet. Now the 
 analytical expression for these errors contained the nine unknown quan- 
 tities of the problem. Putting it, therefore, equal to each numerical error 
 in succession, Le Verrier formed two hundred and seventy-nine equations 
 of condition, and by means of these he proposed to obtain the solution of 
 the problem. With this view he grouped them into thirty-three mean 
 equations, twenty-six of which depended on the modern observations of 
 Uranus, and the remaining seven on those made previous to its recogni- 
 tion as a planet in 1781. He eliminated without difficulty six of the un- 
 known quantities in terms of the three others, these last being the mass 
 of the disturbing planet, and the corrections to the epoch and the mean 
 distance. Pursuing a process which it would be out of place to attempt 
 explaining here, he formed three final equations, involving these three 
 quantities, and then determined their values by successive approximation. 
 This object being once accomplished, it was easy for him to obtain the 
 values of the other six quantities which he had first eliminated. The 
 following are the results relative to the disturbing planet at which he 
 finally arrived : 
 
 Semi-axis of the orbit t 36.154 
 
 Sidereal revolution ..... 217.387 years, 
 
 Eccentricity ...... 0.10761 
 
 Longitude of the perihelion . . . 284 45' 
 
 Mean longitude, 1st January, 1847 . . 318 47' 
 
 True heliocentric longitude, 1st Jan., 1847 326" 32' 
 Distance from the sun 33.06 
 
 Having determined the precise position of the disturbing planet, by 
 assuming that the observations of Uranus were rigorously accurate, Le 
 Verrier next proceeded to investigate the limits within which it must be 
 
HISTORY OF PHYSICAL ASTRONOMY. 189 
 
 included, allowing each of the observations to be affected with an error as 
 great as could possibly be due to it. He found that the mean distance 
 could not be greater than 37.90, nor less than 35.04, and hence he con- 
 cluded that the limits of the periodic time were 207 years and 233 years. 
 Adopting a given value of the mean distance, and supposing all the other 
 elements to vary, he found that the recorded positions of Uranus might 
 still be represented within the limits assigned by the errors of observation. 
 At length the error in one of the positions having become equal to the 
 greatest possible value assigned to the error of observation, the values of 
 the elements were henceforth restricted by the condition that the error in 
 this position should retain its maximum value, and the locus of the 
 disturbing planet for the 1st January, 1847, corresponding to the differ- 
 ent systems of elements derived from this hypothesis, was a continuous 
 curve. By continuing the variation of the elements, the error in 
 another of the positions became as great as possible, and, the values 
 of the elements being henceforth restricted by it, the locus of the 
 planet was transformed into a different curve. Proceeding in this manner, 
 Le Verrier found that the space within which the planet must be included, 
 corresponding to the assumed value of the mean distance, was a curvilinear 
 polygon whose sides were discontinuous, and for different values of the 
 mean distance he obtained different polygons. The amplitude of the 
 polygons diminished as the value of the mean distance approached its ex- 
 treme limits, and when it actually attained either of them the polygon be- 
 came a point. This circumstance indicated that there was only one posi- 
 tion of the planet that could satisfy the observations. When a sufficient 
 number of such polygons was constructed, they might then be all cir- 
 cumscribed by one continuous curve, and tangents drawn to it w r ould 
 necessarily include the disturbing planet. Le Verrier found that the 
 longitude of the tangent, drawn from the sun to the east side of the 
 bounding curve, was 321, whence, as he had already obtained 326 32' 
 for the most precise value of the planet's longitude, it followed that the 
 space to be explored in this direction extended only to about 5^. The 
 western limit was much more remote from the precise longitude, but he 
 remarked that its amplitude might be reduced considerably by assigning 
 a probable limit to the eccentricity. Assuming that the value of the 
 eccentricity did not exceed .125, he obtained 335 for the limiting longi- 
 tude in this direction. He also found that the value of the mass could 
 not be greater than 4^17* nor l ess t ^ an TTTO o- 
 
 We have mentioned that Le Verrier assigned 326 32' as the true helio- 
 centric longitude of the disturbing planet on the 1st January, 1847. This 
 determination, to use his own words, placed the planet about 5 to the 
 east of the star $ of Capricorn. Only twelve days had elapsed since it 
 was in opposition, and on this account strong hopes were entertained by 
 him that astronomers might succeed in discovering it before it plunged 
 again into the rays of the sun. With the view of directing attention more 
 strongly to this point, he made some interesting remarks relative to the 
 apparent magnitude and visibility of the planet. The apparent magnitude 
 depends on the volume of the body and its distance from the sun. The 
 volume, again, is deducible from the mass and density. Now, he had 
 already found that the mass of the planet was two and a half times greater 
 than that of Uranus. There remained, therefore, only the density to be 
 ascertained. He had no established principles to guide him in coming to 
 a conclusion on this point, and therefore he was compelled to have re- 
 
190 HISTORY OF PHYSICAL ASTRONOMY. 
 
 course to analogy. Now it appears, from a comparison of the relative den- 
 sities of the various planets, that, in general, the density is less according 
 as the planet is more distant from the sun. Le Verrier assumed that the 
 density of the new planet was equal to the density of Uranus. This hy- 
 pothesis was manifestly less favourable tt> its visibility than if he had 
 assumed, according to the strict suggestions of analogy, that the density 
 was somewhat less than that of Uranus. Knowing the density and the 
 mass, he obtained the volume, and finally, by means of the latter and the 
 distance from the sun, which he had found to be equal to thirty-three 
 times the earth's distance, he determined the apparent magnitude of the 
 planet. In this manner he found, that at the instant of opposition it 
 would subtend an angle of 3". 3; and, considering in connexion with this 
 fact the light which it would be capable of reflecting, he concluded that it 
 would not only be visible in good telescopes, but that it would be distin- 
 guishable from the fixed stars by its disc. " This," he remarked, " is a 
 very important point. If the object of discovery is liable to be confounded 
 with the fixed stars, it will be necessary, in order to distinguish it from 
 them, to observe all the small stars situated in the region of the heavens 
 assigned for examination, and to establish in one of them a proper motion. 
 This would be a long and troublesome operation. But, on the other hand, 
 if the planet has a disc of sufficient amplitude to prevent it from being 
 confounded with the stars ; if we may substitute, instead of a rigorous de- 
 termination of all the luminous points, the simple study of their physical 
 appearance, the search will proceed with greater rapidity."* 
 
 The elaborate character of Le Verrier 's researches, and the confidence 
 with which he predicted the discovery of the planet, was calculated to pro- 
 duce a strong impression on the minds of astronomers. This remark ap- 
 plies more especially to those who were cognizant of the simultaneous re- 
 searches of Mr. Adams, and who could appreciate the probability in favour 
 of a result in Physical Astronomy that had been deduced from two inde- 
 pendent investigations. The existence of a Trans-Uranian planet ap- 
 peared now to such astronomers to be placed beyond all doubt, and its actual 
 discovery was expected to be not very distant. It was under the impression 
 of the near approach of this great event that Sir John Herschel used the 
 following memorable words in an address to the British Association, at 
 Southampton, on the 10th September, 1846 : " The past year has given 
 to us the new planet Astrea ; it has done more, it has given us the 
 probable prospect of another. We see it as Columbus saw America from 
 the shores of Spain. Its movements have been felt trembling along the 
 . far-reaching line of our analysis with a certainty hardly inferior to ocular 
 demonstration."! 
 
 Before proceeding further with our account, it may not be out of place 
 to consider shortly what were the means which astronomers possessed for 
 the discovery of a body such as theory indicated in the present case to 
 exist. Now there are two peculiarities which generally distinguish planets 
 from the fixed stars, and which serve the purpose of their detection. 
 These are : 1st, their apparent magnitudes, in virtue of which, when ob- 
 served through telescopes, they exhibit well-defined discs ; 2nd, their 
 motion in the zodiac. Le Verrier, by means of reasoning of a very pro- 
 bable character, had come to the conclusion that the planet would have a 
 
 * Recherches sur le Mouvement de la Planete Herschel, p. 237. 
 t Athenaeum, 3rd October, 1846. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 191 
 
 sensible disc. The apparent diameter, however, which he assigned to it 
 was so extremely small that it was manifest only the most powerful tele- 
 scopes would suffice to distinguish it from the fictitious discs exhibited by 
 the fixed stars. The probability, therefore, of discovering the planet by 
 its physical appearance was confined to a limited number of European 
 Observatories. With respect to the method of discovering the planet by 
 its proper motion, the use of the telescope in this case is mainly to render 
 the star visible as a luminous point, and, in consequence, it is more gene- 
 rally practicable than the method just referred to. On the other hand, 
 the operation of carrying it into effect is extremely laborious, unless the 
 astronomer already possesses a map of the region of the heavens which 
 he purposes to examine, including all the stars down to the magnitude of 
 the body he is in search of. With such a guide, however, nothing can be 
 more simple than to ascertain whether the region which he is engaged in 
 exploring can possibly afford any indication of the planet. For this pur- 
 pose the astronomer has only to compare the actual appearance of the 
 heavens on any night with the map. If the stars in both cases correspond, 
 it follows that no change has occurred since the construction of the map, 
 and, as all the objects whose positions were recorded must in consequence 
 have been of a stellar nature, the comparison of the heavens with the 
 map cannot afford any clue to the existence of a planet. If, however, the 
 map contains a star which is not in the heavens, it is clear that the miss- 
 ing star must have been a planet which wandered out of the region under 
 examination during the period that elapsed since the construction of the 
 map, and its discovery may be expected to result from a careful scrutiny of 
 the heavens in the vicinity of the stars designated on the map. On the 
 other hand, if a star appear in the heavens which is not contained in the 
 map, it clearly indicates the entrance of a planet into the designated re- 
 gion subsequently to the construction of the map. In order to conduct a 
 search for the Trans-Uranian planet after this manner, it was necessary to 
 possess a map on which were designated all the stars in the part of the 
 heavens assigned for examination, down to the tenth order of magnitude 
 inclusive. No such map had hitherto been executed for the region compre- 
 hending the theoretical locus of the planet, and the only method of search 
 which remained to be adopted was that already in course of being carried 
 into effect by Professor Challis, and which was indeed tantamount to the 
 actual construction of a map. 
 
 On the 18th September Le Verrier addressed a letter to the astrono- 
 mers of the Berlin Observatory, announcing to them the result of his re- 
 searches, and requesting their co-operation in searching for the planet. By 
 a singular instance of good fortune the Berlin astronomers possessed an 
 advantage in effecting this search which was not yet available to the other 
 astronomers of Europe. For some years past a series of star maps had 
 been in course of publication, under the auspices of the Berlin Academy of 
 Sciences, comprehending different portions of the region of the heavens 
 which extends 1 5 on each side of the equator, and designating the posi- 
 tions of all stars down to the tenth magnitude*. Just as the accounts re- 
 specting Le Verrier's researches reached Berlin, the map of Hora XXI., 
 the part of the heavens containing the theoretical place of the planet 
 which had been executed with great care by Dr. Bremiker was engraved 
 
 * Many astronomers in other countries of Europe, as well as Germany, have lent their 
 aid in the construction of these maps. One of them was executed by Dr. Hussey, the 
 astronomer to whom allusion has been made at the beginning of this chapter. 
 
192 HISTORY OF PHYSICAL ASTRONOMY. 
 
 and published. The Berlin astronomers received Le Verrier's letter on 
 the 23rd September. On the same evening Dr. Galle compared the 
 appearance of the heavens with the map, and found that the latter did not 
 contain a star of the eighth magnitude which was situate very near the place 
 indicated by Le Verrier as the locus of the disturbing body. The observa- 
 tions of the following evening decided that this was the Trans-Uranian 
 planet. It was then retrograding with a daily motion in right ascension 
 amounting to 62". The following is a comparison of the results of obser- 
 vation and theory. 
 
 Observed Right Ascension 23rd September, 12 h O m 15 s 
 
 M.T.Berlin . . . . . . . 328 19' 16" 
 
 Observed Declination South 13 24' 8"2 
 
 Whence 
 
 Geocentric Longitude 325 53' 
 
 Parallax of the Orbit 1 4' 
 
 True Heliocentric Longitude . . . . . 326 5 7' 
 Longitude for the same instant, assigned by Le Ver- 
 rier's theory ....... 326 0' 
 
 Difference between Observation and Theory . . 57' 
 
 Thus it appears that the place assigned by Le Verrier to the disturbing 
 body did not differ by so much as one degree from its actual place as in- 
 dicated by observation. Nor was the agreement less striking with respect 
 to the apparent diameter of the planet. Le Verrier had predicted that it 
 would be equal to 3".3 ; the micrometrical observations of the Berlin 
 astronomers gave 3" as the real value. 
 
 The accounts of the discovery of the Trans-Uranian planet were re- 
 ceived with admiration and delight by all who felt any interest in the 
 cause of science, and the name of Le Verrier was henceforth associated 
 with those illustrious philosophers who have stamped the age in which 
 they lived with the impress of their genius. We shall now give a brief 
 account of the labours of Professor Challis, who had undertaken a very 
 laborious examination of the heavens in search of the planet. We have 
 mentioned that he commenced his observations on the 29th July. His plan 
 was to divide the region to be explored into zones of 9' in declination, this 
 being the breadth of the field of view of the telescope when a magnifying 
 power of 166 was employed, and to note the positions of all the stars in 
 each zone down to the eleventh magnitude. On the 4th August his obser- 
 vations were made wholly in declination, for the purpose of obtaining a 
 number of stars as reference points. On the 1 2th of the same month he 
 noted the positions of all the stars in a zone which he had already ex- 
 amined on the 30th July. He compared to a certain extent the observa- 
 tions of the two evenings, and, having discovered their complete accord- 
 ance, he felt assured that his method of search might be relied upon. He 
 continued his observations throughout the months of August and September. 
 On the 1st October he was made acquainted with the discovery of the planet 
 by Galle. He had then recorded the positions of 3 1 5 stars, and was making 
 preparations to map them. The necessity for this operation having ceased, 
 he proceeded to discuss the observations, with the view of ascertaining 
 
HISTORY OF PHYSICAL ASTRONOMY. ] 93 
 
 whether they had secured the discovery of the planet. Having resumed 
 the comparison of the observations of the 30th July and the 12th August, 
 which both related to the same zone, he found that a star, marked No. 49 
 in the series of the 12th August, was wanting in the series of the 30th 
 July. It followed, as a necessary consequence, that this was the planet : 
 it had wandered into the zone during the period that elapsed between the 
 two observations. He also easily ascertained, by means of the observation 
 of the 12th August, that the planet was included in the stars observed as 
 reference points on the 4th of the same month*. Thus, although the 12th 
 August was only the fourth day of observing, two positions of the planet 
 were already secured. " This is entirely to be attributed," says Professor 
 Challis, " to my having on those days directed the telescope towards the 
 planet's theoretical place, according to instructions given in a paper Mr. 
 Adams had the kindness to draw up for me." f 
 
 It is a remarkable fact that before receiving intelligence of the discovery 
 of the planet by Galle, Professor Challis had also obtained a position of 
 the planet by pursuing the plan of observation recommended by Le Verrier. 
 On the 29th September he received the Comptes Rendus for the 31st 
 August, containing the account of that geometer's researches on the 
 hypothetic planet. Struck with the author's conclusions relative to the 
 limits of the planet's position and the magnitude of its disk, he resolved 
 to attempt the discovery of the body by means of its physical appearance. 
 He possessed an advantage in prosecuting a search of this kind which few 
 astronomers enjoyed in an equal degree, from having at his command the 
 magnificent equatorial belonging to the Observatory. On the evening of 
 the 29th September he examined a zone comprised between the limits of 
 right] ascension, within which Le Verrier had fixed the position of the 
 planet. Among 300 stars which passed through the field of view of his 
 telescope, one especially attracted his attention by its disk. This proved 
 to be the planet ; it shone with the lustre of a star of the eighth magnitude. 
 
 The search commenced by Professor Challis on the 29th July, and 
 prosecuted with so much energy and perseverance during the two follow 
 ing months, is deserving of attention, both on account of its forming the 
 only systematic attempt to detect the planet that had been made previous 
 to the evening of its actual discovery, as well as on account of the results 
 which were obtained by the subsequent discussion of the observations. It 
 appears that not only was the theoretical discovery of the planet first effected 
 at Cambridge, but two positions of it were also secured at the same place 
 six weeks before a telescope was directed to the heavens in search of it at 
 any other observatory in Europe. In estimating how r nearly Professor 
 Challis had arrived at the actual discovery of the planet, it must be borne 
 in mind that the contemplated search for it extended only to a definite 
 region of the heavens, and that it would have been completed within a 
 definite lapse of time. When the observations came to be discussed, the 
 discovery of the planet would infallibly have resulted from a comparison 
 of the observation of the 30th July with that of the 12th August. 
 
 The earliest announcement of Mr. Adams' researches through the 
 
 * The following are the positions of the planet in right ascension and declination, as 
 assigned by these observations : 
 
 M.T.Greenwich. Right Ascension. North Polar distance. 
 August 4 . . 13 h 26 m 25 s .. 21 h 58 m 14 S .70 .. 102 57' 32".2 
 12 . . 13 3 26 .. 21 57 26.13 .. 103 2 0.2 
 *f* Report to the Syndicate of the University of Cambridge. 
 
194 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 medium of the press was contained in a letter from Sir John Herschel to 
 the editor of the Athenceum, which appeared in the number of that 
 Journal for the 3rd October, 1846. The illustrious philosopher, after 
 referring to the words he used at the meeting of the British Association 
 held at Southampton in the previous nfonth, relative to the probable 
 existence of a planet exterior to Uranus and the prospect of its speedy 
 discovery by the aid of analysis, remarked that lie would not have expressed 
 himself in such confident terms on that occasion if he had not been already 
 aware that Mr. Adams, a young mathematician of Cambridge, had been 
 prosecuting researches similar to those in which M. Le Verrier was 
 engaged* but at the same time totally independent of them, and had 
 arrived at results respecting the actual position of the disturbing body 
 which almost coincided with those deduced by the French geometer*. 
 This announcement was followed by a letter from Professor Challis, which 
 appeared in the Athenalim of the 17th of the same month. The writer 
 gave a brief account of Mr. Adams' labours and of the systematic search 
 which had been undertaken at Cambridge with the object of discovering 
 the planet by its zodiacal motion. He also stated that the observations had 
 been discussed, subsequently to the actual discovery of the planet, at Berlin, 
 whence it was found that the discovery of the disturbing body had been 
 secured by means of the observations of the 30th July and 12th of August. 
 He concluded by intimating that the details of Mr. Adams' researches 
 would shortly be published. The statements of Sir John Herschel and 
 Professor Challis were corroborated at the same time by Mr. Airy in a 
 letter addressed to M. Le Verrier. 
 
 In France the announcement of Mr. Adams' researches Oil the Pertur- 
 bations of Uranus gave rise to a strong manifestation of national feeling. 
 Nor can it be denied that the occasion chosen for preferring the claims of 
 the English mathematician was unfavourable to their ready reception in 
 that country. Amid the universal applause so justly excited by the 
 brilliant researches of M. Le Verrier, it could hardly be expected that the 
 announcement of similar researches prosecuted independently of them in 
 another country, terminating in similar results, and therefore claiming by 
 implication an equal degree of credit, would be received without some 
 degree of reluctance, or discussed with a total absence of passion, by a 
 people especially sensitive on points of national glory. But although this 
 circumstance may account for the absurd violence with which a portion of 
 the French press assailed the eminent astronomers who first announced 
 the labours of Mr. Adams, it does not by any means explain, far less 
 does it justify, the ungenerous aspersions that were cast upon the researches 
 of the English geometer while the means of ascertaining their real 
 character had not yet been laid before the public by persons whose 
 position in the scientific world ought to have served as a guarantee for 
 greater discretion. It was at once assumed that Mr. Adams' solution of 
 the inverse problem of perturbation was a crude essay which could not 
 endure the test of rigorous examination, and it was urged with equal 
 precipitancy, that as his researches had not been duly published, it would 
 be impossible to establish their claim to originality. On the other hand, 
 as their 'merits were attested by the first astronomers of England, it was 
 
 * Sir John Herschel was present at the meeting of the Board of Visitors, held at the 
 Observatory of Greenwich on the 29th June, 1846 (see p. 184), when Mr. Airy gave an 
 account of the researches of Messrs. Adams and Le Verrier. 
 
HISTORY OF PHYSICAL ASTRONOMY. 195 
 
 obvious that they could not be treated \vith indifference. Under such 
 circumstances the course obviously suggested by a due regard to the sacred 
 claims of right and the dignity of science, would have been to suspend 
 judgment on the question altogether, pending the publication of Mr. 
 Adams' researches which were announced as speedily forthcoming. M. 
 Arago, actuated, beyond doubt, by a laudable desire to defend the rights of 
 his countryman from what he conceived to be an unjustifiable aggression, 
 took a different view of the matter, and at once Undertook a critical 
 examination of the merits of Mr. Adams in regard to the theoretical 
 discovery of the Trans-Uranian planet. The paper which he drew up on 
 this occasion is inserted in tihe Comptes Rendus for the 19th October, 
 ] 846 *. We shall not here make any allusion to the assumptions which M. 
 Arago so unwarrantably employs in the absence of acknowledged facts, 
 with the view of preserving the consistency of his reasoning. Their 
 fallacy was effectually exposed a few weeks afterwards, without any contro- 
 versy, by the publication of the admirable researches of Mr. Adams, and of 
 the important mass of documentary correspondence in the possession of 
 Mr. Airy, relative to the discovery of the planet. We shall merely 
 make a few remarks on the main principle laid down by him, and the 
 conclusion which he seeks to draw from it. He assumes, as the basis 
 
 * This paper contains a view of certain communications of Professor Challis which 
 tends at first appearance to lead to a conclusion totally inconsistent with the real state- 
 ments of the English astronomer. M. Arago asserts that Professor Challis, writing to him 
 on the subject of the planet, uses the following words : " I became acquainted on the 29th 
 September with the final researches of M. Le Verrier; I conformed strictly to the sug- 
 gestions of that astronomer, and confined my search within the limits assigned by him." 
 He then remarks that Professor Challis in his letter to the Athenaeum^ announces 
 that he was guided in his search for the planet by a paper which Mr. Adams drew 
 up for him. Having placed these two apparently contradictory statements in juxta- 
 position, M. Arago simply contents himself with the following comment upon them: 
 " I will not seek to reconcile these two versions. I will leave to Mr. Challis the task of 
 explaining how the name of Adams, which did not figure in his first communication, is 
 become so prominent in his second." Now, what are the real facts of the case ? In the 
 Comptes Rendus, tome xxiii. p. 764, there appears a letter from Professor Challis to M. 
 Arago, dated the 5th October, 1846, in which the writer gives an account of his search 
 for the planet with the Northumberland telescope, and mentions his having detected it 
 by its disk on the evening of the 29th September. In this letter he alludes to M. Le 
 Verrier in the terms quoted by M. Arago as above stated. Again, in a letter to the editor 
 of the Athenaum, dated the 15th October, 1846, (see Athenaeum, October 17,) Professor 
 Challis gives an account of the laborious search undertaken by him, having for its object 
 to detect the planet by its zodiacal motion. In this letter he states that he was guided in 
 his search by a paper which Mr. Adams drew up for him ; that he commenced his obser- 
 vations on the 29th July ; and that a comparison of the observations of the 30th July 
 and 12th of August, instituted subsequently to the receipt, of the accounts of Galle's dis- 
 covery, shewed him that he had secured the planet. The reader will at once perceive 
 from the foregoing statements that the two communications of Professor Challis referred 
 to two distinct modes of search prosecuted on two distinct occasions. In his letter to M. 
 Arago he mentions the result of observations pursued with the view of detecting the 
 planet by its physical aspect, professing to have been guided by the instructions of M. Le 
 Verrier. In his letter to the Athcnceum he communicates the result of observations 
 anterior to the preceding that had been made with the view of discovering the planet by 
 its zodiacal motion, asserting to have been guided on this occasion by Mr. Adams. It 
 was impossible that the instructions contained in M. Le Verrier's paper of the 31st 
 August, and first made known to Professor Challis on the 29th September, could have 
 been of any service to that astronomer in a search for the planet prosecuted by him in the 
 beginning of the former of these months. A mind much less acute than M. Arago 's will, 
 therefore, see no inconsistency in the two passages which that illustrious philosopher 
 appears to despair of reconciling together. How justly may we remark in his own words, 
 " L' amitie est souvent aveugle, et se laissc fasciner." 
 
 3 
 
196 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of his reasoning, that the only rational mode of writing the history of the 
 sciences is to rely exclusively on publications, the dates of which are well 
 ascertained, and he hence infers that Mr. Adams has no right to be 
 mentioned in connexion with the discovery of the Trans-Uranian planet, 
 either by a detailed citation, or by any alhfsion whatever. It will at once 
 occur to the reader that the force of this proposition depends entirely on 
 the precise meaning applied to the term publication. If it be restricted 
 to printed documents, we conceive that the principle advanced by M. 
 Arago is totally untenable, and that it essentially vitiates any conclusion 
 that may be derived from it. .To limit the test of decision in disputed 
 questions of scientific discovery to such a species of evidence would be at 
 once repugnant to reason and at variance with the common practice of 
 mankind in all ages. Are communications transmitted to learned societies, 
 or documents of an authentic character, addressed to persons of acknow- 
 ledged probity and occupying official positions, to be set at nought as so 
 much waste paper, merely because they have not passed through the 
 ordeal of the printing press ? To admit such a monstrous proposition 
 would be striking at the root of those unalterable principles of common 
 sense upon which our primary notions of evidence are founded, and to 
 introduce in their stead an arbitrary standard of decision which, so far from 
 defining clearly the rights of rival claims, would itself perpetually form the 
 subject of acrimonious controversy. We have no reason however to sup- 
 pose that the illustrious philosopher, who drew up the paper in question, 
 was really of opinion that the evidence which could be of any utility in 
 establishing claims to scientific research rested on so narrow a basis. On 
 the contrary, we are disposed to infer from the acknowledged acuteness of 
 his discriminating powers, and his enlightened zeal in the cause of truth, 
 that his sentiments as above expressed, demand a more liberal interpre- 
 tation, and that in the present instance, had he been in possession of all 
 the facts relating to the disputed question, he would have arrived at a 
 conclusion more consistent with reason and justice than that to which he 
 was conducted by the imperfect statements then accessible to him *. 
 
 The question of Mr. Adams' merits in connexion with the theoretical 
 discovery of the planet exterior to Uranus, was soon placed in a clear light. 
 On the 13th of November, 1846, a paper was read by Mr. Airy before the 
 Astronomical Society, entitled "An Historical Statement of Circumstances 
 connected with the Discovery of the Planet beyond Uranus." This 
 valuable communication, besides containing a large mass of interesting 
 materials bearing more or less on the discovery of the planet, exhibits, in 
 one unbroken chain of correspondence, the progress of Mr. Adams' 
 researches, from the date of Professor Challis' first letter to the Astronomer 
 Royal on the subject in February, 1844, down to the acknowledgment at 
 Greenwich of Mr. Adams' paper, dated the 2nd September, 1846. The 
 independent character of Mr. Adams' researches was now placed beyond 
 all doubt or equivocation, and his claims to the theoretical discovery of 
 the planet established on the incontrovertible evidence of authentic docu- 
 ments. Mr. Adams' Memoir on the Perturbations of Uranus was read 
 before the Astronomical Society on the same day on which Mr. Airy 
 communicated his statement, and was subsequently published in the 
 sixteenth volume of the Memoirs of the Society, and also in the Nautical 
 
 * See in connexion with these remarks the note at the foot of page 214, in the next 
 chapter. 
 
HISTOKY OF PHYSICAL ASTRONOMY. 197 
 
 Almanac for 1850. If anything was wanted to complete the vindication 
 of Mr. Adams' claims, it was amply supplied by this Memoir. Apart from 
 all consideration of the brilliancy of the final result in relation to the 
 planetary system, it exhibits an admirable specimen of the application of 
 analysis to one of the most difficult subjects of physical astronomy, being 
 planned with a sagacious appreciation of the difficulties peculiar to such 
 abstruse researches, and pursued throughout its details with exquisite 
 mathematical skill. 
 
 The impression produced by the communication of Mr. Airy to the 
 Astronomical Society was such as always naturally ensues when truth is 
 presented in the form of a plain statement of facts, stripped of all ingenuity 
 of reasoning or flourish of rhetoric, and relying for acceptance solely on 
 the authenticity and innate strength of the evidence by which it is sup- 
 ported. The most illustrious philosophers, of Europe, while justly acknow- 
 ledging the originality and brilliancy of M. Le Verrier's researches on the 
 perturbations of Uranus, have cordially concurred in awarding a similar 
 tribute to Mr. Adams, and the names of both these geometers are now 
 imperishably associated with the theoretical discovery of the planet by 
 which these perturbations were produced. 
 
 It has been asserted that as M. Le Verrier's researches alone were 
 instrumental in leading to the actual discovery of the planet by Galle, 
 Mr. Adams, whose labours exercised no influence on the observations of 
 the German astronomer, cannot justly be placed in so high a position as 
 his illustrious contemporary. This opinion we imagine to have originated 
 in an imperfect discrimination of the respective functions of the geometer 
 and the observer. The geometer, relying upon the firmly-established 
 principles of the theory of gravitation, recognises in the irregularities of 
 one of the planets unequivocal evidence of the existence of an unseen 
 member of the solar system, and, by a successful application of analysis, 
 he arrives at a knowledge of its position. The observer, guided by the 
 instructions of the geometer, searches the heavens, and succeeds in dis- 
 covering optically what the geometer had previously discovered theoretically. 
 Each has his peculiar duties, totally distinct from those of the other ; and 
 we should be acting in opposition to the plainest maxims of justice by 
 ascribing to the one any credit on account of duties performed by the 
 other. The eclat which so justly surrounds the optical discovery of the 
 Trans- Uranian planet must be shared severally by the Berlin Academy of 
 Sciences under whose auspices the charts of the zodiac have been con- 
 **structed, by Dr. Bremiker who so skilfully designated the region of the 
 heavens in which the planet was moving, and by Dr. Galle, who so 
 promptly availed himself of the publication of Dr. Bremiker's chart. If 
 \ve would look for the real grounds of M. Le Verrier's renown, we must 
 abandon the glorious spectacle of the heavens and enter the solitary 
 chamber of the geometer. It is there that he justly becomes the object of 
 our admiration, as he advances step by step along the intricate maze of 
 his researches, vanquishing each successive difficulty by the ready re- 
 sources of his genius, and cheerfully executing calculations which are 
 almost appalling to contemplate ; until a bright flood of light is finally 
 diffused over his labours, and the distant member of our system, which 
 human eye has not yet seen, discloses itself to his purely intellectual scru- 
 tinies with all the certainty of demonstrative reasoning. If this be the 
 just view of M. Le Verrier's labours in relation to the discovery of the 
 Trans-Uranian planet, we are then constrained by parity of reasoning to 
 
198 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 take a similar view of the equally admirable labours of Mr. Adams. Nor 
 can the award of equal merit be withheld, on the ground that Mr. Adams 
 reserved the secret of his researches to himself, while M. Le Verrier 
 openly promulgated his results to the world, and thereby put astronomers 
 in possession of the means of actually discovering the planet. This 
 objection is untenable, for the simple reason that it is directly at variance 
 with acknowledged facts. Mr. Adams communicated his results to two of 
 the most influential astronomers of England, whose co-operation, as we 
 have already had occasion to remark, sufficed to secure the optical dis- 
 covery of the planet. That the laborious search undertaken at Cambridge 
 was anticipated as regards the final result by the more simple procedure 
 adopted at Berlin, cannot, without a flagrant violation of the rules of jus- 
 tice, be considered derogatory to the merits of Mr. Adams. It was suf- 
 ficient that he had communicated his results to competent astronomers. 
 It would be totally inconsistent with reason to hold his fame responsible 
 for any ulterior proceedings. We have already mentioned the peculiar 
 advantage enjoyed by the Berlin astronomers in searching for the planet. 
 If a similar facility of search had been accessible at the Observatory of 
 Cambridge, it is admitted by all persons that the planet could not fail to 
 have been first discovered there*. This is a question, however, which 
 concerns Professor Chain's, but does not, in the remotest degree, affect the 
 purely theoretical labours of Mr. Adams. 
 
 We have been induced to submit to the reader the foregoing remarks, 
 because we conceive that the brilliant result achieved by the Berlin astro- 
 nomers has had a tendency to foster erroneous ideas relative to the merits 
 of the various persons, whether mathematicians or astronomers, whose 
 labours have been more or less associated with the discovery of the Trans- 
 Uranian planet. It is only, however, by persisting to confound things 
 totally dissimilar in their nature, that any such notions can retain a per- 
 manent hold on the mind. 
 
 Soon after the discovery of the planet, an attempt was made in this 
 country to exhibit in an unfavourable light the conduct of the astronomers 
 to whom Mr. Adams had communicated his results towards the close of 
 the year 1845. They were charged in vehement terms with lukewarm- 
 ness in the cause of science, as well as indifference to the honour of the 
 country and the reputation of Mr. Adams, on the ground that they did not 
 institute an immediate search for the planet which theory had indicated 
 so clearly to exist. It was alleged that the execution of this task de- 
 volved more especially upon them, inasmuch as they were the official 
 astronomers of the country, and that, by neglecting to carry into effect the 
 proposed search, time was allowed for a rival to step into the field and to 
 divide with Mr. Adams the honour attached to the theoretical discovery of 
 the planet. 
 
 It is hardly necessary to state that this accusaticii is the offspring of in- 
 discriminating zeal or personal prejudice, rather than the result of a dis- 
 passionate examination of facts. We are confident that the simple perusal 
 of the foregoing account will be amply sufficient to convince any unbiassed 
 mind of the justness of this assertion. As, however, the charge is not desti- 
 tute of plausibility, and as some of our readers, who have not bestowed 
 
 * " Si M. Challis s'en fut servi (une carte des etoiles) au lieu de suivre une marche plus 
 penible, il n'eut pas manque une decouverte qui echappa en pareille circonstance a Le- 
 monnier et a Lalande." Extract of a Letter from M. Valz to M. Arago, Comptes Rendus, 
 tome xxiv. p. 880. 
 
HISTORY OF PHYSICAL ASTRONOMY, 109 
 
 sufficient attention on the subject, may have been misled to some extent 
 by this groundless clamour, we deem it not altogether out of place to sub- 
 mit a few remarks here in relation to it. We have not indeed the slightest 
 doubt that if a diligent search of the heavens had been instituted in the 
 month of November, 1845, it would have resulted in the discovery of the 
 planet. But, while fully conceding this point, we are by no means pre- 
 pared to admit that existing circumstances would have warranted the im- 
 mediate appropriation of the resources of any official Observatory to such 
 an object. It must be borne in mind that Mr. Adams' results were the 
 fruits of the first solution of the problem of planetary perturbation which 
 the geometer, aided by analysis, had yet arrived at. It was reasonable 
 then to suppose that the position of the planet was not assigned with a 
 high degree of accuracy, and that, in order to secure its discovery, a con- 
 siderable region of the heavens would require to be submitted to a careful 
 examination. In carrying this operation, however, into effect, no aid could 
 be derived from any previous labours in Uranography, since a star map 
 had not yet been constructed for the part of the zodiac in which the planet 
 was then moving. The search, therefore, could only be accomplished by 
 the prosecution of an extensive course of observations, similar to that 
 which Mr. Challis undertook in the following year. Under such circum^ 
 stances it was imperative on the part of the astronomer, charged with 
 official duties, to exercise due discretion in selecting the most favourable 
 period for devoting the resources at his disposal to a systematic search for 
 the planet. This line of conduct was more especially prescribed in the 
 present case, as two months had already elapsed since the planet was in 
 opposition, and the chance of effecting its discovery before it was lost in 
 the rays of the sun had in consequence considerably diminished. The sub- 
 sequent history of the circumstances connected with the discovery of the 
 planet confirm this view of the subject. Although M. Le Verrier an- 
 nounced the existence of the undiscovered body as early as the 1st June, 
 1846, and confidently asserted, as the result of a careful analysis, that the 
 error in the position he assigned to it did not exceed 10, it does not ap- 
 pear that a single telescope was directed to the heavens in search of the 
 disturbing body at any Observatory on the Continent of Europe previous 
 to the night of its actual discovery towards the close of the month of Sep- 
 tember of the same year. Even at the Royal Observatory of Paris, which 
 is under the direction of the illustrious philosopher who originally sug- 
 gested to M. Le Verrier the subject of the perturbations of Uranus, and 
 where it might have been expected that the remarkable results obtained by 
 the geometer would have excited peculiar interest, no steps appear to have 
 been taken towards the actual discovery of the planet, although a month 
 had elapsed between M. Le Verrier's announcement of his final results on 
 the 31st August, 1846, and the receipt of the intelligence from Berlin, 
 containing the accounts of Galle's discovery. That a search for the dis- 
 turbing body would eventually have been undertaken at more than one 
 Observatory is quite certain; but it was not the opinion of any astronomer, 
 that without the aid of a star map, this object could be successfully accom- 
 plished, except by an extensive and systematic course of observation. 
 " Had it not been for the infinitely favourable circumstance," says M. Encke, 
 " of possessing a map whereon one might be sure to find the positions of all 
 the fixed stars down to the tenth magnitude, I do not think that we should 
 have found the planet." * These remarks will appear superfluous to those 
 
 * Comptes Rendus, tome xxiii. p. 662. 
 
200 H1STOBY OF PHYSICAL ASTRONOMY. 
 
 who have any practical knowledge of astronomy. They are addressed 
 especially to the general reader, who might be led by misrepresentation 
 to form inaccurate views on the subject. Men of science have all been 
 delighted and astonished that the planet was discovered so soon. Only 
 those who make the cause of science subservient to the miserable grati- 
 fication of personal feeling have sought to indulge in opprobrious language, 
 because the discovery did not take place sooner. Such persons, true to 
 their instincts, would have been the first to hold up to public ridicule the 
 credulity of the planet hunters, and to raise the charge of a wasteful 
 expenditure of the country's resources, if the speedy discovery of the 
 disturbing body had not indicated a different, though equally unjustifiable, 
 ground of obloquy. 
 
 It would be an invidious task to institute a comparison between the 
 respective merits of Le Verrier and Adams in connexion with the immortal 
 discovery, of which we have endeavoured to give some account in the pre- 
 ceding pages. We are of opinion that the labours of both these geometers 
 are equally calculated to excite admiration. The annals of science do 
 not contain a brighter page than that which records the progress of M. 
 Le Verrier's labours as he advances from the ill-defined irregularities of 
 Uranus to the precise position of the undiscovered planet. The care 
 with which he scrutinizes every fact; the vigilance he exhibits in de- 
 tecting every imaginable source of error, and the thorough manner in which 
 he sifts all its parts; the ingenuity and conclusiveness of his methods, 
 and his indomitable perseverance in calculation indicate, in a high degree, 
 the possession of those qualities which constitute the main elements of 
 success in all researches relating to the physico-mathematical sciences. 
 Nor does a review of Mr. Adams' labours offer a less pleasing picture. We 
 see the obscure undergraduate, while his attention is yet distracted by the 
 routine of academic discipline, seizing with the happy intuition of genius the 
 true theory of Uranus, and forming the bold resolution of tracing it to its 
 final results. The constancy with which he afterwards struggles to effect 
 this object, notwithstanding the manifest disadvantages of his position, is 
 equalled only by the masterly character of his analytical researches and 
 the brilliant termination to which he conducts them. It is gratifying to 
 reflect that the labours of both Le Verrier and Adams, in connexion with 
 the perturbations of Uranus, are so completely dissociated, that no danger 
 of a mis-statement of facts can exist in the discussion of their relative 
 merits. Differences of opinion on this last point will, no doubt, always 
 prevail ; but we are confident that future ages will concur with the present 
 in awarding to each geometer the tribute of unqualified admiration. 
 
 The discovery of the planet Neptune (for such is the name by which 
 Astronomers have agreed to distinguish the Trans-Uranian member of 
 the Solar System) marks an important epoch in the history of physical 
 astronomy. Hitherto the object of the geometer had been to unfold by a 
 deductive process the principles of perturbative influence, and to explain 
 by them the various phenomena of the planetary motions. It was only in 
 the determination of the masses of the planets, and in assigning the ratios 
 of their. polar and equatorial axes, that the order of inquiry was reversed, 
 and an accurate knowledge of the disturbing influence was sought to be 
 established by reasoning upwards from its observed effects. In each of 
 these cases, however, the equations of condition are of extreme simplicity, 
 and the value of the final results is dependent much less upon the skill of 
 the geometer than upon the accuracy of the fundamental observations. The 
 idea of submitting to a similar treatment the problem of three bodies does 
 
HISTOEY OF PHYSICAL ASTEONOMY. 201 
 
 not appear to have occurred to any of the great geometers \vhose names are 
 associated with the development of the theory of gravitation. Nor is this 
 circumstance calculated to excite surprise, for the actual state of Physical 
 Astronomy had not yet demanded such an advanced step. It was only 
 when all the consequences resulting from the mutual action of the planets 
 already known had been fully deduced, and the outstanding irregularities 
 had assumed the form of residual phenomena depending on some foreign 
 influence, that further speculation suggested the expediency of inverting 
 the usual order of investigation. It is manifest from this circumstance, 
 that the complete establishment of the formulae of planetary perturbation 
 must have preceded any attempt to ascend from the effects produced by 
 an unseen planet to the determination of its actual position. The accom- 
 plishment of this latter object is therefore an indication of the highly- 
 advanced state of physical astronomy, since it implies not only that the 
 difficulties peculiar to the inverse problem of perturbation have been 
 successfully overcome, but also that the irregularities occasioned by the 
 mutual action of the planets have been deduced from the principles of the 
 Newtonian theory, and have, in all instances, been found to accord with 
 the results derived from observation. This remark does not, of course, 
 apply to the planet which theory has recently revealed to us, since a con- 
 siderable time must elapse before an accurate knowledge of the inequalities 
 of its motion can be obtained. It will then be an interesting point to 
 ascertain whether these inequalities do not in their turn afford indications 
 of the existence of a still more remote member of the solar system. The 
 astronomer is thus led to speculate on the theoretical discovery of planets, 
 reflecting too feeble a light on account of their immense distance from the 
 sun, to be ever visible, even by the aid of the most powerful telescopes. 
 It is to be hoped, that notwithstanding the abundant harvest, which has 
 been already reaped in Celestial Mechanics, that magnificent region is 
 destined still to afford more profitable fields for the application of the re- 
 sources of analysis than that which the imagination here suggests. 
 
 CHAPTER XIII. 
 
 The Elements of the Planet Neptune deduced from Observation. -They are found to be 
 Discordant with the Results of Theory The cause of Discordance assigned. The 
 Planet observed by Lalande. Theory of its Perturbations Researches on the Value 
 of its Mass. Uncertainty respecting this Element. Researches of M. Hansen on the 
 Lunar Theory. Conclusion of the History of Physical Astronomy. 
 
 As soon as astronomers received intelligence of the discovery of the Planet 
 Neptune, the new member of the solar system was regarded with intense 
 interest, and accurate observations of it were made both in Europe and 
 America. When the elements of the orbit were calculated from these ob- 
 servations, a comparison of the results with those assigned by the theories 
 of Le Verrier and Adams led to rather unexpected conclusions. Although 
 the orbits assigned by these geometers to the disturbing planet did not 
 differ materially from each other, they both, on the other hand, exhibited 
 
202 HISTORY OF PHYSICAL ASTRONOMY. 
 
 a very marked discordance with the real orbit, as indicated by observation. 
 It was found that the orbit in which the planet actually revolved was much 
 smaller than either of those deduced from theory, and that, instead of being 
 very eccentric, it approached very nearly to a circular form. The following 
 are the elements calculated from observation by Mr. Walker of Washing- 
 ton, U.S. : 
 
 Mean distance 30.0363 
 
 M. Long. January 1, 1847; M. T. Greenwich 328 32' 44".20 
 
 Eccentricity . . . -'i 00871946 
 
 Long, of Perihelion , . &*& . . 47 12' 6".50 
 Long, of Ascending Node . . , . 130 4 20 .81 
 Inclination , I 46 58 .97 
 
 Mean Daily Motion . , . . . . 21".55448 
 
 Periodic Time . . . 164.6181 trop. years. 
 
 Elements of the planet's orbit were also calculated by other astronomers, 
 and the results were found to agree very nearly with those above given. 
 It appears that the mean distance, instead of being nearly double the 
 mean distance of Uranus, amounts only to about two-thirds of it. The law 
 of Bode, therefore, which is so remarkably applicable to the other mem- 
 bers of the planetary system, totally fails in this case. The general 
 discordance of the elements with those severally assigned by the two 
 geometers who were led to the theoretical discovery of the planet, at first 
 occasioned considerable surprise, and it was suspected that some difficulty 
 would be experienced in rendering a satisfactory account of its origin. A 
 little reflection, however, served to arrive at clearer views on the subject. 
 In order that the reader may understand how elements so remote from the 
 truth as those of Le Verrier and Adams, could have sufficed to effect the 
 theoretical discovery of the planet, it is necessary to form a distinct con- 
 ception of the nature of the problem, by the solution of which these geo- 
 meters were conducted to their respective results. The data of this 
 problem were the observed perturbations of Uranus, and the main object 
 to be accomplished was to determine the position in the zodiac occupied 
 at any assigned instant by the disturbing body so as to arrive at its actual 
 discovery. Now, the derangement occasioned in the motion of any planet 
 by the action of another planet upon it depends on the intensity and 
 direction of the disturbing force at each instant ; and these again depend 
 on the mass of the disturbing body, and on its distance and longitude with 
 respect to the sun. It is manifest, therefore, that only those elements 
 which will accurately assign the distance and longitude of the disturbing 
 body will render a complete account of the perturbations of Uranus. But 
 if the values of the heliocentric co-ordinates should not be absolutely cor- 
 rect, still, if they approach with tolerable approximation to the true values, 
 it is not difficult to perceive that by a due adjustment of the mass, the 
 intensity and direction of the disturbing force will be represented with a 
 corresponding degree of precision. Under such circumstances the anoma- 
 lies of the disturbed planet will be accounted for with nearly as great 
 fidelity as if the disturbing planet were in its true place, for the error of 
 perturbation is obviously of an order inferior to the error in the place of 
 the disturbing body. Now, although it is impossible permanently to re- 
 present, even with tolerable accuracy, the heliocentric co-ordinates of a body 
 revolving in an elliptic orbit by means of any elements which differ from 
 
HISTORY OF PHYSICAL ASTRONOMY. 
 
 203 
 
 the true elements, still, when the question refers only to a section of the 
 orbit, this object may be accomplished by employing indefinite combina- 
 tions of elements, differing very considerably from each other. This will 
 be readily understood when it is borne in mind that the theory of elliptic 
 motion assigns four arbitrary constants, which may be modified in a variety 
 of ways, so as to answer the purpose of mutual correction ; and that on 
 account of the smallness of the arc described by the body, the outstanding 
 errors, which inevitably exist in all such cases, are not allowed time to 
 develope themselves to any serious extent. In the case of Neptune dis- 
 turbing Uranus, the perturbations are sensible only a little before and 
 after conjunction. Throughout the whole period embraced between 1690, 
 the year of the earliest observation of Uranus, and the commencement of 
 the present century, the action of the disturbing planet has been quite 
 inappreciable ; and consequently the tabular errors of Uranus for that 
 period may be considered as wholly explicable by the errors of the elliptic 
 elements. The last conjunction of the two planets took place in the year 
 1822, and the action of the disturbing planet was sensible only during 
 about twenty years anterior to that event, and the same number of years 
 subsequent to it. It is manifest, therefore, that any elements which will 
 afford a pretty accurate representation of the heliocentric co-ordinates of 
 Neptune during the present century, will account with sufficient fidelity 
 for the perturbations of Uranus during the same period. Conversely, if 
 the perturbations are faithfully accounted for, we may conclude that the 
 theory is capable of representing the co-ordinates of the disturbing planet 
 with considerable precision, and that they may be employed with confidence 
 for the purpose of its actual discovery. That the theories of Le Verrier 
 and Adams were capable of so representing the co-ordinates of Neptune 
 during the whole period when its action was sensible, may be seen from 
 the following table, which exhibits the actual and theoretical values of the 
 longitude and radius vector for the beginning of each of the years specified 
 between the years 1800 and 1860 :^ 
 
 
 
 
 Theory of Adams *. 
 
 
 Planet Neptune. 
 
 Theory of 
 Le Verrier. 
 
 
 
 
 
 
 
 1st Approximation. 
 
 2nd Approximation. 
 
 Year. 
 
 Longitude. 
 
 Rad. Vec. 
 
 Longitude. 
 
 Had. Vec. 
 
 Longitude. 
 
 Rad. Vec. 
 
 Longitude. 
 
 Rad. Vec. 
 
 1800 
 
 226 4' 
 
 30.30 
 
 231 34' 
 
 33.57 
 
 236 46' 
 
 36.31 
 
 238 9' 
 
 34.90 
 
 1810 
 
 247 20 
 
 30.28 
 
 251 10 
 
 32.80 
 
 254 13 
 
 34.75 
 
 256 39 
 
 33.92 
 
 1820 
 
 268 52 
 
 30.23 
 
 271 28 
 
 32.35 
 
 273 11 
 
 33.45 
 
 276 5 
 
 33.25 
 
 1830 
 
 290 31 
 
 30.55 
 
 292 8 
 
 32.29 
 
 293 27 
 
 32.56 
 
 295 54 
 
 32.96 
 
 1840 
 
 312 17 
 
 30.06 
 
 312 36 
 
 32.63 
 
 314 30 
 
 32.22 
 
 316 10 
 
 33.11 
 
 1850 
 
 334 12 
 
 29.96 
 
 332 25 
 
 33.32 
 
 335 36 
 
 32.48 
 
 335 50 
 
 33.67 
 
 1860J 356 14 
 
 29.87 
 
 351 17 
 
 34.26 
 
 356 1 
 
 33.30 
 
 354 39 
 
 34.57 
 
 * Mr. Adams' theory is founded upon a method of successive approximation. A cer- 
 tain value of the mean distance is first assumed, and by a comparison of the results 
 calculated by its aid with those derived from observation, an indication is obtained of the 
 direction in which the error in the mean distance lies, and also of its probable magnitude. 
 The solution is then repeated with a new value of the mean distance, suggested by the 
 original solution, and a further approximation is obtained. This is the method of 
 
204 HISTORY OF PHYSICAL ASTRONOMY. 
 
 It is manifest that any two corresponding co-ordinates of either of the 
 theories contained in the above table might have been employed with suc- 
 cess in searching for the planet. Even twenty years before conjunction the 
 error of its position as assigned by Adams' first approximation amounts to 
 little more than 1 0, a quantity which falls considerably within the range of 
 search proposed by the Astronomer Royal to Professor Challis, in the month 
 of July, 1846. The reader will not fail to remark, that the longitudes are 
 generally represented with greater accuracy than the distances. This cir- 
 cumstance admits of easy explanation. The intensity of the disturbing force 
 in any given configuration of the two planets depends on the mass and dis- 
 tance of the disturbing planet. Now, if the distance be made too great, 
 the disturbing force will be enfeebled in a corresponding degree ; but this 
 effect may be obviated by a suitable increase of the mass. This is pre- 
 cisely what happens in the theories of Le Verrier and Adams. The dis- 
 tances are all too great in both theories ; but, on the other hand, the mass 
 in each case is considerably enlarged beyond its true value. The pertur- 
 bations of Uranus may therefore be accounted for, in so far as the intensity 
 of the disturbing force is concerned, even although the radius vector of the 
 theoretical planet should be considerably erroneous. The mass, however, 
 exercises no influence in determining the direction of the disturbing force ; 
 and if the latter element be erroneous to any great extent, the perturba- 
 tion will be necessarily erroneous also, since it cannot derive compensation 
 from any other source. Hence arises the necessity of a comparatively 
 higher degree of accuracy in the representation of the longitudes of the 
 theoretical planet. 
 
 When the elements of Neptune were determined with a degree of pre- 
 cision sufficient to enable astronomers to trace its motion through the 
 anterior part of its orbit, attempts were made to ascertain whether it had 
 been observed on any occasion previous to its discovery as a planet by Dr. 
 G alle. It was soon found by Dr. Petersen, of Altona, and Mr. S. Walker, 
 of Washington, thatja star in the Histoire Celeste of Lalaude, observed 
 May 10, 1795, and since missing, could be no other than the planet Nep- 
 tune. The place of the star being marked doubtful, the French astrono- 
 mers were' induced to examine the original manuscripts of the Histoire 
 Celeste, which are deposited in the Royal Observatory of Paris. An in- 
 spection of the observation established the identity of the planet with the 
 recorded star, and disclosed an additional fact of extreme interest. It 
 appeared that the planet was also observed on the 8th May, 1795, and 
 that its right ascension and declination were regularly recorded, although 
 they were not subsequently inserted in the printed catalogue. The dis- 
 cordance of the two positions May 8-10, in a case where identity was 
 looked for, beyond doubt suggested to Le Fra^ois Lalande a suspicion of 
 the accuracy of his observations, and induced him to suppress altogether 
 the observation of May 8. A comparison of the two observations clearly 
 
 investigation generally employed in physical astronomy. In his first solution, Mr. Adams 
 assumed that the mean distance of the hypothetic planet was equal to 38.4 ; in his second 
 solution he made it 37.5 ; and in his communication to the Astronomer Royal, dated 
 September 2, 1846, he stated, as the result of further discussion, that 33.6 would 
 probably be a very near approximation. The actual mean distance in fact is 30.04. 
 Thus we see that Mr. Adams was fairly on the track of the true orbit. The method 
 employed by M. Le Verrier is of a more ambitious character, but, unfortunately, it is not 
 adequate to meet all the difficulties of such abstruse enquiries, and in the present instance 
 it had the effect of betraying M. Le Verrier into error with respect to the limits of the 
 mean distance and the other elements of the orbit. 
 
HISTORY OF PHYSICAL ASTRONOMY. 205 
 
 exhibits the retrograde motion of a planet, and assigns differences of 
 right ascension and declination, agreeing almost exactly with those indi- 
 cated by the motion of the planet Neptune. 
 
 An examination of the mutual action of Uranus and Neptune illustrates 
 some very interesting points in the theory of planetary perturbation. 
 In consequence of the mean motion of the former of these planets being 
 only a small fraction less than twice the mean motion of the latter, the 
 perturbations which recur in every synodic revolution of the two planets, 
 assume a resemblance to those which take place in the theories of the 
 first and second, and of the second and third satellites of Jupiter. This 
 near commensurability of the mean motions, in fact, introduces into the 
 orbit of each planet a considerable eccentricity, dependent wholly on per- 
 turbation, and distinguishable from the permanent eccentricity of the orbit 
 by the constant coincidence of the line of apsides with the line of conjunc- 
 tion of the two planets. In the case of Neptune disturbing Uranus, the 
 aphelion of the movable ellipse is constantly turned towards the point of 
 conjunction. On the other hand, when the action of Uranus upon Neptune 
 is considered, it is the perihelion that is turned towards the same point. 
 In another respect the perturbations of the two bodies resemble those of 
 various other primary members of the planetary system. The near com- 
 mensurability of the mean motions, combined with the permanent eccen- 
 tricities of the orbits, gives rise to an inequality of long duration, similar 
 to that in the theories of Jupiter and Saturn, or any of the other long 
 inequalities to which we have had occasion to allude. The magnitude and 
 duration of this inequality cannot be ascertained with precision until 
 astronomers arrive at an accurate determination of the elements of the 
 two planets. This remark applies more especially to the mean distances, 
 a very small error in their relative values producing an enormous influence 
 on the final results. If we adopt 30.2026 for the mean distance of Neptune, 
 being one of the earlier values deduced from observation, the duration of 
 the inequality will be 6820 years. On the other hand, if we employ 
 Mr. Walker's determination of the mean distance, which differs from the 
 preceding value only by T -J^., the duration of the inequality will only 
 extend to 4051 years. The magnitude of the inequality will vary in a still 
 greater proportion with the change of mean distance *. 
 
 The mass of Neptune is an element which, in the present state of the 
 theory of the planet, is still involved in great uncertainty. A satellite 
 which has been discovered by Mr. Lassel fortunately affords the means of 
 determining its value independently of the perturbative action of the 
 planet, but no satisfactory results on this point have been elicited by the 
 researches of astronomers. M. Otto Struve, by means of his own observa- 
 tions, makes the period of the satellite 5 d 21 h 15 m , and the semi-major 
 axis of the apparent orbit 17". 89. These numerical values indicate a 
 mass equal to TT -J-g T , the sun's mass being represented by unity. On the 
 other hand, Professor Pierce of Harvard College, U.S., guided by similar 
 observations of his countryman, Mr. Bond, has obtained -j-g-g-jo f r tne 
 value of the planet's mass. This geometer has executed a detailed calcu- 
 lation of the perturbations which Neptune produces on Uranus, and has 
 found that the mass deduced from Mr. Bond's observations of the satellite 
 
 * It is worthy of remark that the inequality is greater in the former of these cases than 
 in the latter, although the disturbing body is then more distant. Both the magnitude and 
 duration of the inequality increase ad infinitum as the mean distance increases towards a 
 value very nearly equal to 30.45014. 
 
206 HISTORY OF PHYSICAL ASTRONOMY. 
 
 accounts better for the irregularities of the disturbed planet than any 
 other value which has been assigned. When the difficulty of making 
 observations of the satellite is taken into consideration, it is manifest that 
 some time must elapse before the value of this element can be established 
 with a degree of precision conformable to the present condition of Physical 
 Astronomy. 
 
 In one of the preceding chapters allusion has been made to the long ine- 
 quality in the moon's epoch, which was the cause of so much embarrassment 
 to astronomers in the present century, but of which the existence was placed 
 beyond all doubt, and its true nature clearly established, by a discussion of 
 the Greenwich lunar observations consequent upon their recent reduction. 
 The complete explanation of this inequality by the theory of gravitation, 
 was the reward of Professor Hanseix's researches on the subject. Mr. 
 Airy, by the discussion of the same observations, detected also two small 
 periodical inequalities in the moon's motion, neither of which had hitherto 
 been recognised by theory. The greater of these inequalities was in the 
 moon's latitude. It varied with the cosine of the moon's true longitude, 
 amounted at its maximum to 2".17, and was additive. The other 
 inequality was in the longitude. It varied with the cosine of the longitude 
 of the node, had a maximum value equal to 0".97, and was subtractive. 
 These quantities are indeed very small, but such is the high degree 
 of precision which characterizes modern observation, and such is the 
 mathematical refinement attained in the correction of the lunar or planetary 
 elements by the discussion of masses of observations, that the existence 
 and true form of the inequalities was established beyond all doubt by Mr. 
 Airy's researches. Observation and theory were therefore once more at 
 direct issue, and it remained for the geometer to reconcile their discordance 
 by demonstrating the existence of the discovered inequalities, as necessarily 
 due to perturbative action. This important object has recently been ac- 
 complished by the same geometer to whom the explanation of the long 
 inequality in the epoch of the moon is due. Professor Hansen, by a pro- 
 found investigation of the lunar theory, has discovered two inequalities 
 similar to those indicated by observation, and very nearly agreeing with them 
 in their maximum values. The inequality in latitude was found by him to 
 amount to 1".3S. It arises from this circumstance, that the plane to 
 which the lunar orbit is inclined at an invariable angle is not the plane of 
 the ecliptic as has been hitherto supposed, but a plane the position of 
 which Professor Hansen represents by the following conception : "Take 
 the plane of the earth's orbit in the position in which it was about three 
 years ago ; let the nodes of this plane revolve backwards on the present 
 ecliptic through 90, without change of inclination ; the plane so found is 
 the plane to which the uniformity of the inclination of the moon's orbit is 
 to be referred." * The same train of investigation gave also the inequality 
 in longitude. M. Hansen obtained 0".50 for its maximum value. The 
 discordance between M. Hansen's results, and the values assigned to the 
 inequalities by Mr. Airy, are not greater than such as may fairly be 
 ascribed to errors of observation. Thus the clouds which for a moment 
 obscured the Newtonian theory of gravitation have been effectually dis- 
 sipated, and a fresh conquest has been added to the long list of triumphs 
 which adorn its history. 
 
 With the foregoing brief allusion to the recent researches of M. Hansen 
 
 * Letter from Professor Hansen to the Astronomer Royal, Monthly Not. Ast. Soc., 
 June, 1849. 
 
HISTORY OF PHYSICAL ASTKONOMY. 207 
 
 on the lunar theory, our imperfect attempt to trace the history of physical 
 astronomy is now brought to a close. A review of the progress of this 
 sublime department of science from its origin to its present advanced 
 State exhibits three periods, severally characterized by distinctive fea- 
 tures, and separated by Well-defined outlines. The first of the seperiods 
 extends from the commencement of Newton's career to about the middle 
 of the eighteenth century. It comprehends the establishment of the 
 theory of gravitation by that immortal philosopher, the general propaga- 
 tion of its principles, and the efforts pursued by geometers with a view to 
 its future development. The appearance of the Principia in 1689, is one 
 of those conspicuous landmarks in the annals of science which enable the 
 reader to group together a multitude of subordinate events, and to pursue 
 his way with comparative ease along the intricate path of physical re- 
 search. Guided by the maxims of a cautious philosophy in establishing 
 his fundamental principles, and relying on the conclusions of a sublime 
 geometry, the offspring of his own genius, Newton has in that Work un- 
 folded the mechanism of the material universe, and traced with complete 
 success the agency of gravitation in all the grand phenomena of the 
 planetary movements. The dim perceptions of Copernicus, the more 
 searching and comprehensive but equally ineffectual speculations of Kepler, 
 the sober conjectures of Borelli, and the acute surmises of Hooke, were 
 now proved by demonstrative reasoning to be so many indistinct and 
 scattered glimpses of one all-pervading principle which the author had the 
 glory of first revealing to the world. The multitude of complex and 
 apparently unconnected phenomena, which astronomers had detected by 
 means of persevering efforts, prosecuted throughout a long succession 
 of ages, now assumed the character of subordinate truths flowing from one 
 common source. The sagacious generalizations of Hipparchus and 
 Ptolemy among the ancients, and the equally admirable efforts of Tycho 
 Bralie and Kepler among the moderns, were finally emancipated from 
 the empiricism which characterizes mere mathematical inductions, and 
 now stood forth invested with all the grandeur of natural laws. The 
 general adoption of the theory of gravitation which took place towards 
 the close of the period we are considering, affords a lesson at once interest- 
 ing and instructive. Slow at first to admit principles which presented 
 themselves in the austere garb of the ancient geometry, and violated the 
 cherished creations of fancy, the human mind, notwithstanding, was unable 
 effectually to resist the force of demonstrative reasoning, and finally was 
 constrained to bow before the simple majesty of truth. By a rational 
 exposition of their more salient features, the principles of the theory of 
 gravitation were brought home to the understandings of persons unused 
 to processes of scientific inquiry with a power of conviction which the more 
 refined investigations of modern times are calculated only in a small 
 degree to strengthen. With respect to the geometer, the impression 
 produced on his mind by the discoveries of Newton was of a totally different 
 character. Far from recognising a theory already complete in all its parts, 
 he discovered, in the pages of the Principia, an inexhaustible mine of 
 profound research, and already descried, in the dim perspective of futurity, 
 the. magnificent expansion which the sublime principles therein expounded 
 were destined to acquire. But, to use the language of an illustrious living 
 philosopher, the geometry of Newton was like the bow of Ulysses, which 
 none but its master could bend *. The efforts of geometers during this 
 
 * Herschel's Discourse on the Stucly of Natural Philosophy, p 273. 
 
208 HISTORY OF PHYSICAL ASTRONOMY. 
 
 period were therefore mainly directed to the improvement of the transcen- 
 dental analysis, the only instrument that could be expected in future to 
 afford any efficient aid in the ahstruse researches relating to the system of 
 the world, its applications being confined to problems of pure mechanics 
 the branch of science which forms trie connecting medium between 
 analysis and physics. The prodigious mass of original matter that had 
 been presented in the Principia in a synthetic form supplied geometers 
 with an inexhaustible field of delightful speculations of this nature, and 
 gave birth to a multitude of analytical inventions which proved of incalcu- 
 lable service in the future development of the theory of gravitation. 
 
 The second period in the history of physical astronomy extends from 
 the commencement of the labours of Euler and his contemporaries on the 
 lunar theory to the close of the eighteenth century. Less fertile in 
 original ideas than the period to which we have been referring, it notwith- 
 standing exhibits a refinement of conception in fundamental principles, 
 combined with a power of generalization in the methods of research, to 
 which no scientific investigations in any other age can offer a parallel. 
 These brilliant efforts of genius, when applied to Celestial Mechanics, con- 
 ducted the geometer to new solutions of all the great problems of the 
 system of the world, more comprehensive in design, and more fertile in 
 detail, than those derived from the synthetic methods of the Principia. 
 Formula? were assigned exhibiting the oscillations of the planetary move- 
 ments throughout indefinite ages both past and future. The sublime 
 truths relating to the stability of the planetary system were established by 
 Lagrange and Laplace upon the basis of a rigorous analysis. The accurate 
 computation of the motion of the lunar apogee, the equally satisfactory 
 account of the hitherto inexplicable irregularities of Jupiter and Saturn, and 
 of the secular acceleration of the moon's mean motion, the solution of the 
 great problem of the precession of the equinoxes by the strictest principles 
 of mechanical science, and the complete establishment of the theory of 
 Jupiter's satellites, may be ranked among the most brilliant conquests 
 achieved during this period. The actual state of astronomical science 
 was also now brought into more intimate connexion with the researches of 
 the geometer than it had been in the preceding period. The phenomena 
 of the celestial motions discovered by Hipparchus and his successors down 
 to Kepler inclusive, were too broadly traced out in the heavens to excite 
 any doubts respecting their real character. It only remained, therefore, 
 to explain their dependence upon physical principles, a task which devolved 
 exclusively on the geometer. But when the latter proceeded to consider 
 the more recondite parts of the theory of gravitation, it became indis- 
 pensable, in order to obtain a confirmation of his results by an appeal to 
 observation, that the corresponding phenomena of the heavens should be 
 exhibited in a clear form by the astronomer. The objects of research, 
 being now, however, of a more minute character than those hitherto 
 accounted for by theory, were appreciable to the astronomer only by a closer 
 scrutiny of facts and greater delicacy of observation. It was thus that 
 astronomy and abstract science reflected a light upon each other's paths, 
 which conduced materially to their mutual progress. The results achieved 
 by the critical acumen of Halley, the sagacity of Bradley, and the unrivalled 
 practical skill of Maskelyne, advanced at an equal pace with the analytical 
 researches of the geometers on the Continent, and are imperishably asso- 
 ciated with them in the magnificent triumphs which illustrate the history 
 of physical astronomy during this period. The latter aptly closes with the 
 publication of the Mecanique Celeste, a work embodying many of the most 
 
HISTORY OF PHYSICAL ASTRONOMY. %09 
 
 important methods of Euler, Clairaut, D'Alembert, and Lagrange; but in 
 respect to which it has been beautifully remarked by an eminent philo- 
 sopher* that the immortal author might be amply justified in using the 
 words of the prince of antiquity, " et quorum pars magna fui." 
 
 The third period, although distinguished less by intellectual triumphs 
 than by the profusion of its accumulated treasures, notwithstanding 
 exhibits some results which may vie in splendour with the most brilliant 
 efforts of genius in any age. The sublime theory of the variation of 
 arbitrary constants was carried by Lagrange to a state of perfection which 
 will command the admiration of geometers to the latest posterity, and was 
 subsequently applied with success to all the great problems of the system 
 of the world. The vast treasures of analysis which had been amassed by 
 the geometers of the eighteenth century supplied inexhaustible stores for 
 the improvement and extension of the several parts of the theory of gravi- 
 tation ; and, as the objects of research were now of a still more evanescent 
 character than they had been in the preceding period, the labours of the 
 astronomer were characterized by a suitable degree of refinement. The 
 annals of science do not contain the record of more delicate operations 
 than those which have been conducted in the present age for the purpose 
 of determining the ellipticity of the earth by means of the pendulum. 
 The elements of the planetary orbits have also been determined with 
 unexampled precision, a circumstance which has been attended with the 
 twofold advantage of improving the tables of astronomy, and exhibiting, in 
 bold relief, the existence of outstanding irregularities. By these means 
 the long inequalities in the earth and moon, besides various phenomena 
 of minor interest, have been detected and accounted for by the theory of 
 gravitation. A similar process led to a clear definition of the anomalies of 
 Uranus, and suggested those immortal investigations which established the 
 existence of an exterior planet. 
 
 The future prospects of physical astronomy are in accordance with its 
 past triumphs. The theories of the smaller planets and comets, and the 
 inverse problem of planetary perturbation, still continue to offer to the 
 geometer extensive subjects of interesting research. The theories of the 
 secondary systems are also still in an imperfect condition. It is true that 
 the moon and the system of Jupiter's satellites have formed the subjects of 
 elaborate research, and that their complex perturbations have been studied 
 with a degree of success which leaves little further to be desired; but so 
 intricate are the various parts of physical astronomy, and so difficult is it for 
 the geometer to bring them within the reach of his analysis, that methods 
 of investigation devised for any particular problem become totally useless 
 when applied to others apparently similar to it. In the secondary systems 
 of Saturn, Uranus, and Neptune, difficulties will doubtless occur to the 
 geometer, which can only be vanquished by methods of analysis peculiarly 
 adapted to each specific case. But the planetary system does not hold 
 out the exclusive prospect of future advancement in the study of Celestial 
 Mechanics. Already the sublime truth announced by Newton, that every par- 
 ticle of matter in the universe attracts every other particle with a force vary- 
 ing reciprocally as the squares of their mutual distances, has been realised 
 in the motions of those vast bodies which roll in space at an inconceivable 
 distance beyond the limits of the solar system. The recent researches of 
 astronomers on the motions of Double Stars have established this important 
 fact beyond all doubt. An unlimited field of speculation is here presented 
 
 * M. Biot. 
 
 p 
 
210 HISTOBY OF PHYSICAL ASTEONOMY. 
 
 to the contemplative mind. Whether it is allotted for the geometer to 
 transport his analysis effectually to those myriads of bodies which twinkle 
 in the starry heavens, and to calculate the perturbations which the solar 
 system may one day experience as, in the course of its motion through 
 space, it approaches some of the great masses of the universe, are questions 
 which cannot fail to occur to the thoughtful inquirer, but are of the class 
 which time alone can solve. To use the language of an eminent philosopher 
 it would be rash to be too sanguine; it would be unphilosophical to despair. 
 Still more shrouded in mystery is the question relative to the nature 
 and mode of operation of the principle which is thus found to exercise an 
 incessant influence over the constituent particles of matter. That it has a 
 close affinity to heat, light, electricity, and the other imponderable agents 
 of the material creation, nay, that all may be only so many distinct mani- 
 festations of some more general principle, is the prevailing opinion of those 
 who have devoted much attention to physical researches. This opinion 
 may one day ripen into an established truth, and views of nature unex- 
 ampled in magnificence and splendour may be reserved for future genera- 
 tions. In the present state of our knowledge, however, all attempts at 
 generalizations of this kind must be regarded as premature. A multitude 
 of difficulties occur in every subject of physical enquiry, the explanation of 
 which must precede any extensive induction of general principles such as 
 that referred to, but which can only be expected to result from scientific 
 researches prosecuted throughout a long succession of ages. Whether 
 gravitation is a quality inherent in, and necessarily co-existent with, 
 matter, or whether it is a principle essentially distinct from it and 
 operating merely on its constituent parts, is a question which, in all 
 probability, is destined for ever to prove irresolvable to the most penetrating 
 inquiries of the human mind. It is when he thus passes the boundary 
 that circumscribes the province really accessible to his researches, and 
 seeks with prying interest to penetrate into the illimitable region of the 
 unknown, that man with all his boasted philosophy is reminded of his 
 nothingness. He has decomposed the subtle light into its primitive 
 elements, and determined with mathematical rigour the amazing velocity 
 of its transmission through space ; he has measured the distances of the 
 celestial bodies, and traced the laws of their complicated movements but 
 the fall of a decayed leaf suggests to him problems, whose solution 
 transcends the loftiest powers of his understanding, and in the physiology 
 of the humblest moss that presents itself to his contemplation he en- 
 counters mysteries that prove impenetrable to his most searching scru- 
 tinies. To examine, arrange, and classify the countless varieties of 
 physical phenomena to define the character, and unfold the admirable 
 beauty, of the principles that unite them together, and to advance by suc- 
 cessive inductions to relations of a more and more extensive order in the 
 economy of the material universe such are the magnificent enterprises 
 which science proposes to the well-directed efforts of persevering thought 
 such are those alone whose realization is attainable by human research. 
 Ennobled with elevating conceptions of creative grandeur, and fraught with 
 sentiments of pure enjoyment, is the mind of the philosopher, who, while 
 prosecuting the study of nature in the true spirit of rational inquiry, regards 
 his vocation, not as a pursuit designed to gratify his curiosity or minister 
 to his ambition, but as a glorious privilege offered to him, by rightly 
 availing himself of which he is enabled to advance the condition of his 
 fellow creatures, and to discover innumerable illustrations of the power, 
 wisdom, and goodness of the Supreme Being. 
 
HISTORY OF PHYSICAL ASTRONOMY. 211 
 
 CHAPTER XIV. 
 
 Researches on the Solar Parallax. Modern Determinations of this Element Discovery 
 of the Solar Spots Consequences deduced from this Discovery Period of the Sun's 
 Rotation. Theories of the Solar Spots. Wilson. Herschel. Researches on the 
 Lunar Parallax. Ellipticity of Mercury. Researches on the Rotation of Venus. 
 Discovery of the Ultra Zodiacal Planets Micrometrical measures of Jupiter's 
 Satellites. Micrometrical measures of Saturn, and of his Ring. Discovery of the 
 eighth Satellite of Saturn Researches on the Satellites of Uranus. Lassel's Dis- 
 covery of the Satellite of Neptune. Researches on Comets Halley's Comet. 
 Comet of 1843. 
 
 THE determination of the distance from the sun to any of the planets 
 revolving round him, is one of the most important problems of astronomical 
 science. When this object is effected in any individual instance, it is then 
 possible by means of Kepler's third law to ascertain the distances of all the 
 planets from the sun, and hence, also, their distances from the earth cor- 
 responding to any assigned instant. An accurate knowledge of the latter is 
 indispensable in reducing the apparent positions of the planets to the true 
 positions which they would occupy if seen from the centre of the earth. 
 /These results may obviously be all derived from the solar parallax, which is 
 expressed by the reciprocal of the sun's distance from the earth. / The real 
 value of this element has, in all ages, formed an interesting subject of 
 enquiry. Aristarchus of Samos, by observing the angular distance between 
 the sun and moon, when the latter was dichotomized, inferred that the 
 sun is nineteen times more distant from the earth than the moon is. 
 Ptolemy assumed this result to be true, and, combining it with the value 
 of the lunar parallax as determined by his own observations (or rather 
 perhaps those of Hipparchus), he obtained 3' for the amount of the solar 
 parallax. This value was adopted by all his successors down to Tycho 
 Brahe inclusive. Kepler, while engaged in his celebrated researches on 
 the motions of Mars, availed himself of the accurate observations of Tycho 
 Brahe to institute a searching scrutiny into the value of the solar parallax. 
 The conclusion he came to was, that it did not exceed I', and in all pro- 
 bability fell very short of that quantity. The researches of Cassini reduced 
 the superior limit considerably below this value. He attacked the problem 
 not by direct investigation, but by means of researches on the parallax of 
 Mars. When this planet is in opposition, it is much nearer to the earth 
 than the sun is, and consequently its parallax is then a much more 
 appreciable quantity than that of the sun. But if the parallax of any 
 planet is once determined, the parallax of the sun or that of any other 
 planet, becomes known by means of Kepler's third law. The method pro- 
 posed by Cassini for determining the parallax of Mars, was to make simul- 
 taneous observations of the planet when in opposition at two places of the 
 earth considerably distant from each other, and then, by a comparison of 
 the results, to ascertain the amount of displacement arising from the 
 difference of position. For this purpose, Richer was sent by the Academy 
 of Sciences to Cayenne, in Africa, while Cassini, Roemer, and Picard 
 observed the planet at different places in France. A comparison of the 
 
 p 2 
 
212 HISTORY OF PHYSICAL ASTBONOMY. 
 
 positions of the planet as determined by these observations shewed that 
 the effect of parallax was insensible ; whence it was inferred that at the 
 utmost it did not exceed 25". This gave 10" as the greatest value 
 which could be assigned to the solar parallax. Cassini fixed it at 9". 5, 
 a result which formed a very important approximation to the true value. 
 When Lacaille was at the Cape of Good Hope, he made observations of 
 Mars for a similar purpose. A comparison of his results ' with those 
 assigned by similar observations in Europe gave 10". for the amount 
 of the sun's parallax. 
 
 The transits of Venus across the sun's disk in the years 1761 and 1769 
 supplied astronomers with a more accurate method of determining the 
 solar parallax than that to which we have been just alluding. This 
 method was first pointed out by Halley, who, in 1716, suggested to 
 astronomers to carry it into effect on the occasion of the approaching 
 transit of the planet, earnestly imploring them not to neglect so valuable 
 an opportunity of determining so important an element. Astronomers 
 did not fail to appreciate the value of Halley 's proposal; and on their 
 recommendation the principal Governments of Europe fitted out expe- 
 ditions to various parts of the world, both in 1761 and 1769, for the 
 express purpose of observing the transit of the planet. The transit of 
 1761 was imperfectly observed, and the result did not prove satisfactory. 
 The transit of 1769, however, was observed with complete success. A 
 comparison of the results assigned by the various observations gave 8". 7 
 and 8". 5 as the most probable limits within which the parallax is confined. 
 Delambre assigns 8". 6 as the most accurate value, a result which places 
 the sun at the distance of 95 millions of miles from the earth. When we 
 consider the ingenuity of the method employed in arriving at this deter- 
 mination, and the refined nature of the process by which it is carried into 
 effect, we cannot refrain from acknowledging it to be one of the noblest 
 triumphs which the human mind has ever achieved in the study of physical 
 science. 
 
 A comparison of the value of the solar parallax as assigned by observa- 
 tions of the planet Mars, with that obtained by the more accurate method 
 of the transit of Venus, did not lead to so close an agreement as might 
 have been expected from the advanced state of astronomy. With the 
 view of arriving at a more satisfactory result by the former of these 
 methods, the late Mr. Henderson made observations of Mars at the Cape 
 of Good Hope, on the occasion of the opposition of the planet in 1832. 
 Simultaneous observations of the planet were made at Greenwich, Cam- 
 bridge, and Altona. A discussion of all the observations gave for the 
 solar parallax a mean value equal to 9". 125. This result forms a nearer 
 approximation to the generally acknowledged value, than either of those 
 assigned by Cassini or Lacaille, but still it has not altogether satisfied the 
 desire of further research on the subject. A method for determining 
 the solar parallax by means of observations of Venus and Mars has 
 recently been proposed by Dr. Gerling of Marburg. A suggestion which 
 was made to the Government of the United States to lend its co-operation 
 in carrying this method into effect, has been favourably received ; and, in pur- 
 suance of this object, an expedition has been despatched to the State of Chili, 
 in South America, in the month of July of the present year*. It is con- 
 templated to observe Mars at the oppositions of 1849-52; and Venus at 
 
 * 1849. 
 
HISTORY OF PHYSICAL ASTEONOMY. 213 
 
 the inferior conjunctions and stationary points of 1850-&2. The conduct 
 of the observations has been assigned to Lieutenant Gilliss, a young 
 astronomer who has already signalized himself in a most praiseworthy 
 manner. It is to be hoped that the result of this expedition will prove to 
 be as conducive to the advancement of astronomical science as the expedi- 
 tion itself is creditable to the Government under whose auspices it has been 
 undertaken. 
 
 When Galileo first directed his telescope to the sun, he was surprised 
 to find that the surface of that luminary, instead of presenting a uniform 
 appearance, according to the opinion universally entertained by philoso- 
 phers, was diversified with a number of dark spots exceedingly irregular 
 both in form and magnitude. When watched attentively for some days 
 these phenomena were perceived to be in a state of constant change. In 
 some instances two or three spots would unite together and form one large 
 spot ; and on the other hand it happened not unfrequently that a spot of 
 considerable magnitude would break up into two or three smaller ones. 
 In the latter case the spots generally diminished with more or less rapidity, 
 and finally disappeared altogether, when they were succeeded by others of 
 the same irregular and fleeting nature. This remarkable discovery 
 inflicted one of the most effective blows which had yet been dealt against 
 the ancient philosophy by the progress of scientific research ; for it was 
 one of the fundamental doctrines of Aristotle that the heavens are incor- 
 ruptible and immutable ; and, therefore, that the surfaces of the celestial 
 bodies are destitute of any physical changes analogous to those which 
 characterize the operations of nature on the surface of the earth. The 
 announcement of the existence of spots on the sun was therefore received 
 by the adherents of that philosophy with feelings of deep mortification, 
 and various attempts were made to demonstrate its fallacy. By some the 
 spots were alleged to be spurious phenomena arising from the impurities 
 in the glasses with which the observations were made. By others they 
 were maintained to be planets revolving round the sun at small distances 
 from his surface, for when watched some days they were all found to have 
 a motion on his disk from east to west. Observations made with different 
 glasses sufficed to disprove the former of these assertions. With respect 
 to the latter, a fatal objection to it consisted in the irregular aspect and 
 changeful character of the spots. 
 
 Although the name of Galileo is more intimately associated with the 
 discovery of the solar spots than that of any other philosopher, it would 
 appear that one of his contemporaries at least arrived also at a knowledge 
 of these interesting phenomena by original observation. Nay, it has even 
 been alleged that the illustrious Italian was anticipated on this occasion by 
 an astronomer of Germany. It is incontestable that the earliest publica- 
 tion which contains an account of the solar spots is due to John Fabricius, 
 a nephew of David Fabricius, the astronomer and intimate friend of 
 Kepler. The dedication of this work* is dated June 13, 1611. The 
 author asserts that the solar spots were observed by him from the com- 
 mencement of the current year. The work contains internal evidence 
 that some of the observations of these phenomena must have been made 
 at least three months anterior to the date of dedication. Another of 
 Galileo's contemporaries who asserted that he had discovered the spots 
 by his own observations was Christopher Scheiner, a German Jesuit, 
 
 * Johannis Fabricii Phrysii de Maculis in Sole Observatis, &c. Witteburgi, 4to, 1611. 
 
214 HISTORY OF PHYSICAL ASTRONOMY. 
 
 who was Professor of Mathematics in the University of Ingolstadt. This 
 individual published an account of his observations in three letters ad- 
 dressed to Wilser, the chief magistrate of Augsburg, under the anonymous 
 signature of Apelles latens post tabulam. The first of these letters is 
 dated the 12th November, 1611. The amthor states that he first dis- 
 covered the spots seven months previously. This assertion would carry 
 back his observations to the month of April, 1611. He mentions that, 
 upon resuming his observations in the month of October, he suspected 
 that the appearances arose from some defect in the glasses with which he 
 viewed the sun, but that after he had prosecuted his observations for a 
 short time he finally became convinced of the actual existence of the spots*. 
 With respect to his alleged discovery of the spots as early as April, 1611, 
 it is clearly inadmissible, inasmuch as it rests solely on his own assertion. 
 Nor, indeed, even if supported by sufficient evidence, do his observations 
 of that period appear to possess any real merit, since we find him in 
 October still doubting the actual existence of the spots. Galileo first 
 alluded to his discovery of the solar spots in the commencement of his 
 "Dissertation on Floating Bodies," published at Florence in 1612f. A 
 detailed account of his researches on these phenomena is contained in 
 three letters addressed to Welser in reply to the letters addressed to the 
 same individual by Scheiner, whose views of the nature of the solar spots 
 were at variance with those of the Italian philosopher. These letters 
 were published at Rome in January, 1613, under the auspices of the 
 celebrated Lyncean Society J. The first letter is dated the 4th May, 1612. 
 The author asserts in it that eighteen months had elapsed since he 
 originally observed the spots. This statement carries back his discovery 
 to about the beginning of November, 1610. As, however, he has not 
 cited any observations of so early a date, nor mentioned any individuals to 
 whom he communicated his discovery, it is impossible to admit his asser- 
 tion as an historical fact. Evidence of a more reliable character goes to 
 
 * An amusing incident is related in connexion with Scheiner's observations, which 
 indicates the fatal effect with which the authority of Aristotle succeeded in maintaining its 
 ascendancy over men's minds, even when the dogmas of the illustrious Stagyrite were 
 opposed to the testimony of the senses. As soon as Scheiner had assured himself of the 
 actual existence of the solar spots, he communicated his discovery to the Provincial of the 
 Order of Jesuits, but the latter, who was a zealous Peripatician, positively refused to give 
 credit to his assertion. " I have read Aristotle's writings from end to end many times," 
 says he to Scheiner, "and I can assure you that I have nowhere found in them anything 
 similar to what you mention. Go, my son, and tranquillize yourself; be assured that what 
 you take for spots in the sun are the faults of your glasses or your eyes." The inflexible 
 provincial would not allow, him to publish his observations and opinions under his own 
 name. He only consented to an anonymous publication of them, as mentioned in the 
 text. 
 
 {* Discorso intorno alle Cose che stanno in su 1'Acqua. Firenze, 1612. 
 
 | Istoriaet Dimostrazioni intorno alle Macchie Solari et loro accident! dal Signor Galileo 
 Galilei, &c. Roma, 13 gennaro, 1613. 
 
 M. Arago, in his valuable " Analysis of the Life and Discoveries of Sir William 
 Herschel," published in the Annuaire for 1842, has discussed with great ability the claims 
 of the various individuals to whom the discovery of the solar spots has been attributed. 
 He rightly refuses to Galileo the credit of having discovered the spots eighteen months 
 previous to his first letter to Welser, on the ground that the claim to the discovery rests on 
 the bare assertion of its author. He, however, readily admits that if Galileo's letters con- 
 tained the records of any observations made in the preceding year, such records should be 
 considered as fully substantiating his claim to the discovery. The following are the 
 words of M. Arago in reference to this point : " Le meilleur moyen de trancher toute 
 difficulte sur la date de la decouverte des taches cut ete de rapporter de veritables obser- 
 
HISTORY OF PHYSICAL ASTRONOMY. 215 
 
 shew that he observed the spots as early as the month of April, 1611. 
 On some day in that month he announced the existence of the solar spots 
 at a conference of savans, held in the garden of Cardinal Bandini at 
 Rome. This fact was afterwards adduced in support of his claims to the 
 original discovery of the phenomena, and was corroborated by several 
 persons who were present at the conference. A fourth individual to whom 
 the discovery of the solar spots has been attributed is Hariot, the cele- 
 brated mathematician of England. De Zach, who visited this country 
 towards the close of the last century, obtained access to the manuscripts of 
 Hariot, and from an inspection of them he came to the conclusion that the 
 author had observed the solar spots as early as the month of December, 
 1610. The late Professor Rigaud, of Oxford, however, having carefully 
 examined the same manuscripts, found that the observations contained in 
 them could not bear the interpretation put upon them by De Zach. It 
 turns out, in fact, from his researches, that Hariot did not commence his 
 observations of the spots before the month of December, 1611. With 
 respect to the other three individuals whose names are associated with the 
 discovery of the phenomena, it is pretty evident that the claims of two at 
 least are well founded. Fabricius and Galileo appear to have both per- 
 ceived the spots about the same time. The observations of Scheiner were 
 of a later date, but it is not impossible that they may have been quite 
 independent of those of his contemporaries. 
 
 The discovery of the solar spots soon conducted astronomers to the 
 important conclusion that the sun has a rotatory motion round a fixed 
 axis. Fabricius found that all the spots had a common motion on the 
 sun's disk from east to west. Their motion was greatest when they were 
 in the centre of the disk, and it thence gradually diminished until they 
 reached the western limb, when they disappeared from observation. In 
 the course of ten days afterwards the spots reappeared on the eastern 
 limb. Their motion at first was slow, but it continually increased until 
 they reached the centre of the disk, when it again attained its maximum 
 rate. He also found that the magnitude of the spots appeared to be 
 greatest when they were on the centre of the disk, and least when they 
 were near either of the limbs. He remarked, that according to the 
 principles of perspective, all these appearances would ensue on the sup- 
 position that the spots were attached to the surface of the sun, the latter 
 being supposed at the same time to revolve round an axis with a uniform 
 motion from east to west. He does not appear, however, to have formed 
 an adequate conception of the importance of this conclusion, for he did not 
 pursue any further researches in connexion with it. 
 
 Galileo reasoned on the subject with his usual sagacity. The various 
 circumstances connected with the phenomena of the spots soon revealed 
 
 vations. Qui aurait ose concevoir des doutes sur la sincerite d'une declaration de Galilee 
 cor^ue en ces terms : Tel jour, en 161 1, je vis une tache pres du bord oriental du Soleil ; 
 tel autre jour elle etait au centre du disque ; a telle troisieme date je fus temoin de la 
 disparition de la tache derriere le bord occidental ? On trouve des observations de ce 
 genre dans les lettres que 1'illustre physicien ecrivit a Welser d'Ausbourg, mais elles sont 
 toutes des mois d'Avril et de Mai, 1612." (Annuaire, 1842, p. 469.) From the above 
 passage we infer that if M. Arago had been acquainted with Mr. Airy's " Historical 
 Statement of Circumstances connected with the Discovery of the Planet exterior to Uranus " 
 at the time when he was engaged in drawing up the critical remarks on that subject, which 
 appeared in the Comptes Eendus for the 19th October, 1846, he would have conceded 
 substantially to Mr. Adams his right to the discovery of the Trans- Uranian planet, as un- 
 hesitatingly as in the present instance he concedes hypotheticaUy to Galileo his right to 
 the discovery of the solar spots. 
 
216 HISTOEY OF PHYSICAL ASTKONOMY. 
 
 to his acute perception the fact of the sun's motion round a fixed axis. In 
 the remarks on the spots, which appear in the beginning of his " Disserta- 
 tion on Floating Bodies, "he makes the period of rotation to be about a 
 lunar month*. In his third letter to Welser his language is more 
 precise. He states that, having observed*a great number of spots with 
 much attention, he came to the conclusion, that the time during which 
 they remained on the disk was somewhere about fourteen days f. This 
 assigns rather more than twenty-eight days to the period of the sun's 
 apparent rotation. Modern observation makes it 27 d 8 h . He also re- 
 marked that the axis of rotation is not perpendicular to the plane of the 
 ecliptic, but that it deviates from the pole of that circle only by a small 
 angle. Although Scheiner formed very erroneous views of the nature of 
 the solar spots, he studied with great assiduity all the circumstances con- 
 nected with their appearance. In 1630 he published his Rosa Ursina \, 
 an immense work, devoted exclusively to the subject of the solar spots, 
 
 * Che (il sole) in un mese lunare in circa finisce il suo periodo. Opere di Galileo, 
 Edit. Pad. tome i. p. 189. 
 
 + M. Arago, while engaged in discussing the relative merits of Galileo and Scheiner, 
 with reference to their respective researches on the subject of the sun's rotation (An- 
 nuaire, 1842), appears to have been hurried, by the ardour of dispute, into the commission 
 of an act of injustice against the illustrious Italian. The following is a brief statement of 
 the facts connected with this question. Scheiner, in one of his letters, had contended 
 that the spots could not be attached to the surface of the sun, alleging in support of his 
 assertion, that the time occupied by a spot in traversing the sun's disk was greater in some 
 cases than it was in others. Galileo denied the existence of any difference in the duration 
 of the spots on the disk, and proceeds in the following terms to state the grounds of his 
 disbelief: " Perche havendo io circa questo particolare fatte molte, et molte diligentis- 
 sime osservazioni non ho trovato incontro alcuno, onde si possa concluder altro, se non 
 che le macchie tutte indifleramente dimorano sotto '1 solar disco tempi eguali che al mio 
 giudizio sono qualche cosa piu di giorni 14." (Istoria, &c., alle Macchie Solari, p. 116.) 
 It appears by this passage, and also by that cited in the foregoing note, that as early as 
 1612 Galileo had watched with great assiduity the various circumstances connected with 
 the solar spots, and that as nearly as he could possibly judge the period of the sun's rota- 
 tion was 28 days. In 1630, Scheiner published his Rosa Ursina, in which he fixed 
 the period of rotation between 26 and 27 days. Let the reader compare these facts 
 with the following assertion of M. Arago's. " Galileo has never assigned the period of 
 the sun's rotation, whether apparent or real, otherwise than in a vague manner. With 
 respect to the apparent period he fixed it at about a month (nello spazio quasi d'un 
 mese, Dialogues).... Besides, the Dialogues did not appear until 1632, two years after the 
 publication of the Rosa Ursina of Scheiner." Thus it appears that M. Arago entirely 
 overlooks the scientific statement made by Galileo in his letter to Welser, of December, 
 1612, and assumes, as the basis of his reasoning, a remark on the same subject made by 
 the illustrious philosopher in his " Dialogues on the System," a work in which the author 
 avowedly expounds his views rather in the language of familiar explanation than in the 
 strict phraseology of science. Galileo's estimate of the period of rotation is also pre- 
 sented in a very unfavourable point of view by placing it after the publication of Schemer's 
 work, and twenty years subsequent to the stricter statement made by him in his letter to 
 Welser. It may be urged that the language of the Italian philosopher is by no means 
 consistent with the precision due to such researches. This is, no doubt, true, but it cer- 
 tainly does not lose, in this respect, by comparison with the language of Scheiner. Indeed, 
 when we take into account the discordances of the modern determinations of the period of 
 rotation (amounting to seven or eight hours), we cannot refrain from the conclusion that 
 too much reserve cannot be employed in advancing the charge of vagueness against the 
 original explorer of the heavens with the telescope, whose observations were made with a 
 little instrument that magnified only thirty-three times. 
 
 $ Rosa Ursina, sive Sol ex admirando facularum et macularum suarum phenomeno 
 varius, &c. Alluding to this enormous work, Delambre says, " There are few books so 
 diffuse and so void of facts. It contains 784 pages : there is not matter in it for 50 
 pages." Hist. Ast. Mod. tome i. p. 690. 
 
HISTORY OF PHYSICAL ASTRONOMY. 217 
 
 and comprehending observations of these phenomena, which extended 
 over a period of eighteen years. He determined the period of the 
 sun's rotation to be between 26 and 27 days. He also assigned 6 and 
 8 as the two extreme limits of the angle at which the pole of rotation is 
 inclined to the pole of the ecliptic. Modern observation makes it 7 20'. 
 
 The subject of the solar spots is calculated, in a strong degree, to attract 
 the attention of those engaged in the study of physical science. When it 
 is considered that the sun exercises so commanding an influence over the 
 operations of nature on the earth, it is impossible to repress an intense 
 desire of arriving at some knowledge of those mysterious changes which 
 are perpetually taking place at his surface. Notwithstanding its manifest 
 importance, however, there is, perhaps, no department of astronomical 
 science in which less real progress has been made than in that relating to 
 the solar spots. In order that the reader may form a clearer conception 
 of the various theories which have been devised with a view to explain the 
 origin of these interesting phenomena, we shall give a brief statement of 
 the principal facts relating to them which have been established by the 
 observations of astronomers. 
 
 When a spot on the sun's disk is closely examined, it is found not to be 
 uniformly obscure. The central part is characterised by intense blackness, 
 but it is surrounded on all sides by a contour of appreciable breadth, which 
 exhibits a semi-luminous appearance. The more obscure part of the spot 
 is termed the nucleus ; while that which is visible by a faint light has 
 been denominated the penumbra. The nucleus and the penumbra do not 
 shade into each other, but are separated by a well-defined boundary. This 
 important characteristic of the solar spots was first remarked by Scheiner, 
 and has been fully established by the observations of subsequent astrono- 
 mers. A similar remark holds good with respect to the exterior part of 
 the penumbra ; the bounding line between it and the wholly luminous re- 
 gion around it being in general distinctly visible. Sir William Herschel 
 made a series of photometrical experiments with a view to determine the 
 relative quantities of light emitted by the nucleus, the penumbra, and the 
 wholly luminous part of the sun. The conclusion he came to was that, if 
 the full light of the sun be represented by a thousand, the brightness of 
 the penumbra will be represented by four hundred and sixty-nine, and 
 that of the nucleus by seven. 
 
 The formation of a spot is generally indicated by the appearance of a 
 very black pore, which gradually enlarges on all sides. This enlargement 
 of the spot is effected by a simultaneous enlargement of the nucleus and 
 penumbra. When two or more spots appear very close together, they 
 frequently expand towards each other and form one large spot. When a 
 spot is diminishing, previous to its disappearance, the process of diminu- 
 tion is accomplished by an irregular encroachment of the penumbra upon 
 the nucleus. This circumstance causes the form of the nucleus to be very 
 irregular, and not unfrequently leads to its breaking up into two or more 
 distinct nuclei. When a spot is disappearing, the nucleus generally 
 vanishes before the penumbra. 
 
 Sometimes a spot is observed in which the penumbra is wanting. Small 
 spots are generally destitute of these appearances. On the other hand, a 
 penumbra without a nucleus is occasionally seen. Schemer, and the an- 
 cient observers of the spots, were of opinion that the exterior boundary of 
 the penumbra never contained any sharp angles, however irregular the 
 boundary on the side of the hucieus might be. The accurate observations 
 
218 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of Sir William Herscliel have shewn that this is not universally true. On 
 the 18th February, 1801, that astronomer observed a spot on the sun's 
 disk, from the nucleus of which there issued a branch, jutting out sharply 
 upon the penumbra, while on the same side of the spot there appeared a 
 similar projection of the penumbra upon 4he luminous region around it. 
 In the course of a little more than two hours he found that the nucleus 
 had thrown out three branches ; and, in this case also, he found that there 
 were three exactly corresponding branches of the penumbra. A conclusion 
 manifestly deducible from these curious facts was, that the cause which 
 acted upon the nucleus acted also in a similar manner upon the 
 penumbra. 
 
 The magnitude of some of the solar spots is immense. In 1754, Mayer 
 perceived a spot, the dimensions of which amounted to -^th of the sun's 
 apparent diameter. This gives above 45,000 miles for the absolute 
 diameter of the spot. In 1779 there appeared an immense spot on the 
 sun which Herschel was enabled to discern with the naked eye. When 
 observed by him with a seven feet reflector, and a high magnifying power, 
 it was found to be divided into two parts. The larger of the two measured 
 1' 8" in diameter, which indicates an absolute length of 31,000 miles. 
 The rapid changes which these phenomena undergo is very astonishing. 
 Herschel states that, while engaged in observing a spot on the 19th 
 February, 1800, he fixed his attention on several places, but on looking 
 off, even for a moment, the spots he had marked could not be found again. 
 Sir John Lubbock, in a recent communication, states that he has observed 
 spots visible to the naked eye, of which, on the following day, not a trace 
 could be found, even with the aid of a good telescope *. 
 
 A remarkable circumstance connected with the solar spots is their con- 
 stant appearance near the equator. Galileo remarked that their distance 
 from that circle never exceeded 29. Scheiner found by his own observa- 
 tions, that they were all confined to a zone extending 30 on each side of 
 the equator, which was termed by him, on this account, the royal zone. 
 Subsequent astronomers have enlarged the region of the spots, so as to 
 embrace a zone of about 35 north and south of the equator. Occasionally, 
 indeed, spots are observed in the regions exterior to this zone. A large 
 spot, which appeared on the sun's disk in 1783, was found by Mechain to 
 be distant about 41 30' from the solar equator. This is, however, an in- 
 stance of very rare occurrence. Sir John Herschel carefully observed the 
 spots on the sun's disk, towards the close of the year 1836 and the begin- 
 ning of 1837 ; and he has remarked that, during the whole period em- 
 braced by his observations, the most unpractised eye could not fail to per- 
 ceive by the mere allineation of the spots, the situation of the poles and 
 equator of the sun, without watching from day to day their progress across 
 the diskf. 
 
 Besides the phenomena of the spots, the telescope has disclosed other 
 interesting appearances on the sun's disk. Some parts are perceived to 
 be brighter than the rest of the surface, and hence have derived the ap- 
 pellation of faculae. These phenomena were first noticed by Galileo in 
 his third letter to Welser on the spots J. The illustrious philosopher, with 
 
 * Phil. Mag. vol. xxxii. p. 171. 
 
 f Results of Astronomical Observations at the Cape of Good Hope, &c. , &c. London, 
 J. o4 V . 
 
 Posso aggiungere che nella medisima faccia del sole si veggono tal volta alcune 
 piazzettepiu chiare del resto. Istoria, &c., delle Macchie Solari, p. 132. 
 
HISTORY OF PHYSICAL ASTRONOMY. 219 
 
 admirable tact, cites the existence of these phenomena as an irrefragable 
 proof that the spots are attached to the surface of the sun, instead of being 
 planets, as Scheiner, in his " Letters to Welser," supposed them to be ; 
 for, on the latter supposition, he remarks, that the faculae, in virtue of their 
 motion from east to west, ought sometimes to appear as bright spots beyond 
 the limb of the sun, a conclusion which was totally at variance with obser- 
 vation. The faculae generally present an extended luminous appearance, 
 but occasionally they exhibit a round form. On the 3rd December, 1800, 
 Sir William Herschel observed a facula, which measured %' 45".9 in ap- 
 parent length, and therefore extended over a linear space of 75,000 miles. 
 Faculae are for the most part seen in the neighbourhood of spots, hut 
 sometimes they appear alone. In the latter case they are generally the 
 precursors of spots which appear on the disk the following day. Messier 
 was frequently enabled by this circumstance to predict the appearance of 
 spots twenty-four hours before they actually presented themselves on the 
 disk. The faculae are always brightest on the sun's limb, and generally 
 disappear as they approach the centre of the disk. When they enter the 
 disk on the eastern limb they generally continue to be perceived for two 
 or three days, after which they cease to be visible until they reappear on 
 the opposite side of the disk, when they are again perceptible during two 
 or three days before disappearing at the western limb. 
 
 The faculae always appear in the region of the spots. Observers, however, 
 have discovered that the whole surface of the sun is diversified with minute 
 luminous specks of different degrees of brightness and irregular streaks of 
 light of extreme tenuity, bordered by more obscure parts. These pheno- 
 mena are termed luculi. They are always perceptible on the sun's disk, 
 and cause the whole surface to assume a mottled appearance. Sir William 
 Herschel compares the corrugated state of the sun, arising from this cause, 
 to the roughness of an orange. These phenomena are found to be in a 
 state of constant change. The more obscure parts, when submitted to a 
 close examination by Sir William Herschel, presented small pores as 
 black as the nuclei of the spots. 
 
 We now proceed to notice the various explanations of the solar spots 
 which have been advanced by different astronomers. Galileo supposed 
 them to be clouds, of a greater or less degree of opaqueness, which are con- 
 stantly floating in the solar atmosphere, and, by their occasional interposi- 
 tion, prevent the observer from viewing the luminous surface of the sun. 
 This theory, however, is incompatible with certain appearances (to be 
 noticed presently) which indicate that the spots are depressions in the 
 luminous surface of the sun. It is also defective, inasmuch as it does not 
 explain the constant presence and well-defined outline of the penumbra, 
 nor give any account of the existence of faculae. Scheiner, after he was 
 convinced that the spots could not be planets, adopted the opinion that 
 they were the indications of tumultuous movements occasionally agitating 
 the ocean of liquid fire of which he supposed the sun to be composed. La 
 Hire imagined the sun to be a fluid mass, which contained within it nu- 
 merous opaque bodies. Occasionally the latter approached the surface and 
 gave rise to the appearance of spots. When floating on the surface they 
 attracted all the particles of a similar nature around them ; and, conse- 
 quently, when they disappeared the places that had been occupied by them 
 were brighter than the other parts of the surface : hence originated the 
 solar faculae. This explanation agrees with a remark of Cassini's, to the 
 effect, that when a spot disappears it is generally succeeded by a facula. 
 
220 HISTORY OF PHYSICAL ASTRONOMY. 
 
 It gives no account, however, of the numerous faculse which frequently are 
 seen in the vicinity of a spot previous to its disappearance. It is also 
 manifestly defective in many other particulars. Derham was of opinion 
 that the spots are volcanos in the sun, that the nucleus represents the 
 smoke, and that the facula?, which subsequently appear, are the glowing 
 flames of the eruption. A fatal objection to this hypothesis is, that the 
 appearance of the solar faculse, for the most part, precedes the appearance 
 of the spots. 
 
 The theory of the solar spots, propounded by Dr. Wilson of Glasgow, is 
 far more worthy of consideration than any that we have hitherto noticed. 
 This ingenious astronomer maintained that the sun is an opaque mass 
 surrounded by a luminous atmosphere, and that the spots are excavations 
 in the luminous matter, by means of which the observer is enabled to see 
 the dark body of the sun. The reasoning by which he established the 
 important fact that the spots are depressions below the luminous surface 
 of the sun is of a purely inductive character, and is founded upon obser- 
 vations of the great solar spot which appeared in the year ]769. The ac- 
 count he gives of these observations is exceedingly interesting*. He first 
 perceived the spot on the 22nd November. It appeared below the equa- 
 torial diameter, and was not far from the western limb. On the 23rd he 
 observed it again, and found that a remarkable change had taken place. 
 The penumbra, which on the previous day was equally broad on all sides of 
 the nucleus, was now very much contracted on the side which lay towards 
 the centre of the disk, while the other parts retained nearly their former 
 dimensions. On the 24th he again observed the spot. The distance from 
 the limb was now only 24", and the contracted side .of the penumbra had 
 entirely vanished. The breadth of the nucleus on the same side, also ap- 
 peared to be more suddenly impaired than it ought to have been by the 
 motion of the sun across the disk. Dr. Wilson demonstrated, by strict 
 geometrical reasoning, that these are the appearances which would neces- 
 sarily ensue on the supposition that the spot was a vast excavation, of 
 which the nucleus was the bottom, and the penumbra the sloping sides. 
 If it really was an excavation, a similar succession of changes in a reverse 
 order should take place when the spot reappeared on the eastern limb. 
 This was, in fact, what occurred to the observation of Dr. Wilson. On the 
 llth December the spot appeared on the opposite side of the disk. It 
 was then distant about I/ 30" from the eastern limb. The side of the 
 penumbra, next to the limb which formerly vanished, was now wholly 
 visible, while that turned towards the centre of the disk appeared to be 
 wanting. On the 12th December it came into view, and he saw it dis- 
 tinctly, although narrower than the other side. He did not see the spot 
 again until the 17th December, when it had passed the centre of the disk, 
 and the penumbra now appeared to surround the nucleus equally on all sides. 
 
 The interesting facts first announced by Dr. Wilson on this occasion, 
 have been fully established by the observations of Sir William Herschel 
 and all subsequent astronomers who have directed their attention to the 
 phenomena of the solar spots. The conclusion to which they unavoidably 
 lead cannot be any other than that which suggested itself to Dr. Wilson, 
 namely, that the spots are not on the same level with the rest of the solar 
 surface, but are depressions below it, formed by the partial removal of the 
 luminous matter which envelopes the dark body of the sun. This was an 
 
 * Phil. Trans., 1774. 
 
HISTORY OF PHYSICAL ASTRONOMY. 221 
 
 important step in the progress of researches on the solar spots, and it re- 
 commended itself more especially to the attention of astronomers, inas- 
 much as it was not due to any arbitrary assumptions, but was established 
 by a rigorous process of inductive reasoning. With respect to the phy- 
 sical cause which determines the generation of the spots, and the various 
 phenomena connected with them, Wilson candidly acknowledged his in- 
 ability to advance an adequate explanation ; but he propounded his views 
 on the subject in the form of queries, some of which are not unworthy of 
 attention. In order to account for the formation of the spots, he suggests 
 whether an elastic vapour might not be generated in the interior of the 
 sun, which, by escaping at the surface, would diffuse itself in all directions, 
 and, forcing a passage through the luminous envelope, would expose to 
 the eye of an observer the dark body of the sun. This hypothesis, he 
 remarked, would satisfactorily explain the circumstance of the boundary 
 between the nucleus and the penumbra being always distinctly visible and 
 well defined. When the action of the vapour diminished in intensity, the 
 luminous matter, in obedience to the solar gravitation, would flow into the 
 excavation, causing it to contract equally on all sides, and thereby giving 
 rise to the appearance presented by the diminution of a spot. In order to 
 account for the gradual process by which the changes of the spots ap- 
 peared to be effected, Dr. Wilson supposed the luminous matter of the sun 
 to possess rather the consistency of a thick fog than the mobility of a 
 fluid or gaseous envelope. The penumbra indicated the sloping sides of 
 the excavation, which were supposed to be less bright than the rest of the 
 surface, on account of a diminution of lustre experienced by the luminous 
 matter when it diffused itself over them. With respect to the faculse, 
 Dr. Wilson imagined them to be, in all probability, merely phenomena 
 of light and shade, arising from tumultuous movements in the luminous 
 matter, which were occasioned by the intense action of the excavations. 
 He adduced in support of this explanation, the remarkable fact, that the 
 faculae appear always in the vicinity of spots, and are never observed in 
 the polar regions of the sun. 
 
 The foregoing speculations of Dr. Wilson, on the origin of the solar 
 spots, are very ingenious ; but as they involve the assumption of a gaseous 
 vapour, of whose existence we have no proof, they are inadmissible into 
 the rank of physical truths deduced by legitimate reasoning from esta- 
 blished facts, and, therefore, cannot be recognised as really forming a part 
 of astronomical science. But apart from the objection that the principle 
 to which the phenomena of the spots are ascribed is not a vera causa, the 
 hypothesis of Wilson, when submitted to close examination, will be found 
 to afford a very inadequate explanation of these phenomena. One impor- 
 tant defect we shall mention, and it will be unnecessary to point out 
 more ; for unless a theory be capable of representing all the details of a 
 phenomenon, it cannot be considered as a true embodiment of natural 
 facts. Although the boundary between the nucleus and the penumbra is 
 sufficiently well accounted for, the case is very different with respect to the 
 exterior boundary of the latter. It is impossible to conceive how a homo- 
 geneous vaporous substance, such as the luminous matter of the sun is 
 assumed to be composed of, could experience so striking a change of 
 lustre as observation indicates, by a mere change in the inclination of its 
 surface to the visual ray. That the transition is abrupt and not gradual 
 from the nucleus to the penumbra, and from the penumbra to the wholly 
 luminous region around it, is a feature of the solar spots which has been 
 
222 HISTORY OF PHYSICAL ASTRONOMY. 
 
 remarked by all astronomers who have observed these phenomena, from 
 the period of their discovery down to the present day. " This want of 
 graduation," says Sir John Herschel, " this sharply-marked suddenness 
 of transition, is altogether opposed to the conception of a susceptibility of 
 indefinite and easy mixture, in the luminous, non-luminous, and semi- 
 luminous constituents of the solar envelope There is no gradual 
 
 melting of the one shade into the other spot into penumbra-^-penumbra 
 into full light. The idea conveyed is more that of a successive withdrawal 
 of veils, the partial removal of definite firms, than the melting away of a 
 mist, or the mutual dilution of gaseous media." * 
 
 In adverting to the views of Dr. Wilson on the solar spots, it would be 
 unjust to attach to them a degree of importance beyond what they really 
 possessed in the author's own estimation. No philosopher could appre- 
 ciate more fully than he has done, the essential distinction that exists be- 
 tween conclusions drawn from an examination of the real phenomena of 
 nature, and all mere speculations in physical science, however ingenious or 
 probable. In a paper on the same subject, which was subsequently com- 
 municated by him to the Royal Society, and which was written principally 
 with the view of combating certain objections urged by Lalande against his 
 explanation of the spots being excavations in the luminous matter of the 
 sun, we find incidentally thrown out the following series of conjectures 
 respecting the origin of the spots : " Whether their first production and 
 subsequent numberless changes depend upon the eructation of elastic 
 vapours from below, or upon eddies or whirlpools commencing at the surface, 
 or upon the dissolving of the luminous matter in the solar atmosphere, as 
 clouds are melted and again given out by our air; or, if the reader pleases, 
 upon the annihilation and reproduction of parts of this resplendent cover- 
 ing, is left for theory to guess at."f Some of these surmises, when at- 
 tentively considered, will be found to be by no means destitute of probability. 
 
 Allusion has been made to an objection urged by Lalande against 
 Wilson's explanation of the solar spots. The French astronomer, con- 
 ceiving that the supposition of their being excavations, was incompatible 
 with certain observations of Cassini and La Hire, came to the conclusion 
 that they were rather protuberances existing on the solar surface J. In 
 order to account for their formation, he supposed that the luminous fluid 
 which covered the dark body of the sun occasionally subsided, laying bare 
 the projecting eminences. The nuclei of the spots represented the latter, 
 while the penumbrae indicated the surrounding shallows. Without allud- 
 ing to the numerous defects of this theory, a fatal objection to it is. that 
 the penumbra shades insensibly into the luminous region around it. This 
 conclusion, as we have repeatedly had occasion to remark, is totally at 
 variance with observation. 
 
 In 1776 Bode published a theory of the solar spots. He supposed the 
 sun to be surrounded by two atmospheres. One of these was opaque, the other, 
 which was the exterior atmosphere, was luminous. The appearance of a 
 spot was occasioned by a partial opening formed in the luminous atmo- 
 sphere, which disclosed to the eye of an observer the dark substratum 
 beneath. The luminous matter was wholly withdrawn only at the centre 
 of the aperture, occasioning the appearance indicated by the nucleus of the 
 spot. Towards the sides it merely diminished in thickness, and in conse- 
 
 * Results of Astronomical Observations at the Cape of Good Hope. 
 
 f Phil. Trans., 1783, p. 162. J Mem. Acad. des Sciences, 1776. 
 
HISTOKY OF PHYSICAL ASTKONOMY. 
 
 quence exhibited a fainter lustre, whence originated the penumbra. He 
 supposed the faculas to be vast undulations in the luminous atmosphere, 
 in proof of which he remarked that they were most conspicuous towards 
 the limbs of the sun, and ceased to be visible when they approached the 
 centre of the disk. This explanation of the solar spots does not differ 
 materially from that which had been already advanced by Wilson; nor 
 does it remove any of the objections to which the latter is liable. 
 
 The next astronomer whose researches on the solar spots demand a brief 
 notice is Sir William Herschel. That illustrious individual devoted con- 
 siderable attention to this subject, and has presented the result of his 
 labours in two papers, which appear in the volumes of the Royal Society*. 
 In these papers the author has given a detailed statement of a multitude 
 of interesting facts derived from his observations of the solar spots, and 
 has exhibited a complete view of these phenomena which is in the highest 
 degree instructive. The conclusions to which he was conducted by his 
 researches on this subject are entitled in some respects to be ranked with 
 the many other great achievements of his genius. He demonstrated, by 
 means of his admirable observations, that the spots are real depressions in 
 the surface of the sun, and that the faculae are elevations above the 
 ordinary level. He supposed, also, in common with several astronomers 
 who preceded him, that the sun is an opaque mass surrounded by a 
 luminous atmosphere. He maintained, however, that this atmosphere 
 cannot be either gaseous or fluid ; for on either of these suppositions, the 
 luminous matter would flow with great velocity into the depressions, and 
 would occasion an almost instantaneous disappearance of the spots, instead 
 of a gradual diminution as observation indicated. He remarked, also, 
 that the existence of faculas is incompatible with the mobility of a fluid or 
 gaseous substance ; for these luminous ridges sometimes continue to main- 
 tain themselves for several days at a considerable elevation above the 
 ordinary level of the solar surface. In order to account for the various 
 appearances of the spots, he supposed the sun to be surrounded by a tran- 
 sparent atmosphere, in which are suspended two distinct strata of clouds 
 at different elevations. The upper stratum is composed of self luminous 
 clouds, which constitute the source of the solar light. The lower stratum 
 is composed of opaque clouds, which shine only by the reflexion of the 
 luminous regions above them. They are denominated by Herschel the 
 planetary clouds, on account of their supposed resemblance to the clouds 
 of the terrestrial atmosphere. The solid nucleus of the sun is effectually 
 protected from the intense light of the luminous regions by the inter- 
 position of the planetary Clouds. When corresponding apertures are 
 formed in both strata of clouds, the dark body of the sun is perceptible 
 through them, and gives rise to the appearance of a spot. If the apertures 
 be of equal magnitude, the substratum will present an appearance of 
 uniform blackness, and will therefore indicate a nucleus without a penum- 
 bra. If the aperture in the upper stratum be wider than that in the 
 lower, a portion of the latter will be seen surrounding the dark body of 
 the sun ; but as it shines only by reflexion, it will exhibit a fainter lustre 
 than the luminous regions, and therefore the appearance in this case will 
 be that of a nucleus surrounded by a penumbra. If there be no aperture 
 in the stratum of the planetary clouds, the appearance will manifestly be 
 that of a penumbra without a nucleus. In order to account for the for- 
 
 * Phil. Trans., 1795-1801. 
 
224 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 mation of the spots, Herschel supposed a highly elastic gas to be 
 generated in the solid body of the sun. This gaseous substance ascends in 
 virtue of its inferior specific gravity relative to the solar atmosphere, 
 forcing a passage through both strata of clouds, and exposing to the eye of 
 an observer the dark body of the sun. When it reaches the luminous 
 regions, it enters into combination with other gases, whence result decom- 
 positions which give rise to faculas, and cause the solar surface generally 
 to assume a mottled appearance. 
 
 It is scarcely , necessary to state that any theory which involves the 
 agency of a principle, of whose existence we have no positive proof, cannot 
 be recognised as forming a part of the general body of science. The 
 hypothesis of an elastic gas to whose energy the formation of the solar 
 spots is mainly ascribed in the foregoing explanation, may or may not be 
 true ; but in the present state of our knowledge it can only be regarded as an 
 arbitrary assumption, which possesses no stronger claims to our acceptance 
 than many other similar hypotheses that might be adduced. 
 
 It is necessary, therefore, to draw a broad line of distinction between the 
 purely speculative views of Sir William Herschel on this subject, and the 
 important conclusions to which he has been conducted by reasoning from 
 established facts. Indeed, it is quite clear that the illustrious astronomer 
 himself did not attach any value to his hypothesis of the generation of the 
 spots, beyond what it possessed as a convenient medium of connecting to- 
 gether the various results at which he had arrived in the course of his 
 more rigorous researches *. The latter were pursued in the true spirit of 
 inductive investigation, and the results constitute a valuable contribution 
 to our knowledge respecting the interesting subject to which they refer. 
 The facts upon which he has established the existence of two distinct strata 
 of clouds in the solar atmosphere were exhibited by him in a very clear 
 light ; and the reasoning by which he fortifies that conclusion appears to 
 be quite unexceptionable. This step had the effect of conducting him to 
 an explanation of the penumbra of the solar spots phenomena which all 
 preceding astronomers had signally failed to render a satisfactory ac- 
 count of. 
 
 The geometrical relation of the nuclei of the solar spots with respect to 
 the luminous surface, was first pointed out by Wilson. For a similar 
 explanation of the penumbrae, astronomy is indebted to Herschel. With 
 respect to the faculae, the just surmises of Wilson and Bode were 
 fully established by Herschel, on facts derived from accurate observa- 
 tion. A consistent view of the solar spots was thus obtained by a strict 
 process of inductive reasoning. It still remained to render a legitimate 
 account of the origin of these phenomena, by referring them to the 
 operation of some really existing physical cause. Some interesting spe- 
 culations designed to accomplish this object appear in Sir John Herschel's 
 recent work, containing the results of his observations at the Cape of 
 Good Hope. That distinguished philosopher justly remarks that, what- 
 ever be the cause of the spots, it is very evident that these phenomena 
 
 * In confirmation of this remark, the following passages may be cited from the papers 
 of 1795 and 1801. " They (the luminous clouds of the sun) plainly exist, because we see 
 them ; the manner of their being generated may remain an hypothesis, and mine, till a 
 better can be proposed, may stand good ; but whether it does or not, the consequences I 
 am going to draw from what has been said, will not be affected by it." Phil. Trans., 
 1795, p. 61. " I am, however, well prepared to distinguish between facts observed, and 
 the consequences that in reasoning upon them we may draw from them ; and it will be 
 easy to separate them, if that should be hereafter required." Phil Trans., 1801, p. 303. 
 
HISTORY OF PHYSICAL ASTRONOMY. 225 
 
 have an intimate connexion with the rotation of the sun about his axis. 
 The remarkable fact of their absence from the polar regions, and their 
 confinement to two zones, extending to about 35. on each side of the 
 equator, with an intermediate equatorial belt in which they are more 
 rarely perceived, appears to him to afford an indubitable indication that 
 they derive their existence from circulating movements in the atmospheric 
 fluid which encompasses the sun, depending on the rotation of that body 
 about its axis, by a relation similar to that which connects the system of 
 terrestrial trade and anti-trade winds with the earth's rotation. Now if 
 any cause can be assigned which is capable of creating a circulation of the 
 atmospheric fluid between the equator and the poles, the effect of the 
 sun's rotation will be to modify the currents so produced as the trade 
 winds and monsoons on the surface of the earth are modified and to dis- 
 pose all the meteorological phenomena which accompany them as their 
 visible manifestations into two zones parallel to the equator, with a calm 
 equatorial zone interposed. The question then arises, where are we to 
 discover the exciting cause of such circulations in the fluids of the solar 
 atmosphere ? With reference to this point, Sir J. Herschel remarks 
 that the trade winds are occasioned by the unequal effects of the 
 solar rays in heating the equatorial and polar regions of the ter- 
 restrial atmosphere ; but, as no such external cause exists in the 
 present case, we are necessarily led to look for the source of circulation in 
 the economy of the sun itself. He then proceeds to state that if there can 
 be assigned any physical difference in the constitutions of the equatorial 
 and polar regions of the sun, which tends to repress the escape of heat in 
 the one of these regions, and to favour it in the other, the effect will be the 
 same as if these regions were unequally heated and all the phenomena of 
 trade winds mutatis mutandis must arise. Before proceeding to a further 
 exposition of his views, he takes this occasion to remark that the exist- 
 ence of a solar atmosphere cannot admit of any doubt. He adduces 
 in support of his assertion the deficiency of light exhibited by the border 
 of the solar disk, whether when viewed through coloured glasses, or by 
 projecting its image on white paper. But a phenomenon which appears 
 to him to establish still more conclusively the existence of such an atmo- 
 sphere, is that which was witnessed during the total eclipse of the sun which 
 occurred on the 8th of July, 1842*. On that occasion there appeared 
 three rose-coloured protuberances of immense size projecting from the 
 dark limb of the moon, which could not have been any other than clouds 
 floating in, and sustained by, a transparent atmosphere enveloping the 
 sun. To what distance from the surface of that body this atmosphere 
 may extend, it -is difficult to ascertain with precision; but, from the de- 
 ficiency of light exhibited by the exterior part of the disk being gradual, 
 and also perceptible at some distance within the margin, he is induced to 
 suppose that it must be considerable, not merely in absolute measure, but 
 as an aliquot part of the sun's radius. Admitting, then, the existence of 
 such an atmosphere, the laws of equilibrium will cause it to assume the 
 figure of an oblate spheroid, and the gaseous envelope so formed being 
 thicker round the equator than at the poles, a different obstacle will be 
 opposed to the escape of heat from the equatorial and the polar regions of 
 the sun. The manifest result will be, that an habitual difference of tem- 
 perature will prevail in the two regions. 
 
 * For interesting accounts of this eclipse, drawn up from personal observation, see 
 papers by Daily and Airy, in vol. xv. of the " Memoirs of the Astronomical Society." 
 
 Q 
 
226 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 " The spots, in this view of the subject," says the illustrious astronomer 
 referred to, " would corne to be assimilated to those regions on the earth's 
 surface in which, for the moment, hurricanes and tornadoes prevail the 
 upper stratum being temporarily carried downwards, displacing by its im- 
 petus the two strata of luminous matter beneath (which may be conceived as 
 forming an habitually tranquil limit between the opposite upper and under 
 currents), the upper, of course, to a greater extent than the lower, and 
 thus wholly or partially denuding the opaque surface of the sun below. 
 Such processes cannot be unaccompanied with vorticose motions, which, 
 left to themselves, die away by degrees and dissipate, with this peculiarity, 
 that their lower portions come to rest more speedily than their upper, by 
 reason of the greater resistance below, as well as the remoteness from the 
 point of action, which lies in a higher region, so that their centre (as seen 
 in our water-spouts, which are nothing but small tornadoes) appears to 
 retreat upwards. Now, this agrees perfectly well with what is observed 
 during the obliteration of the solar spots, which appear as if filled in by 
 the collapse of their sides, the penumbra closing in upon the spot and dis- 
 appearing after it."* 
 
 The views contained in the foregoing passage are eminently worthy 
 of attention. It is remarkable that no preceding astronomer attempted to 
 establish a connexion between the origin of the solar spots and the rotation 
 of the sun on his axis, although the intimate relation which appeared to 
 subsist between the situation of the spots and the solar equator, pointed out 
 very unequivocally the mutual dependence of the two phenomena. Dr. 
 Wilson, in a paper already cited, alludes to the invariable appearance of the 
 spots in the regions near the solar equator, as a remarkable fact of which 
 he was unable to offer any explanation f. It is curious, however, to find 
 among a series of conjectures thrown out by him respecting the origin of 
 these phenomena, an idea analogous to that propounded in the above passage J. 
 His allusion to their possible generation by means of whirlpools in the 
 solar atmosphere, commencing from the surface, in common with his other 
 conjectures on the subject, shews that he possessed no inconsiderable 
 share of the imaginative faculty which is so necessary in all physical specu- 
 lations ; but, whatever degree of truth may eventually turn out to be in- 
 volved in this surmise, he cannot be entitled to any credit on its account, 
 since he was unable to discover any physical connexion between it and the 
 subject of investigation. The explanation proposed by Sir John Herschel 
 is valuable, inasmuch as it exhibits the solar spots in the character of dy- 
 namical consequences flowing from the operation of established principles 
 in physics. It is one of those conceptions of genius which, being formed by 
 a comprehensive and luminous view of the mutual relations of facts accurately 
 observed, rather than suddenly suggested by the sallies of a lively but 
 wayward imagination, is found not unfrequently to constitute the germ of 
 a theory of indisputable rigour. The distinguishing character of all those 
 speculations in science which have facts for their basis consists in their 
 tendency to promote further research. By a comparison of their results 
 with those deduced from actual observation, the fundamental principles 
 are modified, and a further advance is made towards a true explanation of 
 the phenomena which form the groundwork of inquiry. In the present 
 instance, the question whether the spots recur periodically in the same 
 precise localities of the solar regions, acquires additional interest from the 
 
 * Results of Astronomical Observations at the Capeof Good Hope, p. 434. 
 t Phil. Trans., 1774. J See p. 222. 
 
HISTORY OF PHYSICAL ASTRONOMY. 227 
 
 hypothesis of their origin advanced in the foregoing passage, and suggests 
 the expediency of a continued prosecution of attentive observations of the 
 spots. By these means it is to be hoped that some light will be thrown 
 upon the real nature of these mysterious but singularly interesting pheno- 
 mena, which, in its turn, will lead to a more accurate knowledge of the 
 physical constitution of the sun. 
 
 We have mentioned that Sir William Herschel, in his theory of the 
 solar spots, supposes the solid nucleus of the sun to be effectually 
 screened from the luminous clouds of the superior regions by the interpo- 
 sition of the planetary clouds which possess the property of reflecting the 
 rays that fall upon them. That the clouds of the lower regions shine only by 
 reflection, he infers from their constantly exhibiting a faint and uniform 
 colour; and that they form a continuous envelope round the nucleus of the 
 sun, appears to him equally manifest from his being enabled, by means of 
 his powerful telescopes, to discover them through the minute fissures by 
 which every part of the luminous surface of the sun is intersected *. He 
 considers, therefore, that, notwithstanding the circumstance of the lumi- 
 nous atmosphere of the sun being the source from which light and heat 
 are dispensed in all directions, the solid nucleus of that body may be con- 
 stantly maintained at a moderate temperature. Proceeding upon this view 
 of the physical constitution of the sun, he comes to the conclusion that the 
 central body of the planetary system is eminently fitted to be the abode of 
 animated beings, and that in fact it offers the example of a magnificent self- 
 luminous planet. This opinion has been ably controverted by one of the 
 most illustrious philosophers of the present age." It is indeed incon- 
 ceivable," says Sir David Brewster, " that luminous clouds, yielding to 
 every impulse, and in a state of perpetual change, could be the depository 
 of that devouring flame, and that insupportable blaze of light, which are 
 emitted by the sun ; and it is still more inconceivable that the feeble 
 barrier of planetary clouds could shield the subjacent mass from the de- 
 structive elements that raged above." According to the opinion of the 
 eminent authority just quoted, the heat and light of the sun derive their 
 origin from two distinct sources. The luminous rays are emitted from the 
 phosphorescent mantle which constitutes the exterior envelope of the sun, 
 while the calorific rays proceed wholly from the opaque nucleus. Our 
 limits will not allow us to notice the ingenious arguments which the author 
 of this explanation adduces in its support f. Unfortunately our know- 
 ledge of the nature of both heat and light is so obscure, that every attempt 
 hitherto made to form an hypothesis respecting the physical constitution 
 of the sun, appears to be beset with insuperable difficulties. 
 
 It is remarkable that, at so recent a period as that of the discovery of 
 the solar spots, astronomers were unacquainted with any method by 
 which the sun might be viewed without injury to the eyes. Appian, 
 an astronomer of the fifteenth century, had indeed pointed out the utility 
 of coloured glasses for this purpose, but the hint appears to have been 
 entirely lost sight of by his successors. Fabricius observed the solar 
 spots either by introducing the sun's rays through a small aperture into 
 a dark room, and projecting his image on a piece of white paper, or by 
 viewing him directly through thin clouds and vapours when he was near 
 the horizon. He recommends all those who purpose making direct obser- 
 vations of the spots to admit to the eye at first only a small portion of the 
 
 Phil. Trans., 1802, p. 294. 
 
 f See Brewster's Edin. Encyclop., Art. "Astronomy." 
 
 Q 2 
 
S28 HISTORY OF PHYSICAL ASTRONOMY. 
 
 solar light, and to increase the quantity gradually, until the visual organ 
 becomes so habituated to the effulgence of the light as to be capable of 
 viewing with impunity the whole <3f the solar disk. Galileo was equally 
 ignorant of any method of observing the sun except that which consisted 
 in taking advantage of his horizontal position when rising or setting. In 
 a postscript added to his second letter to Welser, he alludes to an immense 
 spot which appeared on the centre of the sun's disk, and which he, as 
 well as many others to whom he shewed it, was enabled to perceive with 
 the naked eye at sunset, on the 19th, 20th, and 21st of August, 1612*. 
 Scheiner appears to have been the first observer who reduced into 
 practice the method suggested by Appian. In a dissertation on the solar 
 spots, which he published in 1612, he remarks that the sun may be 
 viewed at any altitude by placing before the telescope a piece of glass, of 
 a green or azure colour. He adds that this is the method practised by the 
 Dutch mariners, when they wish to determine the altitude of the sun. A 
 decided improvement of this method was first indicated by Tarde, a 
 Frenchman, who published a work on the solar spots in 1620. He states 
 that when he observed the spots he placed a thick piece of blue or green 
 glass between his eye and the eye-glass of the telescope. By placing the 
 coloured glass in this position, the indistinctness of the image arising from 
 impurities in the structure of the glass, or an imperfect parallelism of its 
 surfaces, was in a great degree removed. 
 
 The theory of the moon's motion is a subject of so much importance, 
 that the attention of astronomers is constantly directed to its improvement. 
 We have already alluded to a method assigned by the theory of gravitation 
 for determining the distance of the moon from the earth. By means of 
 the formula of Laplace, Burchardt (assuming the moon's mass to be -$ 
 of the earth's) found that the constant part of the lunar parallax under the 
 equator amounted to 57' 0". Damoiseau determined the moon's mass to 
 be ^ T , the mass of the earth being represented by unity, and hence de- 
 rived 57' 0"-9 for the constant of parallax. Plana makes the mass -g' T> 
 and hence computes the parallax under the equator to be 57' 3" - l. 
 
 A more obvious method of ascertaining the horizontal parallax of the 
 moon is founded upon a comparison of her apparent positions as deter- 
 mined simultaneously at different places on the surface of the earth. One 
 of the principal objects of Lacaille's voyage to the Cape of Good Hope 
 was to make observations of the moon for this purpose. By comparing 
 his results with simultaneous observations made at different places in 
 Europe, and assuming the ellipticity of the earth to be ^1^, he obtained 
 57' 13"-1 for the constant part of the moon's equatorial parallax. This 
 is equivalent to a parallax of 57' 4"-6, if the ellipticity be supposed equal 
 to -y^ -Q. Lalande, by comparing Lacaille's observations at the Cape of 
 Good Hope with simultaneous observations made by himself at Berlin, 
 fixed it at 57' 3"-7. Burg determined it to be 57' 1" by a similar com- 
 parison of Lacaille's observations with corresponding observations made 
 at Greenwich. Henderson, during his residence at the Cape of Good 
 Hope in the years 1832 and 1833, determined a great number of decli- 
 nations of the moon, with the view of arriving at a more accurate value of 
 this element. By a comparison of his own observations with others, made 
 simultaneously at Greenwich and Cambridge, he obtained 57' 1"'8 for the 
 constant of the equatorial parallax f. This gives 7 -^.^ for the value of the 
 
 * Istoria et Dimostrazione intorno alle Macchie Solari, p. 56. 
 f Mem. Ast. Soc., vol. x., p. 294. 
 
HISTOEY OF PHYSICAL ASTRONOMY. Q29 
 
 moon's mass. Mr. Airy, by a discussion of the totality of the Greenwich 
 observations, instituted subsequently to their recent reduction upon a uni- 
 form plan, has determined the constant part of the equatorial parallax to 
 be 57' 4"-94. This value, considering the broad basis upon which it rests, 
 is more entitled to confidence than any other which astronomers have 
 hitherto arrived at. 
 
 In consequence of her proximity to the earth, the physical consti- 
 tution of the moon offers to astronomers a more favourable subject of re- 
 search than that of any of the other celestial bodies. Galileo's discovery, 
 that her surface is diversified with mountains and valleys, like the sur- 
 face of the earth, was one of the many signal triumphs which that 
 illustrious philosopher achieved in favour of the Copernican system of 
 the world. He concjuded, from his observations, that the mountains of 
 the moon are much higher than those of the earth, when the relative 
 magnitudes of the two bodies are taken into account. Many of them, 
 according to his estimation, attain an elevation of four or five miles 
 above the surrounding plains. Hevelius, Riccioli, and more recently 
 Schroeter, were conducted by their respective observations to similar con- 
 clusions. Sir William Herschel did not discover any grounds for ascrib- 
 ing such an enormous height to the lunar mountains. He inferred, from 
 his observations, that with a few exceptions they did not exceed half a 
 mile in height. This conclusion is undoubtedly more consistent with 
 analogy than that which assigns a higher elevation. It must be admitted, 
 however, that the recent researches of MM. Beer and Madler, on this 
 subject, go to support the remarkable results of Schroeter and the more 
 ancient observers. These astronomers have determined the heights of 
 1093 lunar mountains, principally by means of micrometrical measures of 
 the lengths of their shadows, and have found several of them to attain an 
 elevation of four miles above the neighbouring plains *. 
 
 The numerous spots which appear on the surface of the moon when 
 viewed with the telescope, besides being calculated to throw light on the 
 physical constitution of that body, are of some utility in observations of 
 eclipses, and on this account several astronomers have devoted conside- 
 rable attention to a careful delineation of their relative positions. Charts 
 of the telescopic appearance of the moon were first executed by Scheiner, 
 but Langrenus, Cosmographer of the King of Spain, was the first person 
 whose labours on this subject deserve notice. He constructed, and even 
 actually engraved, thirty maps of different portions of the lunar surface, 
 founded on observations made by himself with a large telescope, at Madrid 
 and Brussels. It was he who introduced the practice of naming the dif- 
 ferent spots after mathematicians, philosophers, and other eminent men. 
 Hevelius about the same time devoted four years to assiduous observa- 
 tions of the lunar spots and delineations of their various configurations. 
 He rejected the nomenclature of Langrenus, and named the spots after 
 continents, seas, islands, and other objects on the earth's surface to which 
 he conceived they bore a resemblance. Riccioli was the next astronomer 
 who constructed charts of the lunar surface. He restored the principle of 
 nomenclature adopted by Langrenus, but, instead of distinguishing the 
 
 * The following are the elevations of a few of the principal lunar mountains, as deter- 
 mined by MM. Beer and Madler : Dorfel, 23,174 feet; Newton, 22,141 feet; Cas- 
 satus, 21102 feet; Curtius, 20,632 feet; Callippus, 18,946 feet; Tycho, 18,748 feet. 
 A mile contains 5280 feet. The four highest of these mountains, therefore, attain seve- 
 rally an elevation of about four miles. The other two are about half a mile lower. 
 
230 HISTORY OF PHYSICAL ASTRONOMY. 
 
 spots by the names of great men indiscriminately, he employed for this 
 purpose only the names of eminent astronomers of ancient and modern 
 times. In 1692 Cassini executed a chart of the full moon. The positions 
 of the spots were determined by means of his own observations of eclipses. 
 Delineations of the moon's appearance have ateo been executed by Schroeter, 
 Lohrmann, and other observers. The most recent work of this kind is the 
 elaborate representation of the lunar surface by MM. Beer and Madler. 
 
 The question whether the moon be surrounded by an atmosphere, has 
 been much discussed by astronomers. Various phenomena are capable 
 of indicating such an atmosphere, but, generally speaking, they are found 
 to be unfavourable to its existence, or at all events they lead to the con- 
 clusion that it must be very inconsiderable. From the uniform appear- 
 ance presented by the lunar spots, when viewed from time to time with the 
 telescope, it is reasonably supposed that they are not liable to be occasion- 
 ally obscured by the interposition of dense clouds between them and the 
 earth, like the different portions of the earth's surface ; and on this ground 
 it has been maintained that the moon cannot be encompassed by a gaseous 
 fluid, analogous in its properties to that which encompasses the earth. 
 Hevelius indeed, who devoted many years to assiduous observations of 
 the moon's surface, has remarked that the spots sometimes appeared to be 
 less bright and less regularly defined than they usually were, even when 
 the air was so clear as to allow stars of the sixth and seventh magnitudes 
 to be distinctly visible *. His assertion, however, has not been borne out 
 by the more searching observations of succeeding astronomers, and there- 
 fore it is not entitled to any weight in discussing so delicate a point as the 
 existence of a lunar atmosphere. 
 
 The occultations of stars by the moon have hitherto afforded only 
 very slight indications of an elastic fluid enveloping the lunar sur- 
 face. If such a fluid really exists, it manifestly follows that, when the 
 moon approaches within a very small distance of a star previous to occult- 
 ing it, the star ought to exhibit a sensible change of colour and diminu- 
 tion of lustre, in consequence of the rays proceeding from it to the eye of 
 the observer being partially absorbed in the course of their passage through 
 the lunar atmosphere. Observation is, generally speaking, at variance 
 with this conclusion, the star being found* in most cases, to retain its 
 ordinary colour and brightness until it actually arrives at the moon's 
 limb. There is not wanting high authority, however, in support of an 
 occasional obscuration of the light of the star. On the 27th March, 
 1811, M. Arago witnessed at the Royal Observatory of Paris, the occulta- 
 tion of a small star in the constellation Taurus. The star, as long 
 as it continued to be visible, retained its usual colour, but it exhibited a 
 very sensible diminution of brightness during a short time previous to its 
 immersion. The occultation took place at the dark limb of the moon, which 
 was only four days old. The dimness of the star could, therefore, hardly 
 be ascribed to the overpowering glare of the moon's light. On a subse- 
 quent occasion the same eminent astronomer perceived that the star 49 
 Libras commenced to diminish in lustre three or four seconds previous to 
 its immersion. Similar instances of obscuration have also been occasion- 
 ally observed by other astronomers, but as the phenomenon is not gene- 
 ral the existence of a lunar atmosphere cannot be considered to be 
 established by it. There is another phenomenon attending the occulta- 
 tions of stars, analogous to that already mentioned, which has been found 
 * Cometographia, p. 363. 
 
HISTORY OF PHYSICAL ASTRONOMY. 231 
 
 to afford similar indications of a lunar atmosphere without placing the 
 question of its existence beyond all doubt. When the star comes up 
 to the moon, it is observed frequently to hang on the margin of the 
 disk for several seconds previous to its disappearance. An effect ana- 
 logous to this would manifestly be produced by the interposition of the 
 denser strata of the moon's atmosphere between the star and the observer. 
 On the occasion of the first of the two observations of M. Arago, above 
 cited, the star appeared to adhere to the moon's limb for the space of three 
 or four seconds after it was perceived to be in contact with it. This 
 circumstance could not be ascribed to the effect of irradiation, since the 
 occultation took place at the dark limb of the moon, which was visible by 
 means of the lumiere cendree, or reflected light of the earth. Numerous 
 similar instances of the star's adherence to the limb of the moon have 
 been recorded by astronomers, but, as in the case of a diminution of lustre, 
 the phenomenon is not general. In the vast majority of occultations the 
 star comes up to the limb of the moon, and then disappears instantaneously. 
 Its occasional adherence to the limb cannot be admitted, therefore, to af- 
 ford any conclusive proof in favour of a lunar atmosphere. There is a third 
 circumstance connected with the phenomena of occultations which is cal- 
 culated to throw light upon this interesting question. It is manifest that 
 if the moon be surrounded by an atmosphere, the refractive power of the 
 latter would cause a star to be visible during a short time subsequent to 
 its immersion, and also during an equal lapse of time previous to its 
 emergence. The interval, therefore, which elapses between the disappear- 
 ance of the star at the moon's limb, and its subsequent re-appearance at 
 the opposite limb, ought to be less than the time which the moon takes to 
 describe an arc equal to her apparent diameter, by twice the horizontal re- 
 fraction of the lunar atmosphere. When the interval, however, is calcu- 
 lated by means of the theory of the moon's motion and her apparent dia- 
 meter, corresponding to the time of occultation, the result is found to ex- 
 hibit an exact accordance with that derived from direct observation. It 
 follows, therefore, that if the moon really be surrounded by an atmosphere, 
 its refractive power must be very inconsiderable. 
 
 The occultation of a planet by the moon suggests a peculiar mode of 
 testing the existence of a lunar atmosphere, in addition to those 
 already alluded to, which are also applicable to the fixed stars. When 
 the planet has so nearly approached the moon as to be almost in 
 contact with her limb, the rays issuing from the margin of its disk will 
 manifestly undergo different degrees of refraction in the course of their 
 passage through the lunar atmosphere, and an apparent distortion of its 
 figure will be the necessary consequence. Observation, however, does not 
 afford any indications of such a phenomenon. In 1679 Cassini and La 
 Hire witnessed an occultation of Jupiter by the moon, and they found that 
 from the time of the planet's approach to the limb until its complete dis- 
 appearance it did not exhibit the slightest indication of a change of figure*. 
 Similar phenomena have been observed by modern astronomers, but on no 
 occasion has any distortion of the round appearance of the planet been 
 distinctly discernible. 
 
 The phenomena of solar eclipses hate also been employed by astrono- 
 mers for the purpose of establishing the existence of a lunar atmosphere. 
 When the dark body of the moon is projected upon the luminous disk of 
 
 * Anc. Mem. Acad. des Sciences, tome i., p 303. 
 
232 HISTOKY OF PHYSICAL ASTRONOMY. 
 
 the sun, the rays of light proceeding from those parts of the sun which 
 are apparently contiguous to the lunar disk, will necessarily graze the 
 moon's surface, and if a lunar atmosphere exists, they ought, by the in- 
 flexion which they suffer in passing through it, to distort the visible por- 
 tion of the solar disk, and to cause the phase of the eclipse corresponding 
 to any assigned instant to be different from what it would be according to 
 the theories of the solar and lunar motions. From observations of a solar 
 eclipse which took place in 1748, Euler concluded that the horizontal re- 
 fraction of the lunar atmosphere amounted to 20"*. His researches, 
 however, were incomplete, inasmuch as he took no account of the effect of 
 irradiation, which, by causing an apparent enlargement of the solar disk, 
 might be expected to exercise a perceptible infl uence on the phase of the 
 eclipse. The latter is, in fact, modified by two distinct causes, which are 
 so interwoven in their operation, that it is impossible to investigate the ef- 
 fects of the one without taking simultaneous cognizance of those of the 
 other. In order to ascertain whether the phenomena of solar eclipses 
 were capable of affording any indications of a lunar atmosphere, Du Se- 
 jour, a French astronomer of the last century, undertook a rigorous inves- 
 tigation of the subject, founded on observations of the solar eclipse of 
 1764. He introduced the effects of irradiation and inflexion into his re- 
 searches in the shape of two unknown quantities, and then, by means of 
 equations of condition, which it was necessary that they should satisfy, he 
 determined the values of them* which accorded best with the totality of the 
 observations. The conclusion at which he finally arrived was, that the 
 effect of irradiation amounted to 3", and that the inflexion which the solar 
 rays suffered in passing through the lunar atmosphere amounted to an equal 
 quantity. This gives l-"5 for the mean horizontal refraction of the lunar 
 atmosphere. The mean refraction of the terrestrial atmosphere at the 
 horizon amounts to 34', a quantity which is 1400 times greater than l"-5. 
 It hence follows that the lunar atmosphere is 1400 times rarer than com- 
 mon atmospheric air, and consequently it exceeds in this respect the most 
 perfect vacuum which has been hitherto formed by means of the air-pump. 
 It appears, therefore, from the phenomena of solar eclipses, that, if a lunar 
 atmosphere really exists, it is quite inconsiderable when compared with the 
 terrestrial atmosphere. 
 
 Auzout first remarked that the moon could not be surrounded by an 
 atmosphere without possessing also a twilight f. This effect ought to 
 manifest itself in a faint light, extending to a short distance within the 
 unenlightened part of the lunar, disk, and thereby rendering a narrow strip 
 of it visible, although not directly illuminated by the solar rays. Astro- 
 nomers having failed to discover any indications of such a phenomenon, it 
 was concluded, -that the moon could not be encompassed by a fluid capable 
 of dispersing and reflecting the sun's rays. The appearance, however, was 
 at length recognised by Schroeter, who was enabled to deduce from it the 
 existence of an atmosphere of a small refractive power J. When the moon 
 exhibited a very slender crescent, he discovered a faint crepuscular light, ex- 
 tending from each of the cusps along the circumference of the unenlightened 
 part of the disk. Its length was I' 20", and its greatest breadth, 2". By 
 means of these data he found that the height of the lunar atmosphere, con- 
 sidered in so far as it was capable of affecting the brightness of a star, or caus- 
 
 * M&n. Acad. Berlin, 1748. 
 
 { Mem. Acad. des Sciences, tome vii., p. 106. 
 
 t Phil. Trans., 1792. 
 
HISTORY OF PHYSICAL ASTKONOMY. 233 
 
 ing a sensible inflexion of the rays of light proceeding from a celestial body, 
 did not exceed 5376 feet. An atmosphere of such a height would form a 
 zone round the circumference of the lunar disk, the apparent breadth of 
 which would amount only to 0'94". The moon would describe this arc in 
 less than two seconds of time. This circumstance has been adduced by 
 Schroeter as affording a sufficient explanation of the difficulty of detecting 
 any traces of a lunar atmosphere in the phenomena of occultations and 
 eclipses. 
 
 In consequence of the intense lustre of Mercury, and its constant vicinity 
 to the sun, astronomers have experienced great difficulty in arriving at 
 any reliable results respecting its physical constitution. According to 
 Schroeter the planet is surrounded by an atmosphere of considerable density. 
 The same astronomer concluded, from his observations, that there exist 
 very high mountains on its surface. It would appear, from the results at 
 which he arrived, that the mountains of this planet are much loftier than 
 those of the Earth, or the Moon, the relative magnitudes of the several 
 'bodies being taken into account. He estimated the height of Chimborazo 
 in South America at -yoVf of the Earth's radius ; the highest mountains 
 of the Moon at -^-^ of the lunar radius ; and those of Mercury at -^-^ of 
 its radius. He also found, by careful observations of the phases of the 
 planet, that it revolves about an axis inclined at a considerable angle to 
 the ecliptic. He determined the period of rotation to be 24 h 5 m 30 s . 
 
 Since Mercury appears to have a rotatory motion, it might be reasonably 
 supposed that her figure would not be that of an exact sphere. Schroeter, 
 however, could not discover any trace of ellipticity in the appearance of 
 the planet. The observations of Sir William Herschel conducted him to 
 a similar conclusion. That illustrious astronomer observed the transit of 
 the planet which took place in November, 1803, but, although he devoted 
 great attention to the appearance of the disk, he was unable to persuade 
 himself that it exhibited even the slightest deviation from a circular form*. 
 He therefore came to the conclusion that, unless the polar axis was turned 
 towards the earth, the planet did not possess any sensible ellipticity. It 
 appears, however, from recent micrometrical measures executed by the 
 Eev. Mr. Dawes on. the occasion of the transit of November, 1848, that 
 the figure of the planet is really spheroidal to a small extent. The mean 
 of several results, obtained by different methods of measurement, indicated 
 an ellipticity equal to -^-gf. 
 
 One of the most interesting of the various phenomena which disclosed 
 themselves to the admiration of Galileo, when he first directed the tele- 
 scope to the heavens, was the appearance presented by the planet Venus. 
 When observed near her inferior conjunction she exhibited a slender 
 crescent of light, like the moon when she is a few days old. As she re- 
 ceded from the position intervening between the sun and the earth, the 
 phase continued to increase in magnitude until, upon approaching her 
 superior conjunction, she acquired a round appearance, like the full moon. 
 The conclusion was irresistible, that the planet was an opaque body, 
 which owed its luminous appearance solely to its power of reflecting the 
 solar rays which fell upon its surface. An important point of resemblance 
 was thus established between it and the earth, which formed the ground 
 of an argument of overwhelming force in favour of the Copernican system 
 of the world. 
 
 * Phil. Trans., 1803, p. 217. f Monthly Pro. Ast. Soc., Dec. 1848. 
 
234 HISTORY OF PHYSICAL ASTRONOMY. 
 
 As in the case of Mercury, the intense lustre of this beautiful planet 
 has proved a serious obstacle to astronomers, in their attempts to arrive at 
 some knowledge respecting its physical constitution. In the years 1666-7 
 Cassini, while still residing under the clear sky of Italy, devoted his atten- 
 tion to a searching examination of the planet,* with the view of detecting pe- 
 riodic changes in its appearance which might indicate a rotation on an axis. 
 On the 21st April, 1667, he at length discovered a bright spot, which, 
 when watched for some time, was found to return to the same position on 
 the disk of the planet at successive intervals of about 23 hours. This would 
 indicate a rotation of the planet agreeing very nearly with the diurnal mo- 
 tion of the earth. Cassini, however, was unable to follow the spot through- 
 out an extent of its course sufficiently large to enable him to ascertain 
 positively whether its change of position arose merely from a libratory mo- 
 tion of the planet, or from a complete rotation on an axis. Upon a subse- 
 quent occasion, during his residence in France, he resumed the examination 
 of the planet, with the view of perfecting his previous researches, but al- 
 though he strove, with great perseverance, to detect the spot on its disk 
 which was visible in Italy, all his efforts were fruitless. In 1 726 Bianchini, 
 the domestic prelate of the Pope, commenced an examination of Venus at 
 Rome, with a powerful telescope constructed by the celebrated Campani, and 
 soon succeeded in detecting several dark spots on the disk of the planet, the 
 motion of which he continued for some time to watch with great attention. 
 The conclusion he arrived at was somewhat anomalous. He announced 
 that the changes in the positions of the spots could not be satisfactorily 
 accounted for without supposing a period of rotation amounting to 24 d 8 h . 
 The researches of astronomers on the rotation of the planet formed the 
 subject of a critical discussion by J. Cassini. He remarked that the con- 
 tinuity of Bianchini's observations was interrupted by the interposition 
 of the Barbariui Palace, which every night concealed the planet from him 
 for some time. Adopting a hypothesis founded on this chasm in the ob- 
 servations, he shewed that if the period of rotation be supposed equal to 
 23 h 20 m , the observations of his father as well as those of Bianchini may 
 be equally well satisfied ; but he remarked that if the period of 24 d 8 h be 
 admitted," his father's observations must be rejected as totally worthless*. 
 
 The value assigned by Cassini to the period of the rotation of Venus has re- 
 ceived a complete confirmation from the researches of modern astronomers. 
 In 1789 Schroeter, having undertaken a careful examination of the planet 
 with a seven-feet reflector, discovered a luminous point in the dark hemi- 
 sphere, a little beyond the southern horn, indicating the existence of a 
 high mountain. By continuing for some time to direct his attention to 
 the periodic changes of this object, he was finally enabled to deduce from 
 them the conclusion, that the planet performs a complete rotation on its 
 axis in a period amounting to 23 h 21 m 19 s . This result agrees with that 
 recently arrived at by the late Sig. De Vico and his associates, of 
 the Observatory of the Roman College. In 1839 they commenced 
 a series of observations of Venus with a magnificent refractor by Cau- 
 choix. In order more effectually to obviate the inconvenience arising 
 from the intense lustre of the planet, the examination was conducted 
 during the day time I. The ancient spots observed by Bianchini were 
 speedily re-discovered, and were found to possess the precise forms assigned 
 
 * Clemens J' Astronomic, p. 526. 
 
 f A similar mode of observing the planet was employed by La Hire. See Mem. 
 Acad. des Sciences, tome x., p. 20. 
 
HISTOKY OF PHYSICAL ASTKONOMY. 235 
 
 to them by that astronomer. The final conclusion was, that the planet 
 performs a complete rotation on its axis, in a period agreeing almost ex- 
 actly with that which Schroeter had deduced from his observations. 
 
 The various astronomers who have determined the rotation of Venus 
 agree in estimating the inclination of the equator to the plane of 
 the ecliptic at 75. No trace of ellipticity has been discovered in the 
 planet ; nor will this appear surprising when the probable smallness 
 of its amount is considered. If the equatorial axis exceeded the polar by 
 only ^ O th of its own length, as in the case of the earth, the difference 
 of the two axes would subtend an angle of only a tenth of a second at the 
 mean distance of the planet from the earth. It is obvious that the 
 most delicate micrometrical measurements are incapable of establishing 
 the existence of so small a quantity. That the ellipticity of the planet 
 does not differ much from that of the earth, is probable from the circum- 
 stance that both bodies are nearly of the same size, and are endued 
 with nearly equal velocities of rotation, 
 
 According to Schroeter there exist mountains of immense height on the 
 surface of Venus. The most considerable of these elevations amounts to 
 r ^ of the radius of the planet. Chimborazo, in South America, which 
 was long supposed to be the highest mountain on the surface of the earth, 
 attains an elevation equal only to T QTT ^ ^ e terrestrial radius. The 
 same astronomer remarks that Venus, as well as Mercury and the Earth, 
 have the highest mountains situate in their southern hemispheres. These 
 results can only be admitted with a certain degree of reserve, when the 
 extreme delicacy of the observations by means of which they are arrived at, 
 is taken into account. Even the great Herschel was unable to deduce 
 any trustworthy results of this nature from his observations of the planet. 
 The remark of Schroeter, that the three planets nearest the sun have the 
 highest mountains situate in their southern hemispheres, is at least no 
 longer applicable to the earth, since the Himalayan range of mountains 
 has been found to be the most elevated region on its surface. 
 
 Various circumstances concur to prove that Venus is surrounded by 
 an atmosphere of considerable density. During the transits of the 
 planet over the sun's disk in 1761 and 1769, the planet was observed, 
 by several astronomers, to be surrounded by a faint ring of light similar 
 to the appearance which would be occasioned by the passage of the solar 
 rays through a circumambient fluid. This indication of the existence of 
 an atmosphere is confirmed by the observations of Schroeter, who dis- 
 covered what appeared to him to be a faint crepuscular light, extending 
 beyond the cusps of the planet into the dark hemisphere *. From micro- 
 metrical measures of the space over which this light was diffused, he con- 
 cluded that the horizontal refraction at the surface of the planet amounts 
 to 30' 34", a quantity agreeing very nearly with the horizontal refraction 
 of the terrestrial atmosphere f. 
 
 When the planet Mars is observed with a telescope of ordinary power, 
 its surface appears to be diversified with spots of an irregular cha- 
 racter, which have conducted astronomers to some interesting conclusions 
 respecting its physical constitution. These appearances were first noticed 
 by Fontana, a Neapolitan astronomer. In 1636 he observed a spot on 
 the disk of the planet, which subsequently re-appeared in 1638. From 
 the changes which it seemed to undergo, he suspected that the planet was 
 
 * Phil. Trans., 1792. 
 
 f The interesting fact of the existence of a twilight in Venus has been confirmed by 
 the observations of Sir William Herschel. (Phil Trans. 1793, p. 214. ) 
 
236 HISTORY OF PHYSICAL ASTRONOMY. 
 
 endued with a rotation on an axis. Hooke is one of the first astronomers 
 who arrived at this conclusion by reasoning of a strictly legitimate cha- 
 racter, founded upon his own observations of the planet. On the 28th of 
 March, 1 666, he communicated a paper to the Royal Society, containing 
 an account of observations of certain spots em the disk of the planet. He 
 mentions that he had seen the spots in the month of February, 1666; 
 but the earliest observation contained in his paper is dated the 3rd of the 
 following month. Having found that the spots returned at regular inter- 
 vals to the same position on the disk, he inferred that the planet accom- 
 plishes a rotation on an axis in a period amounting to 12 or 24 hours *. 
 The contemporaneous observations of Cassini in Italy conducted that astro- 
 nomer to a result of greater precision. He concluded, from the interval 
 which elapsed between the return of the spots to the same position on the 
 disk, that the planet performs a complete revolution round its axis in 24 h 
 40 m . This result received a satisfactory confirmation from the researches 
 of the elder Maraldi. In 1704 that astronomer, having watched the changes 
 in the positions of the spots, inferred a period of rotation equal to 24 h 39 ra . 
 In the autumn of 1719, there occurred a peculiarly favourable opportunity 
 for verifying this conclusion. When the planet arrived in opposition on 
 the 27th August of that year it was only 2^ distant from the perihelion, 
 and on account of its proximity to the earth it shone with such uncommon 
 splendour that many persons supposed it to be a comet or a new star. On 
 the 19th August, Maraldi, having examined the planet with a telescope 
 34 feet long, perceived two obscure bands on the disk, forming with each 
 other an obtuse angle, which exhibited a very conspicuous point f. On the 
 25th September, he again observed the planet,' and perceived the angular 
 point in the same position on the disk. During the interval of 37 days, 
 which had elapsed between the two observations, the planet had therefore 
 completed 36 rotations on its axis. This gave 24 h 40 m for the period of rota- 
 tion, a result agreeing exactly with that arrived at by Cassini. In the 
 years 1777 and 1779, Sir William Herschel carefully observed the changes 
 in the appearance of the planet, and concluded from them that the period 
 of rotation amounted to 24 h 39 m 21 S> 67 J. He also found that the inclina- 
 tion of the planet's equator to the ecliptic amounts to 28 42', and that its 
 ascending node is situate in 19 28' of Sagittarius . The recent researches 
 of MM. Beer and Madler make the period of rotation to be 24 h 37 m 23 s . 
 
 Mars being endued with a rotation on a fixed axis, it is reasonable to 
 conclude that the figure of the planet will be flattened at the poles. It 
 was reserved for Sir William Herschel to establish this interesting fact 
 upon the basis of observation. By micrometrical measurement he deter- 
 mined the lengths of the equatorial and polar axes to be as 1355 to 1272, 
 or as 16 to 15 nearly ||. This indicates an ellipticity considerably greater 
 than what appears necessary to counterbalance the centrifugal force of the 
 equatorial parts of the planet, if its density be supposed homogeneous. 
 The discordance, however, in this as well as in all similar instances, may 
 be explained by an adequate supposition respecting the internal structure 
 of the planet. 
 
 The earlier observers of Mars had remarked the appearance of very bright 
 spots at the poles of his equator. Maraldi, who devoted much attention 
 to these phenomena, suspected that they were the indications of physical 
 changes occurring on the surface of the planet. In 1777-79, Sir William 
 Herschel examined the telescopic appearance of the planet with instru- 
 
 * Phil. Trans., No 14 t Mem. Acad. des Sciences, 1720. 
 
 \ Phil. Trans. 1781, p, 134. Phil. Trans., 1784, p. 273. || Ibid. 
 
HISTORY OF PHYSICAL ASTRONOMY. 237 
 
 merits far superior in power to any that had been hitherto used for a 
 similar purpose, and with the scrupulous attention to accuracy which cha- 
 racterized all the observations of that illustrious astronomer. He sup- 
 posed the bright appearances around the poles to be the light reflected 
 from masses of ice, and snow accumulated in the polar regions ; and he 
 ascribed their occasional diminution to the dissolving influence of the 
 solar rays, when they became exposed to them by the revolution of the 
 planet in its orbit. The changes actually exhibited by the spots afforded 
 a striking confirmation of this view of their origin. Thus, in the year 
 1781, the spot about the south pole was extremely large, but this might 
 naturally have been expected, since the pole had been recently involved in 
 perpetual darkness during the space of twelve months. In 1783 it had 
 become considerably smaller, and it continued to decrease from the 20th 
 May of that year till about the middle of September. During the last- 
 mentioned interval, the south pole had already been above eight months 
 enjoying the benefit of summer, and still continued to receive the sun- 
 beams, though, towards the close of the period, in so oblique a direction as 
 to derive but little benefit from them. On the other hand, in the year 
 1781, the north polar spot which had been enjoying the sunshine for 
 twelve months, and was but lately returning to darkness, appeared small, 
 though increasing in size. It was indeed invisible in the year 1783, but 
 this arose from the position of the axis of the planet, by which it was 
 removed out of sight*. The explanation of Sir William Herschel has been 
 generally adopted by astronomers, as the most probable that can be offered 
 respecting the interesting phenomena to which allusion has just been made. 
 It is hardly necessary to remark that such an explanation implies the ex- 
 istence of an atmosphere about the planet. 
 
 If we consider the arrangement of the planetary system as it was known 
 previous to the discovery of Uranus, it will readily occur, either from a com- 
 parison of the numerical values of the mean distances of the planets, or 
 from an inspection of their orbits when traced concentrically by a graphic 
 process on a sheet of paper, that while the intervals between the succes- 
 sive orbits increase continually outwards from the sun, a vacuity, dispro- 
 portionately larger than any of the others, exists between the orbits of Mars 
 and Jupiter. When Kepler, during the earlier period of his astronomical 
 career, was endeavouring to discover a connexion between the mean 
 distances of the planets from the sun, and their motions in their orbits, 
 he encountered in this anomalous fact an insuperable obstacle to the 
 success of his speculations. The most plausible hypothesis that his fertile 
 imagination could suggest, appeared to require that the vacuity should be 
 filled up by the interposition of another orbit. At length, having despaired 
 of reconciling the actual state of the planetary system with any theory he 
 could form respecting it, he hazarded the assertion that a planet really 
 existed between the orbits of Mars and Jupiter, and that its smallness 
 alone prevented it from being visible to astronomers. This bold surmise 
 of the illustrious discoverer of the laws of the planetary movements, was 
 generally regarded as not the least probable of those transient sallies of the 
 imagination in which he delighted to indulge, and it was favourably alluded 
 to by Lambert in his " Cosmological Letters," published in 1769. In 1772, 
 Bode published a treatise on astronomy in which he first announced the 
 singular relation between the mean distances of the planets from the sun, 
 which has since been distinguished by his name. This relation, to which 
 * Phil. Trans., 1784, p. 261. 
 
238 HISTORY OF PHYSICAL ASTRONOMY. 
 
 allusion has already been made in one of the foregoing chapters, exhibited 
 in a very striking light the exaggerated leap from Mars to Jupiter, and 
 suggested the strong probability of a planet revolving in the intermediate 
 region. This conjecture was rendered still more plausible by the dis- 
 covery of the planet Uranus, in 1781, the distance of which from the sun 
 was found to conform exactly to the law of Bode. In Germany, especially, 
 a strong impression had been produced that a planet really existed between 
 Mars and Jupiter ; and, through the active exertions of De Zach, an asso- 
 ciation of twenty-four astronomers was formed, having for its object to 
 effect the discovery of the unknown body. For this purpose the zodiac 
 was divided into twenty-four zones, one of which was to be explored by 
 each astronomer ; and the conduct of the whole operation was placed under 
 the superintendence of Schroeter. Soon after the formation of this society 
 the planet was discovered, but not by any of those astronomers who were 
 engaged expressly in searching for it. Piazzi, the celebrated Italian 
 astronomer, while engaged in constructing his great catalogue of stars, 
 was induced carefully to examine, several nights in succession, a part of the 
 constellation Taurus, in which Wollaston, by mistake, had assigned the 
 position of a star which did not really exist. . On the 1st January, 1801, 
 Piazzi observed a small star, which, on the following evening, appeared to 
 have changed its place. On the 3rd he repeated his observations, and he 
 now felt assured that the star had a retrograde motion in the zodiac. The 
 daily change of position in right ascension was 4', and the change in decli- 
 nation towards the north pole was 3' 30". On the 24th of January, 
 he transmitted an account of his discovery to Oriani and Bode, communi- 
 cating the positions of the star on the 3rd and 23rd of that month, and 
 adding that its motion, from being retrograde on the llth, had become 
 direct on the 13th of the same month. Piazzi continued to observe the 
 star until the llth of February, when he was seized with a dangerous 
 illness which completely interrupted his labours. His letters to Oriani 
 and Bode did not reach these astronomers until the latter end of March, 
 but the planet had then approached too near the sun to admit of their ob- 
 taining a verification of his discovery by actual observation, and it was 
 necessary for this purpose to wait until the month of September, when the 
 planet would have effectually extricated itself from the solar rays. Its re- 
 discovery, after the lapse of so considerable a period subsequent to the 
 most recent observation, could not be expected to be accomplished without 
 a pretty accurate knowledge of the orbit in which it was moving; but the 
 data communicated by Piazzi were insufficient for this purpose. They 
 merely served to indicate that the body revolved in a circular orbit between 
 Mars and Jupiter, at a distance agreeing very nearly with that assigned 
 by Bodes law, and so far offered a satisfactory confirmation of the views 
 of the German astronomers. Meanwhile Piazzi, fearing lest he should be 
 deprived in any degree of the glory attached to the discovery of the planet, 
 communicated to astronomers all the observations of it made by him down 
 to the llth February. Gauss found that they might be all satisfied 
 within a few seconds, by an elliptic orbit, of which he calculated the ele- 
 ments ; and, with the view of aiding astronomers in searching for the 
 planet, that illustrious geometer also computed an ephemeris of its motion 
 for several months. After a careful examination of its geocentric path, 
 the planet was finally discovered by De Zach on the 31st of December, 
 and by Olbers on the following evening. A year had therefore elapsed 
 between the original discovery of the planet by Piazzi and its subsequent 
 
HISTORY OF PHYSICAL ASTRONOMY. 239 
 
 re-discovery by the German astronomers. Piazzi conferred on it the name 
 of Ceres, in allusion to the titular goddess of Sicily, the island in which it 
 was discovered ; and the sickle has been appropriately chosen for its 
 symbol of designation. 
 
 The mean distance of Ceres, as determined by the calculations of Gauss, 
 was 2* 767. The distance assigned by Bode's law is 2*8. In this respect, 
 therefore, the new member of the planetary system harmonized admirably 
 with the other bodies of which it was composed. In other respects, 
 however, it offered unexpected anomalies. Sir William Herschel found, by 
 micrometrical measures of the planet's apparent magnitude, that its dia- 
 meter at the mean distance of the earth from the sun would subtend an 
 angle of only //- 35. This result makes the linear diameter amount to 
 only 161 miles. The newly-discovered body was, therefore, excessively 
 minute, when compared with any of the older members of the planetary 
 system. Its motion also exhibited peculiarities which in some degree as- 
 similated it to bodies of a cometary nature. Its inclination to the ecliptic 
 excededed 10, and consequently it deviated from that plane to a much 
 greater extent than any other planet. 
 
 The interesting discovery of Piazzi was soon followed by another of a 
 similar nature. Olbers, while engaged in searching for Ceres, had studied 
 with minute attention the various configurations of all the small stars 
 which are situate near the geocentric path of that planet. On the 28th of 
 March, 1802, while examining the north-western part of the constellation 
 Virgo, his attention was directed to a small unknown star of the 7th magni- 
 tude. It was situated very near the place where he discovered Ceres, and 
 it formed an equilateral triangle with two other small stars, whose positions 
 were given in the catalogues of astronomers. From the intimate knowledge 
 he had acquired of the region in which the star appeared, he felt assured 
 that he had not perceived it on any former occasion ; and his first impression 
 was, that in all probability it was a variable star which had attained its 
 maximum state of brightness. After the lapse of two hours, however, he 
 found that it had a proper motion, the right ascension having sensibly 
 diminished during that interval, while, on the other hand, the decimation 
 had increased towards the north. The observations of the following even- 
 ing established beyond all doubt his suspicion that the body was a planet ; 
 its right ascension having diminished to the extent of 10', while the 
 increase of declination was 20'. On the 28th of April, when a month 
 only had elapsed since the discovery of the planet, Gauss assigned the 
 elements of the elliptic orbit in which it was found to revolve, and the re- 
 sults derived from them exhibited a most satisfactory accordance with 
 observation. The mean distance, as determined by Gauss, was 2-670. 
 The planet, therefore, offered in this respect a remarkable analogy to 
 Ceres, the mean distances of both planets agreeing within a small fraction. 
 Like Ceres also, it was remarkable for the minuteness of its volume. 
 From Herschel's estimate of its apparent magnitude, it followed that its 
 linear diameter did not amount to more than 110J miles *. In the form 
 and position of its orbit, it exhibited deviations from the older planets, 
 much more considerable than those by which Ceres was distinguished. 
 The eccentricity was found by Gauss to be 0'24764, and consequently was 
 greater than that of Mercury, the most remarkable of all the older planets 
 in this respect. But the most striking feature of the planet's motion, if 
 
 * Phil. Trans., 1802, p. 218. 
 
240 HISTORY OF PHYSICAL ASTRONOMY. 
 
 we except the coincidence of its mean distance with that of Ceres, was the 
 inclination of its orbit to the ecliptic, which amounted to the very consider- 
 able angle of 34 39'. In consequence of the various peculiarities of the 
 two new bodies, Sir William Herschel proposed to denominate them aste- 
 roids, instead of planets, and this appellation is frequently applied to them 
 as well as to the other bodies which have since been discovered revolving 
 in the same region. 
 
 An examination of the relative magnitudes of the planetary orbits had 
 suggested the existence of an unknown planet, revolving between the orbits 
 of Mars and Jupiter. Instead of one planet, however, two were found, con- 
 forming in this respect to the requirements of analogy. Considering this 
 singular fact, in connexion with the extreme minuteness of the two bodies, 
 and the other circumstances by which they were distinguished from the 
 more ancient planets, Olbers was led to suspect that they might possibly 
 be the fragments of a larger planet, which had once been revolving in 
 the same region, and at an anterior epoch had been shattered to pieces by 
 the energy of some unknown cause. Pursuing this ingenious conception, 
 he was led to conclude that there might be many more similar fragments 
 which had not yet been discovered. He also inferred that the eccentricities 
 and inclinations of their orbits might be very different, but that the mean 
 distances would be nearly equal, and, as they all had a common origin, that 
 their orbits would have two common points of intersection, situate in op- 
 posite regions of the heavens, through which every fragment would neces- 
 sarily pass in the course of each revolution. He proposed, therefore, to 
 search carefully every month the north-western part of the constellation 
 Virgo, and the western part of the constellation of the Whale, being the two 
 opposite regions in which the orbits of the two bodies already discovered 
 were found to intersect each other. Meanwhile the discovery of a third 
 planet tended in a strong degree to confirm the truth of his hypothesis, 
 and to encourage him in his arduous undertaking. In consequence of the 
 extreme smallness of Ceres and Pallas, they are liable to be confounded 
 with the telescopic stars, which lie near their paths, and consequently 
 when any time is allowed to elapse without their being observed, it be- 
 comes a difficult matter to recognise them again. With the view of facili- 
 tating this object, M. Harding, one of the astronomers attached to the 
 Observatory of Lilienthal, had undertaken to construct a series of charts, 
 whereon were laid down the positions of all the small stars which appear 
 near the geocentric paths of the two planets. On the 2nd September, 
 1804, while engaged in exploring the heavens for this purpose, he per- 
 ceived a small star in the constellation Pisces, very near to that part 
 of the constellation of the Whale, through which Olbers had asserted that 
 the fragments of the shattered planet would be sure to pass. On the 4th 
 of September he repeated his observation, and found that the star had 
 changed its place. The observations of the succeeding evenings esta- 
 blished, beyond all doubt, that the star was in reality a new planet. The 
 elements of its orbit were calculated by Gauss, who found, as in the case 
 of the other two planets recently discovered, that it revolved between the 
 orbits of Mars and Jupiter. The mean distance was 2-670, consequently 
 it almost coincided with the mean distances of Ceres and Pallas. The 
 eccentricity amounted to 0-2543, and therefore surpassed that of any other 
 member of the planetary system. Harding conferred on the planet the 
 appellation of Juno, with a sceptre surmounted by a star for the symbol 
 of designation. Like Ceres and Pallas, it is remarkable for its extreme 
 
HISTORY OF PHYSICAL ASTRONOMY. 241 
 
 smallness. Herschel was unable to pronounce -with certainty that its 
 diameter exhibited any sensible magnitude. 
 
 Stimulated by the discovery of Juno, which so remarkably supported his 
 theory, Olbers continued, with unremitting assiduity, to explore the two 
 opposite regions of the heavens, which appeared to him to offer the 
 strongest probability of detecting any additional fragments of the shattered 
 planet. At length, after he had been engaged nearly three years in this 
 laborious pursuit, his admirable perseverance was crowned with success. 
 On the evening of the 28th of March, 1807, as he was proceeding to re- 
 examine the northern wing of the constellation Virgo, his attention was 
 drawn all at once to a brilliant star of the sixth magnitude, which ap- 
 peared a little to the west of the star marked 223 in Bode's catalogue. 
 From his intimate acquaintance with this part of the heavens, he felt per- 
 suaded that the star had not appeared in it on any former occasion, and he 
 concluded, without hesitation, that it was a planet. On the same evening 
 he established this fact beyond all doubt, having ascertained, by means of 
 two observations, that the motion of the body was retrograde. The ele- 
 ments of the orbit were determined by Gauss, who executed the calcula- 
 tions required for this purpose before more than ten hours had elapsed 
 after he obtained possession of the observations. The planet was found 
 to revolve in the same region with Ceres, Pallas, and Juno, its mean dis- 
 tance being somewhat less than that of any of those bodies. Olbers dele- 
 gated to Gauss the privilege of naming the planet. The illustrious geo- 
 meter chose the appellation of Vesta, the symbol of designation being the 
 altar on which burned the sacred fire in honour of the goddess. This 
 planet is even smaller than any of the three others previously discovered 
 in the same region. It is remarkable for the brilliancy of its light. 
 Schroeter states that he once saw it with the naked eye. 
 
 The hypothesis of Olbers respecting the origin of the asteroids was in 
 many respects so plausible that geometers were induced to direct their at- 
 tention to the subject. In the " Connaissance des Temps " for 1814, La- 
 grange has investigated the explosive force which would be necessary to 
 detach a fragment of matter from a planet revolving at a given distance 
 from the sun. Applying his results to the earth, he found that if the 
 velocity of the detached fragment exceeded that of a cannon ball in the 
 proportion of 121 to 1, the fragment would become a comet with a direct 
 motion ; but if the velocity rose in the proportion of 15(5 to 1, the motion 
 of the comet would be retrograde. If the velocity was less than in either 
 of these cases, the fragment would revolve as a planet in an elliptic orbit. 
 For any other planet besides the earth, the velocity of explosion corre- 
 sponding to the different cases would vary in the inverse ratio of the square 
 root of the mean distance. It would, therefore, manifestly be less, as the 
 planet was more distant from the sun. In the case of each of the four 
 smaller planets, the velocity of explosion, indicated by their observed 
 motion, would be less than 20 times the velocity of a cannon ball. 
 
 Although a strong probability existed that many more bodies revolved 
 between the orbits of Mars and Jupiter similar to those already discovered, 
 a considerable period elapsed before the planetary system was enriched by 
 any further accession from this source. This circumstance arose, doubtless, 
 from the immense labour attending the operation of searching for the 
 bodies, and the want of good charts containing a representation of the re- 
 lative positions of all the small stars situate in those regions where it 
 might be expected that the bodies would be discovered. In 1825, a fresh 
 
 R 
 
242 HISTORY OF PHYSICAL ASTRONOMY. 
 
 impetus was given to researches of this nature, by the resolution of the 
 Berlin Academy of Sciences to procure the construction of a series of 
 charts representing the relative positions of all the stars, down to the 
 tenth order of magnitude, in a zone of the celestial regions extending 15 on 
 each side of the equator. All the charts connected with this great under- 
 taking have not yet been executed ; but we have already had occasion to 
 illustrate their great utility, in our account of the discovery of the planet 
 Neptune. It was probably by reflecting on the advantage of such deli- 
 neations of the celestial regions that M. Hencke, an amateur astronomer 
 of Driessen, in Germany, was induced, about the year 1830, to commence 
 a careful survey of those regions wherein it was most likely that any addi- 
 tional planets would be found. During fifteen years he continued with 
 unwearied assiduity to prosecute this object, tracing the relative positions 
 of the small stars, and making himself acquainted with their various con- 
 figurations. At length his unflinching perseverance met with its due reward. 
 On the 8th of December, 1845, while engaged in examining a portion 
 of the fourth hour of right ascension, his attention was directed to a small 
 unknown star which appeared, between two others of about the same size, 
 with it. As he had acquired an intimate acquaintance with this part of 
 the heavens, he felt confident that the star had not been previously visible 
 in it. He therefore suspected that he had discovered a planet, and he 
 wrote to M. Encke, of the Observatory of Berlin, announcing the exist- 
 ence of the unknown star, and communicating to him its position on the 
 day before mentioned. On the evening of the 14th of December, the Berlin 
 astronomers directed the magnificent refractor of the observatory to the 
 part of the heavens in which M. Hencke had asserted he had seen the 
 suspected planet, and presently they discovered a star of the ninth magni- 
 tude, which was not marked in the corresponding chart of the academy, 
 executed by Professor Knorre. The subsequent observations of the same 
 evening shewed it to be a planet. It was then retrograding with a daily 
 motion in right ascension, amounting to 14' 21".2 of arc. On this occasion 
 the elements of the orbit were rapidly determined, not by Gauss indivi- 
 dually, as on previous occasions of a similar kind, but by a host of young 
 astronomers throughout Europe, who had become familiar with the methods 
 of that illustrious master. The results of their calculations shewed the 
 body to be one of the family of asteroids. The honour of naming it was 
 delegated by the discoverer to M. Encke, who conferred on it the appella- 
 tion of Astrasa. 
 
 The industry of M. Hencke was soon again rewarded by a similar 
 discovery. On the 1st of July, 1847, while engaged in examining the 
 seventeenth hour of right ascension, he perceived a small star of about 
 the ninth order of magnitude, which was not marked in the corresponding 
 map of the academy, constructed by Dr. Bremiker. On the 3rd he re- 
 peated his observation, and found that during the intermediate period its 
 right ascension had sensibly diminished, while its southern declination had 
 increased. It proved to be another of the smaller planets. Gauss, who had 
 been invited to choose its name, bestowed on it the appellation of Hebe. 
 
 The year 1847 was not destined to come to a close before it was sig- 
 nalized by two other discoveries of a similar nature. Mr. Hind, the 
 Astronomer attached to the Observatory of Mr. Bishop, Regent's Park, 
 London, had been for some time engaged in revising the Berlin maps, 
 of which the utility had now become so apparent. He had also under- 
 taken the formation of ecliptical charts for a few of the hours of right 
 
HISTORY OF PHYSICAL ASTRONOMY. 243 
 
 ascension, representing the relative positions of all the telescopic stars 
 down to the tenth magnitude. On the 13th of August, 1847, while sur- 
 veying the heavens in the prosecution of these labours, his attention was 
 drawn to a star of the 8.9th magnitude, which was not marked in Hora xix. 
 of the Berlin Maps constructed by Wolfer. He was especially surprised to 
 find that, although the same region had been examined on the 22nd of June, 
 and also on the 31st of July, no note had been made in reference to the un- 
 marked star. Even this circumstance, however, was not considered by him to 
 afford conclusive proof in favour of a proper motion of the star, since it ap- 
 peared to him not improbable that the previous invisibility of the star might 
 arise from its light being variable, having met with a great many new 
 stars of this nature in the course of his observations. The application of 
 the micrometer, however, dispelled all doubts on this point. Before half 
 an hour elapsed he was enabled to satisfy himself, by its change of position, 
 that the star had a proper motion. Subsequent observations shewed that 
 it was one of the ultra-zodiacal planets. At the suggestion of Mr. 
 Bishop, the planet was named Iris. On the 18th of October of the same 
 year, Mr. Hind discovered a star of the tenth magnitude, which was not 
 marked in Hora v. of the Berlin Maps. Micrometrical measures of its 
 position, made after the lapse of about three hours and a half from the 
 time when he first observed it, established the existence of a proper 
 motion. It proved to be another planet of the same class with Iris. 
 Sir John Herschel, having been invited to name the planet, conferred on 
 it the appellation of Flora. The discovery of the two planets Iris 
 and Flora reflects equal credit on the assiduity of Mr. Hind, and on the 
 enlightened zeal of the gentleman under whose auspices he has been 
 prosecuting his observations. It is pleasing to reflect, that in recent times 
 the British Isles have furnished a greater number of examples of the 
 devotion of private resources to the cause of astronomical science than any 
 other country. 
 
 The planet Flora formed the eighth fragment of the hypothetic planet 
 of Olbers which had been discovered since the commencement of the 
 present century. Two more have subsequently been added to this 
 number. One of them was discovered on the 25th of April, 1848, by 
 Mr. Graham, of Mr. Cooper's Observatory, Markree, Ireland. It has 
 received the name of Metis. This planet is remarkable for the near coin- 
 cidence of its mean motion with that of Iris, the difference of their 
 periodic times having been found by the most recent calculations to 
 amount only to five days. The other planet was discovered at Naples, on 
 the 16th of April, 1849, by M. De Gasparis. At the suggestion of Sig. 
 Capocci it has been called Hygeia. This makes ten fragments of the 
 shattered planet which have been already recovered. When it is con- 
 sidered that, since the discovery of six of these fragments, an equal 
 number of years has not yet come to a close, it may reasonably be pre- 
 sumed that a long period is not destined to elapse before many more 
 similar discoveries will be made. 
 
 When Jupiter is observed with a telescope of considerable power, 
 there appear several obscure belts encompassing his body. These 
 belts have been found to vary in number, magnitude, and mutual 
 distance ; but for the most part three only are observed, extending 
 in parallel directions across the centre of the disk. These pheno- 
 mena escaped the observations of Galileo, his telescopes not being 
 
244 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 sufficiently powerful to exhibit them. According to Riccioli, they were 
 first observed by Zucchi, an Italian Jesuit *. On the 17th of May, 1 630, 
 that individual perceived two belts on the disk of the planet. In 1633, 
 Fontana perceived three belts, in 1648, Grimaldi was unable to perceive 
 more than two. He was the first person wno remarked that the direction 
 of the belts is parallel to the plane of Jupiter's orbit. In addition to the 
 belts which surround the body of the planet, the rest of the surface 
 appears diversified with dusky spots of an irregular character. These 
 macula? are generally of transient duration, but some which appear in the 
 vicinity of the belts are of a more permanent nature than the others ; and 
 astronomers, by watching from time to time their position on the disk, 
 have been enabled to establish the interesting fact that the planet revolves 
 round a fixed axis. It is worthy of remark, that the illustrious Kepler, 
 previous to the invention of the telescope, had surmised that Jupiter 
 revolves on an axis, and from a consideration of the rapid motion of the 
 satellites of the planet round their primary, compared with the slower 
 motion of the moon round the earth, he inferred that the period of 
 rotation is less than twenty-four hours. This sagacious conjecture has 
 received a remarkable confirmation from the researches of subsequent 
 astronomers. Hooke appears to have been the first person who was led 
 by observation to suspect that Jupiter revolves on an axis. In the month 
 of May, 1664, he discovered a small spot on the largest of the three 
 belts. In the course of two hours, he found that it had moved from east 
 to west about half the length of the diameter of the planet f. With that 
 fickleness of purpose which characterized his conduct throughout life, he 
 appears to have abandoned all further observations of the planet, leaving 
 to others in this as in almost all similar instances, the glory of sub- 
 stantiating the interesting fact which, by his superior acuteness, he was 
 enabled first to foreshadow. It was reserved for Cassini to prove, beyond 
 all doubt, that Jupiter revolves on an axis, and to assign with considerable 
 precision the period of rotation. In the month of July, 1665, he observed 
 the planet with a telescope constructed by Campani, the object-glass of 
 which had a focal length of thirty-five French feet. He discovered a 
 great number of spots on the disk, some of which were brighter than the 
 rest of the surface, resembling in this respect the solar facula?. They 
 all appeared to have a motion on the disk from east to west, but in every 
 instance they exhibited such rapid variations of form and magnitude, that 
 no certain result could be deduced from them. At length he discovered 
 a permanent spot situated close to the northern border of the most 
 southern of the three belts, which he continued to observe for several 
 months. It appeared largest on the centre of the disk, from which it 
 gradually diminished until, before reaching the margin, it became invisible. 
 Its motion also was swifter on the centre of the disk than towards the 
 circumference. From these facts Cassini concluded that the spot adhered 
 to the surface of the planet, and that the latter consequently revolves on 
 an axis. With respect to the time in which it effected a complete 
 
 * Almag. Nov. tome i., p. 486. Dr. Moll, of Utrecht, in his interesting account of 
 the invention of the telescope, published in the first volume of the Journal of the Royal 
 Institution, ascribes the discovery of Jupiter's belts to Toricelli, the pupil of Galileo. 
 
 t Phil. Trans., No. 1. This communication, consisting of eight lines, is the second which 
 appears in the famous collection of the Transactions of the Royal Society. 
 
HISTOEY OF PHYSICAL ASTKONOMY. 245 
 
 rotation, he found that the belts generally presented a very altered 
 appearance after the lapse of five hours. It followed, therefore, that the 
 time of rotation was somewhere about ten hours. In order to arrive at 
 a result of greater precision, he watched the motion of the spot which 
 appeared near the southern belt, and he found that it returned to the 
 same position on the disk exactly in 12 d O h 4 ni . During this lapse of 
 time it had effected twenty-nine complete rotations, consequently the 
 period of a single rotation was 9 h 56 m . Cassini attempted on subsequent 
 occasions to determine the time of rotation, but the results obtained by 
 him did not exhibit so exact an accordance with each other as was 
 desirable. It appeared, from this circumstance, impossible to withhold 
 the conclusion that the spots, besides participating in the rotatory motion 
 of the planet, had also a proper motion on his surface. The accurate 
 observations of Sir William Herschel lead to a similar conclusion. That 
 illustrious astronomer carefully watched the spots of the planet in the 
 years 1778-79, but the various results at which he arrived relative to the 
 time of rotation fluctuated between 9 h 55 m 40 s and 9 h 50 m 48 s ; the 
 discordance, therefore, amounted, in some instances, to 4 m 52 s , a quantity 
 too great by far to be ascribable wholly to errors of observation *. 
 Schroeter experienced similar anomalies, in the course of his attempt to 
 determine the rotation of the planet. He concluded, from his observations, 
 that the most probable value of the period of rotation is 9 h 55 m 33 8 .6. In 
 the years 1.834-5, Mr. Airy made observations on the planet, at Cambridge, 
 for the purpose of determining the time of rotation. He perceived a dark 
 spot below the apparent lower belt, which seemed to him to be well adapted 
 for establishing this point. His observations comprehended 225 rotations, 
 commencing December 16, 1834, and terminating March 19, 1835. The 
 period of rotation was found by means of them to be 9 h 55 m 2 1 s . 3 f. Mr. 
 Airy considers that the probable error of this result does not exceed 
 four seconds. 
 
 Since Jupiter revolves round an axis, it might be expected that his 
 figure would be flattened at the poles ; and further, it might be inferred, 
 from his immense magnitude and the rapidity of his rotation, that the 
 flattening would exceed that of the terrestrial spheroid. The results of 
 observation have been found to accord with both these conclusions. In 
 1691 Cassini remarked that Jupiter appeared to him to have an oval 
 shape. The greater diameter extended east and west, and it seemed to him 
 to exceed the diameter at right angles to it by about a fifteenth part J. 
 The remark of that illustrious astronomer was soon confirmed by the 
 observations of La Hire, Eoemer, and Picard. The first determination 
 of the ellipticity of the planet by careful measurement is due to Pound, 
 whose results assign to it a mean value equal to -73-^3- . In the present day 
 M. Struve has found, by means of micrometrical measurements made with 
 Fraunhofer's great refractor, that the apparent magnitude of the equa- 
 torial diameter, as seen from the sun, at the mean distance 5.20279, is 
 equal to 38". 327, and that the apparent magnitude of the polar diameter, 
 at the same distance, is equal to 35".538 ||. These results give -y^V-rr f r 
 the ellipticity of the planet. We have seen that Laplace found from 
 theory, that if the equatorial axis of the planet be represented by unity, 
 
 * Phil. Trans., 1781. f Mem. Ast. Soc., vol. ix., p. 5. 
 
 $ Anc. Mem. Acad. des Sciences, tome ii., p. 130. 
 
 Principia, lib. iii., prop. 19. || Mem. Ast. Soc., vol. iii., p. 301. 
 
246 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 the polar axis will be equal to 0.9286. In the present case, by adopting 
 the same unit of length, the polar axis will be found to be equal to 0.9272. 
 A more striking instance of agreement between theory and observation 
 could not be adduced from the whole body of physical science. 
 
 The great distance of Jupiter prevents th*e discovery of any phenomena 
 analogous to those which have rendered the existence of an atmosphere 
 about Yenus so probable ; nor do the polar regions of the planet exhibit 
 any changes of appearance resembling those which have conducted astro- 
 nomers to a similar conclusion with respect to Mars. In the absence of 
 these favourable circumstances, the rapid rotation of the planet comes to 
 the aid of the astronomer; for it can hardly admit of doubt, that the in- 
 tense centrifugal force arising from this cause is intimately connected with 
 the formation of those remarkable bands which encompass the equatorial 
 regions of the planet, in directions parallel to each other and to the plane 
 of rotation. Although, generally, there appear only three obscure belts 
 on the disk of the planet, sometimes a greater variety is perceptible. In 
 1664, Campani perceived four dark belts and two white ones. In 1691, 
 Cassini saw eight obscure belts on the disk of the planet, situate very close 
 to each other *. Sometimes only one belt is visible, and this is always 
 the principal belt, which is situate on the northern side of the planet's 
 equator. On the other hand, the whole surface of the planet has occa- 
 sionally been seen covered with belts. On the 18th of January, 1790, Sir 
 William Herschel, having observed the planet with his 40-feet reflector, 
 perceived two very dark belts, divided by an equatorial zone of a yellowish 
 colour, and on each side of them were dark and bright belts alternating, 
 and continued almost to the poles -j-. A similar appearance was also once 
 observed by Messier J. These phenomena sometimes undergo very rapid 
 transformations, affording thereby a strong proof that they owe their 
 origin to the fluctuating movements of an elastic fluid enveloping the body 
 of the planet. On the 13th of December, 1690, Cassini perceived five belts 
 on the planet, two in the northern hemisphere, and three in the southern. 
 An hour afterwards there appeared only the two belts nearest the centre, 
 and a feeble trace of the remaining northern belt. The same astronomer 
 frequently witnessed the formation of new belts on the planet in the 
 course of one or two hours || . 
 
 The dark spots on the disk of the planet also afford unequivocal indica- 
 tions of the existence of an atmosphere, for it is impossible to reconcile their 
 variable velocities with the supposition of their being permanent spots 
 adhering to the surface of the planet. Cassini found, from his observa- 
 tions, that the spots near the equator of the planet revolved with a greater 
 velocity than those more distant from it If. This fact has been confirmed 
 by the more recent observations of Schroeter. Sir William Herschel 
 found that the velocity of a spot sometimes underwent a very sensible 
 change in the course of a few days. He supposes the spots to be large 
 congeries of clouds suspended in the atmosphere of the planet, and he 
 ascribes their movements to the prevalence of winds on its surface, which 
 blow periodically in the same direction #*. From the circumstance that 
 
 * Mem. Acad. des Sciences, tome x., p. 6. Clemens d' Astronomic, p. 406. 
 
 t Phil. Trans., 1794, p. 30. 
 
 | Delambre, Astronomie Theorique et Pratique, tome iii., p. 77. 
 
 Clemens d' Astronomie, p. 405. 
 
 II Anc. Mem. Acad. des Sciences, tome ii., p. 105. *[[ Ibid., p. 130. 
 
 ** Phil. Trans., 1781, p. 118. 
 
HTSTOEY OF PHYSICAL ASTRONOMY. 247 
 
 the spots generally assign to the planet a period of rotation less than that 
 which appears to be its most probable value, it may be inferred that the 
 wind constantly blows in the same direction as that in which the planet 
 revolves upon its axis. Herschel found that a spot, after its first appear- 
 ance, continued to complete its successive rotations in less and less inter- 
 vals of time, affording thereby a clear indication that its proper motion 
 was constantly increasing. This circumstance, he remarks, may naturally 
 be explained by supposing that a considerable time necessarily elapses 
 before the spot can acquire the full velocity of the wind by which it is im- 
 pelled. It is evident, from the amount of discordance exhibited by a com- 
 parison of the different periods of rotation derived from the movements of 
 the spots, that the currents in the atmosphere of the planet must possess 
 very considerable velocities. Sir William Herschel found, from his observa- 
 tions, that the spots, on one occasion, must have been transported through 
 60 in twenty-two rotations of the planet. This would indicate that the 
 wind on the surface of the planet was travelling at the rate of somewhat 
 more than 200 miles in an hour, a velocity which, however, does not ex- 
 ceed that of occasional winds on the surface of the earth. The nearest 
 approach to the velocity of the wind will of course be indicated by the 
 smallest period of rotation. In 1692, Cassini observed a spot near the 
 equator of the planet, which performed a complete rotation in 9 h 50 m *. 
 Assuming (which is certain to be true) that the period of the planet's real 
 rotation lies between 9 h 55 m and 9 h 56 m f, this would indicate that the cur- 
 rent in the atmosphere of the planet was travelling at the rate of about 
 250 miles in an hour. In general the spots complete their rotations in 
 periods varying between 9 h 50 m and 9 h 56 m , whence it may be concluded 
 that the currents in the atmosphere do not possess a velocity exceeding 
 the hundredth part of the rotatory motion of the planet. 
 
 Although the spots on Jupiter, by their transient existence and variable 
 motion, generally indicate that they are of atmospheric origin, there are 
 some of a more permanent character, whose frequent re-appearance in the 
 same position can only be explained by supposing them to adhere to the 
 surface of the planet. The most remarkable of these is the spot situate 
 close to the northern margin of the southern belt, by watching the appa- 
 rent motion of which Cassini originally succeeded in determining the 
 period of the planet's rotation. From its first discovery in 1665 down to 
 1713, it vanished and re-appeared no less than nine times. When the 
 southern belt disappeared, the spot disappeared also, but the belt was fre- 
 quently perceived without the spot. On no occasion did the spot continue 
 
 * Mem. Acad. des Sciences, tome x., p. 8. Clemens d'Astronomie, p. 406. 
 
 + It appears, from the researches of Cassini, Schroeter, and Airy, that the period of rota- 
 tion is included between 9 h 56'" and 9 h 55 m . Independently of the results arrived at by the 
 two last-mentioned astronomers, it is evident, from observations of the permanent spot 
 originally discovered by Cassini, on the occasions of its successive re- appearances between 
 1665 and 1713, that the period of rotation is somewhat less than 9 h 56 m . In 1672, Cassini, 
 by means of it, made the period of rotation 9 h 55' 11 50 s . In 1708, Maraldi deduced from 
 it a period equal to 9 h 56'" 48 s , and from observations of it in 1713 he made the period 
 equal to 9 h 56 n . On the last-mentioned occasion he compared Cassini's original observa- 
 tions of the spot in 1665 with his own observations in 1713. Assuming the period of 
 rotation to be 9 h 56 m , he found that in 1713 the actual position of the spot was about. 36 
 in advance of the computed position. This would afford a valuable means of determining 
 the period of rotation, if we could be assured of the precise number of complete rotations 
 embraced between the observations of 1665 and 1713; but this is an uncertain datum, 
 on account of the magnitude of the probable error of the element to be determined. 
 
248 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 visible so long as three years*. Its disappearance is manifestly dependent 
 on the same cause which determines the invisibility of the belt. Cassini 
 supposed the belts to indicate currents in the seas of the planets, ana- 
 logous to those which occur in different regions of the earth f ; but this 
 hypothesis affords no explanation of the aingy colour which the belts 
 usually exhibit. A more probable hypothesis of their real nature has 
 been suggested by Sir William Herschel, who considers the light of 
 the bright regions of the planet to arise from dense accumulations of 
 vapours suspended in its atmosphere, while the dark belts, on the other 
 hand, indicate the opaque surface of the planet, which possesses an inferior 
 power of reflecting the solar light, and admits of being seen throagh those 
 regions of the atmosphere that are comparatively free of clouds J. This 
 hypothesis affords a natural explanation of the simultaneous disappear- 
 ance of the southern belt and the spot adjacent to it, for the vapours 
 which close in upon each side of the belt and cover the surface of the 
 planet must necessarily submerge the spot at the same time, and thereby 
 render it invisible also. 
 
 In a former part of this work, we have given a detailed account of the 
 researches of astronomers on the motions of Jupiter's satellites. It is 
 remarkable that, down to the middle of the seventeenth century, there 
 were persons who refused to believe that these bodies actually circulated 
 round the planet. In 1665 Cassini announced his discovery of two 
 phenomena which furnished incontestable proofs that the satellites con- 
 formed in this respect to the analogy offered by the motion of the ter- 
 restrial satellite. By means of the powerful glasses of Campani, he 
 succeeded in perceiving the satellites when, in the course of their orbitual 
 motion, they were interposed between the planet and the earth. On such 
 occasions, they exhibited the appearance of small spots on the disk of the 
 planet ; but he shewed that, from their motion near the margin being 
 the same as on the centre, and from their apparent magnitudes being 
 constant during the time they were visible, they could not be attached to 
 the surface of the planet. He also discovered the shadows which the 
 satellites projected upon the body of the planet while in the act of passing 
 between it and the sun. In order to convince the most sceptical of the 
 real nature of these appearances, he announced, beforehand, the days and 
 the hours in the months of August and September of the year above-men- 
 tioned, when the bodies of the satellites and also their dark shadows would 
 be seen upon the disk of the planet . These predictions having been 
 verified by observation, no doubt could henceforth exist in any mind that 
 the satellites revolve round the planet in the same manner as the moon 
 revolves round the earth. 
 
 In 1707, Maraldi I. discovered that the fourth satellite, on the occasion 
 of passing between the planet and the earth, sometimes appeared brighter 
 than the planet, while at other times it resembled a black spot upon the 
 disk. He further discovered that in the latter case the magnitude of 
 the satellite was frequently less than that of its shadow, which was at the 
 same time visible on the disk, although, according to the laws of optics, it 
 
 * For a curious account of the circumstances attending the successive re -appearances of 
 this spot see Anc. Mem. Acad. des Sciences,tome ii., p. 105, tome x., pp. 1, 513; Mem. 
 Acad. des Sciences, 1708, 1713; also Cassini's Elemens d' Astronomic, p. 405, et seq. 
 
 f Anc. Mem. Acad. des Sciences, tome ii., p. 106. 
 
 j Phil. Trans., 1793, p. 218. 
 
 Journal des Savans, February 21, 1666; see also Phil. Trans., No. 10, p. 171. 
 
HISTORY OF PHYSICAL ASTRONOMY. 249 
 
 ought to have been greater. A similar appearance was witnessed by him 
 in 1713. The conclusion he drew from it was, that there are dark tracts 
 of great extent on the surface of the satellite, which are incapable of re- 
 flecting the light of the sun. It may be remarked that the question with re- 
 spect to the real nature of these spots admitted of two distinct explanations. 
 If the satellite was supposed to perform a complete rotation on an axis, in 
 the precise time which it took to revolve round the planet, it would inva- 
 riably turn the same hemisphere to the observer on the occasion of each 
 transit; and if the spots adhered to the surface, it ought always to exhibit 
 the same appearance on the disk of the planet. The variation of bright- 
 ness, on this hypothesis, indicated that the spots were not of a permanent 
 nature, but were merely transient phenomena, arising probably from 
 physical changes occurring on the surface of the satellite. On the other 
 hand, if the motions of rotation and revolution were not equal, the satel- 
 lite might turn a different hemisphere to the observer on the occasion of 
 each transit, and the variations in its appearance might be accounted for by 
 supposing that there existed permanent tracts of great extent on its surface 
 which reflected only a small portion of the solar light which fell upon 
 them. Sir William Herschel has shewn, from his observations, that the 
 periods of rotation and revolution of the satellite are equal, whence it 
 follows that the spots cannot be permanently attached to its surface. They 
 must, therefore, arise from changes occasionally occurring either on the 
 surface of the satellite or in its atmosphere. The other satellites have 
 been found to exhibit appearances similar to those of the fourth*, and as, 
 in the case of each of them also, the periods of rotation and revolution are 
 equal, a similar conclusion is equally applicable to them. The interesting 
 fact, that each of the four satellites performs a complete rotation on its axis 
 in a period equal to that of its revolution round the planet, was deduced by 
 Sir William Herschel, from a comparison of the relative quantities of light 
 emitted by the satellites in different parts of their orbits. He discovered 
 that all the satellites were subject to great variations of brightness in the 
 course of their revolutions round the planet, but, having carefully watched 
 the appearance of each satellite throughout a great number of revolutions, 
 he invariably found that when it arrived in the same position of its orbit it 
 exhibited the same degree of brightness!. The obvious conclusion was, that 
 the rotatory motion of each satellite was equal to its orbitual motion round 
 the planet. This curious fact had been already established in the case of 
 the moon and the fifth satellite of Saturn, and there is good reason to sup- 
 pose that it forms an essential characteristic of the movements of all 
 the secondary bodies of the planetary system. 
 
 The determination of the magnitudes of the satellites has formed an 
 interesting object of research to astronomers, but it is attended with 
 great difficulty, in consequence of the extreme minuteness of the bodies, 
 
 * Maraldi found that the third satellite, on the occasions of its transit across the disk of 
 the planet, exhibited variations similar to those which he remarked in the fourth satellite 
 (Mem. Acad. des Sciences, 1707, p. 193). According to that astronomer, Cassini had 
 previously noticed similar variations in all the satellites. The observations of Cassini 
 and Maraldi were confirmed soon afterwards by those of Pound (Phil. Trans., 1719, p. 
 902). Bianchini was the first person who discovered that the satellites are subject to great 
 variations of brightness in other parts of their orbits, as well as in conjunction. He 
 remarked that the fourth satellite sometimes became so small as to be almost invisible 
 (Mem. Acad. des Sciences, 1714, p. 32). 
 
 t Phil. Trans., 1797, Part II., p. 332, et seq. 
 
250 HISTORY OF PHYSICAL ASTRONOMY. 
 
 and their immense distances from the earth. It is only when viewed with 
 the exquisite telescopes of the present day that they have finally exhibited 
 real disks of appreciable magnitude, and consequently it was impossible 
 on any previous occasion to ascertain their ^apparent diameters by direct 
 measurement. In 1734, Maraldi II. attempted to determine their mag- 
 nitudes by noting the times which they occupied in entering upon the disk 
 of the planet. In this manner, he found that the linear diameter of the 
 third satellite amounted to T '-g of that of Jupiter, and the diameters of the 
 other three satellites to about -^ of the same unit*. Now Jupiter, at his 
 mean distance from the sun, appears under an angle equal to 36". 7. 
 Hence, according to Maraldi, the apparent diameters of the satellites, 
 when viewed at the same distance, would be 2" for the third satellite, and 
 1".8 for the three others. These results considerably exceed the true 
 magnitudes of the angles as determined by micrometrical measurement. 
 In 1738, Whiston gave a statement of the magnitudes of the satellites, 
 but he does not mention upon what grounds it is founded. He estimated 
 the third satellite to be equal in size to the Earth or Venus ; the first to 
 be equal to Mars ; the second to be somewhat larger than Mercury ; and 
 the fourth only a little larger than the Moonf. Bailly attempted to de- 
 termine the magnitudes of the first three satellites by noting the times 
 which they occupied in entering into the shadow of the planet, or in 
 emerging from itj. This method is not susceptible of great precision, and 
 consequently the results obtained by that astronomer were not regarded as 
 worthy of any confidence. Lalimde subsequently determined the magni- 
 tude of the fourth satellite by the same method . Sir William Herschel 
 determined the magnitude of the second satellite by noting the time which 
 it took to enter upon the disk of the planet. Having found, from obser- 
 vations of the transit which took place on the 28th of July, 1794, that an 
 interval of four minutes elapsed between the instant of the satellite's ex- 
 terior contact with the margin of the planet, and that of its complete pro- 
 jection on the disk, he hence determined by calculation that at the mean 
 distance of Jupiter from the sun it would subtend an angle equal to // .87||. 
 He did not attempt to determine the magnitudes of the other satellites by 
 the same method of strict calculation, but, from a nice estimation of the rela- 
 tive magnitudes of the four bodies, he concluded that the third satellite 
 is considerably larger than any of the others ; that the first is nearly of 
 the size of the fourth ; and that the second is a little smaller than either 
 of the two latter, or the smallest of all. Schroeter and Harding deter- 
 mined the magnitudes of the four satellites by means of observations of 
 their transits over the disk of the planet. According to the results at 
 which they arrived, the apparent diameters of the four satellites, when viewed 
 from the earth, at the mean distance of the planet, are severally 1".068, 
 O r/ .870, 1".543, and 1".074, commencing with the first satellite, and pro- 
 ceeding in the order of their distances from the planet IF. The result for 
 the second satellite agrees very nearly with that deduced by Sir William 
 Herschel. 
 
 In 1826, M. Struve determined the magnitudes of the satellites by mi- 
 crometrical measurements of their disks with the great Dorpat refractor. 
 The following are the apparent diameters which they would severally ex- 
 
 * Mem. Acad. des Sciences, 1734. 
 
 f " The Longitude discovered by means of Jupiter's Satellites," London, 1738, p. 7. 
 
 J Mem. Acad. des Sciences, 1771. Ibid., 1774. 
 
 || Phil. Trans., 1797, Part II., p. 350. ff Mem. Ast. Soc., vol. iii., p. 301. 
 
HISTORY OF PHYSICAL ASTRONOMY. 251 
 
 hibit, supposing them to be viewed at the mean distance of the planet 
 from the earth * : 
 
 Apparent diameter of 1st satellite . . . ]".015 
 
 2nd ... .91] 
 
 3rd ... 1 .488 
 
 4th ... 1.273 
 
 These results present a very satisfactory accordance with those which 
 Schroeterand Harding obtained by a less direct method. They also harmo- 
 nize admirably with the estimations which Sir William Herschel formed of 
 the relative magnitudes of the four bodies. The coincidence in the last-raen- 
 tioned instance is especially valuable, inasmuch as it shews the degree of 
 confidence that may be placed in the apperqus of Herschel, with respect to 
 many delicate points in the science of astronomy, which rest mainly on the 
 sagacity of that great observer. From the above measures of M. Struve 
 it is easy to infer that the linear diameters of the four satellites, commenc- 
 ing with the first and proceeding outwards, are severally 2429 miles, 2180 
 miles, 3561 miles, and 3046 miles. It appears, therefore, that the third 
 satellite exceeds Mercury in magnitude by a small quantity, and that the 
 second is about the size of the Moon. The first and fourth satellites of 
 course occupy, in respect of magnitude, an intermediate position between 
 these two bodies. 
 
 Saturn, when viewed with the telescope, exhibits obscure bands, dis- 
 posed in parallel directions across the centre of his disk, analagous to 
 those which encompass the body of Jupiter, though not so well defined. 
 These bands were first observed by Dominique Cassini, but they appeared 
 so faint and uniform that he was unable to draw any conclusions from 
 them. In the year 1715, when the ring had totally disappeared, J. 
 Cassini examined the planet with a telescope of 114 feet focal length, 
 and perceived two broad bands exactly parallel to the plane of the ring, 
 and extending over a considerable portion of the disk. He searched in 
 vain for a spot which, by observations of its position at different intervals, 
 might indicate a rotatory motion ; but, from the circumstance of all the 
 satellites, except the most distant, revolving in the plane of the ring, he 
 shrewdly suspected that the planet revolved about an axis perpendicular 
 to that plane f. It was reserved for Sir William Herschel to establish 
 this fact by observation, and also to assign the period of rotation. He 
 commenced his examination of the planet in the year 1775. By means 
 of his powerful telescopes, he discovered that the belts were in a state of 
 constant change, and from their arrangement, which was generally parallel 
 to the ringj, he inferred the probability of the planet revolving round an 
 axis perpendicular to the plane of the ring. His suspicion of a rotatory 
 motion was confirmed upon finding that a spot which he discovered on the 
 19th of June, 1780, occupied different positions of the disk on each of the 
 two following evenings . On the llth of November, 1793, having exa- 
 
 * Mem. Ast. Soc., vol. iii., p. 301. 
 
 f Mem. Acad. des Sciences, 1715. 
 
 In the course of his earlier observations of the planet, Sir William Herschel occa- 
 sionally discovered belts which deviated sensibly in direction from the plane of the ring. 
 Cassini had in some instances observed belts on Jupiter's disk disposed in a similar manner. 
 (Anc. Mem. Acad. des Sciences, torn, x., p. 683. ) In the latter case they were generally the 
 precursors of extensive changes in the arrangement and appearance of the equatorial 
 belts. It is very reasonable to suppose that these anomalous belts are the indications of 
 tempestuous movements in the atmospheres of both planets. 
 
 Phil. Trans., 1790, Part I., p. 10. 
 
252 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 mined the planet with his seven-feet reflector, he perceived a bright 
 and uniform belt situated a little to the south of the shadow of the ring. 
 Close to it was a darker belt, in which were two narrow divisions, so that 
 the planet appeared to be encompassed by a quintuple belt, composed of 
 three dark and two bright belts. By watching the variations in the appear- 
 ance of this belt he discovered that the planet revolves round an axis per- 
 pendicular to the plane of the ring in the short period of I0 h 16 m O s .44#. 
 The observations by means of which he arrived at this interesting conclusion 
 extended from December 4, 1793, to January 16, 1794, and included 100 
 rotations of the planet. It is worthy of remark, that Huyghens inferred, 
 from the shortness of the period of the satellite discovered by him, that the 
 planet had a rapid rotation on an axis. We have already mentioned that 
 Kepler had previously hazarded a similar conjecture with respect to Jupiter. 
 
 The discovery that Saturn is compressed at the poles, is also due to 
 Sir William Herschel. In 1782, he determined the lengths of the equa- 
 torial and polar axes of the planet, by micrometrical measurement with his 
 20-feet reflector. He found the apparent equatorial diameter to be 
 22".81, and the apparent polar diameter to be 20". 61, whence it followed 
 that the two diameters were to each other nearly as 11 to 10f. The 
 precise ellipticity indicated by these measures was equal to 0.09645. So 
 far the results of observation presented a satisfactory accordance with 
 those derived from mechanical principles, and Saturn appeared to conform 
 in this respect to the analogy of the other planets. In 1805, however, 
 the same astronomer announced the existence of an unexpected irregu- 
 larity in the figure of the planet. The equatorial diameter appeared to 
 exceed the polar, agreeably to his previous observations, but he now found 
 that the longest diameter occupied an intermediate position between them, 
 so that the planet, in consequence, exhibited the form of a quadrangle 
 with the four corners rounded off. He determined by actual measure- 
 ment that the three diameters were as 36, 35, 32, and that the longest 
 diameter was inclined to the plane of the equator at an angle of 43 20 *. 
 The observations of the following year convinced him that he had made 
 the equatorial diameter too short, and he finally adopted 36, 35.41, and 
 32, as the numbers expressing the relative lengths of the three diameters. 
 By this revisal the anomaly in the figure of the planet was to some extent 
 diminished. It is worthy of remark, also, that the ellipticity assigned by 
 the new values of the equatorial and polar diameters coincides with that 
 deducible from the measures of 1789. This circumstance is the more 
 satisfactory, as the original determination of the ellipticity by the illus- 
 trious astronomer has been found to accord exactly with that derived from 
 the most recent micrometrical measures of the axes of the planet . 
 
 The irregularity in the figure of Saturn, to which allusion has just been 
 made, was regarded by astronomers as an inexplicable anomaly in the 
 planetary system. Herschel ascribed it to the attraction of the ring. It 
 
 * Phil. Trans., 1794, p. 62. f Ibid., 1790, Part L, p. 17. J Ibid., 1805, p. 280. 
 
 In every work which the author has seen containing any allusion to the observations 
 of Herschel on the figure of Saturn, it is stated that the diametral values 36, 35, and 32 
 were the final results at which he arrived. The material revisal mentioned in the text 
 appears to have been totally lost sight of, although nothing can be more distinct than the 
 language of the illustrious astronomer on this point. The following are his express 
 l**words on the occasion : " The equatorial diameter of my last year's figure is, however, a 
 very little too short ; it should have been to the polar diameter as 35.41 to 32, which is 
 the proportion that was ascertained in 1 789, from which I have hitherto found no reason to 
 depart." (PM. Trans., 1806, Part II., p. 461.) 
 
HISTORY OF PHYSICAL ASTRONOMY. 
 
 253 
 
 was found, however, upon investigation, that the ring was not capable of 
 producing an effect similar to that indicated by the observations of Herschel. 
 The subject of the figure of the planet, therefore, excited a lively interest, 
 more especially on account of the high authority upon which the alleged 
 irregularity rested. In 1 832, Bessel resolved to ascertain the figure of the 
 planet by direct measurement. He had been led to suspect that the ob- 
 servations of Herschel were illusive in the first place, because they were 
 at variance with the results of theory, and, in the second place, because 
 they were made under unfavourable circumstances, the contour of the 
 disk having been broken by the ring, which, in 1805, was very open. 
 By careful raicrometrical measurement, he found that the apparent mag- 
 nitude of the equatorial diameter of the planet at the mean distance from 
 the earth, was 17". 05 3, and that the apparent magnitude of the polar 
 diameter was 15".381*. These results gave 0.098047 for the ellipticity, 
 upon the supposition that the figure of the planet was an oblate spheroid. 
 We have seen that Herschel made it 0.09645. The two results do 
 not therefore differ by so much as -J-Q of either. In order to ascer- 
 tain the real figure of the planet, Bessel in the first instance assumed 
 that it was an oblate spheroid whose ellipticity was equal to that indicated 
 by the ratio of the two axes, and having calculated, upon this supposition, 
 the lengths of several diameters inclined at different angles to the plane 
 of the equator, he compared them with the corresponding results ob- 
 tained by direct measurement. A complete accordance was found to 
 subsist between the calculated and measured diameters of the planet, con- 
 sequently no doubt could henceforth exist that the figure of the latter is 
 in reality that of an oblate spheroid. The following are the results at 
 which Bessel arrived : 
 
 Distance from 
 the Equator. 
 
 Measured Diameter. 
 
 Calculated Diameter. 
 
 J 0' 
 
 17". 139 
 
 17". 053 
 
 22 30 
 
 16 .679 
 
 16 .777 
 
 45 
 
 16 .242 
 
 16 .160 
 
 67 30 
 
 15 .605 
 
 15 .607 
 
 90 
 
 15 .332 
 
 15 .394 
 
 It is impossible to contemplate these numbers without a feeling of 
 admiration of the theory which is capable of responding so faithfully to 
 the requirements of nature, and of the exquisite skill displayed by the 
 illustrious astronomer who executed measures so singularly delicate as 
 those above given with a success apparently so complete. 
 
 Sir William Herschel was induced to suspect from his observations 
 that Saturn is surrounded by an atmosphere of considerable extent. 
 Having assiduously observed the belts of the planet during the period in- 
 cluded between the years 1775 and 1780, he found them to be subject 
 to incessant variations, analogous to those which characterize the fluctuat- 
 ing movements of an atmospheric fluid. The phenomena observed by 
 him during the occultations of the satellites were also favourable to the 
 same hypothesis. He found in each instance, that the satellite, after 
 coming up to the planet, continued to hang on its limb for some time before 
 
 * See an account of Bessel's researches on this subject, translated from the original 
 German, in the Connaissance des Temps for 1838. 
 
254 HISTOKY OF PHYSICAL ASTKONOMY. 
 
 it actually vanished. The seventh satellite was observed by him on one 
 occasion to linger in contact with the disk for the space of 20 minutes. 
 This would give 2" for the amount of the horizontal refraction at the 
 surface of the planet*. It would be har.dly safe to draw any positive 
 conclusions from so minute a result. Herschel did not fail to remark that 
 the irradiation of the planet was not taken into account. He, how- 
 ever, discovered other phenomena which afforded more palpable indi- 
 cations of the existence of a Saturnian atmosphere. He perceived an 
 occasional brilliancy in the surface of the planet around both the poles, 
 analogous to that observed in the polar regions of Mars, and he found, 
 as in the case of that planet, that the region around each pole dimi- 
 nished or increased in brightness, according as it was more or less ex- 
 posed to the influence of the solar rays. In 1793, when the south pole 
 had been long turned towards the sun, he perceived that the whole surface 
 around it was of a pale whitish colour, far inferior in brightness to the 
 ring, and not even equal in this respect to the white belts encompassing 
 the equator of the planet. On the other hand, the surface around the 
 north pole, which had been less exposed to the solar rays, was of a bright 
 white colour. In 1806, the north pole having been for some time illumined 
 by the sun, the regions around it had lost much of their lustre, but those 
 around the south pole appeared to him to regain their former bright 
 colour. The latter were now decidedly brighter than the equatorial regions 
 of the planet, as was evident from the appearances they severally exhi- 
 bited when viewed with the telescope. With a magnifying power of 527, 
 the south polar regions continued to appear very white, while, on the con- 
 trary, the regions near the equator assumed a yellowish tinge f. Herschel 
 suggests to future astronomers the prosecution of attentive observations 
 of these interesting phenomena, with the view of establishing a definitive 
 connexion between them and the vicissitudes of the Saturnian year. It 
 is manifest, as in the case of Mars, that such appearances necessarily 
 imply the existence of an atmosphere, whether they be supposed to arise 
 from variations in the temperature of the planet, or from the fluctuating 
 movements of vapours suspended above its surface. 
 
 Among the many objects which excited the admiration of Galileo when 
 he first turned the telescope towards the heavens, there was none which 
 filled his mind with such astonishment as the appearance presented by 
 Saturn. Writing on the 13th of November, 1610, to Julian de Medicis, 
 the Tuscan Ambassador at the Imperial Court, he announced to him 
 having discovered, to his great admiration, that Saturn was not a single 
 planet, but was composed of three bodies, which almost touched each 
 other, and constantly maintained the same relative position. He re- 
 marked that the three bodies were arranged in the same straight line ; 
 that the middle body was the largest, and that the two others were situated 
 respectively on the east and west sides of it. He added that, with tele- 
 scopes of inferior power, the planet did not appear triple, but exhibited an 
 oblong form, somewhat like the shape of an olive J. The illustrious 
 philosopher did not long continue his observations of the planet before 
 he discovered that the lateral bodies did not constantly retain the 
 same apparent magnitudes. In a letter to Castelli, dated the 30th of 
 December, 1610, he mentioned that, since the mouth of July, the two 
 
 * Phil. Trans., 1790, Part I., p. 15. f Ibid., 1806, Part II., p. 464, et seq. 
 $ Opere di Galileo, Edit. Pad., torn, ii., p. 41. 
 
HISTOKY OF PHYSICAL ASTRONOMY. 255 
 
 bodies had been gradually diminishing, although they appeared to be im- 
 moveable, both with respect to each other and to the central body*. They 
 continued to grow less and less during the course of the two following 
 years, at the close of which they finally vanished altogether, leaving 
 the planet quite round, like Jupiter. Galileo announced this mysterious 
 disappearance of the phenomenon in his third letter to Welser, dated 
 December 4, 1612. The astonishment which he felt on the occasion was 
 mingled with a feeling of alarm lest the Aristotelians, taking advantage 
 of his inability to adduce an adequate explanation of the cause of disap- 
 pearance, should attempt to make his observations a subject of derision, 
 by alleging them to have been destitute of any foundation in nature. 
 " What," he remarks, " is to be said concerning so strange a metamor- 
 phosis ? Are the two lesser stars consumed after the manner of the solar 
 spots? Have they vanished and suddenly fled? Has Saturn perhaps 
 devoured his own children ? Or were the appearances indeed illusion or 
 fraud, with which the glasses have so long deceived me, as well as many 
 others, to whom I have shewn them ? Now, perhaps, is the time come 
 to revive the well nigh withered hopes of those who, guided by more pro- 
 found contemplations, have discovered the fallacy of the new observations, 
 and demonstrated the utter impossibility of their existence. I do not 
 know what to say in a case so surprising, so unlocked for, and so novel. 
 The shortness of the time, the unexpected nature of the event, the weak- 
 ness of my understanding, and the fear of being mistaken, have greatly 
 confounded me."f 
 
 During the course of nearly half a century which elapsed after the in- 
 vention of the telescope, the singular vicissitudes which the appendage of 
 Saturn underwent, continued to form an inexplicable enigma to astrono- 
 mers. The only real progress made towards its explanation consisted 
 in arriving at more accurate views of the appearances exhibited by it 
 in the telescope and in ascertaining the time which it occupied in 
 passing through the cycle of its phases. Instruments superior to those 
 of Galileo shewed that the objects composing the appendage were not 
 round like the other celestial bodies, but rather resembled two luminous 
 crescents, attached by their cusps to the planet, and forming, as it were, 
 two handles to it. The conformation of these handles, or anscs, was 
 found to be subject to a slow alteration, which caused the appearance of 
 the planet to be constantly changing. When the ansa3 first became visible, 
 after the planet had passed through its round form, they appeared like two 
 arms extending on each side of the planet, but they continued gradually to 
 open out during the following seven or eight years, at the close of which they 
 again began to contract, and after an equal lapse of time, vanished entirely, 
 when the planet again assumed its round form. The appendage therefore 
 completed the cycle of its various appearances in about fifteen years, or half 
 the period of the planet's revolution round the sun. It was reserved for 
 Huyghens to discover the true cause of these singular changes. He first com- 
 municated to the world his explanation of them, under the form of an enigma, 
 in a small tract, entitled, " De Saturni Luna Observatio Nova," published 
 in 1656 ; but he subsequently gave an explicit announcement of the real 
 nature of the appendage of the planet, with a detailed exposition of its 
 theory, in a book written expressly on the subject which appeared in the 
 year 1659 J. In this work, before proceeding to explain his own theory, he 
 
 * Opere di Galileo, Edit. Pad., torn, ii., p. 46. t Ibid., p. 152. 
 
 \ Systema Saturnium, 4to. Hagse, 1659. 
 
56 HISTORY OF PHYSICAL ASTRONOMY. 
 
 considers the various hypotheses which had been advanced by astronomers 
 with a view to account for the appearances of the planet, and he points out 
 the insuperable difficulties by which each of them is accompanied. 
 Roberval, it must be acknowledged, approached more nearly to the true 
 explanation of the phenomenon than any'of his contemporaries. He 
 supposed that vapours capable of reflecting the rays of the sun escaped 
 from the torrid regions of Saturn, and, after attaining a certain elevation, 
 remained in a state of suspension around his equator. When they filled 
 the whole space included between the surface of the planet and the 
 region of their highest elevation, they caused the planet to assume an 
 elliptic form. When they ascended in less abundance, a wide space was 
 left between them and the planet, and they only reflected the solar light 
 in the parts that were densest, which, relatively to an observer at the 
 earth, were the parts most remote from the centre of the planet. In this 
 case the appendage would resemble two ansae with obscure spaces between 
 them. When no vapours ascended, the planet would appear quite round *. 
 Huyghens objected to this hypothesis that' it made the exhalation of 
 vapours to depend upon the position of the planet in its orbit (since the 
 round phase occurred when the planet was in two opposite points of the 
 ecliptic, and the opening of the ansa3 was greatest when it was about 90 
 distant from either), while at the same time it assigned no cause why the 
 vapours should cease in some parts of the orbit, and in other parts should 
 ascend in great abundance. With respect to the alleged elliptic form of 
 the planet, he had already shewn that it did not exist, being in fact an 
 illusive appearance which the planet assumed when it was observed with 
 telescopes incapable of exhibiting the dark spaces between the ansae. It 
 was therefore a superfluous task to assign its cause. 
 
 Huyghens introduces his own explanation of the phenomenon by re- 
 marking that all the primary bodies of the planetary system, beyond 
 doubt, revolve about fixed axes. He further considers it to be established 
 by observation, that the rotatory motion of each primary is more rapid 
 than the orbitual motion of any of the smaller bodies circulating round it, 
 and he hence concludes that Saturn and his appendage revolve with a 
 rapid velocity round an axis. In 1655, while he was engaged in ponder- 
 ing upon this subject, the planet exhibited an appearance which strongly 
 
 * Delambre appears to have committed a slight, inadvertence in his account of 
 Roberval's theory as explained by Huyghens. The following are the terms in which he 
 notices it: " Roberval avait imagine que Saturne etait rond comme les autres planetes, 
 mais que de son equateur il s'echappait des vapeurs, qui demeuraient suspendues a certain 
 distance et formaient autour de la planete un cercle qui, vu par nous obliquement, devait 
 se montrer comme une ellipse." Hist. Ast. Mod., tome ii., p. 564. It will be seen, 
 however, by reference to the original, that Huyghens makes no allusion whatever to the 
 principle of perspective, that a circle exhibits the form of an ellipse when viewed 
 obliquely with respect to the visual ray. The figure which Roberval ascribes to 
 the planet is a real not an apparent ellipse, being occasioned by the absence of vapours in 
 the polar regions of the planet, in the same manner as the flattening at the poles of 
 Jupiter causes the disk of that planet to assume the form of an ellipse. But although 
 the French astronomer does not appear to have recognized clearly that the opening out and 
 closing of the ansse might be explained by the variable obliquity of the vaporous zone 
 with respect to the visual ray, he very sagaciously conjectured, by the aid of considerations 
 identical with those which conducted Huyghens to a similar conclusion, that, the appendage 
 must encompass the planet equally in every direction. This is candidly acknowledged by 
 Huyghens himself (See Systema Saturnium, p. 42, Opera Varia, vol. ii., p. 562). 
 There was a good deal of truth in Roberval's views, but it is clear that he wanted the 
 vigour of mind necessary to correct his theory by instituting a close comparison between 
 its results and the recorded observations of astronomers. 
 
HISTORY OF PHYSICAL ASTRONOMY. . 257 
 
 attracted his attention. The appendage resembled two arms extending 
 in the same right line on opposite sides of the planet, as if an axis 
 had passed through its centre. As the appearance of this axis was con- 
 stantly the same, when observed from day to day, he concluded that the 
 appendage must encompass the planet similarly in every direction so as 
 to assume the form of a ring; for it was manifest that the rapid 
 rotation of the planet and its appendage was incompatible with any other 
 supposition. On the other hand, if this be once admitted, the appendage 
 obviously would exhibit the same appearance whatever might be the 
 velocity of rotation. When he proceeded to compare the various ap- 
 pearances of which such a ring is susceptible with the recorded observa- 
 tions of the phases of the planet, he soon found that they could not be 
 reconciled without supposing the plane of the ring to be inclined to the 
 ecliptic at a constant angle, similarly to the plane of the terrestrial 
 equator. The existence of the ansae indicated also to him that the ring 
 did not adhere to the surface of the planet, but was everywhere separated 
 from it by an interval of equal breadth. Assuming these particulars 
 with respect to the ring, he found that all the appearances of the planet 
 might be satisfactorily accounted for by means of such an appendage. 
 The logogriphe containing his explanation of the phenomenon was pub- 
 lished by him in the following form : 
 
 aaaaaaa ccccc d eeeee g h iiiiiii 1111 mm nnnnnnnnn oooo pp q rr s ttttt 
 
 uuuuu 
 
 He now restored the letters to their original places, when they stood 
 thus : 
 annulo cingitur, tenui piano, nusquam cohaerente, ad eclipticam inclinato ; 
 
 or, in other words, " the planet is surrounded by a slender flat ring, 
 everywhere distinct from its surface, and inclined to the ecliptic." Nothing 
 can be more convincing or beautiful than the explanation which this 
 theory affords of the various phenomena presented by the planet. When 
 the position of the planet in its orbit is such that the plane of the ring 
 passes through the sun, the edge only of the ring is exposed to the solar rays, 
 and the extent of the illuminated surface being very small, it is incapable 
 of producing a sensible impression on the visual organ. In this position, 
 then, the ring is invisible, and the planet presents a round appearance, like 
 the sun or full moon. The ring also disappears when its plane passes 
 through the earth, for, although one of its sides may then be illuminated by 
 the sun, it is only the edge which is turned towards the observer. Besides 
 these two causes of disappearance, which are of a transient nature, and render 
 the ring invisible only for a few days at most, there is a third cause which 
 generally continues in operation during a longer period of time, and pro- 
 duces a more lasting effect. When the planet is so situated that the plane 
 of the ring passes between the earth and the sun, the unenlightened side 
 of the ring is then turned towards the earth, and consequently during the 
 whole time that the planet is in this position (which frequently extends 
 to several months) the ring will be invisible. The same theory affords an 
 equally satisfactory account of the different phases assumed by the ap- 
 pendage of the planet during the period of its visibility. It is manifest 
 that when the plane of the ring passes through the sun, and when conse- 
 quently the ring ceases to be visible, the planet, if viewed from the sun, 
 would appear in the node of the ring. When the planet revolves from 
 this position, the sun commences to ascend above the plane of the 
 
 s 
 
258 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 ring, and the latter in consequence becomes visible in the form of a very 
 elongated ellipse, gradually opening out in breadth. The ellipse con- 
 tinues to approach towards a circular form, until the planet has reached a 
 distance of 90 from the node of the ring, when the elevation of the sun 
 above the plane of the ring has attained its maximum. The ring hence- 
 forth begins to contract, and the same succession of appearances, in a re- 
 verse order, will obviously ensue, as the planet revolves towards the oppo- 
 site node, where the ring again will cease to be visible. The ring will, 
 therefore, complete the cycle of its phases in a period equal to half a revolu- 
 tion of the planet round the sun, or in about fifteen years. The appearances 
 will not be materially different whether the ring be viewed from the earth 
 or the sun, except during the time that the planet is in the vicinity of 
 either of the nodes of the ring. At such a juncture the combined motions 
 of the earth and the planet may cause the plane of the ring to pass more 
 than once through the earth, and the ring may, in consequence, disappear and 
 re-appear twice, before its plane has entirely swept over the terrestrial orbit. 
 
 Huyghens predicted that the planet would appear round in the month 
 of July or August, 1671. Cassini, in fact, found that the ring totally dis- 
 appeared towards the end of May, in that year. The coincidence was suf- 
 ficiently satisfactory, considering that the position of the node of the ring, 
 upon which the times of the round phase of the planet depends, could not 
 possibly have been determined with a great degree of accuracy. 
 
 The position of the ring is usually determined by the inclination of 
 its plane to the ecliptic and the longitude of its ascending node. If 
 the plane of the ring was perpendicular to the ecliptic, the ring would 
 appear like a luminous line at the node, and would thence gradually 
 open out, until it finally assumed the form of a circle at a distance of 
 90 from the node. Now it appears, from observation, that the minor 
 axis of the ellipse, which the form of the ring usually exhibits, does 
 not become equal to the major axis, even when the opening of the ring is 
 greatest. The obvious conclusion, therefore, is that the plane of the ring 
 is not perpendicular to the ecliptic, but is inclined to it at a sensible 
 angle. It is easy to shew, from the principles of perspective, that when 
 the planet is at a distance of 90 from the node of the ring, the major 
 axis of the ellipse is to the minor axis as radius to the sine of the angle 
 contained between the plane of the ring and the visual ray. Hence by 
 taking into account the elevation of Saturn above the plane of the ecliptic, 
 upon which, to a certain extent, the direction of the visual ray depends, it 
 is easy to determine the inclination of the plane of the ring to the ecliptic. 
 Huyghens originally supposed that the plane of the ring was parallel to 
 the equator, and hence inferred that its inclination to the plane of the 
 ecliptic was 23 30'. In 1668, however, Picard and himself found, by 
 measurements made with a telescope of 21 feet focal length, that the in- 
 clination was 31*. This was a nearer approximation to the true value 
 than any other which astronomers had arrived at previous to the com- 
 mencement of the present century. The longitude of the node of the 
 ring is determined by the position of the planet relative to the sun or the 
 earth, during the disappearance or reappearance of the ring; for it is mani- 
 fest that when the sun or the earth passes through the plane of the ring, 
 the heliocentric longitude of the planet in the one case, and the geocentric 
 longitude in the other, are equal to the longitude of the node of the ring. 
 
 * Phil. Trans., 1669, p. 900. 
 
HISTORY OF PHYSICAL ASTRONOMY. 259 
 
 Huyghens first fixed the ascending node of the ring in 153 of longitude, 
 and afterwards in 170 30'. The elder Maraldi was the first astronomer 
 who gave a complete theory of the method for determining the elements 
 of the ring. From observations of the passage of 1715, he found that the 
 inclination of the plane of the ring was 31 20', and that the longitude of 
 the ascending node was 166 17'*. Lalande adopted Maraldi's value of 
 the inclination, and by means of observations of the passage of 1774, he 
 determined the longitude of the ascending node to be 167 5'f. This 
 result he found to differ from Maraldi's only by 1', taking into account 
 the effect of precession which he estimated at 49' for the interval of 59 
 years which had elapsed between 1715 and 1774. He therefore inferred 
 that the position of the node of the ring is invariable. The researches of 
 subsequent astronomers have shewn, however, that this was an erroneous 
 conclusion. 
 
 In 1811, when the ring was very open, Bessel measured the axes of 
 the ellipse, formed by the ansa3, and hence determined the inclination of 
 the ring to be 28 34'. 1. This evaluation differed considerably from 
 Maraldi's, which had been hitherto adopted by astronomers. It received 
 a strong confirmation, however, from the subsequent measures of M. Struve. 
 In 1826, when the planet was at a distance of 90 from the node of the 
 ring, and when, in consequence, the opening of the ring was again at its 
 maximum, that eminent astronomer executed a series of micrometrical 
 measures of the axes of the ring with Fraunhofer's great refractor, and 
 by means of them he determined the inclination of the ring to be 28 5'.9. 
 He also estimated that the probable error of this result did not exceed 6'. 4 J. 
 
 The value assigned by Bessel to the inclination of the ring was deduced 
 from measures executed with a micrometer attached to a 16-inch tele- 
 scope, by Dollond. At a subsequent period, having obtained possession of 
 a splendid heliometer, he resolved to employ it in determining the ele- 
 ments of the ring with greater precision. In pursuance of this design he 
 executed a great number of micrometrical measures of the apparent posi- 
 tion of the ring during the period embraced between the years 1830 and 
 1834. He also introduced into his investigation all the recorded disap- 
 pearances and re-appearances of the ring, from the passage of the planet 
 through the node of the ring in 1701, down to the passage of 1832. By 
 a comprehensive and masterly treatment of the subject, he finally arrived 
 at the conclusion that the longitude of the ascending node of the ring in 
 the year 1800 was 166 53' 8".9, and that the inclination of its plane to 
 the ecliptic was 28 10' 44 // .7. He also found that the node of the ring 
 retreats upon the plane of the ecliptic at the rate of 46 // .462 annually . 
 The result which he obtained for the inclination of the ring agrees with 
 that deduced by M. Struve within the limits of error assigned by the latter 
 astronomer. It may, therefore, be regarded as the most accurate deter- 
 mination of that element which has yet been arrived at. 
 
 In 1675 Cassini, having observed Saturn after his emergence from the 
 rays of the sun, discovered that the ring was divided into two parts by a 
 black band, so that it appeared to be composed of two concentric rings ||. 
 This fact was confirmed by subsequent observations of the planet in differ- 
 ferent parts of its orbit, from which it appeared that the band was constautly 
 
 * Mem. Acad. des Sciences, 1715. f Ibid., 1774. 
 
 J Mem. Ast. Soc., vol. ii., p. 583. Connaissance des Temps, 1838. 
 
 |[ Anc. Mem. Acad. des Sciences, tome x., p. 583. 
 
260 HISTORY OF PHYSICAL ASTRONOMY. 
 
 visible, and that its position on the northern side of the ring corre- 
 sponded exactly to its position on the southern side *. Sir Willliam 
 Herschel, without being aware of the reasons which induced Cassini and 
 Maraldi to suppose an actual division of the ring into two smaller con- 
 centric rings, undertook a most searching examination of the appear- 
 ance of the dark band, with the view of deciding this delicate point. 
 Various facts were detected by this great observer which afforded un- 
 equivocal indications of the duplicity of the ring. He found that the 
 band was of the same colour as the space between the ring and the 
 planet, and was equally well denned on both its borders. It also 
 constantly exhibited the same breadth, colour, and sharpness of outline 
 throughout the whole period of ten years, during which he observed the 
 northern side of the ring. The passage of the planet through the 
 descending node of the ring in 1789 having rendered the southern side 
 of the ring henceforth visible, he found that the band existed on it, as 
 well as on the northern side, and exhibited similar characteristics. He 
 also perceived, agreeably to the observations of preceding astronomers, 
 that the divisions on both sides of the ring corresponded exactly to each 
 other. It was impossible, therefore, to avoid the conclusion, that the dark 
 band indicated a material division of the ring, and that in fact, the planet 
 was surrounded by two concentric rings, separated from each other by a 
 space, through which the open heavens were visible f. The observa- 
 tions of succeeding astronomers have afforded a complete confirmation of 
 the justness of this conclusion. Some persons have even asserted that 
 they have perceived a great number of concentric dark lines on the ring. 
 This indication of the ring being divided into numerous parts was observed 
 by Short and some of his contemporaries. In more recent times a similar 
 phenomenon has been witnessed by De Vico, Encke, Lassel, and other 
 observers. On the other hand Sir William Herschel and M. Struve, not- 
 withstanding the high optical qualities of their telescopes have not dis- 
 covered any traces of the existence of such a subdivision of the ring. 
 
 The determination of the dimensions of the ring has formed an interest- 
 ing object of research to astronomers. Huyghens concluded, from his 
 own observations, that the diameter of the ring was to that of the planet 
 as 9 to 4 J. In 1719 Pound found, by means of a telescope of 123 feet 
 focal length, that the two diameters were as 7 to 3 . In more recent 
 times the micrometrical measurements of Sir William Herschel and M. 
 Struve have led to an accurate knowledge of the magnitude of this stupen- 
 dous zone. The following are the dimensions of the exterior and inte- 
 rior rings, as assigned by M. Struve : 
 
 1. Exterior diameter of the exterior ring . . . 40".095 
 
 2. Inner diameter of the exterior ring .... 35".289 
 
 3. Exterior diameter of the interior ring . . . 34".475 
 
 4. Interior diameter of the interior ring . . . 2 6". 6 68 
 
 5. Equatorial diameter of Saturn 17".991 
 
 6. Breadth of the exterior ring ".403 
 
 7. Breadth of the division between the rings . . . 0".408 
 
 8. Breadth of the interior ring . 3".903 
 
 9. Distance of the interior ring from the ball . . 4". 339 
 10. Equatorial radius of Saturn ..... 8". 995 
 
 * Mem. Acad. des Sciences, 1715, p. 13. f Phil. Trans., 1792. 
 
 J Systeraa Saturnium, p. 78. Phil. Trans., 1719. 
 
HISTORY OF PHYSICAL ASTRONOMY. 261 
 
 These measures are adapted to the mean distance of the planet from the 
 earth. We may form an estimate of the linear dimensions of the ring 
 from the fact that an object situated at the same distance, in order to sub- 
 tend an angle of only 1", would require to have an absolute diameter of 
 4387 miles. It is easy hence to infer that the exterior ring will have an 
 absolute diameter of 175,928 miles! The dimensions of the other parts 
 will of course bear a similar relation to their apparent magnitudes. 
 
 Various circumstances concur to prove that the thickness of the ring must 
 be very inconsiderable. When its plane passes through the earth or the 
 sun (on either of which occasions its edge only is capable of reflecting the 
 solar rays to the observer) it has been generally found to disappear, even 
 when the most powerful telescopes have been directed towards it. When 
 it is about to vanish, or when it begins to re-appear, after being for some 
 time invisible, it resembles an excessively-narrow luminous line, before and 
 behind which the satellites are observed to pass in the course of their 
 revolution round the primary. Being sometimes apparently situated on 
 the ring, these bodies were employed by Sir William Herschel as standards 
 of comparison whereby to estimate its thickness. On such occasions the 
 satellite was invariably found to project on the opposite sides of the ring, 
 whence it followed that the ring could not be so thick as the diameter of 
 the satellite. On the 29th of August, 1789, (when only three days had 
 elapsed since the plane of the ring passed through the earth,) having per- 
 ceived the third satellite upon the ring, he concluded that the thickness of 
 the ring was not equal to one-third of the diameter of the satellite *. He 
 estimated the diameter of the latter to be less than \" ; consequently the 
 thickness of the ring did not subtend an angle so great as 0".3. If we 
 suppose the planet to have been at its mean distance from the sun, this 
 would indicate a thickness of 1462 miles. Even the seventh satellite, 
 notwithstanding its extreme minuteness, was observed by Herschel to 
 project upon opposite sides of the ring. When the edge of the ring was 
 almost completely turned towards him, the satellite, to use his own beau- 
 tiful comparison, appeared like a bead moving upon a thread. He was of 
 opinion that the diameter of the satellite did not exceed a thousand miles. 
 It was probable, therefore, that the ring was not more than a few hundred 
 miles in thickness. The illustrious astronomer did not fail on this occa- 
 sion to remark, that if the ring was surrounded by an atmosphere, the 
 refraction which it would exercise upon the rays of light proceeding from 
 the satellite to the observer, would cause an apparent projection of the 
 satellite similar to that indicated by observation, even although its dia- 
 meter considerably fell short of the thickness of the ring. It appears, 
 however, from other considerations, that the projection of the. satellite is 
 in reality due to the extreme thinness of the ring. Schroeter, from, obser- 
 vations of the breadth of the shadow which the ring threw upon the planet, 
 when it was about to disappear, concluded that its apparent thickness at 
 the mean distance of the planet amounted only to O'MSSf. This indi- 
 cates a real thicknes of rather more than 500 miles. Sir John Herschel 
 estimates the thickness not to exceed the half of this quantity. He is of 
 opinion that if it even subtended an angle of 0".05 the ring would have 
 been visible when the planet was observed by him, with a 20-feet re- 
 flector, on the 29th of April, 1833 J. 
 
 Phil. Trans., 1790, Pt. I., p. 6. + Mem. Ast. Soc., vol. ii., p. 517. 
 
 f Outlines of Astronomy, p. 315. Only three days had then elapsed since the plane 
 of the ring passed through the earth. 
 
262 HISTORY OF PHYSICAL ASTRONOMY. 
 
 While engaged in observing the planet when the edge of the ring was 
 turned towards him, Sir William Herschel perceived several lucid protu- 
 berances upon the ring, the positions of which could not be reconciled with 
 the actual motion of any of the satellites. His suspicion that they were 
 phenomena of a distinct character was strengthened by the fact that they 
 never came off the ring and showed themselves as satellites. The ques- 
 tion occurred to him whether they might not be the indications of an 
 eighth satellite revolving between the seventh satellite and the planet. 
 By comparing together the different positions of the brightest of the spots, 
 he found that they might be accounted for, by supposing the spot to 
 revolve round the planet in a period equal to 10 h 32 m 15 S .4. Having 
 then computed, by means of Kepler's third law, the distance at which a 
 satellite would require to be placed, in order that it might accomplish a 
 complete revolution round the planet in the same time, he found the re- 
 sult to be 17".227. This distance would bring the satellite precisely 
 upon the plane of the ring. It followed, therefore, either that the parti- 
 cles of the ring possessed sufficient mobility to allow the satellite to 
 revolve through them, or that the variable positions of the lucid protube- 
 rances arose from a revolution of the ring itself around the planet. That 
 the ring was not fluid, but, on the contrary, was composed of a substance 
 as solid as the materials of the planet itself, appeared to him evident, from 
 the sharp definition of its borders, the brilliancy of the light reflected by 
 it, and the darkness of the shadow which it threw upon the body of the 
 planet. It was impossible, therefore, to withhold the conclusion that the 
 ring is endued with a rotatory motion round the planet, which it completes 
 in the short period of 10 h 32 m 15 s . 4*. This result presents a complete 
 accordance with that which Laplace deduced about the same time, from 
 an investigation of the mechanical conditions which are necessary to assure 
 the stability of the ring. It must be acknowledged, however, that the 
 observations of Schroeter and Harding, on the occasion of the disappear- 
 ances of the ring in ] 803, are in direct contradiction to a rotatory motion 
 of the ring about the planet. These astronomers observed several lucid 
 points upon the ring which continued immovable during a period of 
 eight hours. When watched also from night to night, the points were al- 
 ways found to retain the same position f. A similar objection to the 
 rotation of the ring has been indicated by the observations of Prof. Bond, 
 of Cambridge, U.S., on the occasion of the disappearance of the ring in 
 1848 }. Another fact has been established by the observations of astrono- 
 mers which, although essentially explicable by the principles of mechani- 
 cal science, is accompanied by a phenomenon totally at variance with the 
 supposition of a rotatory motion of the ring. In 1826 M. Struve found 
 that the ring is not concentrically situate with respect to the planet. It 
 appeared from micrometrical measurements, that the distance* of the outer 
 edge of the ring from the body of the planet was equal to ll".288 on the 
 east side of the planet, and only to 11".073 on the west side. The ring 
 was, therefore, nearer to the west side of the planet than it was to the east 
 side by 0".215 . That the ring should revolve eccentrically with respect 
 to the planet, is a condition which accords admirably with the principles 
 upon which its conservation depends ; but the fact of its invariably de- 
 viating towards the same side of the planet cannot be reconciled with the 
 
 * Phil. Trans., 1790, Pt. II., p. 480. f Connaissance des Temps, 1808. 
 
 J Month. Proc. Ast. Soc., December, 1849. 
 Mem. Ast. Soc., vol. iii., p. 301. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 263 
 
 supposition of a revolution of any kind whatever. Lastly, there is a 
 circumstance attending the disappearances and re-appearances of the ans 
 which is unfavourable to the existence of a rotatory motion of the ring. 
 It has heen frequently found on such occasions that one ansa alone was 
 visible, and in by far the greater number of cases this was the western 
 ansa. It is difficult to reconcile this fact with the rapid rotation assigned 
 to the ring by Herschel, since, upon the supposition of such a movement, 
 a complete alternation ought constantly to take place in the appearance of 
 the ans* at the close of every five hours. There are, indeed, some obser- 
 vations of this kind, such as those of Cassini and Maraldi to be noticed 
 presently, which positively favour the hypothesis of a rotatory motion of 
 the ring. The interesting observations of the Rev. W. R Dawes, on the 
 occasion of the passage of the plane of the ring across the terrestrial orbit, 
 in 1848-9, also lead unequivocally to the same conclusion. The rotation 
 of the ring can hardly, therefore, admit of any doubt, although there are 
 some difficulties attending the subject which remain to be explained. 
 
 Sir William Herschel first remarked that the light of the ring is brighter 
 than that of the planet. With a high magnifying power the light of the 
 planet assumed a yellowish tinge, while that of the ring still continued 
 white *. By means of the superior brilliancy of the ring he was enabled 
 to trace it in those parts where it crossed the luminous disk of the 
 planet f. It has been already mentioned that Cassini found the interior 
 ring to be brighter than the exterior ring. He compared the difference 
 between the two rings in brightness to that which subsists between 
 polished and unpolished silver J. The observations of succeeding astro- 
 nomers lead to a similar conclusion. Sir William Herschel discovered 
 that the interior ring gradually diminishes in brightness towards the inner 
 edge, the light of which, according to him, does not exceed in intensity 
 that of the dark equatorial belts of the planet . A similar remark has 
 been made by M. Struve, who considers that the inner edge of the interior 
 ring is less sharply defined and less regular in its construction than the 
 outer edge ||. In all calculations relative to the disappearance and re- 
 appearance of the ring, it has been assumed by astronomers that the 
 appendage of the planet is regular in its construction, and that it is 
 bounded by parallel planes. Observations of the ansa?, however, when 
 they are about to disappear, or when they first begin to re-appear after a 
 period of invisibility, afford grounds for suspecting that the actual con- 
 formation of the ring is irreconcilable with such an hypothesis. In 
 1671, when the ring was about to disappear, the ansa? were observed by 
 Cassini to contract considerably. This circumstance was ascribed by him 
 to the inferior brightness of the exterior ring which caused it to disappear, 
 while the interior ring was yet visible If. He remarked also that, on the 
 same occasion, one of the ansa? was partially visible when no trace of the 
 other could be discerned, but he found that the visible remnant was not al- 
 ways on the same side of the planet **. A similar phenomenon was wit- 
 nessed by Maraldi. On the 9th of October, 1714, (six days previous to 
 the passage of the plane of the ring through the earth,) that astronomer 
 perceived that the ansa?. were reduced to half their ordinary dimensions. 
 The eastern ansa appeared also to be somewhat broader than the western. 
 
 * Phil. Trans., 1790. Part I., p. 5. f Ibid., 1805. Part II., p. 273. 
 
 J Mem. Acad. des Sciences, tome x., p. 583. Phil. Trans., 1794, p. 53. 
 
 |j Mem. Ast. Soc., v.ol. ii., p. 517. ^| Mem. Acad. des Sciences, tome x., p. 583. 
 ** Mem. Acad. des Sciences, 1705, p. 18. 
 
264 HISTORY OF PHYSICAL ASTRONOMY. 
 
 On the 12th of the same month, the planet was attended by the western 
 ansa only. Maraldi remarked that these anomalous appearances might 
 be accounted for by supposing that the ring is not wholly situated in one 
 plane, or that its surface is very irregular, and that the western ansa, 
 which from either of these causes appeared fainter than the eastern on the 
 9th of October, was subsequently transported by the rotation of the ring, so 
 as to occupy the eastern side of the planet on the 12th of the same month *. 
 The observations of succeeding astronomers generally agree in indi- 
 cating a similar inequality in the construction of the ring. On the 29th 
 of November, 1743, Heinsius perceived that the eastern ansa was shorter 
 than the western f. On the 6th of October, 1773, the planet was observed 
 at Cadiz with the western ansa only J. On the llth of January, 1774, 
 Messier perceived that the eastern ansa was longer than the western . 
 On the 4th of January, 1803, Harding witnessed the re-appearance of the 
 western ansa, while the eastern was yet totally invisible ||. On the 16th 
 of June, 1803, Schroeter, with great difficulty, observed the western ansa; 
 but the eastern had some time previously disappeared H. It would seem, 
 from these observations, that the western ansa is in general more easily 
 discernible than the eastern. This fact, although at variance with the 
 alleged rotation of the ring, does not affect the question under considera- 
 tion, namely, the irregularity of the surface of the ring, which is unequivo- 
 cally indicated by all the observations. There is another circumstance which 
 abundantly serves to prove that the bounding surfaces of the ring are not 
 composed of parallel planes. If such were the case, it is manifest that the 
 instants of the disappearance and re-appearance of the ring would be con- 
 stantly regulated by the motion of the planet, and a determinate position 
 of the plane of the ring. Bessel, however, found, by a strict analytical 
 investigation, that the recorded observations of these phenomena were 
 incompatible with the results derived from the supposition of such a 
 plane **. It is impossible, therefore, to admit that the bounding sides 
 of the ring are composed of parallel planes. 
 
 Sir William Herschel was induced to suspect, from his observations, 
 that the ring is encompassed by an atmosphere. In 1807 he perceived 
 that the two poles of the planet did not exhibit the same shape. There 
 appeared a protuberance about the regions of the south pole which he had 
 not witnessed on any previous occasion, while, on the other hand, the north 
 polar regions retained their usual shape. By careful observation he satis- 
 fied himself that this appearance did not arise from any irregularity in the 
 surface of the planet. It was, therefore, evidently an optical phenomenon, 
 due to some cause which did not similarly affect the regions about both poles. 
 In reference to this point, he remarked that the ring was differently situ- 
 situated with respect to the opposite sides of the equator of Saturn, 
 being before the planet in the southern hemisphere, and behind it in 
 the northern. The rays of light proceeding from the south polar re- 
 gions to the earth passed pretty close to the ring, while those issuing 
 from the regions in the vicinity of the north pole traversed an open- 
 space remote from any external influence. Hence, if the ring be sup- 
 posed to be surrounded by an atmosphere, it would refract the rays 
 proceeding from the regions about the south pole, and would thereby 
 
 * Mem. Acad. des Sciences, 1715, p. 12. 
 
 f Lalande, Astronomic, Art. 3373. \ Ibid. 
 
 Ibid. II Connaissance des Temps, 1808, p. 429 
 
 ^ Connaissance des Temps, 1838. ** Ibid. 
 
HISTORY OF PHYSICAL ASTRONOMY. 265 
 
 occasion an apparent distortion of the figure of the planet similar to the 
 observed protuberance *. Herschel was more especially inclined to adopt 
 this explanation of the phenomenon, as he had previously been led to sus- 
 pect the existence of an atmosphere about the ring, from the fact of the 
 satellites projecting on each side of it during the period when it resembled 
 a luminous line. The recent observations of astronomers go to support 
 the same conclusion. It has been already mentioned that the ring is 
 found to disappear when its plane passes either through the earth or the 
 sun. To the greater number of observers it has also continued invisible, 
 as might naturally be expected, during the whole time that the unen- 
 lightened side is turned towards the earth. It is a remarkable fact, how- 
 ever, that Sir William Herschel succeeded in perceiving the ring when its 
 plane was interposed between the earth and the sun, and when conse- 
 quently the bright side was turned away from himf. It was also re- 
 peatedly seen under similar circumstances, by the Rev. W. R. Dawes in 
 this country, and by Mr. Bond in America, during the passage of its plane 
 across the terrestrial orbit in 1 848-9 J. Now, since it would seem that 
 the edge of the ring is invisible when it is turned directly to the observer, 
 it ought, a fortiori, to be invisible in every other position. Hence it fol- 
 lows, that the visibility of the ring, during the time that its plane was in- 
 terposed between the earth and the sun, did not arise from the light re- 
 flected by its edge. The inference is therefore unavoidable, that the ring 
 was visible by means of the surface which was turned away from the sun, for 
 the opposite surface upon which the rays of that luminary directly fell, was 
 then turned away from the earth. The observations of Mr. Dawes are 
 especially conclusive with respect to this point. When the plane of the 
 ring was interposed between the earth and the sun (on \vhich occasion the 
 bright side of the ring was turned away from the earth), the ring was still 
 faintly visible ; but as the earth continued to approach the plane, the ring 
 was seen with greater difficulty, and when it was actually situated in the plane, 
 the ring was invisible, even when the planet was viewed with Mr. Lassel's 
 20-feet reflector . Now, if the visibility of the ring in the above instance 
 was due to the light reflected by its edge, a succession of appearances the 
 very reverse of that indicated by observation ought to have taken place ; 
 for as the earth approached the plane of the ring, the edge of the ring was 
 turned more directly towards the observer, and therefore it ought to have 
 been seen with increased facility. That the visibility of the ring, when its 
 plane was interposed between the earth and the sun, was occasioned by 
 
 * Phil. Trans., 1808, p. 162. + Phil. Trans., 1790, Part I., p. 8. 
 
 f When Saturn is proceeding from the ascending to the descending node of the ring, 
 the north side of the ring is that which is enlightened by the sun ; and on the contrary, 
 when he is proceeding from the descending to the ascending node, it is the south side 
 which is enlightened by that luminary. The planet having passed through the descend- 
 ing node of the ring on September 3, 1848, it follows that the north side of the ring, from 
 being hitherto the illuminated side, became, henceforward, the dark side. Now, on the 
 22nd of April, 1848, the earth met the plane of the ring advancing in the opposite direc- 
 tion, and passed from the north to the south side of the ring. On the 12th of September, 
 1848, it overtook the same plane, and passed from the south to the north side of the ring. 
 On the 18th of January, 1849, having again reversed its motion, it met the plane of the 
 ring a second time, and passed from the north to the south side of the ring. It is easy to 
 infer from these particulars, that throughout the whole period embraced between April 22, 
 1848, and January 18, 1849, the unenlightened side of the ring was turned towards the 
 earth, with the exception of the few days that elapsed between the 3rd and 12th of Sep- 
 tember, 1849. 
 
 Month. Proc. Ast. Soc., January, 1850. 
 
266 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 light reflected from its obscure surface, and not from its edge, was still 
 further proved by the observations of Mr. Dawes during the interval when 
 the earth was receding from the plane of the ring; for, in this case, the ring 
 became more and more distinctly visible, according as the elevation of the 
 earth above the plane continued to increase/ 
 
 With respect to the physical explanation of the interesting appearance 
 above alluded to, Sir William Herschel suggested that it might arise from 
 the light reflected by the planet upon the dark surface of the ring. Mr. 
 Dawes, however, considers that the quantity of light derived from this 
 source would not suffice to render the ring so distinctly visible as the 
 observations indicated, especially in those parts that were less exposed 
 .to the illuminated hemisphere of the planet. He proposes, therefore, to 
 account for the phenomenon, by supposing the ring to be surrounded by 
 an atmosphere which occasions a twilight sufficiently strong to render the 
 ring visible, even after the sun has descended below the surface turned 
 towards the earth. He remarks, in support of this explanation, that 
 during the whole period embraced by his observations, the depression of 
 the sun below the obscure surface of the ring, did not exceed 1. It is 
 manifest, therefore, that a twilight of considerable brightness might arise, 
 even without the necessity of assigning a high degree of density to the 
 atmosphere of the ring. This explanation was still further strengthened 
 by the colour of the obscure surface of the ring, which appeared to Mr. 
 Dawes to have a ruddy tinge, somewhat resembling the appearance of the 
 western sky after sunset*. The observations of Mr. Dawes, and the 
 interesting conclusion which he so reasonably draws from them, go to 
 support the assertion of Sir William Herschel relative to the protuberance 
 about the south pole of the planet, observed by him in the year 1807. 
 The establishment of the elliptical figure of the planet by Bessel, and still 
 more recently by the Rev. Mr. Main, of the Royal Observatory of Green- 
 wich, cannot of course invalidate the existence of that apparent anomaly; 
 since the observations of both these astronomers were made at a time when 
 the atmosphere of the ring could exercise no optical influence on the figure 
 of the planet f. 
 
 * Granting that the visibility of the ring, when its plane is interposed between the earth 
 and the sun, is due to the twilight occasioned by a circumambient atmosphere, it is mani- 
 fest that the effect so produced will be greatest when the sun is just depressed below the 
 obscure surface of the ring, and the earth at the same time has attained its maximum ele- 
 vation above that surface. From the position assigned to the ascending node of the ring 
 by Bessel, it is easy to infer that this condition will be satisfied, if the passage of the 
 planet, through either node of the ring should take place on the 7th of June, or the 9th of 
 December. A juncture of this kind occurred in the year 1832, the planet having passed 
 through the ascending node of the ring about the beginning of December. On the other 
 hand, the twilight will be viewed to least advantage if the planet should pass through the 
 ascending node of the ring on the 7th of March, or through the descending node on the 
 9th of September. It appears, therefore, that the recent passage of the planet which took 
 place on the 3rd of September, 1848, was unfavourable for witnessing this interesting 
 phenomenon. In fact, at the very time when the sun was about to ascend to the level of 
 the obscure surface of the ring, the earth had almost overtaken the plane of the ring, so 
 that the twilight, when strongest was viewed when the edge only of the ring was turned 
 towards the observer. If the planet should pass through the ascending node of the ring 
 on the 9th of September, or through the descending node on the 7th of iMarch, there will 
 be only one brief disappearance of the ring ; but as the planet on either of such occasions 
 will be in conjunction with the sun, it will be invisible, as well as its appendage, so that, 
 in point of fact, there will be no disappearance at all, in the usual sense of the term. 
 
 f It is interesting to know that the result at which Bessel arrived, relative to the ellip- 
 tical figure of Saturn, has been completely verified by means of similar observations 
 
HISTORY OF PHYSICAL ASTRONOMY. 267 
 
 The singular appendage with which Saturn is furnished has naturally 
 given rise to speculations respecting its physical origin, and various hypo- 
 theses, characterized by more or less ingenuity, have been formed in con- 
 nexion with this subject. Maupertius supposed the materials of the ring 
 to be composed of the tail of a comet, which happening to revolve in the 
 vicinity of the planet was arrested by its attractive force, and compelled to 
 circulate as a satellite round it. According to De Mairain, Saturn was 
 formerly a body of much greater dimensions than it now is, the ring being 
 the residue of the equator of the ancient planet. Buffon supposed, that 
 while the planet was yet in a liquid state the equatorial parts were driven 
 to a considerable distance from its centre by the centrifugal force arising 
 from its rotation, and that having subsequently become solid by cooling, 
 they encompassed the planet in the form of a ring. Du Sejour adopted 
 this view of the origin of the ring, but he further maintained that a con- 
 tinuance of the rotatory movement was necessary to assure its conser- 
 vation. He remarked that while the ring was yet in a liquid state, its 
 constituent particles being exposed to the incessant action of the planet 
 had a constant tendency to precipitate themselves upon its surface. It 
 was necessary, therefore, to suppose that the ring was endued with a 
 rotatory movement, sufficiently great to generate a centrifugal force 
 capable of counterbalancing the gravity of the planet. He asserted 
 further that, as the attraction of the planet on the more distant parts 
 of the ring was less, while the centrifugal force, cceteris paribus, was 
 greater, it was indispensable towards maintaining the equilibrium of the 
 two forces, that the parts of the ring, at different distances from the 
 centre, should revolve with different velocities. He, therefore, supposed 
 that the ring was formed of several concentric solid zones, endued with 
 different rotatory movements round the planet, the velocity of rotation 
 being less according as the zone was more remote from the centre of the 
 planet. This very plausible hypothesis has been borne out to a certain 
 extent by the researches of subsequent astronomers, as we have already 
 had occasion to mention. 
 
 On the 25th of March, 1655, when Huyghens was engaged in examin- 
 ing Saturn with a telescope of 12 feet focal length*, which he had con- 
 structed with his own hands, his attention was drawn to a small star which 
 appeared to the west of the planet, at a distance from it of about 3'. He 
 remarked that the star was disposed in the same right line with the ring, 
 which then resembled a luminous line extending on opposite sides of the 
 planet. He also perceived a small star to the east of the planet, which 
 was nearly at the same distance from it with the other, but declined 
 sensibly from the plane of the ring. His impression was that the latter 
 was merely a fixed star; but from its peculiar position with respect to the 
 ring, he suspected that the star on the west side of the planet, was a 
 satellite. On the following evening, having again directed his telescope 
 to the planet, he found that the star on the east side was removed to 
 twice its previous distance, while the one on the west side still retained 
 the same position, relative to the planet which it occupied, when he first 
 saw it. It was now obvious that the former was a fixed star which the 
 planet had left farther behind in the course of its retrograde motion, while 
 the latter was a satellite which accompanied its primary round the sun. 
 
 which Mr. Main made on the occasion of the last disappearance of the ring. See Month. 
 Proc. Ast. Soc., vol. ix. 
 * Cosraotheoros, p. 99. 
 
S68 HISTORY OF PHYSICAL ASTRONOMY. 
 
 He found by a rough estimation, that the satellite completed its synodic 
 revolution in 16 days, and that its greatest apparent distance from the 
 planet was rather less than 3'. A few years afterwards he fixed the period 
 of revolution more accurately at 15 d 23 h 13 m *. A curious remark was 
 made by Huyghens in connexion with this discovery, which strikingly il- 
 lustrates the tenacity with which the ancient notions respecting the per- 
 fectibility of the heavens, and the harmony of numbers, continued to cling 
 to minds even of the very first order. He asserted that as the planets 
 and satellites were now equal in number, and as the aggregate of both 
 amounted to twelve, which was universally admitted to be a perfect 
 number, it was reasonable to suppose that the planetary system was com- 
 plete, and upon this ground he ventured to predict that no more satellites 
 would in future be discovered f. Twelve years only elapsed when the dis- 
 covery of two additional satellites of Saturn served to expose the fallacy of 
 a prediction so unworthy of the genius of its author. Since the epoch of 
 that discovery, the satellites have constantly kept in advance of the 
 planets, in respect of number, until the present day, when the ultra-zodiacal 
 planets have at length come to the rescue of the more ancient members of 
 the system, and a relation of equality again subsists between the planets 
 and satellites, with this material difference, however, that the number of 
 each, instead of being only six, now amounts to eighteen. 
 
 The passage of Saturn through the node of his ring in 1671 was an 
 event of peculiar interest to astronomers, inasmuch as it formed the cri- 
 terion which was to establish the truth or fallacy of Huyghens' theory of 
 the appendage being composed of a ring ; and the appearance of the planet 
 on that occasion was, in consequence, an object of more than ordinary at- 
 tention. On the 25th of October, 1671, while Cassini was engaged in 
 observing Saturn with a telescope of 17 feet focal length, he perceived a 
 small star to the west of it, in a position which very nearly coincided with 
 the plane of the ring. Having repeated his observations on the following 
 evenings, he soon discovered a sensible change in the position of the star 
 with respect to the other stars around it. He continued to observe it on 
 twelve successive nights, at the close of which he established various pro- 
 perties of its motion which convinced him that it was a satellite. He 
 found that its greatest elongation from the planet exceeded three times 
 that of the satellite discovered by Huyghens. He estimated the time of 
 its synodic revolution to be equal in round numbers to 80 days J . Having on 
 a subsequent occasion instituted a comparison between observations which 
 embraced 150 revolutions of the satellite, he determined the period to be 
 79 d 22 h 4 m . The satellite thus discovered by Cassini arrived at its 
 greatest elongation about the end of October, 1671. He continued to 
 observe it till the month of December, when his labours were interrupted 
 by unfavourable weather, and when he afterwards resumed them the 
 satellite could not be found. Having procured a new telescope of 34 feet 
 focal length, he succeeded in rediscovering the satellite on the 13th of 
 December, 1672 ; but a few days afterwards it again disappeared, and it 
 continued invisible for some time, notwithstanding that he made the most 
 persevering efforts to obtain a sight of it. We shall presently give a more 
 detailed account of the curious property of the satellite which causes it to 
 be periodically invisible to the greater number of observers. 
 
 * Opera Varia, torn, ii., p. 551. 
 
 f Systema Saturnium, Ded. ; Opera Varia, torn, ii., p. 530. 
 
 \ Mem. Acad. des Sciences, tome x., p. 584, et seq. Ibid., 1705, p. 24. 
 
HISTORY OP PHYSICAL ASTRONOMY. 269 
 
 On the 23rd of December, 1672, Cassini, while engaged in searching 
 for his lost satellite, discovered a small star near the place where he ex- 
 pected to find it, but still in a position which did not accord sufficiently 
 well with the theory of the satellite's motion. This turned out to be a 
 third satellite, revolving nearer the planet than either of the two others. 
 It completed its revolution in about four days and a half. Subsequently 
 he determined the period with greater precision to be 4 d 12 h 27 m . He 
 also found that its greatest distance from the planet did not amount to 
 more than a diameter and two-thirds of the ring *. 
 
 In the month of March, .1684, Cassini discovered two more satellites cir- 
 culating round Saturn. They were both nearer the planet than any of the 
 others previously discovered. The interior of the two satellites, at its 
 greatest elongation, receded from the planet to a distance measuring only 
 two-thirds of the diameter of the ring, and revolved completely round it 
 in l d 21 h 19 m . The exterior satellite attained an elongation equal to 
 three-fourths of the diameter of the ring, and completed its revolution in 
 3 d 17 h 43 m f. It is obvious that these discoveries could not have been 
 made without telescopes of very considerable optical power. Before, how- 
 ever, any means were devised of obviating the effects of chromatic aberra- 
 tion, it was found to be impossible to construct refracting telescopes of a 
 high power without assigning such an enormous focal length to the object 
 glass as to render the instrument totally unmanageable. Cassini eluded 
 this difficulty by setting aside the tube of the telescope altogether, and 
 placing the object glass in a suitable position for viewing the object through 
 it. A similar mode of observing was also practised about the same time by 
 Huyghens J. Cassini discovered the two interior satellites of Saturn with 
 object glasses of 136 and 100 feet focal length ; but he afterwards succeeded 
 in observing them with glasses of 90 and 70 feet focal length. These glasses 
 were constructed by Campani, at Rome. Cassini first placed them in an 
 aperture, which he had caused to be left for that purpose in one of the 
 towers of the Royal Observatory of Paris at the time of its erection. 
 As this mode of observing could not be conveniently practised at all alti- 
 tudes, he afterwards adopted the expedient of placing the object glasses 
 sometimes on the top of a pole, and at other times on a wooden tower 
 of great height . 
 
 In order to distinguish the different satellites from each other, Cassini 
 proposed to denominate them according to their distances from the planet, 
 the innermost being the first satellite, the one next to it the second, and so 
 on to the outermost satellite, which was the fifth. According to this nomen- 
 clature, the satellite discovered by Huyghens, although the first in the 
 order of discovery, was denominated the fourth satellite. 
 
 The reader will not fail to remark that the five satellites of Saturn were 
 discovered at the times of the disappearance of the ring, or at least on the 
 occasions during which it assumed the form of a luminous line. This cir- 
 cumstance is doubtless to be ascribed partly to the superior attention with 
 which the planet was observed at those junctures, and partly to the greater 
 
 * Mem. Acad. des Sciences, tome x., p. 586. + Ibid., p. 694, et seq. 
 
 J The credit of first practising this mode of observation has been generally ascribed 
 to Huyghens, but Cassini distinctly asserts that his observations of Saturn's satellites were 
 the first that had been made without employing the tube of the telescope. He states that 
 he had already discovered the two interior satellites in that manner when Huyghens pub- 
 lished his l Atroscopium,' in which he explains a method analogous to his, though much 
 more troublesome in detail. (Mem. Acad. des Sciences, 1705, p. 23.) 
 
 Mem. Acad. des Sciences, tome x., p. 702; 1705, p. 23. 
 
270 HISTORY OF PHYSICAL ASTRONOMY. 
 
 facility of making such discoveries, in consequence of the planet being 
 then disencumbered of its appendage. Six passages of the planet through 
 the node of its ring had occurred without leading to any similar results, 
 when the seventh was at length illustrated by Sir William Herschel's 
 discovery of two additional satellites. On 'the 28th of August, 1789, 
 having directed to the planet his 40-feet reflector, which he had just com- 
 pleted, that astronomer perceived six small stars, which, from their bright 
 appearance, and their arrangement in the plane of the ring, he at once 
 suspected to be all satellites*. The planet was then retrograding with 
 great rapidity, and the opportunity was therefore favourable for deciding 
 this point. A very short time served to convince him that his suspicion 
 was well founded. After the lapse of about two hours and a half he dis- 
 covered, to his great delight, that the planet had carried away all the six 
 stars from their original positions. They proved to be the five old satellites 
 of the planet, and a sixth, which for the first time, had revealed itself to 
 mortal eyes. This satellite was nearer the planet than the innermost or 
 first satellite of Cassini. By a comparison of his observations, Herschel 
 found that it completed a sidereal revolution round the planet in 
 l d 8 h 53 m 9 s . The addition of this satellite to the Saturnian system was 
 succeeded by that of another, which Herschel was enabled, by means of 
 the same powerful telescope, to detect on the 17th of the following month. 
 He found this satellite to revolve still nearer the planet than any of the 
 others. He determined the time of its revolution to be & h 40 m 46 s . 
 According to the principle of nomenclature adopted by Cassini, the last- 
 mentioned satellite of Herschel should be denominated the first satellite 
 of the planet, the other satellite discovered by that astronomer should be 
 denominated the second, and so on, proceeding outwards from the planet. 
 As a rigorous adherence to this principle would have the effect of altering 
 the designations of the five old satellites, Herschel proposed to call the 
 two satellites discovered by him the sixth and seventh satellites, counting 
 inwards with respect to the planet. Hence the seventh satellite is the 
 nearest to the planet, while the fifth is the most remote from it f. The 
 two satellites discovered by Herschel are visible only in telescopes of ex- 
 traordinary power. The seventh satellite was estimated by that astro- 
 nomer to be beyond all comparison smaller than the sixth. Even in the 40- 
 feet reflector it appeared only like a very small lucid point J. On account 
 of its vicinity to the planet, it is hidden by the ring throughout the greater 
 part of each revolution. Schroeter, who never could obtain a sight of it, 
 was induced to doubt its existence. It has, however, been repeatedly seen 
 in several of the powerful telescopes of the present day. 
 
 It will be readily seen, by a comparison either of the distances or the 
 periodic times of the satellites of Saturn, that a disproportionately-wide 
 interval exists between the orbits of the fourth and fifth satellites. The 
 vacuity hence arising has been to a certain extent filled up by the discovery 
 
 * Phil. Trans., 1790, Part I., p. 10. 
 
 t As an improvement in the nomenclature of the Saturnian system was very desirable, 
 Sir John Herschel has recently proposed to denominate the satellites after the Titanian 
 divinities. The names of the seven satellites, commencing with the one most remote 
 from the planet, and proceeding regularly inwards, are contained in the following line: 
 
 Japetus, Titan, Rhea, Dione, Tethys, Enceladus, Mimas. 
 
 This mode of distinguishing the satellites seems in a fair way of being generally adopted. 
 The discovery of an eighth satellite has shown the absolute necessity of some such nomen- 
 clature. 
 
 t Herschel, however, succeeded in seeing it with his 20-feet reflector. 
 
HISTORY OF PHYSICAL ASTRONOMY. 271 
 
 of an eighth satellite of the planet, on the occasion of the recent passage of 
 the plane of the ring across the earth's orbit. This interesting result is due 
 to the independent labours of two astronomers, who although residing 
 in different hemispheres, recognized the satellite on the very same day, 
 viz., the 19th of September, 1848. On the 16th of the month just men- 
 tioned, Prof. Bond, of Cambridge, U. S., while engaged in observing Saturn, 
 perceived a small star of the seventeenth magnitude, situated nearly in the 
 plane of the ring. On the 19th he discovered that the star was retro- 
 grading with the planet, whence its real nature at once suggested itself to 
 him. Mr. Lassel, of Starfield, Liverpool, arrived at the discovery of the body 
 in the same manner. He first observed it as a star on the 18th of Sep- 
 tember, and on the following evening he detected such indications of its 
 motion as enabled him to establish, beyond all doubt, that it was a satellite. 
 Thus, although Mr. Bond first saw the satellite as a star, he discovered its 
 real nature only on the same night with Mr. .Lassel. But, indeed, 
 although either of these astronomers had discovered the satellite several 
 days previous to the other, it would be absurd in such a case to draw any 
 distinction between their respective merits. Of course the discovery of 
 Mr. Lassel was generally announced throughout Europe, before the sur- 
 prising intelligence of Mr. Bond's simultaneous discovery of the satellite 
 was wafted across the Atlantic*. It is a curious fact that Huyghens, as if 
 to atone for his unfortunate prediction relative to the secondary planets on 
 a former occasion, suggested the probability of a satellite revolving in the 
 interval included between the orbits of the fourth and fifth satellites of 
 Saturn f. In conformity with the nomenclature proposed by Sir John 
 Herschel, the new satellite has received the name of Hyperion. Its period 
 has been estimated to be 22 d 12 h , but this can only be considered a provi- 
 sional evaluation. 
 
 The only fact which has been established relative to the physical consti- 
 tution of the satellites of Saturn is, the remarkable variation of the light of 
 the fifth satellite. It has been already mentioned that this satellite disap- 
 peared soon after its discovery in 1671, and that after Cassini recovered 
 a sight of it in the following year, it again speedily eluded his observations. 
 Having watched it throughout a great number of revolutions, that astro- 
 nomer found that it was invariably invisible in the eastern part of its 
 orbit. It regularly disappeared two or three days after passing its superior 
 conjunction, and did not re-appear until two or three days before its arrival 
 in inferior conjunction. As the period of the satellite is nearly equal to 
 80 days, it continued consequently invisible for about a month during each 
 revolution. Two interesting conclusions were deducible from this fact. 
 In the first place, it was obvious that there existed extensive tracts on the 
 surface of the satellite that were incapable of reflecting a sufficient 
 quantity of the solar light to render them visible. In the second place, 
 since these dark tracts were constantly turned towards the sun when the 
 satellite was in the same parts of its orbit, it followed that the satellite 
 presented the same hemisphere towards the planet, during each synodic 
 
 * Mr. Lassel discovered the satellite with a Newtonian reflector of 20-feet focal length, 
 and 24- inches aperture. Prof. Bond effected its discovery with a magnificent refracting 
 telescope, the object glass of which has a diameter of 15 inches. 
 
 t Cum enim inter extremas duas, spatium amplius pateat quam pro distantns caete- 
 rarum; posset hoc insidere sextus satelles. Cosmotheoros, p. 99, Opera Varia, torn, ii., 
 p. 698, 
 
272 HISTORY OF PHYSICAL ASTRONOMY. 
 
 revolution, and consequently its motion upon its axis was equal to its 
 motion round its primary, as in the case of the earth's satellite. 
 
 The curious discovery of Cassini, above referred to, has been verified by 
 the observations of subsequent astronomers. Sir William Herschel, with a 
 view to establish beyond all doubt the variation of the light of the satellite, 
 observed it with the most scrupulous attention throughout a great number of 
 revolutions. By means of his powerful telescopes, he was enabled to per- 
 ceive it throughout the entire course of its revolution round the planet, but 
 he found that it constantly experienced a great diminution of lustre when it 
 was passing through the eastern half of its orbit. He also discovered, 
 by a nice comparison of its light with that of each of the other satellites, 
 that it varied much in brightness throughout each revolution, but that it 
 always exhibited the same degree of brightness when it appeared in the 
 same part of its orbit. This interesting fact accords admirably with the 
 conclusion previously suggested by the observations of Cassini, namely, 
 that the satellite rotates completely on an axis in the same time which it 
 takes to accomplish its revolution round the planet. Herschel concluded 
 from his observations, that the light of the satellite is in full splendour 
 when it is traversing the part of its orbit which is between 68 and 129 
 past the inferior conjunction. He estimated that, in passing through this 
 arc, it does not fall above one magnitude short of the brightness of the 
 fourth satellite. On the other hand, from about seven degrees past the 
 opposition till towards the inferior conjunction, it is not only less bright 
 than the third satellite, but it hardly rivals the second or even the first. 
 Upon the whole, the alteration of brightness appeared to him to be 
 equivalent to a change from the fifth to the second magnitude #. 
 
 On the evening of the 13th of March, 1781, when Sir William 
 Herschel was engaged in examining the small stars in the neighbourhood 
 of H Geminorum, his attention was attracted towards a star which 
 appeared sensibly larger than any of those around it. Being struck with 
 its unusual size, he instituted a comparison between it and two other 
 small stars, and finding it to be much larger than either, be began to 
 entertain a suspicion that it was a comet. In order to obtain a stronger 
 assurance on this point, he had recourse to a delicate criterion, by means 
 of which astronomers are usually enabled to distinguish a fixed star 
 from a planet or comet. The apparent diameters of both the fixed stars 
 and planets are generally found to increase when a higher magnifying 
 power is applied to the telescope with which .they are observed ; but there 
 is this essential distinction between the two classes of objects, that while 
 the apparent diameters of the planets are enlarged in the exact propor- 
 tion of the magnifying power, those of the fixed stars do not increase at 
 so rapid a rate. At the same time, however, the light of the planet 
 becomes fainter, and its outline appears ill defined ; while, on the other 
 hand, the fixed stars, under similar circumstances, retain their usual lustre 
 and distinctness. When Herschel first saw the star, he had been using 
 a magnifying power of 227. He now applied to his telescope (which was 
 a seven feet reflector) magnifying powers of 460 and 932, and he found, 
 agreeably to his conjecture, that the star acquired successively a duller 
 and more confused appearance, and was in each case enlarged in the 
 exact proportion of the magnifying power, while the stars with which he 
 compared it, retained their usual aspect, and exhibited a less rapid varia- 
 
 * Phil. Trans., 1792, p. 14. 
 
HISTORY OP PHYSICAL ASTRONOMY. 273 
 
 tion of magnitude. Having now felt a strong persuasion that the object 
 was a comet, he determined, by careful estimation, its position with 
 respect to a telescopic star near to it, intending to make observations of 
 it on the following evenings, for the purpose of ascertaining whether it 
 had a proper motion. A very brief lapse of time served to dispel all 
 doubts upon this point, the star having been found by him to be revolving 
 with a slow motion, according to the order of the signs, in an orbit which 
 deviated very little from the plane of the ecliptic. He continued to 
 observe the star until the 19th of April, determining its position on each 
 occasion by measuring, with a micrometer, its distance from a telescopic 
 star near to it, and also its angle of position with respect to the same 
 star, or in other words, the angle contained between an imaginary line 
 joining the two stars and the parallel of declination passing through the 
 telescopic star. He also executed several naicrometrical measures of its 
 apparent diameter. Having drawn up an account of his observations, he 
 communicated it to the Royal Society in a paper, which was read before 
 that body on the 26th of April, 1781. In this paper he does not appear 
 to entertain a suspicion that the object of his discovery was any other 
 than a comet *. 
 
 Previous to transmitting the above-mentioned communication to the 
 Royal Society, Herschel had taken an opportunity of announcing his 
 discovery to Dr. Maskelyue, the Astronomer Royal, who in his turn gave 
 due notice of it to the astronomers of France. Messier commenced his 
 observations of the supposed comet on the 16th of April, 1781, and his 
 example was speedily followed by Lalande, Lemonnier, Mechain, and 
 DAgelet, as well as by Reggio, De Cesaris, Bode, Wargentin, and 
 various other astronomers on the Continent. As soon as a few observa- 
 tions of it were obtained at Paris, an attempt was made by means of 
 them to determine the elements of the parabolic orbit in which it was 
 presumed to revolve. A serious difficulty, however, soon presented itself 
 to those engaged in this enquiry. It was found that although a parabola 
 might be assigned, which would represent with tolerable fidelity a limited 
 number of observations of the comet, yet in a few days afterwards, the 
 positions of the body> when calculated upon the same hypothesis, appeared 
 to be totally irreconcilable with the actual motion. Various attempts 
 to discover an orbit which would permanently represent the motion of the 
 body were made by Mechain, the President de Saron, Laplace, Boscovich, 
 and others, but in all instances they proved to be equally unavailing for 
 this purpose. Nor is their failure at all to be surprised at, for, since the 
 body was universally supposed to be a comet, it was concluded, by reason- 
 ing from analogy, that the perihelion, at the utmost, would not extend 
 beyond the orbit of Jupiter, and that in all probability it was situated far 
 within the terrestrial orbit f. The attention of each calculator was 
 therefore constantly directed towards constraining the body to move in an 
 orbit the perihelion distance of which, even upon the most extravagant 
 supposition, was imagined not to amount to four times the radius of the 
 
 * Phil. Trans., 1781, p. 492, et seq. 
 
 f In Delambre's catalogue of 116 comets, comprehending all the bodies of this nature 
 whose elements have been determined down to the year 1813, there is only one comet, 
 viz., that of 1729, whose perihelion distance (4.0698) exceeds four times the terrestrial 
 orbit. There are only six comets in the catalogue which, at their perihelia, passed 
 beyond the orbit of Mars, and the whole number which passed beyond the earth's orbit 
 does not amount to more than twenty-three. Ast. Theor. et Prat., tome 3, p. 416. 
 
 T 
 
274 HISTORY OF PHYSICAL ASTRONOMY. 
 
 terrestrial orbit. It was never suspected all the while, that the nearest 
 distance of the body from the sun exceeded the same standard of measure- 
 ment at least eighteen times. 
 
 The President de Saron appears to have been the person who threw 
 the first glimmering of light on this perplexing subject. On the 8th of 
 May, 1781, he announced that the comet was in reality much more 
 remote from the sun than astronomers had hitherto supposed it to be. 
 He estimated its perihelion distance to be equal to at least twelve times 
 the radius of the terrestrial orbit *. This was an important suggestion, 
 for it had the effect of directing the attention f enquirers to the region 
 of the heavens in which the body was actually revolving. By adopting 
 it, the observations were represented with greater precision than they had 
 been on any previous hypothesis, and hopes began to be entertained of 
 arriving at a determination of the real orbit of the body. 
 
 The next step in the enquiry was made by Lexell, who happened to be 
 in England at the time of Herschel's discovery. In an account of his 
 researches which he communicated to the Academy of St. Petersburg, 
 he mentions that Dr. Maskelyne, and the other English astronomers who 
 observed the body, agreed with him in supposing that in all probability it 
 was a planet f. Various circumstances, he remarks, concurred in suggest- 
 ing this view of its nature. In the first place, observation shewed it to 
 be a well-defined object, whereas comets generally have a nebulous 
 appearance. Again, although very small, it was not difficult to discern a 
 difference in its light from that of the fixed stars. Lastly, its slow 
 motion in latitude (indicating that its inclination to the ecliptic was very 
 inconsiderable), and its motion in the zodiac according to the order 
 of the signs, were two independent facts which both strongly supported 
 the hypothesis of its being a planet. Taking two extreme observations 
 of the body, one by Herschel, dated March 17, 1781, and the other by 
 Maskelyne, dated May 11 of the same year, Lexell found that they 
 might be both satisfied by a circular orbit, \vhose radius was equal to 
 18.93, the mean distance of the earth from the sun being supposed equal 
 to unity. In the month of June'or July, while still residing in England, 
 he wrote a letter to one of his friends in Paris, in which he stated, that the 
 motion of the body which formed the subject of so much anxious investi- 
 gation might be represented by a circular orbit, whose radius was equal 
 to eighteen times the mean distance of the sun from the earth. " From 
 that time," says Lalande, " it appeared to me that the body ought to be 
 called the new planet." J Lexell soon afterwards found that on account 
 of the slow motion of the body, and the consequent sniallness of the arc 
 described by it within a limited interval of time, the observations in- 
 cluded between March 17 and May 28 might be satisfied by an infinite 
 number of parabolas, whose perihelion distances varied from 6 to 22 times 
 the radius of the terrestrial orbit. From this circumstance it appeared 
 evident to astronomers, that until the planet had described a larger arc, 
 it would be impossible to arrive at an accurate knowledge of the elements 
 of its orbit." 
 
 After the lapse of a few months, when the motion of the planet began 
 to be developed more clearly, its distance from the sun, upon the suppo- 
 
 * Mem. Acad. des. Sciences, 1779, p. 529. 
 f Nov. Act. Acad. Petrop., torn, i., p. 69, et seq. 
 
 J " Des lors il me parut qu'on devait lui donner le nom de nouvelk planete, Mem. 
 Acad. des Sciences, 1779, p. 530. 
 
HISTORY OF PHYSICAL ASTRONOMY. 275 
 
 sition of a circular orbit, was determined with considerable precision ; but 
 from the discordances which still existed between the computed and the 
 observed positions, it was plainly apparent that the real orbit was an 
 ellipse of small eccentricity. Elliptic elements of the planet were first 
 calculated by Laplace, and were communicated by him to the Academy of 
 Sciences, in the month of January, 1783. 
 
 When it was ascertained beyond all doubt that the body discovered by 
 Herschel was a planet, it became desirable to distinguish it by some 
 special name. As the privilege of choosing a name in all such cases is 
 the incontestable right of the discoverer, Herschel, urged by a feeling of 
 gratitude towards his royal patron, George III., proposed to confer on the 
 planet the appellation of the Georgium Sidus. Lalande, influenced by an 
 equally honourable motive, suggested the name of Herschel. Both these 
 names sounded incongruously with the prevailing nomenclature of the 
 planetary system, and neither of them consequently met with much 
 favour on the part of astronomers. The names of various heathen divinities 
 were proposed as more appropriate for this purpose. After some time 
 had been spent in discussing the rival claims of different deities, the 
 name of Uranus, suggested by Bode, was finally adopted by astronomers, 
 and has always since been employed to distinguish the planet. 
 
 A point of great interest to be determined was, the magnitude of the 
 body, by tbe discovery of which the planetary system had just been en- 
 riched. For this purpose two data were indispensable, namely, the 
 distance of the planet from the earth at any assigned instant, and the 
 angle subtended by its diameter when viewed at that distance. The 
 former of these could be determined with facility, and with a considerable 
 degree of precision ; the case was very different with respect to the latter. 
 Herschel's first measures of the apparent diameter of the planet, exhibited 
 a remarkable discordance with each other. On the 17th of March he fixed 
 it at 2".53'", on the 2nd of April he made it 4".25 /// , and on the 18th of 
 the same month he determined it to be 5". 2"'*. A similar discordance 
 existed between the measures of other astronomers. Maskelyne was in- 
 duced to fix the magnitude of the apparent diameter at 3". The as- 
 tronomers of Milan fixed it between 6" and 7". Mayer of Manheim esti- 
 mated it to be as high as 1 0". Lexell, despairing of the possibility of 
 determining the apparent diameter of the planet by micrometrical 
 measurement, attempted to ascertain its value by comparing the planet 
 with another body whose apparent diameter was known. For this purpose 
 he compared it with Mars, at a time when that planet was near the 
 position of apogee, and when his apparent diameter in consequence did 
 not exceed 5". Finding that Uranus appeared to be less than the planet 
 with which he compared it, he hence concluded that its apparent diameter 
 fell certainly below 5", and in all probability did not exceed 3" f. The 
 mean of these two extremes gives 4" for the apparent diameter of the 
 planet, a result which forms a closer approximation to the true value than 
 any other that had been hitherto assigned by astronomers. In order to 
 remove all doubts upon this subject, Herschel in 1782 undertook a series 
 of measures of the planet with two micrometers, one of which, called the 
 lamp micrometer, was an instrument of his own invention. He thus ob- 
 tained a number of results, from which it appeared that the mean value 
 of the angle subtended by the diameter of the planet was somewhere 
 
 * Phil. Trans., 1781, p. 494. f Nov. Act. Acad. Petrop., torn, i., p. 78. 
 
 T 2 
 
27G HISTORY OF PHYSICAL ASTRONOMY. 
 
 about 4" *. On a subsequent occasion he instituted a strict comparison 
 between these results, and hence concluded that the apparent diameter of 
 the planet, when viewed at its mean distance from the earth, was equal to 
 3".91. By combining this result with the distance of the planet as 
 recently ascertained (viz., 19.08, the mean distance of the earth being 
 supposed equal to unity), he was enabled to determine its linear dimen- 
 sions and volume. In this manner he found that the diameter of the 
 planet measured 34217 miles. It therefore exceeded the diameter of the 
 earth in the proportion of 4.3 to 1. It was easy also to infer that in vo- 
 lume it exceeded the same body in the proportion of 80 to 1 f. From these 
 results it appeared that the newly -discovered body was, after Jupiter and 
 Saturn, by far the most considerable of those bodies hitherto recognised as 
 revolving round the sun. 
 
 The enrichment of the planetary system consequent on the accession of 
 Uranus to it, marks the commencement of the long series of brilliant dis- 
 coveries and sublime speculations which adorned the astronomical career of 
 Sir William Herschel J. It has been frequently asserted that this noble 
 achievement was the effect of chance, and the inference has been hastily 
 drawn, that the merit associated with it is of a very inferior order compared 
 with that due to the same astronomer on account of the many other efforts 
 of his genius. It is true that the discovery was accidental, inasmuch as it 
 did not result from an examination of the heavens, instituted in pursuance 
 of any theoretical views respecting the existence of the body ; but if it is 
 thereby meant that the planet might with equal probability have presented 
 itself as such to any observer, there cannot we conceive be a more vulgar 
 error. A few remarks upon the subject will amply illustrate the justness 
 of this conclusion. In the first place, it may be asserted that the dis- 
 covery was no other than the legitimate reward which might be expected 
 eventually to crown the exertions of an astronomer, who continued from 
 night to night with unwearied enthusiasm to explore the heavens, with 
 optical appliances which owed their exquisite character solely to the re- 
 sources of his own genius. Upon this ground alone, therefore, the author 
 of the discovery, even if he had not borne the immortal name of Herschel, 
 would have been entitled to a high place among those who have success- 
 fully explored the celestial regions. Nor would a less generous award be 
 in unison with the natural promptings of the human heart. The motto 
 of one of England's most illustrious sons, " palmam qui meruit ferat," ex- 
 presses, in appropriate language, the spontaneous response of the mass of 
 mankind in all ages, to every result achieved, whether in arts or arms, by 
 a well-directed course of skilful energy and unflinching perseverance. 
 But the planet, in fact, was involved in an extensive field of observation, 
 which the astronomer had conceived the design of submitting to a syste- 
 matic scrutiny ; and it only required the application of his mental powers 
 to the realisation of this design to conduct him inevitably to the wander- 
 ing body . The occasion was, therefore, favourable for detecting the 
 planet, but this would have been a useless advantage without the man. 
 Similar junctures must frequently offer themselves to every person who 
 devotes his attention to physical phenomena, but how few are sagacious 
 enough to discern their presence, and extract from them their legitimate 
 
 * Phil. Trans., 1783, p. 13. f Ibid., 1788, p. 378. 
 
 J Born at Hanover 1738; died at Slough, in England, 1822. 
 
 Herschel was engaged in a series of observations with a view to the investigation of 
 the annual parallax of the stars, when his attention was first drawn to the planet. 
 
HISTORY OF PHYSICAL ASTRONOMY. 277 
 
 consequences ! The circumstances attending the discovery in the present 
 instance, abundantly serve to prove that its author was no ordinary 
 observer. The singling out of the planet from among the multitude 
 of similar objects by which it was surrounded, was an operation of the 
 utmost delicacy, which demanded extraordinary powers of discernment. 
 Lalande has expressed his astonishment that Herschel should have been 
 led to direct his attention especially to the planet, considering that with 
 an instrument of his own, which magnified 120 times, the appearance of 
 the body did not differ from that of a star of the seventh magnitude *. 
 The language of Messier is equally decisive upon this point. "Nothing," 
 says that astronomer, writing to Herschel, " was more difficult than to 
 recognise the body ; and I cannot conceive how you have been induced to 
 return repeatedly to that star or comet, for it has been absolutely neces- 
 sary for me to observe it several days in succession, in order to obtain an 
 assurance that it had a proper motion."! 
 
 The different sets of elements which Laplace and his contemporaries 
 had calculated for Uranus, soon after its discovery, could only be consi- 
 dered as provisional, the motion of the planet not having been yet suffi- 
 ciently developed to justify the hope of determining with precision the 
 form and position of the orbit in which it revolved. In 1790, the 
 Academy of Sciences, with the view of eliciting a definitive determination 
 of the orbit of the planet, proposed its theory as the subject of a prize. 
 It has been already mentioned in one of the foregoing chapters, that the 
 prize was awarded to Delambre. An account has also been given, in the 
 same chapter, of the subsequent researches of astronomers on the theory of 
 the planet, and of the memorable consequence which ensued from the 
 study of the irregularities of its motion. 
 
 The immense distance of Uranus precludes all hopes of discovering any 
 phenomena indicative of its physical constitution, analogous to those in- 
 teresting appearances, which an examination of the other principal planets 
 with the telescope has revealed to astronomers. Sir William Herschel was 
 induced to suspect that the figure of the planet is sensibly spheroidal. 
 Observations with his 7-feet, 10-feet, and 20-feet reflectors, all concurred 
 in suggesting the same conclusion relative to this point. The longer axis 
 of the planet also appeared to him, agreeably to the analogy of Jupiter 
 and Saturn, to be situated in the plane of the orbits of the satellites. 
 Assuming the ellipticity of the planet to be an established fact, he hence 
 concluded that the planet revolves with considerable velocity upon an 
 axis J. M. Arago has naturally expressed his surprise that an observer so 
 scrupulous as Herschel should have contented himself with a simple esti- 
 mation of the figure of the planet, when he might have obtained a defini- 
 tive assurance upon this point, by direct measurement of the equatorial 
 and polar axes with a micrometer . There are two distinct circum- 
 stances, however, which concur in rendering the determination of the ellip- 
 ticity of Uranus an operation of extreme difficulty. In the first place, 
 the smallness of the apparent magnitude of the planet has a tendency to 
 cause a small error in the measurement of either of the axes to exercise a 
 
 * Mem. Aead. des Sciences, 1779, p. 528. 
 
 f " Rien n'etait plus difficile que de la reconnaitre; et je ne puis pas concevoir com- 
 ment vous avez pu revenir plusieurs fois sur cette etoile ou comete, car absolument il a 
 fallu 1'observer plusieurs jours de suite pour s'appercevoir qu'elle avait un mouvement." 
 Phil. Trans., 1781, p. 500. 
 
 | Phil. Trans., 1798, p. 11, Annuaire, 1842, p. 579, 
 
278 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 very material influence on the ellipticity. Til the case of Jupiter, the 
 difference between the equatorial and polar axes, at the mean distance of 
 the planet from the earth, is equal to 2". 789 ; and as the ellipticity is 
 measured by the ratio of this quantity to the equatorial axis, it is obvious 
 that an error of a tenth of \" , committed in its determination, will entail 
 on the ellipticity an error less than o'jth of its real value. Now, if we 
 assume the ellipticity of Uranus to be equal to that of Jupiter, the differ- 
 ence between the equatorial and polar axes (supposing the former to be 
 equal to 4") will amount only to 0".2916. It follows, therefore, that an 
 error equal to a tenth of 1" committed in the measurement of either 
 of the axes would occasion an error in the ellipticity greater than one- 
 third of its true value. M. Madler, indeed, has obtained for the planet an 
 ellipticity equal to -g.^, indicating a difference between the equatorial and 
 polar axes amounting to 0".435. But even upon such a supposition, an 
 error of measurement equal to that assumed in the two previous cases 
 would produce an alteration to the extent of one-fourth in the value of the 
 ellipticity. There is another circumstance, however, which operates un- 
 favourably in attempting to determine the ellipticity of Uranus. The re- 
 mark of Herschel, that the longer axis of the planet extends in the plane 
 of the orbits of the satellites, leads to the curious conclusion that the 
 equator of the planet is nearly perpendicular to the plane of the ecliptic, 
 since tbe satellites have been found to revolve in orbits which are nearly 
 perpendicular to that plane. The consequence of this anomalous condition 
 \vill be, that the planet will exhibit the full quantity of its ellipticity only 
 in two opposite points of its orbit, namely, those wherein the plane of its 
 equator passes through the earth, for the planet in such positions alone is 
 projected upon a plane passing almost through its poles. On the other 
 hand, there are two opposite points, 90 distant from these, in Which the 
 planet will assume nearly a circular appearance, since the plane of projec- 
 tion almost coincides with the plane of the equator. In any intermediate 
 position the apparent ellipticity will be less than the true, and it will 
 continually diminish as the planet recedes to a greater distance from 
 either node of its equator. It is obvious from this circumstance, that 
 even if the ellipticity of the planet should be very considerable, it is 
 not liable to be detected except when the planet is passing through 
 either of the nodes of its equator, an event which can only occur at 
 successive intervals of half a revolution of the planet, or about forty-two 
 years. 
 
 It follows from the foregoing remarks that, even if the ellipticity of 
 Uranus should be considerable, the difference between the lengths of the 
 apparent equatorial and polar axes, which is at all times very small, on ac- 
 count of the minute dimensions of the disk, is in general rendered still 
 smaller by the peculiar position of the equator of the planet. Perhaps 
 this circumstance may explain the reluctance of Herschel to determine the 
 ellipticity of the planet by actual measurement, the small difference be- 
 tween the apparent lengths of the equatorial and polar axes not offering 
 any chance of his obtaining a trustworthy result by this means. It ap- 
 pears, indeed, as already stated, that M. Madler has obtained for the 
 planet an ellipticity equal to -g.\^ M. Otto Struve, however, who ob- 
 served the planet still more recently with the magnificent refractor of 
 Pulkowa, was unable to discern the slightest trace of ellipticity. 
 
 Sir William Herschel at one time was inclined to suspect that Uranus 
 is surrounded by one or two rings. On the 4th of March, 1787, 
 
HISTORY OF PHYSICAL ASTRONOMY. 279 
 
 having examined the planet with his 20-feet reflector, he perceived 
 two projecting points, at opposite extremities, of a diameter extending 
 east and west, and also two similar points, though somewhat smaller, 
 at a distance of 90 from the others. The same appearance having been 
 witnessed by him on several successive evenings, he suspected that the 
 planet might be encompassed by two rings at right angles to each 
 other*. Subsequent observations, however, shewed him that the ap- 
 pearance was illusory. The suspicion of a ring returned to his mind on 
 a future occasion; but in this instance also it proved to be unfounded. 
 Indeed, he remarked that during the interval of ten years, extending 
 from 1782 to 1793, which his observations of the .planet embraced, 
 whatever might have been the position of the node of the ring, the 
 planet must have removed to a sufficient distance from it at some time 
 during that period, to cause such an opening of the ring as would render 
 it pretty visible, if it had existed at all. 
 
 Soon after his discovery of Uranus, Herschel endeavoured to ascertain 
 whether it was attended by satellites; but although he repeatedly ex- 
 amined the planet for this purpose, with his most powerful telescopes, he 
 was unable to discover any trace of the existence of such bodies. He 
 ascribed his failure to the want of a sufficient quantity of light to render 
 visible such faint objects as he presumed the satellites of so remote a 
 planet would be. As soon, however, as he experienced the advantage of em- 
 ploying the front view in his telescopes, from the additional quantity 
 of light which he gained by this contrivance, he again resolved to pro- 
 secute this interesting enquiry. Accordingly, on the llth of January, 1787, 
 he directed one of his telescopes f to the sweep, including the planet, and 
 when it arrived on the meridian he perceived several faint stars near 
 to it, the positions of which he noted down with great care. On the 
 following evening, when the planet returned to the meridian, he 
 looked out with eager scrutiny for his stars, and he found that two 
 of them were missing. He repeated his observations on the 14th, 
 17th, 18th, and 24th of January, and also on the 4th and 5th of 
 February, carefully delineating on each occasion the configurations of the 
 small stars in the Vicinity of the planet, Although he had no longer any 
 doubt of the existence of one satellite at least, he deferred making any 
 communication respecting it, until he had seen it actually hi motion. Ac- 
 cordingly he directed his telescope to the planet on the 7th of February, 
 and having fixed his attention on the satellite at six o'clock in the evening, 
 he steadily kept it in view until 3 o'clock in the following morning. During 
 the course of nine hours that he remained at the telescope, he had the 
 gratification of perceiving that the satellite continued faithfully to attend 
 the planet, while at the same time it described a considerable arc of its 
 proper orbit. He did not omit following another star which, from his pre- 
 vious observations, he suspected to be a satellite, but from his attention 
 having been $/> strongly directed to the object already mentioned, he could 
 not be so well assured of its motion. The observations of the 9th of Feb- 
 ruary removed all doubts from his mind, the star, during the interval 
 which elapsed since his previous observation, having advanced in the same 
 direction with the other star already recognised as a satellite, but with a 
 
 * Phil. Trans., 1798, p. 67. 
 
 f This appears, from the context, to have been his 20-feet reflector, although he does 
 not expressly mention that it was that instrument. 
 
280 HISTORY OF PHYSICAL ASTRONOMY. 
 
 quicker motion. From this circumstance he inferred that it revolved be- 
 tween the latter and the planet. He, therefore, called it the first satellite 
 while the one more remote, although the first that had been discovered, 
 received from him the name of the second satellite. 
 
 Herschel communicated an account of his discovery of the satellites of 
 Uranus to the Koyal Society, in a paper which was read before that body 
 on the 15th of February, 1787 *. A sufficient interval of time had not yet 
 elapsed to enable him to determine the elements of their motion ; but by 
 a rough estimation, he found that the first satellite completed its synodic 
 revolution in about eight days and three quarters, and the second in 
 thirteen days and a half. He also remarked that the orbits were inclined 
 at considerable angles to the ecliptic. As soon as he obtained an adequate 
 number of observations .of the two satellites, he undertook a rigorous 
 determination of their elements. The results of his researches are con- 
 tained in a paper which was read before the Royal Society on the 142nd of 
 May, 1788 f . He found the time of a synodic revolution of the first satel- 
 lite to be 8 d 17 h l m 19 s . 3, and that of the second to be 13 d ll h 5 m 1 s . 5. 
 He determined the apparent distance of the second satellite at the mean 
 distance of the planet from the earth to be 44". 23. It was a matter 
 of such extreme difficulty to obtain even a sight of the first satellite, that 
 he did not attempt to establish its distance from the planet by obser- 
 vation ; but knowing the periodic time, and knowing also the periodic 
 time and distance of the second satellite, he was enabled to deduce it from 
 these data by means of Kepler's third law. In this manner he found the 
 apparent distance of the satellite from the planet to be 33". 09. He de- 
 termined the inclination and the longitude of the node of the second satel- 
 lite, but the results exhibited an ambiguous character, in consequence of 
 an uncertainty in the observations, which could not be removed until the 
 planet had revolved round the sun through an arc sufficiently large to oc- 
 casion a sensible change in the position of the satellite's orbit relative to 
 the earth. The ambiguity involved an extraordinary alternative, to which 
 we shall presently have occasion to allude more particularly. Herschel 
 found from his observations of the first satellite, that the position of its 
 orbit did not deviate sensibly from that of the second. On account of the 
 great inclinations of their orbits, the satellites could only be eclipsed when 
 the planet was passing through either of their nodes. Herschel an- 
 nounced that they would undergo eclipses in either of the years 1799 or 
 1818, adding that they would appear, on such an occasion, to ascend out of 
 the shadow of the planet, in a direction almost perpendicular to the plane 
 of the ecliptic. This interesting phenomenon was predicted with a re- 
 markable degree of accuracy, considering the extreme difficulty of obtain- 
 ing reliable observations of the satellites, and the short interval of time 
 which elapsed since their discovery ; but from a circumstance connected with 
 the visibility of these minute bodies, which the illustrious astronomer was 
 the first to point out, it has not been hitherto allotted to mortal eyes to 
 witness it. 
 
 We have mentioned that the results at which Sir William Herschel 
 arrived, relative to the position of the orbits of the satellites, were to a 
 certain extent ambiguous. It was manifest that the orbits were almost 
 perpendicular to the plane of the ecliptic, and that the planet was advanc- 
 ing towards their ascending node; but there were two positions of the orbits, 
 
 * Phil. Trans., 1787, p. 125, et secj. f Phil. Trans., 1788, p. 364, et se<j. 
 
HISTORY OF PHYSICAL ASTRONOMY. 281 
 
 either of which would satisfy the observations. This will be easily under- 
 stood when it is borne in mind that a circle viewed obliquely assumes 
 the form of an ellipse, whose eccentricity depends upon the degree of 
 obliquity, and that it is possible to assign two different positions to a 
 circle, in each of which it will be equally oblique with respect to the visual 
 ray. As an illustration of this remark let the circle A B c D represent the 
 orbit of the satellite, and let the plane of the paper be perpendicular to 
 
 the visual ray. Let us now suppose the orbit to turn through a certain 
 angle round the axis A c, so that the semicircle ABC shall, by this means, 
 be elevated above the plane of the paper, while the opposite semicircle, 
 A D c, is equally depressed below it. When the orbit is viewed in this 
 new position, it will be projected upon the plane of the paper, and will 
 appear to coincide with the ellipse A b c d, the eccentricity of which 
 will increase as the orbit revolves through a greater angle, or, in other 
 words, according as its plane becomes more oblique with respect to the 
 visual ray. If, however, we had supposed the orbit to revolve in the 
 opposite direction through an equal angle, so that the semicircle ABC 
 was depressed below the plane of the paper, while the opposite semicircle, 
 ADC, was equally elevated above it, the projected orbit, in this case also, 
 would manifestly coincide with the ellipse A I c d. It will, therefore, 
 be impossible for an observer, by simply viewing the motion of the satel- 
 lite from a remote point situate above the plane of projection, to ascertain 
 whether the semicircle A B c is turned towards him, or whether it is 
 turned away from him. It is manifest, however, that the position of the 
 orbit of the satellite, with respect to a fixed plane, will be very different 
 in the two cases. The true position can only be decided by the motion 
 of o, the common centre of the two circles, which causes one of the assumed 
 orbits of the satellite to become more, and the other to become less 
 oblique with respect to the visual ray ; whence, by confronting the two corre- 
 sponding ellipses with the results of observation, it is possible to ascertain 
 which of the circles represents the real orbit of the satellite. For example, 
 let us suppose o (representing the planet) to revolve from right to left 
 round the eye of the observer as the centre of motion, the plane of 
 the circle A B c D, constantly moving parallel to itself, it is then mani- 
 fest that if the semicircle A B c be turned towards the observer it will 
 become more and more oblique with respect to the visual ray, and, there- 
 fore, the ellipse Abed will gradually contract in width. On the other 
 hand, if the semicircle A B c be turned away from the observer, the 
 motion of o will cause the plane of the orbit A B c D to become less and 
 less oblique with respect to the visual ray, and the ellipse will gradually open 
 out. Herschel accordingly remarked in 1788, that although the position of 
 the orbit of the second satellite was then doubtful, the true position would be 
 ascertained in the course of a few years by the opening or closing of the 
 
282 HISTORY OF PHYSICAL ASTRONOMY. 
 
 apparent ellipse of the satellite. If the ellipse should contract, the longi- 
 tude of the ascending node of the satellite would be 168 0' 3".9, and 
 the planet would pass through it in 1799 ; but on the other hand, 
 if the ellipse should open out, the longitude of the ascending node would 
 be 246 2' 2". 3, and the passage of the planet through it would not 
 take place before the year 1818*. The most interesting circumstance 
 connected with this ambiguity referred to the motion of the satellite, 
 which would be direct or retrograde, according as the ellipse was observed 
 to open or close. A similar remark was applicable to the first satellite, 
 the position of whose orbit was found to coincide with that of the second. 
 Herschel found from observations of both satellites, subsequent to 1788, 
 that their apparent ellipses continued for some time to contract, and he 
 hence drew the legitimate conclusion that their motion is retrogade. He 
 formally announced this result for the first time in a paper which he com- 
 municated to the Royal Society towards the close of the year 1797 f. This 
 singular anomaly in the planetary system has been confirmed by the 
 observations of subsequent astronomers. Herschel was now enabled 
 definitively to announce that the ascending node of the satellites was 
 situated in 108 0' 3". 9 of longitude, and that the planet would pass 
 through it in the year 1799. The common inclination of their orbits to 
 the orbit of the planet had been found by him in 1788 to be 80 20' ll".l J. 
 On a future occasion he arrived at a more accurate determination of the 
 position of the orbits. 
 
 In the paper above referred to, Herschel announced his discovery of 
 four additional satellites of Uranus. The number of the satellites of the 
 planet therefore now amounted to six. One of the new satellites was the 
 nearest of all to the planet; another revolved in the space included 
 between the orbits of the two satellites already discovered ; the remaining 
 two were exterior to both the old satellites. Conformably to the practice 
 of naming the satellites according to the order of their distances from the 
 planet, Herschel, in this paper, distinguished the two satellites discovered 
 in 1787, by the names of the second and fourth satellites . With respect 
 to the four new satellites, although confidently asserting their existence, 
 he did not venture to give an exact determination of their distances from 
 the planet or their periodic times, on account of the small number of 
 undoubted observations of them which he possessed, but he assigned, as 
 provisional data, certain approximate values of these elements, remarking 
 that future observations might require that they should be considerably 
 modified. These results, including the elements of the second and fourth 
 
 * Phil. Trans., 1788, p. 375. f Phil. Trans., 1798, p. 47, et seq. 
 
 J Phil. Trans., 1788, p. 375. Herschel, indeed, assigned in this paper two values 
 of the inclination, corresponding to the two values of the longitude of the node, and it was 
 by means of these results that he expressed the ambiguity in the position of the orbits. 
 As, however, the^other value of the inclination, viz. 99 39' 48 '.9, is the supplement of that 
 mentioned in the text, it is manifest that the conclusion at which Herschel arrived may be 
 equally well expressed by adopting the smaller inclination in both cases, and supposing 
 the motion to be retrograde in the case wherein the supplement was assigned. For the 
 Sake of simplicity this mode of interpretation has been employed. 
 
 The illustrious astronomer did not, however, invariably adhere to this nomenclature, 
 for in all discussions relating exclusively to the two old satellites, he applied to them their 
 original appellations. In order not to introduce confusion into the text, we shall con- 
 tinue to denominate each satellite according to the order of its distance from the primary, 
 assuming the existence of the six satellites to be an established fact. 
 
HISTOKY OF PHYSICAL ASTRONOMY. 
 
 283 
 
 satellites, as determined by him in 1788, are contained in the following 
 table. 
 
 Order of Distance. 
 
 Date of Discovery. 
 
 Distance from 
 the Planet. 
 
 Periodic Time. 
 
 1st satellite 
 
 January 18, 1790 
 
 25". 5 
 
 5 d 2 ]h 25 m 
 
 2nd do. 
 
 January 11, 1787 
 
 33 .09 
 
 8 17 1 
 
 3rd do. 
 
 March 26, 1794 
 
 38 .57 
 
 10 23 4 
 
 4th do. 
 
 January 11, 1787 
 
 44 .23 
 
 13 11 5 
 
 5th do. 
 
 February 9, 1790 
 
 88 .46 
 
 38 1 49 
 
 6th do. 
 
 February 28, 1794 
 
 177 .92 
 
 107 16 40 
 
 The distance of the first satellite was the result of a micrometrical 
 measure executed by Herschel at a time when he supposed the satellite 
 to be at its greatest elongation from the planet. The distance of the third 
 satellite was determined by assuming its orbit to bisect the linear interval 
 included between the orbits of the two older satellites ; the fifth satellite 
 was supposed to be twice as distant from the planet as the fourth, and the 
 sixth satellite to be four times as distant as the same satellite was. 
 
 The periodic times were not deduced from observation, but were calcu- 
 lated by means of Kepler's third law*. 
 
 In 1815 Herschel communicated to the Royal Society his fourth and 
 last paper on the satellites of Uranus f. The passage of the planet through 
 the ascending node of the satellites had supplied him with a favourable 
 opportunity of obtaining a more accurate determination of the elements of 
 the two old satellites, their apparent orbits on that occasion having assumed 
 the form of straight lines. He found from observation, that the planet 
 passed through the ascending node of the satellites on the 12th of March, 
 1798. The longitude of the node was, therefore, 165 30'. He fixed the 
 inclination of the orbits of the satellites to the ecliptic at 78 58'. A new 
 investigation of the synodic revolutions of the two satellites gave him 
 8 d 16 h 56 m 5 S .2 for the period of the second satellite, and 13 d ll h 8 m 59 s 
 for the period of the fourth. With respect to the question of the distances 
 of the satellites from the planet, he did not undertake to correct the 
 results he had already arrived at, but he assigned certain measures of 
 both satellites, which he considered might be useful in future enquiries 
 relative to this point. 
 
 The passage of the planet through the node of the satellites in 1798, 
 enabled Herschel to obtain a few more observations of the satellites whose 
 existence he first announced in 1797. He still continued to assert his 
 firm belief in the existence of other satellites besides those of 1787, but 
 it was a matter of such extreme difficulty to obtain even occasional glimpses 
 of these remote atoms, and still more so to distinguish them from one 
 another, that he did not venture to give a rigorous determination of 
 their elements, or even to assign the precise number of satellites. He 
 therefore confined himself to the communication of all the observations indi- 
 
 * Herschel's observations of the supplementary satellites appear to have been made 
 with his 20-feet reflector. In a subsequent paper (Phil. Trans., 1815) he explains the 
 grounds upon which he was induced not to make more frequent use of his gigantic 
 telescope of 40 feet focal length, which conducted him, immediately after its completion 
 in 1789, to the discovery of the two interior satellites of Saturn. 
 
 f Phil. Trans., 1815, p. 293, et seq. 
 
284 H1STOKY OF PHYSICAL ASTHONOMY. 
 
 cative of their existence, leaving to future astronomers the task of deducing 
 positive results respecting them, when a more complete system of data for 
 this purpose should be obtained by means of additional observations. 
 
 Sir William Herschel found that the interior of the two old satellites 
 was brighter than the exterior satellite, wnence he concluded that it was 
 the more considerable of the two in point of magnitude *. It appeared 
 from his observations, that both satellites were subject to great varia- 
 tions of brightness. It happened, in consequence, that the exterior satel- 
 lite was sometimes more distinctly visible than the interior. Herschel 
 concluded, from this variation in the brightness of the two satellites, either 
 that there existed dark tracts on their surfaces which were turned in suc- 
 cession towards the earth by the rotation of the bodies on their axes, or 
 that each satellite was enveloped in an atmosphere which, by its fluctu- 
 ating movements, occasionally laid bare the dark surface of the satellite, 
 as in the case of the Sun, Jupiter, and Saturn f. 
 
 Herschel found that both satellites invariably disappeared when they 
 arrived within a certain distance of the planet. The limit of visibility, 
 however, was different for each satellite. The interior satellite generally 
 vanished at a distance of 18" from the planet. The exterior satellite 
 ceased to be visible at the distance of 20" J. A dense atmosphere envelop- 
 ing the planet would explain the disappearance of the satellites, did it not 
 happen that they were lost sight of, when traversing the nearest half of their 
 orbits as well as the opposite half. The only satisfactory explanation which 
 could be given of the phenomenon was, that the feeble light of the satellites 
 was overpowered by the superior lustre of the planet. Herschel remarked, 
 that, owing to a similar cause, the Earth, Venus, and Mercury, would for 
 ever remain invisible to the "inhabitants of Uranus, being constantly lost 
 in the effulgence of the Sun's light. It is interesting to trace the progress 
 of optical science (or rather its application to practical purposes) in con- 
 nexion with the question of the visibility of the smaller bodies of the 
 planetary system. Huyghens generally lost sight of the satellite dis- 
 covered by him, two days before its arrival in conjunction with the planet, 
 and did not again perceive it until two days after conjunction . Cassini 
 was unable to perceive the satellite immediately interior to that of 
 Huyghens, except at its greatest elongation from the planet, even when 
 its orbit was so open that at the time of conjunction it passed quite clear 
 of both the planet and the ring ||. Sir William Herschel, however, suc- 
 ceeded in keeping sight of every one of the seven satellites of Saturn 
 until they actually arrived in contact with his diskH. Perhaps some 
 future observer may succeed in accomplishing for the satellites of Uranus 
 what that illustrious astronomer achieved in respect to those of Saturn **. 
 The satellites of Uranus require telescopes of such a high degree of 
 perfection to render them barely discernible that, after Sir William 
 Herschel ceased to direct his attention to these remote bodies, any further 
 observations of them were for a long time neglected. This remark applies 
 
 * Phil. Trans., 1798, p. 78. f Ibid., 1815, p. 356. 
 
 $ Ibid., 1798, p. 76; ibid., 1815, p. 355. 
 
 Opera Varia, torn, ii., p. 524. 
 
 || Anc. Mem. Acad. des Sciences, tome x., p. 586. 
 
 f Phil. Trans., 1790, Part I., p. 7 ; also 1798, p. 74. 
 
 ** It results from the invisibility of the satellites of Uranus near conjunction, that the 
 eclipses of these bodies (which, on account of the great inclination of their orbits can 
 only take place on the occasion of the passage of the planet through either of the nodes) 
 >vill necessarily be invisible also. 
 
HISTORY OF PHYSICAL ASTRONOMY. 285 
 
 not merely to the four satellites alluded to by Herscliel at a later period 
 of his researches, the existence of which might be regarded as proble- 
 matical, but also to the two satellites originally discovered by him in 
 1787, the theory of whose motions he had brought to a state of consider- 
 able perfection. It does not appear that any astronomer obtained even a 
 sight of these faint objects until the year 1828, when Sir John Herschel 
 detected them with a 20-feet reflector. In order to verify the general 
 character of the views of his illustrious father, relative to the orbits of the 
 two satellites, and to obtain a fresh correction of their periodic times, the 
 same astronomer executed a series of observations of their angles of posi- 
 tion with the meridian, throughout the years 1830, 1831, and 1832. By 
 a skilful discussion of his father's observations of the second satellite, and 
 a similar treatment of his own, he obtained two epochs of the passage of 
 the satellite through the ascending node of its orbit, which embraced an 
 interval of 15122 d . 4 h 17 m , and included 1737 revolutions of the satellite. 
 Having calculated the duration of 1737 revolutions of the satellite, from 
 the periodic time, as determined by his father, he found it to be 
 15121 d 15 h 42 m 32 S .4. This was less than the time deduced from the 
 observations, by 12 h 34 ra 28 s . It followed, therefore, that the assumed 
 period was a little too short ; and from the number of revolutions com- 
 prehended between the^two epochs, it was easy to conclude, that the time 
 of each revolution required to be lengthened by 26 S .06. In this manner 
 Sir John Herschel obtained 8 d 16 h 56 m 3 1 s . 3 for the corrected period of 
 the satellite. By pursuing a similar process with respect to the fourth 
 satellite, he determined its periodic time to be 13 d ll h 7 m 12 s . 6. In 
 this case, therefore, his father's period required to be shortened by 
 l m 46 9 .4. The positions of the satellites, when calculated from their 
 corrected periods, and the inclination and node of their orbits, as deter- 
 mined by Sir William Herschel, exhibited an accordance with the corre- 
 sponding observations sufficiently close to establish the general accuracy 
 of the theory of both bodies. Sir John Herschel found that the observations 
 of the second satellite afforded pretty strong indications of ellipticity. He 
 also considered it very probable that the data of the fourth satellite might 
 prove to be equally indicative of elliptic motion, although it would be 
 premature to attempt the investigation of this part of the subject*. 
 
 The next astronomer who directed his attention to the satellites of 
 Uranus was M. Lamont, of Munich, who, in the autumn of 1837, made 
 several accurate observations of the second and fourth satellites with a 
 refractor of 15 feet focal length and 10 J inches aperture. The main object 
 of his observations was to determine the greatest elongations of the 
 satellites, with the view of arriving at an accurate knowledge of the mass 
 of the planet. He did not, however, omit to derive a new determination 
 of the periodic times of both satellites, by a comparison of his own obser- 
 vations with those of Sir William Herschel and his son. By means of 
 a series of micrometrical measures he determined the greatest elongation 
 of the second satellite to be 31".35, and that of the fourth to be 40".07. 
 He also obtained 8 d 16 h 56 m 28 S .5, and 13 d ll h 7 m 5 S .9 for the times of 
 the synodic revolutions of the two satellites f. 
 
 M. Lamont states, in his memoir, that he saw the most distant of the 
 six satellites of Uranus on the 1st of October, 1837. This was the only 
 verification that had been hitherto obtained of Sir William Herschel's 
 observations relative to the existence of other satellites of the planet 
 
 * Mem. Ast. Soc. vol. viii. p. 1, et seq. t Ibid., vol. xi. p. 51, et seq. 
 
286 HISTORY OF PHYSICAL ASTKONOMY. 
 
 besides those discovered by him in 1787. Additional light has been thrown 
 upon this interesting subject by the observations of astronomers during 
 the last few years. The first satellite, or the nearest of the six to the 
 planet, has been repeatedly observed by Mr. Lassel in this country, 
 and also by M. 0. Struve in Russia. Mr. -Lassel first saw the satellite on 
 the 14th of September, 1847. The observations of M. Otto Struve 
 date from the 8th of October of the same year. The Rev. W. R. 
 Dawes having instituted a comparison between the results of both these 
 astronomers, came to the conclusion that they are incompatible with 
 each other upon any supposition whatever relative to the elements of the 
 satellite, and upon this ground he has suggested the probability of there 
 being two satellites instead of one, revolving within the interior of the two 
 old satellites. By a discussion of the observations of Mr. Lassel, he found 
 that the apparent distance of the satellite is only 11", and the time of its 
 revolution 2 d 2 h 43 m 6 s . M. Otto Struve, from his own observations, 
 deduced 17". 5 for the distance of the satellite, and 3 d 22 h 10 ra for the 
 time of its revolution. The hypothesis of the existence of two distinct 
 satellites derives additional support from the fact that Mr. Lassel con- 
 stantly saw the satellite on the north side of the planet, while M. Otto 
 Sltruve, on the other hand, invariably saw it on the south side. The latter 
 of these astronomers has suggested that the satellite observed by him, like 
 the fifth satellite of Saturn, might lose much of its light in the northern 
 half of its orbit. Of course a similar remark is applicable, mutatis mu- 
 tandis, to the satellite observed by Mr. Lassel. It would appear, there- 
 fore, that, besides the observations of Mr. Lassel and M. Struve being 
 irreconcilable with each other, in so far as the motion of the body is con- 
 cerned, there exists*an essential distinction between the indications which 
 they severally afford, of the physical constitution of the satellite. 
 
 The third, or intermediate satellite, of Sir William Herschel, included 
 between the two satellites of 1787, was observed by Mr. Lassel on the Gth 
 of November, 1847. No indications of its existence appear to have since 
 been obtained by any observer. It is clear that much yet remains to be 
 done before anything like a satisfactory view of the Uranian system can 
 be arrived at. In the meantime it offers to the astronomer an interest- 
 ing field of observation and research; while it holds out in still more 
 distant prospective to the geometer, the grounds of one of the most curious 
 problems in physical astronomy. 
 
 The telescopic discovery of the planet Neptune by Dr. Galle, to which 
 allusion has been made in one of the preceding chapters, was soon 
 followed by the discovery of a satellite of the planet. The science of 
 astronomy is indebted for this interesting acquisition to Mr. Lassel, whose 
 important discovery in connexion with the Saturnian system (although 
 subsequent to the present in the order of time) we have already had 
 occasion to mention. On the 10th of October, 1846, Mr. Lassel, while 
 engaged in observing Neptune, perceived a small star near it which he 
 suspected to be a satellite, but as the planet was seon afterwards lost in 
 the rays of the sun, he was unable to obtain an assurance on this point 
 until the following year. Observations made on the 8th and 9th of July, 
 1847, proved to him, beyond all doubt, that the object he originally 
 perceived was in reality a satellite, and this conclusion was further 
 strengthened by repeated observations of it during the course of the two 
 following months. It was also observed soon afterwards, at Pulkowa, by 
 M. Otto Struve, and at Cambridge, U. S., by Prof. Bond. This inte- 
 resting discovery was made by Mr. Lassel, with a Newtonian reflector of 
 
HISTORY OF PHYSICAL ASTBONOMY. 287 
 
 20 feet focal length, and 2 feet aperture, which he had constructed with 
 his own hands. It was the first reward that crowned his successful 
 exertions to provide himself with the means of effectually exploring the 
 heavens, and it was one to which his ingenuity and perseverance had well 
 entitled him *. 
 
 As the satellite of Neptune supplies a method for determining the mass 
 of the planet, independent of that founded on the perturbations occasioned 
 hy the planet, its periodic time and greatest elongation are elements 
 the ascertainment of whose true values is manifestly an object of great 
 importance. Prof. Pierce of Harvard College, U. S., by combining the 
 observations of Messrs. Lassel and Bond, has found the periodic time of 
 the satellite to be 5 d 21 h 12 m .4 s and its greatest elongation to be 16".5. 
 The corresponding results which M. Otto Struve has deduced from his 
 own observations of the satellite, do not exhibit so close an agreement 
 with these numbers as is desirable. According to that astronomer the 
 periodic time of the satellite amounts to 5 d 21 h 15 m , and its greatest 
 elongation to 18". These different determinations of the periodic time 
 and distance of the satellite, of course, indicate different values of the mass 
 of the planet. The element which offers the principal difficulty to the 
 astronomer is the distance. Perhaps some time may elapse before its 
 value will be ascertained with sufficient precision, to justify the hope of 
 deducing from it the true value of the mass of the planet, an element of 
 so much importance in all researches relative to the movements of those 
 bodies upon which the planet exercises a sensible influence. From the 
 observations of the satellite, it appears that its orbit is inclined to the 
 ^)lane of the ecliptic at an angle of about 35, but it has not yet been 
 ascertained whether the motion is direct or retrograde. 
 
 Neptune offers an interesting analogy to the Earth, arising from the 
 circumstance of its being attended by only one satellite. When, how- 
 ever, the rapid advancement of astronomical science in recent times is 
 taken into consideration, it will readily be admitted, that it would be 
 unsafe to reckon upon the permanence of this analogy. Huyghens upon 
 his discovery of a satellite revolving round Saturn alluded with conscious 
 exultation to the resemblance existing between the planet and the earth 
 in this -respect, as furnishing an argument in favour of the Coperriican 
 system of the world of a much more conclusive kind than that supplied 
 by the satellites of Jupiter f . Saturn, however, had only accomplished half 
 a revolution in his orbit after this remark was made, when Cassini, by his 
 discovery of two additional satellites, put a term to the fancied resem- 
 blance between that planet and the earth. It must be admitted that 
 on this occasion at least, the advocate of the immobility of the earth for 
 such Cassini may be accounted to be gave an effectual reply to the 
 reasoning of his unwary antagonist. 
 
 * In connexion with the brief allusion in the text to Mr. Lassel's labours, it may not 
 be out of place to cite the following passage from the Report of the Council 
 of the Astronomical Society, setting forth the grounds upon which it was resolved to 
 award to him the gold medal of the Society for the year 1848. " The simple facts are, 
 that Mr. Lassel cast his own mirror, polished it by machinery of his own contrivance, 
 mounted it equatorially in his own fashion, and placed it in an observatory of his own 
 engineering. A private man, of no large means, in a bad climate, and with little leisure, 
 he has anticipated, or rivalled, by the work of his own hands, the contrivance of his own . 
 brain, and the outlay of his own pocket, the magnificent refractors with which the Em- 
 peror of Russia and the citizens of Boston have endowed the observatories of Pulkowa 
 and the Western Cambridge." Month. Proc. Ast. Soc., Feb. 1849. 
 
 f Opera Varia, torn, ii., p. 531. 
 
288 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Of the eighteen satellites which at present are recognised as belonging 
 to the planetary system, seventeen would have for ever remained unknown, 
 were it not for the aid afforded to human vision by the telescope. Nine 
 of these satellites have been discovered exclusively with the refracting, 
 and seven exclusively with the reflecting telescope. The remaining 
 satellite was discovered by the independent use of two telescopes, one 
 of which was constructed upon the refracting, and the other upon 
 the reflecting principle. Of the satellites discovered with the refract- 
 ing telescope, four (and these by far the most important of the seven- 
 teen) were discovered by the aid of a little instrument resembling in 
 principle the modern opera glass. Five were discovered with telescopes 
 of immense focal length, constructed upon the principle originally recom- 
 mended by Kepler. The achromatic telescope can boast of only one 
 triumph, and even that is shared with the reflecting telescope. Of the 
 satellites discovered with the reflecting telescope, two were discovered with 
 an instrument of 40 feet focal length, and 4 feet aperture ; two, including 
 the satellite discovered also with the refracting telescope, with an instru- 
 ment of 20 feet focal length, and 2 feet aperture ; and four with an 
 instrument of 20 feet focal length and 18 inches aperture. 
 
 There is no department of astronomical science which has been culti- 
 vated more assiduously in recent times than that relating to the move- 
 ments of Comets. The highly-improved state of the methods of calculation 
 relative to this subject, enable the astronomer with comparative ease to 
 trace back the motions of comets throughout anterior ages, and by con- 
 fronting the results so obtained with the contemporary records of ancient 
 comets, in many instances to deduce conclusions of an interesting and 
 valuable character. In this manner, it has been recently found that the 
 famous comet of Halley was observed by the Chinese astronomers on the 
 occasion of its passage of the perihelion in the year 1378. The earliest 
 authentic account of this comet, contained in European records, relates 
 to its passage of the perihelion in the year 1456. Halley suspected that 
 a comet which appeared in 1380 might be identical with the one of 1682, 
 but from the vague terms in which the ancient comet was alluded to, he 
 found it impossible to arrive at any trustworthy conclusions on this point. 
 No doubt, however, can exist with respect to the comet recorded in the 
 Chinese annals. It appears from the researches of M. E. Biot, that a 
 very conspicuous comet was observed in China in the year 1378. Tit first 
 appeared on the 26th of September, and it continued to be visible during 
 forty-five subsequent days. In the work containing the account of this 
 comet, there is also a minute description given of the route which it 
 traversed among the fixed stars during the period of its visibility. In 
 order to ascertain whether this comet was identical with Halley V, M. 
 Laugier reduced the elements of the latter comet to the perihelion 
 passage previous to that of 1456. The most delicate point of this en- 
 quiry was the determination of the time of the passage of the perihelion, 
 which, after various trials, he finally fixed on Nov. 8.77, 1378. Having 
 then calculated the position of the comet on the 26th of September, 1378, 
 and also various positions corresponding to the period included between 
 that date and the 10th of November (on which day the recorded comet 
 was. last visible), he found that the apparent path pursued by it agreed 
 exactly with that indicated by the observations of the Chinese Astrono- 
 mers*. The interval embraced between the perihelion passages of 1378 
 
 * Comptes Rendus, tome xvi., p. 1004; Connaissance des Temps, 1846. 
 
HISTORY OF PHYSICAL ASTltONOMY. 289 
 
 and 1456, is longer than any other period of the comet that has been 
 hitherto determined by observation *. 
 
 Besides the comets to which allusion has already been made in con- 
 nexion with the theory of gravitation, there are several other bodies of the 
 same class which have also been found to revolve in elliptic orbits. It 
 may be remarked that the question whether a comet returns periodically 
 to perihelion, or whether, after having once visited the solar system, it 
 then passes off definitively into the boundless regions of space, may admit 
 of being resolved in two different ways. The elements of two or more 
 comets may be compared together, and if they should present a close re- 
 semblance, it may be inferred that each set of elements refers merely to a 
 different return of the same body. This circumstance will, therefore, 
 serve to establish the periodicity of the comet, and the interval included 
 between two consecutive apparitions will indicate the time of revolution. 
 It was by means of such a comparison that Halley succeeded in establish- 
 ing the periodicity of the famous comet which bears his name, and in 
 predicting the time of its next return to perihelion. This was the only 
 mode of determining the time of a comet's revolution which Newton con- 
 sidered to be practicable, for he was of opinion that all comets, without 
 exception, revolve in very elongated ellipses, although for the sake of 
 simplicity it might be assumed that towards the perihelion the path of 
 each comet did not deviate sensibly from a parabola. The great im- 
 provements which have been effected in the methods of calculation since 
 Newton's time have emboldened astronomers in many instances to an- 
 nounce the periodicity of a comet, and to assign the time of its revolution 
 by means of observations made on the occasion of only one apparition. 
 This method is undoubtedly more direct and more generally applicable 
 than that founded on the comparison of different apparitions ; but the 
 results obtained by the employment of it have seldom turned out to be 
 satisfactory. The errors of observation bear so large a proportion to 
 the deviations from parabolic motion, which, in this case, form the real 
 data of the problem, and the arc described by the comet, during the period 
 of its being visible, is usually so small, that the values assigned to the 
 periodic time by different computers, have frequently exhibited a great 
 discordance. With respect to many of those comets to which elliptic orbits 
 have been assigned, their movements admit of being equally well repre- 
 sented by parabolas. It is only in those cases in which it is found to be 
 impossible to reconcile the actual motion of the comet with any parabola 
 whatever, that the application of the elliptic method maybe expected to 
 lead to trustworthy results. 
 
 The great comet of 1680 has been supposed to revolve in an elliptic 
 orbit. Halley, by comparing it with several ancient comets, was induced 
 to conclude that it accomplished a complete revolution in 575 years. 
 Euler and Pingre, severally, calculated its period from the observations 
 of 1680 ; but the results at which they arrived differed materially 
 
 * The following are the periods which have been derived from the recorded observa- 
 tions of the comet. 
 
 From 1378 to 1456 77.58 years. 
 
 1456 1531 , 75.21 
 
 1531 
 
 1607 
 1682 
 1759 
 
 1607 76.15 
 
 1682 74.91 
 
 1759 76.49 
 
 1835 . . . 76.68 
 
 The mean of these periods is 76.1 years. Comptcs Rendus, tome xvi. p. 1006. 
 
 U 
 
290 HISTORY OF PHYSICAL ASTBONOMY. 
 
 from each other, as well as from the period which Halley had deduced by 
 the light of historical records. 
 
 In the year 1264, A. D., there appeared a splendid comet, which was 
 visible both in Europe and China, From the resemblance of its appa- 
 rent path to that of a comet observed in 1556, it has been concluded 
 that the two bodies are identical. Such is the view of the subject which 
 has been taken by Pingre, Lalande, and various astronomers of the present 
 day. Mr. Hind, by a skilful discussion of the recorded observations, has 
 arrived at results which render still more probable the identity of the two 
 comets, If this be true, the comet ought to return again to perihelion 
 about the year 1848, the period being somewhere about 292 years. 
 Such would be the case if the motion of the comet was effected solely by 
 the central action of tfre sun. It is necessary, however, to take into ac- 
 count the effects of planetary perturbation in determining the precise time 
 of return to perihelion. This arduous task has been recently executed by 
 M. Bomme, a geometer of the Netherlands, who has found that the action of 
 the planets will retard the comet's arrival in perihelion until the year 1858 
 or 1860 *, It is to be hoped that the expected stranger will, in due time, 
 respond" to the elaborate calculations of which it has formed the subject. 
 
 The great comet of 1811 was found by Bessel to have a period of 3383 
 years. Several other astronomers who have calculated the elliptic ele- 
 ments of this comet have obtained results agreeing very nearly with each 
 other and also with that deduced by Bessel. Corqets which take such an 
 immense length of time to accomplish a single revolution, lose much of 
 the interest which the periodic character of their movements is otherwise 
 calculated to excite. The case is quite different with respect to such 
 comets as those of En eke, Biela, Faye, and De Vico, which may be ex- 
 pected frequently to return to perihelion during the average period of 
 human life. Two other comets have recently been found to revolve in 
 elliptic orbits of comparatively small dimensions. One of these was dis- 
 covered by M. Brorseu, on the 26th of February, 1846. Its period has 
 been determined to be about five years and a half. The last passage of 
 the perihelion took place on the 25th of January, 1846. The other 
 comet of short period was discovered by M. Peters, on the 26th of June, 
 1846. It has been found by M. D'Arrest that the observations of this 
 comet are capable of being represented by an elliptic orbit, with a period 
 of 5804 days, or about sixteen years. 
 
 The most splendid comet of the present century was that which appeared 
 in the early part of the year 1843. The following elements of its motion, 
 calculated by Sig. Capocci, will serve to give an idea of the orbit in which 
 it moves. They have been selected for this purpose on account of the peri- 
 helion distance coinciding almost exactly with the mean of the perihelion 
 distances arrived at by various other astronomers who have computed the 
 elements of the comet : 
 
 Passage of the perihelion, February 27,5643 
 
 Perihelion distance . 0.00538 
 
 Longitude of the Perihelion 277 52' 35" 
 
 Longitude of ascending Node 354 48' 50" 
 
 Inclination 35 56' 55" 
 
 Motion Pietrograde. 
 
 * Mr. Hind's elements of the comet of 1556, when employed as the basis of calcula- 
 tion, fix the passage of the perihelion in the year 1858. Halley's elements make the 
 passage two years later. 
 
HISTOBY OF PHYSICAL ASTBONOMY. 291 
 
 It appears from the above value. of the perihelion distance that the 
 comet approached nearer the sun than any other comet recorded in his- 
 tory. The great comet of 1680 had been hitherto the most remarkable 
 in this respect of all those comets whose elements had been determined, 
 having approached the sun's surface within one-third of his diameter. 
 The least distance of the comet of 1843 from the sun's surface did not 
 amount to more than one-seventh of the solar diameter. The comet, there- 
 fore, approached twice as near the sun as the comet of 1680. 
 
 The immense velocity of the comet of 1843, when revolving in the 
 neighbourhood of the sun, arising from the smallness of its perihelion dis- 
 tance, occasioned some extraordinary peculiarities in its motion. Thus 
 between the 27th and 28th of February it described upon its orbit an 
 arc of 292. Supposing it to revolve in an elliptic orbit, this would leave 
 only 68 to be described during the time which elapses until the next 
 arrival in perihelion. On the evening of the 27th of February it de- 
 scribed the whole of the northern part of its orbit, having occupied only 
 2 h ll m in passing from the ascending to the descending node. It was 
 twice in conjunction with the sun on the 27th of February. The first 
 conjunction took place at 9 h 24 m p. M. The comet was then revolving 
 beyond the sun. The second conjunction took place at 12 h 15 m p. M. 
 The comet was then passing between the sun and the earth. The time at 
 which this interesting event occurred, prevented astronomers from ascer- 
 taining whether the comet would have been visible when projected upon 
 the solar disk *. 
 
 It has been suspected that the comet of 1843 is identical with another 
 great comet which appeared in the same region of the heavens in the 
 year 1668, and which was visible at San Salvador in Brazil, at Bologna, 
 and Lisbon. On the evening of the 5th of March the comet was seen at 
 San Salvador by Father Valentine Estancel. It then appeared a little 
 above the western horizon. The tail measured 23 in length, and resem- 
 bled a huge beam of light, extending nearly in a horizontal direction 
 from west to south. Its light was so vivid that persons standing on the 
 shore were enabled to discern its reflexion on the sea ; but the head was 
 so small as to be scarcely visible f . The comet was observed by the same 
 individual on the 7th of March. Cassini observed it at Bologna on the 
 10th and 14th of the same month. Drawings of the direction of its tail, 
 as determined by him on those days, were afterwards communicated by 
 Maraldi to the Academy of Sciences J. It is a remarkable fact that if this 
 comet be supposed to have passed its perihelion on the 27th of February, 
 1668, the Brazilian observations, as well as those of Cassini, will be repre- 
 sented with sufficient accuracy by the orbit of the comet of 1843. This 
 would assign to the comet a period of exactly 175 years. 
 
 The elements of the comet of 1843 presented also a strong resem- 
 blance to those of a comet observed in 1689. The most discordant ele- 
 ment was the inclination, which, in the case of the latter comet, amounted 
 to 69 17' according to the calculations of Pingre. The same astronomer 
 found the passage of the perihelion to have taken place on December 1.6, 
 1689. Sig. Capocci, however, remarked, that if the comet be supposed 
 to have passed its perihelion on December 3, all the recorded obser- 
 vations will be accurately satisfied by the elements of the comet of 1843. 
 
 * Comptes Rendus, tome xvi., p. 642. f Cometographie, tome ii., p. 22. 
 
 Mem. Acad. des Sciences, 1702, p. 107. 
 
 u 2 
 
HISTORY OF PHYSICAL ASTRONOMY 
 
 Hence, in order to reconcile this conclusion with that arrived at relative 
 to the comet of 1668, it would be necessary to diminish the period of the 
 comet to 21 years. But there are other comets which astronomers have 
 suspected to be identical with the cornet of 1843, especially those of 
 1618 and 1702. Capocci, therefore, suggested the probability of the 
 period of the comet being somewhere about seven years, remarldng that 
 this hypothesis would afford a satisfactory account of numerous apparitions 
 of comets recorded in history. The opinions of this astronomer have re- 
 ceived a remarkable confirmation from the subsequent researches of Prof. 
 Pierce and M. Clausen. Prof. Pierce having recomputed the elements 
 of the comet of 1689, obtained 30 25' for the inclination of the orbit. 
 This result agreed almost exactly with that obtained for the inclination 
 of the comet of 1843. He also found the passage of the perihelion to 
 have taken place on December 2.1463, 1689. M. Clausen having 
 discussed the totality of the observations of the comet of 1843, found that 
 they would be best represented by supposing the comet to revolve in an 
 elliptic orbit, the period of which he fixed at 6.8 years. It is not easy to 
 reconcile this conclusion with the fact of the comet not having been 
 more frequently recognised on former occasions of its return to peri- 
 helion. This circumstance may be accounted for in some instances by 
 the peculiar position of the orbit of the comet, in others, perhaps, by 
 changes in its physical constitution, which may exercise a material in- 
 fluence on its visibility. 
 
 The physical constitution of comets forms a subject of research at once 
 so varied and extensive that it has been deemed expedient to devote a 
 separate chapter to an account of the labours of astronomers in con- 
 nexion with it. 
 
 CHAPTER XV. 
 
 General Aspect of Comets. Translucency of Cometic Matter Structure and Di- 
 mensions of the Envelope. Description of the Tail. Its Direction and Curva- 
 ture. Peculiarities of Structure Dimensions. Phenomena Observed during the 
 Passage of Comets through their Perihelia. Comet of Halley. Comet of 1799 . 
 Variation of the Volume of Comets. Hevelius. Newton. Struve. Herschel. 
 Dissolution of Comets. Historical Statement of Ephorus. Comet of Biela. Deve- 
 lopement of the Tail. Comet of 1680. Comet of 1769. Anomalous Appearances in 
 the Tail Instances of Remarkable Comets. Hypotheses respecting their Physical 
 Constitution. Theories of the Variation of a Comet's Volume. Newton. Valz. 
 Herschel. Theories of the Tails of Comets. Kepler. Newton. Electrical Theory. 
 Light of Comets. Appearance of Phases. Cassini. Cacciatore. Polarization of the 
 Light of Comets. Researches of Arago. Question respecting the Solidity of Comets. 
 Newton. Laplace. Smallness of a Comet's Mass. Ultimate condition of Cometary 
 Bodies. Opinions of Newton, Laplace, and Herschel on this point. 
 
 THE question relative to the constitution of Comets is one of the most in- 
 teresting in the whole range of celestial physics. There is something in 
 the sudden apparition and strange aspect of these bodies which is calcu- 
 lated to arrest the attention of the most careless observer of nature. In 
 former ages they were regarded with superstitious dread, as manifestations 
 of divine displeasure, and the harbingers of impending calamities. Every 
 feature in their appearance was gazed upon with intense anxiety, and was 
 assimilated, by the influence of an excited imagination, to the awe-inspiring 
 lineament of a supernatural phantom. In recent times, when a more ad- 
 
HISTORY OF PHYSICAL ASTRONOMY. 293 
 
 vaiiced state of civilization has led to juster views of celestial phenomena, 
 it has become an interesting branch of study to enquire into the nature of 
 comets, and the purposes which they fulfil in the economy of the material 
 universe. And although it must be acknowledged that little progress has 
 hitherto been made towards obtaining a satisfactory solution of these ques- 
 tions, still a multitude of facts have been disclosed by the observations of 
 astronomers, which have formed the groundwork of much ingenious specu- 
 lation, and have tended to throw some degree of light on the mysterious 
 subject to which they relate. 
 
 Comets exhibit various peculiarities by means of which they are readily 
 distinguishable from other bodies. The light by which they shine is 
 generally pale, compared with that of the planets or stars. The principal 
 part of their structure is the head, which presents the appearance of a ne- 
 bulous body, more or less condensed towards the centre. Within the head 
 a bright point is seen, approaching in lustre to a planet. This is called the 
 nucleus of the comet. The nebulosity of the head is surrounded by a 
 hazy contour, termed the coma. But the most remarkable part in the 
 structure of a comet is the tail, which appears as a long train of light 
 issuing from the head. Although these are the more prominent features 
 by which comets are in many instances characterised, they are found actu- 
 ally to exhibit a great variety of aspect. Multitudes of comets, which are 
 visible only in telescopes, present neither tail nor nucleus ; but merely re- 
 semble a round mass of vapours slightly condensed towards the centre. 
 Even of those comets which are visible to the naked eye there have been 
 some which did not exhibit the usual features of these bodies. The comet 
 of 1585, observed by Tycho Brahe, possessed neither tail nor coma, but 
 appeared perfectly round like a planet *. Various examples of the same 
 sort are to be found in the records of astronomical observation. 
 
 The substance of which comets are composed is characterised by an 
 extreme degree of tenuity. This has been inferred from the fact that 
 stars have been seen through them without exhibiting any sensible dimi- 
 nution of lustre. Even as early as the time of Seneca it was remarked 
 that stars were occasionally visible through the substance of comets. It 
 might well be supposed that the rude observations of ancient times would 
 be incapable of indicating delicate alterations of brightness, even although 
 they should exist. Modern astronomers, however, universally agree in 
 representing the translucency of cometic matter to be in most cases so 
 perfect as to offer no obstacle to vision. .Numerous observations might be 
 cited in confirmation of this fact. Thus, on the 9th of November, 1795, 
 Sir William Herschel observed the comet of that year pass centrally over 
 a telescopic double star of the eleventh or twelfth magnitude ; but, not- 
 withstanding this circumstance, the smaller of the two component stars 
 continued, during the whole time of the transit, to be distinctly visible f. 
 Olbers perceived a star of the tenth magnitude through the comet of 
 1802 ; but he was unable to persuade himself that it exhibited any dimi- 
 nution of its usual brightness. On the 7th of November, 1828, M. 
 Struve perceived a star of the tenth magnitude within a few seconds of 
 the brightest part of Encke's comet ; but the light of the star did not 
 seem to be enfeebled in the slightest degree. Sir John Herschel, in a 
 
 * Plane rotunda extitit ; nee ullam caudam aut barbam in unam magis quam in aliam 
 partem portendebat. (Epist. ad Landgrav. p. 13.) 
 
 *h Phil. Trans. 1796, Pt. I., p. 133. This comet was discovered by Miss Caroline 
 Herschel ; it has since been ascertained to have been an apparition of Encke's comet. 
 
294 HISTORY OF PHYSICAL ASTRONOMY. 
 
 paper on Biela's comet, which appears in the " Memoirs of the Astrono- 
 mical Society," has mentioned a fact which strikingly illustrates the trans- 
 parency of the substance of which comets are composed. The comet 
 having passed over a small cluster of stars of the sixteenth or seven- 
 teenth magnitude, the appearance presented was that of a nebula, partly 
 resolvable into stars. The most trifling fog would have effaced the stars ; 
 but in the present instance they still continued to be visible, although 
 the cometic matter interposed between them and the observer must have 
 been at least 50,000 miles in thickness*. It might be expected that a 
 star when seen through the substance of a comet would suffer an appa- 
 rent displacement, from the refraction exercised by the cometic matter 
 upon the rays of light proceeding from the star to the observer. No such 
 phenomenon, however, has ever been detected by any astronomer. An 
 important observation was made by Bessel, with the view of deciding this 
 interesting point, on the occasion of the last apparition of Halley's comet. 
 On the 39th of September, 1835, a star of the tenth magnitude ap- 
 proached within 7". 78 of the nucleus of the comet, but its apparent 
 position was not affected in the slightest degree f. It is manifest from 
 this circumstance that, unless the matter of which a comet is composed 
 differs in its essential properties from other material substances, it must 
 possess a degree of tenuity which is quite inconceivable. 
 
 The nebulosity in which a comet appears enveloped is, in some in- 
 stances, separated from the head by a dark space, indicative of a trans- 
 parent atmosphere. This formed one of the most striking features of the 
 great comet of 1811 J. On the side turned towards the sun there appeared 
 a semicircular ring of light enveloping the head, but maintained quite dis- 
 tinct from it by a dark interval of uniform breadth, through which small 
 stars were visible. The opposite extremities of the luminous semicircle 
 extended beyond the head in two slightly-diverging streams of light, occa- 
 sioning the appendage of the tail. By an attentive examination of the 
 different parts of the comet during the period of its visibility, Sir William 
 Herschel was conducted to a remarkable conclusion respecting its struc- 
 ture. From the circumstance of the semicircular envelope constantly 
 exhibiting the same appearance, he inferred that it was in reality a hollow 
 hemisphere ; for he justly remarked that, if it was similar in structure 
 to the ring of Saturn, it could not fail to undergo a sensible change of 
 apparent form, in consequence of the variable position which it assumed, 
 arising from the combined motions of the earth and the comet. The 
 darkness of the space between the luminous semicircle and the head arose 
 from the line of vision not traversing a sufficient depth of the nebulous 
 matter to render that part of the envelope visible. This will appear 
 manifest when it is considered that the hemispherical envelope was viewed 
 towards the centre in a direction almost perpendicular to its surface, 
 whereas in those parts where the semicircle was visible, the line of vision, 
 being a tangent to the surface of the envelope, traversed a much greater 
 depth of matter, and thereby occasioned a greater concentration of light. 
 From the transparency and uniform breadth of the dark interval which 
 
 * Mem. Ast. Soc., vol. vi., p. 99, et seq. 
 
 f Connaissance des Temps, 1840, Addit., p. 97. 
 
 t The year 1811 was distinguished by the apparition of two comets, of which by far 
 the more conspicuous was that which first became visible. This is the comet to which 
 allusion will be made on every future occasion, when speaking of the comet of 1811, 
 uuless the second comet be expressly mentioned. 
 
HISTORY OF PHYSICAL ASTRONOMY. 295 
 
 separated the envelope from the head, Herschel concluded that the 
 comet was encompassed by an elastic atmosphere. In accordance with 
 this supposition, the semicircular ring of light would represent a stratum of 
 nebulous matter suspended in the atmosphere of the comet, at a consider- 
 able distance from the head . 
 
 Observations of many other comets lead to the belief that they essen- 
 tially resemble in structure this comet of 1811, but in every case the 
 apparent form is modified by circumstances depending on the peculiar 
 constitution of each body. Thus although the dark interval interposed 
 between the envelope and the head was very apparent in the comet of 
 1811, yet in most instances such a phenomenon is not discernible. Its 
 absence may be accounted for by supposing the stratum of nebulous matter 
 to be of sufficient depth to cause it to be everywhere visible. Hence, 
 although it be suspended at a considerable elevation above the more con- 
 densed portion of the comet, the intermediate space will not be anywhere 
 apparent. 
 
 The extreme tenuity of the matter composing the head and the sur- 
 rounding nebulosity of comets has been already mentioned. On the other 
 hand, the dimensions to which these parts swell out is frequently enormous. 
 Herschel found that the head of the comet of 1811 had a diameter of 
 i'27,000 miles*. The diameter of the envelope was found by the same 
 astronomer to be at least 643,000 miles f. 
 
 It has been stated that within the head of a comet there is usually a 
 bright point termed the nucleus. This is the only part of its structure 
 which excites any suspicion of a solid substance. Some astronomers, 
 however, maintain that the nucleus is composed of nebulous matter, like 
 the other parts of the comet, differing from them only in the superior 
 condensation of its particles. An observation of the comet of 1825, by- 
 Sir John Herschel, tends to support this opinion. Having examined the 
 comet with a 10-feet Newtonian telescope, he perceived a stellar point 
 which seemed to indicate a solid nucleus. When he sought, however, to 
 obtain a stronger assurance on this point, by the aid of a 20-feet reflector, 
 the illusion was speedily dispelled. The comet now assumed the appear- 
 ance of a milky irresolvable nebula, the centre exhibiting a round disk, 
 with a brightness equal almost to that of a planet, but without a definite 
 outline or the least suspicion of a brilliant point J. Bessel's observations 
 of Halley's comet conducted him to a similar conclusion. When the 
 comet was examined with a low magnifying power, there appeared within 
 it a bright nucleus of measurable dimensions, but when a higher power 
 was applied to the telescope, no such phenomenon was any longer per- 
 ceptible . 
 
 It would seem from the observations of astronomers, that any indication 
 of a solid substance presented by cometary bodies is invariably dispelled 
 when the comet is examined with a magnifying power adequate to disclose 
 its nebulous structure. A decisive test of the real nature of the nucleus 
 of a comet would be afforded by an observation of its transit over a star. 
 Phenomena of this kind are of very rare occurrence ; but instances have 
 been mentioned by astronomers which go to support the opinion that the 
 nucleus of a comet is composed of a solid substance. Messier has stated, 
 that on the 18th of August, 1774, while engaged in observing the comet 
 
 * Phil. Trans., 1812, p. 121. f phil - Trans> > 1812 > P- 12a 
 
 | Mem. Ast. Soc., vol. ii., p. 486, et seq. 
 
 Connaissance des Temps, 1840, Addit., p. 81. 
 
296 HISTOBY OF PHYSICAL ASTEONOMY. 
 
 which Montaigne had recently discovered, he perceived a very small star 
 near it, and that after the lapse of about four hours another star became 
 visible in its vicinity. He remarked that the circumstance of the one 
 star being seen before the other could not be accounted for by supposing 
 the second star to have been originally obscured by the glare of the moon's 
 light, since it was equally bright with the first, and he, therefore, came to 
 the conclusion that it must have been actually hid behind the solid nu- 
 cleus of the comet *. Wartmann has also mentioned that in the year 1828 
 he witnessed the extinction of the light of a star of the eighth magnitude 
 by the passage of Encke's comet over it. Neither of these observations 
 have been deemed sufficiently trustworthy to warrant the conclusion that 
 the nucleus of a comet is in any instance a real indication of a solid body. 
 On the other hand, there is no decisive proof that the nucleus is wholly of 
 nebulous structure, for in all those cases that have been cited to demon- 
 strate the extreme tenuity of cometic matter, there has either been no ap- 
 pearance of a nucleus at all, or the comet has not passed centrally over the 
 celestial body. Bessel is of opinion that until some unequivocal transit of 
 the nucleus of a comet over a star be observed, it will be impossible to 
 arrive at any positive conclusion respecting its physical structure f. 
 
 Attempts have been made to determine the absolute magnitude of the 
 nucleus of a comet by the measurement of its apparent diameter. In 
 this manner Schroeter found that the nucleus of the comet of 1799 had a 
 diameter of 373 miles. Sir William Herschel, by a similar process, found 
 that the nucleus of the comet of 1807 had a diameter of 538 miles. The 
 same astronomer computed that the nucleus of the second comet of 1811 
 measured 2637 miles in diameter. These results are very uncertain, 
 in consequence of the smallness of the angles which the nuclei of comets 
 usually subtend ; moreover, the phenomenon of a nucleus may be wholly 
 illusory, as certain observations already cited would seem to indicate. 
 
 It has been stated that the tail of a comet usually appears as an exten- 
 sion of the nebulosity enveloping the head. The two luminous streams 
 composing it continue to appear quite distinct even at some distance from 
 the head, but towards their extremities they gradually become confounded 
 together by means of scattered light pervading the space between them. 
 An attentive examination of the appearance presented by the tail of the 
 comet of 1811, during the period of its visibility, led Sir William 
 Herschel to a conclusion respecting its structure, analogous to that which 
 corresponding observations of the envelope had suggested to him. He 
 found, in fact, that the two luminous streams proceeding from the op- 
 posite sides of the envelope continued to form the bounding sides of the 
 tail in every position in which the comet was viewed. This is the con- 
 sequence that would ensue if the tail had been in reality composed of 
 a hollow cone of matter attached at its narrower extremity to the hemi- 
 spherical envelope ; for the line of vision, being a tangent at the sides, 
 traversed a much greater depth of matter than towards the middle, 
 where it was perpendicular to the surface of the cone. 
 
 The direction in- which the tail extends relatively to the head is gene- 
 rally opposite to that in which the sun is situated. Appian is the first of 
 European astronomers who remarked this fact, having been led to its 
 discovery by his observations of the comet of 1531, and of four other 
 
 * Mem. Acad. des Sciences, 1775, p. 446. 
 
 f Connaissance des Temps, 1840, Addit., p. 98. 
 
HISTORY OF PHYSICAL ASTRONOMY. 297 
 
 comets which appeared between 1531 and 3539. Strictly speaking, in- 
 deed, the axis of the tail does not coincide exactly with the prolongation of 
 the line joining the sun and the comet. It generally inclines towards the 
 region in which the comet has been recently moving, and as the inclina- 
 tion increases with the distance from the head, it will necessarily exhibit 
 a slight curvature. This deviation of the tail from a rectilinear direction 
 is more especially remarkable when the comet is near the perihelion. It 
 has been generally found, also, that the tail appears brighter and better 
 denned on the convex or preceding side, than it does on the opposite 
 side *. 
 
 Although Appian has undoubtedly the merit of being the first of Euro- 
 pean astronomers who discovered that the direction of the tails of comets 
 is usually opposite to that of the sun, it appears from the researches of the 
 late M. Ed. Biot, that the same fact was known to the Chinese astronomers 
 at a much earlier date. In the annals of the Dynasty of Thong, which 
 reigned in China between the years 618 and 907 of the Christian era, 
 there is an account of a comet which appeared on the 22nd of March, 837, 
 and the following days. The account concludes with this remark, "In 
 general when a comet (literally a broom) appears in the morning, the tail 
 extends towards the west; when it appears in the evening it extends 
 towards the east. This is a constant rule."f 
 
 Comets have occasionally been observed, the tails of which have been 
 characterised by remarkable peculiarities ; Chesaux states, that the comet 
 of 1744 had six tails spread out in the form of an immense fan. Accord- 
 ing to Bessel, the comet of 1807 had two tails, one making an angle of 8 
 with the prolongation of the radius vector ; the other, which was fainter, 
 making an angle of 29 with it. The comet which appeared towards the 
 close of 1823 had tw r o tails, one extending in the usual direction, the 
 other turned almost towards the sun. Lateral tails have also been occa- 
 sionally seen. Thus, during the first three days of March, the great 
 comet of 1 843 was observed at Chili to have a lateral tail issuing from the 
 original one at a distance of L0 from the head, and extending to a much 
 greater length than the other J. 
 
 The tails of comets frequently exhibit an imposing aspect in conse- 
 quence of their immense apparent lengths. According to Longomontanus, 
 the great comet of 1618 extended over an arc of the heavens equal to 
 104. The tail of the comet of 1680 measured 90 at Constantinople. 
 Chesaux states that the six tails of the comet of 1744 varied in length 
 from 30 to 44. According to Pingre, the tail of the comet of 1769 
 appeared 97 long in tropical countries. The tail of the comet of 1843 
 was observed, under the same favourable circumstances, to extend over 
 an arc of 65. 
 
 It is to be remarked that the foregoing measures cannot be considered 
 as possessing the character of definitive results. The tail of a comet is, 
 in fact, found to vary in apparent length in different climates, indicating 
 thereby that its aspect depends, to a certain extent, on the state of the 
 
 * This phenomenon appears to have been first remarked in the great comet of 1618. 
 Wendelin, in a passage cited by Hevelius, describes it with great perspicuity in the fol- 
 lowing terms: " Cauda pro motu capitis tracta, instar cornu incurvabatur modice, 
 atque ad earn partem qua findebat sibi aetherem plane glabra densior erat ac compaction 
 retro vero solutior ac villosior." ( Cometographia, p. 455.) 
 
 f Comptes Rendus des Sciences, tome xvi. , p. 751. 
 
 Ibid., tome xvii., p. 362. 
 
298 HISTORY OF PHYSICAL ASTRONOMY. 
 
 atmosphere through which it is viewed. Thus, at Paris, the tail of the 
 cornet of 1680 was 62 long; at Constantinople it was 90. The tail of 
 the comet of 1769 was 43 long at London on the 9th of September. On 
 the same day it was 55 long at Paris ; at>the Isle of Bourbon it was 60; 
 at Teneriffe it was 75. On the llth of September it was 90 at sea ; at 
 the Isle of Bourbon it was 97*. The tail of the comet of 1843 did not 
 measure more than 40 in England or France ; in tropical countries it was 
 found to extend over an arc of 65. 
 
 The absolute lengths of the tails of some comets are still more calcu- 
 lated to excite surprise than their apparent lengths. The tail of the great 
 comet of 1680 was 96 millions of miles long. The tail of the comet of 
 1769 had an absolute length of 38 millions of miles. According to 
 Herschel, the tail of the comet of 1811 must have been more than 100 
 millions of miles long on the 15th of October. The tail of the comet of 
 1843 attained a length of 150 millions of miles. 
 
 The apparent breadth of the tail of a comet seldom exceeds a few 
 degrees. Each of the six tails of the comet of 1744 Was 4 broad. The 
 tail of the comet of 1811 was found by Herschel, on the 12th of October, 
 to have a maximum breadth of 6 45'. Small as these measures may 
 appear to be, they indicate absolute dimensions of very considerable mag- 
 nitude. Thus Herschel found that, on the 12th of October, the greatest 
 annular section of the tail of the comet of 1811 had an absolute diameter 
 of 1 5 millions of miles f. 
 
 It is obvious, from the foregoing results, that the volumes of the tails of 
 comets must be enormous. Nor is there any difficulty in accounting for 
 such vast emanations from the comparatively small dimensions of the 
 head, for such is the excessive tenuity of the substance composing the tail 
 of a comet, that a very small quantity of matter would suffice for its pro- 
 duction. Newton, with the view of illustrating this point, calculated that 
 if a globe of common atmospheric air, one inch in diameter, was expanded 
 so as to have an equal degree of rarity with the air situated at an elevation 
 above the earth's surface equal to the earth's semi-diameter, it would fill 
 the whole planetary regions as far as the sphere of Saturn, and would even 
 extend a great deal farther j. 
 
 The phenomena exhibited by one of the more conspicuous comets during 
 the period of its apparition afford unequivocal indications of the powerful 
 influence exercised by the sun upon the physical constitution of these 
 bodies. When a comet first becomes visible previous to its passage of the 
 perihelion, it usually presents the appearance of a pale nebulous body with 
 a point more or less bright in the centre, but without any trace of coma or 
 tail. As it continues to approach the sun the nebulosity becomes more 
 apparent, and the head exhibits an increased degree of brightness, on the 
 side which is turned towards the sun, subject, however, to variations of an 
 exceedingly irregular character. The tail at the same time comes into 
 view, and gradually increases in length. After the passage of the peri- 
 helion, the same succession of changes occurs in a reverse order, the comet 
 finally assuming the appearance presented by it when it first became 
 visible, and soon afterwards vanishing altogether from observation. The 
 phenomena witnessed on the occasion of the last apparition of Halley's 
 comet, both before and after the passage of the perihelion, are highly 
 
 * Cometographie, tome ii., p. 194. f Phil. Trans., 1812, p. 124. 
 
 J Princip., lib. iii., prop. 41. 
 
HISTORY OF PHYSICAL ASTRONOMY. 299 
 
 interesting and suggestive. Previous to the 2nd of October, 1835, the 
 comet presented merely a round nehulous disk, with a faint nucleus in the 
 centre. When observed by Bessel on the evening of that day, the nucleus 
 was found to have suddenly acquired a high degree of brilliancy, and from 
 it there appeared to issue, on the side towards the sun, a cone of light 
 which, after extending to a short distance from the head, was observed to 
 curl backwards, as if impelled by a force of great intensity directed from 
 the sun. This outstreaming cone continued to be visible, in the form of 
 a luminous sector of a circle, until the 22nd of October. When observed 
 from night to night it was found to vary constantly in magnitude and 
 brightness. The direction of the axis of the cone was also variable. 
 Bessel discovered, by a strict analytical investigation, founded on its 
 observed positions, that it oscillated to and fro on each side of the line 
 joining the comet and the sun. These oscillations were generally very 
 rapid, the lapse of a few hours in some instances sufficing to render them 
 sensible. It is a remarkable fact, that the night on which these inte- 
 resting phenomena first manifested themselves, was also signalized by the 
 commencement of the tail of the comet. It is impossible to doubt that 
 this appendage derived its origin from the nebulous matter which had 
 been in the first instance raised from the head by a force directed to the 
 sun, and was subsequently impelled by a powerful force in the opposite 
 direction. While these curious phenomena were in course of being 
 developed, the nucleus of the comet exhibited great variations of bright- 
 ness. On the 12th of October it presented to Bessel a measurable 
 diameter, when observed with a magnifying power of 179; it did not 
 even lose its planetary aspect until a power of 290 was applied. On the 
 14th it suddenly became much fainter. W T ith a power of only 90 it lost 
 the appearance of a solid body *. 
 
 When the comet was observed by Sir John Herschel at the Cape of 
 Good Hope, after its passage of the perihelion, the appearance presented 
 by it was totally different from what it had been a few months previously. 
 When examined through a telescope on the 25th of January, it did not 
 exhibit any trace of a tail, but simply resembled a round nebulous body 
 about 2' in diameter, surrounded by a coma of great extent. Within the 
 disk there appeared a small bright point, in a position somewhat eccentric, 
 from which there issued towards the circumference, in the direction opposite 
 to that of the sun, a ray of highly condensed light. The comet, in fact, 
 seemed to contain within it another miniature comet, having a nucleus, 
 head, and tail of its own, perfectly distinct from the surrounding nebu- 
 losity f. As the comet receded from the sun the head began to dilate. 
 
 * Connaissance des Temps, 1840, Addit., p. 82. 
 
 f A similar appearance was remarked in the great comet of 1618. The following 
 account of it, extracted from Kepler's " Treatise on Comets," may, perhaps, not prove 
 uninteresting to the reader: " Et quid probat evidentius eundem effluxum caudae 
 capite, quam illud mirabile, quod ut in cometa anni 1618, nucleus quidam, interior, 
 solidior, et luminosior ; sic in cauda radius singularis, specie medullee in arbore, A Romanis 
 inter initia in medio, a me et Schickardo posterioribus diebus ad alterum latus, est obser- 
 vatus ; quasi ut tota cauda toto capite, sic ilia conspicua pars caudae a conspicuo capitis 
 nucleo de lapsa sit (De Cornells, p. 103). The above description presents a remarkable 
 agreement in several points with Sir John Herschel's account of the curious phenomenon 
 witnessed by him in Halley's comet. From the circumstance of the nuclear ray having 
 been seen by Kepler towards one of the sides, instead of in the middle, as at Rome, 
 Pingre seems disposed to believe that it was no other than the ordinary luminous edge of 
 the comet's tail. Without insisting, as an objection to this conclusion, that there was 
 only one ray visible, it is evident, from Kepler's remark respecting the direct emanation of 
 
300 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 while at the same time its light grew fainter ; also, in consequence of suc- 
 cessive additions to its length, it gradually assumed the form of a section 
 of a paraboloid. The head, or rather the paraboloidal envelope, continued 
 to enlarge with extraordinary rapidity, maintaining all the while the utmost 
 regularity of form and sharpness of outline. At the same time it gradually 
 diminished in brightness, until at length it disappeared simply from want of 
 light to render it visible. In the direction of the axis of the paraboloid a faint 
 elongation finally appeared, indicative of a tail ; but no decided manifesta- 
 tion of such an appendage was witnessed on any occasion subsequent to the 
 passage of the perihelion. The nuclear ray continued to emit the same 
 vivid light, increasing in length and constantly maintaining a position 
 coincident with the axis of the paraboloid, until, after some time, it 
 gradually grew fainter, and finally ceased to be visible. The nucleus, on 
 the other hand, which at first did not seem to undergo any change, ulti- 
 mately exhibited a decided increase of relative brightness. When the 
 comet was last seen, on the 5th of May, 1836, it presented exactly the 
 same aspect as it did when it first became visible in the month of August 
 of the previous year. 
 
 Phenomena more or less resembling those above describe.d have been 
 found to manifest themselves on the occasion of the passage of all great 
 comets through their perihelia. It seems to be pretty well established, 
 that the more tumultuous changes usually take place during the period 
 when the comet is approaching the sun. Those which occur after the 
 passage of the perihelion appear to be of a more quiescent nature, indi- 
 cating the gradual relapse of the body into the condition in which it was 
 when originally seen after returning from aphelion. This circumstance 
 clearly points to the sun as the exciting cause of these wonderful 
 changes in the constitution of comets, whatever be the nature of the forces 
 which are called into operation by his agency. Sometimes, indeed, pheno- 
 mena of a rapidly fluctuating character are observed a little after the 
 passage of the perihelion. Such was the case with respect to the comet 
 of 1799, according to Schroeter. This comet passed its perihelion on the 
 7th of September. Nothing unusual in its appearance was remarked 
 until the 16th of that month, when Schroeter perceived that the nucleus 
 was suddenly reduced to two-thirds of its former size. Between the 20th 
 and 2 1st of the same month, the surrounding nebulosity had diminished 
 to the extent of one-fourth. On the 22nd the nucleus burst out with 
 renewed splendour, and continued to exhibit the same brilliant appearance 
 until the 25th, when it again became extremely faint. The fact of these 
 changes occurring after the comet had passed its perihelion is, doubtless, 
 to be ascribed in some degree to the peculiar constitution of the comet, 
 which may have rendered it less susceptible to the influence of the sun 
 than is usually the case; but more especially to the circumstance that the 
 accumulated effect of the sun's action may naturally be supposed not to 
 have attained its maximum until a little after the comet had begun to 
 recede from the sun. 
 
 It has been stated that the paraboloidal envelope of Halley's comet was 
 
 the ray from the nucleus, that the phenomenon was one of a totally different nature. 
 It is worthy of notice that the ray was first seen on the 30th of November, 1618. Its 
 appearance was, therefore, subsequent to the comet's passage of the perihelion, which, 
 according to Halley, took place on the 8th of the same month. Here, then, is another 
 point of resemblance between the phenomenon and the appearance of Halley's comet in 
 the early part of the year 1836. 
 
HISTOKY OF PHYSICAL ASTHOJSOMY. 301 
 
 observed to increase rapidly in dimensions after the passage of the peri- 
 helion. A similar enlargement of the comet of 1652 was found by Heve- 
 lius to take place as it continued to recede from the sun. According to 
 the calculations of that astronomer, the linear diameter of the comet had 
 increased, between December 20 and January 12, in the proportion of 
 1 to 24*. He mentions that when it was about to disappear it almost 
 equalled the sun in absolute magnitude. 
 
 The curious fact of a comet swelling out in dimensions as it continued 
 to recede from the sun, did not escape the attention of Newton. While 
 admitting it to be true, upon the authority of Hevelius, he remarked, on 
 the other hand, that comets diminish in volume in the course of their 
 approach to the sun, attaining their minimum dimensions a little after the 
 passage of the perihelion. Thus the comet of 1680, in the month of 
 November, appeared like a star of the first or second magnitude ; but in 
 the following month it did not exceed a star of the third magnitude f. 
 
 The interesting fact of a variation of the absolute magnitude of a comet 
 depending on its distance from the sun, does not appear to have attracted 
 any attention for a long time after the publication of the Principia. Pingre, 
 in his great work on Comets, denies the truth of Hevelius' statement respect- 
 ing the enlargement of the comet of 1652 in the course of its recess from the 
 sun, upon the ground that the observations of the comet, when rightly inter- 
 preted, do not lead to such a conclusion |. On the other hand, he appears 
 disposed to admit that comets diminish in volume as they approach the sun. 
 Both the alleged diminution previous to the passage of the perihelion, and 
 the subsequent enlargement, have been confirmed by the observations of mo- 
 dern astronomers. M. Struve established beyond doubt, by a series of micro- 
 metrical measures, that Encke's comet continually diminished in volume as it 
 approached the sun, on the occasion of its passage of the perihelion towards 
 the close of the year 1828. On the 28th of October, when the distance 
 of the comet from the sun was 1.4617, the diameter of the head was 79.4. 
 On the 24th of December, when the comet had arrived in perihelion, and 
 the distance was only 0.5419, the diameter of the head was 3.1 1|. The 
 comet, therefore, during the intermediate period, had diminished in linear 
 dimensions in the ratio of 25 to 1, and consequently it had collapsed into 
 about the sixteen-thousandth part of its original volume. Sir John Her- 
 schel's observations of Halley's comet are equally conclusive with respect 
 to an enlargement of volume having taken place simultaneously with the 
 recess of the comet from the sun. During the interval embraced between 
 the 25th of January, 1836, and the 1st of the following February, the 
 volume of the comet was found by that astronomer to have increased in 
 the proportion of 1 to 41.605 II. The different explanations which have 
 been advanced of the variation of a comet's volume depending on its dis- 
 tance from the sun will be noticed presently. 
 
 Since comets in some instances approach nearer the sun than any of the 
 planets, they experience a degree of heat Curing their passage of the perihe- 
 lion of which it is difficult to form an adequate conception. Newton calcu- 
 lated that the great comet of 1680, when passing through its perihelion, was 
 subjected to a heat 2000 times greater than that of red-hot iron. The comet 
 of 1843, which approached still nearer the sun, must have been exposed to 
 a heat of even greater intensity. Sir John Herschel has computed that the 
 
 * Cometographia, p. 331. f Principia, lib. iii., prop. 41. 
 
 $ Cometographie, tome i., p. 125. Ibid., tome ii., p. 193. || Annuaire, 1832. 
 1 Results of Astronomical Observations at the Cape of Good Hope, p. 404. 
 
302 HISTORY OF PHYSICAL ASTRONOMY. 
 
 heat received by its surface during the passage of the perihelion was 
 equal to that which would be received by an equal portion of the earth's 
 surface, if it were exposed to the influence of 47,000 suns, placed at the 
 common distance of the actual sun. He has also shown that the heat 
 to which the comet was subjected on the* same occasion must have ex- 
 ceeded the heat concentrated in the focus of Perkins' great lens in the 
 proportion of J24J to 1 ; although the heat in the latter instance was so 
 great as to have melted cornelian, agate, and reck crystal * ! It is not easy 
 to conceive how a flimsy substance such as that of which a comet appears 
 to be composed, can effectually resist such an intense heat so as not 
 to pe dissipated in space. The ingenious views of Laplace on this point 
 will be mentioned when we come to speak of the various hypotheses which 
 have been advanced relative to the physical constitution of comets. 
 
 A signal manifestation of the influence of the sun is sometimes afforded 
 by the breaking up of a comet into two or more separate parts on the occa- 
 sion of its approach to the perihelion. Seneca relates that Ephorus, an 
 ancient Greek author, makes mention of a comet which, before vanishing, 
 was seen to divide itself into two distinct bodies f. The Roman philoso- 
 pher appears to doubt the possibility of such a fact ; but Kepler, with cha- 
 racteristic sagacity, has remarked that its actual occurrence was exceedingly 
 probable *. The latter astronomer further remarked that there were some 
 grounds for supposing that two comets, which appeared in the same re- 
 gion of the heavens in the year 1618, were the fragments of a comet that 
 had experienced a similar dissolution. Hevelius states that Cysatus per- 
 ceived in the head of the great comet of 1618 unequivocal symptoms of a 
 breaking up of the body into distinct fragments. The comet, when first 
 seen in the month of November, appeared like a round mass of concen- 
 trated light. On the 8th of December it seemed to be divided into several 
 parts. On the 20th of the same month it resembled a multitude of small 
 stars . Hevelius states that he himself witnessed a similar appearance in 
 the head of the comet of 1661 ||. 
 
 The foregoing statements respecting the dissolution of comets cannot 
 be admitted without a certain degree of reserve, in consequence of the 
 imperfect nature of astronomical observation in early times. The case is 
 different with respect to Biela's comet, which was observed to separate itself 
 into two parts on the occasion of its approach to perihelion in 1846. The 
 circumstances relating to this remarkable event have been already alluded 
 to in a former chapter 11. It is impossible to doubt that it arose from the 
 divellent action of the sun, whatever may have been the mode of ope- 
 ration. 
 
 The developement of the tail of a comet is usually regulated by the 
 changes which occur in the head and nucleus. Its formation generally 
 commences when the comet is descending towards the sun, but in most 
 instances it does not acquire its greatest length, nor does it shine with its 
 full splendour, until a little after the passage of the perihelion. This is 
 what might naturally be expected, if the sun be supposed to be the prin- 
 cipal agent in the production of the tail. The following account of the 
 progress of the tail of the great comet of 1680 is extracted from Newton's 
 Principia. This comet passed its perihelion on the 8th of December. On 
 the 6th of November it exhibited the aspect of a round nebulous body. 
 
 * Outlines of Astronomy, p. 370. f Qusest. Nat., lib. vii., cap. xvi. 
 
 | De Cometis, p. 50. Cometographia, p. 341. 
 
 Cometographia, p. 417. II See p. 136. 
 
HISTOBY OF PHYSICAL ASTRONOMY. 303 
 
 On the llth the tail just became visible. When observed through a ten- 
 feet telescope it appeared half a degree long. On the 17th it was observed 
 at Rome to be more than 15 in length. On the 18th it appeared 3Q long 
 in New England. On the 12th of December it was observed at Rome to 
 be 70 long. On the 5th of January its length was found by Newton to 
 be 40, On the 25th it measured only 6 or 7, and appeared very faint. 
 On the 10th of February it was only 2 long. On the 25th the comet was 
 seen without a tail, and shortly afterwards disappeared entirely from 
 observation. 
 
 The following account of the progress of the tail of the great comet of 
 ] 769 will afford a still more striking illustration of the agency of the sun 
 in the developement of these singular appendages, inasmuch as all the 
 observations of the comet were made at the same place and by the same 
 individual. On the 8th of August, 1769, Messier, while engaged in explor- 
 ing the heavens with a two-feet telescope, perceived a round nebulous 
 body which turned out to be a comet. On the 15th of the same month 
 the tail became visible to the naked eye, and appeared to be about 6 in 
 length. On the 28th it measured 15. On the 2nd of September it was 
 36 long. On the 6th it was 49. On the 10th it was 60. The comet 
 having now plunged into the rays of the sun, ceased to be visible. On the 
 8th of October its passage of the perihelion took place. On the 24th of 
 the same month it reappeared, after emerging from the rays of the sun. 
 The tail now measured only 2 in length. On the 1st of November it 
 measured 6. On the 8th of the same month it was only 2| long. On 
 the 30th it measured 1^. The comet henceforward ceased to be visible*. 
 
 Sometimes the luminous streams which form the bounding sides of the 
 tail of a comet appear to undergo variations in their length of considerable 
 rapidity and magnitude. Phenomena of this nature were noticed by Her- 
 schel in the tail of the comet of 1811. He suspected that they arose from 
 a rotatory motion of the tail, which caused its different parts to be trans- 
 ported in succession to the apparent sides, whence, by supposing the hollow 
 cone of which it was composed to be irregularly terminated, a succession 
 of apparent changes would take place, resembling those actually perceived. 
 Similar variations, indicative of a rotatory motion, were also witnessed in 
 the tail of the comet of 1825, by Mr. Dunlop, at Paramatta. 
 
 Phenomena of a still more fleeting and irregular nature are alleged to 
 have been observed in the tails of comets. Kepler states that the tail of 
 the comet of 1607, which atone time appeared short, would, in the twink- 
 ling of an eye, become very longf. According to Cysatus, the tail of the 
 comet of 1618 exhibited undulations, as if it had been agitated by the wind. 
 Hevelius has mentioned that he perceived similar undulations in the tails 
 of the comets of 1652 and 1661 ; and Pingre has still more recently 
 asserted the same thing with respect to the comet of 1769. To this class 
 of phenomena may be referred a remarkable appearance witnessed in the 
 great comet of 1843. On the llth of March Mr. Clerihew, who observed 
 the comet at Calcutta, found that since the previous evening it had darted 
 forth a new tail, nearly twice as long as the original one, and forming with 
 it an angle of 18. This supplementary tail was not seen on any other 
 night during the visibility of the comet. 
 
 Before attempting to describe the various hypotheses that have been 
 formed respecting the physical constitution of comets, it may not be out 
 
 * Mem. Acad. des Sciences, 1775, p. 392, et seq, t De Cometis, p. 102. 
 
304 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of place to give a brief account, by way of illustration, of some of the more 
 remarkable apparitions of bodies of this class which have been recorded in 
 history. 
 
 Diodorus Siculus has stated that in the first year of the 102nd Olym- 
 piad (or the year 371 A.C.) there appeared in the heavens a train of light 
 of extraordinary splendour. This remarkable phenomenon was believed to 
 have presaged the destruction of the Achaian cities Helix and Buris. Aris- 
 totle alludes to the same comet in his treatise on Meteors. He says that 
 on the first night the head was not seen, having been too near the sun. 
 On the second night it had removed a little from the sun, and was visible 
 for a short time in the evening. After it set the tail was still seen as a 
 brilliant train of light, extending over a third of the heavens, or, in other 
 words, over an arc of 60. 
 
 In the year 43 A.C., during the celebration of the games in honour of 
 Venus, there appeared a comet at Rome, which could be discerned before 
 sunset. This celestial prodigy continued to be visible for eight successive 
 days. The poets flattered Augustus with the belief that it was the 
 departed soul of his great relative Julius Caesar, who had been recently 
 assassinated. It has been already mentioned that Halley suspected this 
 to be an apparition of the great comet of 1680. 
 
 In the year 1106, A.D., there appeared a magnificent comet, which was 
 visible over all Europe. Matthew Paris says that it was seen at a distance 
 of only one cubit from the sun. It is easy to conclude from this remark 
 that the comet was visible in the daytime. The head was small and 
 obscure, but the tail is stated by various writers to have been an object of 
 terrific splendour, which was seen like a fiery beam stretching from the 
 west towards the north-east regions of the heavens. This is also believed 
 to have been an apparition of the comet of 1680. 
 
 In the summer of 1264 a great comet appeared, which is mentioned by 
 almost every contemporary historian of Europe. An account of it is also 
 contained in the Chinese Annals, which presents a satisfactory agreement 
 with the statements of the western writers respecting it. This magnificent 
 comet is said to have been accompanied by a tail 100 long. It was gene- 
 rally believed that the object of its apparition was to announce the death 
 of Pope Urban IV., who expired in the following October. We have 
 already mentioned that this comet is supposed to be identical with a comet 
 which appeared in 1556, and that its return in the present day is expected 
 with a considerable degree of confidence by astronomers. 
 
 The year 1402 was distinguished by the appearance of two of the most 
 splendid comets recorded in history. The first became visible about the 
 middle of February. As it continued to approach the sun it increased in 
 magnitude and splendour, until at length, towards the end of March, it 
 became visible in broad daylight. The tail when first seen was short, but 
 it increased with great rapidity, and ultimately exhibited an immense 
 apparent length. 
 
 The second comet of 1402 appeared in the month of June. It was ob- 
 served in Italy, Germany, and the countries of the East. Like the first 
 comet of the same year, it was visible in the daytime. After sunset the 
 tail was seen extending from the horizon to the zenith. It is said to have 
 been so bright as to have eclipsed the light of the stars, but this is a mani- 
 fest exaggeration. 
 
 In the year 1456 there appeared a magnificent comet, which was visible 
 over all the countries of Europe. The tail is stated to have been 60 long. 
 
HISTORY OF PHYSICAL ASTRONOMY. 305 
 
 This comet spread universal consternation, in consequence of its apparition 
 being simultaneous with the capture of Constantinople by the Turkish 
 army. In order to ward off the evil consequences which might ensue from 
 its influence, Pope Calixtus II. ordered prayers to be offered up in all 
 the Western churches. He also issued a bull, in which he anathematized 
 both the Turks and the comet. It is hardly necessary to state that while 
 the followers of the crescent did not fail to acquire permanent possession 
 of the ancient capital of the Eastern Empire, notwithstanding the means 
 that were employed by the Papal Church to arrest their progress, so in like 
 manner the comet continued with the same tranquillity as formerly to pur- 
 sue its path throughout the heavens. This is now known to have been an 
 apparition of the famous comet of Halley. 
 
 According to Cardan, a cornet which appeared in 1532 was seen by the 
 inhabitants of Milan in full sunshine. This comet is supposed to be iden- 
 tical with one of those which appeared in 1402, and also with a comet 
 which subsequently became visible in 1661. 
 
 The comet of 1577 was one of the most conspicuous of modern times. 
 It was first seen by Tycho Brahe before sunset, as he was returning home 
 after taking some fish out of a pond. This comet is remarkable for being 
 the first that was demonstrated to revolve beyond the moon's orbit. 
 
 The seventeenth century is peculiarly fertile in great comets. It was 
 distinguished by two apparitions of Halley 's comet, namely, those of 1607 
 and 1682. The third comet of 1618 was one of the most splendid of 
 modern times. Its more remarkable features have been already mentioned. 
 The comet of 1652 is said by Hevelius to have been of such magnitude as 
 to have resembled the moon when half full ; only it shone with a pale 
 and dismal light. This comet is otherwise interesting to the astronomer 
 on account of the minuteness with which the various phenomena relating 
 to it have been described by the assiduous observer just mentioned. An 
 account has already been given of the huge comet of 1668, which was seen 
 in the countries of the south of Europe and in Brazil. The comet of 1680 
 is memorable for the magnificent tail by which it was accompanied ; for its 
 near approach to the sun ; but above all, for having furnished the data by 
 means of which the immortal Newton succeeded in demonstrating that 
 comets are guided in their movements by the same principle as that 
 which controls the planets in their orbits. The comet of 1689, which 
 was visible only in southern countries, had a tail 68 long. It has been 
 already mentioned that there exist good grounds for believing it to have 
 been identical with the great comet of 1843. 
 
 Although the eighteenth century is less prolific in apparitions of great 
 comets than that immediately preceding, it is notwithstanding distin- 
 guished by two of the most remarkable recorded in history. The comet of 
 1744 is one of the few comets which have been seen in full sunshine. On 
 the 1st of February it appeared more brilliant than Sirius. On the 8th it 
 equalled Jupiter. On the 1st of March it was visible to the naked eye at 
 one o'clock in the afternoon, five hours only having then elapsed since its 
 passage of the perihelion. The singular appearance of the tail of this 
 comet has been already mentioned. The comet of 1769 is especially me- 
 morable for the immense tail by which it was accompanied. 
 
 The first comet of 1811 was one of the most conspicuous of the present 
 century. It is especially remarkable for the length of time during which 
 it continued to be visible. The comet of 1843, to which allusion has been 
 so frequently made, was in many respects one of the most remarkable of 
 
 x 
 
306 HISTORY OF PHYSICAL ASTEONOMY. 
 
 modern times. Like a few other comets, it was visible in broad daylight. 
 At noon on the 28th of February it was distinctly seen without the aid of 
 glasses, by numerous persons congregated in the streets of the city of Bologna 
 in Italy. It then appeared to the east of the sun, at a distance from his disk 
 of about two diameters. On the same day it was seen under similar cir- 
 cumstances, in various parts of the world. When it had sufficiently extricated 
 itself from the rays of the sun to be visible in the evening, it appeared with 
 extraordinary magnificence, especially in tropical countries. The head 
 was very conspicuous, but the most striking part of the comet was the tail, 
 which resembled an immense beam of light, extending over an arc of 60 
 or 70. Unfavourable weather prevented this magnificent comet from 
 being visible in England or any of the northern countries of Europe previous 
 to the J 7th of March. On the evening of that day, a little after sunset, 
 the tail became visible in the western horizon, but the head had already 
 set. On the following evening the whole of the comet was seen. The 
 head was small, but the tail was a brilliant object, extending over an arc 
 of the heavens of about 40. It continued to appear with great splendour 
 on the following evenings, but it rapidly grew fainter, and finally disap- 
 peared altogether from observation about the beginning of April*. It has 
 been already mentioned that this comet is remarkable for having approached 
 nearer the sun than any other comet recorded in history. 
 
 It now remains to give some account of the various hypotheses that have 
 been formed respecting the physical constitution of comets, and of the 
 explanations that have been founded upon them, of the more prominent 
 phenomena exhibited by these bodies. Although Tycho Brahe, by prov- 
 ing that comets traverse the regions beyond the moon's orbit, transferred 
 them from the category of substances generated in the terrestrial atmo- 
 sphere, he still left the question undecided whether they are bodies 
 forming permanent members of the solar system, or whether they are 
 mere masses of vapour, liable to be dissipated into space by the action of 
 the sun or any other similar body near which they may happen to pass in 
 the course of their erratic movements. That comets are either wholly or 
 partially composed of a gaseous substance, appears to be admitted by every 
 philosopher who has sought to arrive at some definitive conclusion respecting 
 their physical structure. Kepler supposed them to be bodies of transient 
 duration, which spin out their fleeting existence by a process Of evapora- 
 tion conducted through the medium of their tails. Newton, on the other 
 hand, was of opinion that comets are composed of a partially solid sub- 
 stance. He imagined that the matter susceptible of evaporation forms an 
 extensive atmosphere round the comet, which is gradually dissipated into 
 space by the action of the solar heat, the vaporised particles, as in Kepler's 
 theory, occasioning the appendage of the tail in the course of their recess 
 from the head. According to another hypothesis, the nebulous matter thus 
 raised from the comet is not wholly projected into space, the greater por- 
 tion being again precipitated upon the head, in consequence of the dimi- 
 nution of temperature which takes place during the comet's recess from 
 the sun. 
 
 It has been already mentioned that the assertion of Hevelius, respecting 
 the variation of the volume of comets depending on their distance from 
 the sun, has been confirmed to a certain extent by the observations of 
 
 * For a great number of interesting particulars relative to this remarkable comet, see 
 the Comptes Rendus, tome xvi., pp. 597, 605, &c. &c. &c, 
 
HISTORY OF PHYSICAL ASTflONOlUY. 307 
 
 modern astronomers. Newton's theory of the projection of the cometic 
 atmosphere into the tail, and its subsequent dispersion into space, suffi- 
 ciently accounts for the diminution of volume previous to the passage of 
 the perihelion ; but it is difficult to explain by the same theory the enlarge- 
 ment observed to take place during the comet's recess from the sun. It 
 was probably with a view to obviate this difficulty that he threw out the 
 conjecture of the comet being enveloped in a dense smoke during its pas- 
 sage of the perihelion, arising from the intense heat to which it was then 
 exposed. The presence of such a smoke would cause the comet to appear 
 less in perihelion than it really was ; while its gradually less abundant 
 emission as the comet continued to recede from the sun would give rise to 
 an apparent enlargement of volume. It is hardly necessary to state that 
 this is a mere surmise to which no importance can be attached as an expla- 
 nation of a fact established by accurate observation. M. Valz has recently 
 attempted to account for the diminution of the volumes of comets on 
 approaching the sun, and their subsequent enlargement, by the compres- 
 sion which they undergo in the course of traversing the solar atmosphere. 
 This view of the origin of the phenomenon necessarily implies that the 
 comet is absolutely impermeable to the highly-attenuated fluid through 
 which it is assumed to revolve, a condition which is utterly incompatible 
 with all that observation has revealed to us respecting the structure of 
 these bodies. A more probable explanation has been suggested by Sir 
 John Herschel. According to that astronomer, as the comet approaches 
 the perihelion the action of the solar heat will be constantly transforming 
 the nebulous matter of which it is composed into the condition of a trans- 
 parent invisible gas ; and as this process necessarily commences at the 
 exterior of the nebulosity, where the solar rays impinge, the immediate 
 consequence will be a diminution of the volume of the comet. After the 
 passage of the perihelion, the radiation of heat from the surface of the 
 more condensed portion of the comet will not be sufficiently compensated by 
 the solar heat, and the diminution of temperature hence arising will occa- 
 sion a precipitation on the surface of the nebulous matter suspended in a 
 gaseous state in the atmosphere of the comet. This precipitation of 
 nebulous matter will continue to go on under the influence of the cooling 
 process occasioned by the increasing distance of the comet from the sun, 
 and the manifest result will be a rapid enlargement of the visible dimen- 
 sions of the comet. According to the laws of equilibrium the lighter par- 
 ticles of the precipitated vapour will arrange themselves so as to form the 
 superior stratum of the enveloping nebulosity of the comet. It is evi- 
 dent also that as this bounding stratum continues to diminish in density 
 it will attain a higher and higher elevation, while at the same time its 
 increased tenuity will cause it to assume a more and more filmy aspect *. 
 This view of the physical condition of the nebulosity of a comet subsequent 
 to the passage of the perihelion has received a strong confirmation from 
 the observations of Halley's comet by Sir John Herschel, who found that 
 simultaneously with the increase of its dimensions the envelope continually 
 grew fainter, until at length from this cause alone it ceased to be visible. 
 
 According to the above theory the growing faintness of the envelope is, 
 in a great degree, occasioned by the gradual absorption of the vaporous 
 matter composing it, into the nucleus of the comet. This was clearly 
 indicated in the case of Halley's comet by the brilliant appearance of the 
 
 * Mem. Ast. Soc., vol. vi., p. 99, et seq. 
 
308 HISTORY OF PHYSICAL ASTRONOMY. 
 
 nuclear ray during the earlier observations of the comet, and the increase 
 of relative brightness exhibited by the nucleus itself when the ray finally 
 disappeared. The conclusion naturally suggested by these physical 
 changes was, that the nebulous matter composing the paraboloidal enve- 
 lope of the comet was conducted again to the nucleus along the axis of 
 the paraboloid, and that the ultimate brightness of the nucleus was due to 
 the increased condensation of its constituent molecules, resulting partly 
 from the accession of the matter composing the envelope, and partly from 
 an actual diminution of volume consequent on its diminishing tempera- 
 ture. 
 
 The foregoing theory of the variation of the volume of a comet depend- 
 ing on its distance from the sun, is mainly founded on the principle that 
 the nebulous matter of the comet is susceptible of being transformed by 
 the heat of the sun into the condition of a transparent invisible gas ; and 
 that so long as the comet is in the neighbourhood of its perihelion it is 
 actually encompassed by such an atmosphere. It has been already men- 
 tioned that the observations of the comet of 1811 afforded unequivocal 
 evidence of the existence of a transparent atmosphere ; for upon no other 
 supposition could the dark interval which separated the envelope from the 
 head be satisfactorily explained. When the precipitation of the nebulous 
 matter of the envelope rendered this' interval no longer visible, it was im- 
 possible to obtain any direct assurance respecting the atmosphere ; but 
 that it still continued to surround the comet Herschel received an indu- 
 bitable proof in the re- appearance of the envelope on the 9th of December, 
 1811*. This indication of a second stratum of nebulous matter lasted 
 only a few days, and was doubtless occasioned by some circumstance 
 peculiar to the constitution of the comet. 
 
 In all speculations on the physical constitution of comets the most 
 interesting point of enquiry is that relating to the origin of the tails of 
 these bodies. The earlier astronomers, including Appian, Cardan, and 
 Tycho Brahe, supposed the phenomenon of a comet's tail to arise simply 
 from the passage of the solar rays through the nebulosity of the head, 
 comparing it to the appearance presented by a beam of light which has 
 been transmitted through a small aperture into a dark chamber. It does 
 not seem to have occurred to these theorists, that the beam of light in the 
 latter instance becomes visible only in consequence of the presence of 
 floating molecules of matter which obstruct the solar rays and reflect 
 them to the eye of the spectator t. 
 
 The opinion of the Cartesians, although based on a more rational 
 principle, involved conclusions totally inconsistent with observation. 
 They imagined the tail of a comet to be occasioned solely by the refrac- 
 tion which the ether of the celestial regions exercised upon the rays of 
 - light proceeding from the comet to the observer. If this were true, the 
 light of the tail ought to exhibit the various colours of the prismatic 
 spectrum. Upon the same supposition the planets and fixed stars should 
 also be accompanied by tails. Neither of these conclusions, however, are 
 borne out by the observations of astronomers. Moreover, according to 
 this hypothesis, the deviation of the tail from the prolongation of the 
 
 * Phil. Trans., 1812, p. 129. 
 
 t Pingre, alluding to this absurd hypothesis, cites Newton and Gregory as having 
 remarked that it was at variance with the fundamental principles of optical science. The 
 same objection, however, had already been clearly pointed out by Kepler. (JDe Co- 
 metis, p. 101.) 
 
HISTORY OF PHYSICAL ASTfiOKOUY. 309 
 
 radius vector should always be in the same direction when the comet 
 appears in the same region of the heavens. Newton, however, has 
 remarked that, although the comet of 1577 occupied the same apparent 
 position on the 28th of December which the comet of 1680 occupied on 
 the 29th of the same month of the year, and although the earth, in both 
 cases, was consequently in the same part of her orbit, the tail of the 
 comet of 1577 deviated 21 towards the south, whereas on the other hand 
 the tail of the comet of 1680 deviated 4^ towards the north*. It follows, 
 therefore, that the supposition of the phenomenon being due to the 
 refraction which the light of the comet suffers in passing through the 
 celestial regions is inconsistent with observed facts, and is consequently 
 untenable. Another opinion respecting the tails of comets is that which 
 supposes them to be appearances similar to the aurora borealis. A theory, 
 founded upon this view of the subject, was proposed by Mairan, but its 
 inconsistencies were too glaring to secure even its partial adoption. 
 
 According to the various hypotheses hitherto considered, the tail of a 
 comet is merely an optical illusion, having no real foundation in nature. 
 Another class of hypotheses is that according to which they are imagined 
 to be composed of a material substance similar to the nebulosity of the 
 comet. Some persons, adopting the maxims of the Aristotelian philosophy, 
 respecting light and heavy bodies, supposed that the matter composing 
 the atmosphere of comets was an essentially light substance; that in 
 virtue of its inherent levity it had a constant tendency to recede from the 
 sun ; and that hence originated the appendage of the tail. It is hardly 
 necessary to state that this hypothesis is at variance with the fundamental 
 property of the inertia of matter and the recognised principle of universal 
 gravitation. 
 
 The first approach to anything resembling a rational explanation of the 
 tails of comets is unquestionably due to Kepler. According to that 
 illustrious astronomer a comet is composed wholly of a nebulous substance, 
 the constituent parts of which are gradually broken and dispersed by the 
 incessant action of the solar rays upon them. The lighter particles yield 
 to the impulse of the rays, and, proceeding to an immense distance from 
 the head of the comet, occasion the appendage of the tail. The denser 
 particles remain behind and form the nebulosity surrounding the headf. 
 This hypothesis furnished a satisfactory account of the general direction 
 of the tails of comets. It also afforded an explanation of their curvature 
 and their concavity with respect to the region which the comet was 
 leaving ; for it is manifest that as the comet continued to revolve in its 
 orbit, the nebulous particles impelled by the solar rays would lag some- 
 what behind the prolongation of the radius vector, and that the effect so 
 produced would be greatest for the particles which had ascended the 
 earliest, or, in other words, for the particles most remote from the head. 
 Another advantage of this hypothesis was that of referring the phenomenon 
 to a true physical cause ; for it can hardly be doubted, whatever be the 
 mode of the propagation of light, that the solar rays, if interrupted in 
 their progress by a material substance, must communicate to it an impact 
 of some degree of intensity. On the other hand it must be admitted that 
 the cause assigned, although founded in nature, cannot, with any degree 
 of probability, according to Kepler's view of it, be considered sufficient to 
 produce the observed appendage of the comet. A material improvement 
 
 * Princip., book iii., prop. 41. t De Cometis, p. 100. 
 
310 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of the hypothesis of that astronomer consisted in introducing the solar 
 heat as one of the exciting causes of the phenomenon. The first person 
 who appears to have explained the formation of the tails of comets upon 
 this more enlarged view of the action .of the sun was Claude Comiers, 
 a French writer, who flourished ahout the middle of the seventeenth 
 century. He supposed the particles composing the nebulosity of the 
 comet to be rarefied to so great a degree by the heat of the sun, as to yield 
 with facility to the impulse of the solar rays, and, acquiring from this 
 cause a motion in the direction opposite to the sun, to form an appendage 
 to the comet represented by the phenomenon of the tail*. The theory of 
 Kepler, thus improved, presented itself to the mind of the enquirer under 
 a much more favourable aspect than previously ; for, however feeble might 
 be the dynamical influence of the solar rays, it was possible, without ex- 
 ceeding the bounds of a rational probability, to ascribe the phenomenon to 
 their agency, by supposing an adequate attenuation of the nebulous matter 
 of the comet, arising from the calorific power of the rays. No further 
 notice appears to have been taken of this theory until the time of Whiston, 
 who explained it with great clearness in his work entitled " A New Theory 
 of the Earth, "f It was soon afterwards referred to by Euler as the most 
 satisfactory explanation of the phenomenon that had been hitherto devised; 
 and upon the same ground it has been favourably mentioned by many 
 subsequent astronomers and mathematicians, including in more recent 
 times Sir William Herschel, Laplace, Delambre, and Arago. 
 
 Newton, in the Principia, has entered into some interesting speculations 
 on the physical constitution of comets, in the course of which he discusses 
 the various hypotheses that had been formed with a view to account for 
 the origin of the tails of these bodies J. Of these, the hypothesis of Kepler, 
 founded on the impulsion of the solar rays, appeared to him to be the only 
 one which offered any degree of probability ; but his mind was too much 
 pre-occupied with an hypothesis of his own upon the subject, to allow him 
 to give the full sanction of his authority to it. Newton's view of the 
 origin of the tail of a comet was this: he supposed the rays of the sun, 
 by their calorific influence, to raise the temperature of the nebulous 
 particles of the comet, which, in their turn, communicated a portion 
 of the heat thus acquired to the contiguous particles of the ethereal 
 fluid composing the solar atmosphere. This increase of temperature 
 being accompanied by a corresponding diminution of density, the par- 
 ticles of the ether ascended to a greater distance from the sun, 
 carrying along with them the more volatile particles of the comet in 
 the same manner as an upward current of air causes smoke to ascend 
 in the terrestrial atmosphere . The general direction of the tail, its de- 
 
 * Traite de la Nature et Presage des Cometes, p. 81. 
 
 f- See p. 52 of the work cited. f Prin., lib. iii., prop. 41. 
 
 L" Newton," says Lalande ( Ast., tome iii., art. 3212), " supposed the tails of comets 
 emanations from their atmospheres. He remarked that smoke and vapours may 
 
 rays, or, more probably, from the rarefaction which the solar heat produces in their atmo- 
 spheres." It does not seem to have occurred to the astronomer just cited, (unless in- 
 deed he threw the responsibility of the omission upon Newton,) that without the additional 
 supposition of a solar atmosphere, the vapours of the comet, if rarified by heat, would 
 extend equally in all directions from the head. In the very next article of the work 
 cited, he gives a clear description of Newton's theory, ascribing it, however, not to that 
 philosopher, but to Boscovich, and stating that it first appeared in a work published by 
 him at Rome in the year 1746. 
 
HISTORY OF PHYSICAL ASTRONOMY. 311 
 
 viation from a straight line, and its convexity with respect to the region 
 towards which the comet was advancing, were explained by this theory 
 with the same facility as by Kepler's. Notwithstanding these advantages, 
 it met with a reception from men of science, which forms a striking con- 
 trast with that experienced by the other physical theories of its author. 
 This circumstance is, perhaps, in some degree attributable to Newton's 
 assumption of a principle whose existence was unsupported by any positive 
 evidence, a fault which that illustrious philosopher so cautiously avoided 
 in all his other speculations. It may be remarked, however, that cometary 
 phenomena are not altogether wanting in indications of a solar atmosphere, 
 or some such ethereal fluid, pervading the celestial regions. It has been 
 already mentioned that the motion of Encke's comet seems to indicate the 
 existence of such a fluid-. Another fact, which has been more generally 
 established, tends also to suggest the suspicion of the comet moving 
 through a resisting medium. It has been mentioned that the tail of a 
 comet is usually brighter and better defined on the convex than on the 
 concave side. Now, this is the result which might naturally be expected 
 to be produced by the motion of the comet through a resisting medium ; 
 for as the convex side of the tail is also the preceding side, it is the part 
 that would be mainly exposed to the pressure of the ethereal fluid ; and 
 being, in consequence, more condensed, it ought to appear more luminous, 
 and to present a sharper outline than the concave side. Newton, indeed, 
 gave a different explanation of this phenomenon. He considered it to 
 arise from the circumstance that the particles composing the preceding 
 side of the tail, had more recently ascended from the head of the comet 
 than the other particles, and therefore that less time was allowed for their 
 diffusion in space f. It is not improbable that the superior brightness 
 and clearer definition of the convex side of the tail may be due to the 
 combined operation of both these causes. 
 
 Newton's theory of the tails of comets may perhaps be considered 
 equally satisfactory with that which refers them to the action of the solar 
 rays upon the more volatile particles of the cometic atmosphere; but 
 neither the one nor the other can be regarded as anything else than a 
 vague hypothesis, which, although it affords an explanation of a few of the 
 more prominent features of the phenomenon, is incapable of conducting 
 to results of any precision, and totally fails to render an account of minute 
 details. Thus, although the general direction of the tails of comets is 
 accounted for sufficiently well either by the dynamical action of the solar 
 rays upon the cometic atmosphere, or by their calorific agency, assuming 
 the existence of a solar atmosphere, it is utterly impossible to explain, by 
 either of these principles, such a phenomenon as that presented by the 
 comet of 1823, which had one tail extending in the usual direction, and 
 another turned almost completely towards the sun. Many other anoma- 
 lous appearances are equally inexplicable by either of the two hypotheses 
 just mentioned. A more recent view of the subject is founded upon the 
 supposition of the phenomenon being due to electrical agency. One of 
 the earliest advocates of this mode of explanation was the German astro- 
 nomer Olbers. In more recent times it has been favourably noticed by 
 Bessel, Biot, and Sir John Herschel. The limits of this work prevent 
 any further allusion to it here. It may be remarked that in the present 
 state of our knowledge respecting the nature and mode of operation of the 
 
 * Seep. 135. f Princip., lib. iii., prop. 41. 
 
HISTORY OF PHYSICAL ASTRONOMY. 
 
 electrical principle, it is utterly hopeless to arrive at any reliable con- 
 clusions by means of a theory founded upon the supposition of its 
 agency. 
 
 The question whether comets are self luminous, or whether they are 
 indebted for their light solely to the sun, has often been discussed by 
 astronomers. The high magnifying powers that these bodies in some 
 instances support, tend to favour the conclusion that they are self lumi- 
 nous. It was upon such grounds that Herschel concluded that the comet 
 of 1807, and the first comet of 1811, shone by a light essentially inherent 
 in their respective substances *. Bessel was of opinion that the sudden 
 variations of brightness exhibited by Halley's comet in the month of 
 October, 1835, could with difficulty be accounted for by any other suppo- 
 sition than that of a developement of light by the substance of the comet f. 
 It is manifest that the appearance of phases in comets, if established be- 
 yond doubt, would afford a decisive proof that these bodies shine only by 
 reflection. It has been asserted that phases, in some instances, have 
 been actually observed, but such statements have not been supported by 
 the observations of contemporary astronomers. Delambre mentions that 
 the registers of the Royal Observatory of Paris exhibit unequivocal indi- 
 cations of phases in the comet of 1682. It is to be remarked, however, 
 that neither Halley, nor any 'other astronomer who observed this comet, 
 makes mention of such a fact. Again, James Cassini states that the 
 comet of 1744 exhibited phases which would have been as distinct as 
 those of Venus if the disk had been somewhat larger J. On the other 
 hand, Heinsius and Chesaux, who both observed the comet with especial 
 attention, have explicitly denied the existence of any indications of such 
 a phenomenon. In more recent times Cacciatore, the celebrated Italian 
 astronomer, expressed his positive conviction that the comet of 1819 
 presented the appearance of a crescent. It was found, however, that the 
 position he assigned to the line joining the horns of the crescent was in- 
 compatible with the supposition that the comet shone by the light of the 
 sun. Sir William Herschel was unable to discover anything resembling 
 a phase in the comet of 1807, although he assured himself, that a con- 
 siderable portion of the disk could not have been illuminated by the sun 
 at the time of observation . The observations of subsequent astronomers 
 have also been generally unfavourable to the existence of phases ||. 
 
 Although observations indicating the existence of phases in comets 
 would establish beyond all doubt that these bodies shine by reflected 
 light, it must be admitted on the other hand that the absence of such 
 phenomena does not warrant the conclusion that comets are self luminous. 
 With reference to this point it is to be remarked, in the first place, that 
 if a comet consists of a mere globular mass of vapours, it will offer no 
 effectual opposition to the passage of the solar rays, and, consequently, it 
 will reflect light with equal facility from every part of its surface. Nay, 
 if the comet should offer unequivocal indications of the existence of a 
 nucleus, since in every such case the surrounding nebulosity is of im- 
 mense extent, it is difficult to conceive how a different result can take 
 
 * Phil. Trans., 1808, p. 157; ibid., 1812, p. 119. 
 
 f Connaissance des Temps, 1840. Addit. p. 98. 
 
 | Mem. Acad. des Sciences, 1744, p. 303. Phil. Trans., 1808, p. 156. 
 
 || Sir John Herschel has remarked that nothing which could bear the least resemblance 
 to a phase was perceptible in Halley's comet. (Results ofAst. Obs. at the Cape of Good 
 Hope, p. 397. ) 
 
HISTORY OF PHYSICAL ASTRONOMY. 013 
 
 place, even if the nucleus be composed of a solid substance. But, in fact, 
 the nuclei of comets are so very small, that even under the most favour- 
 able circumstances the discovery of phases might naturally be expected to 
 elude the most delicate observations *. 
 
 A very different method has been devised by M. Arago for ascertaining 
 the nature of the light by which comets shine. It is well known that 
 Avhen light is reflected from a body at certain angles, it acquires properties 
 different from those which characterize light emitted directly from a self lu- 
 minous body ; or, in other words, the light thus reflected becomes polarized. 
 By means of experiments on the light of the comet of 1819, M. Arago 
 found that it contained polarized, and therefore reflected light. Similar 
 experiments on Hal ley's comet, made on the occasion of its apparition in 
 1835, afforded still clearer indications of the existence of reflected light f. 
 In other instances, as in the case of the great comet of 1843. no trace of 
 polarized light was discernible J. It may be remarked that experiments 
 of this nature, however unequivocal their results may be, are not capable 
 of deciding the question with respect to the nature of the light by which 
 comets shine, since a body, although self luminous, does not with less 
 facility on that account reflect the light of other bodies. There is a ques- 
 tion of another kind, however, upon which such experiments are calculated 
 to throw a decisive light. It has been mentioned as a proof of the trans- 
 lucency of the matter of which comets are composed, that the smallest 
 stars have been occasionally seen through them without undergoing any 
 diminution of lustre. This, however, has not been the invariable result 
 that has occurred, under such circumstances, to the observation of astro- 
 nomers. In some instances the star has appeared sensibly fainter from 
 the interposition of the comet. For example, on the 31st of October, 
 1807, Sir William Herschel found that small stars, seen through the tail 
 of the comet of that year, exhibited a considerable diminution of bright- 
 ness as they became'more involved in the nebulosity of the cornet. This 
 diminution of brightness is readily accounted for by the obstruction Which 
 the particles of the cometic matter offer to the rays of light proceeding 
 from the star to the observer. It is to be remarked, however, that ac- 
 cording to a principle of optics, a feeble light when projected upon an 
 illuminated ground, suffers an apparent diminution of brightness ; and 
 the question, therefore, arises whether the faintness of a star, when seen 
 through a comet, is not wholly referable to this cause. In the instance 
 above cited, Herschel felt a disposition to adopt this as the true explana- 
 tion of the phenomenon, on the ground that the brightness of the tail of 
 the comet was a fact palpable to observation, whereas, on the other hand, 
 there was no evidence to prove the existence of floating particles of matter 
 interposed between the star and the observer . Now the experiments of 
 M. Arago on the light of comets establish beyond doubt that the substance 
 of which the tails of these bodies are composed, is sufficiently dense to ob- 
 struct the rays of light proceeding from a luminous body ; for the pheno- 
 menon of reflected light necessarily implies that the cometic particles 
 
 * According to Sir William Herschel the nucleus of the comet of 1807 had an appa- 
 rent diameter of I" (Phil. Trans,, 1808, p. 156). The same astronomer found the 
 apparent diameter of the nucleus of the first comet of 1811 to be only 0". 775. (Phil. 
 Trans., 1812, p. 118.) 
 
 f Comptes Rendus, tome i., p. 257. J Ibid., tome xvi., p. 597. 
 
 Herschel at this time was inclined to believe that the tail of a comet was merely an 
 optical phenomenon resembling the aurora borealis. (Phil. Trans., 1808, p. 159.) 
 
314 HISTORY OF PHYSICAL ASTRONOMY. 
 
 possess this power of obstruction. It results, therefore, that the faintness 
 which small stars occasionally exhibit, when perceived through any part 
 of the substance of a comet, may, and in all probability does, to some extent, 
 arise from the resistance which the cometic particles oppose to the rays of 
 light proceeding from the star to the observer *. 
 
 When the flimsy nature of the substance of a comet is taken into con- 
 sideration, it is difficult to conceive how such a body is not entirely dissi- 
 pated in space by the enormous heat of the sun during its passage of the 
 perihelion. Mention has already been made of Newton having calculated 
 that the great comet of 1680, when it arrived at its least distance from the 
 sun, was subjected to a heat 2000 times greater than that of red-hot iron f. 
 He considered that the circumstance of a comet being able to maintain its 
 existence after passing through such a terrible ordeal, formed an irre- 
 sistible argument in favour of its being a solid body. Laplace, availing 
 himself of Black's beautiful discovery of latent heat, shewed that the 
 durability of the existence of a comet might be accounted for, without 
 having recourse to a principle which, to say the least respecting it, did not 
 receive any support from observation. It was established by the eminent 
 philosopher just cited, that when a body is in the course of passing from 
 the liquid to the gaseous state, the particles, as they become successively 
 volatilized, abstract from the body a large quantity of caloric which con- 
 tinues insensible to the thermometer. Laplace supposed that the heat 
 thus carried off by the volatilized particles of the comet during its passage 
 of the perihelion, would serve to moderate the temperature of the more 
 condensed portion ; and conversely, the heat given out by the same par- 
 ticles, in the course of their return to the liquid state, would have the 
 effect of counteracting the intense cold to which the comet would be 
 exposed in the more distant parts of its orbit J. 
 
 Whether a comet be composed of a partially solid substance, or whether 
 it consist of a mere collection of vapours, is a question which has not yet 
 been resolved to the satisfaction of astronomers; but one thing is certain, 
 that the masses of comets must be very small. This was strikingly 
 evinced in the case of Lexell's comet by its passage through the middle of 
 the system of Jupiter's satellites, in the year 1779, without occasioning the 
 slightest perceptible derangement in the motion of either of those bodies. 
 
 * It seems difficult to account for the extreme faintness of the stars seen by Sir William 
 Herschel through the comet of 1807, without supposing it to have been in some degree 
 produced by the interposition of the cometic substance. On the other hand, Sir John 
 Herschel has remarked that, although innumerable stars of all magnitudes, from the ninth 
 downwards, were seen by him through the substance of Halley's comet, there never ap- 
 peared the least ground for presuming any extinction of their light in traversing it. 
 " Very small stars were, indeed, obliterated," says that eminent astronomer, "as they 
 would have been by an equal illumination of the field of view ; but in no case to a greater 
 extent than they would have been by so much lamp-light, artificially introduced. {Results 
 ofAst. Obs. at the Cape, p. 401.) 
 
 f As this result of Newton's is often cited, it may not be out of place briefly to state the 
 grounds upon which he established it. When the comet was in perihelion, on the 8th 
 of December, its distance from the centre of the sun was to the earth's distance as 6 to 1000. 
 Now, since the intensity of the sun's heat is reciprocally as the square of the distance from his 
 centre, it follows that the sun's heat on the comet was to the heat of the summer sun as 
 1,000,000 to 36, or as 28,000 to 1. But he also found by experiment that the heat of 
 boiling water is about three times greater than the heat which dry earth acquires from the 
 summer sun ; and he moreover conjectured that red-hot iron is about three or four times 
 hotter -than boiling water. His final conclusion consequently was that the comet must 
 have been subjected to a heat 2000 times greater than that of red-hot iron. 
 
 f Systeme du Monde, tome i., book ii., chap. v. 
 
HISTOBY OF PHYSICAL ASTHONOMY. 31 5 
 
 The question with respect to the end which comets are designed to serve 
 in the economy of creation, appears to be involved in a degree of obscurity 
 greater even than that which surrounds any other enquiry connected with 
 these mysterious bodies. Newton asserted that all those comets which 
 descend so low as to come within the solar atmosphere, would suffer a re- 
 tardation of their motion on each occasion of their passage through their 
 perihelia, and being, in consequence, less capable of resisting the attrac- 
 tion of the sun, would gradually approach that body until they ultimately 
 fell upon his surface. Generalising this idea, he supposed that the fixed 
 stars might be occasionally recruited by the falling of comets into 
 them, and that the conflagration hence arising might account for 
 those temporary stars which, at different times, have appeared with great 
 splendour in the heavens. With respect to the tails of comets he was 
 of opinion that after being dissipated in space they were absorbed by the 
 planets, and entering into a multitude of chemical combinations with other 
 substances, tended thereby to repair the waste of fluids occasioned by the 
 evaporating influence of the sun. It would, perhaps, be as difficult to 
 disprove these surmises as to demonstrate their truth, for in fact, they 
 can only be regarded as mere sallies of the imagination into regions of 
 thought, beyond the reach of legitimate reasoning. The speculations of 
 succeeding astronomers on this subject do not lead to conclusions of a 
 more satisfactory kind than those above hinted at. Sir William Herschel 
 was of opinion that a comet on the occasion of each perihelion passage 
 acquires a more perfect state of condensation in consequence of the action 
 of the solar heat upon the nebulous matter of which it is partially 
 composed. This hypothesis pointed out to the probability of a comet 
 eventually acquiring the consistency of a solid body and assimilating itself 
 in all respects to a planet. A similar view of the ultimate state of comets 
 was adopted by Laplace, who remarked that the comet of 1759 was the 
 only one which had hitherto exhibited any indications of having arrived at 
 a fixed condition. He was probably led to this conclusion by a 
 comparison of the recorded apparitions of the comet, from which it would 
 seem that it had been diminishing in splendour on the occasion of each 
 return to perihelion, until at length, in 1759 it almost ceased to exhibit 
 the more striking peculiarities of a cometary body. Much of the awful 
 magnificence of the comet on the occasion of its apparition in 1456 is 
 doubtless attributable to the effect upon the imagination of a phenomenon 
 that was universally regarded with feelings of terror, as a visible mani- 
 festation of divine displeasure; but it is an indisputable fact that the 
 comet was a much more conspicuous object in 1607, than it was in 1684 
 or 1759. Thus, in 1607, Kepler distinctly perceived the tail with the 
 naked eye, thirty days before the comet's arrival in perihelion*. In 1682 
 the comet, even for some time after it became visble to the naked eye, 
 did not exhibit any vestige of a tail, for Cassini has remarked that its disk 
 was as round, as well defined, and as devoid of nebulosity as that of the 
 planet Jupiter f. Perhaps the circumstance of its appearing so soon after 
 the great comet of 1680 may have caused its cometic features to be in 
 some degree overlooked by astronomers. This could not be said on the 
 occasion of the return of the cornet in 1759, for although Messier carefully 
 
 * The comet with its tail was seen at Prague by many persons as well as Kepler on 
 the 26th of September (De Cometis, p. 25). According to Halley it passed its peri- 
 
 r\ n A. ^ i 
 
 helion on the 26th of October. 
 
 f Mem. Acad. des Sciences, 1699, p. 39. 
 
31& HiSTOEY OF' PHYSICAL ASTKONOMY. 
 
 observed it with a telescope twenty-six days before the passage of the 
 perihelion, he was unable to discern the slightest trace of a tail. So far, 
 therefore, the remark of Laplace appears to be supported by observation. 
 Unfortunately, however, the comet during its last apparition exhibited a 
 decidedly less planetary aspect than it did in 1759; for on the 12th of 
 October, 1835, the tail was already visible to the naked eye as a very con- 
 spicuous object, although the passage of the perihelion did not take place 
 until 35 days afterwards. 
 
 The foregoing account of speculations on the physical constitu- 
 tion of comets may serve to shew how much yet remains to be done in 
 this interesting department of astronomy. It is clear that a more ex- 
 tensive collection of facts than that at present in the possession of astro- 
 nomers, must be formed by a long course of accurate observation ; and that 
 more mature views of the great agents of nature must be arrived at by an 
 assiduous cultivation of the various branches of physical science, before 
 any hopes can be entertained of coming to a definitive conclusion respect- 
 ing the more essential properties of these mysterious bodies, or the pur- 
 poses they are designed to accomplish in the economy of the material 
 universe. 
 
 CHAPTER XVI. 
 
 Importance of Facts in the Cultivation of Physics. Astronomy a Science of Observation. 
 
 Inequalities which affect the apparent positions of the Celestial Bodies. Preces- 
 sion. Its Discovery by Hipparchus. Researches of Modern Astronomers on its 
 Value. Bessel. Peters. Otto Struve. Refraction. Its effect upon the Place of a 
 Celestial Body first remarked by Ptolemy. Opinion of Tycho Brahe respecting its 
 
 Nature The first Theory of Refraction due to Cassini. His Table of Refractions 
 
 Newton. His Correspondence with Flamstead on the subject of Refraction For- 
 mula of Bradley French Tables of Refraction. Researches of Bessel. Aberration. 
 
 Its discovery by Bradley. Modern Determinations of its Value. Nutation dis- 
 covered by Bradley. Its most Approved Value. Researches on Parallax. Methods 
 for facilitating the Reduction of Observations. Method of Bessel. Physical Causes 
 which more especially affect the Aspect of the Celestial Bodies. Diffraction. Irradia- 
 tion. 
 
 IT does not require a profound aquaintance with the history of any branch 
 of physical science, to arrive at the conviction that its advancement has 
 been invariably effected by reasoning upon facts whose existence had been 
 already established either by observation or experiment. Astronomy is 
 essentially a science of observation. Even in the earliest stages of its 
 progress some interesting results were deduced, by simply noting the 
 periodical recurrence of the more obvious phenomena. It was by pur- 
 suing a process of this sort that the Chaldeans succeeded in obtaining rude 
 approximations to the times of revolution of the sun and moon, and in 
 predicting the occurrence of lunar eclipses. The earlier philosophers of 
 Greece, misled by erroneous views with respect to the mode of discovering 
 truth, imagined that it would be inconsistent with the dignity of the 
 human mind, to recognise any alliance between the lofty speculations of 
 abstract science and the monotonous task of observation. It followed, as 
 a necessary consequence, that during many years of Grecian history, not 
 
HISTORY OF PHYSICAL ASTRONOMY. 317 
 
 even excepting the palmy days of Athenian civilisation, no progress was 
 made in the study of astronomy. It was only when Alexandria became 
 the capital of the civilised world, and learning in all its departments was 
 liberally patronised by the Ptolemies, that the phenomena of the heavens 
 were observed with regularity and care by the aid of instruments invented 
 for that express purpose. Accordingly, astronomy, considered as a science 
 of strict calculation, was during this period established on a durable basis. 
 It cannot be asserted, indeed, that even yet the metaphysical notions of the 
 speculative philosophers had been wholly banished from the science. The 
 Aristotelian dogmas respecting the essential nature of the celestial move- 
 ments were still regarded as indisputable axioms, between which on the one 
 hand, and nature on the other, a sort of compromise was effected by means 
 of the famous mechanism of epicycles. So long, indeed, as the discord- 
 ances between its results and the actual phenomena of the heavens did not 
 exceed the probable errors of observation, this system, however compli- 
 cated, might fairly be regarded as a legitimate representation of established 
 facts. It was only when the advanced state of practical astronomy allowed 
 the repudiation of discordances of such magnitude, that the arbitrary crea- 
 tions of the human mind, and the immutable laws of the physical universe, 
 might be said to have come into direct collision. The triumphant esta- 
 blishment of the true system of nature by the immortal Kepler, led to the 
 complete emancipation of astronomical science from the thraldom of the 
 Schools, and its subsequent history has in consequence been one of unin- 
 terrupted progress down to the present day. 
 
 Since the laws which regulate the movements of the celestial bodies 
 constitute the principal subject of research in the study of astronomy, it is 
 manifest that the establishment of a series of facts relating to their apparent 
 positions, forms an indispensable preliminary to all such enquiries. Accord- 
 ingly, the sun, moon, and planets have in all ages been carefully observed 
 with this object in view ; and all the resources of mechanical skill, as well 
 as the most profound investigations of physical science, have been applied 
 towards assuring the accuracy of the results. The stars, too, have been ob- 
 served with equal care, not merely on their own account, but also because 
 they form fixed points, to which the positions of the various bodies of the 
 solar system may be on all occasions referred. 
 
 But the simple determination of the apparent positions of the celestial 
 bodies does not suffice to produce results immediately available towards the 
 purposes of astronomy. Certain inequalities of small, but variable magni- 
 tude, affect the position of every celestial body, the values of which must 
 be carefully ascertained for each observation, in order to arrive at a know- 
 ledge of the mean position of the body, which alone can be employed in 
 forming the basis of ulterior research. These minute displacements arise 
 from the combined operation of various distinct principles, the investi- 
 gation of the laws of which forms one of the most important departments 
 of astronomical science. When considered with respect to their origin, 
 they admit of a threefold division. In the first place there are inequali- 
 ties which depend upon the principle of gravitation; such are the pheno- 
 mena of Precession and Nutation. The second class of inequalities includes 
 those which are explicable by reference to the properties of light ; such are 
 the phenomena of Refraction and Aberration. Lastly, there is the dis- 
 placement occasioned by Parallax, 
 
 It appears from the foregoing remarks that every celestial body is sub- 
 ject to an apparent displacement arising from the combined influence of 
 
318 HISTORY OF PHYSICAL ASTKONOMY. 
 
 five distinct inequalities, of which four derive their origin from physical 
 causes ; while, on the other hand, the fifth depends upon considerations of 
 a purely mathematical nature. The apparent position of a body is re- 
 duced to the mean by applying to it, with an opposite sign, the numerical 
 value of each inequality, corresponding t'o the time of observation. A 
 brief account of the researches of astronomers in connexion with each of 
 these five inequalities or corrections, as they are technically termed, may, 
 perhaps, not prove uninteresting to the reader. This will be best effected 
 by alluding to each correction according to the order of its discovery. 
 
 Of the various inequalities which require to be taken into account in 
 reducing the apparent position of a heavenly body to its mean position, 
 the one which first became known to mankind is the increase of longitude, 
 arising from a slow regression of the equinoctial points upon the plane of 
 the ecliptic. As this constant shifting of the intersection of the ecliptic 
 and equator causes the annual arrival of the sun in either of the equinoxes 
 to be a little earlier than it would otherwise be, it has in consequence been 
 denominated " the Precession of the Equinoxes." The discovery of this 
 apparent movement is due to Hipparchus, who arrived at it about the 
 year 125, A. c., by a comparison of his own observations with those of 
 Timocharis, made about 170 years earlier. Its existence was afterwards 
 established beyond doubt by Ptolemy, between whom and Hipparchus 
 there elapsed an interval of nearly 300 years. It has been already men- 
 tioned that Copernicus was the first who gave the true explanation of this 
 phenomenon. The discovery of its physical cause by Newton, and the 
 researches of his successors on its laws, have also been briefly noticed. It 
 only remains to give some account of the successive determinations of its 
 quantitative value by astronomers. 
 
 The earliest statement of the value of precession is to be found in the 
 Syntaxis. Ptolemy mentions, in the seventh chapter of that work, that 
 having observed several bright stars in the zodiac, he found that while 
 their relative positions were the same as in the days of Hipparchus, they 
 had all increased in longitude to the extent of 2 40' during the interval 
 that elapsed between that astronomer and himself. He hence inferred 
 that the increase of longitude amounted to 1 in 100 years, which implies 
 an annual precession of 36"; he moreover stated that Hipparchus had 
 arrived at the same result. This was a very erroneous determination, 
 for, according to the researches of modern astronomers, the annual amount 
 of precession is a little in excess of 50". The interval between Hip- 
 parchus and Ptolemy comprehended a period of 267 years, so that the total 
 increase of longitude must in reality have amounted to 3 37', a quantity 
 greater nearly by 1 than that assigned by Ptolemy. As the discordance 
 seems too great to be accounted for by errors of observation, except by 
 adopting an extravagant supposition with respect to their probable magni- 
 tude, many eminent astronomers have come to the conclusion that Ptolemy 
 made no observations at all ; that in fact his catalogue of the stars is no 
 other than the catalogue of Hipparchus reduced to the epoch of 137 A.D., 
 by increasing all the longitudes to the extent of 2 40'. Unfortunately 
 there are circumstances which strongly tend to justify this serious charge. 
 Delambre compared together the longitudes of 312 stars as assigned by 
 Ptolemy with the longitudes of the same stars inserted in Flamstead's 
 catalogue, and supposing the interval between these two astronomers to 
 comprehend a period of 1553 years, he hence deduced 5 2". 4 for the annual 
 value of precession. This result exceeds the true value by rather more 
 
HISTOEY OF PHYSICAL ASTRONOMY. 319 
 
 than 2"; but such a discordance would necessarily ensue if Ptolemy 
 simply derived his catalogue from that of Hipparchus, since in reducing 
 the longitudes to his own epoch he supposed the quantity of precession to 
 be too small. In order to obtain a stronger assurance on this point, 
 Delambre diminished Ptolemy's longitudes of the same stars by 2 40', 
 and supposing the results to be the longitudes of Hipparchus, he in- 
 stituted a comparison between them and Flamstead's longitudes. As- 
 suming the interval between Hipparchus and Flamstead to include a 
 period of 1820 years, he now obtained 50".12 for the resulting value of 
 precession, a quantity agreeing almost exactly with the modern determina- 
 tion. Delambre obtained results of a similar nature by pursuing the 
 same process with respect to several other sets of stars common to the 
 catalogues of Ptolemy and Flamstead. 
 
 The Arabian astronomers generally estimated the quantity of precession 
 at 1 in 66 years. This gave 54" for the annual precession, a result which 
 formed a much closer approximation to the true value than that which 
 Ptolemy had arrived at. 
 
 The efforts of modern astronomers have been constantly directed 
 towards obtaining a more accurate value of this element. Tycho Brahe 
 fixed the annual precession at 51". Flamstead made it 50". Lalande, by 
 comparing the longitude of Spica Virginia as assigned by Hipparchus with 
 its longitude deduced from observations made in 1750, obtained 50". 5 for 
 the resulting value of precession. Delambre, by a comparison of the ob- 
 servations of Bradley, Mayer, and Lacaille with his own observations, was 
 induced to fix the annual precession at 50". 1. 
 
 As the theory of gravitation began to acquire a more complete state of 
 developement, it became apparent that the precession of the equinoxes is a 
 phenomenon of a much more complicated nature than it had hitherto been 
 supposed to be. It has been already mentioned, that the action of the 
 planets on the earth occasions a secular displacement of the terrestrial 
 orbit, in virtue of which the equinoctial points have a constant tendency 
 to advance with a very slow motion upon the plane of the ecliptic, and that 
 hence arises a distinction between lunisolar precession, which refers ex- 
 clusively to the action of the sun and moon, and general precession, which 
 is equal to the lunisolar precession diminished by the small effect of an 
 opposite nature, arising from planetary perturbation. Now as the diplace- 
 ment of the terrestrial equator, by constantly altering the position of the 
 zero points, to which the celestial bodies are referred on the ecliptic, 
 affects their longitudes but not their latitudes ; so the displacement of the 
 plane of the ecliptic affects the right ascensions of all the celestial bodies, 
 but does not exercise any influence upon their declinations. It is manifest, 
 therefore, that the variation of the right ascension of a star is an effect pro- 
 duced principally by the action of the sun and moon, but in some degree 
 also by the action of the planets; whereas, on the other hand, the change of 
 declination depends exclusively upon lunisolar action. Hence by com- 
 paring together the mean right ascensions of a great number of stars, 
 as determined at two distant epochs, the quantity of general precession 
 may be ascertained, and by instituting a similar comparison with respect 
 to mean declinations, the resulting quantity is the value of lunisolar pre- 
 cession. Both the regression of the equinoctial points, occasioned by the 
 conical motion of the earth's axis and the progression due to the displace- 
 ment of the ecliptic are in a state of slow variation, and consequently 
 neither the general nor the lunisolar precession retains in every age the 
 
t-f 
 
 820 HISTORY OF PHYSICAL ASTRONOMY. 
 
 same value. The researches of the illustrious Bessel led to a more accu- 
 rate determination of the constants of precession than any which had been 
 hitherto arrived at. His earliest investigation, which obtained for him 
 the prize of the Berlin Academy, appeared in the year 1815. He re- 
 turned to the subject on several subsequent occasions, and his final results 
 are contained in the Tabula Regiomontance, which was published in 1830. 
 The materials of his researches were the observations of Bradley, which 
 formed the most ancient reliable data that were available to him ; and 
 those of Piazzi, as well as many of his own observations, with which he 
 compared the determinations of the English astronomer. The values 
 which he assigned to the constants of lunisolar and general precession 
 have, until very recently, been universally used by astronomers. The 
 annual value of lunisolar precession at the beginning of the year 1750 
 was fixed by him at 50".37572, and the annual value of general precession 
 at 50".21129. 
 
 The importance of an accurate knowledge of precession in determining 
 by observation the positions of the celestial bodies has been the main 
 cause of those repeated investigations that have been undertaken by astro- 
 nomers in modern times, for the purpose of obtaining further corrections 
 of the constants upon which its annual value for any given year, and its 
 total magnitude corresponding to any assigned distance from a given epoch, 
 depend. The truth of this remark will appear evident from a considera- 
 tion of the mode by which the absolute position of a celestial body is 
 usually ascertained. This object is effected, not by a direct process, which 
 would be generally impracticable, but by determining the relative position 
 of the body with respect to certain fundamental stars whose absolute posi- 
 tion has been already ascertained with great care at some anterior epoch. 
 Now the absolute position of a body in the celestial sphere is usually ex- 
 pressed by means of its right ascension and declination ; but, as both these 
 co-ordinates have reference to the position of the vernal equinox, they are 
 in a state of continual variation from the effects of precession. It is 
 of no use, therefore, for the astronomer to be acquainted with the original 
 right ascension and declination of the star with which he compares the 
 object of observation, unless he possesses a sufficient knowledge of the ex- 
 tent to which the equinoctial points have retreated upon the ecliptic during 
 the intermediate period, to enable him to compute the values of the same 
 co-ordinates corresponding to the time of observation. 
 
 But there is another circumstance which in recent times has rendered 
 an accurate knowledge of precession indispensable. The researches that 
 have been prosecuted in the present day, with the view of establishing the 
 motion of the solar system in space, have suggested the necessity of ascer- 
 taining with the utmost precision the real nature of those secular varia- 
 tions which affect the apparent positions of the stars. It is not difficult 
 to see that a small error committed in the determination of the nume- 
 rical values of the constants of precession, would, by always acting in the 
 same direction on the position of a star, be liable to become confounded 
 with the proper motion of the star, which is also characterised by a similar 
 peculiarity. The elaborate researches of the Russian astronomers, MM. 
 Peters and Struve, have led to a modification of Bessel 's constants of 
 precession, which, although very slight, may not improbably exercise an 
 important influence on the delicate investigations of sidereal astronomy. 
 
 Ptolemy was the first who remarked that a ray of light proceeding from 
 a star to the earth underwent a change of direction in passing through the 
 
HISTORY OF PHYSICAL ASTRONOMY. 3rfl 
 
 atmosphere, and that, in consequence of the deflection, the star would ap- 
 pear to be elevated above its true place. He further asserted that the dis- 
 placement would be less according as the altitude of the star increased, and 
 that it would vanish altogether when the star was in the zenith ; but he did 
 not attempt to determine its magnitude in any instance, although he made 
 some excellent experiments on the refractive powers of glass and water. 
 Albazen, the Arabian astronomer, reasoned very judiciously on the same 
 subject, in his " Treatise on Twilight," and Waltherus, a German astro- 
 nomer, who flourished towards the close of the fifteenth century, made 
 some attempts to determine the magnitude of refraction near the horizon. 
 Tycho Brahe was the first astronomer who applied refraction as a correc- 
 tion to the apparent positions of the celestial bodies. Having found that 
 the latitude of Uraniburg, as deduced from the least and greatest altitudes of 
 circumpolar stars, differed to the extent of 4' from the latitude indicated 
 by observations of the sun at the solstices, he was led to attribute the 
 discordance to the effect of refraction, which he supposed to have been 
 mainly influential at the winter solstice when the sun attained only a 
 very low altitude. Pursuing the subject, he deduced from his observations 
 a table of refractions, which, although by no means remarkable for ac- 
 curacy, possessed the merit of being the first of the kind that had been 
 constructed by any astronomer. He supposed the refraction to be 34' at 
 the horizon, and 5" at 45 of altitude. His views of the nature of refrac- 
 tion were by no means so accurate as those of Ptolemy or Alhazen, with 
 whose works on the subject he does not seem to have been acquainted. 
 Under an impression that the refraction of the rays of light proceeding 
 from a heavenly body, was occasioned by the vapours which accumulate 
 near the horizon, he asserted that it did not extend so far as the zenith. 
 He also supposed that the refraction of the stars was different from that 
 of the sun or any of the planets ; and that while in the former case it 
 ceased at 20 of altitude, in the latter it was sensible as far as 45. These 
 opinions, although erroneous in an extreme degree, did not admit of 
 being corrected by an appeal to observation, on account of the imperfect 
 condition of practical astronomy. 
 
 Kepler, by means of an empirical rule of his own invention, cal-' 
 dilated a table of refractions, which was found to be considerably more 
 accurate than Tycho's table. Delambre has shown that for all zenith dis- 
 tances less than 70 the errors do not surpass 9" *. 
 
 The researches of philosophers on the subject of refraction were facili- 
 tated in a vast degree by the discovery of Snell, that when a ray of light 
 enters a transparent medium the sines of the angles of incidence and 
 refraction bear a constant ratio to each other. By means of this principle 
 it was easy, in all cases of a ray of light entering a homogeneous medium, 
 to ascertain the subsequent direction of the ray, whatever might be the 
 angle of incidence, when the direction corresponding to any given angle 
 was once determined by experiment. The first theory of astronomical 
 refraction is due to Cassini. He supposed the atmosphere to possess 
 a uniform density, and to extend to a definite height above the surface of 
 the earth. According to this hypothesis, the refraction of a ray of light 
 proceeding from a celestial body, takes place wholly at its entrance into 
 the spherical shell of air which encompasses the earth ; whence it follows 
 that the path pursued by the ray in its subsequent passage through the 
 
 * Hist. Ast. Mod, tome i., p. 3C7. 
 
3$W HISTOEY OF PHYSICAL ASTRONOMY. 
 
 atmosphere must necessarily be a straight line. In order to adapt his 
 hypothesis to the calculation of a table of refractions, it was necessary for 
 Cassini to determine the height of the homogeneous atmosphere, and the 
 refraction corresponding to a given angle of incidence. The data which 
 he used for this purpose were the observed refractions for two given 
 zenith distances. These were, the horizontal refraction, which he made 
 equal to 32' 20", and the refraction at 80 of zenith distance, which he 
 determined to be 5' 28". Being now in possession of tbe elements of his 
 theory, he calculated a table of refractions extending from the horizon to 
 the zenith. Besides this table, which was designed to represent the re- 
 fractions in summer, he calculated two other tables, one of which was 
 adapted to the winter season, and the other to the intermediate seasons of 
 spring and autumn. It was found that by estimating the solar parallax at 
 I/, agreeably to Kepler, the triple table was indispensable when the object 
 was to represent the observed refractions throughout the year. Cassini, 
 however, was induced to suspect from observations of the moon when in 
 the dichotomies, that the solar parallax fell considerably short of V ; nay, 
 he even did not scruple to assert that in point of fact it might be regarded 
 as insensible. By adopting this supposition, he found that the table 
 which he had calculated for summer, was likewise applicable to the other 
 seasons of the year ; but it was impossible to pronounce with absolute cer- 
 
 , tainty whether his view of the subject was the right one or not. The 
 table, in its triple form, first appeared in the Solar Ephemerides, published 
 
 j by Malvasia, at Bologna, in the year 1662. The results were found to re- 
 present the observed refractions with a remarkable degree of accuracy. 
 
 L This will appear somewhat surprising when the erroneous nature of the 
 hypothesis from which they were deduced is taken into account ; for it is 
 manifest that, so far from the atmosphere being homogeneous, the succes- 
 sive strata of air increase in density towards the surface of the earth, 
 by reason of the pressure of the superincumbent strata, and the ray of 
 light being in consequence deflected continually from a rectilinear direc- 
 tion, the path pursued by it through the atmosphere will, in reality, be a 
 curve which is concave with respect to the earth. 
 
 Notwithstanding the success of Cassini's attempt to represent the 
 derangements in the apparent positions of the celestial bodies, arising 
 from the combined influence of parallax and refraction, it was still desir- 
 able, for the advancement of astronomical science, to arrive at a precise 
 knowledge of the independent effects of each of these two elements. To 
 accomplish such an anatysis, however, by means of observations made at 
 Paris, was found to be impracticable, in consequence of the refractions at 
 the solstices being so considerable as to render uncertain any conclusion with 
 respect to the effect occasioned by parallax. In order to obtain a satis- 
 factory solution of this question, the Academy of Sciences resolved to 
 determine the distance between the tropics by means of observations of 
 the sun at some place near the equator, where, the refractions being 
 insensible on account of the great zenith distance of the object, the effects 
 of parallax alone would become apparent. In pursuance of this design 
 they selected a small island on the coast of Africa, lying about 5 north of 
 
 [ the equator, as a suitable locality for the proposed observations, and 
 assigned the conduct of them to Richer, one of the members of their own 
 body. Richer executed his task in the year 1672. The result of his 
 observations afforded a complete verification of Cassini's views, by shewing 
 that the solar parallax was insensible. Cassini, in consequence, adopted 
 
HISTORY OF PHYSICAL ASTRONOMY. JJgJJ 
 
 the table of refractions for summer as true for the whole year, and com- 
 municated them to the Academy of Sciences as the definitive result of his 
 researches'*. This table was inserted in the Con na usance des Temps, 
 and continued for a long time to be published annually in that JEphemeris. 
 
 It appears from the foregoing account of Cassini's researches, that the 
 calculation of a triple table of refractions adapted to the different seasons 
 of the year, was forced upon him by the erroneous value of the solar 
 parallax, generally prevalent in his time, and that the adoption of his own 
 views with respect to the value of that element, made the refractions 
 invariable throughout the year. It is, therefore, inconsistent with the 
 facts of the case, to assert, as some writers have done, that we owe origin- 
 ally to Cassini the remark that the refractions vary with the season of 
 the year. The first suspicion of this fact is undoubtedly due to his contem- 
 porary, Picard. At one of the meetings of the Academy of Sciences, held 
 in 1669, having been invited to state the objects of research which ap- 
 peared to him to be most conducive to the advancement of astronomical 
 science, he suggested the desirableness of calculating a table of refractions 
 for Paris, adapted to the different seasons of the year, and even according 
 to the different changes of the weather, marking, on each occasion, the 
 winds and the state of the thermometer, in order to ascertain whether the 
 variations in the quantity of refraction are not accompanied by phenomena 
 affording unequivocal indications of their existence f. Picard, on a future 
 occasion, gave a more distinct explanation of his views on the subject. 
 Having found from observations of the sun, that the refractions are more 
 in excess after the winter solstice than before it, he attributed the differ- 
 ence to the greater degree of cold which usually prevails in the more 
 advanced part of the winter season. Upon the same grounds he concluded 
 that the refractions during the night are greater than those which take 
 place during the day J. These views must be regarded as highly credit- 
 able to the sagacity of Picard, especially when it is considered that, with the 
 exception of Newton, no other person appears to have formed an adequate 
 conception of the importance of taking into account the influence of tempe- 
 rature upon refraction until towards the middle of the eighteenth century. 
 The subject of refraction is too closely connected with physical astro- 
 nomy not to have occupied the attention of Newton. In the fourteenth 
 section of the first book of the Principia he has shewn that when a ray of 
 light enters a transparent medium, the attraction of the molecules com- 
 posing the medium will deflect it from its original direction, and, by 
 supposing them to act according to a given law, he has deduced the 
 fundamental theorem of Snell, that the sines of the angles of incidence 
 and refraction bear a constant ratio to each other. In his Treatise on 
 Optics, he has alluded more particularly to atmospheric refraction , but 
 he does not attempt to determine the amount of deflection experienced 
 from that cause by a ray of light proceeding from a celestial body to 
 the surface of the earth. In the year 1721 Halley communicated to the 
 Royal Society a table of refractions which he asserted to have been 
 calculated by Newton j|. This table exhibits the refractions from the 
 horizon to 75 of apparent altitude. The refraction at the horizon is 
 assigned equal to 33' 4.5"; the refraction at 45 amounts to 54". No 
 
 * Anc. Mem. Acad. des Sciences, tome viii., p. 81. 
 
 f Histoire Celeste, p. 17. \ Ibid., p. 19. 
 
 Optics, book ii., part iii., prop. x. |j Phil. Trans., 1721, p. 169. 
 
 y 2 
 
324 HISTORY OF PHYSICAL ASTRONOMY. 
 
 information was given by Halley with respect to the way in which the 
 table was constructed, so that it long continued to be an interesting 
 question with astronomers, whether it rested solely upon observation, 
 or whether it was derived from some physical theory of refraction. There 
 existed indeed strong reasons to suspect, from Newton's mode of consider- 
 ing refraction as a result of dynamical agency, that the table was con- 
 structed upon theoretical principles. This has been established beyond 
 all doubt in recent times, by the publication of Baily's Life of Flamstead, 
 which contains some interesting particulars relative to Newton's re- 
 searches on the theory of astronomical refraction*. It appears from 
 certain correspondence between Newton and Flamstead, published in that 
 work, that during the period which elapsed between October, 1694, and 
 March, 1695, Newton was engaged in a profound investigation of the 
 subject referred to, and that he finally transmitted to Flamstead a 
 table of refractions, which, there is every reason to suppose, was identical 
 with the one subsequently communicated by Halley to the Royal Society. 
 A short notice of this correspondence, the publication of which has had 
 the effect of throwing additional lustre around the genius of Newton, 
 already immortalised by so many great discoveries, may perhaps not 
 prove uninteresting to the reader. 
 
 In a letter, dated October 11, 1694, Flamstead points out to Newton 
 the discordances between the refractions near the horizon, as assigned by 
 various astronomers, and the corresponding results which he had deduced 
 from his own observations. He remarks, also, that, at the same altitudes, 
 he found that the refractions were different on different nights. He in- 
 vites the attention of Newton to the subject, and requests that he will 
 communicate to him the result of his reflections upon it. The reply of 
 Newton is valuable, inasmuch as it shews that he had already formed a 
 true conception of the physical principles upon which atmospheric refrac- 
 tion depends. In a letter, dated October 24, 1694, he thus explains his 
 views on the subject: " The reason of the different refractions near the 
 horizon, in the same altitude, I take to be the different heat of the air in 
 the lower region. For when the air is rarefied by heat, it refracts less ; 
 when condensed by cold, it refracts more. And this difference must be 
 most sensible when the rays run along in the lower region of the air for a 
 great many miles together; because 'tis this region only which is rarefied 
 and condensed by heat and cold ; the middle and upper region of the air 
 being always cold. I am of opinion also, that the refraction in all greater 
 altitudes is varied a little by the different weight of the air discovered by 
 the baroscope. For when the air is heavier, and by consequence denser, 
 it must refract something more than when 'tis lighter and rarer. I could 
 wish, therefore, that in all your observations, where the refraction is to be 
 allowed for, you would set down the weight of the baroscope and heat of 
 the air, that the variation of the refraction by the weight and heat of the 
 air may be hereafter allowed for, when the proportion of the variation by 
 those causes shall be known. "f 
 
 Flamstead was unable to appreciate the importance of the sagacious 
 hints thrown out by his illustrious contemporary. Although possessing many 
 of the qualities requisite for constituting an accurate observer of celestial 
 
 * Account of the Rev. John Flamstead, compiled from his own manuscripts and 
 other authentic documents never before published. 4to, London, 1835. 
 f Ibid., p. 137. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 325 
 
 phenomena, he was naturally unfitted for the loftier task of investigating 
 the various physical causes upon whose combined operation they depend. 
 It is due to him, however, to state that, in the present instance, he does 
 not appear to have been insensible to the advantages which might accrue 
 to astronomical science from the theoretical researches of Newton, although 
 he failed to profit by the counsel of that philosopher, in so far as his own 
 practice as an observer was concerned. 
 
 The subsequent progress of Newton's labours on the subject of refraction 
 is clearly exhibited in his letters to Flamstead. It has been already men- 
 tioned that he succeeded in explaining the refraction of a ray of light by the 
 attraction of the transparent medium into which it enters. In the present 
 case the medium was composed of an infinite number of concentric spherical 
 strata of air, increasing in density towards the surface of the earth ; so 
 that, in point of fact, it was necessary to investigate the effect produced by 
 an infinite number of media, all of which possessed different degrees of 
 refractive power. This circumstance rendered the problem of refraction 
 vastly more difficult than it had been on the hypothesis of Cassini ; but on 
 the other hand it was manifest that the condition of a variable density was 
 that which accorded with the actual constitution of the atmosphere. Newton, 
 by a happy application of dynamics to his doctrine of refraction, reduced the 
 problem to a form which tended greatly to facilitate its solution. As each 
 stratum of air acted uniformly upon the incident ray*, the resultant 
 attraction of the particles was a force directed to the centre of the earth, 
 since no reason could be assigned why it should deviate to one side more 
 than to another. Hence the investigation of the path pursued by the ray 
 of light through the atmosphere, was brought under the theory of central 
 forces, the principles of which Newton had already fully established in 
 the first book of the Principia. One of the conditions of the problem 
 was, the relation between the density of the air find its refractive 
 power; another of equal importance was, the law according to which the 
 density of the air diminished in ascending from the surface of the earth. 
 Newton rightly supposed the refractive power of the air to be proportional 
 to its density. The ascertainment of the law of density in ascending 
 from the earth's surface was attended with much greater difficulty, since it 
 depended upon a knowledge of the physical constitution of the atmosphere. 
 Newton commenced his researches by supposing the density to diminish 
 by equal degrees with equal increments of altitude. Upon this hypothesis 
 he calculated three tables of refraction, one for winter, another for summer, 
 and a third for the intermediate seasons of spring and autumn. These 
 tables do not, by any means, exhibit a satisfactory accordance with the 
 corresponding results indicated by observation. Newton, in fact, soon 
 afterwards discovered that the law of density upon which they rested was 
 erroneous, inasmuch as it supposed " the refracting force of the atmo- 
 sphere as great at the top as at the bottom."! He accordingly aban- 
 doned it, as manifestly at variance with the actual state of nature, and 
 
 * The forces of the molecular particles are supposed to be sensible only at insensible 
 distances. 
 
 f Flamstead's Life, p. 147. The truth of this remark will appear from the following 
 consideration. When a ray of light passes from one stratum of air into another, it is at- 
 tracted in opposite directions by the two strata with forces proportional to their respective 
 densities. It is clear, therefore, that the whole force which is effectual in refracting the 
 ray is proportional to the difference of densities of the strata. Now, according to the hy- 
 pothesis mentioned in the text, this difference is a constant quantity. Hence the re- 
 fractive force is also constant. 
 
326 HISTORY OF PHYSICAL ASTRONOMY. 
 
 proceeded to the consideration of another hypothesis, founded upon the 
 constitution of the atmosphere, described by him in the 22nd proposition 
 of the second book of the Principia. In this proposition the density 
 of the air is supposed to be proportional to the pressure, and hence is 
 readily deduced the theorem, that, if the Distances from the centre of the 
 earth increase in arithmetical progression, the densities of the correspond- 
 ing strata of air will diminish in geometrical progression *. This hypothesis 
 is more conformable to the real constitution of the atmosphere than that 
 adopted by Newton in the first instance, for it has been demonstrated by 
 experiment, that the density of air is proportional to the compressing 
 force. On the other hand it is to be remarked, that the influence of tem- 
 perature is left wholly out of consideration, although it is manifest that 
 the superior heat of the lower regions of the atmosphere, by rarefying the 
 air, tends inevitably to derange the law of density which would otherwise 
 ensue. It may, therefore, easily be imagined that the new hypothesis of 
 Newton did not yield results much more satisfactory than those derivable 
 from the original one. In fact, he found that for low altitudes the refrac- 
 tions assigned by it were all by far too great. The cause of this dis- 
 cordance did not fail soon to disclose itself to his penetrating intellect. 
 " I have found," says he, " that if the horizontal refraction be 84', the 
 refraction in the apparent altitude of 3 will be 1 3' 3" ; and if the refraction 
 in the apparent altitude of 3 be 14', the horizontal refraction will be 
 something more than 37'. So that, instead of increasing the horizon- 
 tal refraction by vapours, we must find some other cause to decrease it. 
 And I cannot think of any other cause besides the rarefaction of the lower 
 region of the atmosphere by heat." Having calculated a table of refrac- 
 tions upon this hypothesis, he transmitted a copy of it to Flamstead, in- 
 closed in a letter dated March 15, 1695. The letter is preserved in the 
 library of Corpus Chnsti College, Oxford ; but the table of refractions 
 which accompanied it has nowhere been found. 
 
 The question naturally arises, was the table of refractions which New- 
 ton transmitted to Flamstead, similar in all respects to the one communi- 
 cated by Halley to the Royal Society ? In order to establish this point in 
 the affirmative, it is necessary, in the first instance, to shew that both 
 tables were calculated upon the same hypothesis respecting the constitu- 
 tion of the atmosphere. M. Biot was the first who proved by strict cal- 
 culation, that a theory of atmospheric refraction, in which the densities of 
 the successive strata of air are supposed to be proportional to the pressures, 
 is capable of furnishing results identical with the refractions contained in 
 Halley 's tablef. This was soon afterwards demonstrated still more un- 
 equivocally by Ivory *. It appears, therefore, that both tables in ques- 
 tion were constructed upon the same principles. The sole object that 
 still remained to be accomplished, in order to dispel all doubts respecting 
 their common origin, was to establish the identity of their numerical 
 results. This has been effected by the aid of a passage of Newton's letter to 
 Flamstead, wherein he mentions that if the refraction at 3 of altitude be 
 13' *JO" the table may be relied upon as exact to a second for all altitudes 
 
 * Strictly speaking, the theorem requires that the distances from the centre of the 
 earth should be in harmonical proportion ; but on account of the immense magnitude of 
 the terrestrial radius, compared with the altitudes of the successive strata of air, they may, 
 without any sensible error, be taken in arithmetical progression. 
 
 f Connaissance des Temps, 1839. Addit, p. 105. 
 
 J Phil. Trans., 1838, p. 183. 
 
HISTOBY OF PHYSICAL ASTRONOMY. 
 
 above 10. Now it appears by reference to Halley's table that the refrac- 
 tion at 3 is therein also equal to 13' 20". The conclusion, therefore, is 
 unavoidable, that the refractions communicated by Newton to Flamstead 
 and Halley, were both copies of the same original table, and that the latter 
 was calculated upon the hypothesis that the densities of the successive 
 strata of air are proportional to the pressures. This hypothesis neces- 
 sarily implies a uniform temperature of the atmosphere. 
 
 It may well excite surprise, that, after Newton had established a theory 
 of refraction which agreed in so many of its fundamental principles with the 
 actual constitution of the atmosphere, and had also succeeded in accurately 
 working out its results, he declined, notwithstanding, to communicate an 
 account of his researches to the world. He was probably induced to adopt 
 this course from a consciousness of the inadequacy of his theory to repre- 
 sent the actual refractions with all the accuracy demanded by the existing 
 state of practical astronomy. We have seen that he did not fail to per- 
 ceive that the rarefaction of the air in the lower regions of the atmosphere, 
 would cause the refractions near the horizon to be in reality less than 
 those assigned by theory. It does not appear, however, that he attempted 
 to correct his results by taking into consideration the influence of tempera- 
 ture. He, doubtless, was of opinion that the law of the variation of this 
 element in ascending from the surface of the earth, was too imperfectly 
 known to justify the hope of ascertaining its effect upon refraction by a 
 process of strict calculation. Indeed it may be asserted that the question 
 with respect to the mean influence of temperature upon the constitution 
 of the atmosphere, has proved a stumbling-block to every astronomer and 
 mathematician who has undertaken to investigate the laws of refraction, 
 from Newton's time down to the present day. 
 
 Although Cassini's table of refractions was generally adopted by astro- 
 nomers, on account of its satisfactory agreement with the results of obser- 
 vations, it was well known that the hypothesis of a homogeneous atmosphere, 
 upon which it rested, did not truly represent the actual state of nature. 
 In 1702 La Hire attempted to determine the path pursued by a ray of 
 light through the atmosphere, by taking into account the variable density 
 of the air; but his investigation not being grounded upon accurate 
 physical principles, the conclusion at which he arrived was necessarily 
 erroneous *. In 1714, J. Cassini sought to effect the same object by arbi- 
 trarily assuming several curves as representatives of the path of a ray 
 of light through the atmosphere, and trying which of them agreed best 
 with the observed refractions. He fouiid that by supposing the path of 
 the ray to be circular, the refractions were represented better than by his 
 father's theory j. It is hardly necessary to remark, that a problem so 
 intricate as that of atmospheric refraction, does not admit of even an 
 approximate solution by a process so purely tentative as that above 
 hinted at. 
 
 The first investigation of the problem of astronomical refraction upon 
 sound physical principles, or at any rate the one which was first commu- 
 nicated to the world, is due to the celebrated mathematician, Brooke 
 Taylor. At the end of his treatise, " Methodus Incrementorum," pub- 
 lished in 1715, he employs Newton's doctrine of refraction, as expounded 
 in the sixth section of the first book of the Principiu, to investigate the 
 curve described by a ray of light in its passage through the atmosphere. 
 
 * Mem. Acad. des Sciences, 1702, p. 18'2. t Ibid., 1714, p. 33, 
 
338 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Assuming that the refractive power of the air is proportional to its density, 
 and that the densities of the successive strata of air are proportional to 
 the pressures, he succeeded, by the aid of analysis, in obtaining a rigorous 
 solution of the problem ; but the results a,t which he arrived were not ex- 
 hibited in a form that was commodious for calculating a table of refractions. 
 It is a remarkable fact, that while Taylor deduced the expression for 
 the differential of refraction with all desirable accuracy, he stood in this 
 respect almost alone, until Kramp published his researches on refraction 
 towards the close of the eighteenth century *. 
 
 In 1729 Bouguer investigated the theory of astronomical refraction in a 
 memoir which obtained for him the prize of the Academy of Sciences of 
 that year. Instead of adopting the Newtonian doctrine of refraction, he 
 imagined the incessant deflection of a ray of light proceeding from a 
 celestial body through the atmosphere, to be occasioned by the action of 
 a substance pervading the aerial fluid, which he termed the refractive 
 matter, and which he supposed to dilate gradually in ascending from the 
 surface of the earth. Assuming a certain hypothesis with respect to the 
 dilatation of the refractive matter, he deduced a theorem for computing 
 the refraction corresponding to any assignable altitude. The values of 
 the constants upon which the practical application of this theorem rested, 
 were determined by means of two observed refractions. These were the 
 horizontal refraction, which he fixed at 33', and the refraction at 26 of 
 altitude, which he made equal to % 12'' '. He then computed a table of 
 refractions extending from the horizon to the zenith, which was found to 
 exhibit a tolerably satisfactory agreement with observation. 
 
 In 1743 Thomas Simpson published his " Mathematical Dissertations, 1 ' 
 which contained an investigation of the problem of astronomical refraction. 
 He remarked that the hypothesis respecting the constitution of the atmo- 
 sphere which assumed the densities of the successive strata of air to be 
 proportional to the pressures, was manifestly erroneous ; for although it 
 was quite true in the case of a uniform distribution of heat, it was inappli- 
 cable to the actual state of nature, in consequence of the air in the upper 
 regions of the atmosphere being colder, and therefore less elastic, than 
 the air near the surface of the earth. Hence, instead of supposing the 
 densities of the successive strata of air to diminish in geometrical progres- 
 sion, which is the law corresponding to a uniform temperature, he sup- 
 posed them to diminish by equal degrees as the altitude above the earth's 
 surface increased, or, in other words, he supposed them to diminish in 
 arithmetical progression relative to the altitude. Assuming the Newtonian 
 doctrine of refraction as the basis of his investigation, he deduced a veiy 
 concise theorem for calculating the refraction corresponding to any assigned 
 zenith distance. The constants involved in this theorem were determined 
 by means of two observed refractions, for which he was indebted to Dr. 
 Bevis, a contemporary astronomer. These were the horizontal refraction, 
 which was valued at 33', and the refraction at 30 of altitude, which was 
 
 * M. Matthieu, in his interesting note on the theory of astronomical refraction, inserted 
 at the end of Delambre's " Histoire de 1' Astronomic au Dixhuitieme Siecle," has remarked 
 that the expression for the differential of refraction assigned by Taylor is not rigorously 
 true. M. 1'lana, however, has very plainly shewn that this remark* is not correct, being 
 quite irreconcilable with the process of investigation, as well as the numerical data of 
 Taylor. (Mem. Acad. Tur., vol. xxxii., p. 61.) M. Matthieu's mistake arose from attach- 
 ing too literal a signification to a verbal expression employed by the English mathema- 
 tician. 
 
HISTOKI OF PHYSICAL ASTKONOMY. 329 
 
 fixed at ]/ 30".5. By the aid of these data Simpson calculated a table of 
 refractions, which was found to agree sufficiently well, under certain 
 restrictions, with the results of observation in all those cases wherein 
 the altitude was considerable. Another table was calculated by him, 
 in which the fundamental refractions were somewhat larger than those 
 above stated. This modification of the original table was intended to 
 meet the case of a low temperature of the atmosphere. M. Matthieu was 
 the first who shewed that Simpson's theorem is in point of fact identical 
 with the one which Bouguer had deduced a few years previously, by 
 means of an investigation founded on a totally different conception of the 
 nature of refraction. 
 
 While mathematicians were engaged in researches on the theory of 
 atmospheric refraction, astronomers were endeavouring, by the aid of ob- 
 servation, to calculate tables which should be capable of assigning the 
 magnitude of refraction at any altitude above the horizon. It was long, 
 however, before they perceived the necessity of taking into account the 
 corrections depending upon the variations of the pressure and temperature 
 of the air. Halley was the first who remarked that the quantity of refrac- 
 tion must necessarily vary with the weight of the atmosphere. In 1720 
 he read before the Royal Society a paper relating to J. Cassini's researches 
 on the parallax of Sirius, wherein he asserted that Hawksbee having 
 demonstrated by experiment that the refractive power of the air is propor- 
 tional to its density, it followed that if the barometer were supposed to 
 vary from 28 to 30 inches, or one-fifteenth part, the quantity of refraction 
 at every altitude would undergo an equal degree of variation, and hence 
 he inferred that the refraction of Sirius, which was ]/ 55", might fluctuate 
 from this cause to the extent of 1" or 8" *. We have already seen that 
 Picard found reason to suspect that the refractions were affected by the 
 variations of temperature. La Hire denied that observation afforded any 
 proof of the refractions being liable to fluctuate from such a cause. No 
 further notice of the subject appears to have been taken by any astro- 
 nomer until Le Monnier directed attention to it on the occasion of his 
 publication of the Histoire Celeste, in the year 1741. In the introduction 
 to that work he asserted that the variations in the temperature of the 
 atmosphere exercised a sensible influence on the refractions of the celestial 
 bodies. From a great number of observations of circumpolar stars, made 
 by him during the greatest heat of summer and the most intense cold 
 of winter, he inferred that, at 4 44' of altitude, the variation of refraction 
 was 2', corresponding to a variation of the thermometer amounting to 36: 
 
 The three celebrated astronomers, Bradley, Lacaille, and Mayer, whose 
 labours, in so many respects, form the commencement of a new era in the 
 history of astronomy, simultaneously introduced the practice of applying 
 to a mean table of refractions, the corrections depending upon the daily 
 fluctuations of the barometer and thermometer. From observations of the 
 least and greatest altitudes of circumpolar stars, and of the altitude of the 
 sun at the equinoxes, Bradley deduced a theorem of great simplicity and 
 elegance for computing the mean quantity of refraction corresponding to 
 any given altitude. The variable effect depending on the pressure of the 
 atmosphere offered no difficulty, being simply proportional to the oscilla- 
 tions of the barometer. The correction for the variation of temperature 
 was a delicate point of investigation. By instituting a careful comparison 
 
 * Phil. Trans., 1720, p. 3. 
 
380 HISTOEY OF PHYSICAL ASTKONOMY. 
 
 between the actual refractions, as determined at the extreme degrees of 
 heat and cold throughout the year, Bradley deduced a rule for com- 
 puting its values, which was found to present a remarkable agreement 
 with the results of observation. The application of the corrections for 
 pressure and temperature to the theorem Tor computing the mean refrac- 
 tions, furnished him with a general rule for computing the quantity of 
 refraction, corresponding to any apparent altitude, and under every condi- 
 tion of the atmosphere, with respect to pressure and temperature. The 
 refraction at 45, when the barometer stood at J29.6 inches, and the 
 thermometer at 50 Fahrenheit, was fixed by him at 56".8. The general 
 rule assigned by him was found to give results of remarkable accuracy, 
 as far as 80 of zenith distance, and until about the beginning of the 
 present century it was almost universally used in the computation of 
 astronomical refractions. 
 
 Mayer's formula for refraction appeared in a posthumous work, contain- 
 ing his solar and lunar tables, which was published at London in the 
 year 1770*. The main peculiarity of this formula was the thermometric 
 correction, which, although somewhat different from Bradley 's, was found 
 to represent the effects produced by the variations of temperature with 
 very great accuracy. Lacaille's researches on refraction were founded on 
 a comparison of a great number of observations made by him at the 
 Cape of Good Hope with corresponding observations made at Paris. By 
 a comprehensive and skilful discussion of these observations he succeeded 
 in forming a table of refractions extending from the zenith to a distance 
 of 6 from the horizon. He made the refraction at 45 equal to 6 6". 5, the 
 barometer being supposed to stand at 28 French inches, and the thermo- 
 meter at 10 Reaumur. This determination was manifestly too great by 
 6" or 1", a circumstance which seemed inexplicable when the acknow- 
 ledged accuracy of Lacaille, as an observer, was taken into account. 
 Maskelyne was tho first who traced the error to its true source, namely, 
 to a defect in the instrument of Lacaille K Delambre, by various calcula- 
 tions, has fully verified the assertion of the English astronomer];. 
 
 The theory of astronomical refraction continued throughout the whole 
 of the eighteenth century to exercise the talents of the most eminent 
 geometers of Europe. Its slow improvement is mainly attributable to 
 the imperfect knowledge that prevailed respecting the actual constitution of 
 the atmosphere. In 1799, Kramp, a German mathematician, published a 
 work containing a more complete investigation of the subject than any 
 which had hitherto appeared. It had been already ascertained that, ex- 
 cept for low altitudes, there were several hypotheses respecting the law 
 of the density of the air that were capable of representing the observed 
 refractions with almost the same degree of accuracy, provided the values of 
 the constants were determined with sufficient precision. Kramp com- 
 menced his researches by supposing that the densities of the successive 
 strata of air diminish in the same ratio with the pressures, an hypothesis 
 which implied that the temperature of the air is uniform. By a rigorous 
 analysis he deduced an expression for refraction involving two constants, 
 the values of which it was possible to determine without having recourse to 
 astronomical observation. These were the refractive power of the air, and 
 its density at the surface of the earth corresponding to a given height of the 
 
 * Tabulae Motuum Solis et Lunse. Lond., 1770. 
 
 f Phil. Trans., 1787, p. 173. 
 
 \ Hist. Ast. au Dixhuitteme Si^cle, pp. 485-89. 
 
HISTOEY 01<' PHYSICAL ASTRONOMY. 331 
 
 barometer. We have seen that Cassini, Bouguer, and Simpson succeeded 
 in determining the elements of their respective theories, only by means of 
 two observed refractions of a celestial body. Kramp imagined that the 
 formula he had deduced from the hypothesis of a uniform temperature 
 would serve to represent the observed refractions as far as 84 of zenith 
 distance. This, however, was awarding to it a greater degree of accuracy 
 than it was really entitled to. For the refractions near the horizon he 
 adopted a more comprehensive view of the subject, by taking into account 
 the influence of temperature in modifying the law of the density of the 
 air. 
 
 The illustrious Laplace was the next person who contributed by his 
 labours to the improvement of the theory of astronomical refraction. By 
 pursuing a method of investigation founded upon the omission of small 
 quantities, the influence of which, under certain conditions, would be 
 insensible, he deduced a formula for refraction, which possessed the advan- 
 tage of being independent of any hypothesis respecting the constitution of 
 the atmosphere. The constants were the same as those which Kramp 
 had introduced into his results. The importance of such a formula as 
 that discovered by Laplace must be very obvious, when the difficulty of 
 ascertaining the law of the density of the atmosphere is taken into con- 
 sideration. It is but just, however, to state that the illustrious geometer 
 referred to was anticipated on this occasion by Oriani, who had been con- 
 ducted, by an investigation of the subject, to a similar result several 
 years previous to the publication of the Mecanique Celeste *. 
 
 Laplace found, by strict investigation, that no appreciable error would 
 be entailed on the final results by the peculiar mode of procedure which 
 he employed in deducing the above-mentioned formula, so long as the zenith 
 distance did not exceed 74. The investigation of the law of refraction 
 towards the horizon was attended with extreme difficulty, since it de- 
 pended upon the peculiar constitution of the atmosphere, which in a great 
 degree was unknown, on account of the uncertainty that prevailed respect- 
 ing the precise influence of temperature. Having remarked that an 
 atmosphere whose density diminished in geometrical progression made 
 the refractions towards the horizon too great, while, on the other hand, 
 one whose density diminished in arithmetical progression made the same 
 refractions too small, Laplace was led to believe that an hypothesis which 
 should combine both laws of progression would probably afford an accurate 
 representation of the true constitution of the atmosphere. Pursuing this 
 idea he investigated the law of refraction for low altitudes, and deduced a 
 formula which he adapted so as to represent the observed refraction at the 
 horizon. By means of this formula, which was designed to represent the 
 refractions of all zenith distances greater than 74, and the formula 
 already referred to, which was applicable to the remaining part of the 
 quadrant, a table of refractions was calculated under the superintendence 
 of the French Bureau ties Longitudes, and was first published in the year 
 1806. The refractive power of the air was determined astronomically, 
 
 * The investigation alluded to in the text, according to Plana, appeared in the Milan 
 Ephemeris for 1788. (Mem. Acad. Tur., tome xxvii.) Oriani's remarks upon the ex- 
 pression deduced by him are very clear in reference to the question of its generality. 
 The following are his words, as cited by the philosopher just mentioned: " Quae ex- 
 pressio a nulla pendet hypothesi, vel circa caloris legem in atmosphtera, vel circa aeris 
 densitatem in variis a telluris superficie distantiis." 
 
33 2 HISTORY OF PHYSICAL ASTRONOMY. 
 
 and also by direct experiments \vith the prism. Delambre, by a dis- 
 cussion founded upon a great number of Piazzi's observations of circum- 
 polar stars, and also several hundreds of his own observations of the sun, 
 determined the refraction at 45 of altitude to be equal to 57". 58, the 
 barometer being supposed to stand at 29.6 inches, and the thermometer 
 at 50 Fahrenheit. MM. Arago and Biot, by means of experiments with 
 the prism, obtained a result indicating that, at the same altitude, and 
 under the same conditions of temperature and pressure, the refraction 
 of the atmosphere was equal to 57".65. The agreement of this quantity 
 with that found by Delambre must be regarded as very satisfactory, 
 especially when the widely different nature of the methods employed in 
 determining them is taken into account. 
 
 The table of refractions calculated upon the basis of Laplace's formula 
 was found to represent the observed refractions better than any other that 
 had been hitherto used by astronomers. It has since been published 
 annually in the Connaissance des Temps, and has always been held in 
 great esteem for its accuracy. From the zenith to a distance of 80 " the 
 results agree with the observed refractions to within 1". For lower 
 altitudes they exhibit a small error in excess, which increases continually 
 towards the horizon*. In the Connaissance des Temps for 1851, M. 
 Caillet has calculated the table anew upon the same basis, the results 
 being worked out to a greater degree of accuracy, so as to adapt them to 
 the present advanced state of astronomical science. 
 
 From the relation between the density and pressure of the atmosphere, 
 assigned by his theory, Laplace deduced the law of the diminution of 
 temperature in ascending from the surface of the earth. He endeavoured 
 to verify his theory in this respect by comparing it with a thermometric 
 experiment made by Gay Lussac at an altitude of 6980 metres above the 
 level of the Seine, on the occasion of his famous ascent from Paris in a 
 balloon. The result of this comparison was considered by Laplace to 
 afford a satisfactory confirmation of his theory, for a near agreement be- 
 tween the actual and calculated temperatures could not be expected to 
 take place, on account of the oscillations that incessantly occur in the 
 atmosphere. It must be admitted, however, that in the present instance 
 the representation of the actual constitution of the atmosphere was far less 
 satisfactory than in the case of the refractions, even after assigning their 
 due weight to such temporary causes of discordance f. 
 
 In 1814, Dr. Brinkley communicated to the Pvoyal Irish Academy a 
 paper on the theory of astronomical refraction. Assuming, as facts esta- 
 blished by experiment, that the sines of the angles of incidence and re- 
 fraction bear a constant ratio to each other when the media remain the 
 same, and that for media of different densities the refractive power is pro- 
 portional to the density, he deduced the formulae for refraction correspond- 
 ing to various hypotheses respecting the constitution of the atmosphere, 
 without having recourse to the Newtonian doctrine relative to the attraction 
 of particles at insensible distances. From 525 of his own observations of 
 circumpolar stars, he determined the refraction at 45 to be 57" '.42, the 
 barometer standing at 29.6 inches, and the thermometer at 50 Fahren- 
 heit. Tables were given by him in the same paper to facilitate the calcu- 
 lation of refractions J. 
 
 * Phil. Trans., 1838, p. 186. f See Mec. Cel., tome iv., p. 265. 
 
 Trans. Roy. Irish Acad., vol. xii., p. 77, et seq. 
 
IITSTOftY OF PHYSICAL ASTRONOMY. 333 
 
 In 1823 the late Mr. Ivory communicated to the Royal Society an im- 
 portant paper containing an account of his researches on the theory of 
 astronomical refraction *. Its chief peculiarity consisted in the mode in 
 which the influence of temperature was considered. Laplace, as we have 
 seen, did not introduce this element explicitly into his researches. He 
 merely assumed an hypothesis respecting the constitution of the atmo- 
 sphere, which he conceived would be adequate to account for the effects 
 depending upon the combined variations of temperature and pressure 
 in ascending from the surface of the earth. But although the results 
 calculated on this hypothesis exhibited a remarkable accordance with ob- 
 servation, in so far as regards the refractions of the celestial bodies, still 
 it was desirable to attain the same degree of accuracy by means of a 
 theory in which the temperature of the air appeared in an explicit form as 
 one of the fundamental elements upon which the ultimate results were 
 based. In the outset of his researches Mr. Ivory supposed the tempera- 
 ture of the air to diminish at a uniform rate corresponding to equal 
 increments of altitude. In order to calculate the refractions upon this 
 hypothesis, it was necessary to ascertain the actual diminution of tempera- 
 ture corresponding to a given elevation above the surface of the earth. 
 Mr. Ivory determined the value of this element by a comparison of 
 thermometric experiments made at various altitudes by Gay Lussac, 
 Ramond, and Humboldt. The resulting refractions agreed very well with 
 the corresponding quantities deduced from observation ; but as the hypo- 
 thesis upon which they rested, assigned to the atmosphere a height 
 considerably less than was otherwise probable, Mr. Ivory rejected it, and 
 adopted another founded upon a somewhat different law of temperature, 
 the accuracy of which he verified by shewing its agreement with the actual 
 temperature and pressure of the air as deduced from experiments made at 
 various altitudes above the level of the sea. The initial rate of the 
 diminution of temperature, being a fact established by experiment, was 
 necessarily the same in this as in the previous hypothesis. Mr. Ivory 
 having deduced the results of his theory by a process in which his 
 mathematical genius is strikingly conspicuous, employed them in calcu- 
 lating a new table of refractions. The elements were identical with those 
 of the French tables, except that the constant representing the initial rate 
 of the diminution of temperature was used instead of the horizontal 
 refraction. The resulting refractions were found to agree with observation 
 as nearly as any that had been hitherto calculated. 
 
 Mr. Ivory's theory of refraction possessed the advantage of being 
 founded upon elements, the values of which it was possible to ascertain 
 without having recourse to astronomical observation. It was also found to 
 present a closer, as well as a more general, agreement with the actual 
 diminution of temperature in ascending from the surface of the earth than 
 any previous theory had done. Moreover, the results were obtained by 
 employing an expression for the variation of the density of the atmosphere 
 that was characterised by an extreme degree of simplicity. M. Plana is 
 inclined to doubt whether any new theory of refraction, whatever peculiar 
 advantages it may seem to hold forth, will be found which shall be capable 
 of assigning results of the same degree of accuracy by means of an equally 
 simple law of density f. The same distinguished philosopher has shewn that 
 
 * Phil. Trans., 1823, p. 409, et seq. 
 t Mem. Acad. Tur., vol. xxxii., p. 172. 
 
384 HISTORY OF PHYSICAL ASTBONOMY. 
 
 by applying Ivory's law of the diminution of temperature to the superior 
 regions of the atmosphere, the result agrees very nearly with that deduced 
 by M. Fourier, relative to the mean temperature of the planetary regions 
 depending upon the radiation of heat from.the celestial bodies. Mr. Ivory 
 developed his theory more fully in a paper which he communicated to the 
 Royal Society in the year 1838*. 
 
 No essential improvement has been made in the theory of astronomical 
 refractions since the publication of Mr. Ivory's remarkable results. The 
 labours of those eminent geometers who have subsequently directed 
 their attention to the subject, serve only to shew that the most con- 
 summate mathematical skill, apart from experimental researches, is no 
 longer adequate to this end. A review of the progress of this interesting 
 branch of physical enquiry cannot fail to suggest the conclusion that the 
 steps which have led to its present advanced condition are mainly due 
 to the successive labours of Newton, Taylor, Oriani, Kramp, Laplace, and 
 Ivory. With respect to Newton, we allude solely in this remark to his 
 exposition of the doctrine of refraction generally upon physical principles, 
 since his unpublished researches on astronomical refraction, considered as 
 a special branch of enquiry, could not possibly exercise any influence on 
 the labours of his successors. On the other hand it is impossible to 
 peruse without feelings of intense admiration the account of that illus- 
 trious philosopher's researches, as exhibited in his correspondence with 
 Flamstead. The accurate conception which he forms of the relation 
 between the phenomenon of refraction and the density of the refractive 
 medium, the acuteness which he displays in detecting the various sources 
 of its incessant fluctuations, and the sagacity with which he combines the 
 physical elements upon which it depends, so as to form the groundwork 
 of a profound mathematical investigation are all unequivocal indica- 
 tions of a genius of the most exalted order, and such as proclaim, in no 
 unworthy language, the immortal author of the Principia. Previous to 
 the publication of his correspondence with Flamstead, it was supposed 
 that his researches on the subject did not extend beyond the explanation 
 of the general phenomena of refraction by mechanical principles, and the 
 determination of the law of the density of the atmosphere upon the hypo- 
 thesis of a uniform temperature. It now appears that, by a beautiful 
 application of his theory of central forces, he completely solved the 
 problem of atmospheric refraction upon more than one hypothesis respect- 
 ing the law of density. The only real step in advance that has been made 
 by Newton's successors consists in the introduction of the element of tem- 
 perature into the researches on the subject f. The intimate connexion of 
 this principle with the density of the atmosphere, and its consequent 
 influence upon the refraction of a celestial body, did not fail to be discerned 
 by him ; but the imperfect state of thermotics in his time rendered 
 hopeless any attempt to investigate the effects produced by it. 
 
 Whatever improvements may be effected in the theory of astronomical 
 refraction by future enquiry will, in all probability, depend upon the 
 
 * Phil. Trans., 1838, p. 169, et seq. 
 
 f It is worthy of remark that those geometers who refused to admit the Newtonian 
 princ-iple of the attraction of the molecules of matter, failed by means of any other hypo- 
 thesis to deduce the rigorous expression for the differential of refraction. Thus Plana 
 has shewn (Mem. Acad. Tur., tomes xxvii, xxxii.) that the expressions assigned by D. Ber- 
 noulli, Euler, Lambert, and Lagrange were all more or less erroneous, Kramp, Laplace, 
 and all modern enquirers, except Brinkley, have employed the Newtonian theory. 
 
HISTORY OK PHYSTCAL ASTRONOMY. 386 
 
 success of experimental researches on the constitution of the atmosphere, 
 instituted mainly with a view to ascertain, with a greater degree of preci- 
 sion, the mean law of the density of the air and the influence of the 
 aqueous vapour diffused throughout the different strata. It is a fortunate 
 circumstance that, except in those cases wherein the zenith distance is 
 considerable, theory is capable of representing the observed refractions 
 independently of a knowledge of the law of density. The question rela- 
 tive to the influence of the aqueous vapour suspended in the atmosphere 
 is still involved in great obscurity, notwithstanding the researches of 
 several eminent modern philosophers on the subject*. 
 
 On account of the imperfect state of the theory of refraction, many 
 astronomers have been induced to rely mainly upon their own observations 
 for the means of constructing tables which shall assign with precision the 
 numerical value of this correction, corresponding to any given altitude. 
 Allusion has already been made to the labours of Bradley and his con- 
 temporaries, with a view to the attainment of this end. In more recent 
 times the subject has occupied the attention of many eminent astronomers. 
 Piazzi, while engaged in the construction of his great catalogue of stars, 
 employed a table of refractions which he deduced wholly from his own 
 observations. Groombridge, Carlini, and many other astronomers of the 
 present age, have distinguished themselves by researches of a similar 
 nature. The labours of Bessel on this subject were worthy of his com- 
 manding powers of investigation. In the Berlin Epliemeris for 1813, 
 he determined the refractions deducible from Bradley : s observations. He 
 resumed the subject in the Fundamenta Astronomies, employing the 
 suggestions of theory to aid him in his researches. In the Tabula 
 Ecgiomontanfu he has given a table of refractions extending from the 
 zenith to a distance of 83. This table, being founded upon a skilful discus- 
 sion of a great number of accurate observations, is regarded as one of the 
 most trustworthy that has been hitherto calculated, and in consequence 
 is generally used by the astronomers of the present day. 
 
 No table has yet been calculated which is capable of representing the 
 refractions near the horizon with a degree of precision adequate to the re- 
 quirements of astronomical observation. The physical constitution of the 
 atmosphere, which fails to exercise any sensible influence on the refrac- 
 tions at considerable altitudes, plays an important part when the rays of 
 light from the celestial bodies enter the refracting medium in very 
 oblique directions ; and, being liable to incessant oscillations from meteoro- 
 logical causes, it occasions thereby corresponding variations in the re- 
 fractions -h Irregularities in this manner arise which are found to be 
 
 * The refractive power of aqueous vapour exceeds that of air of the same density ; but 
 it has been found that under the same pressure of the atmosphere, the density of air exceeds 
 that of the vapour suspended in it, nearly in the same proportion. Hence the influence 
 of aqueous vapour upon refraction has been generally supposed to be insensible. 
 
 t If the earth was bounded by a plane surface, and the air was arranged in strata 
 parallel to it, the refraction suffered by a ray of light proceeding from a celestial body, 
 would be the same as if it had at once passed from the ethereal regions into the air 
 at the earth's surface. Hence, in such a case, the quantity of refraction corresponding to 
 any given altitude might be deduced simply from researches on the density of the air 
 at the earth's surface, independently of a knowledge of the law according to which (the 
 density varied. Now, when a ray of light proceeds from a celestial body near the zenith, 
 it is manifest that, although the strata of air are in reality disposed in concentric spherical 
 shells, they are nearly parallel to each other at the points where the ray impinges upon 
 them. On the other hand, if the ray proceeds from a celestial object, situate near the 
 horizon, it enters the atmosphere in a very oblique direction, and consequently the strata 
 
036 HISTORY OP PHYSICAL ASTRONOMY. 
 
 altogether independent of the usual indications of the barometer and 
 thermometer. Such anomalous effects are doubtless attributable to 
 changes in the upper regions of the atmosphere, the nature and extent of 
 which the observer is unable to ascertain even with the smallest degree of 
 success. It would, therefore, appear t& be a work of supererogation to 
 calculate the mean refractions for low altitudes when the appropriate 
 corrections to be applied to them do not exhibit sufficient indications 
 whereby their values may be determined. The mode of procedure that 
 appears to be best adapted for overcoming this difficulty, consists in an 
 extensive study of meteorological phenomena, with a view to ascertain the 
 laws of those oscillations which affect the mean condition of the atmo- 
 sphere at different altitudes above the surface of the earth. It is 
 gratifying to think that this branch of physical enquiry is at length 
 beginning to receive an amount of attention adequate in some degree to 
 its paramount importance. 
 
 The grand discovery of the Aberration of Light resulted in an attempt 
 to detect the annual parallax of the fixed stars. Although the facts re- 
 vealed by the invention of the telescope and the discovery of gravitation, 
 had the effect of establishing beyond all doubt the truth of the Copernican 
 system of the world in the minds of astronomers, still it was desirable to 
 obtain an assurance on this point, founded upon an argument which ap- 
 pealed more directly to the senses than any that had been hitherto adduced. 
 The absence of any appreciable change in the positions of the fixed stars, when 
 observed at opposite extremities of the terrestrial orbit, was one of the earliest, 
 as it was unquestionably the most serious objection that had been urged 
 against the earth's motion ; and it was always considered that the detection 
 of such a change by observation would furnish an irrefragable proof that 
 the earth is not the centre of the solar system. Astronomers in various ages 
 had attempted to accomplish this object, but all their efforts had hitherto 
 proved fruitless. One of the methods which seemed to be best adapted 
 for this purpose was that employed by Hooke, of observing stars whose 
 zenith distance is small, since the effects arising from any uncertainty 
 in the value of refraction are thereby avoided. That astronomer had 
 selected for the object of his enquiry the bright star y Draconis, which 
 passes within a few minutes of the zenith of Gresham College, where 
 his instrument was erected ; and by observing it carefully at different 
 seasons of the year, he came to the conclusion that it had a sensible 
 parallax. It was with the view of verifying the interesting result an- 
 nounced by Hooke that, towards the close of the year 1725, Molyneux, 
 an amateur of astronomy, resolved to undertake a series of observations 
 of the same star. In pursuance of this design he caused a large zenith 
 sector to be constructed by Graham, the famous mechanician, which he 
 erected at Kew, his place of residence. On the 3rd of December, 
 1725, the instrument was for the first time employed in determining 
 the position of the star as it passed the zenith. Similar observations 
 were also made on the 5th, llth, and 12th of the same month, but no 
 change in the position of the star having been detected, a circumstance 
 which was naturally accounted for by the position which the earth then 
 occupied in its orbit, it was deemed unnecessary to make any further 
 
 at the points of impact rapidly diverge from parallelism. It is manifest, therefore, that 
 while in the former case the law of the density of the atmosphere may be dispensed with, 
 in computing the quantity of refraction, without entailing any material error, the same 
 course of procedure cannot be pursued with equal safety in the latter case. 
 
HI8TOEY OF PHYSICAL ASTRONOMY. 337 
 
 observations until the season of the year should arrive when the effect 
 produced by parallax would be most readily apparent *. It was, therefore, 
 more from curiosity than any other motive, according to his own state- 
 ment, that Bradley, who was then at Kew, was induced to observe the 
 star on the 17th of December. On this occasion the position of the star 
 was found to be somewhat more southerly than it appeared to have been 
 from the previous determinations. Suspecting that the discordance arose 
 from an error in the observations, Molyneux and Bradley again determined 
 the position of the star on the 20th of December, when to their great 
 surprise they discovered that it had advanced still further towards the 
 south f . This circumstance was the more surprising, as the direction of 
 the star's apparent motion was opposite to that which would have resulted 
 if the effect had been occasioned by parallax. The star continued 
 to advance towards the south until about the beginning of March, 1726, 
 when it attained a distance of 20" from its original position. It now ap- 
 peared for some time to be stationary, no sensible change of position having 
 been indicated by several successive observations. About the middle of 
 April it appeared to be returning towards the north, and by the middle of 
 June it again passed the meridian at the same distance from the zenith 
 as it did in the beginning of December. It continued to pursue the 
 same direction until September, when its displacement towards the north 
 became as great as it had been towards the south in the beginning of 
 March. After remaining for some time stationary, it again reversed its 
 motion, and finally arrived, in the beginning of December, in the same 
 position which it occupied twelve months previously, allowing for the 
 small change of declination, occasioned by the precession of the 
 equinoxes. 
 
 The great regularity with which the phenomenon passed through its 
 successive phases, clearly indicated that it was not accidental, but, on the 
 contrary, that it arose from the uniform operation of some unknown 
 physical cause. A nutation of the earth's axis suggested itself as probably 
 capable of explaining the observed motion ; but although this hypothesis 
 accounted sufficiently well for the change of declination of y Draconis, it 
 was soon found to be inconsistent with similar observations of other stars. 
 This -was more especially true with respect to a small star opposite in 
 right ascension to y Draconis. In this case the direction of the apparent 
 motion of the star was indeed such as would have resulted from a nutation 
 of the earth's axis ; but the actual change of declination was equal only 
 to half that of y Draconis, whereas, if the phenomenon had been really 
 due to a nutation of the earth's axis, the change of declination would have 
 been nearly the same for both stars. Their attempt to explain the 
 phenomenon by refraction was also equally unsuccessful ]. 
 
 * The annual parallax of a fixed star in latitude, is at its maximum when the earth is 
 situate in the plane of a great circle to the ecliptic passing through the star. In such a 
 position it is manifest from the mathematical nature of a maximum or minimum, that the 
 variation of parallax must be insensible. Now, since the star y Draconis is situate near 
 the solstitial colure (in 1700 its right ascension was about 267), it is easy to see that 
 the above condition would be nearly fulfilled about the time when Molyneux commenced 
 his observations. 
 
 f The loose piece of paper upon which Bradley made the memorandum of this famous 
 observation, has been found among his manuscripts. A fac-simile of this highly in- 
 teresting relique is given by Rigaud in his Miscellaneous Works and Correspondence 
 of Bradley. 
 
 \ Their conjecture respecting the probability of the displacement being occasioned by 
 
338 HISTOKY OF PHYSICAL ASTRONOMY. 
 
 Being anxious to ascertain the laws of this singular phenomenon 
 and to discover its physical cause, Bradley resolved to procure an in- 
 strument for himself, so that he might make observations for that pur- 
 pose with greater convenience. He therefore made Graham construct 
 for him a zenith sector which measured 12 feet in length, and had an 
 arc of 6J. By means of so large an arc he was enable to make choice 
 of more than 900 stars of different magnitudes contained in Flamstead's 
 Catalogue*; but his principal reason for having recourse to such a con- 
 struction was, that he might observe Capella, which was the only star of 
 the first magnitude that passed near his zenith. 
 
 The instrument having been erected at Wansted in Essex, on the 19th 
 of August, 1727, Bradley proceeded forthwith to make observations with 
 it, selecting such stars as appeared to be best adapted for throwing light 
 upon the phenomenon f. Of these there were twelve that could be observed 
 at all seasons of the year, being bright enough to be seen in the day-time 
 when nearest the sun. He had not long continued his observations when 
 he found that only those stars which were situated near the solstitial 
 colure were farthest north and south when the sun was about the equi- 
 noxes ; and he finally discovered it to be a general law that each star was 
 farthest north when it passed the zenith about six o'clock in the evening, 
 and farthest south when it passed about six in the morning. When his 
 observations had extended over a whole year, he proceeded to compare 
 them together, and having obtained a satisfactory knowledge of the laws 
 of the phenomenon, he began to enquire into its probable cause. He had 
 already arrived at the conviction that it could not be due to a nutation 
 of the earth's axis. He had also ascertained that it could not in any way 
 arise from refraction. He now considered the effect of an alteration in 
 the direction of the plumb line, but he soon found it was inconsistent with 
 his observations. At length the happy idea occurred to 
 'his mind, that the phenomenon might be completely ac- 
 counted for by the gradual propagation of light, combined 
 with the motion of the earth in its orbit. The following 
 is a brief exposition of the mode in which he conceived 
 it to originate. 
 
 Let c A be a ray of light falling perpendicularly upon 
 the line DB. Then, if the eye is at rest at A an object 
 at c must appear in the direction A c whether light be 
 propagated in time or in an instant. But if the eye is 
 moving from B towards A, and if light at the same time is 
 propagated with a velocity that is to the velocity of the 
 eye as c A to B A, then the particle of light which 
 enters the eye at A must have been at c when the eye 
 was at B. Hence, if B c be a tube capable of admitting 
 only one particle of light, it is manifest that the particle 
 at c will descend along the tube if it be inclined at the 
 angle ABC, but that it will not reach the eye if the tube be inclined 
 at any other angle. In like manner, if B c represent the tube of a 
 telescope through which the object is viewed, it must be inclined at 
 
 refraction, was founded on the supposition of an annual change in the figure of the at- 
 mosphere, produced by the motion of the earth through a resisting medium. 
 
 * The instrument of Molyneux had a range of only a few minutes ; its length, how- 
 ever, was twice that of Bradley's. 
 
 t Molyneux assisted Bradley in erecting his sector, On the 22nd of August, 1727, 
 
HISTORY OF PHYSICAL ASTRONOMY. 339 
 
 the angle ABC, in order that the particle of light entering the eye 
 at A, shall have descended along the optical axis of the telescope. If 
 the eye had been moving with the same velocity but in the contrary 
 direction, viz., from D towards A, then the tube must have been in- 
 clined at the angle ADC, which is equal to the former angle. Although, 
 therefore, the true place of the object at c, when viewed from A, is perpen- 
 dicular to the direction in which the eye is moving, it will appear in the 
 direction of the tube, and the magnitude of the displacement hence arising 
 will manifestly depend upon the relation between the velocity of light and 
 the velocity of the eye. If light moved 1000 times faster than the eye, 
 the angle ABC would be equal to 89 56^', and the displacement of the 
 object would consequently amount to 3|'. 
 
 Admitting that the earth revolves round the sun in an annual orbit, 
 and that the velocity of light exceeds that of the earth, in the ratio of 
 1000 to 1 , it follows from what has been already stated, that an object 
 situate in the pole of the ecliptic would appear during the course of a 
 year to describe a small circle whose radius is equal to 3^', its true place 
 being the centre of the circle. Bradley further ascertained that an object 
 situate in any other position of the celestial sphere would describe annually 
 a small ellipse round its true place, the minor axis of which would coincide 
 with the circle of longitude passing through the object. He also inferred 
 from his hypothesis that the major axis of the ellipse would be equal to 
 the radius of the small circle which an object situate in the pole of the 
 ecliptic would describe, and that the minor axis would be to the major 
 axis as the sine of the latitude to radius. 
 
 Since the radius of the small circle, which an object situate in the pole 
 of the ecliptic would thus seem to describe, depends upon the ratio of the 
 velocity of light to the orbitual velocity of the earth, it is manifest that 
 if the radius of this circle be determined by observation, the ratio in 
 question may hence be readily ascertained. Now Bradley found from 
 observations of y Draconis that the radius of the small circle amounted to 
 20". 2, whence he concluded that the velocity of light exceeds the velocity 
 of the earth in its orbit in the ratio of 10,210 to 1. Knowing the velocity 
 of the earth he hence obtained 8 m 12 s for the time which light occupies in 
 passing from the sun to the earth. By means of similar observations of 
 various other stars he found that the major axis of the apparent ellipse 
 described by each star, or in other words the diameter of the little circle 
 which a star situate in the pole of the ecliptic would describe, was con- 
 tained somewhere between 40" and 41 V . Assuming its true value to be 
 40|" he hence inferred that light occupied 8 m 13 s in passing from the 
 sun to the earth. This appeared to him to afford an interesting con- 
 firmation of his hypothesis, being a mean of the results deduced at dif- 
 ferent times from the eclipses of Jupiter's satellites. 
 
 Having determined the maximum value of the inequality, Bradley next 
 
 he thus writes in the journal of his observations at Kew : " Now Mr. Bradley's instru- 
 ment is set-up and we go on comparing notes from this time." This plan of observing 
 together was not, however, realised to any great extent. Only six observations subse- 
 quent to the erection of Bradley's instrument, are recorded in the Kew Journal. The 
 last is dated the 29th of December, 1727. Molyneux, having been appointed one of the 
 Lords of the Admiralty a few months previously, doubtless found it to be incompatible 
 with the due discharge of his official duties, to continue his astronomical observations. He 
 died in April, 1728. (Rigaud's Miscellaneous Works and Correspondence of Bradley.) 
 
 7. 2 
 
340 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 proceeded to compare its variations throughout the year, with the cor- 
 responding numbers assigned by his hypothesis. The result of this 
 comparison was in the highest degree satisfactory. Of seventy decima- 
 tions of y Draconis determined in the course of a year, one only differed 
 more than 2" from the hypothesis, and even in this case the observation 
 was marked doubtful on account of clouds. The comparison of the ob- 
 served and computed declinations of n Urscs Majoris exhibited an equally 
 gratifying accordance *. 
 
 The phenomenon referred to in the foregoing account received from 
 Bradley the name of Aberration. Its discovery is universally regarded as 
 one of the most important accessions which astronomical science has ever 
 received. The sagacity which Bradley evinced as well in the establish- 
 ment of its laws, as in the detection of its physical cause, would entitle 
 him to a place among the greatest philosophers of ancient or modern 
 times, even if no other triumphs had adorned his career. 
 
 It has been mentioned that Bradley estimated the maximum of 
 aberration at 20".25. Upon further consideration he was induced to fix 
 it at 20" f. The delicacy of modern researches on astronomy has ren- 
 dered a closer approximation to the true value indispensable, even although 
 the corrections assigned by the various enquirers who have devoted their 
 attention to the subject, do not in any case exceed a few tenths of a 
 second. Delambre, by comparing together observations of a thousand 
 eclipses of Jupiter's first satellite, deduced 20".255 as the most probable 
 value of the coefficient of aberration. This result, as we have seen, agrees 
 very nearly with that originally obtained by Bradley. Various deter- 
 minations of this element, have been assigned by modern astronomers, 
 which generally fluctuate between 20". 7 080 and 20".2116. In 1844, 
 Baily, having compared together all those that were known to him, de- 
 duced 20". 4192 as the most probable value. This result has received a 
 strong confirmation from the recent researches of MM. Peters and Struve. 
 M. Peters, by means of a great number of observations made at Pulkowa, 
 with a vertical circle constructed by Ertel, has determined the maximum 
 value of aberration to be 20".481. M. Struve makes it 20".445 by a dis- 
 cussion of observations made also at Pulkowa, with a transit fixed in the 
 prime vertical J. 
 
 * Bradley's account of this brilliant discovery is contained in the volume of the Philoso- 
 phical Transactions for 1729. It will be seen that his researches are wholly founded on 
 observations of the declinations of the stars. It does not appear that he attempted to 
 verify his theory by means of right ascensions. At any rate he makes no especial allu- 
 sion in his paper to the effect which the displacement would produce upon those co- 
 ordinates, although the fact announced by him, that every star described an apparent, 
 ellipse necessarily implied variations in right ascension, corresponding to those in decli- 
 nation. It is evident that he deemed observations of right ascension not to be sufficiently 
 trustworthy for so delicate an investigation. In 1730 Manfred! asserted that his obser- 
 vations, although subject to occasional irregularities, exhibited a motion in right ascen- 
 sion, analagous to that which Bradley had detected in declination. (Comm. Acad. 
 Bonon, vol. i. p. 634.) 
 
 t Phil. Trans. 1748, p. 23. 
 
 | Struve's Etudes d' Astronomic Stellaire, p. 96. In the same work it is stated 
 that M. Peters obtained 20' .676 for the maximum value of aberration with a probable 
 error of I". 11, by a discussion of certain observations of Flamstead's which are contained 
 in a letter from that astronomer to Wallis, published in the third volume of the Opera 
 Mathematica of the latter. Flamstead was under the impression that the variations of 
 the star observed by him {Polaris') were occasioned by parallax. 
 
HISTOBY OF PHYSICAL ASTKONO.MY. 841 
 
 When Bradley was engaged in investigating the phenomenon of aberra- 
 tion, he found that in the case of some stars near the equinoctial colure, 
 the change of declination was greater than that \vhich would have resulted 
 from a mean annual precession of 50". Similar observations of stars 
 near the solstitial colure, indicated an effect of a contrary nature, the change 
 of declination being less than the quantity due to the same value of pre- 
 cession. It was manifest, from this circumstance, that the phenomenon 
 could not be attributed to an error in the motion of the equinoctial points. 
 Bradley made repeated observations with the view of discovering its real 
 nature from the year 1727, when his instrument was first erected at 
 Wansted, until 1732, the year of his removal to Oxford. During this 
 interval of time some of the stars near the solstitial colure had changed 
 their declination 9" or 10'' less than the quantity due to a precession 
 of 50" ; while others near the equinoctial colure had exhibited an equal 
 change of decimation in the opposite direction. The north pole of the 
 equator appeared to have approached the stars which came to the meridian 
 with the sun about the vernal equinox and the winter solstice, and to 
 have receded from those which came to the meridian with the sun about 
 the autumnal equinox and the summer solstice. 
 
 After pondering for some time on the phenomenon, Bradley began to 
 suspect that it might arise from the variable action of the moon on the 
 matter accumulated round the terrestrial equator. On account of the 
 motion of the moon's nodes, the inclination of the lunar orbit to the earth's 
 equator is in a state of perpetual change, whence it might readily be in- 
 ferred that the efficacy of the moon to disturb the earth would be subject 
 to a corresponding variation. During a revolution of the moon's nodes the 
 inclination of the lunar orbit passes through all its values, increasing during 
 the half of this period to the extent of 10, and then returning during the 
 other half to its original state. It therefore occurred to Bradley that the 
 motion of the equinoctial points, which partly depends upon the disturbing 
 action of the moon, would be subject to an oscillatory movement of sensible 
 magnitude, the period of which would coincide with the time of a complete 
 revolution of the moon's nodes. Upon comparing the observations of stars 
 near the solstitial colure that were almost opposite in right ascension, he 
 found that the change of declination, though opposite in direction, was 
 equal in quantity ; for while 7 Draconis had advanced northward, the 
 small star 35 Camelopardali appeared to have moved as far towards the 
 south. A nutation of the earth's axis was, therefore, in this case, capable 
 of explaining the phenomenon, although it was found to be inadequate to 
 that end, when the question referred to aberration. The same conclusion 
 followed from a comparison of observations of other stars that, taken two 
 and two, were nearly opposite in right ascension. 
 
 In J727, when Bradley commenced his observations, the moon's ascend- 
 ing node was in Aries, and the inclination of the lunar orbit was at its 
 maximum. In 1736 the lunar node was in the beginning of Libra, 
 having completed half a revolution in virtue of its retrograde motion, 
 and the inclination of the orbit had consequently now descended to its 
 minimum. During the intermediate period the change in the declina- 
 tion of stars near the solstitial colure, was less by 18" than that which 
 would have resulted from an annual precession of 50"; for y Draconis, 
 which ought to have advanced about 8" farther towards the south, was ob- 
 served in 1736 to be situate 10" more to the north than it was in 1727. If 
 the phenomenon was supposed to arise from a change in the obliquity of 
 the ecliptic, it would indicate a diminution equal to V in 30 years. As this 
 
343 HISTORY OF PHYSICAL ASTKONOMY, 
 
 quantity greatly exceeded the rate of diminution which had hitherto been 
 deduced from the observations of astronomers, Bradley was induced to 
 ascribe the phenomenon to an oscillation of the earth's axis, occasioned by 
 the disturbing action of the moon upon the terrestrial equator. Being 
 unable, however, by means of observations, extending only over a period 
 of nine years, to judge whether the axis would recover its former position, 
 he found it necessary to continue his observations throughout a whole 
 revolution of the moon's nodes. In the year 1745, when the moon's 
 ascending node had again arrived in Aries, he had the satisfaction to find 
 that the stars returned to the same position which they would have 
 occupied, if the inclination of the terrestrial axis had been the same as it 
 was in 1727. This circumstance appeared to him an indubitable indica- 
 tion that he had detected the true cause of the phenomenon. 
 
 Machin, to whom Bradley communicated an account of his discovery, 
 devised a geometrical theory of the phenomenon, by the aid of which he 
 computed a table of its numerical values. He supposed that while the 
 mean pole of the equator described a circle round the pole of the ecliptic, 
 at the rate of 50" in a year, occasioning thereby the uniform motion of 
 precession, the apparent pole of the equator described round the mean 
 pole, a small circle whose radius was equal to 9", being in that part of the 
 circle which is farthest from the pole of the ecliptic when the moon's 
 ascending node was in the beginning of Aries, and in the opposite point 
 w T hen the same node was in Libra. 
 
 Bradley proceeded to establish a strict verification of his hypothesis, by 
 comparing it with a great number of his observations. The result of 
 this comparison afforded a complete confirmation of his views. Having 
 computed the mean declination of y Draconis from 300 distinct obser- 
 vations, by applying to each observation the appropriate corrections of 
 precession, aberration, and nutation, he obtained a series of results which 
 presented a remarkable agreement with each other. Eleven only were 
 found to differ so much as 2' from the mean of the whole, while not 
 one differed so much as 3" from it. The result was equally satisfactory 
 in the case of several other stars, which he employed in testing his hypo- 
 thesis*. 
 
 It has been stated that Bradley fixed the coefficient of nutation at 9". 
 The researches of subsequent enquirers seem to indicate that the true 
 value exceeds this quantity by a few tenths of a second. Maskelyne made 
 it 9".55. Laplace, by the aid of theory, deduced 9".40 as its most pro- 
 bable value. Lindenau, by a discussion of a vast number of observations, 
 extending from 1750 to 1815, and consequently including three complete 
 revolutions of the moon's nodes, obtained 8". 989 for the coefficient of 
 nutation. This result is now generally supposed by astronomers to fall 
 below the true value. Dr. Brinkley, by comparing 1618 observations of 
 different stars, made it 9".25. Henderson, from the value of the moon's 
 mass, indicated by his researches on the lunar equatorial parallax, deter- 
 mined the coefficient of nutation to be 9".28. Dr. Robinson, from up- 
 wards of 6000 observations with the mural circle, made by Pond at 
 Greenwich, between the years 1812 and 1835, deduced 9".23913 as its 
 most probable value. Various similar evaluations have been effected by 
 modern astronomers. Baily, by a careful comparison of all the results, 
 came to the conclusion that the most probable value of the coefficient is 
 
 See the original Memoir of Bradley (Phil, Trans., 1748, p. 1 et seq.). 
 
HISTOEY OF PHYSICAL ASTEONOMY. 343 
 
 In order to render observations of the planets available as elements of 
 theoretical research, it is necessary to reduce them from the place of ob- 
 servation to the sun, the physical centre of the planetary system. Two 
 steps are requisite for this purpose. The first consists in reducing the 
 apparent position of the planet from the place of observation to the centre 
 of the earth. To this end it is indispensable to obtain a knowledge of 
 the diurnal or geocentric parallax, in other words, the apparent displace- 
 ment occasioned by viewing the body from a point on the surface of the 
 earth instead of its centre. The second step in the reduction of a planetary 
 observation, consists in transferring the position from the centre of the 
 earth to the centre of the sun. This object is effected by means of the 
 annual or heliocentric parallax. When once the absolute magnitude of the 
 terrestrial orbit has been determined by means of the solar parallax, the 
 heliocentric parallax of any planet, is readily ascertained by the aid of 
 Kepler's third law. The reduction of a planetary observation is thus 
 ultimately made to depend upon the evaluation of the solar parallax. The 
 progress of researches on this important subject has already been briefly 
 alluded to in one of the preceding chapters. 
 
 After the astronomer has succeeded in tracing the laws of the various 
 principles which exercise an influence on the apparent positions of the 
 celestial bodies, and has determined their maximum effects with all 
 desirable precision, there still remains the laborious task of computing the 
 displacement occasioned by them corresponding to any assigned instant. 
 Various expedients have been devised with a view to abbreviate the 
 toilsome calculations attendant upon this operation. In the Connaissance 
 des Temps for 1760, there appeared tables having for their object, to faci- 
 litate the computation of aberration and nutation for a few of the principal 
 stars. Similar tables continued to be published in the volumes for the 
 subsequent years, the numbers of stars to which they were adapted, gradu- 
 ally increasing, until at length it amounted to 510 in the volume for 1806. 
 In the same year tables designed to facilitate the calculation of aberration 
 and nutation were published by Cagnoli and De Zach. Cagnoli's tables 
 appeared in the form of an appendix to a catalogue of 501 stars which he 
 published at the same time *. They were applicable only to the stars con- 
 tained in the catalogue. De Zach's tables were attached to a catalogue of 
 1830 zodiacal stars ; but their application was confined to 494 of the prin- 
 cipal stars in the catalogue")-. In 1812, the last-mentioned astronomer 
 gave an important extension to his previous labours by the publica- 
 tion of tables of aberration and nutation, adapted to a catalogue of 1440 
 stars j. A defect of these tables consisted in the omission of the solar 
 nutation, an element of displacement which, although of inconsiderable im- 
 portance compared with the other corrections, is capable of exercising a 
 very sensible influence on the delicate investigations of sidereal astronomy. 
 
 It cannot fail to excite surprise that, until a very recent period, no 
 general methods were devised by astronomers, having for their object 
 to facilitate the reduction of observations, by combining together in one 
 homogeneous system of calculation, as far as was practicable, the separate 
 processes for determining the various inequalities which affect the ap- 
 parent positions of the celestial bodies. With respect to refraction, its 
 
 * Catalogue de 501 etoiles, suivi des Tables relatives d' Aberration et de Nutation ; 
 Mod., 1807. 
 
 *h Tabulae Speciales Aberrationis et Nutationis, &c. ; 2 torn. 8vo., Gotha, 1807. 
 
 { Nouvelles Tables d' Aberration et de Nutation pour 1440 etoiles, 8vo., Marseille, 
 1812. 
 
344 HISTORY OF PHYSICAL ASTKONOMY. 
 
 magnitude in any particular instance depends upon the altitude of the 
 object above the horizon, and the state of the barometer and thermometer 
 at the time of observation. It is obvious, therefore, that it cannot be 
 conveniently combined in calculation with precession, aberration, or nuta- 
 tion, the respective values of which depend on the position of the object 
 in the celestial sphere and on the time of observation. An objection of 
 a similar nature occurs, when the question relates to the combination 
 of the geocentric parallax with any other correction. 
 
 On the other hand, the inequalities of precession, aberration, and nuta- 
 tion, offer obvious facilities for the invention of a method which may em- 
 brace them all in one uniform process of calculation. For a long time, 
 however, no vigorous effort appears to have been made with a view to the 
 attainment of this desirable end. Astronomers continued to calculate the 
 three inequalities by separate processes, notwithstanding the analogy they 
 bore to each other when considered merely in reference to the determina- 
 tion of their numerical values. The reduction of any single observation, 
 could, therefore, be effected only by executing a variety of distinct pro- 
 cesses of calculation ; and it was doubtless owing to the labour necessarily 
 demanded by such an operation, that vast masses of observations came to 
 be accumulated without being reduced at all. 
 
 About the year 1820 the subject began to attract serious attention, and 
 methods designed to facilitate the reduction of observations upon the prin- 
 ciple of combination above referred to, were suggested by various astrono- 
 mers, both in this country and on the Continent. Bessel at 'length pro- 
 posed a method which, on account of its superior advantages, has supplanted 
 all the others. The complete correction of a star's place (in so far as pre- 
 cession, aberration, and nutation are concerned), whether in right ascension 
 or in declination, is by this method expressed in terms of four products, each 
 product being composed of two factors, one of which depends on the place 
 of the star in the celestial sphere, and the other on the time of observation. 
 The factors which depend on the time of observation are the same both 
 for right ascension and declination, but those depending on the place of the 
 star are different. Hence the reduction of an observation, at least as far 
 as relates to the three corrections above-mentioned, demands the com- 
 putation of twelve constants, eight of which depend on the place of the 
 star, and four on the time of observation. Now, when the mean place of a 
 star is once determined, the constants of the first-mentioned group may be 
 computed by an easy process, and it is manifest that when this is once ac- 
 complished, the results will serve equally well for all observations of the 
 star. On the other hand the four constants which depend on the time of 
 observation, will vary for every day of the year, and will even be different 
 on the same day of each successive year. Hence these constants, unlike 
 the former, will require to be calculated for each day of observation. 
 They possess this peculiar advantage, however, that when once cal- 
 culated for any day of the year, they will apply equally well to any star in 
 the heavens on that day. 
 
 The facility with which this method adapts itself to the computation of the 
 apparent places of the stars by the aid of a catalogue of their mean places is 
 very obvious. The eight constants depending on the place of each star, may 
 be calculated once for all, and inserted in the catalogue. The four constants 
 depending on the time of observation, cannot, of course, be included absolutely 
 in any catalogue; but their successive values may be calculated for a definite 
 peroid of time, so as to be applicable to any day of observation comprehended 
 within that period. These objects being accomplished, the determination 
 
HISTORY OF PHYSICAL ASTKONOMi'. 345 
 
 of the complete correction of any star in the catalogue for any day of the 
 year, and the consequent ascertainment of its apparent place on the same 
 day, is an operation -which may be performed in two or three minutes. 
 The advantage \vhich the theoretical astronomer must possess, in being 
 thus relieved at the outset of his researches from a vast amount of 
 tedious calculation, is too obvious to require further notice. The values 
 of the four constants depending on the time of observation, are calcu- 
 lated for each day of the year, and are published annually in the Nau- 
 tical Almanac*. Mr. Airy has recently proposed a modification of 
 Bessel's method, designed to obviate certain inconveniences which in 
 some respects attend its practical application f. 
 
 The Uranographical principles, to which allusion has already been made 
 in this chapter, exercise a direct influence on the apparent positions of the 
 celestial bodies, and therefore an accurate knowledge of the effects pro- 
 duced by them is indispensable in all those questions which concern the 
 relations of space and time. Moreover, the principle of refraction, by 
 affecting the aspect of phenomena, demands attention in various researches 
 relating to celestial physics. 
 
 But the principles of Diffraction and Irradiation are also known to ex- 
 ercise an influence similar to that ascribed to refraction in the latter 
 instance. These, indeed, by occasioning an alteration in the apparent 
 magnitudes of the celestial bodies might be supposed in some cases ulti- 
 mately to affect their apparent positions. Their influence in this respect, 
 however, has been hitherto found to be inappreciable. On the other hand 
 it cannot be doubted, that they sensibly affect the aspect of eclipses both 
 of the sun and rnoon, as well as transits, occultations, and varions other 
 phenomena. A brief historical account of researches on these principles, 
 considered only in so far as their influence on astronomical science is con- 
 cerned, may, perhaps, not be out of place on the present occasion. 
 
 The discovery of the Diffraction of Light is due to Grimaldi, an Italian 
 philosopher of the seventeenth century J. Having admitted a beam of light 
 through a very small aperture into a dark room, he found that the 
 shadows of bodies placed in the cone of light thus formed, when received 
 upon a screen, were larger than they would have been if the rays of light 
 had passed by the edges of the bodies in right lines. He perceived also 
 around the shadows three fringes of coloured light. The fringe nearest 
 the shadow in each case was the broadest; the one most distant from 
 it was the narrowest and faintest of the three. Grimaldi concluded from 
 these facts that light was deflected when it passed by the edges of bodies. 
 He first gave an account of his experiments in a work published at 
 Bologna, in the year 1665 . 
 
 The phenomena of diffraction did not escape the attention of Newton. 
 In the third book of his Optics he gives some account of his researches on 
 the subject. He mentions, however, that he was interrupted in the midst 
 of his experiments, and that at no subsequent period could he find leisure 
 to resume them. This part of the researches of the illustrious philo- 
 sopher must therefore be considered as left in an unfinished state. 
 
 Newton repeated Grimaldi's experiment, by admitting a beam of light 
 
 * These are the constants denominated A, B, c, D, the numerical values of which are in- 
 serted in succession at page xx. of each month, in the first part of the Ephemeris. 
 t Mem. Ast. Soc., vol. xvi., p. 256, et seq. 
 
 $ This property of light is also sometimes distinguished by the term " Inflexion." 
 Physico Mathesis de Lumine. Bonon, 1665. 
 
346 HISTOEY OF PHYSICAL ASTEONOMY. 
 
 into a dark room, through a small hole about the 42nd part of an inch in 
 diameter, and he found, like that philosopher, that slender bodies, placed 
 in the cone of light, threw upon a screen, shadows of much larger dimen- 
 sions than they ought to have done if light had passed in right lines. A. 
 human hair, equal in breadth to the QSOtn of an inch, placed at a distance 
 of 12 feet from the hole, threw a shadow upon a screen 4 inches beyond 
 it, which was equal to the 60th part of an inch in breadth *, and conse- 
 quently was more than four times broader than the hair itself. Newton 
 established, by a variety of experiments, that the phenomena of diffraction 
 were absolutely independent, both of the nature of the substance which 
 threw the shadow, and of the form of its edge. They appeared to him, 
 therefore, to depend upon some principle quite distinct from refraction. 
 He made some interesting experiments on the fringes which surround the 
 shadows of diffracting bodies, and concluded his labours on the subject 
 with certain queries suggestive of the nature of diffraction. 
 
 The phenomena of the diffractive fringes have engaged the attention of 
 many eminent philosophers of the present century, but an account of their 
 labours does not come within the province of this work. The principle of 
 diffraction has been supposed in various ways to affect the aspect of celes- 
 tial phenomena ; but the case in which its influence has been most com- 
 pletely established, is that wherein the object-glass of the telescope con- 
 stitutes the diffracting body. The disks and rings exhibited by the fixed 
 stars, when viewed in telescopes of high power, have been fully accounted 
 for in this manner, by adopting as the basis of enquiry, the principles of the 
 undulatory theory of light. In the next chapter we shall have occasion 
 to mention several phenomena which philosophers have endeavoured to 
 explain by the diffraction of light. 
 
 A principle which is supposed to exercise a more varied and extensive 
 influence on celestial phenomena than the diffraction of light, is that 
 which has been distinguished by the term " Irradiation." In virtue of 
 its operation a luminous object projected upon a dark ground is dilated 
 in all directions, so as to appear somewhat enlarged in dimensions. A 
 striking example of the effect of irradiation is afforded by the appearance 
 of the moon when only a few days old. In this case the luminous crescent 
 is seen to form part of a much larger circle than the remaining portion of 
 the disk, the outline of which is rendered distinctly visible by means of the 
 lumiere cendree, or reflected light of the earth. As might be expected, a 
 phenomenon the converse of this is exhibited, when an opaque body is seen 
 projected upon a luminous surface. The object then appears to be con- 
 tracted in dimensions, from the light encroaching upon it on all sides. 
 
 Some of the phenomena of irradiation are so palpable to observation, 
 that they could not fail to have attracted notice at a very early age. It 
 appears, however, that Kepler was the first who pointed out the conse- 
 quence generally arising from the operation of this principle. His re- 
 marks on the subject are contained in his " Supplement to Vitellion," a 
 treatise on Optical Science which he published in the year 1604 f. After 
 citing the case of the new moon as above referred to, he remarked that 
 the aspect presented by the lunar eclipse of May 25, 1603, afforded a 
 similar illustration of the effect produced by irradiation. Again, it was 
 found that during eclipses of the sun, the deficient segment of the solar 
 
 * Optics, p. 114 (4to., Lond., 1704). 
 
 t Ad Vitellionem Paralipomena quibus Astronomise pars optica traditur, 4to. ; Franc., 
 1604 
 
HISTORY OF PHYSICAL ASTEONOMY. 347 
 
 disk always appeared too small, in consequence of the light. of the visible- 
 segment dilating in all directions and encroaching on the dark limb of the 
 moon. As a simple mode of exhibiting the influence of irradiation, he 
 remarked that if a ruler be held before the eye so as to intercept the light 
 of the moon, it will appear narrower at the part where it is projected upon 
 the lunar disk. 
 
 We owe also to Kepler an explanation of the physical cause of irradia- 
 tion. He supposed that the rays of light from remote objects converged 
 before reaching the retina, and then proceeded in a divergent course, so 
 that each pencil of rays depicted upon the optic membrane a small sur- 
 face instead of a point. It followed as an obvious consequence of this 
 theory, that the object would appear somewhat enlarged. Kepler, how- 
 ever, was of opinion that unless the retina was very sensitive, no impres- 
 sion was produced upon it beyond the central point of the small area 
 corresponding to each pencil of rays. Hence, according to this view of the 
 subject, the phenomena of irradiation would be visible only to a particular 
 class of individuals *. 
 
 The foregoing explanation is exceedingly plausible, but a slight examina- 
 tion will suffice to show that it is inconsistent with the results of observation. 
 In the first place, it is not true that the rays of light emanatiag from remote 
 objects, converge before reaching the retina. The eye in fact possesses a 
 power of adaptation which enables it to bring the rays to a focus upon the 
 optic membrane, however great may be the distance at which the object is 
 placed. Secondly, it is to be remarked that even if this assumption was 
 well founded, the hypothesis would still be inadequate to explain the phe- 
 nomena of irradiation, since the latter do not fail to present themselves to 
 observation at the distance of distinct vision. Lastly, the phenomena of 
 irradiation are generally visible to all persons, although they exhibit 
 themselves with greater intensity to some persons than they do to others. 
 
 The irradiation of luminous bodies was a subject which attracted the 
 attention of Galileo on many occasions in the course of his physical inves- 
 tigations, and a variety of interesting remarks upon it are to be found in- 
 terspersed throughout his writings. In the " Sidereus Nuncius " he 
 asserts that the fixed stars, when viewed with the telescope, are not en- 
 larged in the proportion of the magnifying power. In explanation of this 
 fact he remarks, that the telescope has the effect of stripping the star of 
 the false light by which it is usually surrounded when viewed with the 
 naked eye. This spurious corona is ascribed by him. to the influence of 
 irradiation. It generally increases with the brightness of the field upon 
 which the luminous object is projected. Thus at sunset, when the ob- 
 scurity of the heavens is tempered by the influence of the twilight, the 
 stars, even of the first magnitude, appear excessively minute. So with 
 respect to Venus, notwithstanding the splendour with which she usually 
 shines, she does not exceed a star of the sixth magnitude on those occa- 
 sions when she happens to be visible at noon f . 
 
 Galileo next alludes to irradiation in one of his letters to Welser on the 
 solar spots. Scheiner had remarked that Venus would appear as large on 
 the sun's disk, as she does when she is near her superior conjunction. 
 Galileo, however, denied the truth of this statement. He asserted, in the 
 first place, that the irradiation of the planet usually causes her to appear 
 
 * Ad Vitellionem Paralipomena, p. 217, et seq. 
 
 f Opere di Galileo, torn, ii., p. 13, Edit. Pad., 1747. 
 
o48 HISTORY OF PHYSICAL ASTRONOMY. 
 
 much larger than she really is. In confirmation of this fact he remarked 
 that even when the planet assumes the form of a very slender crescent, she 
 appears round like any other star, her true figure heing masked by the 
 effulgence of her irradiation. On the otfrer hand, when she appears pro- 
 jected on the luminous surface of the sun, she ought to exhibit a corre- 
 sponding diminution of magnitude, from the irradiation of the solar light 
 encroaching everywhere upon her disk. Upon these grounds he con- 
 tended that the planet ought to appear considerably less on the solar disk 
 than she does in any other position*. 
 
 In his " Discourse upon Comets," he finds occasion to refer to the irra- 
 diation of light in refuting an argument used hy his opponents, which was 
 based upon an absurd opinion respecting the theory of the telescope f. It 
 was contended that comets are very remote bodies, because when viewed 
 in the telescope they did not exhibit any sensible enlargement. This 
 fallacy was suggested by the analogy of the fixed stars, for as these bodies 
 did not appear sensibly enlarged in the telescope, and at the same time were 
 well known to be very remote, so it was hastily concluded that the small 
 effect produced upon their appearance in the telescope was due to their 
 great distance. Galileo demonstrated by an appeal to experiment, and by 
 reasoning of invincible force, that the element of distance did not exercise 
 the slightest influence on the enlargement of an object seen through 
 the telescope];. The fact that some bodies were enlarged in a greater 
 degree than others, was ascribed by him to the irradiation of light. The 
 telescope in most cases deprives the body of the false light arising from 
 this cause, so that although it does not fail to enlarge the real angular 
 dimensions of the body in the proportion of the magnifying power, the 
 spurious diminution may so far neutralise the actual enlargement, that the 
 appearance presented by the body in the telescope, may not differ sensibly 
 from that which it exhibits to the naked eye. It is to be remarked, how- 
 ever, that the irradiation exhibited by an object to the naked eye, depends 
 upon the darkness of the ground upon which it appears projected ; while on 
 the other hand, since it is the object itself freed from irradiation that we 
 perceive in the telescope, its aspect will not be affected in this case by the 
 ground of projection. Hence the apparent magnitude of a star will vary to 
 the naked eye with the obscurity of the heavens, while in the telescope it will 
 not undergo any change. As an illustration of the truth of this remark, 
 Galileo cites the case of Sirius, the brightest star in the heavens. A few 
 
 * Opere di Gal., torn, ii., p. 129 ; Istoria e Dimostrazioni intorno alle Macchie So- 
 lari, p. 110. 
 
 f Discorso delle Comete di Mario Guiducci, Firenze, 1619. This dissertation upon 
 comets, although professedly written by Guiducci, was well known at the time of its pub- 
 lication, to have proceeded from the pen of Galileo, and it has always been included in 
 the successive editions of the complete works of the illustrious philosopher. 
 
 \ The following passage referring to this principle, may serve to illustrate Galileo's 
 mode of exposing the fallacies of his opponents: " Place an opaque disk at a certain 
 distance, and directly behind it, but four or six times farther off, place a white disk of so 
 much greater dimensions than the other, as just to allow its circumference to be seen 
 like a white ring. Now, if the telescope be directed to the two disks, it ought to follow, 
 if the more remote disk be magnified in a less proportion than the nearer one, that the 
 former will be altogether covered by the latter, and the ring will totally disappear. Hence, 
 by applying the same reasoning to eclipses of the sun, it might happen that an eclipse 
 which would appear partial to the naked eye, would become total by viewing it through 
 the telescope ; so that while with the optical instrument, we found ourselves plunged in the 
 darkness of night, we should be enjoying the brightness of daylight with the unassisted 
 eye!" Opere di Gal, torn, ii., p. 221 ; Discorso delle Comete, p. 26, 
 
HISTORY OF PHYSICAL ASTRONOMY. 349 
 
 hours before sunrise it does not appear much larger in the telescope than 
 when viewed with the naked eye. As the approaching sun, however, 
 begins to chase away the darkness of night, the star appears less and less 
 to the naked eye, until at length, when the sun is about to ascend above 
 the horizon, it dwindles to a mere point of light, and then disappears. 
 On the other hand, during all this time the star constantly exhibits the 
 same magnitude in the telescope *. 
 
 Galileo makes some interesting remarks on irradiation in his letter to 
 Grienberger, on the subject of the lunar mountains f. It had been asserted 
 that, as the full moon always presented a well-defined outline, whether 
 when viewed with the naked eye or through a telescope, it was impossible 
 that there could exist any inequalities around her circumference. Galileo, 
 however, maintained that the irradiation of the moon's light, by obliterat- 
 ing any asperities around her edge, might effectually conceal the real 
 nature of that part of her surface. With respect to irradiation generally, 
 he remarked that it increases with the brightness of the object. It is 
 from this cause that the planets near the sun have a greater irradiation 
 than those that are more remote. So intense is the irradiation of Mer- 
 cury, that it is impossible, even with the most powerful telescope, to de- 
 prive him of his brilliant corona. The same is true, though in a less 
 degree, with respect to Mars. On the other hand, Jupiter, and especially 
 Saturn, being more feebly illuminated by the solar light, lose their irradi- 
 ation in; the telescope, and disclose their true figures. "With respect to 
 Venus, when she is near her inferior conjunction, she resembles the new 
 moon, but such is the intensity of her irradiation, that she appears to the 
 naked eye, like any other star. In this position, however, as the extent of 
 the illuminated surface is small, and the light is at the same time enfeebled 
 by the obliquity of the surface, it is possible, by means of a telescope, to 
 discern the real appearance of the planet. When, however, she is near 
 her superior conjunction, she presents a complete hemisphere of vivid 
 light towards the earth, of such intensity, that even the most perfect 
 telescope does not suffice to destroy her irradiation, and reveal to us her 
 true figure. 
 
 Galileo, therefore, contends that since the effect of irradiation is so 
 great, as to conceal from the unaided eye the immense cavity of Venus 
 when she assumes the form of a crescent, it is much more probable that 
 even the telescope will fail so completely to efface the irradiation of the 
 moon, as to disclose the small eminences and cavities which may be situate 
 near the edge of her disk. With the view of illustrating the fact that the 
 irradiation of objects whose apparent magnitude is small, may produce so 
 strong an effect as totally to obliterate any asperities of outline, he de- 
 scribes the following experiment : Take a thin plate of metal in which are 
 inserted two chinks, the one with smooth and the other with rugged edges. 
 Let the piece of metal be illuminated behind by a brilliant light, and let 
 the observer place himself in front, the only light accessible to him being 
 that which is transmitted through the chinks. If he view the piece of 
 metal at only a short distance, the asperities of the rugged chink will be 
 easily perceptible to the naked eye. If he remove to a distance of a 
 hundred or a hundred and fifty paces, the asperities cease to be visible to 
 the naked eye, but they may still be discovered by the aid of the telescope. 
 Finally, if he view the piece of metal at a distance of about a mile, the 
 
 * Opere di Gal., torn, ii., p. 219 ct se? t Ibid., torn, ii., p. 419 et seq. 
 
350 HISTORY OF PHYSICAL ASTRONOMY. 
 
 asperities of the rugged chink will no longer be discernible even with a 
 telescope, so that the edges of both chinks will assume the same smooth- 
 ness of outline. 
 
 Galileo remarked on frequent occasions, that irradiation produced a 
 more sensible effect according as the apparent magnitude of the object 
 was less*. This, indeed, is manifest to any person, when it is considered 
 that the false light arising from irradiation, being the same whatever be 
 the magnitude of the object, cannot fail to affect small objects in a greater 
 degree than large ones. It was upon this ground he explained the fact 
 that while the aspect of the stars varied with the obscurity of the heavens, 
 the moon continued to retain the same apparent magnitude, whether seen 
 in the brightness of noon or in the darkness of midnight. 
 
 With respect to the cause of irradiation, Galileo imagined it to reside 
 in the eye, but he does not seem to have entertained a very decided 
 opinion with respect to its mode of operation. In his " Discourse upon 
 Comets " he conceived the irradiation of luminous objects to arise from 
 the refraction of the rays of light by the humours diffused over the eye f. 
 In his Dissertation, entitled " 11 Saggiatore," he enters more fully into the 
 same question. It had been supposed by some persons, that irradiation 
 was occasioned by objects illuminating the surrounding air, so that the 
 corona of light thus formed were confounded with the objects themselves. 
 Galileo admits that when the sun or moon are near the horizon, they 
 illuminate the vapours through which they are seen ; but he denies that 
 the illumination is so intense as to render the vapours liable to be con- 
 founded with the actual disks of either of those bodies. He then remarks, 
 that the refraction of the moisture diffused over the eyes, causes a 
 luminous appearance to surround the object, but being very feeble, com- 
 pared with the original light, it does not affect the apparent magnitude. 
 It will be seen that he here disavows the opinion previously enter- 
 tained by him, to the effect that irradiation proceeded wholly from refrac- 
 tion. He now considers the irradiation of luminous objects to arise from the 
 rays of light being reflected by the extremities of the eyelids, and then 
 being dispersed over the pupils J. He reproduces this opinion in his 
 famous " Dialogues on the System of the World, " but in a subsequent 
 part of the same work he ascribes the phenomena of irradiation to either 
 of the two causes he had already assigned, or to some other unknown 
 cause residing in the eye ||. 
 
 The irradiation of luminous objects being, according to Galileo, attribut- 
 able to some ocular cause, it was clear that phenomena of this nature 
 could not be affected by the magnifying power of the telescope. He ex- 
 plained by this principle the fact that the irradiation generally disappeared 
 when the object was viewed through a telescope, the spurious light being 
 masked by the enlargement of the apparent dimensions of the object. 
 
 The sagacity with which Galileo discusses the subject of irradiation, 
 cannot be sufficiently admired. The least satisfactory part of his specula- 
 tions is that relating to the physical cause of the phenomenon. It must 
 be acknowledged that his views on this point are very obscure and vague. 
 The reader cannot fail to remark that he concurs with Kepler in placing 
 the source of irradiation in the eye. 
 
 * Opere di Gal., torn, ii., p. 350 ; Ibid., torn, iv., p. 242. 
 t Ibid., torn, ii., p. 223 ; Discorso delle Comete, p. 32. 
 j: Ibid., torn. ii.,'p. 348; II Saggiatore, p. 212. 
 Ibid. ; torn, iv., p. 69, || Ibid., torn, iv., p. 242. 
 
HISTORY OF PHYSICAL ASTRONOMY. 851 
 
 Gassendi is the next person who occupied his attention with the subject 
 of the irradiation of light. This philosopher entertained very erroneous 
 views respecting the physical cause of irradiation, but he made some inte- 
 resting experiments for the purpose of ascertaining the laws by which it 
 is regulated. In order to ascertain the effect produced upon the enlarge- 
 ment, according as the field upon which the luminous object appeared be- 
 came brighter, he measured the successive magnitudes of the moon's ap- 
 parent diameter, as visible to the naked eye, from midnight till noon, and 
 obtained the following results. At midnight the apparent diameter was 
 found to be 38'; at dawn it was 36f ' ; in clear daylight, 34J-' ; after 
 the sun arose, but before he had emerged above the vapours of the 
 horizon, 341'; at mid-day, when the sun shone with all his splendour, 
 33'*. 
 
 Descartes, in his Dioptrics, published at Leyden in 1 637, at length gave 
 the explanation of irradiation which is now generally received. He sup- 
 posed that the extremities of the fibres of the optic nerve, though small, 
 have some magnitude, and that in consequence, the impression produced 
 by each pencil of rays which converged upon the retina, had a tendency 
 to propagate itself to a certain distance on all sides, although it would be 
 strongest at the point where the rays converged. When the light of the 
 object was feeble, the impression might practically be supposed to be con- 
 fined to the central point; but in the case of very bright objects, the im- 
 pact of the rays might be so intense as to make the lateral impression 
 very sensible. It followed as an obvious consequence of this mode of 
 viewing the subject, that all luminous bodies would appear somewhat 
 enlarged beyond their true apparent dimensions. 
 
 Newton, having discovered the unequal refrangibility of light, did not 
 fail to perceive that the aberration arising from this cause alone, would 
 have the effect of vitiating all observations of the apparent magnitudes 
 of bodies, as seen through telescopes. In fact the rays of different colours 
 belonging to each pencil of light, instead of converging to a point by the 
 refraction of the object-glass of the telescope, were so dispersed as to 
 assume the appearance of a small coloured circle at the focus, and hence 
 obviously would arise an enlargement of the image beyond its true magni- 
 tude. Newton remarked that the enlargement arising from the unequal 
 refrangibility of light would be less according as the focal length of the 
 telescope was increased. In the Principia, he states that the apparent 
 diameter of Jupiter, at his mean distance from the earth, was found by the 
 aid of Huyghens' telescope of 123 feet focal length to be 39"; while, on the 
 other hand, its value deduced from the times of the satellites crossing the 
 planet's disk, amounted only to 87 J". He, therefore, concluded that the 
 chromatic aberration of the telescope was somewhere about 2".f Hence 
 in reference to the apparent diameter of Saturn, which was found by 
 means of the same telescope to be 18", he remarks that " if all false 
 light be rejected, the diameter of the planet will not remain greater 
 than 16"."J 
 
 It is remarkable that Newton makes no allusion to irradiation in the 
 course of his enquiries relative to the true apparent diameters of the 
 planets. It is difficult to say, whether his silence arose from an absolute 
 
 * Opera Omnia, torn, iii., p. 395; Flor., 1727. 
 f Prin., lib. iii., Phenom. i. 
 $ Prin., lib. iii., Phenom. ii. 
 
352 HISTORY OF PHYSICAL ASTRONOMY. 
 
 disbelief in the existence of any enlargement arising from this cause, 
 or from an impression that the enlargement, which generally appeared less 
 in the telescope, was in the present instance totally inappreciable, in conse- 
 quence of the immense focal length of. the instrument by the aid of 
 which the measurements were effected. But whatever may have been the 
 opinion of Newton on this point, it is certain that after his discovery of 
 the unequal refrangibility of light, the subject of irradiation ceased to as- 
 sume the same degree of importance which induced Galileo so repeatedly 
 to refer to it in the course of his researches, its effects being for a long 
 time confounded with those depending on the aberration of the telescope. 
 
 The phenomena exhibited during the transits of Venus across the sun's 
 disk in the years 1761 and 1769, had the effect of again directing the 
 attention of astronomers to the subject of irradiation. Lalande found by 
 calculations based 011 the times which Venus actually occupied in crossing 
 the sun's disk during the transits of 1761 and 1769, that the apparent dia- 
 meter of the sun, as assigned by the solar tables, was too great by 6" or 7" *. 
 Du Sejour was conducted to the same result by his elaborate researches on 
 the annular eclipse of 1764. He found that the observations of the eclipse 
 could not be satisfied, except by supposing that the apparent diameter of 
 the sun, as deduced from the solar tables, was too great by 9" or 6". 6, ac- 
 cording as the tables of Clairaut or those of Mayer were employed f. 
 Lalande seems disposed to consider the enlargement of the solar diameter 
 as due to the aberration of the telescope. Du Sejour applies the term 
 irradiation to the enlargement, asserting, however, at the same time, that 
 he does not mean thereby to announce any opinion respecting its physical 
 origin. 
 
 In 1782, while Sir William Herschel was engaged in a series of experi- 
 ments for the purpose of determining the apparent diameter of the planet 
 he had recently discovered, he noticed an interesting fact illustrative of 
 the irradiation of light. The method he employed for measuring the 
 planet's disk consisted in comparing its image as seen through a telescope 
 with an artificial lucid disk, formed by making a circular aperture in paste- 
 board, and covering it with transparent paper illuminated behind by a 
 flame. The image of the planet was observed in the telescope with the 
 right eye, while the lucid disk was viewed directly with the left, its dis- 
 tance being made to vary until it appeared exactly of the same size as 
 the image in the telescope. Hence, the linear diameter and distance 
 of the artificial disk being known, it was easy to deduce its apparent 
 diameter, and by combining this datum with the magnifying power of the 
 instrument, the apparent diameter of the planet was also readily ascertained. 
 In order to ensure an accurate comparison of the disks, Herschel pre- 
 pared a series of circles, varying in diameter from 2 to 5 inches, and 
 increasing successively by tenths of an inch. He remarked, that as the 
 brightness of the image in the telescope varied with the altitude of the 
 planet and the magnifying power of the instrument, so it was necessary, in 
 these experiments, to alter in a corresponding degree the brightness of 
 the lucid disk, for he found that the magnitude of its apparent diameter 
 was very sensibly affected by this cause. In fact, having placed several 
 of the artificial disks together and illuminated them at the same time, 
 he found that a very small quantity of additional light was necessary, in 
 
 * Mem. Acad. des Sciences, 1770, p. 403. f Ibid., 1775, p. 365. 
 
HISTORY OF PHYSICAL ASTRONOMY. 353 
 
 order to cause one of the disks to differ in magnitude by one or even two 
 tenths of an inch *. 
 
 Dr. Robinson, in a paper communicated to the Astronomical Society in 
 1831, gives an interesting account of some experiments which he made 
 for the purpose of ascertaining the amount of influence exercised by irra- 
 diation on the apparent diameters of the sun and moon f. The method 
 he employed consisted in observing lucid disks of different magnitudes, 
 and measuring their apparent diameters when subjected to different 
 degrees of illumination. A slip of brass with a small circular hole in it 
 was placed in the focus of an object-glass, and the hole being illuminated 
 by a lamp placed behind it, was then viewed through the object-glass by 
 means of a telescope directed to it. By this contrivance the image of the 
 hole seen in the telescope was rendered similar to that which would have 
 been formed by a remote object like the sun or moon, since the rays 
 of light transmitted through the hole emerged in parallel directions 
 from the object-glass. On looking through the telescope, the aperture 
 assumed the appearance of a luminous disk about 17' in diameter; but, on 
 interposing a slip of oiled paper between it and the lamp, it assumed 
 a much duller appearance, resembling the aspect of the moon in a dense 
 fog. In this state Dr. Robinson brought the wires of the micrometer so 
 as to be tangents to the disk; and then, having caused the oiled paper to 
 be removed, he instantly saw the opposite segments of the disk extend 
 beyond the wires. Bringing the latter again into a tangential position 
 with respect to the disk, he determined the apparent diameter anew, the 
 excess of which over the previous measure manifestly gave him twice the 
 breadth of the annular enlargement arising from the increased brightness 
 of the disk. In this way he obtained a series of results, the mean of 
 which indicated an irradiation amounting to about 2".6. He repeated the 
 experiment with apertures of different apparent diameters, and obtained a 
 similar result in each case. Dr. Robinson was induced to conclude from 
 his experiments that the main source of irradiation is in the eye; at the 
 same time he admitted that the aberration of the telescope might in some 
 degree contribute to the apparent enlargement of the object. The tele- 
 scopes which he employed on this occasion did not appear to be affected 
 by any sensible aberration, from the distinctness with which they ex- 
 hibited very close double stars, so that the enlargement indicated by his 
 experiments must be considered as referable almost wholly to irradiation. 
 
 In one of his experiments it appeared to Dr. Robinson, that the bright- 
 ness of the lucid disk was equal to that of the sun as seen in his transit. 
 It might be expected, therefore, that the irradiation would be nearly the 
 same in both cases. The experiment gave him 2". 8 for the difference 
 between the least and greatest apparent diameters of the disk. This 
 result presents a satisfactory agreement with two values of the solar 
 irradiation deduced from astronomical researches of a more recent date 
 than those of Lalande and Du Sejour. By a discussion of the transits of 
 Venus in the years 1761 and 1769, Encke obtained a value of the solar 
 diameter which was less than that of the tables by 2".95 J. Wurm, by 
 
 a similar discussion of the annular eclipse of 1820, deduced a result indi- 
 ting that the solar diameter of the tables was too great by 3".3'2 . 
 In one of his experiments, Dr. Robinson illuminated the field of view 
 
 Phil. Trans., 1783, p. 1, et seq. f Mem. Ast. Soc., vol. v., p. 1, et seq. 
 
 J Mem. Ast. Soc., vol. v., p. 7. Ibid., p. 8 
 
354 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 for the purpose of ascertaining whether any effect would be produced on 
 the irradiation. When the disk was in its state of greatest illumination 
 no change was perceptible ; but on turning off the light from the field of 
 view, when the disk was obscured by the interposition of the oiled paper, a 
 manifest enlargement was immediately apparent. The absence of any 
 sensible enlargement in the first instance, arose doubtless from the circum- 
 stance of the brilliant light of the disk effectually overpowering the fainter 
 light diffused over the field of view. 
 
 As it appeared evident from these experiments that the irradiation of 
 an object was sensibly influenced by the brightness of the ground on which 
 the object was projected, Dr. Robinson imagined that its effect might be 
 eliminated altogether from observations of the sun and moon by sufficiently 
 illuminating the field of view of the telescope. To effect such an illu- 
 mination, however, by an artificial process was absolutely impossible, when 
 the question related to observations of the sun, nor was it even generally 
 practicable in the case of the moon. Under these circumstances, Dr. 
 Robinson hit upon the ingenious idea of illuminating the field of view by 
 deriving the light from the luminary itself. In pursuance of this design 
 he proposed to cover the object-glass of the telescope with a semi-trans- 
 parent diaphragm, leaving a small central aperture to admit the rays 
 which formed the image at the focus, while the rest of the diaphragm served 
 to fill the field with scattered light. This method was applied by Dr. Robin- 
 son to observations of the sun, and the results obtained by him in a few 
 instances, appear to have been very satisfactory ; the value of the solar 
 diameter determined by means of the transit instrument, exceeding only 
 by a- very small quantity, the value assigned by the tables. 
 
 One curious fact noticed by Dr. Robinson, in the course of his experi- 
 ments, is worthy of mention. Having examined the luminous disk with a 
 double image micrometer, he was surprised to find that the contact of the 
 two images was not affected by the intensity of their illumination. He 
 expressed himself as somewhat doubtful of the result, the experiment 
 having been hastily made. It would appear, however, to be supported by 
 experiments of a similar nature made by other astronomers, M. Arago 
 had previously attempted to ascertain the influence of irradiation by 
 measuring with a rock crystal micrometer the apparent diameters 
 of luminous disks, and then comparing them with the corresponding 
 results obtained by combining the absolute diameters with the distance of 
 the disks from the eye ; but in all such experiments he found that the 
 irradiation was insensible, even when the illumination of the disks was 
 more intense than that of the full moon*. A similar result was obtained 
 by M. Bessel when he sought by means of his great heliometer to deter- 
 mine the influence of irradiation on the occasion of the transit of Mercury 
 across the sun's disk in the year 1832. Since, in this case, the effect of 
 irradiation is to dilate the apparent diameter of the sun, and dimmish that 
 of the planet, it is not difficult to see that if such an effect really existed 
 in any sensible degree, the luminous thread which succeeds the first in- 
 terior contact of the two bodies ought to acquire instantaneously a certain 
 degree of breadth at the point of contact ; and similarly the luminous 
 thread which precedes the second interior contact ought to exhibit a sudden 
 rupture at the point of contact as if some protuberance had all at once 
 been formed on the planet. Bessel was unable to discern the slightest 
 
 * Traite d'Astronomie Physique, par M. Biot; 2 ieme edit., tome ii., p. 534. 
 
HISTORY OF PHYSICAL ASTRONOMY. 355 
 
 indication of either of these phenomena during the transit of the planet 
 above referred to. But he obtained a still more unequivocal proof that 
 the effect of irradiation was insensible. Since the first interior contact of 
 the two bodies is indicated by the sudden closing together of the two 
 extremities of the luminous border of the sun, while the second interior 
 contact is made apparent by the equally sudden rupture of the opposite 
 border, it is manifest that the interval of time included between the two 
 contacts when taken in conjunction with the relative motion of the planet, 
 as assigned by the tables, will serve to determine the apparent diameter 
 of the sun. Now Bessel, by employing this method, arrived at a re- 
 sult which coincided exactly with that obtained by direct measurement of 
 the solar diameter with a micrometer during the transit of the planet. 
 
 Thus it appears that the experiments of Bessel concur with those of M. 
 Arago and Dr. Robinson in indicating that the effect of irradiation is in- 
 sensible when the instrument employed in measuring it is one which gives 
 a double image of the luminous body. We shall presently have occasion 
 to mention that experiments of this nature have been supposed to furnish 
 only particular illustrations of a general law affecting the irradiation of 
 two luminous objects placed in juxtaposition. 
 
 In the year 1838 M. Plateau communicated to the Royal Academy of 
 Brussels, an elaborate memoir, containing an account of a variety of ex- 
 periments performed by him with the view of elucidating the nature and 
 laws of irradiation *. A very simple mode of exhibiting the enlargement 
 arising from this cause was devised by him. A white card was divided 
 into six rectangular compartments, by drawing two parallel lines pretty 
 close to each other down the middle of the card, and then bisecting these 
 by a third line, drawn at right angles to them. The middle rectangle in 
 ,the upper half of the card, and the broad lateral rectangles in the lower half, 
 were then painted black, so that there appeared in the middle of the card 
 a band composed of two parts, the one black, (in the upper half of the 
 card,) projected upon a white ground, the other white, (in the lower half,) 
 projected upon a black ground. This contrivance manifestly tended to 
 render the effect of irradiation more perceptible ; for while the white band 
 in the lower half of the card was liable to dilate from the encroachment of 
 the light upon the black ground, the black band in the upper half was 
 equally liable to contract from the encroaching irradiation of the white 
 light on each side of it. The card being placed vertically near a window, 
 so as to be well exposed to the light, was then viewed at the distance of 
 a few yards, when the effect of irradiation was clearly exhibited by the 
 white band in the middle of the lower half appearing sensibly broader 
 than the black band above it. The following are the more important 
 conclusions to which M. Plateau was conducted by his experimental re- 
 searches on the subject of irradiation. 
 
 1 The quantity of irradiation increases with the brightness of the ob- 
 ject, but in a much less rapid proportion. It has very nearly attained its 
 maximum when the brightness is equal to that exhibited by the northern 
 region of the sky. 
 
 2 Two irradiations in close proximity tend to neutralize each other. The 
 diminution arising from this cause is greater in each case, as the interval 
 between the luminous objects is less. 
 
 3 The quantity of irradiation augments with the time of contemplating 
 
 * Nouv. Mem. de 1'Acad. Royal dc Bruxelles, tome xi., p. 1, et seq. 
 
 A A 2 
 
356 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the object. It is different for different individuals, and for the same 
 individual it varies from one day to another. 
 
 4 When an object is viewed through a telescope, the apparent enlarge- 
 ment exhibited by it arises from two distinct causes, viz., ocular irradiation, 
 and the aberration of the telescope. The part due to ocular irradiation de- 
 pends on the magnifying power of the telescope, on the brightness of the 
 image, and on the physiological qualities of the eye of the observer. More- 
 over, the interposition of the eye-glass of the telescope tends to produce a 
 peculiar effect on the enlargement. 
 
 5 The part of the enlargement due to the aberration of the telescope 
 varies necessarily with the instrument employed. For the same instru- 
 ment, it may be considered as constant. 
 
 The most remarkable of these propositions is that wherein it is an- 
 nounced that the irradiations of two luminous objects are diminished by 
 their mutual proximity. M. Plateau extends this principle to the pheno- 
 mena of irradiation seen with the naked eye as well as to those observed 
 in the telescope. He rests its demonstration upon various experiments, 
 some of which are of a very convincing nature, and do not seem to be liable 
 to any objection. He refers to this principle the absence of any sensible irra- 
 diation in the experiments of Arago, Robinson, and Bessel, above alluded 
 to. Without expressing a formal opinion on its origin he seems disposed 
 to consider it as due to the fact, that there does not exist in either case a 
 sufficient contrast between the luminous object and the ground upon which 
 it appears projected. M. Plateau concurs with most other philosophers 
 in placing the source of irradiation in the eye, but he does not express any 
 opinion respecting the mode by which the effect is produced. 
 
 The most recent account of experimental researches on Irradiation, is 
 contained in a paper communicated by Professor Powell to the Astronomi- 
 cal Societ}', in the year 1849*. That distinguished philosopher appears 
 disposed to regard the phenomena of irradiation as due, in a great degree, 
 to some cause extraneous to the eye. While admitting that the irregular 
 scintillation of a star may arise from some physiological affection of the 
 organ of vision, and may vary in different individuals, he considers that 
 the enlargement exhibited by a well-defined disk, capable of exact mea- 
 surement, cannot reasonably be ascribed to a cause of so fluctuating a 
 nature. He then proceeds to describe various experiments which tend to sup- 
 port this assertion. One of the most unequivocal results derived from these 
 experiments consisted in this, that an image of the object, formed in the focus 
 of a lens, is affected by irradiation in an equal degree with the object itself. 
 A card, similar to that employed by M. Plateau, being exposed to a mode- 
 rately strong light, and its image being then thrown by reflexion upon a 
 ground glass placed in the focus of a lens, the image of the card was seen 
 painted on the ground glass, with precisely the same enlargement as that 
 which it exhibited to the naked eye. It might be urged against this ex- 
 periment, that the brightness of the light at the focus of the lens might in 
 its turn produce its irradiation, so as to occasion the apparent enlargement 
 of the image. With reference to this objection Prof. Powell remarks, that 
 the image on the ground glass was in general by far too faint to produce any 
 such secondary effect. That the irradiation could not be due to this cause 
 was proved further beyond all doubt by the fact, that when a dark glass 
 was interposed between the eye and the image of the card in the focus, 
 
 * Mem. Ast. Soc., vol. xviii., p. 69, et seq. 
 
HISTORY OF PHYSICAL ASTRONOMY. 357 
 
 the enlargement still continued to be equally perceptible. Prof. Powell, 
 upon the grounds of such experiments, considers the conclusion to be un- 
 avoidable, that the enlargement is occasioned by some optical cause acting 
 upon the formation of the focal image, and independent of any organic 
 affection of the eye. 
 
 Pursuing this view of the origin of irradiation, he conceived that a strik- 
 ing verification of it would be obtained, if a photographic image of the ob- 
 ject could be formed, exhibiting the enlargement. An experiment which he 
 made with a view to decide this point, was attended with complete success. 
 The image of the card when formed by a photographic process, either in 
 the light of the bright sky or in the full sun, was found to exhibit a mani- 
 fest enlargement. 
 
 Irradiation may be greatly diminished, or even completely destroyed, 
 by the interposition of a lens between the object and the eye. Prof. 
 Powell found that with ordinary daylight a lens which magnified three or 
 four times was sufficient to extinguish every trace of the phenomenon. 
 He states, as the result of his experience generally, that magnifying powers 
 varying from ten to twenty effectually destroy the irradiation occasioned 
 by the brightest light which the eye can bear. 
 
 M. Plateau experienced great difficulty in reconciling the effect produced 
 by the interposition of a lens with the theory of irradiation, which as- 
 cribes its origin to some ocular cause. Prof. Powell is of opinion that it 
 may be accounted for by the diffusion of light, resulting from the ap- 
 plication of the lens, rendering the enlargement too faint to be percep- 
 tible. Upon the same principle he explains the absence of irradiation in 
 experiments made with a double image micrometer. In this case, each of 
 the images possesses only half the original brightness, and being at the 
 same time viewed with a high magnifying power, the effect of irradiation 
 might, by the combined operation of both these causes, be rendered in- 
 sensible. 
 
 In observations with the telescope it has been found, that the regular 
 enlargement occasioned by irradiation is mainly dependent on the aperture, 
 focal length, and magnifying power of the instrument. With respect to 
 the new moon, Prof. Powell remarks, that when viewed with a 30-inch 
 achromatic, and very low powers, the projection of the illuminated crescent 
 beyond the dark part of the disk was distinctly seen ; with a power of 50 it 
 was barely visible ; and with 80 not at all. The following passage of a letter 
 from Prof. C. Piazzi Smyth, cited by that philosopher, affords an interesting 
 confirmation of the same fact : " On a particularly fine night at the Cape, 
 when the enlargement of the bright part of the new moon beyond the dark 
 was unusually striking to the naked eye, amounting to two or three 
 minutes of space, a 14-foot reflector was turned to the object, and, with 
 every increase of power, the apparent projection was more" and more cut 
 down definition was very good that night. With power of 300 the pro- 
 jection was barely sensible; it did, however, still absolutely exist, but to 
 perhaps not more than two or three tenths of a second of space." * 
 
 It is generally admitted that the irradiation of bodies is affected by the 
 dimensions of the aperture of the telescope. When the aperture is dimin- 
 ished, the apparent enlargement of the object is diminished also. This, 
 doubtless, arises from the less intense brightness of the image. It is to 
 be remarked, however, that when the aperture is reduced to very small 
 
 * Mom. Ast. Soc., vol. xviiii., p. 80. 
 
550 HISTORY OF PHYSICAL ASTRONOMY. 
 
 dimensions, the diffraction of the object-glass begins to affect the apparent 
 magnitude of the image in the opposite direction, so that when the aper- 
 ture has reached a certain degree of contraction, the enlargement arising 
 from this cause may compensate for the. diminished effect of irradia- 
 tion. Prof. Powell is of opinion that this may account for Dr. Robinson 
 having found the interval between the transits of the sun's limbs to be 
 unaltered by contracting the aperture of the telescope, and also for the 
 fact that Mr. Dawes, during the transit of Mercury over the sun's disk 
 in 1848, found that the apparent diameter of the planet was the same, 
 when observed with different apertures. 
 
 A review of the progress of researches on irradiation cannot fail to sug- 
 gest the conclusion, that the knowledge we possess respecting its nature 
 and laws is still very imperfect and obscure. On the other hand, no doubt 
 can exist that it exercises a sensible influence on the observations of the 
 astronomer. It is manifest also, that as the art of observation continues 
 to advance towards perfection, it will become more and more imperative 
 on the part of the astronomer to attend to the effects produced by it. In 
 the present state of the subject the inquirer is impeded at the very outset 
 of his researches, by the want of data of sufficient completeness and pre- 
 cision upon which he might establish his reasoning. It is to be hoped 
 that amid the activity which pervades every department of astronomical 
 science, this branch of enquiry will not fail to receive an amount of atten- 
 tion adequate to its growing importance. 
 
 We shall now proceed to give a brief account of the researches of astro- 
 nomers, with a view to the explanation of various interesting phenomena, 
 by means of some of the principles alluded to in this chapter. 
 
 CHAPTER XVII. 
 
 Eclipses of the Sun and Moon Historical Statement of total Eclipses of the Sun. 
 Annular Eclipses observed in modern times. Change of Colour which the sky under- 
 goes during an Eclipse. Its explanation by M. Arago. Corona of Light observed 
 around the Moon. Allusions made to it by Ancient Authors. Explanations of its 
 Physical Cause by different Individuals. Protuberances on the Moon's Limb. Their 
 most, probable nature. Observations on the surface of the Moon during Eclipses 
 Undulations observed on the occasion of the Eclipse of 1842. Similar Phenomena 
 observed during the Eclipse of 1733. Explanation of their Origin. Optical 
 Phenomena observed during Solar Eclipses. Threads, Beads, &c. Explanation of 
 their Origin. Lunar Eclipses Transits of Venus. Physical appearances observed 
 during their Occurrence. Transits of Mercury. Spot observed on the Planet's disk. 
 Its explanation by Professor Powell. Occultations of the Planets and Stars. 
 
 AMID the variety of grand and beautiful phenomena which flow from 
 the operation of nature's laws, exciting alternately the admiration and 
 delight of the attentive observer, there are some whose surpassing magni- 
 ficence extorts universal homage, and awakens in the spectator a feeling of 
 reverential awe. It is impossible for the most frivolous mind to regard 
 with indifference the irresistible impetuosity of the hurricane as in its 
 wild career it sweeps along every opposing obstacle, or to contemplate 
 without emotion the sublime spectacle of the ocean when its billows are 
 agitated by the fury of the tempest. The everlasting noise of the cataract, 
 the deep roll of the thunder storm, or the sudden apparition of the 
 eccentric cornet in the heavens with its pale aspect and " horrid hair," 
 
HISTORY OF PHYSICAL ASTRONOMY. 359 
 
 seldom fails to arouse the apathy of the most listless votary of nature. 
 But perhaps on no occasion does the display of stupendous power in the 
 economy of the physical universe exercise so subduing an influence over 
 the mind, or produce so humiliating a conviction of the impotence of all 
 human efforts to control the immutable laws of nature, and arrest the 
 course of events, as when the glorious orb of day, while riding in the hea 
 vens with unclouded splendour, begins to melt away from an unseen cause, 
 and soon totally disappears, leaving the whole visible world wrapped in 
 the sable gloom of nocturnal darkness. The scene is rendered still more 
 impressive by the circumstances accompanying so remarkable an occur- 
 rence. The heavens assume an unnatural aspect, which excites a feeling 
 of horror in the spectator; a livid hue is diffused over all terrestrial 
 objects ; the plants close up their leaves as on the approach of night ; the 
 fowls betake themselves to their resting-places ; the warbling of the grove 
 is hushed in profound silence. Universal nature seems to have relaxed 
 her energies, as if the pulse which stimulated her mighty movements had 
 all at once stood still. 
 
 During the early history of mankind, a total eclipse of the sun was 
 invariably regarded with a feeling of indescribable terror, as an indication 
 of the anger of the offended deity, or the presage of some impending 
 calamity; and various instances are recorded of the extraordinary effects 
 produced by so unusual an event. In a more advanced state of so- 
 ciety, when science had begun to diffuse her genial influence over the 
 human mind, these vain apprehensions gave place to juster and more 
 ennobling views of nature ; and eclipses generally came to be looked 
 upon as necessary consequences flowing from the uniform operation of 
 fixed laws, and differing from the ordinary phenomena of nature, only 
 in their less frequent occurrence. To the astronomer they have in all 
 ages proved valuable in the highest degree, as tests of great delicacy 
 for ascertaining the accuracy of his calculations relative to the place of 
 the moon, and hence deducing a further improvement of the intricate 
 theory of her movements. In modern times, when the physical consti- 
 tution of the celestial bodies has attracted the attention of many emi- 
 nent astronomers, observations of eclipses have disclosed several in- 
 teresting facts, which have thrown considerable light on some important 
 points of enquiry respecting the sun and moon. 
 
 In the present advanced state of astronomy, the records of ancient 
 eclipses have been successfully employed in fixing the dates of contem- 
 porary events, and thereby rescuing history, in many instances, from the 
 confusion usually incident to a remote antiquity. It is thus that pheno- 
 mena, which, at the time of their apparition, were regarded as the 
 mysterious heralds of some impending calamity in the moral world, 
 totally independent of the ordinary course of nature, and which would 
 have been allowed to pass unnoticed, had it not been for the terror which 
 they inspired, have become subservient in illustrating many obscure pas- 
 sages in the writings of the persons who record them, and establishing 
 our knowledge of ancient times upon a more satisfactory basis. This is 
 justly regarded as one of the most remarkable triumphs of modern science. 
 
 Before entering upon the history of total eclipses of the sun it may not 
 be out of place to give a brief description of the nature of eclipses in 
 general, and of the various circumstances which determine their occur- 
 rence. 
 
 The moon, in the course of her monthly revolution round the earth, 
 
360 HISTORY OF PHYSICAL ASTRONOMY. 
 
 appears to describe a great circle in the heavens, inclined at an incon- 
 siderable angle to the ecliptic. Hence it happens that, when the time of 
 her conjunction with the sun coincides with her passage across the 
 ecliptic, she appears projected upon the region of the heavens occupied by 
 the sun, and, being an opaque body, conceals the whole or a portion of his 
 disk from a spectator on the earth. The defect of light arising from this 
 cause is what is termed a solar eclipse. It is manifest that the moon 
 cannot wholly intercept the solar light, unless during conjunction her 
 apparent diameter exceed the apparent diameter of the sun. This condi- 
 tion, however, is not always fulfilled, for, as the moon revolves in an orbit 
 of considerable eccentricity, her distance from the earth varies in a 
 sensible degree, and hence arises a corresponding variation in her apparent 
 diameter, causing it sometimes to exceed the apparent diameter of the 
 sun, and other times to fall short of it. Hence, when the centres of 
 the sun and moon are projected upon the same point in the heavens, 
 and the apparent diameter of the moon at the same time exceeds that 
 of the sun, the solar disk will be entirely concealed from the view of 
 the spectator, and a total eclipse will be the consequence. If, however, 
 while all other circumstances are alike, the apparent diameter of the moon 
 be less than that of the sun, the solar disk will not wholly cease to be 
 visible, but the opaque body of the moon will appear projected centrally 
 on it, leaving a narrow ring of light exposed to view. In this case, there 
 occurs the interesting phenomenon of an annular eclipse. When the 
 moon does not pass centrally over the sun, but merely overlaps a segment 
 of his disk, a portion of his light only is prevented from reaching the 
 place where the spectator is situate, and a partial eclipse then ensues. 
 
 During a total eclipse of the sun it is manifest that the place on the 
 surface of the earth which happens from this cause to be obscured, is then 
 situated within the moon's shadow. When only a portion of the solar light 
 is intercepted by the moon as in the case of an annular or partial eclipse, 
 the place to which the eclipse is visible is situate beyond the limits of the 
 lunar shadow in a partially-obscured region termed the penumbra. 
 
 Since the moon in passing between the sun and the earth intercepts the so- 
 lar light, either wholly or partially from some place on the surface of the latter 
 hody, so when, in the course of her synodic revolution, she arrives in the op- 
 posite point of her orbit, the earth being now interposed between her and the 
 sun, she is deprived in her turn of the solar light, and the phenomenon of 
 a lunar eclipse is the consequence. It is to be remarked that in all lunar 
 eclipses, the solar rays are supposed to be n-Jiolly intercepted from the 
 obscured surface, those cases in which a partial deprivation of light only 
 occurs, being left out of consideration, on account of the difficulty of deter- 
 mining the exact instant when the obscuration begins or ends. Hence a 
 lunar eclipse corresponds to a total eclipse of the sun in regard to its specific 
 character, the surface obscured being, in each case, actually immersed in 
 the shadow of the eclipsing body. 
 
 If the moon revolved in the plane of the ecliptic, she would necessarily 
 pass between the sun and the earth at every conjunction, while again at 
 every opposition, the earth would be interposed between the sun and moon. 
 Hence a solar eclipse would take place at every new moon, and a lunar 
 eclipse at every full moon. The lunar orbit being, however, inclined at an 
 angle of about 5 to the plane of the ecliptic, an eclipse, whether solar or 
 lunar, can only occur, when the moon during conjunction or opposition is 
 near either of the nodes of her orbit. Astronomers have found by calcula- 
 
HISTORY OP PHYSICAL ASTRONOMY. 361 
 
 tion that a solar eclipse cannot take place unless the moon during conjunc- 
 tion be within 17 21' 27" of her node; nor a lunar eclipse unless during 
 opposition her distance from the node be less than 11 25' 40". The 
 question with respect to the specific nature of the eclipse which may 
 happen in either case, whether it be total or partial, will depend, cateris 
 paribus, upon the distance of the moon within the assigned limit. 
 
 It follows from the foregoing remarks that, whenever the lunar node 
 returns to the same position with respect to the sun and moon, an eclipse 
 of the same nature will always recur. It is manifest that the frequent 
 occurrence of eclipses in general, will depend on the condition of the lunar 
 nodes with respect to their being fixed or moveable. Now, it appears 
 from observation, that they regress with a rapid motion on the ecliptic, 
 making a complete tour of the heavens in about 18 years. A remarkable 
 relation subsists between the synodic revolution of the moon, and the mo- 
 tion of her nodes, which causes the phenomena of eclipses to return within 
 a definite period nearly in the same order. It appears, in fact, that while 
 223 lunations include 6585.321 days, the nodes return to the same posi- 
 tion with respect to the sun in 6585.772 days. The difference amounts 
 to .451 of a day, or barely 12 hours, during which interval of time the sun 
 describes an arc of 28' 6" relative to the lunar node. -Hence at the end of 
 6585.321 clays the moon will have returned to the same position with respect 
 to the sun, and will only be at a distance of 28' 6" from the same position 
 with respect to the node. This period of 223 lunations or 18? 10 d 7 h 43 m *, 
 which occasions a recurrence of eclipses in the same order, was known 
 to the Chaldeans, who arrived at its discovery by comparing together the 
 records of eclipses extending throughout a long succession of agesf. It 
 appears from theory that seven eclipses may and that two must take place 
 in the course of every year. When the number of eclipses is the greatest 
 possible, both eclipses are solar. Out of seventy eclipses which usually 
 take place within a period of 18 years, the average number of solar eclipses 
 is forty-one, and of lunar twenty-nine. 
 
 Although solar eclipses, generally speaking, occur very frequently, a 
 total eclipse of the sun is an event which happens only on very rare occa- 
 sions. This arises from the circumstance of the moon being so small a 
 body compared with the sun, that her shadow frequently does not extend 
 so far as the earth, and even when it does, its dimensions are so inconsi- 
 derable that only under conditions of the most favourable nature, can any 
 portion of the earth pass through it. In fact, although an eclipse recurs 
 nearly about the same time within a period of 223 lunations, it will not 
 be exactly of the same magnitude, and the alteration, although small, may 
 suffice to transform it from a total to a partial eclipse. 
 
 If a total eclipse of the sun is an event of rare occurrence even any- 
 where on the surface of the earth, still more especially is this true when 
 
 * It will be 18v 10 d 7 h 43", or 18? ll d 7 h 43 ', according as four or five leap years 
 happen within the cycle. 
 
 f In these calculations it is only the mean synodic revolution of the moon, and the mean 
 motion of her node, that arc considered. It is clear, therefore, that even although the 
 two periods alluded to in the text were precisely equal, the inequalities both of the moon's 
 longitude and of her node would cause the corresponding eclipses in each cycle to he of 
 somewhat different magnitudes, and also to recur with more or less irregularity. The 
 cycle is sufficiently true, however, to enable a person by means of it to predict eclipses in 
 a rough way, and this is all that the Chaldean astronomers aspired to accomplish. 
 
36-2 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the question relates to some particular place. Halley, in a paper on the 
 total eclipse of the sun which happened at London on the 3rd of May, 
 1715, has remarked that there had not previously occurred a total eclipse 
 of the same body, which was visible in thaj; city, since the 20th of March, 
 1140 A.D. In connexion with this circumstance it is to be borne in 
 mind that the cycle of 223 lunations has respect to the centre of the 
 earth, .and not to any point on its surface. Now, in virtue of the diurnal 
 motion, the position of any point on the earth's surface relative to the sun 
 and moon, is generally different from the position of the centre of the 
 earth relative to the same bodies. Moreover, since the earth is a body of 
 considerable magnitude, while on the other hand the region obscured by 
 the moon's shadow, generally does not exceed 180 miles in diameter, it 
 follows that only a comparatively narrow zone of the earth's surface can 
 be eclipsed during any particular conjunction of the sun and moon. It is 
 clear, therefore, that a total eclipse of the sun may recur regularly at the 
 prescribed time within the cycle, and yet may not be visible at the same 
 place of the earth's surface. 
 
 Although a solar eclipse may last several hours, counting from the 
 commencement to the end of the obscuration, the interval of time during 
 which the sun is completely hidden behind the dark body of the moon is 
 very limited. The duration is greatest when the moon is in perigee and 
 the sun in apogee ; for the apparent diameter of the moon being then the 
 greatest possible, while that of the sun is the least possible, the excess of 
 the former over the latter, upon which the totality of the eclipse depends, 
 has then attained its maximum. Now the perigean diameter of the moon 
 is equal to 33' 31", and the apogean diameter of the sun is equal to 
 31' 30". The difference, 2' V, is the arc which the moon in this case 
 describes during the totality of the eclipse. It is manifest, therefore, 
 when the rapidity of the moon's motion, especially in perigee, is taken 
 into account, that even under the most favourable circumstances the sun 
 will not continue totally eclipsed for more than a few minutes. 
 
 The duration of a total eclipse of the sun varies, when all other cir- 
 cumstances are the same, with the latitude of the place obscured, being 
 greatest at any place under the equator. Du Sejour found from theory 
 that the utmost possible duration of a total eclipse of the &un is 7 m 58 s 
 under the equator, and 6 ra 10 s in the latitude of Paris*. 
 
 The duration of an annular eclipse is greatest when the moon is in 
 apogee, and the sun is in perigee, for the apparent diameter of the sun is 
 then the greatest, while that of the moon is the least possible, and con- 
 sequently the excess of the former over the latter, upon which the annular 
 appearance depends, is then a maximum. The greatest apparent diameter 
 of the sun is 32' 35", and the least apparent diameter of the moon is 
 29' 22". Hence the difference, 3' 13", is the arc described by the moon 
 while the eclipse continues annular. The maximum duration of an 
 annular eclipse exceeds that of a total eclipse for two reasons : first, because 
 the excess of the perigean diameter of the sun over the apogean diameter 
 of the moon (3' 13") is greater than the excess of the perigean diameter 
 of the moon over the apogean diameter of the sun (2' 1") ; secondly, 
 because when the moon is in apogee her motion over the sun's disk is 
 much slower than when she is in perigee. Da Sejour found by actual 
 
 * Mem. Acad. des Sciences, 1777, p. 318. 
 
HISTORY OF PHYSICAL ASTRONOMY. 868 
 
 calculation that the utmost possible duration of an annular eclipse under 
 the equator, is 12 m 24 s *, and under the latitude of Paris is 9 m 56 8 f. 
 
 The writings of ancient authors contain some interesting allusions to 
 eclipses, both of the sun and moon. The most remarkable is a total 
 eclipse of the sun, which Herodotus relates to have happened while the 
 Medes and Lydians were actually engaged in battle. According to the 
 statement of the Greek historian, "the war between the two nations had 
 continued during five years with alternate advantages to either party. In 
 the sixth there was a nocturnal combat ; for after an equal fortune on both 
 sides, and while the two armies were engaged, the day suddenly became 
 night."{ He mentions that Thales the Milesian had predicted this pheno- 
 menon to the lonians, and had ascertained the time of the year in which 
 it would happen. He then adds that the Lydians and the Medes, seeing 
 that the night had thus taken the place of day, desisted from the combat, 
 and became desirous, on both sides, of making peace. 
 
 This remarkable eclipse is alluded to by several ancient writers who 
 nourished subsequently to Herodotus. As the last-mentioned author has 
 not assigned the time of its occurrence, the ascertainment of this point 
 has given rise to a good deal of discussion. Cicero and Pliny both con- 
 cur in asserting that it happened in the fourth year of the forty-eighth 
 Olympiad. This would place it in the year 585 A.C. This date has been 
 adopted by Riccioli, Newton, and various other authorities of modern times. 
 On the other hand, Scaliger found by actual calculation that it happened 
 on the 1st of October, 583 A.C.; Usher placed it in the year 601 A.C. ; 
 Bayer, Costard, and several others, have maintained that a total eclipse 
 of the sun, which appears from theory to have happened on the 18th of 
 May, 603 A.C., was the one alluded to by Herodotus. 
 
 The question with respect to the date of the eclipse, continued in this 
 state of uncertainty until the year 1811, when Baily finally communicated 
 a paper to the Royal Society containing its true solution. By a skilful 
 criticism of the passage in which the Greek historian alludes to the event, 
 he has proved beyond all doubt that it could not have happened earlier 
 than 629 A.C., or later than 595 A.C. Out of seventy eclipses which hap- 
 pened within that period, he found only one which was total in the 
 peninsula of Asia Minor. That eclipse happened on the 30th of Septem- 
 ber, 610 A.C. It was central and total to part of Asia Minor, Armenia, 
 and Media, and the moon's shadow passed over the very locality where 
 the two armies most probably were engaged . It seems impossible to 
 withhold the conclusion that this is the eclipse mentioned by the Greek 
 historian as having produced so memorable an impression on those who 
 were spectators of it. 
 
 Herodotus also mentions a total eclipse of the sun, which happened 
 when Xerxes was advancing with his army from Sardis to Abydos. He 
 states that the sun became invisible, although the heavens everywhere 
 presented a serene and cloudless aspect; and, that in consequence, night 
 took the place of day||. The date of this eclipse has been referred to the 
 year 480 A.C. The question of its actual occurrence is liable, however, to 
 some doubt, arising from a difficulty experienced in reconciling the state- 
 ment of the historian with calculations founded on the solar and lunar 
 tables. 
 
 Thucydides the historian alludes to an eclipse of the sun which hap- 
 
 * Mem. Acad. des Sciences, 1777, p. 317. f Ibid., 1777, p. 316.' 
 
 J Herod., lib. i., sec, 74. Phil. Trans., 1811, p. 220, et seq. |] Herod., lib. vii. 
 
364 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 pened in the first year of the Peloponnesian war. He mentions that it 
 took place about noon, and that several stars were visible*. The language 
 of the writer is somewhat equivocal with respect to the question whether 
 it was a total or a partial eclipse. Kepler considers it to have been total t. 
 It occurred on the 3rd of August, 431 A.C. 
 
 Diodorus Siculus relates that a total eclipse of the sun happened when 
 Agathocles, king of Syracuse, was proceeding with his fleet to Africa. 
 He affirms that the darkness was so great as to bring on the appearance 
 of night, and that stars were visible in all directions. This eclipse is 
 computed to have occurred on the 15th of August, 310 A.C. 
 
 Philostratus, in his " Life of Apollonius," mentions that the death of 
 Domitian, the Roman emperor, was previously announced by a pheno- 
 menon which appears to have been no other than a total eclipse of the 
 sun. "In the heavens," says he, "there appeared a prodigy of this 
 nature : a certain corona, resembling the Iris, surrounded the orb of the 
 sun and obscured his light." It follows from a remark which he after- 
 wards makes in reference to this event, that the darkness w T as so great as 
 to cause the appearance of night. The corona to which Apollonius alludes 
 is a phenomenon that is generally seen around the dark body of the moon 
 during a total eclipse of the sun. A more detailed account respecting it 
 will be given presently. This eclipse has been referred to the year 
 95 A.D. 
 
 Plutarch, in his " Dissertation on the Lunar Spots," alludes to a total 
 eclipse of the sun which had recently happened about mid-day. The 
 darkness was so great as to cause the day to resemble night. Stars were 
 everywhere visible. This eclipse must have occurred towards the close of the 
 first century, or early in the beginning of the second. Kepler states that 
 he calculated a great many eclipses which occurred about the year 100 A.D., 
 and that he found no one which agreed better with the words of Plutarch 
 than a total eclipse of the sun which happened in the year 113 A.D. 
 It is not improbable, however, that it is identical with the eclipse men- 
 tioned by Philostratus, the date of which is necessarily antecedent to the 
 month of September, 96 A.D. 
 
 Total eclipses of the sun are also recorded to have happened in the 
 years 237, 300, 418, 484, 787, 842, 878, 957, 1113. 
 
 It has been mentioned that Halley, in a paper communicated to the 
 Royal Society, alludes to a total eclipse of the sun which happened at 
 London on the 20th of March, 1140 A.D. The illustrious astronomer 
 does not state in very explicit terms whether his knowledge of this 
 eclipse is founded upon records of its actual occurrence, or upon a strict 
 calculation of its date by means of the solar and lunar tables. Neither 
 Kepler nor Riccioli makes any allusion to a total eclipse of the sun having 
 occurred in this year. The following passages extracted from the works 
 of contemporary writers will shew, however, that it was not allowed to 
 pass unrecorded. 
 
 In the section of the Saxon Chronicle which relates to the events of the 
 year 1140, there appears this statement : " In the Lent the sun and the 
 day darkened about the noontide of the day, when men were eating ; and 
 they lighted candles to eat by. That was the thirteenth day before the 
 calends of April. Men were very much struck with wonder. "{ The 
 
 * Thucyd., lib. ii. + Ad Vitellionem Paralipomena, p. 292. 
 
 \ Ingram' s Translation of the Saxon Chronicle, p. 371. 
 
HISTOBY OF PHYSICAL ASTRONOMY. 365 
 
 annalist then proceeds to relate the dire consequences which followed this 
 event. 
 
 In reference to the same eclipse, William of Malrnesbury, states, that 
 " while persons were sitting at their meals, the darkness became so great 
 that they feared the ancient chaos was about to return, and upon going out 
 immediately, they perceived several stars about the sun."* 
 
 Total eclipses of the sun are recorded to have happened in the years 
 1187, 1241, and 1415. A remarkable total eclipse of the sun occurred 
 on the 17th of June, 1433. This eclipse was visible in Scotland, and 
 the time of its occurrence was long remembered by the people of that 
 country as the Black Hour. Maclaurin states, that there is an account of 
 it in a manuscript, preserved in the library of the University of Edin- 
 burgh. It is therein mentioned that the eclipse took place about three 
 o'clock in the afternoon, and that the darkness was so profound that 
 nothing was visible. The latter remark is manifestly an exaggeration. 
 It appears, however, that it was an eclipse of a very unusual kind, for 
 Maclaurin found that at the time of its occurrence the sun was only .2 
 from his apogee, and the moon not more than 13 from her perigee t. 
 This eclipse is not in Riccioli's Catalogue, but he refers to it in another 
 part of his work \. 
 
 History makes mention of total eclipses of the sun which occurred in 
 the years 1485, 1506, 1530, 1514, 1560, 1567, 1598, 1605, 1652 1|, 
 1699 IT. 
 
 Down to the beginning of the eighteenth century, the accounts respecting 
 total eclipses of the sun, contain very few remarks which are of advantage 
 in forming the basis of any physical enquiry. The descriptions of similar 
 phenomena which have been observed in more recent times derive consider- 
 able value from the interesting details by which they are accompanied. 
 
 The first total eclipse of the sun, respecting which the accounts have 
 any pretension to fulness or precision, was one which happened on the 12th 
 of "May, 1706. It was observed at Montpellier by MM. Plantade and 
 
 * Histories Novella, lib. ii. ; Rerum Anglicarum post Bedem Prcccipui Scriptores, p. 
 105. 
 
 + Phil. Trans., 1737, p. 194. J Almag. Nov., lib. v.,cap. ii., SchoL 
 
 This eclipse was total in the British Isles. The moon's shadow seems to have passed 
 over the border counties of England and Scotland. The day of the eclipse was long 
 remembered in both countries as Black Saturday. 
 
 || This eclipse was also total in the British Isles. It was observed hy Dr. Wyberd at 
 Carrickfergus in the north of Ireland (see Wing's Astronomia Britannica, p. 355). The 
 day of its occurrence gave rise to the expression Mirk Monday among the people of Scot- 
 land, which is even still used in some parts of that country, although the eclipse itself has 
 long ago fallen into oblivion. 
 
 ^f This eclipse happened on the 24'. h of September, and was observed at various places 
 in the north of Europe. It is mentioned by several of the Swedish observers of the total 
 eclipse of 1733. (Act a Lit. et Scien. Suecia, torn, iv., Upsal., 1742.) At Leipsic, 
 where it was very nearly total, a correspondent of the Royal Society states, that " when 
 ten digits were obscured, the sky, being otherwise very clear, began to appear of a more 
 livid or wan complexion, and more sad than it usually looks, with a clear sky when the sun 
 is set, or below the horizon. The cocks also which had hitherto crowed very frequently, 
 as if silenced, going to roost, left, off crowing and did not renew it, till by the recovery of 
 the sun's light they had recovered their former gaiety and mirth." (Phil. Trans., 1700, 
 p. 624.) Louville, in his account of the total eclipse of 1715, to be presently mentioned, 
 has noticed a similar fact. He says, that a little before the sun was totally eclipsed, the 
 cocks of London began to crow as" at daybreak ; that they were silent during the total ob- 
 scuration ; and that the sun had no sooner reappeared than they commenced again to crow 
 with greater vivacity than before. (Mem. Acad. des Sciences, 1715, p. 98.) 
 
366 HISTOEY OF PHYSICAL ASTEONOMY. 
 
 Capies*, at Geneva by Duillierf, at Nuremburg, by Wurtzelban J, and at 
 a variety of other places. At Montpellier the total obscuration lasted 
 4 m 10 s . During the time that the sun was totally hidden, there appeared 
 a corona of light around the dark body of 4he moon. The planets Venus, 
 Mercury, and Saturn, as well as Aldebaran, and several other fixed stars, 
 were visible to the naked eye. The effects produced upon the animated 
 creation by the sudden transition from day to night Avere remarkable. 
 " The bats flew about as at dusk. The fowls and pigeons betook them- 
 selves in great haste to their resting-places. The little birds which sung 
 in cages were silent and put their heads under their wings. The animals 
 which were at labour stood still." At Geneva the total obscuration lasted 
 3 m . Duillier states, that the Council which had been engaged in delibera- 
 tion when the eclipse came on, arose from their seats, because they were 
 unable to read or write. Bats were seen flying about, and swallows look- 
 ing in amazement for a place of refuge. In several parts of the city there 
 were seen persons prostrate on the ground and offering up prayers, under 
 the impression that the last day was come. On the tops of some of the 
 mountains of Switzerland, where the view of the heavens was not ob- 
 structed by the gross vapours that accumulate in the lower regions of the 
 horizon, the stars appeared as thickly strewed as in the time of full moon. 
 The aspect of the heavens could neither be compared to the darkness of 
 night, or the chastened hue of twilight . Wurtzelban states, that it was 
 impossible for any person not to feel appalled at the spectacle | . 
 
 Halley has given an interesting account of the total eclipse of the sun 
 which happened at London on the 3rd of May, 171511. The total ob- 
 scuration lasted 3 m 22 s . The planets Jupiter, Mercury, and Venus, as well 
 as Capella and Aldebaran, were visible to the naked eye. There appeared 
 a luminous ring around the moon as on the occasion of the eclipse of 
 1706. " I forbear," says Halley, " in his communication to the Royal 
 Society, " to mention the chill and damp which attended the darkness of 
 this eclipse, of which most spectators were sensible and equally judges. 
 Nor shall I trouble you with the concern that appeared in all sorts of 
 animals, birds, beasts, and fishes, upon the extinction of the sun, since 
 ourselves could not behold it without some sense of horror." ** 
 
 Louville, who repaired from Paris to London, for the express purpose 
 of witnessing this eclipse, has also given an account of it which appears 
 in the "Memoirs of the Academy of Sciences," for 171 5 ft. In various 
 places of England which were more favourable for observing the phenome- 
 non than London, as many as twenty stars were seen with the naked eye 
 during the totality of the eclipse JJ. The direction of the shadow was 
 towards the north-east. At Upsal, in Sweden, the total obscuration lasted 
 4"9 S . 
 
 On the 22nd of May, 1724, a total eclipse of the sun happened, which 
 was visible in France and Germany. It was observed by Maraldi and J. 
 
 * Mem. Acad. des Sciences, 1706, p. 113 (Hist.). 
 
 t Phil. Trans., 1706, p. 2241, et seq. 
 
 $ Miscellanea Beroliniensis, torn, i., p. 219, et seq. 
 
 Mem. Acad. des Sciences, 1706, p. 118 (Hist.). 
 
 || Miscellanea Beroliniensis, torn, i., p. 223. 
 
 H Phil. Trans., 1715, p. 245, etseq. ** Phil. Trans., 1715, p. 261. 
 
 ft Mem. Acad. des Sciences, 1715, p. 89, et seq. JJ Phil. Trans., 1715, p. 250. 
 
 Ibid., 1715, p. 256. 
 

 HISTORY OF PHYSICAL ASTRONOMY. 367 
 
 Cassini, at Trianon *, and by Delisle, at Paris f. At Trianon, the total ob- 
 scuration lasted Q m 16 s . Venus, Mercury, and a few of the fixed stars, 
 were visible to the naked eye. The obscurity does not seem to have been 
 so great as on some former occasions. Wagner states, that when it was 
 at its maximum, there was still light enough to enable a person to deci- 
 pher written characters and to discern objects at a moderate distance offj. 
 On this occasion also a corona of light was seen to encompass the dark 
 body of the moon, during the totality of the eclipse. 
 
 On the 2nd of May, 1733, there happened a total eclipse of the sun, 
 which was visible in the north of Europe. At Forshem, in Sweden, 
 the total obscuration lasted 3 m 8 s . Jupiter, the stars of Ursa Major, 
 Capella, and several other stars, were visible to the naked eye. It 
 was generally remarked, however, that the darkness was not so great 
 as during the total eclipses of 1699 and 1715 ||. The luminous ring 
 formed a conspicuous phenomenon during the total obscuration. It was 
 sufficiently bright to be seen distinctly with the naked eye IF. Three or 
 four spots of a reddish colour were also perceived near the limb of the 
 moon, but not in immediate contact with it **. These interesting pheno- 
 mena will be alluded to presently in more detail. 
 
 On the 9th of February, 1766, a total eclipse of the sun occurred, which 
 was observed in the Southern Ocean by the persons on board the French 
 ship of war the Comte d'Artois. The total obscuration lasted only 53 s . 
 There was seen a luminous ring about the moon, which had four remark- 
 able expansions situate at a distance of 90 from each other ff. 
 
 On the 24th of June, 1778, there happened a total eclipse of the 
 sun, which was observed at sea by the Spanish Admiral Don Antonio 
 Ulloa, while passing from the Azores to Cape St. Vincent \\. The total 
 obscuration lasted four minutes. The luminous ring presented a very 
 beautiful appearance. Before it became very conspicuous, the stars of the 
 first and second magnitude were distinctly visible; but when it attained 
 its greatest brilliancy, those of the first magnitude alone could be per- 
 ceived. The darkness was such, that persons who had been asleep in the 
 afternoon, having awoke, imagined to their great astonishment that the 
 night was already far advanced . The fowls, birds, and other animals on 
 board, took their usual position for sleeping, as if it had been night. 
 
 On the 16th of June, 1806, a total eclipse of the sun occurred, which 
 was visible in North America. At Kinderhook, in the State of New 
 York, it was observed by the Spanish astronomer, Don Joachim Ferrers || ||. 
 The total obscuration lasted 4 m 37 s . One or two of the planets and a few 
 stars of the first magnitude were visible. The moon appeared to be sur- 
 rounded by a luminous ring. There was a slight fall of dew, while the 
 sun was totally hidden. 
 
 * Mem. Acad. des Sciences, 1724, p. 176, 178. f Ibid., 1724, p. 316, et seq. 
 
 Miscellanea Beroliniensis, torn, iii., p. 287. 
 
 Acta Lit. et Scien., Sueciro, torn, iv., p. 61, Upsaliae, 1735. 
 
 II Acta, Upsal., torn, iv., pp. 60, 63, 64. f Acta, Upsal., torn, iv., p. 64. 
 
 ** Phil. Trans., 1733, p. 135; Acta, Upsal., vol. iv., p. 65. 
 
 ft The officers of the Comte d'Artois gave a detailed description of this eclipse to Le 
 Gentil, who has briefly alluded to it in the beginning of the second volume of his work. 
 Voyage dans les Mers de Vlnde. Paris, 1781 . 
 
 Jt Phil. Trans., 1779, p. 105, et seq. 
 
 The total obscuration commenced at 44 minutes past three o'clock in the afternoon. 
 (Phil. Trans., 1779, p. 107.) 
 
 HII Amer. Phil. Trans., vol. vi., p. 264, et seq. 
 
368 HISTORY OF PHYSICAL ASTKONOMY. 
 
 On the 30th of November, 1834, there happened a total eclipse of the 
 sun, which was visible in Georgia and South Carolina, U.S. At Milledge- 
 ville, Georgia, the phenomenon was observed, by the French astronomer, 
 Nicollet*. The total obscuration lasted V* 15 s . At Beaufort, South Ca- 
 rolina, two planets and four stars of the first magnitude were visible to the 
 naked eye f. 
 
 A total eclipse of the sun depends upon the concurrence of so many 
 circumstances, that an opportunity of observing a phenomenon of this 
 nature seldom occurs to the astronomer, even if the place where it is 
 visible were invariably favourable for that purpose. When it is con- 
 sidered, however, that the track of the lunar shadow is not infrequently 
 confined to a region remote from the great centres of European science, 
 it may easily be conceived that an astronomer may pass his whole life- 
 time without enjoying the gratification of witnessing so impressive a 
 spectacle. An intense interest was therefore naturally excited by the 
 approaching occurrence of the total eclipse of July 8, 1842, which was 
 announced to be visible in the north of Italy, and in the southern pro- 
 vinces of France, Germany, and Russia. Many of the most eminent as- 
 tronomers of Europe repaired to different stations upon the track of 
 the lunar shadow, with the intention of observing the phenomenon. 
 M. Arago awaited its occurrence at Perpignan; M. Valz, at Marseilles; 
 M. Petit, at Montpellier; the late Mr. Baily, at Pavia; Mr. Airy, 
 at the Superga, near Turin ; M. Carlini, at Milan ; MM. Santini, 
 and Conti, at Padua ; MM. Schumacher and Littrow, at Vienna ; 
 and MM. Otto Struve, and Schidlowsky, at Lipesk. It was witnessed 
 under favourable circumstances at all these stations, as well as at 
 several other places; and detailed statements respecting it were drawn up 
 by the various observers, which have formed the groundwork of much 
 interesting speculation];. The following account of the occurrence of the 
 eclipse, by M. Arago, cannot fail to repay perusal by the reader. 
 
 " At Perpignan, persons who were seriously unwell, alone remained 
 within doors. As soon as day began to break, the population covered the 
 terraces and battlements of the town, as well as all the little eminences 
 in the neighbourhood, in hopes of obtaining a view of the sun as he as- 
 cended above the horizon. At the citadel we had under our eyes, besides 
 numerous groups of citizens established on the slopes, a body of soldiers 
 about to be reviewed. 
 
 " The hour of the commencement of the eclipse drew nigh. More 
 than twenty thousand persons, with smoked glasses in their hands, were 
 examining the radiant globe projected upon an azure sky. Although 
 armed with our powerful telescopes, we had hardly begun to discern 
 the small notch on the western limb of the sun, when an immense 
 
 * Silliman's Amer. Journal, vol. xxviii., p. 193. 
 
 f Silliman's Journal, vol. xlii., p. 175. 
 
 J Messrs. Baily and Airy have given descriptions of the eclipse, in vol. xiv. of the 
 Memoirs of the Astronomical Society. The observations of the French Astronomers 
 are all given by M. Arago in the Annuaire for 1845. In vol. iv. of the Giornale dell' 
 Istituto Lombardo, there are interesting communications respecting the phenomenon, 
 by MM. Piola, Carlini, Belli, Santini, and Confighliachi. M. Schumacher has given an 
 account of the eclipse in No. 457 of the Astronomische Nachrichten. An account of 
 the observations of M. Otto Struve and his colleague is inserted, in No. 470 of the last- 
 mentioned Journal. In the Annuaire for 1845, M. Arago has collected and arranged all 
 the observations of the eclipse, and has discussed them in the same volume, with the 
 ability which characterizes all the labours of that illustrious philosopher. 
 
HISTORY OF PHYSICAL ASTRONOMY. 3C9 
 
 exclamation, formed by the blending together of twenty thousand dif- 
 ferent voices, announced to us that we had anticipated by only a few 
 seconds, the observation made with the unaided eye by twenty thousand 
 astronomers equipped for the occasion, whose first essay this was. A lively 
 curiosity, a spirit of emulation, the desire of not being outdone, had the 
 privilege of giving to the natural vision an unusual power of penetration. 
 During the interval that elapsed, between this moment, and the almost 
 total disappearance of the sun, we remarked nothing worthy of relation, in 
 the countenances of so many spectators. But when the sun, reduced to a 
 very narrow filament, began to throw upon the horizon only a very feeble 
 light, a sort of uneasiness seized upon all ; every person felt a desire to 
 communicate his impressions to those around him. Hence arose a deep 
 murmur, resembling that sent forth by the distant ocean after a tempest. 
 The hum of voices increased in intensity as the solar crescent grew more 
 slender ; at length the crescent disappeared, darkness suddenly succeeded 
 light, and an absolute silence marked this phase of the eclipse, with as 
 great precision as did the pendulum of our astronomical clock. The phe- 
 nomenon in its magnificence, had triumphed over the petulance of youth, 
 over the ievity which certain persons assume as a sign of superiority, over 
 the noisy indifference of which soldiers usually make profession. A pro- 
 found stillness also reigned in the air ; the birds had ceased to sing. 
 
 " After an interval of solemn expectation, which lasted about two minutes, 
 transports of joy, shouts of enthusiastic applause, saluted with the same 
 accord, the same spontaneous feeling, the first reappearance of the rays 
 of the sun. To a condition of melancholy produced by sentiments of an 
 indefinable nature, there succeeded a lively and intelligible feeling of 
 satisfaction which no one sought to escape from, or moderate the impulses 
 of*. To the majority of the public, the phenomenon had arrived at its 
 term. The other phases of the eclipse had few attentive spectators beyond 
 the persons devoted especially to astronomical pursuits."! 
 
 The interval of time during which the sun was totally hidden behind the 
 dark body of the moon was comparatively brief, even at those places which 
 were most favourably situated for observing the phenomenon. At Perpig- 
 nan, which was close to the centre of the lunar shadow, the total obscura- 
 tion lasted only 2 m 11 s . At Pavia, the duration of the totality was 2 m 24 s . 
 At Venice, which was situate near the southern limit of the shadow, the 
 duration was only 43 s . In the regions of eastern Europe, the total obscu- 
 rity lasted somewhat longer. At Lipesk the duration extended to 3 m 5 s . 
 
 The luminous ring usually seen around the moon during a total eclipse 
 of the sun, appeared on this occasion with great splendour. There were 
 also perceived, three rose-coloured protuberances of sensible magnitude 
 in apparent contact with the moon's limb. The darkness which prevailed 
 during the totality of the eclipse was considerable. Sig. Piola states that 
 at Lodi, the planet Mars, two stars of the constellation Gemini, Aldebaran, 
 
 * In connexion with this remark, the following anecdote, which, according to M. 
 Arago, appeared in the Journal of the Lower Alps, of July 9, 1842, cannot fail to prove 
 interesting to the reader. A poor child of the commune of Sieves was watching her flock 
 when the eclipse commenced. Entirely ignorant of the event which was approaching, 
 she saw with anxiety the sun darken by degrees, for there was no cloud or vapour visible 
 which might account for the phenomenon. When the light disappeared all at once, the 
 poor child, in the height of her terror, began to weep, and call out for help. Her tears 
 were still flowing when the sun sent forth his first ray. Reassured by the aspect, the 
 child crossed her hands, exclaiming, in the patois of the province, " O beou Souleou /" 
 (O beautiful Sun!) 
 
 f Annuaire, 1846, p. 303. 
 
 13 B 
 
370 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Capella, as well as several other stars of the first magnitude, were visible. 
 The citizens of Venice remarked, with respect to a steamboat which was 
 passing on the Lagunes, during the totality of the eclipse, that the column 
 of smoke which usually issues from the funnel was 110 longer visible. The 
 sparks of flame which the column draws 'along with it, appeared in conse- 
 quence to be isolated, and produced a very beautiful effect *. 
 
 The appearance presented by surrounding objects during the eclipse was 
 very remarkable. M. Lentheric has stated that, at Montpellier, a little 
 before the commencement of the totality of the eclipse, the light had 
 acquired a livid and ashy tint, imparting to the human countenance an 
 aspect which was painful to contemplate. MM. Pinaud and Boisgirard 
 remarked that at Narbonne, as the eclipse advanced, the obscurity 
 assumed a character quite peculiar. It had a wan and livid hue, 
 a shade of greyish olive, which seemed to throw over nature a veil of 
 mourning. At Lodi the aspect of the heavens, according to Sig. Piola, 
 was very striking. There were seen two reddish zones extending along 
 the horizon, one in the southern and the other in the northern region of 
 the heavens. They were of a dull copper colour, totally different from 
 the ruddy hue of the aurora or the twilight. The rest of the* heavens 
 passed without any degradation to a dark azure inclining to violet. Its 
 light reflected by the waters of the Po and the Lake of Lecca imparted to 
 them an aspect which inspired terror. At Lipesk the heavens appeared 
 of a greyish violet. The stars Aldebaran and a. Orionis, which are 
 usually red, appeared quite white. It was remarked by all observers, that 
 the spectacle presented during the totality of the eclipse was of a very 
 appalling nature. 
 
 A great number of interesting facts were noticed respecting the effects 
 produced upon animals, by the sudden transition from day to night. M. 
 Arago states, that in many instances, horses and other animals employed 
 in labour, halted all at once when the eclipse became total, lay down, and 
 obstinately refused to move in spite of whip or spur. At Montpellier, 
 according to M. Lentheric, the bats, thinking that night was come, left 
 their retreats. An owl was seen to leave the tower of St. Peter and fly 
 over a part of the town; the swallows disappeared; the fowls went to 
 roost ; a herd of cattle feeding in a field, formed themselves into a circle, 
 their heads directed outwards, as if to resist an attack. At Venice swal- 
 lows were caught in the streets, the terror with which they were seized, 
 having taken from them the power of flight. On the other hand, M. 
 Arago states it to be a well-ascertained fact, that the horses employed 
 in the diligences continued to pursue their courses, without seeming to be 
 in the slightest degree affected by the phenomenon. 
 
 The effect of the obscurity upon those plants which usually close up 
 their leaves during night, was very apparent. At Prades in France, at 
 Milan, and at Vienna, it was found that several plants had closed up 
 during the totality of the eclipse. 
 
 With respect to the variation of the thermometer during the eclipse, 
 M. Arago remarks that it was not so considerable as might have been 
 supposed from the impression of cold upon the hands and face. At 
 Perpignan a thermometer, placed in the shade, descended 3 on the cen- 
 tigrade scale. With respect to the thermometers exposed to the direct 
 action of the solar rays, the variation, of course, was much greater. A 
 thermometer with a black bulb, contained in a globe of glass, from which 
 * Giornale dell' Istituto, del Lombardo, torn, iv., p. 310. 
 
HISTOEY OF PHYSICAL ASTEONOMY. 371 
 
 the air was exhausted, heing exposed to the sun, was found to have de- 
 scended 8. 7 between 5 h 6 m and 5 h 48 m *. A thermometer with a bulb of 
 ordinary glass descended 5. 5 between 5 h 10 m and 5 h 48 m . At the 
 various places of Italy, where observations of this nature were made, the 
 mean descent of the thermometer was 2. 5 Keaumur. At Lipesk, M. 
 Otto Struve found that a thermometer placed in the shade fell 3 Reau- 
 murf. At Perpignan, Turin, Vienna, and several other places, a heavy 
 dew fell during the obscuration. 
 
 The total eclipse of July 8, 1842, afforded an interesting illustration of 
 the high state of perfection which astronomical science has attained, in the 
 fidelity with which it responded to the calculations that had been pre- 
 viously made respecting the time of its occurrence. The coincidence 
 which subsisted in this respect, combined with the remarkable phenomena 
 which presented themselves during the obscuration, were also well cal- 
 culated to elevate the mind to a contemplation of the Eternal Being 
 who directs the movements of the celestial bodies with such unerring 
 regularity, and exercises such an all-pervading influence over the in- 
 numerable arrangements of creation. Although in European countries 
 a total eclipse of the sun is no longer regarded with feelings of super- 
 stitious terror, it would be forming an opinion of human nature equally 
 erroneous and ignoble, to suppose that in the present advanced state of 
 civilisation, a spectacle of such sublimity could be viewed with sceptical 
 indifference. "All the accounts respecting this eclipse," says Sig. 
 Piola, " contain reflections on the perfection of that great machine of 
 the universe, whose movements are so regular that the astronomer is en- 
 abled, long beforehand, to predict their effects with unfailing precision ; and 
 from contemplating the machine, it was natural to ascend to the Supreme 
 Artificer. While this idea swells in the mind, there is another which, at 
 the same time, shrinks into insignificance that suggested by contem- 
 plating the position of man in the midst of creation. The magnificence 
 of the scale upon which the phenomena of the eclipse, whether atmo- 
 spheric or celestial, took place, was patent to every spectator. The exten- 
 sive coloration of an unusual hue, that was visible, the rapid changes 
 which occurred, above all the obscurity which settled over nature like 
 the funereal pall thrown over a dead body, and whose subsequent with- 
 drawal in an instant, operated like a resurrection all this produced on 
 the mind a mixture of profound and indefinable impressions which it 
 will be pleasing to hold long in remembrance."! 
 
 Among the various eclipses of the sun recorded as having happened in 
 ancient times, some were, in all probability, annular; but in no instance 
 is the description of the writer sufficiently clear to establish, beyond 
 all doubt, the actual occurrence of an eclipse of this nature. The earliest 
 eclipse, which is unequivoccally asserted to have been annular, was one 
 which occurred in the year 1567. Clavius, who observed it at Rome, has 
 stated that, when the obscuration was greatest, there still remained 
 around the moon's limb a very narrow ring of the solar light . Kepler, 
 however/found by calculation, that the sun must have been totally covered 
 by the moon on that occasion, and upon this ground he maintained that 
 the luminous ring, observed by Clavius, was no other than the corona 
 
 * The total obscuration commenced at 5 U 4G m 51 s A.M. 
 t Bibliotheque Universelle de Geneve, vol. xliv., p. 309. 
 \ Giornale dell' Istituto del Lombardo, torn, iv., p. 320. 
 Sphrera Sacrobosci, cap. iv. 
 
 BBS 
 
372 HISTOBY OF PHYSICAL ASTEONOMY. 
 
 of light which usually appears around the moon during a total eclipse of 
 the sun*. 
 
 Tycho Brahe, misled by an erroneous determination of the apparent 
 diameters of the sun and moon, came to the conclusion that a total eclipse 
 of the sun was impossible, and that, in fact, all central eclipses of that 
 body were necessarily annular. In accordance with this view of the 
 subject, he contended that the eclipse of 1560, observed at Coimbra by 
 Clavius, as well as the eclipse of 1598, observed at various places in the 
 North of Europe, both of which were reputed to have been total, were in 
 reality annular. It has been ascertained, however, that in each of these 
 instances, the apparent diameter of the moon was less than that of the 
 sun ; and, therefore, it follows that during a short interval of time the 
 sun must have been totally concealed from observation. 
 
 In 1601 there happened an eclipse of the sun, which appears, beyond 
 all doubt, to have been annular in Norway. Longomontanus asserts, 
 upon the authority of Fossius, Bishop of Bergen, that the fishermen on 
 the neighbouring coast perceived with great admiration the whole body of 
 the moon projected upon the sun, leaving uncovered a uniform ring of 
 the solar disk, about a digit and a half in breadth f. An annular eclipse 
 was also observed by Bouillaud, in the year 1639 J. 
 
 The first annular eclipse respecting which we possess a detailed account, 
 was one which happened on February 18, 1737. It was observed in 
 Scotland by the celebrated mathematician, Maclaurin, who communicated 
 to the Royal Society an interesting paper respecting it, which appears in 
 the volume of the Transactions of that body for the same year. The 
 annular eclipses which have since been observed are those of 1748, 1764, 
 1791, 1820, 1831, 1836, 1838, and 1847. 
 
 We now proceed to notice, in detail, the phenomena which generally 
 characterise solar eclipses, and to give a brief account of the various specu- 
 lations that have been propounded respecting their physical origin. 
 
 It has been universally remarked that during the progress of eclipses 
 the colour of the sky undergoes a change. Halley, in his account of the 
 total eclipse of 1715, speaks very explicitly upon this point. " When 
 the eclipse," says he, " was about ten digits (that is, when about five-sixths 
 of the solar diameter were immersed), the face and colour of the sky 
 began to change from perfect serene azure blue to a more dusky livid 
 colour, intermixed with a tinge of purple, and grew darker and darker till 
 the total immersion of the sun."[| The observers of the total eclipse of 
 July 8, 1842, all concur in asserting that the colour of the sky underwent 
 a remarkable change during the progress of the obscuration ; but they 
 differ materially in the details which they furnish respecting the pheno- 
 menon. M. Arago remarks that these discordances are mainly attributable 
 to physiological causes connected with the organ of vision ; and as it is 
 impossible to arrive at an adequate appreciation of the influence of these 
 causes, he considers that any enquiry founded upon the statements of the 
 various observers would be altogether useless, more especially as they are 
 for the most part destitute of precision. He, therefore, undertakes simply 
 to investigate the effect which the progress of the eclipse tends to produce 
 upon the colour of the atmospheric light, in any particular region, without 
 
 * Ad Vitellionem Paralipomena, p. 299. 
 
 f Astronomia Danica, lib. i., cap. 9. { Astronomia Philolaica, lib. ii., p. 210, 
 
 Phil. Trans., 1737, p. 177, et seq. || Ibid., 1715, p. 247. 
 
HISTORY OF PHYSICAL ASTRONOMY. 373 
 
 taking into account the modifying influence of extraneous causes, selecting 
 for this purpose the region which is vertical relative to the spectator. 
 He remarks that every particle of the atmosphere, although illuminated 
 mainly by the direct rays of the sun, is also affected in some degree by 
 the light reflected in every direction from the other particles. During 
 the progress of the eclipse, the region of the atmosphere which lies verti- 
 cally above the spectator, ceases gradually to be illuminated by the direct 
 rays of the sun, while, on the other hand, it is constantly exposed to the 
 same intensity of reflected light from the region which lies in the horizon 
 of particles situate at a great altitude above the place of observation, for 
 the sun still continues to shine upon that region with all his force. The 
 proportion of direct to reflected light continues to diminish as the eclipse 
 increases in magnitude, until at length the reflected light produces a 
 more intense effect than the direct, and thereby determines the visible 
 colour of the sky. Now it is a fact which cannot fail to have come under 
 the observation of every person, that the rays of light proceeding from 
 those regions of the atmosphere that lie near the horizon, invariably differ 
 in hue from those which are transmitted from the more elevated regions. 
 It follows, therefore, as a necessary consequence, that the colour of the 
 sky in the region which is vertical relative to the spectator will undergo 
 a perceptible change *. 
 
 This explanation is very ingenious, but it does not give a satisfactory 
 account of the unnatural aspect which the sky exhibits during an eclipse, 
 and which has been universally remarked to be totally different from the 
 appearance of the dawn or twilight. It is to be borne in mind, however, 
 that the circumstances which determine the faint illumination of the 
 atmosphere during an eclipse, although analogous to those upon which 
 the phenomenon of the dawn or twilight depends, are not absolutely 
 identical with them ; and hence it is not improbable that the different 
 condition of the light, arising from this cause, may produce the pallid hue 
 which is visible during an eclipse. 
 
 It has been found that while the colour of the sky changes very sen- 
 sibly during eclipses of the sun, a similar effect is also produced upon 
 terrestrial objects. Even as early as the year 840, A.D., it was remarked 
 that during the total eclipse of the sun which happened in that year, the 
 colours of objects on the earth were changed f. Kepler mentions that 
 during the solar eclipse which happened in the autumn of 1590, the 
 reapers in Styria noticed that everything had a yellow tinge J. It was 
 remarked by MM. Plantade and Clapies, on the occasion of the total 
 eclipse of 1706, that as the obscuration increased or diminished, objects 
 changed their colour. When two-thirds of the solar diameter were 
 eclipsed, they assumed the colour of orange yellow ; when there was only 
 about the twenty-fifth part of the diameter visible they assumed a reddish 
 tinge, resembling water that has been diluted with wine. 
 
 Sir John Clarke, in an account of the annular eclipse of 1737, states, 
 that there was no considerable darkness, but that the ground was covered 
 with a kind of dark greenish colour . 
 
 In Le Gentil's brief description of the total eclipse of 1766, it is stated 
 that during the greatest obscuration objects assumed a tinge of livid 
 yellow, which produced a very remarkable effect ||. 
 
 * Annuaire, 1846, p. 296. f Ad Vitellionem Paralipomena, p. 294. 
 
 f Ad Vitellionem Paralipomena, p. 303. Phil. Trans., 1737, p. 197. 
 
 || Voyage dans les Mers de PInde, tome ii., p. 16. 
 
374 HISTORY OF PHYSICAL ASTRONOMY. 
 
 During the total eclipse of 1842, it was universally remarked that the 
 colours of terrestrial objects were changed. 
 
 M. D'Hombres-Firmas perceived that when three-fourths of the sun 
 were eclipsed, objects of a reddish colour, and the human countenance 
 especially, appeared paler, and acquired an olive hue. According to M. 
 Lordat, a few minutes before the commencement of the totality of the 
 eclipse, objects appeared to have a slight tinge of yellow ; the light anon 
 became wan and livid ; in certain positions the human countenance had 
 a cadaverous aspect *. 
 
 Sig. Piola states that the observers of the eclipse in Italy generally 
 remarked that towards the total obscuration objects assumed a greenish 
 tinge, which passed gradually to a saffron hue, or to violet, as some of the 
 observers asserted f. According to Mrs. Airy, the effect produced was 
 like looking at objects through a very dark greenish glass J. 
 
 It is manifest that the aspect of terrestrial objects cannot fail to be affected 
 by the change of colour which the atmospheric light undergoes during the 
 progress of an eclipse. It cannot be doubted, however, that the phe- 
 nomena above mentioned are, to a considerable extent, attributable to the 
 influence of contrast. Moreover, it is to be remarked that the physio-- 
 logical constitution of the eye tends to produce a modifying effect upon 
 the specific hue of objects. Under these circumstances, it would obviously 
 be premature to make such observations as those above cited, the ground- 
 work for deducing any sound conclusions of a general nature. 
 
 The darkness which prevails during a total eclipse of the sun is not so 
 profound as might be expected, nor as it is generally supposed to be. 
 Ferrer, in his account of the total eclipse of 1806, states, that even when 
 the effect produced by the interception of the solar rays was at its 
 maximum, the light which still remained, was equal to that of the full 
 moon. In general, it has been found that the darkness is sufficiently 
 intense to prevent a person from reading, although there have not been 
 wanting several instances of a contrary nature. Mr. Airy has remarked 
 that the illumination during the total eclipse of 1842 was so small, that 
 he could with difficulty read the divisions on the watch-plate, which was 
 within eight inches of his eye. The faint visibility which continues to 
 subsist even when the sun is totally concealed behind the dark body of 
 the moon, arises mainly from the light reflected by those regions of the 
 atmosphere which are still illuminated by the direct rays of the sun. It 
 is evident, however, that the corona around the moon will also contribute 
 in some degree towards producing the effect. The observation of Don 
 Ulloa, relative to the darkness which prevailed during the total eclipse of 
 1778, is very decisive upon this point. It has been mentioned that at 
 the commencement of the total obscuration he was enabled to perceive 
 the stars of the second magnitude, but that, after the appearance of the 
 luminous ring, only those of the first magnitude were visible. 
 
 * Annuaire, 1846, p. 291. 
 
 f Giornale dell' Istituto del Lomb., tome iv., p. 304. 
 
 | Mem. Ast. Soc., Vol. xv., p. 17. In thus using the liberty of divesting the obser- 
 vation cited by Mr. Airy, of the anonymous character in which he has presented it in his 
 paper on the eclipse, the author pleads the example of M. Arago, upon whose authority 
 alone he has been induced to adopt a course which is at all times desirable, but more 
 especially so when the subject is of an historical nature, as it happens to be in the pre- 
 sent instance. 
 
 Trans. Amer. Phil. Soc., vol. vi,, p. 266. 
 
HISTORY OP PHYSICAL ASTRONOMY. 375 
 
 The darkness which prevails during the total obscuration of the sun, 
 does not appear to be equally profound, when the observations of different 
 eclipses are compared together ; nor even at different places where the 
 same eclipse has been observed. This arises partly from the variable 
 condition of the atmosphere, and partly from the circumstance that during 
 an eclipse all places are not equally immersed in the moon's shadow. It 
 is manifest that all those places which are situate close to the boundary 
 of the lunar shadow, are exposed in a greater degree to the light reflected 
 from the regions of the atmosphere upon which the sun is still shining, 
 than are the places contiguous to the centre of the shadow. It was upon 
 this principle that Halley explained the fact that at London the obscurity 
 during the total eclipse of 1715, was less intense than that which pre- 
 vailed in various other parts of England that were more deeply immersed 
 in the lunar shadow*. 
 
 A fact was noticed during the total eclipse of 1842, which deserves to 
 be mentioned. Sig. Piola states, that at Lodi, the darkness during the 
 totality of the eclipse was equal to that by which the stars of the second 
 magnitude are usually discerned, and yet only those of the first magnitude 
 were visible f. A similar remark was made by M. Otto Struve, with 
 respect to the same eclipse. He states that at Lipesk the darkness 
 surpassed in a small degree that which reigns at St. Petersburg during 
 the summer solstice ; but that, while in the latter case the stars of the 
 third magnitude are usually discernible without any difficulty, in the 
 former case those of the first alone could be perceived J. Sig. Belli 
 explains this curious fact by reference to a physiological principle. He 
 remarks that during the short interval of total obscuration, the eye has 
 not sufficient time to recover from the dazzling effect of the sun's rays, 
 and consequently is unable to take due advantage of the obscurity which 
 actually pre vails . This is, doubtless, the true explanation of the anomaly 
 observed on such occasions. 
 
 The suddenness with which day succeeds night, upon the reappearance 
 of the sun after undergoing a total eclipse, has been remarked by all 
 persons who have witnessed a phenomenon of this nature. The first ray 
 of the sun darts forth from behind the moon's limb with a velocity that 
 has been compared to the swiftness of an arrow, a flash of lightning, or 
 some such emblem of extraordinary speed ||. According to Sig. Piola, so 
 rapid was the effect produced by the reappearance of the sun on the 
 occasion of the total eclipse of 1842, that it might be said to have been 
 night, and in an instant it was day IT. The same observer states, that it 
 
 * Phil. Trans., 1715, p. 250. Sig. Piola has stated that persons stationed upon the 
 hills around Brescia, during the total eclipse of 1842, enjoyed the beautiful prospect of 
 the peaks of Rosa and Cimone brilliantly illuminated by the sun's rays, while they them- 
 selves were involved in the obscurity of the moon's shadow. (Gior.deU' 1st. Lomb., 
 p. 310.) 
 
 t Giorn. dell' 1st. Lomb., tome iv., p. 341. 
 
 | Bibliotheque Universelle de Geneve, tome xliv., p. 368. 
 
 Giorn. dell' 1st. Lomb., tome iv., p. 341. 
 
 I) *' Instar fulgoris" " instar sagittarum radii solis repente prorumpentes " "radius 
 solis instar sagittse prevolavit" " radius admodum illustris prorupit," &c., c. Such are 
 the terms employed by the Lutheran pastors of Sweden, in describing the reappearance 
 of the first rays of the sun on the occasion of the total eclipse of 1733. 
 
 ^ " Talche si pote dire che in momento era notte e fu giorno " ( Giornale dell J. R. 
 Istituto del Lombardo, tome iv., p. 314). Attempts have been made to detect the 
 motion of the moon's shadow in the course of its passage over the surface of the earth. 
 To effect such an object, however, is manifestly a very difficult matter, on account of the 
 
376 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 was universally remarked by the spectators of the eclipse at Lodi, that 
 the light emitted by the sun previous to the total obscuration, produced a 
 much less dazzling effect than that which distinguished his emersion from 
 behind the dark body of the moon. In the former case, the spectator 
 was enabled to look upon the sun for several minutes previous to the total 
 obscuration, without experiencing any inconvenience ; in the latter case, 
 it was impossible for the naked eye to withstand the violent impact of the 
 first rays of the sun. This fact had been already noticed by Halley, on 
 the occasion of the total eclipse of 17.15. The English astronomer had 
 suggested two distinct causes, to whose combined operation it might be 
 ascribed. One of these was of a physiological nature ; the other implied 
 the existence of a lunar atmosphere. He remarked, in the first place, 
 that previous to the total obscuration, the pupil of the eye might be very 
 much contracted by viewing the sun, and, consequently, the organ of 
 vision would be less liable to suffer from the effulgence of the light than 
 at the instant of emersion, when the pupil had again expanded. Secondly, 
 he suggested that, as the eastern margin of the moon, at which the sun 
 disappeared, had been exposed for a fortnight to the direct action of the 
 solar rays, the heat generated during this period might cause vapours to 
 ascend in the lunar atmosphere, which, by their interposition between the 
 sun and the earth, would have the effect of tempering the effulgence of 
 the solar rays passing through them. On the other hand, the western 
 margin of the moon, at which the sun reappeared, had just experienced a 
 night of equal length, during which the vapours suspended in the lunar 
 atmosphere, had been undergoing a course of precipitation upon the 
 moon's surface under a process of cooling. In this case, therefore, the 
 solar rays would meet with less obstruction in passing through the lunar 
 atmosphere, and, consequently, it was reasonable to suppose that they 
 would produce a more intense effect*. 
 
 It is clear that both causes above mentioned might conspire together in 
 producing the observed effect. As, however, there are no reasons for 
 supposing that the moon possesses an atmosphere capable of exercising 
 any appreciable influence, it is probable that the true explanation is to be 
 sought in the different dimensions of the pupil of the eye, at the com- 
 mencement and the end of the total obscuration. 
 
 The luminous ring that appears around the moon is one of the most 
 interesting features of a total eclipse of the sun. The earliest allusion to 
 it is probably to be found in the passage of the Life of Apollonius, already 
 cited, wherein the author mentions that the death of the emperor 
 Domitian had been previously announced by a total eclipse of the sun. 
 " In the heavens," says Philostratus, " there appeared a prodigy of this 
 
 immense velocity with which the shadow sweeps over any particular place of observation. 
 Halley calculated that the shadow of the eclipse of 1715 passed over England at the 
 rate of fifty-nine geographical miles in a minute (Phil. Trans., 1715, p. 260). Mr. 
 Airy has mentioned in his account of the total eclipse of 1842, that he endeavoured to 
 detect the progress of the lunar shadow as it passed over the immense plain of Lom- 
 bardy, but that his efforts were unsuccessful. He adds, however, that Messrs. Plana and 
 Forbes felt assured that they saw the darkness travel over the country. The only remark 
 of a similar nature which the author has met with in the accounts of former eclipses is 
 contained in the following extract from Duillier's paper on the total eclipse of 1706: 
 " A little before the total obscuration, the country on the west side did already seem 
 overcast with darkness; and after the total obscuration, the darkness ivas seen to leave us 
 more and more, and to fly eastward" (Phil Trans., 1706, p. 2243). 
 * Phil. Trans., 1715, p. 248. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 377 
 
 nature. A certain corona, resembling the Iris, surrounded the orb of the 
 sun, and obscured his light." 
 
 Plutarch, also, about the same time, alludes in one of his works to the 
 phenomenon of the luminous ring. Speaking of a total eclipse of the 
 sun which had recently happened, he endeavours to show why the dark- 
 ness arising from occurrences of this nature is not so profound as that 
 which usually prevails when the sun is below the horizon. He begins 
 by assuming, as the basis of his reasoning, that the earth greatly exceeds 
 the moon in dimensions. After citing various authorities in support of 
 this assertion, he then proceeds thus: "Whence it happens that the 
 earth, on account of its magnitude, entirely conceals the sun from our 
 
 sight But even although the moon should at any time hide 
 
 the whole of the sun, still the eclipse is deficient in duration as well as 
 amplitude, for a peculiar effulgence is seen around the circumference, 
 which does not allow a deep and very intense shadow."* It cannot 
 admit of any doubt that the phenomenon alluded to in the above pas- 
 sage is the luminous ring that has been invariably observed around 
 the moon in modern times on the occasion of a total eclipse of the 
 sunf. 
 
 It would seem that Clavius observed the luminous ring at Rome during 
 the eclipse which happened on April 9, 1567, although he was not con- 
 scious of its real nature. It has been already mentioned, that when the 
 obscuration was greatest, he perceived a narrow ring of light around the 
 moon, which he supposed to be the margin of the solar disk. Kepler, 
 however, maintained that the luminous circle seen by Clavius, could not 
 really be a portion of the sun. He found, in fact, by calculation, that 
 during the eclipse, the moon was at her mean distance from the earth, in 
 which position, he remarked, her apparent diameter exceeds that of the 
 sun even when he is in perigee ; while at the same time the sun was 
 approaching towards apogee, where his apparent diameter is the least 
 possible. He therefore came to the conclusion that the sun must have 
 been totally covered by the moon during the eclipse, and, consequently, 
 that the appearance observed by Clavius could not have been produced 
 by the direct transmission of the solar rays. The explanation which that 
 
 * It will be seen that the passage in the text differs materially from that cited by 
 M. Arago, in the Comptes Rendus, tome xiv., p. 848, which is to the following effect : 
 " La Lune laisse deborder autour d'elle, dans les eclipses, une partie du Soleil, ce qui 
 diminue Vobscurite" It is merely on the strength of the last part of this sentence, and 
 in direct contradiction to the first part, that M. Arago ventures to suggest that the 
 phenomenon of the luminous ring is probably that to which Plutarch alludes. It is 
 manifest, however, that the sentence may be supposed, with greater plausibility, to apply 
 to annular eclipses. With respect to the passage cited in the text, there cannot exist a 
 shadow of a doubt that it refers to the luminous ring that is visible around the moon 
 during a total eclipse of the sun. The following are the express terms in which Plutarch 
 alludes to the phenomenon : n & fftX^n xv oXov wort xgu-^y rov %Xiov, elx i%u 
 ovdt vrXa,To$, w i'xXs/^/j, XXa fiityctiviTKi <r;j a.Lyrt vfi(>i rrjv "<rvv, ovx iwffa, fixfaTctv 
 
 TYIV ffxixv x] axrov. (Plut., Opera Mor. et Phil., vol. ix., p. 682, Edit. Lips., 1778). 
 M. Arago docs not mention the part of Plutarch's works in which the original of the 
 translation given by him is to be found. It is not improbable, therefore, that he may 
 refer to some less unequivocal passage of the Greek author than that above cited. 
 
 f This eclipse is sometimes referred to the year 98, A.D. ; Kepler, however, is dis- 
 posed to believe that it happened in the year 113, A.D. (Tabul. Rudotp. Prcecept., 
 p. 104). 
 
378 HISTORY OF PHYSICAL ASTRONOMY. 
 
 illustrious astronomer has given of the physical cause of the phenomenon 
 will be noticed presently. 
 
 The luminous ring was visible around the moon during the total eclipse 
 of 1598. Jessenius, who observed the ^eclipse at Torgau in Germany, 
 remarked that during the greatest obscuration there appeared a bright 
 light shining around the moon*. On this occasion, also, the phenomenon 
 was generally supposed to arise from a defect in the totality of the eclipse, 
 although Kepler strenuously contended that such an explanation was at 
 variance with the relation between the values of the apparent diameters 
 of the sun and moon, as computed for the time of the eclipse by the aid 
 of the solar and lunar tables. He considered the phenomenon to be 
 identical in its nature with that observed during the eclipse of 1567, and 
 to be a usual accompaniment of total eclipses of the sun. 
 
 The views of Kepler respecting the eclipses of 1567 and 1598 first 
 appeared in his " Supplement to Vitellion," which was published in the 
 year 1604. They received a striking confirmation from the observations 
 of the total eclipse of the sun which happened in the following year. 
 On this occasion the eclipse was observed at Naples, under circumstances 
 which did not admit of any doubt respecting the existence of the ring. 
 " The whole body of the sun was effectually covered for a short time. 
 The surface of the moon appeared quite black ; but around it there shone 
 a brilliant light of a reddish hue, and uniform breadth, which occupied a 
 considerable part of the heavens. "f 
 
 During the total eclipse of the sun which happened on the 29th of 
 March, 1652, and which was visible in the British Isles, the moon was 
 seen surrounded by a ring of light. Dr. Wyberd, who observed this eclipse 
 at Carrickfergus in the north of Ireland, has stated that when the sun was 
 reduced to a very slender crescent of light, the moon all at once threw her- 
 self within the margin of the solar disk with such agility, that she seemed 
 to revolve like an upper millstone, affording a pleasant spectacle of rotatory 
 motion ! He remarks, however, that in reality the sun was totally eclipsed, 
 and that the appearance was due to a corona of light around the moon, 
 arising from some unknown cause. He adds, that it had a uniform 
 breadth of half a digit, or a third of a digit at least, that it emitted a bright 
 and radiating light, and that it appeared concentric with the sun and moon 
 when the two bodies were in conjunction \. 
 
 The luminous ring formed a conspicuous accompaniment of the total 
 eclipse of the sun which happened on the 12th of May, 1706. The de- 
 scription of it given by MM. Plantade and Capies, who observed the 
 eclipse at Montpellier, is clearer and more precise than any other that 
 had been hitherto recorded. As soon as the sun was totally eclipsed, there 
 appeared around the moon a very white light forming a kind of corona, the 
 breadth of which was equal to about 3'. Within these limits the light was 
 everywhere equally vivid, but beyond the exterior contour, it was less in- 
 tense, and was seen to fade off gradually into the surrounding darkness, 
 forming an annulus around the moon of about 8 in diameter . 
 
 * Ad Vitellionem Paralipomena, p. 299. 
 
 f Kepler, De Stella Nova, p. 116, 4to., Prag., 1606. 
 
 \ Wing, Astronomia Britannica, p. 356. 
 
 Mem. Acad. des Sciences, 1706, p. 251. 
 
HISTORY OF PHYSICAL ASTEONOMY. 379 
 
 Halley's account of the total eclipse of the sun which happened at 
 London in 1715, corroborates the testimony of preceding observers with 
 respect to the existence of the luminous ring, and also contains some in- 
 teresting particulars relative to its physical aspect. " A few seconds," 
 says he, " before the sun was all hid, -there discovered itself round the 
 moon a luminous ring about a digit, or perhaps a tenth part, of the moon's 
 diameter in breadth. It was of a pale whiteness or rather pearl colour, 
 seeming to me a little tinged with the colours of the Iris, and to be con- 
 centric with the moon." He remarked, moreover, that the ring appeared 
 much whiter and more brilliant near the body of the moon than at a dis- 
 tance from it, and that the exterior boundary was very ill denned, seem- 
 ing to be determined only by the extreme rarity of the luminous matter*. 
 
 The account of the appearance of the ring on this occasion, given by 
 the French astronomer Louville, tends to confirm the truth of Halley's 
 remarks. He has stated, however, that there were interruptions in its 
 brightness, causing it to resemble the radial glory with which painters en- 
 circle the heads of the saints. He asserted with confidence that it ap- 
 peared to be concentric with the moon f. 
 
 The luminous ring formed a conspicuous feature of the total eclipse of 
 the sun which occurred on the 22nd of May, 1724. Maraldi has stated, 
 that at the commencement of the total immersion, the ring appeared 
 broader on the east than on the west side ; but, on the other hand, that at 
 the end of the total immersion, it appeared broader on the west side. He 
 remarked also that the breadth of the ring where it bordered upon the 
 northern limb of the moon, was greater than the breadth at the part bor- 
 dering upon the southern limbj. 
 
 The luminous ring appeared with great splendour on the occasion of the 
 total eclipse of 1733. A great many interesting observations relative to 
 it, due chiefly to Lutheran pastors, are to be found in the fourth volume of 
 the Transactions of the Royal Society of Sweden . The following are a 
 
 * Phil. Trans., 1715, p. 249. 
 f Mem. Acad. des Sciences, 1715, p. 90. \ Ibid., 1724, p. 178. 
 
 Nothing can be more praiseworthy than the zeal with which the clergymen in the 
 rural districts of Sweden responded to the invitation of the Royal Society of that country 
 to note the various phenomena connected with the occurrence of the total eclipse of 
 1733. The observations transmitted by them to the Society on this occasion, were all 
 arranged methodically by Celsius, previous to their insertion in the volume referred to 
 in the text. Although they cannot pretend to much precision, still it may be asserted 
 without hesitation, that they form the most complete description of a total eclipse of the 
 sun which is to be found in the records of astronomical observation previous to the total 
 eclipse of 1842. This is more especially remarkable, as only a few years 
 
 other two total eclipses of the sun had happened (in fact, during the intermediate period 
 the moon's node in the one case had made only half a revolution, and in the other not 
 more than a whole revolution), by means of which the inhabitants of the two countries of 
 western Europe, which boast of their superior civilization, had an opportunity of making 
 similar observations. With respect to the total eclipse of 1715, the account given by 
 Halley is the only one due to an English observer which contains a single remark of a 
 physical nature. The other descriptions, relating to the duration and magnitude of the 
 eclipse, merely served the purpose of enabling Halley to determine the precise track of 
 the lunar shadow as it passed over England. Something might have been expected 
 from Cotes, who observed the eclipse at Cambridge ; but, according to Halley, he had 
 the misfortune to be oppressed with too much company. The accounts given by the 
 French observers of the total eclipse of 1724, are still more meagre and unsatisfactory; 
 since in this case there is not even one description which might compensate, in some 
 degree by its merits, for the barrenness of the others. 
 
380 HISTORY OF PHYSICAL ASTRONOMY. 
 
 few details respecting it, which have been extracted from the paper by 
 Celsius embodying them. 
 
 The pastor of Stona Malm states, that at Catherinesholm, during the 
 total obscuration, there was seen a ring ground the sun about a digit in 
 bread th,from which there issued rays of light*. According to the pastor 
 of Forshem, the ring appeared of a reddish colour, similar to that which is 
 perceived in the Iris. At the commencement of the total obscuration it 
 appeared broadest towards the west ; in the middle it presented a uniform 
 aspect; and at the close it was broadest towards the north f. Vallerius, 
 another pastor, states, that the ring was more ruddy and compact close to 
 the sun, and that at a distance from that body it appeared of a greenish 
 colour. The pastor of Smoland affirms, that during the total obscuration 
 the limb of the moon resembled gilded brass, and that the faint ring 
 around it emitted rays in an upward as well as in a downward direction, 
 similar to those seen beneath the sun when a shower of rain is impending \. 
 M. Edstrom, Mathematical Lecturer in the Academy of Charlestadt, as- 
 serts, that the ring appeared everywhere of equal breadth, that it emitted 
 rays from above as well as from below, that these rays were equal in 
 brilliancy, but of unequal length, and that they plainly maintained the 
 same position until they vanished along with the ring upon the reappear- 
 ance of the sun's limb . At Lincopia the ring appeared of a bright white 
 colour, but it did not exhibit a radial aspect ||. From the descriptions given 
 by several observers, it would seem that at the commencement of the total 
 obscuration, the ring appeared brighter and broader at the part of the 
 moon's limb where the sun had disappeared, but that towards the close 
 of the obscuration it was more conspicuous in both these respects at the 
 part where the sun was about to emerge. 
 
 It has been already mentioned, that a luminous ring was seen around 
 the moon during the total eclipse of the sun which happened on the 9th 
 of February, 1766. The most remarkable feature exhibited by it con- 
 sisted of four luminous expansions, separated from each other by equal 
 intervals of 90. Two of them were situate in the plane of the ecliptic; 
 the other two were at opposite extremities of a diameter of the ring per- 
 pendicular to that plane. A copy of a drawing of the ring by the officers 
 of the French ship of war, the Comte d'Artois, appears at the beginning of 
 the second volume of Le Gentil's Voyage dans les Mers de VInde. 
 
 A very interesting account of the luminous ring as it appeared during 
 the total eclipse of 1778, is given by the Spanish Admiral Don Antonio 
 Ulloa. He states, that five or six seconds after the commencement of the 
 total obscuration, a brilliant luminous circle was seen surrounding the 
 moon, which became more vivid as the centre of that body continued to 
 approach the centre of the sun. About the middle of the eclipse, its breadth 
 was equal to one-sixth of the moon's diameter. There appeared issuing 
 from it, a great number of rays of unequal length, which could be discerned 
 to a distance equal to the lunar diameter. It seemed to be endued with a 
 rapid rotatory motion, which caused it to resemble a firework turning round 
 its centre. The colour of the light was not uniform throughout the whole 
 breadth of the ring. Towards the margin of the lunar disk, it appeared 
 of a reddish hue ; then it changed to a pale yellow, and from the middle 
 
 * Acta Lit. et Scien. Suec. Upsal., torn, iv., p. 56. f Ibid., p. 61. 
 
 Ibid., p. 62. Ibid., p. 57. || Ibid., p. 59. 
 
HISTORY OP PHYSICAL ASTRONOMY. 331 
 
 to the outer border, the yellow gradually became fainter, until at length it 
 seemed almost quite white *. 
 
 Ferrer, in his account of the total eclipse of 1806, has given a brief 
 description of the luminous ring. He states, that the colour of the light 
 emitted by it resembled pearl colour, and that it had a breadth of about 6'. 
 From the exterior margin there were seen luminous rays extending out- 
 wards to a distance of more than 3. The light was brightest at the edge 
 of the moon, and terminated very confusedly at the outer border. With 
 respect to its relative position, the ring seemed to be concentric with the 
 sun f. De Witt, who observed the same eclipse at Albany in the State of 
 New York, states, that " the luminous circle on the edge of the moon, 
 as well as the rays which were darted from her, were remarkably pale, and 
 had that bluish tint which distinguishes the colour of quicksilver from a 
 dead white." j 
 
 The luminous ring appeared with great splendour during the total 
 eclipse of July 8, 1842. It was of uniform brightness in those parts 
 that bordered on the moon's limb, whence it faded imperceptibly out- 
 wards, terminating so confusedly, that it was impossible to trace its ex- 
 terior limit. The difference between the inner and outer parts of the 
 ring appeared to M. Arago to be sufficiently marked to sanction the 
 subdivision of the ring into two concentric zones, the inner zone being 
 everywhere of equal density and well defined at the outer border, while on 
 the other hand the exterior zone, although the broader of the two, was 
 fainter even at the inner border, and gradually diminished in brightness 
 until it was lost in the surrounding darkness. The interior zone was a 
 conspicuous object at all the stations where the eclipse was observed, and 
 everywhere presented the same aspect. The exterior zone, being much 
 fainter, did not exhibit the same degree of magnitude at the different places 
 of observation. Indeed it was only under favourable conditions of the 
 atmosphere that it was visible at all. 
 
 With respect to the dimensions of the corona, it could not be expected 
 that the observations would present a very close agreement, owing to the 
 indefinite nature of its structure. At Perpignan, M. Silva found by means 
 of a repeating circle, that the interior zone had an invariable breadth of 3' 
 during the whole time of complete obscuration. Mr. Airy estimated its 
 breadth at an eighth part of the lunar diameter, or about 4'. From the 
 statements of the various observers, it would appear that this part of the 
 luminous ring, or in other words the part exhibiting a uniform condensation, 
 extended from the moon's limb to a distance of between 3' and 4'. 
 
 The exterior zone of the corona being more or less perceptible accord- 
 ing to the condition of the atmosphere, there naturally arose considerable 
 discordances in the observations relative to its breadth at the different 
 stations. At Montpellier, M. Petit obtained 8' 45" for the distance to 
 which the corona was visible. This would indicate the breadth of the ex- 
 terior part to be about 5'. Mr. Baily estimated the breadth of the whole 
 corona at half the moon's diameter, or about 16'. At Lipesk, where it 
 appeared with great splendour, M. Otto Struve found that it was visible 
 to a distance of 25' from the moon's limb. 
 
 At several stations the regularity of the contour of the ring appeared 
 to be interrupted by two or more expansions of light. In France there 
 
 * Phil. Trans., 1779, p. 108. 
 
 t Trans. Amer. Phil. Soc., vol. vi., p. 2CC. t l bid -> P- 301. 
 
383 HISTORY OF PHYSICAL ASTRONOMY. 
 
 were generally two such expansions visible. They were situate at oppo- 
 site extremities of a diameter, passing through the point at which the sun 
 went in behind the moon's limb, and the opposite point at which he 
 reappeared. At Milan, Sig. Picozzi observed two jets of light occupying 
 a similar position. It was, doubtless, from the same cause that the ring 
 appeared slightly eccentric at Novara, for it was remarked that its 
 greater axis coincided with the direction of the moon's motion*. A 
 similar elongation of the ring was also observed at Padua, by Sig. Biela, 
 and several other persons f . Sig. Pietropoli, who observed the eclipse at 
 that city, remarked that the ring sensibly bulged out at the opposite 
 extremities of a diameter inclined to the horizon at an angle of about 
 10 | . M. Otto Struve perceived several luminous jets, which in some 
 instances extended as far as 4 from the moon's limb . 
 
 From the ring there were generally seen to issue diverging rays of un- 
 equal length. At Perpignan, M. Mauvais found that some of these rays 
 extended as far as 33' from the moon's limb. Mr. Baily, in his account 
 of the eclipse, remarks, that at Pavia the diverging rays had the effect 
 of depriving the corona of the appearance of a ring ||. On the other, 
 Mr. Airy states, with respect to the aspect of the corona, when viewed 
 from the Superga, that, although a slight radiation might have been per- 
 ceptible, it was not sufficiently intense to affect in a sensible degree the 
 annular structure by which the luminous appearance was plainly distin- 
 guished 11. These discordances are doubtless mainly attributable to the 
 different conditions of the atmosphere at the various places of observation. 
 
 Phenomena of a still more anomalous nature were remarked by several 
 observers in France. At Perpignan, M. Arago, distinctly perceived with 
 the naked eye, a little to the left of the diameter, passing through the 
 highest point of the moon's limb, a luminous spot composed of jets, en- 
 twined in each other. He states, that " in appearance, they resembled 
 a hank of thread in disorder." A similar phenomenon was observed at 
 Montpellier. It was remarked, also, at some stations, that the direction 
 of the diverging rays was not in all instances perpendicular to the moon's 
 limb. Some of these rays when prolonged towards the moon, instead of 
 passing through the centre of that body, cut off only a small segment of 
 her disk. 
 
 The prevailing colour of the ring at the different stations was white. 
 At Perpignan it assumed a yellowish hue in the telescope, but it appeared 
 white to the naked eye. According to Mr. Airy, it had a close resemblance 
 to peach colour. Mr. Baily and M. Otto Struve both found it quite white. 
 
 The different degrees of brilliancy which the ring exhibited at the 
 various places of observation is worthy of remark. At Perpignan, its 
 lustre resembled that of the moon. The aspect which it presented to 
 Mr. Airy, at the Superga, was somewhat similar. On the other hand, 
 at Pavia it appeared with a splendour which excited the admiration of 
 every spectator. " I had imagined," says Mr. Baily, " that the corona, 
 as to its brilliant or luminous appearance, would not be greater than that 
 faint crepuscular light which sometimes takes place on a summer's even- 
 
 * Giorn. dell' 1st. del Lomb., torn iv., p. 307. Sig. Configliachi also affirms, that at 
 Monguzzo two expansions of light were visible at opposite extremities of a diameter of 
 the ring. (See the volume above cited, p. 368.) 
 
 f Giorn. dell' 1st. del Lomb., torn, iv., p. 381. J Ibid., p. 383. 
 
 Annuaire, 1846, p. 329. II Mem. Ast. Soc., vol. xv., p. 5. 
 
 1 Ibid., p. 15. 
 
HI9TOBY OF PHYSICAL ASTRONOMY. 388 
 
 ing, and that it would encircle the moon like a ring. I was, therefore, 
 somewhat surprised and astonished at the splendid scene which now so 
 suddenly burst upon my view."* At Lipesk, the brilliancy of the ring 
 was still more vivid. According to M. Otto Struve, it was so intense as 
 to be barely supportable to the naked eye. So strong was the impression 
 which it produced upon the spectators of the eclipse, that many of them 
 could with difficulty be persuaded that the whole of the solar disk was 
 actually concealed behind the body of the moon f. 
 
 These extraordinary variations in the brightness of the ring are doubt- 
 less attributable to the more or less favourable condition of the atmosphere 
 at the different places of observation. In connexion with this explanation, 
 M. Arago has suggested, with great probability, that the intense brilliancy 
 which the ring exhibited at Lipesk, may have arisen from the compara- 
 tively high altitude of the sun during the totality of the eclipse. As an 
 illustration of this remark it may be stated that at Perpignan, where the 
 ring resembled the moon in lustre, the altitude of the sun at the time of 
 his total immersion was 11 59'; whereas at Lipesk the altitude of the 
 same body was 41 19', when the totality of the obscuration took place. 
 Now it is very manifest that the atmospheric medium of air through which 
 the eclipse was observed, was much less favourable for discerning the 
 brightness of the ring in the former case, than it was in the latter J. 
 
 At Montpellier, there were many persons who asserted that the ring 
 turned continually round its centre. We have seen that a similar remark 
 had been already made with respect to the corona which appeared during 
 the total eclipses of 1652 and 1778. At Lipesk, the light of the ring 
 seemed to M. Otto Struve to be in a state of violent agitation. Mr. Baily 
 states, that the rays had a flickering appearance, somewhat like that which 
 a gas illumination might be supposed to assume, if formed into a similar 
 shape. 
 
 The ring generally became visible a few seconds previous to the total 
 immersion of the sun, and it continued to be perceived during an equal 
 interval of time subsequent to his reappearance. This circumstance sug- 
 gested to M. Arago an interesting method of determining the intensity of 
 the light of the ring relative to the light diffused throughout the atmo- 
 sphere by the full sun. It is manifest, that at the instant when the ring 
 first becomes visible, its light must exceed, in intensity, the atmospheric 
 light which appears around it. In order that an object may become 
 barely visible, it is necessary that its brightness should exceed that of the 
 ground upon which it appears projected by a certain determinate quan- 
 tity . In this manner, then, the light of the ring becomes directly com- 
 parable in intensity with the light diffused around it. Now, the atmo- 
 spheric light around the ring varies in the direct ratio of the solar segment, 
 which remains uncovered by the moon. Hence, knowing the magnitude 
 of the visible segment of the sun, it is easy to compare the light diffused 
 by it through the atmosphere with the light diffused by the full sun, and 
 when this point has been ascertained, the relative intensities of the light 
 of the ring and the light diffused by the full sun become comparable also. 
 Now, the magnitude of the solar segment may obviously be deduced from 
 
 * Mem. Ast. Soc., vol. xv., p. 4. 
 
 f Annuaire, 1846, p. 336. \ Ibid., p. 336. 
 
 At p. 381 of the Annuaire for 1846, M. Arago asserts, as the result of experiment, 
 that in such a case the brightness of the object must exceed that of the ground upon 
 which it is projected by a sixtieth part. 
 
384 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the interval of time which elapses between the instant of the ring becom 
 ing visible, and that of total obscuration, for the time which the moon 
 takes to cover the segment will at once afford an indication of its breadth. 
 
 It appears from the foregoing remarks, that the comparison of the 
 light of the ring with the light diffused in the atmosphere by the full 
 sun, depends upon the determination of the precise time which elapses 
 between the commencement of the visibility of the ring, and the instant 
 of total obscuration. On this point, however, the observations do not 
 agree sufficiently well with each other, to be of much utility to enquirers 
 in resolving so delicate a question. At Montpellier, M. Petit perceived 
 the ring, five or six seconds before the sun had totally disappeared behind 
 the dark body of the moon. At Salon it was seen by M. Largetau, four 
 or five seconds previous to the total immersion. Mr. Baily has remarked, 
 that only three or four seconds were wanting to complete the total immer- 
 sion of the sun when he first saw the ring. 
 
 The luminous ring was seen at some places that were situate actually 
 beyond the limits of the lunar shadow, and where consequently a segment 
 of the solar disk continued visible, even during the time of greatest obscu- 
 ration. In such cases it is manifest that the magnitude of the solar seg- 
 ment visible, upon which the relative intensity of the light of the ring, as 
 determinable by the foregoing method, depends, may be obtained by cal- 
 culating the maximum phase of the eclipse at the place under considera- 
 tion. M. Arago cites an interesting observation of this nature, made by 
 M. D'Hombre Firmas, at Alais, which was contiguous to the lunar shadow, 
 but not actually involved in it. " Every one," says the last-mentioned 
 individual, " remarked the circle of pale light which encompassed the 
 moon when she almost entirely covered the sun*. It would appear that 
 this is not the only instance in which the ring has been seen during a 
 partial eclipse of the sun t. 
 
 The ring at first was only partially visible, being incomplete on the 
 side of the solar disk which was still uncovered by the moon. As soon, 
 however, as the total obscuration was effected, the ring appeared entire. 
 " A bright line," says Mrs. Airy, " seemed to form round the right side 
 of the moon before the disappearance, but not quite round, so that the 
 ring was not complete ; but at the moment of the total disappearance, the 
 ends seemed suddenly to join and form the complete ring."{ At Milan, 
 Sig. Majocchi, and his companions, perceived a fragment of the ring a 
 few seconds before the total obscuration, situate in the region where the 
 first contact of the two bodies took place ; and they continued to discern a 
 faint trace of it in the opposite region, a short time after the reappearance 
 of the sun . This tallies exactly with the observation just cited. 
 
 It was remarked that the ring first appeared brightest on the side 
 of the solar disk, which was just covered by the moon, but that previous 
 to the close of the total obscuration, it was brightest at the part where 
 the sun was about to reappear. This interesting fact is alluded to by 
 several of the observers of the eclipse. There was no defined edge 
 to the ring ; it changed sensibly, being brightest first on the left 
 
 * Annuaire, 1846, p. 339. 
 
 f Thus in an account of the solar eclipse of November 27, 1722, communicated by 
 an observer in America to the Royal Society, it is stated that at Barnstable, on Cape 
 Cod, there was but a little left of the sun, and that nearer the head of the Cape, there 
 was a ring of light quite round the moon (Phil. Trans. 1724, p. 69). 
 
 Mem. Ast. Soc., vol. xv., p. 16. Annuaire, 1846, p. 340. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 385 
 
 side where the sun had gone in, then below, and then on the right 
 side ; the light coming out at each place successively, like little beams 
 from the moon's edge. Such are the terms in which the variation of 
 the appearance of the ring as viewed from the Superga, is described*. 
 Sig. Piola states, that at St. Angelo, near Lodi, the same remark was made 
 by every person who witnessed the eclipse f. It has been already mentioned 
 that a similar fact was noticed, with respect to the appearance of the 
 ring, during the total eclipses of 1724 and 1733. 
 
 The question relative to the physical cause of the luminous ring has 
 given rise to much speculation. Some persons have supposed it to derive 
 its origin from the moon, while others again have maintained that it is 
 purely a solar phenomenon. A brief historical statement of the different 
 hypotheses that have been advanced in connexion with this subject may 
 not, perhaps, prove uninteresting to the reader. 
 
 Various explanations of the luminous ring have been advanced in ac- 
 cordance with the supposition of its being an appendage of the moon. 
 The earliest is that which ascribes it to the influence of a lunar atmo- 
 sphere. It was first suggested by Kepler, as a probable mode of ac- 
 counting for the phenomenon. He conjectured [that the rays of 
 light proceeding from the sun to the earth, might be refracted in passing 
 through the moon's atmosphere, and might thereby occasion an appearance 
 resembling the luminous ringj. This view of the origin of the pheno- 
 menon was regarded with favour by Halley, although at the same time 
 he admitted that it could not be considered as fully established. If the 
 ring was due to the existence of a lunar atmosphere, it ought invariably 
 to appear concentric with the moon. On the other hand, if it arose 
 from the presence of an atmosphere about the sun, it could only surround 
 the moon equably at the instant when the centres of the two bodies were 
 in conjunction. In the latter case, it is manifest that the ring ougfet to 
 appear broadest first at the point where the sun had just disappeared 
 behind the moon's limb, and afterwards at the opposite point where he 
 was about to emerge. It is easy to see, therefore, that observations on 
 the position of the ring during an eclipse, if executed with precision, might 
 afford a valuable criterion for deciding the question, whether the ring was an 
 appendage of the sun or moon. All such observations have, however, been 
 hitherto so vague and contradictory, that no reliable conclusion can be 
 deduced from them. The ring fades off so imperceptibly from the moon's 
 limb, that the establishment, beyond all doubt, of a variation in its breadth 
 during the passage of the moon across the solar disk, if even such a varia- 
 tion existed, would seem to be impracticable. In some instances it has 
 been affirmed that the ring appeared concentric with the moon, while in 
 others it has been maintained with equal confidence, that it was concentric 
 with the sun. The observations in general are decidedly more favourable 
 to the supposition of the ring being concentric with the sun, than to its 
 holding a similar relation with respect to the moon. But indeed it is 
 
 * Mem. Ast. Soc., vol. xv., p. 16. 
 
 + Gior. dell' 1st. del Lomb., torn, iv., p. 306. 
 
 J Ad Vitellionem Paralipomena, p. 302 ; Epitome Astronomiae, p. 893. 
 
 Halley, while inclined to suppose that the luminous ring which appeared during the 
 total eclipse of 1715, arose from the presence of an atmosphere about the moon, did not 
 deny at the same time, that some persons found the ring to increase in breadth as the 
 emersion approached. " This circumstance," says he, " together with the contrary sen- 
 timents of those whose judgment I shall ahvays revere, makes me less confident" (Phil. 
 Trans. 1715, p. 249). It is not improbable that Halley here alludes to the illustrious 
 Newton, with whom he lived on terms of intimate friendship. 
 
 C C 
 
386 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 evident, from a multitude of other considerations, that the moon does not 
 possess an atmosphere so extensive as that which the ring would assign to 
 her. Assuming the ring which was visible during the total eclipse of 1806 
 to be really due to such a cause, Ferrer calculated, from the apparent 
 breadth of the ring, that the atmosphere must have attained an elevation 
 of 348 miles above the moon's surface, whence it would seem to be fifty 
 times more extensive than the earth's atmosphere. He remarked, however, 
 that the refraction of the lunar atmosphere, as indicated by observations of 
 occultations and eclipses, is so small, as to prove, beyond all doubt, that its 
 density is 1980 times less than the density of the terrestrial atmosphere*. 
 The observations of the total eclipse of 1842, tend also to shew that if a 
 lunar atmosphere really exist, its effects are totally inappreciable f. It is 
 impossible, therefore, to avoid the conclusion that the luminous ring 
 cannot proceed from such a cause. 
 
 Finding that the hypothesis of a lunar atmosphere was incapable of ac- 
 counting for the phenomenon of the luminous ring, La Hire suggested, 
 that it might be produced by the reflexion of the solar rays from the in- 
 equalities of the moon's surface contiguous to the edge of her disk, com- 
 bined with their subsequent passage through the terrestrial atmosphere. 
 In order to obtain an experimental illustration of this view of the origin 
 of the ring, he took a round unpolished stone of a yellowish colour, which 
 was about two inches in diameter ; and having suspended it in the air, at 
 the window of his chamber, so as to appear in the direction of the sun, he 
 retired within the chamber, keeping his eye in the centre of the shadow, 
 until the stone covered the sun and extended a little beyond it. Ob- 
 serving the stone at this distance, he perceived around it a bright 
 margin of light which he ascribed to the reflexion of the solar 
 rays from the asperities of its edge, and upon the same principle 
 he asserted that the luminous ring which appeared around the moon 
 during a total eclipse of the sun, might be accounted for}. Delisle, how- 
 ever remarked, as a proof of the fallacy of this explanation, that the same 
 appearance would be produced if the stone was perfectly smooth, nay, he 
 even asserted, that if instead of the stone, a piece of black pasteboard, cut 
 out into any shape approaching to a circle was employed, there would ap- 
 pear a similar line of light around its edges. It was clear, therefore, that 
 the hypothesis of La Hire was untenable. 
 
 Delisle was the first who conjectured that the luminous ring might be 
 occasioned by the diffraction of the solar rays which passed near the 
 moon's edge. He exhibited an illustration of the effect so produced by 
 
 * Trans. Amer. Phil. Soc., vol. vi., p. 274. 
 
 -j- Louville has stated, that at London, during the progress of the total eclipse of 1715, 
 the part of the solar disk contiguous to the eastern limb of the moon appeared to grow 
 continually paler, so as to announce beforehand that it. was about to be eclipsed (Mem. 
 Acad. des Sciences, 1715, p. 94). This circumstance was considered by him to afford a 
 very convincing proof of the existence of an atmosphere about the moon. It is to be re- 
 marked, however, that modern observations of eclipses have not indicated the slightest trace 
 of a phenomenon analogous to that which Louville asserts to have noticed. The luminous 
 ridges termed faculce, which occasionally appear on the surface of the sun, are especially 
 favourable for such observations, on account of their uniform aspect, and the consequent 
 ease with which any variation in their brightness, resulting from the interposition of the 
 lunar atmosphere, or any change in their form due to the refraction of the solar rays in 
 passing through it, might be detected ; but although M. Arago and his colleagues watched 
 several of such ridges with great attention during the progress of the total eclipse of 
 1 842, they were unable to discern the slightest change in their appearance as they ap- 
 proached the moon's limb (Annuaire, 1846, p. 351). 
 
 J Mem. Acad. des Sciences, 1715, p. 161, et seq. 
 
HISTORY OF PHYSICAL ASTRONOMY. 387 
 
 admitting the sun's light through a very small aperture into a dark room, 
 and then receiving the cone of light thus formed upon a metal disk of some- 
 what larger dimensions than the circular section of the cone. Upon then 
 viewing the metal disk from behind, either with the naked eye or with a 
 small telescope, he perceived around it a bright margin of light, exactly 
 resembling that which was visible in the experiment of La Hire *. 
 
 The explanation of the luminous ring proposed by Delisle has been 
 favourably received by several enquirers in recent times, but the attempts 
 to obtain an experimental illustration of it have not been attended with 
 uniform success. In some instances the sun was artificially eclipsed by 
 placing an opaque disk at the focus of the telescope ; but no appearance 
 resembling the luminous ring was discernible around the edge of the 
 disk. In 1846 Prof. Powell communicated to the Astronomical So- 
 ciety, a paper containing an account of a series of experiments executed 
 by him, with the view of elucidating this interesting subject f. He as- 
 cribes the failure of some of the previous experiments of the same nature 
 to the circumstance that the origin of light which was situate in the focus 
 of the telescope was made to coincide with the opaque disk eclipsing it, 
 whereas, in all cases of diffraction it is an indispensable condition that 
 the intercepting body should be at some distance from the origin of light. 
 Before proceeding to describe his own attempts to produce the pheno- 
 menon of the luminous ring, he remarks that in all those experiments 
 which have for their object the exhibition of the ordinary diffractive fringes, 
 it is essentially necessary, in the first place, that the origin of light be a 
 point, or as nearly as possible so ; and, secondly, that the area of the 
 diverging rays extend beyond the edge of the opaque diffracting body J. 
 Having admitted the sun's light through a series of apertures varying 
 from -J^ to of an inch in diameter, he found that the fringes ceased to 
 be distinctly visible when the diameter exceeded of an inch. Moreover, 
 he remarked, that in all such experiments the fringes could only be seen 
 directly, as forming an optical image in the air, which was magnified by 
 an eye-lens. 
 
 A phenomenon of a different kind was, however, perceptible, which 
 continued to be discerned even when the conditions of the experiment 
 were esentially varied. When a circular disk was employed to intercept 
 the light, it was seen with the naked eye, or in a telescope, at a distance, 
 bordered by a luminous ring, even in those cases wherein the diameter of 
 the aperture exceeded \ of an inch, and whether the area of the rays fell 
 without or within the opaque disk. It was found also, that although the 
 ring was distinctly visible with the telescope when in focus for the opaque 
 disk, it could not be seen with the eye-lens. Upon this ground Prof. 
 Powell concludes that the phenomenon of the ring is not an optical 
 image like that formed by the diffractive fringes, and, therefore, that it 
 cannot be ascribed to the principle of diffraction, at least when considered 
 according to the usual acceptation of the term. 
 
 Prof. Powell found that the ring ceased to be discernible when 
 the area of the rays fell short of j- of the diameter of the diffracting 
 disk, and that it increased in breadth as the area approached to an equa- 
 
 * Mem. Acad. des Sciences, 1715, p. 166, et seq. 
 
 f Mem. Ast. Soc. vol. xvi., p. 301, et seq. 
 
 It was in consequence of employing too large an aperture that Mariotte failed 
 to verify the experiment of Grimaldi, and was hence led to doubt the reality of the 
 principle of diffraction ( Traitt des Couleurs, p. 33). 
 
 C C 2 
 
388 HISTORY OF PHYSICAL ASTEONOMY. 
 
 lity with the disk. When the area of the rays was not concentric with 
 the disk, the luminous ring appeared broadest at the part where the rays 
 approached nearest the edge of the disk. 
 
 In order to establish the experiment /nore fully, the ring was examined 
 in a telescope with a magnifying power of 20, furnished with cross wires 
 in its focus. Before the light was allowed to fall upon the opaque disk, 
 the edge of the latter was made to coincide with the intersection of the 
 wires ; but as soon as the light was admitted through the aperture, the 
 ring was seen extending sensibly beyond. The intersection of the wires 
 was now made to coincide with the outer edge of the ring, and upon the 
 exclusion of the light the disk was seen to have fallen sensibly ivithin. 
 
 When the aperture of the telescope was diminished to J of an inch, the 
 ring still continued to be distinctly seen, but the diffraction produced by 
 the contraction of the aperture now caused the fringes to be also visible. 
 
 According to Prof. Powell, the colour of the ring was yellowish. There 
 also appeared a faint bluish light extending within the dark circular area 
 encompassed by it. 
 
 The circumstances of the above-mentioned experiment, abstractedly con- 
 sidered, bear a considerable resemblance to those which determine the ap- 
 pearance of the luminous ring around the moon during a total eclipse of 
 the sun. Moreover, the results may be said also to agree in their main 
 features. It would seem, therefore, not improbable, that they are attri- 
 butable to the same physical cause. This conclusion, however, has been 
 objected to, on the ground of the resemblance between the natural and 
 artificial eclipses not being sufficiently perfect, since, in the case of the arti- 
 ficial eclipse, the diffracting body is surrounded by a medium possessing a 
 considerable power of reflecting the solar light. Again, it has been re- 
 marked by Sir David Brewster, that in all experiments similar to those 
 above alluded to, the breadth of the ring is totally independent of the 
 magnitude of the diffracting body, and therefore the unavoidable con-- 
 elusion is, that in the case of the natural eclipse, the ring would be 
 utterly invisible on account of the comparatively immense distance of 
 the moon from the earth *. This must be considered as a fatal objection 
 to the above explanation, if the principle upon which it is founded be 
 admitted to be true. But besides, the diffraction theory is incapable of 
 offering any account whatever of many of the subordinate features of 
 the ring, and therefore upon this ground alone, it cannot be considered 
 as affording a faithful representation of the phenomenon. 
 
 While some persons have sought to explain the luminous ring, by as- 
 suming it to be an appendage of the moon, others have endeavoured to 
 effect the same object by referring its origin to the sun. It has been 
 already mentioned that the illustrious Kepler, who had the merit of first 
 directing the attention of astronomers to the ring, suggested that it might 
 arise from the refraction of the lunar atmosphere. Another hypothesis 
 advanced by him, as probably involving the true explanation of the pheno- 
 menon was to the effect that it was occasioned by the combustion of the 
 ether in immediate contact with the sun {-. It cannot be denied that, at 
 
 * Brewster's Edin. Encyclop., Art. "Astronomy." 
 
 + Ad Vitellionem Paralipomena, p. 301 ; Epitome Astronomic, p. 893. In order 
 to account for the circumstance of the darkness not being equally intense during all total 
 eclipses of the sun, Kepler imagined the ether to be sometimes very dense, and therefore 
 easily inflamed ; while, on the contrary, at other times being very rare and limpid, it was 
 less liable to be affected by the action of the solar rays. In his explanation of this hypo- 
 thesis, he mentions an experiment which it may not be uninteresting to describe, as it ap- 
 
HISTORY OF PHYSICAL ASTRONOMY. 389 
 
 first sight this explanation appears very plausible, but it is to be remarked 
 that the principle of an ethereal fluid pervading the celestial regions, upon 
 which it is founded, is unsupported by any positive evidence of a trust- 
 worthy character, and therefore it cannot be viewed in any other light than 
 as a gratuitous assumption. 
 
 Other persons have sought an explanation of the luminous ring in the 
 zodiacal light. It is to be remarked respecting this appendage of the sun, 
 that it does not encompass his disk symmetrically, being somewhat elon- 
 gated in the direction of the ecliptic. Dominic Cassini, to whom its dis- 
 covery is due, remarked, that if it were palpably visible, it would probably 
 appear as a faint chevelure about the sun*. Some slight traces of an elonga- 
 tion of the luminous ring which appears around the moon during a total 
 eclipse of the sun, have led to the surmise that it may possibly be no 
 other than the zodiacal light. In the vast majority of cases, however, 
 the ring has been found to be quite circular ; and even in those cases 
 wherein luminous expansions have been observed at opposite extremities 
 of a diameter of the ring, the elongation resulting therefrom does not take 
 place in the direction of the ecliptic. 
 
 The most probable explanation of the luminous ring is that according 
 to which it arises from the presence of an atmosphere about the sun. Its 
 round figure, its nebulous structure, and its gradually-diminishing density 
 outwards, are all favourable to the supposition of its being due to an elastic 
 fluid encompassing the solar orb, and gravitating everywhere towards its 
 centre. It is true that precisely similar results would ensue from the 
 existence of an atmosphere about the moon ; but, in fact, there is no reason 
 to suppose that the moon possesses an atmosphere capable of producing 
 an appreciable effect. On the other hand, the hypothesis of a solar atmo- 
 sphere is not only warranted by the analogy of the other bodies of the 
 planetary system, but is also supported by evidence of a positive nature 
 derived from observations on the physical constitution of the sun. The 
 changes presented by that body when viewed in the telescope can only be 
 consistently accounted for by the supposition of two dissimilar envelopes 
 of matter suspended in a transparent atmosphere at different altitudes 
 above his surface. That such a circumambient fluid really exists is 
 shewn most unequivocally by the gradual diminution of the brightness of 
 the solar disk towards the margin. With respect to this fact, Mr. Airy 
 states it is so palpable to observation, that when in the course of his ex- 
 periments he had occasion to throw a portion of the sun's disk upon a small 
 screen, he was always able to determine whether the limb was approaching 
 the edge of the fully-illuminated screen simply by the change of the inten- 
 
 pears to contain the germ of the discovery of the diffraction of light usually ascribed 
 to Grimaldi. Having inserted two small apertures in the window of a dark chamber, one 
 of which was about the size of a grain of millet, and the other equal in magnitude to a pea, 
 he drew two circles upon a screen placed opposite, the diameters of which bore the same 
 proportion to each other as those of the apertures. The light of the sun being then ad- 
 mitted through the larger aperture, depicted an image on the screen which exactly coin- 
 cided with the larger circle ; but when this aperture was closed, and the light was admitted 
 through the smaller one, the image was no longer well defined, its margin was somewhat 
 dusky, and finally it surpassed in magnitude the smaller circle. 
 
 * Cassini first began to see the zodiacal light in March, 1683 ; and in the Journal des 
 Savans for June of the same year, he made the remark alluded to in the text. For an 
 account of the observations (extending over several years) by means of which he defi- 
 nitely established the existence of this phenomenon, See Anc. Mem, Acad. des Sciences, 
 torn, viii., p. 121, et seq. 
 
390 HISTORY OF PHYSICAL ASTEONOMY. 
 
 sity of illumination *. Now it is very manifest that the presence of an 
 atmosphere about the sun would occasion a variation in the brightness of 
 his disk similar to that above alluded to, since the rays emanating from the 
 edge, by reason of their obliquity, would pass through a greater depth of the 
 elastic fluid, and therefore would undergo a more considerable absorption 
 than those proceeding from the regions nearer his centre. Again, it is to 
 be remarked, that there are not, as in the case of the moon, any facts at 
 variance with the supposition of an atmosphere about the sun, so extensive 
 as that which the luminous ring would seem to indicate. Moreover, the 
 hypothesis of a solar atmosphere adapts itself to the modifying phenomena 
 by which the ring is occasionally characterised, with greater facility than 
 any other. Thus what can be more natural than the conclusion that the 
 reddish macula observed during the total eclipses of 1733 and 1842 
 were clouds suspended in the solar atmosphere ? These phenomena are 
 so intimately connected with the question relative to the existence of the 
 luminous ring, that it will be desirable to present the reader with a 
 detailed account of the more prominent features by which they were dis- 
 tinguished. 
 
 With respect to the spots which appeared during the total eclipse of 
 1733, Vassenius gives the following description of them in a short paper 
 on the eclipse which he transmitted to the Koyal Society of London : 
 " But what seemed in the highest degree worthy not merely of the admira- 
 tion, but also of the attention of the illustrious Royal Society, were some 
 reddish spots which appeared in the lunar atmosphere without the periphery 
 of the moon's disk, amounting to three or four in number, one of which 
 was larger than the others, and occupied a situation about midway be- 
 tween the south and west. These spots seemed in each instance to be 
 composed of three smaller parts or cloudy patches of unequal length, 
 having a certain degree of obliquity to the periphery of the moon. Having 
 directed the attention of my companion to the phenomenon, who had the 
 eyes of a lynx, I drew a sketch of its aspect. But while he, not being 
 accustomed to the use of the telescope, was unable to find the moon ; I 
 again, with great delight, perceived the same spot, or, if you choose, rather 
 the invariable cloud occupying its former situation in the atmosphere near 
 the moon's periphery." He adds, that he continued to observe the phe- 
 nomenon for the space of 40 seconds, until it finally vanished with the 
 appearance of the first rays of the sun f . 
 
 Vassenius, in the foregoing account, assumes without hesitation, that 
 the luminous ring arises from the existence of a lunar atmosphere. His 
 interesting statement respecting the reddish spots which he perceived in 
 it, is corroborated by the pastor of Marstroom, who appears also to have 
 witnessed a similar phenomenon. The following are the terms in which 
 Celsius, while citing the observation of Vassenius, alludes to its confirma- 
 tion by that individual : " In the luminous ring itself, he (Vassenius) 
 perceived three or four lucid macula of unequal form and magnitude 
 near the lunar periphery, but still not adhering to it. He also affirms, 
 that at Marstroom, M. Brag, the pastor of the place, also saw the same 
 maculcs near the moon's limb, through an English telescope of excellent 
 construction."]; 
 
 * Mem. Ast. Soc., vol. xv. p. 11. f Phil. Trans., 1733, p. 135. 
 
 $ Acta Lit. et Scien. Suec., vol. iv., p. 65. As it has been considered that the observation 
 of the Swedish pastor, cited in the text, tends to throw some ambiguity (quelque louche) 
 
HISTORY OF PHYSICAL ASTRONOMY. 391 
 
 It is probably a similar phenomenon which is alluded to by Sueblius, 
 another Swedish pastor residing at Calmaria on the Baltic Sea, In his 
 account of the same eclipse, he states that, " on the right of the sun 
 towards the north, he perceived two lucid streaks parallel to each other 
 and inclined to the horizon."* 
 
 The following is a description, by M. Mauvais, of the phenomena of 
 a similar nature which appeared during the total eclipse of 1842, as 
 they were seen by him at Perpignan. 
 
 " A few seconds after the total obscuration, while attempting to deter- 
 mine the breadth of the ring, I perceived a reddish point at the inferior 
 limb of the moon, which did not, however, project sensibly. When fifty-six 
 seconds had elapsed from the total obscuration, the reddish point of which 
 I have been speaking transformed itself into two protuberances, similar to 
 two contiguous mountains, perfectly well defined. They were not of a 
 uniform colour; upon their flanks were seen streaks of a deeper tint. I 
 cannot give a more exact idea of their aspect than by comparing them to 
 the peaks of the Alps illuminated by the setting sun and seen afar off. 
 One minute and ten seconds had elapsed from the total obscuration, when 
 a third mountain was perceived to the left of the two others. It exhibited 
 the same aspect as far as regards colour. It was flanked by some smaller 
 peaks, but all were perfectly well defined. 
 
 " While this third mountain was in the process of issuing forth, the 
 first two continued all the while to increase. They attained a height 
 which, according to my estimation, subtended an angle of about 2'. 
 
 " The interval between the two groups appeared to embrace an arc of 
 about 25 upon the moon's limb. The most considerable group, the most 
 western in appearance, seemed to me to be a few degrees to the left of the 
 lowest point of the lunar disk."f 
 
 M. Mayette, a captain of the French Engineers, who also observed the 
 eclipse at Perpignan, compared the protuberances to beautiful sheaves of 
 flames. He states, that he continued to see the most northern sheaf a 
 few seconds after the emersion of the sun. 
 
 M. Petit states, that at Montpellier the two inferior points first ap- 
 peared, the more western before the other. They gradually but rapidly 
 increased in magnitude, as well-defined objects would have done, emerging 
 from behind the lunar disk. By actual measurement M. Petit obtained 
 I 7 45" for the angular magnitude of the largest of the luminous protu- 
 berances. 
 
 At Toulon, which was near the southern limit of the lunar shadow, 
 Captain Berard, of the French Marine, remarked that, during the interval 
 of total obscuration, there was seen beyond the moon's limb, near the 
 region where the sun was about to emerge, a very slender red land, 
 irregularly indented, or as it were furrowed here and there with hollows. 
 
 M. Flaguergues, who observed the eclipse at the same place, remarked, 
 
 upon the statement of Vassenius, inasmuch as it represents the spots to be in contact with 
 the moon's limb, it may be desirable to give the precise words in which it is expressed in 
 the original by Celsius, which are to the following effect : " Has etiam maculas Marstrandii 
 per Anglicanum optimse notse telescopium juxta lunse limbum perceptas esse refer t a pas- 
 tore loci Dn. Brag." It is clear from the words in italics (which however are not marked 
 so in the original) that the observation of M. Brag, so far from contradicting that of Vas- 
 senius, affords a most satisfactory confirmation of it. 
 
 * Acta Lit. et Scien. Suec., torn, iv., p. 63. 
 
 f Annuaire, 1846, p. 409. 
 
392 HISTORY OF PHYSICAL ASTRONOMY. 
 
 that previous to the reappearance of the sun, he perceived first one lu- 
 minous point, then a second, and soon afterwards a third, all visible in the 
 region where the sun was about to emerge. 
 
 M. Valz thus describes the appearance presented at Marseilles during 
 the totality of the eclipse. " Forty seconds previous to the end of the 
 total obscuration, I perceived near the part of the moon's limb where I 
 expected the sun to reappear, two points near each other of very great 
 brilliancy, more brilliant even than stars of the first magnitude. Their 
 light was white like that of the sun. There was seen issuing from each of 
 these points a train of light resembling that which is perceived in a dark 
 room, into which the solar light penetrates through an aperture, but only 
 more divergent; and coinciding in direction with the rays issuing from the 
 luminous ring. . . . Fifteen seconds afterwards, a third brilliant 
 point appeared, more to the north, accompanied also with a diverging 
 train of light, and contributing to form a portion of the radial glory of the 
 ring." M. Valz, who supposed that the luminous points perceived by him 
 were situate a little within the margin of the lunar disk, was under the im- 
 pression that they were occasioned by the sun shining through deep 
 valleys on the moon's surface, which in each instance appeared to be 
 closed at the top, by the projection of one of the sloping sides of the valley 
 upon the opposite side. He states, that according to the relative move- 
 ment of the sun and moon, the first luminous points were situate about 
 20" within the moon's border. 
 
 At Visan, which was situate close to the northern limit of the lunar 
 shadow, M. Guerin perceived, immediately after the total obscuration, 
 seven or eight very distinct indentations, which might have been taken for 
 so many stars of different magnitudes. They were redder but less bril- 
 liant than Mars. If the whole periphery of the lunar disk had been bor- 
 dered with similar luminous points, it would have presented the appear- 
 ance of a box of ebony garnished with rubies. 
 
 At Digue, M. Eugene Bouvard perceived two brushes of light at the 
 lower part of the moon's limb. They were formed of rays of a beautiful 
 red mingled with some rays of orange colour. They gradually became 
 broader and fainter as they receded from the moon's limb*. 
 
 The accounts respecting the appearance presented by the luminous pro- 
 tuberances in Italy, do not differ materially from those of the French 
 observers. Mr. Airy remarked, that in form they somewhat resembled 
 saw teeth in the position proper for a circular saw, inclined in the same 
 direction as that in which the hands of a watch turn. Their height was at 
 least equal to a fourth of the breadth of the ring, or 1'f. 
 
 According to Mr. Baily, the luminous protuberances had the appear- 
 ance of mountains of a prodigious elevation. Their colour was red, tinged 
 with lilac or purple. " Perhaps," says he, "the colour of the peach blossom 
 would more nearly represent their aspect." They somewhat resem- 
 bled the snowy tops of the Alpine mountains when coloured by the 
 rising or setting sun. Their light was perfectly steady, having nothing 
 of the flickering appearance observable in the corona. The most con- 
 siderable was bifurcated down to its base, insomuch that one might have 
 said, there were two protuberances, the one being projected upon the 
 other j. 
 
 * Annuaire, 1846, p. 420. 
 
 f Mem. Ast. Soe., vol. xv., p. 16. Ib., p. 6. 
 
HISTORY OF PHYSICAL ASTRONOMY. 
 
 At several of the stations in Lombardy, where the eclipse was observed, 
 only two protuberances were \isible. 
 
 Sig. Santini states, that at Padua, the luminous protuberances pre- 
 sented the appearance of irregular columns of smoke, undulating upon 
 broad bases, and seeming to ascend from behind the body of the moon *. 
 
 Sig. Biela, who observed the eclipse at the same city, states, that there 
 appeared at the lower part of the moon's limb, three pyramids of a dark 
 reddish colour, resembling burning coal, or rather approaching to the 
 colour of purple. Two of these pyramids were near each other; the 
 third, which was the largest, was more to the left, but still was to the 
 right of the point at which the sun was about to reappear. The light of 
 the sun first appeared in isolated points, which in a few instants united 
 together, and formed an excessively slender lunule. The lunule had already 
 been formed a few seconds, when the reddish pyramids disappeared f. 
 
 The following interesting account of the luminous protuberances is given 
 by M. Littrow of Vienna. 
 
 " Shortly after the formation of the ring there appeared luminous spots 
 in several points of the contour of our satellite. Three of these spots 
 were particularly remarkable. Their colour was red with a tinge of blue. 
 They very much resembled the summits of the glaciers gilded by the 
 rising or setting sun ; only they did not terminate in peaks. The largest 
 spot was about 5' in height, and was about %' broad at its base. Their as- 
 pect, which was first white, changed to rose colour and then to violet ; and 
 afterwards passed in a reverse order through the same tints. . . . The 
 protuberances were visible before they assumed a coloured hue, and they 
 continued to be visible after their colour was dissipated."! 
 
 M. Otto Struve has stated, that at Lipesk, a little before the reappear- 
 ance of the sun, M. Schidlowsky perceived several rose-coloured flames 
 which appeared suddenly to burst out at several parts of the lunar disk. 
 They resembled mountains, whose height, by estimation, appeared to be 
 about 2'. A very large part of the lunar disk was garnished with a similar 
 reddish bordering. M. Schidlowsky was unable to examine the entire 
 contour of the moon, for soon after he observed the phenomenon, the 
 sun reappeared. 
 
 The first question which naturally suggests itself upon the perusal of 
 the foregoing statements is this do the luminous protuberances noticed 
 by the various observers belong to the sun or to the moon ? Admitting 
 that they were appendages of the moon, they may be conceived as repre- 
 senting either mountains on her surface or clouds suspended in her atmo- 
 sphere. To adopt the former of these explanations, however, would be 
 assigning to the lunar surface inequalities, vastly exceeding those dedu- 
 cible from other phenomena of a less doubtful nature. Nor is the sup- 
 position of a meteorological origin more probable, since it appears from a 
 multitude of considerations that if an atmosphere really exist about the 
 moon, it is utterly incapable of holding in suspension clouds of such 
 enormous magnitude as the apparent dimensions of the protuberances 
 would indicate. The conclusion, therefore, seems to be unavoidable, that 
 whatever be the real nature of the phenomena, they cannot be referable to 
 the moon. 
 
 But, on the other hand, if they be admitted to be clouds suspended in 
 
 * Giornale dell' J, R. Istituto del Lombardo, torn, iv., p. 378. 
 t Ib., p. 382. J Annuaire, 1846, p. 434. 
 
394 HISTOEY OP PHYSICAL ASTRONOMY. 
 
 the solar atmosphere, the explanation of the various facts relating to them 
 becomes more consistent and probable. 
 
 1. That they are solar and not lunar phenomena is evident from their 
 being invisible for some time after the4otal obscuration, as well as from 
 their appearance as luminous points, and their subsequent gradual increase 
 of magnitude. All these facts are stated with great precision by M. 
 Mauvais. They are the results which would obviously follow from the 
 contiguity of the protuberances to the sun at the upper and western part 
 of the limb, and their gradual disclosure by the motion of the moon 
 towards the east. The last-mentioned fact of the protuberances being 
 gradually brought into view by the motion of the moon over the suns disk 
 is distinctly asserted by M. Petit as having been very palpable to ob- 
 servation *. 
 
 2. Near the southern limit of the lunar shadow the moon would project 
 considerably beyond the superior part of the sun's limb, and therefore it 
 might be expected that the large protuberances seen elsewhere would con- 
 tinue to be almost totally concealed, so as to appear only as luminous 
 points. This circumstance would prevent them from attracting more 
 peculiarly the attention of the observer, who might consequently be led to 
 discover similar points of equal minuteness, which might otherwise have 
 escaped his notice. The truth of this remark will be more apparent to 
 the reader when he takes into consideration the extreme shortness of the 
 interval of total obscuration, even at those places that were situate in the 
 very centre of the shadow, and the variety of circumstances which call for 
 the vigilant attention of the observer during the lapse of that interval. 
 The phenomena observed at Toulon, which was situate only a short dis- 
 tance within the south boundary of the shadow, is quite consistent with the 
 above conclusion. 
 
 3. Towards the northern limit of the shadow, where the moon pro- 
 jected only in a small degree over the superior part of the sun's limb, it 
 might be expected that the protuberances would become visible imme' 
 diately after the commencement of the total obscuration. This circum- 
 stance actually occurred at Visan, as has been already mentioned. It is 
 difficult, however, to account for the smallness of the angular dimensions 
 under which the protuberances appeared at that place. Perhaps it arose 
 from the shortness of the interval of total obscuration, not allowing the 
 eye sufficient time to recover from the dazzling effect of the sun's light, 
 so as to take due advantage of the obscurity which actually prevails. We 
 have seen that the nonvisibility of the stars of the second magnitude during 
 the total obscuration has been referred with great probability to the same 
 cause. 
 
 Admitting, then, that the phenomena had an intimate connexion with 
 the sun, there are various facts which render the supposition of their 
 meteorological origin extremely probable. 
 
 1. The reddish colour of the light emitted by them indicates that they 
 possess the property of absorbing in a great degree all the rays of the 
 
 * It is not to be denied that the size which the protuberances ultimately acquired, when 
 taken into consideration with the fact of their first appearance after the total obscuration, 
 as mere luminous points, considerably exceeds that which this explanation of their appa- 
 rent growth would assign to them. It is to be remarked, however, that when they first 
 became visible, the eye had not in all probability recovered from the dazzling effect of the 
 sun's rays, so as to discern fully the portion of each protuberance that was already disclosed 
 to view. 
 
HISTORY OF PHYSICAL ASTRONOMY. 395 
 
 spectrum, except the red, as in the case of the terrestrial clouds when 
 they are seen illuminated by the sun after his disappearance under the 
 horizon. 
 
 2. The radial appearance which the protuberances exhibited to M. 
 Eugene Bouvard can only be explained by the supposition of the rays of 
 the sun forcing their way through the interstices of the clouds contiguous 
 to his luminous surface, and illuminating the particles of the solar atmo- 
 sphere situate beyond in the line of their emanation. So also with respect 
 to the luminous points observed by M. Valz, it is impossible otherwise to 
 account for the constant emanation of the rays outwards in a direction 
 normal to the moon's limb. 
 
 3. The zone of a deep red colour observed at Toulon towards the part 
 of the moon's limb where the sun was about to emerge, clearly indicates 
 the accumulation of nebulous matter in the lower regions of the solar 
 atmosphere, as well as the condensation of the circumambient fluid of 
 which the latter is composed, towards the surface of the sun, arising from 
 the pressure of the superincumbent strata. 
 
 The indications of a solar atmosphere afforded by phenomena bearing 
 a strong resemblance to clouds and nebulous strata, as well as by the ap- 
 pearance of rays in a direction normal to the suns limb *, although 
 chiefly conspicuous during the total eclipses of 1733 and 1842, have pre* 
 sented themselves on numerous other occasions in a greater or less de- 
 gree of developement. As this is a point of considerable importance in 
 the question relative to the physical constitution of the sun, it perhaps 
 may not be out of place to give a brief statement of all those observations 
 which tend more especially to illustrate it. 
 
 Captain Stannyan, who observed the total eclipse of 1706 at Berne, 
 states, that the emersion of the sun icas preceded by a blood-red streak of 
 light from its left limb, which continued not longer than six or seven 
 seconds of time f. 
 
 A similar phenomenon was remarked by both Halley and Louville on 
 the occasion of the total eclipse of 1715. Halley, in his account of the 
 eclipse, states, that about two or three seconds before the emersion, a long 
 and very narrow streak of a dusky but strong red light, seemed to colour 
 the dark edge of the moon on the western side where the sun was just 
 coming outj. Louville states that, towards the end of the total ob- 
 scuration, there was seen about the moon's limb, at the place where the 
 sun was about to emerge, an arc of a deep red colour. In order to obtain 
 an assurance that the phenomenon was not due to the aberration of the 
 telescope, he took the precaution of viewing it through the very centre 
 of the object-glass, when he found that it exhibited the same colour as 
 before . 
 
 Don Ulloa, in his account of the total eclipse of 1778, speaks of a point 
 of red light which appeared on the edge of the moon's disk near the place 
 where the sun was about to emerge. It first became visible about a 
 minute and a quarter before the reappearance of the sun. It then 
 
 * It has been mentioned in the account of the appearance presented by the luminous 
 ring during the total eclipse of 1733, that there were seen emanating from it rays of 
 unequal length, which constantly maintained the same position. This description is 
 clearly at variance with the supposition of the phenomenon being due to the irregular 
 scintillation of a luminous object. 
 
 t Phil. Trans., 1706, p. 2240. i Phil. Trans,, 1715, p. 250. 
 
 Mem. Acad. des Sciences, 1715, p. 93. 
 
396 HISTORY OF PHYSICAL ASTRONOMY. 
 
 equalled a star of the fourth magnitude, but it gradually became larger. 
 When it attained the size of a star of the second magnitude, the edge of 
 the sun emerged from behind the moon, and it then ceased to be visible. 
 He remarks that it appeared so near the dge of the moon as to leave no 
 doubt of its belonging to the body of the sun*. He, in fact, supposed the 
 phenomenon to arise from the sun being visible through a hole in the 
 body of the moon. There can be no doubt, however, when we take into 
 consideration the contiguity of the luminous point to the edge of the 
 lunar disk, as well as its deep red colour and its gradual increase of 
 apparent magnitude, that it was exactly of the same nature with those 
 luminous points that were seen at several places during the total eclipse 
 of 1842. 
 
 With respect to the total eclipse of 1806, Ferrer remarks that, a few 
 seconds before the emersion of the sun, he observed a zone to issue con- 
 centric with the sun, similar to the appearance of a cloud illuminated by 
 the solar rays f . 
 
 It has been mentioned that, during the total eclipse of 1842, there was 
 seen at Toulon a band of red light around a portion of the moon's limb. 
 The following observations of the same eclipse afford evidence of a 
 similar phenomenon. 
 
 * Signer Santini states, that while engaged in watching the last fragment 
 of the solar light, in order to determine the instant of total immersion, 
 there appeared on the right as well as on the left several luminous streaks 
 separated by obscure and even absolutely dark intervals, which vanished a 
 little before the immersion of the last point of the solar disk J. 
 
 Signer Conti mentions in his account of the eclipse, that, previous to 
 the emersion of the sun, there appeared a reddish arc of light on the right 
 side of the lunar disk. When it became a little brighter, he perceived 
 another vivid light separated from the former by a dark interval. The 
 phenomenon was visible only for a short time . 
 
 Sig. Pietropoli, who also observed the eclipse at Padua, states that pre- 
 vious to the total immersion, he perceived below to the right two very 
 beautiful patches of light \\. 
 
 Sig. Radman, another observer at Padua, appears to have witnessed the 
 phenomenon both before and after the total obscuration. He asserts 
 that no sooner was the sun totally obscured, than there appeared a very 
 slender streak of a reddish light, surrounding somewhat less than half the 
 circumference of the moon, disposed equally on each side of the place 
 where the last ray of the sun was extinguished. He adds, that it soon 
 vanished, but that it reappeared at the instant of the emersion of the 
 sun If. 
 
 M. Schumacher thus describes the appearance presented by the moon's 
 limb immediately previous to the termination of the totality of the eclipse. 
 " A little before the emersion of the sun, there appeared near that part 
 
 * Phil. Trans., 1779, p. 110. 
 
 + Trans. Amer. Phil. Soc., vol. vi., p. 274. The following account of this phenomenon 
 is given by Mr. Garnett, \vho assisted Ferrer in his observations. " Before the end of the 
 total eclipse, the west limb of the moon begun to be illuminated, and the light increased 
 so rapidly, that I at last mistook it for the sun's egress, and called the time to Mr. Ferrer ; 
 but he saw the error, and still kept his eye to the glass, when the first solar ray nearly 
 blinded him. " Tilloctis Journal of Natural Philosophy, vol. xix. , p. 322. 
 
 | Giorn. dell' 1st. del Lomb., torn, iv., p. 379. Ibid., p. 380. 
 
 || Ibid., p. 303. f Ibid., p. 384. 
 
HISTOKY OF PHYSICAL ASTBONOMY. 397 
 
 of the lunar disk from behind which the first ray of light was about to 
 issue, a narrow streak of rose-coloured red light, which extended, perhaps, 
 over an arc of 70 or 80 along the moon's limb, and which disappeared 
 with the luminous ring and the rose-coloured mountains as soon as the 
 first ray of the sun darted forth *. 
 
 M. Otto Struve was under the impression that, immediately before the 
 disappearance of the sun, he perceived a red streak of light along the 
 moon's limb, about 45 from the point where the total immersion took 
 place f. 
 
 The radial appearance noticed during the total eclipse of 1842, imme- 
 diately before and after the complete obscuration, is also a phenomenon 
 which obviously indicates the existence of a solar atmosphere. Thus, in 
 the description of the eclipse ascribed to Mrs. Airy, it is affirmed, that with 
 respect to the place where the sun had gone in, and that where he was 
 about to emerge, the light came out successively like little learns from the 
 moon's edge *. Moreover, it is stated that the light of the ring did not 
 present any remarkable change until the little flame-coloured beams shot 
 out for a few seconds before the reappearance. This emanation of red rays 
 in a direction perpendicular to the moon's limb, can only be accounted for 
 by supposing the rays of the sun to be obstructed in their progress out- 
 wards, by a dense atmosphere enveloping the solar surface and exercising 
 an influence on the primitive rays of the spectrum similar to that pro- 
 duced by the terrestrial atmosphere. 
 
 The accounts respecting annular eclipses are not wanting in allusions 
 to phenomena indicative of a solar atmosphere, analogous to those which 
 have been already noticed. A brief review of those which more especially 
 bear on the subject, cannot fail to prove interesting to the reader. 
 
 Maclaurin, in his account of the annular eclipse of 1737, states that a 
 little before the formation of the ring, a remarkable point or speck of 
 pale light appeared near the middle of the part of the moon's limb that 
 was not yet come upon the disk of the sun, and that a gleam of light more 
 faint than this light seemed to be extended from it to each horn. This 
 phenomenon was seen about fifteen seconds previous to the projection of 
 the whole body of the moon upon the solar disk . 
 
 Maclaurin also states that Lord Aberdour, who observed the same 
 eclipse, remarked that a narrow streak of a dusky red light coloured the 
 dark edge of the moon, immediately before the ring was completed, and 
 after it was dissolved ||. 
 
 Van Swinden, in his account of the annular eclipse of September 7, 
 1820, as observed by him at Amsterdam, states that just before the 
 annulus was formed, he perceived above the yet immersed limb of the 
 sun, a very small arch of light, which was no part of the solar disk. He 
 also adds that the space between it and the moon's dark limb was not 
 illuminated. It might have been compared, as to colour and appearance, 
 with the end of the flame of an argand lamp projecting beyond the 
 chimney or glass tube IT. 
 
 * Annuaire, 1846, p. 437. f Ibid., p. 437. 
 
 \ Mem. Ast. Soc., vol. xv., p. 16. 
 
 Phil. Trans., 1737, p. 181. || Ibid., p. 182. 
 
 ^ Mem. Ast. Soc. vol. 5., p. 145. Van Swinden mentions, in the account of his 
 observations, that during the annular eclipse of 1764, a similar arc of faint light was seen 
 around the moon's limb at Toulouse, by M. Darquier. 
 
398 HISTORY OP PHYSICAL ASTRONOMY. 
 
 The late Mr. Henderson, who observed the annular eclipse of May 15, 
 1836, at Edinburgh, states, in an account of his observations of the 
 phenomenon, that, previous to the formation of the annulus, when the 
 cusps were about 30 or 40 from each, other, an arc of faint reddish 
 light was seen extending between them. This appearance lasted several 
 seconds *. 
 
 The observations made in the United States of America during the 
 annular eclipse of February 10, 1838, furnish additional illustrations of 
 the same phenomenon. Prof. Henry, who observed the eclipse at 
 Princeton College, New Jersey, states that about two minutes before the 
 formation of the ring, he perceived an arch of faint light between the 
 cusps, and shortly afterwards a brush of greater intensity, projecting from 
 near the lower cusps f. A similar appearance was witnessed by Prof. 
 Johnson, who observed the eclipse at Philadelphia. About a minute 
 before the formation of the ring, he perceived an arch of faint light 
 beyond the cusps, with a speck or brush in the centre extending outwards 
 to a distance of two degrees. At the instant of the formation of the 
 annulus, the arch of light had much increased in brightness. The 
 brush which was originally in the centre, now extended from cusp to cusp, 
 radiating outwards to the extent of nearly three digits J. 
 
 Two observations at least, tending to illustrate the subject under con- 
 sideration, were made during the annular eclipse of October 9, 1847. 
 Dr. Forster, who witnessed the eclipse at Bruges, has stated in an account 
 of his observations that there was visible a very remarkable luminous arc or 
 ridge of light, differently coloured from the rest of the sun, extending along 
 and immediately on the limb of the moon between the cusps. The appear- 
 ance lasted nearly five minutes . Captain Jacob, who observed the eclipse 
 at Bombay, states, that shortly before the annular phase, a faint ray or 
 brush of light was seen issuing from, the sun's northern cusp, which soon 
 after extended in both directions as a tangent to the suns limb ||. 
 
 It might be expected, that the arcs and specks of light observed around 
 the moon's dark limb during the total and annular eclipses of the sun, 
 might be also occasionally seen during partial eclipses of considerable 
 magnitude. The following are a few instances in which phenomena of 
 this nature appear to have been visible. 
 
 It has been already mentioned that an eclipse of the sun happened in 
 the year 1605, which was total at Naples. Kepler states that at Antwerp, 
 where the upper limb of the sun projected about a digit beyond the 
 moon's limb, the circumference of the lower limb of the moon was ren- 
 dered visible by means of a ruddy light bordering it 11. 
 
 On the 22nd of June, 1666, there occurred a partial eclipse of the sun 
 which was visible at London. In an account of the phenomenon as observed 
 by Hooke and several other individuals, it is stated that " about the middle 
 between the perpendicular and westward horizontal radius of the sun, 
 viewing it through Bayle's 60-feet telescope, there was seen a little of the 
 limb of the moon without the disk of the sun, which seemed to some of 
 
 * Mem. Ast. Soc., vol. x., p. 37. 
 
 f Silliraan's Journal, vol. xxxviii., p. 166. J Ibid., vol. xxxviii., p. 159. 
 
 This statement is contained in a letter to Prof. Powell (Brit. Ass. Rep., 1848; 
 Transactions of the Sections, p. 4). 
 || Monthly Proc. Ast. Soc., vol. viii., p. 27. f De Stella Nova, p. 116. 
 
HISTORY OF PHYSICAL ASTRONOMY. 399 
 
 the observers to come from some shining atmosphere about the body 
 either of the sun or moon." * 
 
 The eclipse of September 24, 1699, which was total in some parts of 
 the north of Europe was very considerable at Leipsic, where 11 -20 digits 
 of the solar diameter was immersed. In an account of the eclipse, as it 
 appeared at that city, it is asserted that when the cusps of the moon were 
 almost parallel to the horizon, the extremity of the moon looking down- 
 wards was somewhat enlightened, and of a kind of saffron colour f. 
 
 The solar eclipse of July 14, 1748, although seen annular in various 
 parts of Scotland, failed in a small degree from being so at Aberdour 
 Castle, where it was observed by Lord Mortoun the proprietor, Lemonnier 
 the French astronomer, and Short the famous optician. In his account 
 of the eclipse, Short states that when the interval between the moon's 
 cusps did not exceed one-seventh of the moon's circumference, a brown 
 light was plainly perceived both by Lord Morton and himself, to extend 
 from each cusp about one-third of the whole distance between them. He 
 adds also, that he perceived at the extremity of this brown light, which 
 came from the western cusp, a larger quantity of light than usual J. 
 
 The following is an account of the appearance presented by the partial 
 eclipse of February 12, 1831, at Burlington, New Jersey, United States, 
 where it was observed by Mr. Gummere : " At the time of greatest ob- 
 scuration," says that individual, " the cusps were very sharp and well 
 defined, but a thread of light extended from each along the circumference 
 of the suns disk. About a minute after a spot of light was observed a 
 few degrees from the south-western cusp, extending inwards from the 
 thread which proceeded from that cusp." 
 
 Bessel thus describes the appearance presented during the solar eclipse 
 of May 15, 1836, which failed in a small degree to be annular at 
 Konigsberg, where that astronomer observed it ; although in reality it 
 was of the annular species : " About twenty-live seconds before the 
 nearest approach of the centres of the two bodies, I perceived near the 
 extremity of the superior cusp a luminous point, which, without having 
 the brightness of the sun, was very distinctly visible with the powerful 
 heliometer. As the cusps were then approaching each other, I hoped 
 that the annulus was about to form, but this did not happen. With 
 respect to the point which I have just alluded to, it became more luminous 
 Other similar points appeared which soon united together, and rendered 
 visible all the portions of the moon's limb, included between the extremi- 
 ties of the cusps. "|| 
 
 Captain Smyth, who observed the same eclipse at Bedford, where it was 
 also partial, has given the following description of a similar phenomenon : 
 " A little before the greatest obscuration, the sun having then an altitude 
 of about 40, the southern cusp was considerably the brightest, and I then 
 distinctly perceived a small portion of the lunar limb outside the solar 
 orb. As the moon passed over, her following limb was brightened by a 
 fine line of light." ^l 
 
 The eclipse of February 10, 1838, although seen annular in several 
 parts of the United States, slightly failed to appear so at New York. An 
 
 * Phil. Trans., 1666, p. 295. f Ibid., 1700, p. 622. J Ibid., 1748, p. 586. 
 
 Trans. Amer. Phil. Soc., New Series, vol. iv., p. 128. 
 
 II Mem. Ast. Soc., vol. x., p. 32. 
 
 J Smyth's Cycle of Celestial Objects, vol. i., p. 142. 
 
400 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 intelligent observer of the eclipse at that city alludes in a note contain- 
 ing suggestions relative to the total eclipse of 1 842 to a phenomenon 
 which he says may indeed have been observed at other times and recorded, 
 although he has no knowledge that ithasJbeen. On that occasion he noticed 
 several minutes before the time of the nearest completion of the ring, the 
 fine cusps of the sun's unobscured crescent prolonged by a hair breadth 
 line of brightness, totally diverse in colour and intensity from the sun's disk. 
 As the cusps approached, the line or thread of light in advance of each 
 shot round the moon's edge, between them rapidly, till, at a certain time, 
 the threads from the two, met and joined in one thus uniting the 
 cusps *. 
 
 The foregoing observations relative to the appearances noticed during 
 annular and partial eclipses of the sun, present a satisfactory agreement 
 with those made during total eclipses, in so far as they indicate the 
 existence of a solar atmosphere. With respect to the luminous arc seen 
 around the moon's dark limb, it would appear in some cases to indicate 
 the ruddy streak of light which is usually perceived during total eclipses 
 of the sun a few seconds before and after the complete obscuration ; but 
 in general the phenomenon in all probability represents a fragment of 
 the luminous ring, rendered visible in consequence of the atmospheric 
 light diffused around it being enfeebled by the partial obscuration of the 
 solar disk. The specks or points of light observed on so many occasions 
 are manifestly analogous to those seen at Toulon and elsewhere during the 
 total eclipse of July 8, 1842. The brush of light observed during the 
 annular eclipse of 1838 is very instructive. Its direct emanation outwards 
 from & faint speck of light situate in the luminous arc, shows that it was 
 not the consequence of any irregular scintillation, but rather that it was 
 occasioned by some extraneous cause acting constantly in a determinate 
 direction, and totally independent of the brightness of the source from 
 which it seemed to issue. In fact, it can only be explained by supposing 
 the luminous speck to be a collection of nebulous matter, through which 
 the rays of the sun had partially penetrated, so as to illuminate the par- 
 ticles of the solar atmosphere situated beyond in the line of their 
 transmission. 
 
 According to the usual theory of the physical constitution of the sun, 
 that body consists of an opaque nucleus, surrounded by an atmosphere in 
 which are suspended at different elevations two enveloping substances of 
 dissimilar physical properties, the lower envelope being imperfectly 
 luminous, but capable in a high degree of reflecting light, while, on the 
 other hand, the upper envelope forms a resplendent canopy of clouds, 
 which are luminous in themselves, and constitute the source of the light 
 diffused in every direction by the sun. The observations of solar eclipses 
 would seem to indicate, that above the luminiferous envelope there exists 
 a stratum of nebulous matter, which is visible only by means of reflected 
 light. Various interesting questions present themselves for solution in 
 connexion with the admitted existence of such a stratum. In the first 
 place, does this third envelope exercise an influence in the production of 
 any of the other phenomena which have been disclosed by observations on 
 the physical constitution of the sun? M. Arago has very ingeniously 
 suggested that the solar spots which exhibit the aspect of a penumbra 
 without a nucleus, may arise from the superposition of masses of this 
 
 * Silliman's Journal, vol. xlii. , p. 396. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 401 
 
 nebulous matter above the luminiferous envelope. Secondly, the ques- 
 tion arises, does any relation subsist between this non-luminous substance, 
 which floats in the upper regions of the solar atmosphere, and either of 
 the other two envelopes ? Sir John Herschel, in his ingenious theory of 
 the physical origin of the solar spots, supposes a perpetual circulation to 
 be kept up in the solar atmosphere, analogous to that which in the case 
 of the terrestrial atmosphere produces the phenomenon of the trade winds. 
 Now, is it not reasonable enough to suppose that such a circulation will have 
 the effect of continually agitating the non-luminous matter constituting the 
 envelope nearest the solid nucleus of the sun, and throwing up masses of 
 it above the luminiferous surface ? This view of the subject, while it carries 
 with it considerable probability, obviates the necessity of introducing into 
 the theory of the physical constitution of the sun, the idea of a third 
 envelope independent of the two others. Future observation, prosecuted 
 more especially with reference to the position of the solar spots during 
 the occurrence of eclipses of the sun, can alone be expected to throw any 
 light upon this interesting question. 
 
 Although the physical connexion of the solar spots with the nebulous 
 matter which appears to exist above the luminous surface of the sun, is a 
 point which remains to be established definitively by future enquiry, there 
 is some reason to suppose from the observations of Sig. Santini on the 
 occasion of the total eclipse of July 8, 1842, that such a connexion really 
 subsists. 
 
 In his account of the eclipse, that excellent astronomer states, that a 
 few days previous to its occurrence, he observed a very extensive chain of 
 spots on the sun, five of which appeared near the western margin of his 
 disk. He adds that, although he unfortunately omitted to determine 
 their precise position, he felt assured that at the time of the eclipse, they 
 could not have been very far removed from the singular columns of smoke 
 which appeared during the total obscuration *. 
 
 The aspect presented by the moon during eclipses of the sun, has led 
 to some curious speculations. Kepler has stated in one of his works, that 
 during the obscuration consequent upon a total eclipse of the sun, the 
 moon's surface is occasionally distinguishable by a ruddy light \. A similar 
 appearance has been noticed in modern times during the occurrence of 
 annular eclipses. Thus Mr. Baily, in his account of the annular eclipse 
 of 1836, states, that " previous to the formation of the ring, the face of the 
 moon was perfectly black; but on looking at it through the telescope, 
 during the annulus, the circumference was tinged with a reddish purple 
 colour, which extended over the whole disk, but increased in density of 
 colour according to the proximity to the centre, so as to be in that part 
 nearly black. "J 
 
 * Giorn. dell' 1st del Lomb., torn, iv., p. 378. It has been already mentioned that the 
 luminous protuberances seemed to Sig. Santini to resemble irregular columns of smoke, 
 undulating upon broad bases. " Come irregulari colonne de fuoco ondeggiante a larga 
 base." 
 
 + Epitome Astronomise, p. 895. 
 
 Mem. Ast. Soc., vol. x., p. 17. Mr. Baily states that at the same time the globular 
 form of the moon was very perceptible ; he adds that Mr. Veitch (the gentleman at whose 
 residence he observed the eclipse) also noticed the phenomenon, and that both agreed in 
 the impression that the moon had the aspect of a globe of purple velvet. It is a remark- 
 able fact, that an appearance exactly resembling that described by Mr. Baily was witnessed 
 during the total eclipse of 1733; thus M. Tissel states, that at Skepshat in Sweden, "the 
 moon's surface was brighter at the margin near the luminous ring ; towards the middle it 
 
 D D 
 
402 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Kepler ascribes the visibility of the moon's surface during her conjunc- 
 tion with the sun, to the light transmitted by reflexion from the earth, or 
 the earth-shine, as it would be termed by the inhabitants of the moon*. 
 This is doubtless the true explanation of the phenomenon. 
 
 The illustrious philosopher, just cited, while alluding to the visibility of 
 the moon by a faint light during conjunction, does not affirm that the 
 irregularities of her surface have been discerned on any such occasion. 
 The first person who makes mention of this fact is Bigerus Vassenius the 
 Swedish astronomer, to whose interesting observations of the total eclipse 
 of 1733, allusion has already been made. In the account of that eclipse 
 which he transmitted to the Royal Society, he asserts that with a telescope 
 of 21 feet focal length, he perceived several of the principal spots on the 
 moon during the total obscuration f. Ferrer also states, that during the 
 total eclipse of 1806, the irregularities of the moon's surface were plainly 
 discernible J. 
 
 The foregoing are the only two instances in which it appears that the 
 irregularities of the moon's surface have been perceived during a central 
 eclipse of the sun, whether total or annular. M. Arago, and several other 
 observers, carefully sought to effect the same object during the total 
 eclipse of 1842, but all their efforts proved fruitless. The fact of the 
 lineaments of the lunar disk being discernible in some cases and not in 
 others, is obviously attributable to no other cause than the variable con- 
 dition of the atmosphere . 
 
 A singular appearance was noticed at Washington, U.S., during the 
 progress of the partial eclipse of February 12, 1831. Mr. F. R. Hassler 
 states, in an account of that eclipse, that " the most remarkable phe- 
 nomenon was the distinctly painted inequalities of the moon, by the 
 reflected light and shade upon its disk, presenting apparently elevations 
 brilliantly illuminated, and intervals shaded in an ash-coloured shade, 
 more or less dark and distinct as they were nearer to or farther from the 
 sun, the edge of the moon towards the sun being always fully dark." He 
 asserts moreover that the appearance, beginning when about one-eighth of 
 the diameter of the sun was immersed, extended itself, with more or less 
 variation, to about one-third of the moon's diameter, when it gradually 
 faded into indistinctness, and the whole of the moon's surface appeared 
 equally dark ; the same phenomenon was witnessed in an inverted order 
 towards the end of the eclipse ||. 
 
 The singular phenomenon alluded to appears to be totally inexplicable 
 
 became black; and at the centre seemed to protuberate. " Ada Lit. et Scien. Suec., torn, 
 iv., p. 59. Sig. Piola also mentions that on the occasion of the total eclipse of 1842, as 
 the moon advanced upon the solar disk, she seemed to all the spectators who were present 
 with him to protuberate at the centre, and to be compressed at the sides. He adds that 
 a similar appearance was noticed at Belluno. (Giorn. dell 1st. del Lomb., torn, iv., p. 303.) 
 
 * Epitome Astronomic, p. 895. f Phil. Trans., 1733, p. 135. 
 
 J Trans. Amer. Phil. Soc., vol. vi., p. 267. 
 
 The following remark by Sig. Magrini relative to the appearance presented by the 
 moon during the total eclipse of 1842, has some resemblance to the description contained 
 in the text. " The light of the moon, termed ashy, seemed to be brighter towards the 
 disk of the sun both before the immersion and after the emersion." (Annuaire, 1846, p. 
 375, cited from the Gazetta Privileygiata of Milan.) 
 
 || Trans. Amer. Phil. Soc., New Series, vol. iv., p. 131. The only explanation 
 of this phenomenon that appears to possess any degree of plausibility is the follow- 
 ing. It has been found, that during total eclipses of the sun, the irregularities of the 
 lunar disk are sometimes discernible when the whole of the solar disk has been immersed. 
 Let us suppose, that during the eclipse of 1831 the condition of the atmosphere was 
 
HISTOEY OF PHYSICAL ASTKONOMY. 403 
 
 by any known physical principles. That it is connected in some way with 
 the magnitude and relative position of the segment of the sun which has 
 not undergone immersion, would seem obviously to follow from its mode 
 of variation ; but it is difficult to assign any cause why the moon's surface 
 should appear more distinct on the side on which the sun is visible, than 
 on the opposite side. 
 
 A phenomenon of a somewhat similar nature, but one admitting of a 
 satisfactory explanation, was noticed by M. Arago during the total eclipse 
 of 1842. Forty minutes after the commencement of the eclipse, while a 
 considerable portion of the sun was still visible, he observed the dark con- 
 tour of the moon projected upon the bright sky; it corresponded exactly 
 with the portion of the limb that appeared upon the sun ; he remarked 
 also, that it was brighter at the parts where it met the solar disk*. 
 He ascribes the phenomenon to the projection of the moon upon the solar 
 atmosphere, the brightness of which, by an effect of contrast, rendered 
 the outline of the moon's dark limb discernible. This explanation ac- 
 counted for the fact of the limb being brighter towards the sun, since it 
 appeared from all the observations of total eclipses, that the luminous 
 ring exhibited the greatest concentration of light at those parts where 
 it bordered upon the solar disk. 
 
 The contour of the dark limb of the moon was also visible to M. Eugene 
 Bouvard at Digne, and to M. Flaguerges at Toulon ; but it is remarkable 
 that no other observer of the total eclipse of 1842 makes mention of a 
 similar appearance. 
 
 Halley remarked, that during the total eclipse of 1715, he observed per- 
 petual flashes, or coruscations of light, which seemed for a moment to dart 
 out from behind the moon, now here and now there, on all sides, but 
 more especially on the western side a little before the emersion f . Louville 
 alludes to a similar phenomenon in his account of the same eclipse; he 
 states, that during the time of the total obscuration, it seemed as if there 
 had been a succession of trains of gunpowder constantly exploding on the 
 
 so favourable for observation, that if the whole of the solar disk had undergone immer- 
 sion, the dark and bright parts of the moon's surface would have been as plainly dis- 
 tinguishable as Ferrer states they were on the occasion of the total eclipse of 1806. 
 According to M. Arago, the light by which the bright parts are visible in such a case, 
 must exceed the light of the more obscure parts, by at least a sixtieth part. Now, 
 at the commencement of the eclipse, the moon's surface is illuminated unequally by the 
 lumiere cendree, or ashy light, and equally by the atmospheric light diffused by the full 
 sun; and the former of these lights (or rather the excess of the light emitted by the 
 bright parts over the light of the more obscure parts) bears so small a proportion to the 
 latter, that the whole of the moon's surface is almost equally illuminated, and the various 
 irregularities by which it is diversified will be completely effaced. As the eclipse, how- 
 ever, increases in magnitude, the light diffused by the visible segment of the solar disk 
 diminishes at an equal rate, and in consequence, the light of the lumiere cendree con- 
 tinually bears an increasing ratio to the atmospheric light. At length, the latter is so 
 much enfeebled, that the excess of the light of the bright parts of the lunar disk over the 
 light of the more obscure parts, arising from the lumiere cendree, amounts to the sixtieth 
 part of the atmospheric light, whereupon, according to the above remark, the irregularities 
 of the lunar disk will become distinguishable. The American observer states, that the 
 moon's surface became distinctly visible as soon as one-eighth of the solar diameter was 
 immersed. It is difficult to conceive that at so early a stage of the eclipse the atmospheric 
 light would be so much enfeebled, that the lumiere cendree would form a sensible frac- 
 tion of it. Admitting, however, that the phenomenon was due to such a cause, it 
 follows that the lunar surface will appear more illuminated towards the sun, on account 
 of the greater intensity of the atmospheric light, except at the part bordering on the solar 
 segment, where it ivill naturally appear dark from the effect of contrast. 
 * Annuaire, 1846, p. 372. f Phil. Trans., 1715, p. 249. 
 
 D D % 
 
404 HISTORY OF PHYSICAL ASTKONOMY. 
 
 moon's surface. He remarks that the fulminations had a serpentine 
 appearance, causing them to resemble flashes of lightning*. 
 
 Weidler, in an account of the partial eclipse of August 4, 1739, as 
 observed by him at Wurtemberg, makes-mention of a similar phenomenon. 
 He states that a friend of his, well skilled in astronomical observations, 
 having viewed the moon towards the commencement of the eclipse with 
 a telescope 9 feet long, noticed bright lights like flashes of lightning in- 
 terspersed here and there upon her dark surface ; and that after the lapse 
 of one hour and nineteen minutes he again saw the same appearance f. 
 
 Attempts were made during the total eclipse of 1842 to verify the fore- 
 going observations, but it was only at Venice that any analogous corus- 
 cations of light were discerned. Sig. Zantedeschi, who observed the 
 eclipse at that city, states, that from time to time there were visible upon 
 the moon's surface faint illuminations of an intermittent character, re- 
 sembling flashes of phosphoric light, intermingled with black streaks 
 A similar appearance was noticed by M. Wullerstorf j. 
 
 The phenomena above referred to have been explained in various ways 
 by different enquirers. Louville attributed them to the prevalence of 
 electric storms in the lunar atmosphere ; other persons suppose them to 
 have been produced by volcanic energy. M. Arago is of opinion that 
 they may have arisen from the occasional passage of aerolites across the 
 field of view of the telescope. In support of this view of their origin, he 
 cites one or two instances in which, during the total eclipse of 1842, there 
 were seen meteoric lights traversing the regions of the heavens in which 
 the sun and moon were then situate. From the circumstance of the 
 phenomena having been visible only on two or three occasions, it is clearly 
 impossible to arrive at any trustworthy conclusions on the subject. 
 
 At various places in France, a singular undulation of the solar light was 
 remarked on the occasion of the total eclipse of 1842. In a letter to M. 
 Arago, dated July 9, 1842, M. Fauvelle gives the following account of the 
 phenomenon as witnessed by him at Perpignan : " At the moment when 
 the eclipse was about to become total, I perceived the last rays of the sun 
 undulate with great intensity and rapidity upon a white wall of one of the 
 military establishments of the rampart of St. Dominique. The effect 
 might be compared with that which is observed when the light of the sun 
 falls upon a wall or a ceiling after having been reflected from the surface 
 of a sheet of water in a state of agitation. The same phenomenon re- 
 appeared at the instant of the emersion of the sun ; the undulations which 
 at first were very intense gradually died away, and disappeared altogether 
 at the end of five or six seconds."! 
 
 M. Arago remarks also that during the few seconds which could be 
 devoted by his colleagues and himself to the observation of such a pheno- 
 menon, the facade of the great tower of the citadel of Perpignan appeared 
 to be illuminated by a singularly -fluctuating light. 
 
 M. Lentheric thus describes the phenomenon as observed by him at 
 Montpellier : " A little before the commencement of the total obscura- 
 tion, there were seen on the ground and on walls undulating shadows 
 composed of a succession of arcs of three or four decimetres in length, 
 but of much less breadth, which seemed to turn upon themselves. The 
 effect was analogous to that produced by those moveable shadows which 
 
 * Mem. Acad. des Sciences, 1715, p. 96. f Phil. Trans., 1739, p. 228. 
 
 \ Annuaire, 1846, p. 364. Annuaire, 1846, p. 392. 
 
HISTORY OF PHYSICAL ASTRONOMY. 405 
 
 are seen at the bottom of a shallow basin filled with clear water, when the 
 surface, slightly agitated, is illuminated by the rays of the sun." 
 
 A phenomenon similar to that mentioned in the foregoing accounts was 
 also observed at Narbonne, Alais, and several other places in France. 
 The following description of the appearance, as witnessed by M. Savournin 
 at Seyne, is somewhat different from the other statements : 
 
 " There were seen here shadows and luminous patches running after 
 each other, the effect of which was similar to that produced by the passage 
 of a succession of small clouds over the sun. These patches were not all 
 of the same colon?'. Some of them were red ; others were yellow, blue, or 
 white. The children amused themselves in running after them, and 
 trying to put their hands upon them. This extraordinary phenomenon 
 was remarked only a few instants before the complete disappearance of 
 the sun."* 
 
 It is remarkable that no observers of the total eclipse of 1842, out of 
 France, make any allusion to the singular appearances noticed in that 
 country, before and after the total obscuration. Almost equally silent 
 upon this point are the observers of former eclipses of the sun. The 
 following observations of the total eclipse of 1733, appear to have refer- 
 ence to an undulatory movement similar to that above mentioned. 
 
 Rydhenius, pastor of Forshem, states that " when the sun was about to 
 lose his light, and also when he was about to recover it, he emitted rays 
 that undulated like the aurora borealis, and were of & fiery red colour "\ 
 
 Again the pastor of Flo, in his account of the same eclipse, affirms that, 
 " towards the total obscuration stars were visible, and also a singular fluctu- 
 ation in the air. "I 
 
 It might be supposed, although it is by no means probable, that the 
 first cited of these two observations has reference to the appearance of the 
 sun when viewed directly, a little before and after the total obscuration, 
 and not to the effect which might be produced upon a surface illuminated 
 by the solar rays. With respect to the second observation, it is still less 
 improbable that it can be any other than a phenomenon of the same 
 nature as that witnessed during the total eclipse of 1842; since it is 
 difficult to believe that any agitation in the air could be recognised, 
 except by viewing its undulations as projected upon some wall or building. 
 The observation of the pastor of Forshem would also seem to have some 
 analogy to that of M. Savournin, relative to the moveable shadows of 
 different colours which appeared at Seyne during the total eclipse of 1842. 
 As, however, the curious phenomenon witnessed in the latter instance 
 does not seem to have been noticed, except at the place just cited, it 
 would be desirable to obtain a more satisfactory verification of it by 
 reference to some previous eclipse. The following statement made by 
 Delisle, while citing some observations which appeared to him to support 
 his theory of the luminous ring seen around the moon on the occasion of 
 a total eclipse of the sun, manifestly refers to a phenomenon of a similar 
 nature : 
 
 " The second observation is one which a curious individual acquaints 
 
 * Annuaire, 1846, p. 393. 
 
 f Acta Lit. et Scien. Suec., torn, iv., p. 61. The following are the express words of 
 the original: " Sol lucem penitus amissurus eanderuque recuperaturus, radios ejaculabat 
 rluctuabundos, instar aurorce borealis, et rutilos." 
 
 J Acta Lit. et Scien. Suec., torn, iv., p. 61. The words of the observer are these: 
 " Sub qua (obscuratione) stellse apparebant et singularis qusedam in sere fluctuatio." 
 
406 HISTORY OF PHYSICAL ASTRONOMY. 
 
 me with having made, by mere accident *. Having directed his atten- 
 tion to a large white wall, at the moment of the total immersion of an 
 eclipse of the sun, he saw the moon's shadow pass upon the wall, tinged 
 with different colours ."f 
 
 The three observations just cited are the only ones that have been 
 found in the records of solar eclipses, confirmatory of the phe- 
 nomenon remarked exclusively in France, during the total eclipse of 
 1843. The question naturally arises, to what physical cause are the 
 singular undulations noticed on such occasions to be ascribed? It is 
 reasonable enough to suppose that, towards the time of total obscuration, 
 the equilibrium of the atmosphere is very much disturbed by the change 
 of temperature consequent upon the rapid diminution of the visible 
 segment of the solar disk. Hence will arise a sudden intermingling of 
 strata of air of different densities, and consequently of different refractive 
 powers, which may obviously tend to produce a succession of undulatory 
 movements similar to those actually perceived. It is not improbable also 
 that the continuous obstruction of the solar light by innumerable foreign 
 substances floating in the atmosphere, and subject to incessant displace- 
 ments from the agitation of the air, may contribute towards producing 
 *the observed effect. The extreme smallness of the solar crescent cannot 
 fail to render the interposition of any such particles of matter, more 
 readily perceptible than it would otherwise be. It is to be remarked also 
 that the effects in all such cases will be magnified by diffraction. That 
 the phenomenon is to a certain extent dependent on the operation of this 
 principle, would seem to be indicated by the variety of colour which 
 distinguishes the moveable shadows. Moreover, if light be propagated by 
 means of undulations in a highly-elastic medium, it is not improbable 
 that, as the origin of light rapidly diminishes in magnitude, causes of 
 interference may arise leading to a conflict of undulatory movements, 
 whence may ultimately result phenomena analogous to those alluded to 
 in the foregoing observations. 
 
 A phenomenon which seems to be of a totally different nature from any 
 of those hitherto alluded to, has been occasionally observed during solar 
 eclipses, especially such as are of the annular species. In the latter case, 
 previous to the formation of the annulus, the western limb of the moon 
 exhibits an indented appearance, resembling a succession of beads. 
 Almost immediately the beads become elongated, assuming the aspect of 
 long, black, parallel streaks, uniting the limbs of the sun and moon. In 
 the next instant these lines give way, as if they had been snapped 
 asunder by the eastward motion of the moon, and the annulus then 
 appears completely formed. A similar phenomenon ensues in a reverse 
 order, when the eastern limb of the moon is approaching the sun's limb, 
 
 * " Par le plus grand hasard du raonde." 
 
 f Memoires pour servir a VHistoire et au Progres de I' Astronomic, p. 258, 4to., St. 
 Petersbourg, 1738. M. Arago states that having searched, page by page, the volumes of 
 the various academic collections, he found only one observation corroborative of those 
 made in France relative to the undulations which occurred on the occasion of the total 
 eclipse of 1842; but that he was unable to cite it in detail, in consequence of the loose 
 leaf, to which he had consigned the memorandum of it, having been mislaid. 
 (Annuaire, 1846, p. 399.) It is not probable that either of the two Swedish observa- 
 tions cited in the text was that which fell under his eye ; since, if he had met with the 
 one, the other could hardly have escaped him. It is evident, at any rate, that the 
 observation cited by Delisle, in a work which does not form part of any academic 
 collection, cannot be the one referred to by the illustrious philosopher. 
 
HISTORY OF PHYSICAL ASTRONOMY. 407 
 
 previous to the dissolution of the annulus. At first several dark lines 
 dart forward from the moon's limb, and unite themselves to that of the 
 sun ; then they suddenly contract so as to assume the appearance of beads, 
 and immediately afterwards the annulus is dissolved. On the occasion of 
 the annular eclipse of May 15, 1836, this phenomenon was especially 
 observed in Scotland by Mr. Baily, who has given a lively description of 
 it in a paper on the eclipse which appears in the tenth volume of the 
 Memoirs of the Astronomical Society. It may not be uninteresting, 
 however, to show that an appearance more or less analogous to it has been 
 witnessed on several previous occasions, both of total and annular eclipses. 
 
 Halley mentions, in his account of the total eclipse of 1715, that about 
 two minutes before the total immersion the sun was reduced to a very 
 slender crescent of light, the extremities of which seemed to lose their 
 acuteness and to become round like stars *. 
 
 During the total eclipse of 1724, Delisle remarked that the part of the 
 moon's limb, where the total immersion was about to take place, appeared 
 to him irregular and indented f. 
 
 But, as has been already mentioned, it is during annular eclipses of the 
 sun, that the phenomenon witnessed by Mr. Baily is more especially 
 conspicuous. 
 
 In his account of the annular eclipse of 1737, Maclaurin cites a letter 
 addressed by Professor Bayne to Lord Aberdour, containing the following 
 statement : " What appeared to me most entertaining, considered as an 
 object of sight, was when the extremities of the horns, formed upon the 
 face of the sun, seemed as if they had been in the action of uniting their 
 points; the inequalities on the extremity of the moon's disk gave the 
 appearance as it were of small bodies in particular motion |. 
 
 In Short's paper on the annular eclipse of 1748, which has been already 
 referred to, there appears a statement from the Rev. Mr. Irvine, who 
 observed the eclipse at Elgin, in which he asserts that, previous to the 
 joining of the cusps of the sun, as also at the breaking up of the annulus, he 
 perceived a quick tremulous motion and several irregular bright spots between 
 the cusps, which disappeared in a few moments. He adds that both the 
 formation and breaking (of the annulus) were very sensibly to be observed 
 and parted in a moment ; affording a very pleasant sight, by the irregular 
 tremulous spots of the sun . 
 
 The following description of the phenomenon as witnessed in America 
 by Mr. S. Webber, during the annular eclipse of April 3, 1791, is more 
 precise than any that has been hitherto cited : " At both the internal 
 contacts there was a curious and striking appearance of what may be 
 called drops, on account of their resemblance to drops of a fluid. At the 
 first contact, when the horns of the sun were forming a ring about the 
 moon, these luminous drops suddenly appeared, at several different points, 
 with very little difference of time. At first they were nearly circular ; 
 but they rapidly extended themselves along the limb of the sun, till, 
 uniting, they completed the annulus. At the second contact several 
 breaches in the annulus almost instantaneously succeeded the first, at 
 different distances from each other; and the oblong drops included 
 between them contracted and vanished." || 
 
 A similar phenomenon was witnessed by Nicolai at Maiiheim, during 
 
 * Phil. Trans., 1715, p. 248. f Mem. Acad. des Sciences, 1724, p. 317. 
 
 Phil. Trans., 1737, p. 182. Ibid., 1748, p. 594. 
 
 || Mem. Amer. Acad. of Arts and Sciences, vol. ii., part i., p. 20. 
 
408 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 the annular eclipse of September 7, 1820. In his account of the eclipse, 
 he states that about a second before the annulus was formed, the fine 
 curve of the moon's disk, then immediately in contact with the edge of 
 the sun, appeared broken into several parts ; and in a moment these parts 
 flowed together like drops of water or quicksilver near each other. At the 
 dissolution of the annulus, a similar appearance presented itself; for the 
 delicate thread of light then formed by the annulus, instead of being 
 broken into one place only, was in an instant divided into several places 
 at once."* 
 
 The phenomenon was also observed on the occasion of the same eclipse 
 at Bologna, by De Zach, who has given the following interesting descrip- 
 tion of it : " The most beautiful spectacle was the end of the annular 
 eclipse or the instant of the formation of the annulus. The mountains 
 of the moon appeared very distinct. Her limb seemed to be indented, 
 and when it was upon the point of touching the sun's limb, it appeared like a 
 comb or a saw biting the edge of the solar disk. Before the contact of the 
 two limbs was effected, there was visible, not a continuous thread of light, 
 but a number of luminous points, resembling a row of so many pearl 
 beads, separated by dark intervals. This beautiful phenomenon lasted 
 only an instant ; for the contact of the limbs, and the total disappearance 
 of the last trace of light, was instantaneous."! 
 
 The same appearance was also witnessed at Amsterdam by several ob- 
 servers of the eclipse, accompanied in some instances with new features, but 
 the description given by Mr. Baily, of the phenomenon as it presented itself 
 to him on the occasion of the annular eclipse of May 15, 1836, embodies all 
 the particulars by which it has been hitherto distinguished. He states that 
 when the cusps of the sun were about 40 asunder, a row of lucid points, 
 like a string of bright beads, irregular in size and distance from each 
 other, suddenly formed round that part of the circumference of the moon 
 that was about to enter on the sun's disk. Its formation was so rapid that 
 it presented the appearance of having been caused by the ignition of a 
 fine train of gunpowder. Mr. Baily was under the impression that this 
 phenomenon indicated the correct formation of the annulus, and he was 
 accordingly about to note the time of its occurrence. " My surprise, 
 however, was great," says he, " on finding that these luminous points, as 
 well as the dark intervening spaces, increased in magnitude, some of the 
 contiguous ones appearing to run into each other, like drops of water; for 
 the rapidity of the change was so great, and the singularity of the appear- 
 ance so fascinating and attractive, that the mind was for the moment 
 distracted and lost in the contemplation of the scene, so as to be unable to 
 attend to every minute occurrence. Finally, as the moon pursued her 
 course, these dark intervening spaces (which at their origin had the 
 appearance of lunar mountains in high relief, and which still continued 
 attached to the sun's border) were stretched out into long, black, thick, 
 parallel lines, joining the limbs of the sun and moon ; when all at once 
 they suddenly gave way, and left the circumference of the sun and moon 
 in those points, as in the rest, comparatively smooth and circular; and the 
 moon perceptibly advanced on the face of the sun." In fact the phe- 
 nomenon could not be more accurately imagined than by supposing, for 
 
 * Mem. Ast. Soc., vol. i., p. 142. 
 
 f Correspondance Astronomique, vol. iv., p. 171 j Smyth's "Cycle of Celestia 
 Objects," vol. i., Appendix. 
 
HISTORY OF PHYSICAL ASTRONOMY. 409 
 
 the moment, that the edge of the moon was formed of some dark, 
 glutinous substance, which by its tenacity adhered to certain points of 
 the sun's limb, and by the motion of the moon was thus drawn out into 
 long threads, which suddenly broke and wholly disappeared *. 
 
 Mr. Baily remarks that the scene so riveted his attention, that he could 
 not take his eye away from the telescope to note down anything during 
 the progress of the phenomenon. He estimated, however, that the whole 
 took up six or eight seconds or ten at the utmost. The same phenomenon 
 occurred in a reverse order at the dissolution of the annulus. While the 
 limb of the moon was yet at some distance from the edge of the sun, a 
 number of long, black, thick, parallel lines suddenly darted forward from 
 the moon, and joined the two limbs as before. As these dark lines got 
 shorter, the intervening bright parts assumed a more circular and irregular 
 shape, and at length terminated in a fine curve line of bright beads, as at 
 the commencement, till they ultimately vanished, and the annulus ceased 
 to exist. 
 
 Mr. Baily also states that, although the parallel dark lines ought not to 
 have exhibited any perceptible difference of length, the outer lines imme- 
 diately before their rupture seemed to be nearly double the length of 
 those in the middle. This circumstance manifestly indicated a pro- 
 tuberance on the moon's limb at the point where it had just entered upon 
 the sun's disk. A similar phenomenon had been noticed on the occasions 
 of the transit of Venus across the sun's disk in the last century. 
 
 The phenomenon of which Mr. Baily gave so vivid a description 
 excited great interest among astronomers, and future opportunities of 
 verifying it were anxiously looked forward to. The annular eclipse of 
 Feb. 18, 1838, which was visible in the United States of North America, 
 was peculiarly favourable for this purpose. On this occasion, however, 
 the phenomenon was only partially observed. In several instances, the 
 beads witnessed during previous annular eclipses at the instants of the 
 formation and rupture of the annulus, were plainly visible, but no trace of 
 the long black threads alluded to by Mr. Baily could be discerned by any 
 observer. Moreover, it was found that even the beads were not per- 
 ceptible in every case, their visibility seeming to be dependent on the 
 colour of the screen glass employed in observing the sun. With a red 
 glass the phenomenon was generally perceived ; but, when a green glass 
 was used, only a faint trace of it could be obtained, and in many cases it 
 was altogether invisible. Thus Prof. Henry, who observed the eclipse 
 at Princeton College, New Jersey, with a 3^ feet achromatic telescope, 
 and a red screen glass, states that " an appearance similar to a row of 
 beads was regarded as the formation of the ring." He adds that the 
 drops endured only for a second or twof. On the other hand, Mr. R. T. 
 Paine, who observed the eclipse at Washington with a telescope having a 
 green glass applied to it, was unable to discern the slightest vestige of the 
 phenomenon. "The ring," he remarks, "formed instantaneously, and 
 broke nearly so. No beads were seen, nor the dark lines mentioned by 
 Mr. Baily, nor the light round the moon, although all were looked for. 
 No distortion of the moon's limb could be seen, and the cusps of the sun, 
 before the ring formed, were as sharp as needles."! 
 
 It was expected that the observations of the total eclipse of July 8, 
 
 * Mem. Ast. Soc., vol. x., p. 7. 
 j- Silliman's Journ., vol. xxxviii., p. 167. f Ibid., vol. xxxviii., p. 164. 
 
410 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 1842, would serve to throw some light upon this interesting phenomenon. 
 On this occasion, however, astronomers were disappointed. In some 
 instances a faint resemblance to beads of light was seen previous to the 
 total immersion, but, generally speaking, the phenomenon was totally 
 invisible. Even Mr. Baily, whose principal motive for proceeding to Italy 
 was to verify, by means of this eclipse, his previous observations, was 
 unable to discern any trace of the phenomenon. 
 
 The observations of the annular eclipse of October 9, 1847, afforded a 
 partial verification of the phenomenon witnessed by Mr. Baily in 1836. 
 Captain Jacob, who observed the eclipse at Bombay, states, that when the 
 annulus was about being formed, the moon's limb seemed to be united with 
 that of the sun by a dark ligament about 1' in breadth, which became more 
 elongated as the moon advanced upon the sun. The moon's limb was 
 perfectly well denned, except at the part where the ligament was perceived. 
 This phenomenon lasted about three or four seconds, when the ligament 
 at length suddenly gave way, and the annulus was seen complete. The 
 phenomenon exhibited at the dissolution of the annulus was somewhat 
 different. When the moon's limb approached very close to that of the 
 sun, a portion of it, about 30 in extent, suddenly flowed over in dark lines, 
 leaving bright spaces between. This appearance lasted only about two 
 seconds *. 
 
 The same eclipse was observed at several stations in Europe, but no de- 
 cisive indication of the beads or dark lines which exhibited so striking an ap- 
 pearance during the annular eclipse of 1836, was obtained in any instance. 
 
 The question relative to the physical cause of the phenomena above 
 mentioned has naturally excited considerable speculation, but it cannot 
 be said that any definitive conclusion has yet been arrived at upon this 
 head. That they are mainly illusions of an optical nature is generally 
 admitted by all enquirers, but the modus operandi seems to be involved 
 in much obscurity. The most probable hypothesis of their origin is that 
 which refers them to the influence of irradiation. The enlargement of 
 the apparent magnitudes of the celestial bodies, arising from this cause, 
 has been already alluded to. The observations of solar eclipses tend es- 
 pecially to corroborate the truth of this remark. It has been already 
 mentioned that Kepler adduced the appearance presented during the solar 
 eclipse of 1590, as affording an obvious proof of the influence of irradiation. 
 The extraordinary agility with which, according to Wyberd, the moon 
 threw herself upon the solar disk on the occasion of the total eclipse of 
 March 29, 1652, can only be accounted for by supposing that the sun was 
 fringed with a border of spurious light which disappeared all at once as 
 soon as the last portion of his limb was immersed. In his account of the 
 annular eclipse of Feb. 18, 1737, Maclaurin states that the breadth of the 
 aunulus appeared much greater to the naked eye than could have been 
 expected from the difference of the semi-diameters of the sun and moon. 
 "This appearance," he remarks, "proceeded chiefly, I suppose, from the 
 light encroaching on the shade, as is usual ; but whatever was the cause, 
 everybody seemed surprised that the moon appeared so small upon the 
 disk of the sun."| 
 
 The enlargement produced by irradiation is also indicated by a remark 
 of Mr. Fullarton, who, in a description of the same eclipse as it appeared 
 at Crosby, near Ayr, states that the annulus was of a uniform breadth, 
 
 * Monthly Proc. Ast. Soc., vol. viii., p. 27. f Phil. Trans. 1737, p. 183. 
 
HISTORY OF PHYSICAL ASTRONOMY. 411 
 
 during the greater part of the time of its continuance, but seemed to go off 
 very suddenly; so that when the disk of the moon approached the concave 
 line of the sun's disk, they seemed to run together like two contiguous 
 drops of water on a table, when they touch one another."* A similar 
 remark was made by the Rev. Mr. Irvine, of Elgin, relative to the annular 
 eclipse of 1748. In his account of the eclipse, as cited by Short, he states 
 that the moon's body seemed to pass quicker about the time of the annulus, 
 than at any other time during the eclipse f. 
 
 The observations of solar eclipses in more recent times have, in general, 
 afforded similar indications of an enlargement of the apparent magnitude 
 of the sun from the irradiation of his light. 
 
 The dark ligament observed by Capt. Jacob during the annular eclipse of 
 October 9, 1847, is obviously an effect of irradiation, for when the moon is 
 wholly within the solar disk, except at the point of interior contact where 
 it still projects in a very small degree over the sun's limb, the enlarge- 
 ment produced by irradiation will be wholly wanting at this point, whereas, 
 on the other hand, the rest of the limb being uncovered by the moon will 
 exhibit its usual appearance. The sudden deficiency of light arising from 
 this cause will manifestly produce an appearance resembling a dark liga- 
 ment or neck, uniting the limbs of the sun and moon at the point where 
 the contact of the two bodies is about to take place J. 
 
 Prof. Powell's explanation of the beads and threads witnessed at the 
 formation and dissolution of the annulus, is perhaps less liable to objection 
 than any other that has hitherto been proposed. It is based upon two 
 principles, the real existence of which has been established beyond doubt 
 by observation and experiment. These are, the rapid degradation of the 
 sun's light towards the margin of his disk, and the law of irradiation in 
 virtue of which the intensity of its influence increases with the brightness 
 of the luminous object. Admitting these two principles, it is easy to see 
 that a series of fissures in the moon's limb will give rise to so many patches 
 of light, which cannot fail to acquire a more elongated appearance as the 
 moon advances upon the solar disk. 
 
 It is to the inferior brightness of the sun towards the margin of his 
 disk, and the consequent diminution of the effect produced by his irradi- 
 ation, that Prof. Powell ascribes the protuberance on the moon's limb 
 towards the point of her interior contact with the sun, observed by Mr. 
 Baily during the annular eclipse of 1836, when the ring was just formed, 
 and when it was about to be dissolved. In this case it is clear that the 
 solar light, being less intense towards the point of contact than at the 
 other parts where it borders upon the moon's limb, will encroach less by 
 irradiation upon the dark body of the moon than elsewhere ; and that hence 
 will arise an apparent protuberance of the contour of the lunar disk, which 
 which will be most sensible at the point where the limbs of the sun and 
 moon are nearest to each other . 
 
 The foregoing modes of explaining the phenomena observed during annu- 
 lar eclipses are not wanting in plausibility, but they cannot be said to afford 
 a satisfactory account of all the observations. A difficulty which attends 
 these, as well as all other explanations of the same nature, consists in the 
 fact of the phenomena being visible in some cases and not in others, al- 
 though sought for with the utmost care. In some instances the absence of 
 
 * Phil. Trans., 1737, p. 183. f Phil. Trans., 1748, p. 594. 
 
 J Lalande was the first who gave this explanation of the dark ligament. 
 Monthly Proc. Ast. Soc., vol. viii., p. 28. 
 
412 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the phenomena may be explained in accordance "with the above-mentioned 
 principles. Thus, in the case wherein they have not been seen, when 
 the image of the sun has been received upon a screen, it may justly be 
 supposed that this circumstance arose from the feeble irradiation of the 
 solar image, whose brightness is so much inferior to that of the actual sur- 
 face of the sun. In the great majority of cases, however, no explanation 
 can be assigned, which is capable of reconciling the conflicting state- 
 ments of different observers. 
 
 Eclipses of the moon, although neither so impressive in their nature, 
 nor so important in their results as those of the sun, attracted the at- 
 tention of astronomers at a very early age, as in the absence of more 
 refined methods of observation, they served to fix the moon's place in 
 the heavens with considerable precision. Hipparchus did not fail 
 to perceive that observations of lunar eclipses would furnish a solution of 
 the great problem of the longitude. It was accordingly by means of such 
 phenomena, that the difference between the meridians of places on the 
 earth's surface was ascertained during a long succession of ages. The 
 results so obtained were, however, very inaccurate, on account of the diffi- 
 culty which is experienced in determining, by observation, the exact time 
 of the occurrence of a lunar eclipse. The method was therefore speedily 
 abandoned in modern times, upon the invention of others of a more trust- 
 worthy nature. Ptolemy, in his great work the Syntaxis, has determined 
 the elements of the lunar orbit by means of observation of eclipses of the 
 moon, made by the Chaldeans, at Babylon, about 700 years before the 
 commencement of the Christian era. It has been already mentioned 
 that, by a comparison of the same eclipses with others observed in more 
 recent times, Halley was led to suspect the famous inequality of the 
 secular acceleration of the moon's mean motion. 
 
 Observations of lunar eclipses are chiefly interesting in modern times 
 on account of the physical peculiarities which they occasionally exhibit. 
 The ruddy hue, by means of which the moon is rendered visible, even 
 when she is totally immersed in the earth's shadow, was a phenomenon, 
 the cause of which was long involved in great obscurity. By some persons 
 it was supposed to arise from a light naturally inherent in the moon's 
 surface, but it seemed impossible to reconcile this explanation with the 
 appearance of the moon in other parts of her orbit. The illustrious Kepler 
 was the first who shewed that the phenomenon was occasioned by the 
 refraction of the earth's atmosphere, which had the effect of turning the 
 course of the solar rays passing through it so as to fall upon the moon 
 even when the earth was actually interposed between her and the sun *. 
 
 The deep red colour of the moon's surface arises from the absorption 
 of the blue rays of light in passing through the terrestrial atmosphere, in 
 the same manner as the western sky is seen frequently to assume a ruddy 
 hue when illuminated in the evening by the solar rays. On account of the 
 variable condition of the terrestrial atmosphere, the quantity of light which 
 is actually transmitted through it to the moon is liable to fluctuate con- 
 siderably, and hence arises a corresponding variation in the appearance 
 presented by the moon's surface during her immersion in the earth's 
 shadow. If the region of the atmosphere through which the solar rays 
 pass, be everywhere deeply loaded with vapours, the red rays will be almost 
 totally absorbed as well as the blue, and the illumination of the moon will 
 
 * Ad Vitellionem Paralipomena, p. 276. 
 
, HISTOEY OF PHYSICAL ASTRONOMY. 413 
 
 be too feeble to render her surface visible. The records of lunar eclipses 
 present several examples of this kind. Thus Kepler states that during the 
 lunar eclipse which happened on the 15th of June, 1620, the moon totally 
 disappeared, although the fixed stars of the fourth arid fifth magnitudes in 
 her immediate vicinity were plainly distinguishable *. Hevelius also men- 
 tions that during the lunar eclipse of April 25, 1642, the place of the moon 
 could not be ascertained even with the aid of the telescope, although the 
 air was sufficiently pure to discern the stars of the fifth magnitudef. 
 
 The account given by Wargentin, of the lunar eclipse of May 18, 1761, as 
 observed by him at Stockholm, furnishes an interesting illustration of the 
 same remark. The total immersion of the moon took place at 10 h 41 m P.M. 
 The part of the margin of the lunar disk which had last entered the shadow 
 was pretty conspicuous by means of a bright light for five or six minutes 
 after the immersion, and to the naked eye exhibited a lustre equal to 
 that of a star of the second magnitude ; but at 10 h 52 m , this part, as 
 well as the whole of the rest of the moon's body, disappeared so com- 
 pletely, that not the slightest trace of any portion of the lunar disk could 
 be discerned either irith the naked eye or with the telescope, although the 
 sky was very clear and the stars in the vicinity of the moon were distinctly 
 visible in the telescope. After a long search for the missing body of the 
 moon, the Swedish astronomer at length discovered it at ll h 30 ra with a 
 two-feet telescope, by means of a faint light which was visible about the 
 eastern border of the disk. At ll h 33 m , persons of acute vision were able 
 to discern a trace of it with the naked eye, like an exclusively thin vapour ; 
 but more than half of the disk was still invisible. The boundary between 
 the visible and invisible portions was very irregular ; the light was also more 
 intense at the margin of the moon than it was towards the centre. During 
 the progress of the emersion, which commenced at 12 h 15 m , the part of 
 the moon which was still involved in the earth's shadow was by no means 
 palpable to observation, as is usually the case on similar occasions];. 
 
 If the region of the atmosphere, through which the solar rays pass, be 
 everywhere very transparent, the red rays will be transmitted to the moon 
 in great abundance, and her surface will, in consequence, appear strongly 
 'illuminated. Thus, during the lunar eclipse of December 22, 1703, the 
 moon, when totally immersed in the earth's shadow, was visible at Avignon 
 by a ruddy light of such brilliancy, that one might have imagined her body 
 to be transparent, and to be enlightened by the sun from behind . A 
 similar appearance was remarked on the occasion of the total eclipse of 
 the moon, which happened on the 19th of March, 1848. Mr. Forster, of 
 Bruges, states, in an account of the eclipse, that during the totality of the 
 immersion, the light and dark places on the face of the moon could be almost 
 as well made out as in an ordinary dull moonlight night. So intense was 
 the illumination of the moon's surface, that many persons could not be 
 persuaded that she really was eclipsed ||. Mr. Walkey, who observed the 
 eclipse at Clyst St. Lawrence, near Collumpton, states that the appearance 
 was as usual until 20 minutes to nine, when the whole of the moon's sur 
 face became very quickly and very beautifully illuminated, so as to 
 resemble the glowing heat of fire from the furnace, rather tinged with a 
 deep red. This appearance lasted about an hourlT. 
 
 Sometimes it happens that the region of the terrestrial atmosphere 
 
 Ep. Ast., p. 825. t Selenographia, p. 117. Ph. Tr., 1761, pt. i., p. 208, et seq. 
 
 . (Hist.) 
 
 132. 
 threescore years have passed with myself," 
 
 * n>p. ASI., p. ozo. T aeienograpnia, p. 
 
 Mem Acad. des Sciences, 1704, p. 59. 
 
 || Monthly Proc. Ast. Soc., vol. viii., p. 1 
 
 ^ Ibid., vol. viii., p. 132. " More than 
 
414 HISTORY OF PHYSICAL ASTRONOMY. 
 
 through which the solar rays pass, is so loaded with vapour in some parts 
 as in a great degree to absorb the rays, while in other parts it allows them 
 to be transmitted with facility to the moon's surface. Hence during the 
 totality of a lunar eclipse, the moon's surface will appear quite obscure in 
 some parts, and in other parts will exhibit a high degree of illumination. 
 Thus Kepler states that during the total eclipse of the moon, which hap- 
 pened on the 16th of August, 1598, while one-half of her disk was seen 
 only with great difficulty, the other half was discernible by a deep red 
 light of such brilliancy, that at first he was doubtful whether it was im- 
 mersed in the shadow at all*. If dense clouds be interspersed throughout 
 the whole of the atmospheric zone through which the rays pass, there will 
 manifestly ensue an irregular distribution of light and darkness over the 
 whole of the moon's surface. Such was the appearance, which, according to 
 Sir John Herschel, the moon presented during the total eclipse of October 
 13, 1837f. 
 
 The phenomena presented by the transits of the inferior planets over 
 the sun's disk are among the most interesting that arise from the relative 
 movements of the various bodies composing the solar system. The im- 
 portance of the transits of Venus, in determining the solar parallax, has 
 been already referred to. The physical features of such phenomena tend 
 also to attract the attention of the enquirer. The transits of Mercury are 
 of less utility than those of Venus in ascertaining the absolute dimensions 
 of the solar system ; but, as in the case of that planet, the phenomena 
 accompanying such occurrences are calculated to throw some light on the 
 physics of the celestial regions. 
 
 Long before the invention of the telescope it was asserted that Mercury 
 had been seen upon the sun's disk. Even as early as the ninth century, 
 it was stated by the author of the " Life of Charlemagne " that the planet 
 had been visible upon the sun for eight days. As it was impossible, from 
 the rapidity of his orbitual motion, that Mercury could have remained so 
 long visible upon the sun, Kepler suggested that the expression octo dies, 
 or eight days, might have been erroneously substituted for the barbaric 
 Latin octoties, or eight times. It is now well known, however, that the 
 angular magnitude of the planet is by far too small to allow its being seen 
 with the naked eye on such an occasion, so that in all probability the 
 phenomenon referred to was no other than a solar spot of more than ordi- 
 nary magnitude. Coming down to a more recent age, Averroes, a famous 
 physician of Cordova, in Spain, who wrote a commentary on the Alma- 
 gest, positively asserted that he had seen Mercury on the sun at a time 
 when, from the motion of the planet, it ought to have been passing 
 through its inferior conjunction J. This statement, however, must be 
 rejected as unworthy of belief, for the same reason as that alluded to in 
 the case just cited. Kepler himself was induced to believe on one occasion 
 that he had seen the planet on the sun, but the invention of the telescope 
 a few years afterwards having speedily led to the discovery of spots on the 
 sun's disk, he retracted his opinion, and candidly acknowledged that the 
 phenomenon seen by him was, in all probability, no other than one of such 
 macula. 
 
 says Mr. Walkey, "and during that period I have several times beheld an eclipse of 
 the moon, but never before did my eyes behold the moon positively give good light from 
 her disk during a total eclipse." 
 
 * Ad Vitellionem Paralipomena, p. 276. f Outlines of Astronomy, p. 256. 
 
 \ Copern., Revol., lib. x. The real name of this individual, who was of Moorish 
 origin, was Ebn Roschd. 
 
HISTORY OF PHYSICAL ASTRONOMY. 415 
 
 In his " Supplement to Vitellionem," Kepler remarked that from the 
 position of Mercury's nodes, it was possible that he might frequently pass 
 over the sun's disk*. With respect to Venus, he asserted that although 
 she might sometimes be interposed directly between the earth and sun, 
 the instances of such an occurrence were very rare. He announced, in 
 fact, that a transit of this planet would not take place during the whole of 
 the seventeenth century f. 
 
 The completion of the Eudolphine Tables in the year 1627, having 
 enabled their illustrious author to calculate the motions of the inferior 
 planets upon a more accurate basis than any hitherto employed by him, 
 he now arrived at results of considerable precision relating to the times of 
 their transits over the sun's disk. In 1639 he published a small tract, in 
 which he ventured to predict that both Mercury and Venus would pass 
 over the sun's disk in the year 1631, the former on the 7th of November, 
 and the latter on the 6th of December J. He announced at the same time 
 that there would not happen another transit of Venus before the year 1761. 
 This, however, was a mistake, as we shall presently have occasion to show 
 more particularly. 
 
 The transit of Mercury, which Kepler had predicted, was actually wit- 
 nessed by Gassendi, at Paris. He has given an interesting account of 
 his observations in a letter to Shickhard, Professor of Mathematics in the 
 University of Tubingen. "The crafty god," says he, "had sought to 
 deceive astronomers by passing over the sun a little earlier than was 
 expected, and had drawn a veil of dark clouds over the earth in order to 
 make his escape more effectual. But Apollo, acquainted with his knavish 
 tricks from his infancy, would not allow him to pass altogether unnoticed. 
 To be brief, I have been more fortunate than those hunters after Mercury 
 who have sought the cunning god in the sun. I found him out, and saw 
 him, where no one else had hitherto seen him." 
 
 Gassendi made preparations to observe the transit of the planet, by 
 admitting the solar light into a dark chamber through a small aperture in 
 the window, and receiving the image of the sun upon a white screen, 
 having a circle described upon it adapted exactly to the magnitude of the 
 image. The diameter of the circle was three-fourths of a French foot in 
 length, and was divided into sixty parts, so that by supposing the apparent 
 diameter of the sun to be 30', each of the subdivisions would represent an 
 apparent magnitude of 30". The circumference of the circle was also 
 divided into 360 degrees. In order to obtain an accurate knowledge of 
 the time, he placed a person in the room above him, with a quadrant of 
 two feet radius, charging him to observe the altitude of the sun whenever 
 he should hear him stamp with his foot. In order that the transit of the 
 planet might not escape him, he resolved to commence his observations a 
 day or two earlier than that which Kepler had fixed for its occurrence. 
 The 5th of November proved unsuitable for this purpose, being all day 
 rainy. The 6th turned out to be equally unfavourable, the sky being 
 overcast during almost the whole day. The 7th, which was the day ap- 
 pointed for the transit of the planet, was very changeable in the morning, 
 
 * Ad Vitellionem Paralipomena, p. 306. f Ibid, p. 305. 
 
 J The following is the title of this small tract : " Admonitio ad Astronomos rerumque 
 celestium studiosos, de miris rarisque anni 1631 phsenomenis, Veneris puta et Mercurii 
 in solem incursu." Lips., 1629. 
 
 Opera Omnia, torn, ii., p. 537. 
 
416 HISTOEY OF PHYSICAL ASTKONOMY. 
 
 but was for most part cloudy. A little before eight o'clock the sun was visible 
 through the openings of the denser clouds, but a thin veil of nebulous 
 matter still rendered it impossible to distinguish any minute object, either 
 upon the actual disk of the sun or upon his image in the dark chamber. 
 Towards nine o'clock, the sun being distinctly visible, he perceived a black 
 spot upon the image. It was a little to the east of the vertical diameter, 
 and about a fourth of its length from the lower extremity. He roughly 
 marked its position, not having the remotest suspicion that it was Mercury 
 on account of its extreme smallness, for its diameter scarcely seemed to 
 exceed the half of one of the minute parts into which he had divided the 
 diameter of the white circle. He was rather inclined to believe that it 
 was a solar spot, which, although not visible on the preceding day, might 
 have been formed during the intermediate interval, as had happened on 
 several previous occasions, in the course of his experience. The sun having 
 again appeared through the clouds at nine o'clock, he measured the distance 
 of the spot from the centre of the image, intending to compare its position 
 with that of the planet, if the latter should eventually enter upon the sun, 
 for it occurred to him that an observer at some other station might be 
 induced to do so likewise, and that suitable data would thereby be obtained 
 for determining the parallax of the planet. A little afterwards, when the 
 sun again became visible, he measured anew the distance of the spot from 
 the centre of the image, and was surprised to find that it had considerably 
 increased during the intermediate interval. From its rapid motion, he 
 felt assured that it could not be one of those ordinary spots that appear 
 from time to time on the surface of the sun, and he now began to enter- 
 tain some suspicion of its real nature, but still he could not persuade him- 
 self that it was Mercury, so much was his mind pre-occupied with the idea 
 that the planet would exhibit a larger apparent magnitude. While he 
 was pondering whether he had not made a mistake in his first measure- 
 ment, the sun shone forth, whereupon, having again ascertained the posi- 
 tion of the spot, he found its distance from the centre to be even greater 
 than on the previous occasion. He now concluded without hesitation, that 
 it was in reality the planet which the black spot represented. He there- 
 fore immediately gave the preconcerted signal to his assistant in the 
 chamber above him, but unfortunately he had abandoned his post, and 
 for some time could not be found. He returned, however, before the planet 
 had gone off the sun, and made the necessary observations. 
 
 Gasseudi states that the planet, as seen depicted on the solar image, 
 was somewhat diluted, and of a ruddy colour around the margin. Its 
 diameter seemed to be equal to about two-thirds of the interval between 
 two consecutive points of the diameter of the image. The apparent 
 diameter of the planet was therefore only 20". This was far below the 
 angular magnitude which astronomers usually assigned to it. 
 
 The planet had nearly gone off the sun when Gassendi first saw it. 
 From its observed motion during the short interval of its visibility, he 
 calculated that it had entered upon the sun's disk at 5 h 28 m A.M., and 
 that its final egress took place at 10 h 28 m A.M. The transit had therefore 
 lasted five hours precisely. By reducing the calculations of Kepler to the 
 meridian of Paris, he found that the observed time of the transit was in 
 advance of the computed time by 4 h 49 m 30 s . 
 
 The transit of Mercury observed by Gasseudi, took place when the 
 planet was passing through the ascending node of its orbit. The second 
 
HISTORY OF PHYSICAL ASTRONOMY. 417 
 
 transit of the same planet that was actually observed, happened on Novem- 
 ber 3, 1651. On this occasion also the planet was passing through its 
 ascending node *. The phenomenon was observed at Surat in India, by 
 Shakerley, a young Englishman, who, having found by calculation that it 
 would be visible only in Asia, proceeded to India for the express purpose 
 of witnessing its occurrence f. 
 
 The third transit of Mercury recorded by astronomers, happened on 
 the 3rd of May, 1661. Hevelius, who observed it at Dantzic, was asto- 
 nished to find that the apparent diameter of the planet was so small. 
 We have seen that Gassendi estimated it to be equal to 20" ; Hevelius 
 made its greatest value to amount only to 12", and the mean value to 
 6" 3"'J. These results agree very nearly with the modern determinations 
 of the apparent magnitude of the planet. The same transit was observed 
 at London by Huyghens, Street, and Mercator. 
 
 The fourth transit of Mercury that is recorded to have been observed, 
 was that of November 7, 1677. It was witnessed by Halley at St. 
 Helena, where he was then residing, as well as by several persons in 
 Europe. Halley was the first who observed both the ingress and egress 
 of the planet. 
 
 The transits of Mercury that have been subsequently observed, are 
 chiefly interesting on account of the indications they afford of the accuracy 
 of the existing tables of the planet. With respect to the physical pheno- 
 mena accompanying such occurrences, they are not of such importance as 
 might be expected. It is only on a few rare occasions, indeed, that any 
 peculiarity worthy of notice has been seen. In each of such instances, 
 the phenomenon is manifestly referrible to some optical illusion. A brief 
 description of the appearances observed during two or three transits of the 
 planet will serve to confirm the truth of this remark. 
 
 In an account of the transit of Mercury which happened on the 6th of 
 May, 1753, M. De Barros, a Portuguese, who witnessed the phenomenon 
 at Paris, states that when the planet was about to leave the sun's disk, he 
 perceived the interior contact through a green glass placed before the 
 smoked glass of his telescope (which was an excellent Gregorian reflector, four 
 feet long), and that immediately afterwards, viewing the planet through the 
 smoked glass alone, he found that a small thread of light was still visible 
 between the limbs of the two bodies. A second interior contact of the 
 planet was therefore observed at the commencement of the egress, which 
 did not take place till four seconds after the first contact. A similar ap- 
 pearance presented itself at the completion of the egress. The exterior 
 contact was first observed by means of the two glasses ; but upon removing 
 the green glass, the planet was again brought upon the sun's disk, and did 
 not go off until six or seven seconds afterwards ||. 
 
 The phenomena above referred to are, in all probability, connected with 
 the irradiation of light. It has been already mentioned that the colour of 
 
 * The transits of Mercury happen necessarily, from the heliocentric position of its 
 nodes, always in May or November. When the transit takes place in May, the planet is 
 passing; through the descending node of its orbit. The occurrence of the transit in 
 November indicates the passage of the planet through the ascending node. 
 
 f Wing, Astronomia Britannica, p. 312. 
 
 J " Mercurius in Sole Visus." Gedan, 1662, p. 92. 
 
 Wing, Astronomia Britannica, p. 312. This transit, happened on the day of the 
 coronation of Charles II. The observations of Huyghens and his companions are said by 
 Wing to have been made at Long Acre, with a telescope of excellent workmanship. 
 
 || 'Phil. Trans., 1753, p. 362. 
 
 E E 
 
418 HISTOEY OF PHYSICAL ASTKONOMY. 
 
 the glass employed in viewing a luminous object, exercises a material in- 
 fluence on the enlargement arising from this cause. The observation of 
 De Barros was called in question by several of his contemporaries, but 
 when the extraordinary phenomena of a. similar nature witnessed in more 
 recent times are taken into consideration, there seems no reason to doubt 
 the authenticity of his statement. 
 
 Plantade remarked that, during the transit of 1736, the disk of Mer- 
 cury, when projected upon the sun, appeared to be surrounded by a lumi- 
 nous ring. A similar phenomenon has been witnessed during several 
 subsequent transits. MM. Schroeter and Harding, who observed it on 
 the occasion of the transit of 1799, describe it as a nebulous ring of a 
 dark tinge approaching to violet colour*. A ring agreeing with this 
 description was noticed by Dr. Moll, of Utrecht, during the transit of 
 1832 f. On the other hand, many persons who observed the transits above 
 mentioned, did not perceive any indications ojf a ring around the planet, nor 
 have the observations of more recent transits of the planet served to con- 
 firm the existence of such a phenomenon. It is therefore very probably 
 a spurious appearance depending upon some optical cause. 
 
 A curious phenomenon noticed by Schroeter and Harding on the occasion 
 of the transit of Mercury which occurred May 7, 1799, consisted in the 
 appearance of two small spots of a greyish colour on the disk of the 
 planet J. A similar phenomenon was witnessed by Dr. Moll during the 
 transit of 1832, except that in this instance only one spot was visible . 
 During the transit of 1 848, a spot was also seen on the planet's disk by 
 the Rev. J. B. Reade and Mr. Dell. It is described as a greyish spot, 
 shading off indefinitely on all sides from the centre ||. It appears, also, 
 from a statement made by Captain Sir Edward Belcher, R.N., to Prof. 
 Powell, that it was seen in Sir James South 's great refracting telescope, 
 the aperture of which (11.95 inches) had been reduced by a diaphragm 
 outside to 3 inches IT. 
 
 Prof. Powell has proposed an ingenious explanation of the above-men- 
 tioned phenomenon, founded upon the principle of the diffraction of light**. 
 It is a consequence naturally flowing from the theory of the diffraction of 
 the object glass of a telescope, as explained by Mr. Airy, that a small 
 opaque disk, projected upon a luminous surface, should not only undergo 
 a diminution of apparent magnitude, but should also exhibit one or more 
 bright concentric rings in the interior, and if the disk be very small, it is 
 not difficult to conceive that the rings might condense into a bright spot 
 in the centre. Prof. Powell verified this result experimentally, by viewing 
 a small opaque disk, on a ground glass, strongly illuminated behind, with 
 a telescope having its aperture reduced to one-fourth of an inch. Within 
 the disk he distinctly perceived a ring concentric with it, which contracted 
 into a spot in the centre when the disk was very small. 
 
 Nothing can be more satisfactory than the agreement between the 
 result of the above-mentioned experiment and the phenomenon observed 
 during the transit of 1848. So far the explanation of Prof. Powell ap- 
 pears to be unexceptionable. Unfortunately, the same degree of con- 
 sistency does not present itself when the question relates to the phenome- 
 non of a similar nature witnessed on previous occasions of the transit of 
 Mercury. Thus, although Dr. Moll saw a small spot on the disk of the 
 
 * Mem. Ast. Soc., vol. vi. p., 116. f Ibid. Ibid. 
 
 Ibid. || Monthly Proc. Ast. Soc., vol. ix., p. 23. 
 
 f Mem. Ast. Soc., vol. xviii., p. 88. ** Ibid., p. 87. 
 
HISTORY OF PHYSICAL ASTRONOMY. 419 
 
 planet during the transit of 1832, it is quite clear from the drawing he has 
 given of its position, as well as from the terms in which he alludes to it, 
 that it was not situate in the centre of the disk. The explanation of Prof. 
 Powell, however, requires that the spot should be exactly in the centre. 
 Again, we have seen that, on the occasion of the transit of 1799, two spots 
 were seen on the disk of the planet, but, according to the diffraction theory, 
 there should be only one visible. It is manifest that the observations of 
 future transits of the planet can alone throw additional light upon the 
 subject. 
 
 On the occasion of the transit of Mercury in November, 1848, the limb 
 of the planet was seen by one of the observers at Greenwich to be con- 
 nected for some time with the sun's limb by black lines, similar to those 
 noticed by Mr. Baily during the annular eclipse of 1836. It is worthy 
 of remark, however, that although seven other individuals observed the 
 transit with separate telescopes, no such phenomenon was seen by either 
 of them* . These dark lines seem much more difficult to explain than 
 either the dark ligament or the protuberance observable when the moon 
 or planet appears upon the solar disk wholly detached from the sun's 
 limbf. 
 
 The transits of Venus across the sun's disk are phenomena of much 
 rarer occurrence than those of Mercury. It has been already mentioned, 
 that in 1629, Kepler predicted the occurrence of a transit of this planet 
 on Dec. 6, 1631. According to his calculation, it appeared that the planet 
 would not enter upon the sun's disk till towards sunset ; it was not im- 
 probable, therefore, that the phenomenon would be altogether invisible in 
 Europe. Gassendi, however, was not without hopes that in the present 
 instance, as had previously happened with respect to Mercury, there might 
 be a considerable error in the calculated result, and that in reality the 
 planet would begin to be visible on the sun's disk several hours earlier 
 than the time assigned by the tables. He accordingly made arrangements 
 to observe the transit similar to those which he had employed so success- 
 fully in the previous month on the occasion of the transit of Mercury. 
 He has given an account of his fruitless observations on this occasion in 
 a second letter to Schickhard. He intended to watch the appearance of the 
 sun on the 4th and 5th of the month, but an impetuous storm of wind 
 and rain rendered the face of the heavens invisible on both of those days. 
 On the 6th he continued to obtain occasional glimpses of the sun, till a 
 little past three o'clock in the afternoon, but no indication of the planet 
 could be discerned upon his disk as depicted upon the white circle. On 
 the 7th, he saw the sun during the whole forenoon, but he looked in 
 vain for any trace of the planet. It is now well known that the transit 
 of the planet took place during the night between the 6th and 7th of 
 December J. 
 
 It has been mentioned that Kepler had announced that, after the transit 
 of 1631, Venus would not again be seen upon the sun's disk previous to 
 the year 1761. Astronomers were therefore under the impression, after 
 
 * Monthly Proc. Ast. Soc., vol. ix., p. 69. 
 
 f Dr. Foster, who observed this transit, at Bruges, states that the planet, when seen on 
 the sun, had rather the appearance of a globe than a disk. (Monthly Proc. Ast. Soc., vol. 
 ix., p. 4.) A similar remark has been made on the occasion of solar eclipses, see p. 401, 
 (Note). 
 
 J The two letters of Gassendi to Schickhard respecting the transits of Mercury and Venus 
 were published under the title of "Mercurius in Sole Visus et Venus invisa." (Opera 
 Omnia, torn, iv., p. 537, et seq.) 
 
 E E 2 
 
420 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the failure of Gassendi's attempt to obtain a view of the planet during the 
 transit of 1631, that the existing generation of the human race would long 
 have passed away before another occasion would present itself of observing 
 a phenomenon of so interesting a nature* In the year 1639, however, the 
 planet passed again over the sun's disk. On this occasion the transit 
 took place unknown to any person living, with the exception of two in- 
 dividuals who enjoyed the gratification of witnessing the phenomenon. 
 The fortunate observers were Jeremiah Horrocks and William Crab tree, 
 two young men residing in the north of England, devoted enthusiastically 
 to the study of astronomy. Horrocks has given an account of the transit 
 of the planet, as seen lay himself and his friend Crabtree, in an interesting 
 little dissertation on the subject entitled " Venus in Sole visa." He had 
 been engaged in calculating the places of the planets by means of 
 Lansberg's tables, which their author had boasted to be unequalled in 
 point of accuracy; but, on comparing the results with observation, he was 
 mortified to find that the discordances were of such magnitude, as to 
 render his labours almost of no value. This circumstance calls forth the 
 indignation of the young astronomer, who contrasts the tumid arrogance of 
 the Belgian calculator with the unobtrusive merits of the illustrious Kep- 
 ler. Lansberg, with as little modesty as truth, had vauntingly cited the 
 words of the Roman poet, 
 
 " Quantum lenta solent inter viburna cuprcssi," 
 
 as affording a just idea of the superiority of his tables over all other ex- 
 isting labours of a similar kind. Horrocks remarks, that however inap- 
 propriate the simile of the poet may be when so applied, it may be used 
 very justly to represent the surpassing excellence of the Kudolphine 
 Tables. Indeed, there could not be wanted a clearer indication of the 
 genius of Horrocks than is afforded by the intuitive sagacity with which 
 he seems to appreciate the value of Kepler's discoveries ; for it is to be 
 borne in mind that the prejudices in favour of the ancient system of as- 
 tronomy had not yet been wholly eradicated from men's minds *. 
 
 It is a curious fact, however, that the tables of Lansberg, however 
 erroneous, were instrumental in revealing to Horrocks the interesting fact 
 that Venus would pass over the sun's disk in the month of December, 
 1639. He had found that Kepler's tables displaced the planet in lati- 
 tude about 8' towards the south, while on the other hand the tables of 
 Lansberg indicated a much larger error in the opposite direction. During 
 its conjunction with the sun in December, 1639, the planet appeared by 
 Kepler's tables to pass a little below the sun, while, on the other hand, 
 those of Lansberg brought it upon the upper part of his disk. He sus- 
 pected, therefore, that the planet would actually pass over the solar disk 
 towards its lower extremity, and a more complete investigation of the sub- 
 ject assured him of the accuracy of his surmise. By an exact calculation 
 of the time of conjunction, he found, in fact, that the planet would enter 
 upon the solar disk on the 24th of November, O.S., 1639, a little before 
 sunset. Owing to the shortness of the interval that was to elapse pre- 
 vious to the actual occurrence of the transit, he was unable to announce 
 with sufficient publicity the interesting result at which he arrived, so as 
 
 "* Montucla states, that Riccioli, Bouillaud, and many other celebrated astronomers, who 
 were contemporary with them, read Kepler's works without comprehending them. (His- 
 toire des Mathematiques, torn, ii., p. 254.) 
 
HISTORY OF PHYSICAL ASTRONOMY. 421 
 
 to induce astronomers generally to observe the phenomenon. He did not 
 fail, however, to acquaint his friend Crabtree, who lived in the neighbour- 
 hood of Manchester, with the approaching transit, and accordingly these 
 two individuals made suitable preparations, each at his own residence, to 
 observe its occurrence. 
 
 Horrocks employed a mode of observation similar to that practised by 
 Gassendi on the occasion of the transit of Mercury in 1631, as already 
 explained. He divided the diameter of the white circle upon which he 
 received the image of the sun into 30 parts, and each of these into 4 
 smaller parts, so that by supposing the apparent diameter of the sun to 
 be 30', each of the more minute subdivisions would represent an apparent 
 magnitude of 15". After rectifying the motion of the planet, he found 
 that its conjunction would not take place before three o'clock in the after- 
 noon of the 24th of November. However, as all the tables of the planet 
 indicated the conjunction to be earlier some of them even made it to take 
 place on the 23rd he did not consider it prudent to trust too implicitly 
 to his own calculations. He therefore did not omit to examine attentively 
 the image of the sun from time to time on the 23rd. 
 
 On the 24th he continued to observe the solar image from sunrise till 
 the hour appointed for going to church*. During all this time, he saw 
 nothing upon the sun except an ordinary spot of small dimensions which 
 he had noticed on the preceding days, and which could not, therefore, be 
 Venus. At a quarter past three o'clock in the afternoon, as soon as he 
 was again at leisure, he proceeded to resume his observations. " At this 
 time," says he, "an opening in the clouds, which rendered the sun dis- 
 tictly visible, seemed, as if divine Providence encouraged my aspirations, 
 when, Oh most gratifying spectacle! the object of so many earnest wishes\, 
 I perceived a new spot of unusual magnitude, and of a perfectly round form, 
 that had just wholly entered upon the left limb of the sun, so that the mar- 
 gins of the sun and the spot coincided with each other, forming the angle of 
 contact" The planet, in fact, had then entered upon the eastern limb of 
 the sun, at the distance of 62 30' from the lower extremity of the vertical 
 diameter of his disk. By a careful comparison of the relative magnitudes 
 of the image and the round spot visible upon it, he concluded their 
 diameters to be in the proportion of 30 to 1-J- or 1^- at the utmost. The 
 apparent diameter of the planet did not therefore exceed 1' 12". 
 
 Owing to the near approach of sunset, Horrocks was unable to observe 
 the planet longer than half an hour. During this brief interval, he mea- 
 sured its distance from the sun three different times. His observations 
 of the phenomenon were made at Hoole, a small village in Lancashire, 
 about fifteen miles to the north of Liverpool. 
 
 Crabtree, who resided at Broughton near Manchester, had made ar- 
 rangements for observing the transit similar to those employed by Hor- 
 rocks. The sky, however, unfortunately continued overcast during the 
 whole day, and he had abandoned all hopes of witnessing the phenomenon, 
 when, just a little before disappearing below the horizon, the sun burst 
 through the clouds. Repairing immediately to the chamber in which he 
 had made preparations to receive the image of the sun, he beheld, to his 
 
 * The words of Horrocks on this occasion, " ad major a avocatus quce utique ob hcec 
 parerga negllgi non decuit," manifestly have reference to religious duties, and this in- 
 ference is further confirmed by the fact that the 24th of November, 1639, fell upon 
 Sunday, as will be apparent to any person by a slight computation. 
 
 f " Ecce gratissimum spcctaculum et tot votorum materiem!" 
 
422 HISTORY OF PHYSICAL ASTRONOMY. 
 
 unspeakable delight, the round black spot representing the planet depicted 
 upon the white circle. According to Horrocks, he was so captivated by 
 the spectacle, that he gazed upon it immovably for some time, and when 
 he recovered himself, the clouds had agaia obscured the sun, so that he 
 was unable to make any accurate measurements. He, however, drew a 
 diagram of the position of the planet, which Horrocks found to agree 
 exactly with his own observations. He estimated the diameter of the 
 planet at T ^ ^ths of the solar diameter, or about 1' 3", supposing with 
 Horrocks that the latter was equal to 30'. 
 
 Thus did two young men, cultivating astronomy together in a state of 
 almost complete seclusion in one of the northern counties of England, 
 enjoy the privilege of witnessing a phenomenon which human eyes had 
 never before beheld, and which no one was destined again to see until 
 more than a hundred years had passed away*. Unfortunately, a prema- 
 ture death deprived their country of the two individuals who exhibited 
 such enthusiasm in the cause of science. Horrocks was a young man of 
 extraordinary genius, whose name would assuredly have formed a house- 
 hold word to future generations, if his career had not been so soon brought 
 to a close. It may perhaps not be uninteresting to mention some of the 
 few facts which are known respecting the two youthful astronomers. 
 
 Jeremiah Horrocks was born at Toxteth, near Liverpool, in the year 
 16 L9, of parents who appear to have been in rather straitened circum- 
 stances. Having received the rudiments of instruction at his native 
 place, he subsequently completed his education at Emmanuel College, 
 Cambridge. About the year 1633, he seems to have been first led to 
 turn his attention to astronomical pursuits. In one of his posthumous 
 fragments, he has described, with all the fervour of youthful enthusiasm f, 
 the state of his feelings at this time, and the means by which he suc- 
 ceeded in vanquishing the difficulties of his position; for it must be 
 borne in mind that, in those days, there was no branch either of mathe- 
 matical or physical science taught at Cambridge. " I felt great delight," 
 says he, " in meditating upon the fame of the great masters of science, 
 such as Tycho Brahe and Kepler, and sought at least to emulate them 
 in my aspirations. I imagined that nothing could be nobler than to 
 contemplate the manifold wisdom of my Creator amid so great a pro- 
 fusion of works ; and to behold the pleasing variety of the celestial mo- 
 tions, the eclipses of the sun and moon, and other phenomena of the 
 same kind, no longer with the unmeaning gaze of vulgar admiration, but 
 with a desire to know their causes, and to feed upon their beauty by a 
 closer inspection of their mechanism. " I Serious obstacles, however, opposed 
 themselves to the realisation of these ideas by Horrocks. His humble 
 condition in life was by no means favourable to the tranquil prosecution 
 of astronomical researches. He had no teacher who could give him any 
 
 * The transits of Venus happen invariably either in June or December, according as 
 the planet is passing through the descending or the ascending node of its orbit. The 
 intervals between the successive transits counted in years are 8, 105|; 8, 121 1; 
 8, 105j ; &c., &c. Two transits of the planet at the ascending node will happen in the 
 nineteenth century, one on Dec. 8, 1874, and another on Dec. 6, 1882. The transit of 
 1639, witnessed by Horrocks and Crabtree, is the only phenomenon of this kind that has 
 been hitherto observed at the ascending node. 
 
 t " On voit que Horrocks etait jeune et enthousiaste, mais cette jeunesse et cette 
 enthousiasme annoncaient un homme vraiment distingue." (Delambre, Hist. Ast. Mod., 
 torn, ii., p. 497.) 
 
 J Opera Posthuma, p. 2. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 423 
 
 instruction in the elements of the science, nor even a companion to co- 
 operate with him in his studies. But these disadvantages did not effectually 
 depress his ardour. He resolved to cultivate the science alone, by the 
 aid of such books as his limited means could from time to time supply 
 him with. About the year 1636, he at length had the good fortune to 
 obtain the acquaintance of Crab tree, who had already been engaged in 
 similar pursuits. The two young friends corresponded together for several 
 years on astronomical subjects, occasionally communicating with Samuel 
 Foster of London, who was subsequently Professor of Astronomy in 
 Gresham College-. In a letter dated October 3, 1640, Horrocks stated 
 to his friend that he intended soon paying him a visit, but he wished pre- 
 viously to bring to a conclusion his Dissertation on the transit of Venus. 
 On the 12th of December following, he expressed in another letter his 
 regret that the inconstant state of his affairs, and the daily performance of 
 duties of a harassing nature, prevented him so long from enjoying the 
 gratification of a personal interview with his friend. At length, on the 
 19th of the same month, he wrote to say that if nothing unusual should 
 prevent him (nisi quid prater insolitum impediat], he would be at Brough- 
 ton on the 4th of January. Alas ! his expectations were not destined to 
 be realised. Dr. Wallis found 011 the back of this letter a statement in 
 Crabtree's own handwriting to the effect that his dear friend Horrocks 
 died very suddenly on the morning of the 3rd of January, being the very 
 day previous to that on which he intended to visit him. Crabtree survived 
 his friend only a very short time. Dr. Wallis, in 1672, was unable to 
 obtain any authentic particulars respecting his death. The general belief 
 was, that he had perished in the civil wars which soon afterwards broke 
 out. 
 
 Amid the angry din of political commotion, the name of Horrocks was 
 completely forgotten, until at length, after the lapse of twenty years, the 
 manuscript of his " Venus in Sole Visa " having been shown to several 
 members of the Koyal Society, which had just been instituted, a general 
 feeling of admiration was excited by its perusal, and a strong desire was 
 expressed that it should be published. Huyghens, who happened to be 
 then in London, was so much struck with the genius of the youthful 
 author of the Dissertation that he caused a copy of it to be taken, and trans- 
 mitted it to Hevelius, who published it at Dantzic in 1662, along with his 
 own "Mercurius in Sole Visus." It does not redound to the credit of 
 England, that this exquisite relic of one of her most gifted sons should 
 have been allowed first to see the light in a foreign landf. Nor can 
 it assuredly be urged, in extenuation of her indifference, that its author, 
 
 * It appears from Ward's " Lives of the Professors of Gresham College," that Samuel 
 Foster completed his education at Emmanuel College, Cambridge, so that in all probability 
 he was a fellow student of Horrocks. 
 
 t In fact, it has never since been published anywhere else. Delambre expresses his 
 astonishment at not finding it in the work edited by Wallis. A short postscript to the 
 preface, however, serves to explain the omission. It is stated therein that Flamsteed 
 purposed soon publishing a new and more correct edition of the tract " Venus in Sole 
 Visa," from a manuscript in the author's own handwriting. It is well known that Flam- 
 steed never fulfilled the expectation thus held out respecting him. In the list of MSS. 
 of Flamsteed's, preserved in the Royal Observatory of Greenwich, and inserted at the 
 beginning of Daily's " Life of Flamsteed," there is mention of a copy of Horrocks' 
 " Venus in Sole Visa," which, in all probability, is the very copy alluded to by Wallis. 
 If such be the case, it would be only paying a just tribute to the memory of the author to 
 publish it. Delambre states that the work of Hevelius, in which it originally appeared, 
 is now excessively rare. 
 
424 HISTORY OF PHYSICAL ASTRONOMY. 
 
 less fortunate than some of his successors, was struck down by the re- 
 morseless arm of death at the very commencement of his brilliant career. 
 - Having thus been made acquainted with the loss which their country 
 had sustained from the premature deathof Horrocks, the Royal Society 
 took steps to collect together all the memorials respecting himself and 
 his friend Crabtree, which might still be in existence, with a view to their 
 publication. It was found that much of what Horrocks had written was 
 irrecoverably lost. Some of his papers, which, for greater security, had 
 been kept in a secret place during the civil wars, were burned by a 
 party of soldiers who entered his father's house in quest of plunder. 
 Some were carried to Ireland by his brother, who died there and was no 
 more heard of. Another portion, which had been deposited in a book- 
 seller's shop in London, was destroyed during the great fire of 1666. The 
 task of editing all the remaining fragments that could be procured was 
 committed to Dr. Wallis, who was then Savilian professor of geometry 
 in the University of Oxford. They were finally published at London, in 
 the year 1672, under the title of t( JeremiaB Horroccii Opera Posthuma." 
 They consist of a defence of the Keplerian astronomy, a selection of letters 
 from Horrocks to Crabtree, astronomical observations of the two friends, 
 and an exposition of the lunar theory of Horrocks by Flamsteed. In the 
 preface to the work, Dr. Wallis has mentioned such facts as came to his 
 knowledge respecting the life of Horrocks, nor has he failed to allude, in 
 terms of burning indignation, to the apathy with which for more than 
 twenty years the manuscripts of the youthful astronomer were regarded 
 by his countrymen*. It must be acknowledged, however, that the act 
 of reparation which was finally effected forms a bright episode in the 
 early history of the Royal Society, and that throughout all the proceedings 
 connected with the execution of the task assigned to him, Dr. Wallis ex- 
 hibited a spirit of disinterestedness and zeal which reflects the highest 
 honour on his character f. 
 
 When the early death of Horrocks is considered, his posthumous 
 fragments may be readily supposed to derive their interest rather from 
 the indications they afford of what might have been expected from him 
 if a longer term of life had been granted to him, than from any positive 
 influence which they were calculated to exercise on the progress of 
 physical science. In the lunar theory, however, he effected an im- 
 provement which would alone suffice to obtain for him an imperishable 
 reputation. His beautiful explanation of the inequality in the moon's 
 longitude, termed the evection, by means of a libratory motion of the 
 apsides and a variable eccentricity, was the last great step made in the 
 development of the laws of the planetary movements previous to the 
 establishment of the theory of gravitation by Newton ; and there can be 
 little doubt that it afforded material aid to that philosopher in his expo- 
 sition of the general principles of perturbation as detailed by him in the 
 sixty-sixth proposition of the first book of the " Principia " and its famous 
 corollaries. Horrocks has thus won for himself a place among those great 
 
 * "Non possum, inquavn, tion indignari, pretiosum hoc spectaculum (Venus in Sole 
 Visa) nullo auro redimendum, descriptum, preloque paratum,delituisse per annos integros 
 viginti duo ; neniinemque interea repertum esse, qui tarn bellam patris mortui prolem 
 susciperet, qui rem tanti ad astronomiam momenti in lucem mitteret, qui nostrse gentis 
 famse, vel omnium commodo, eatenus inserviret." 
 
 f The account of the various proceedings connected with this matter will be found 
 scattered through the first two volumes of Birch's " History of the Royal Society." 
 
HISTORY OF PHYSICAL ASTRONOMY. 425 
 
 men who, from Hipparchus downwards, by their successive efforts, esta- 
 blished the fundamental facts relative to the movements of the planets 
 without reference to their physical cause. 
 
 Although the posthumous works of Horrocks can only be regarded as 
 mere fragments, their perusal cannot fail to excite a feeling of deep 
 regret that astronomy was so soon deprived of the benefit of his labours. 
 It would be inconsistent with the object of this work to attempt a com- 
 plete analysis of their contents, but a glance over some of his letters to 
 Crabtree may serve to confirm the truth of Delambre's remark, that if their 
 author had lived he would have proved himself the worthy successor of 
 Kepler. These letters were written originally in English, but were 
 translated into Latin by Dr. Wallis. 
 
 In a letter dated November 23, 1637, Horrocks states that he had re- 
 cently spent some time in meditating upon the physical principle in virtue 
 of which the planets revolve in oval orbits. " Kepler," says he, " attri- 
 butes their movements to the action of magnetic fibres, but I entertain 
 serious objections to this hypothesis. It appears to me, however, that I 
 have fallen upon the true theory, and that it admits of being illustrated 
 by means of natural movements on the surface of the earth, for nature 
 everywhere acts according to a uniform plan, and the harmony of creation 
 is such that small things constitute a faithful type of greater things." 
 
 In a letter dated July 25, 1638, he ascribes the motion of the lunar 
 apsides to the disturbing force of the sun. This very remarkable idea of a 
 perturbative influence, exercised by the various bodies of the planetary sys- 
 tem upon each other, had not yet been suggested by any philosopher. The 
 circumstance of its being perfectly true in the particular case alluded to 
 by Horrocks, tends in a still greater degree to enhance the merit of the 
 surmise. In the same letter he exhibits an illustration of the planetary 
 movements by suspending a weight from a fixed point by a long cord, and, 
 having drawn the weight a little aside from the vertical direction, apply- 
 ing to it a slight tangential impulse. This beautiful experiment, illustra- 
 tive of the action of a central force, has been generally ascribed to Hooke, 
 who merely reproduced it, at a meeting of the Royal Society, about thirty 
 years after Horrocks had devised it *. Horrocks remarked that the pen- 
 dulous body would describe an ellipse, the apsides of which would advance 
 slowly in the direction of the body's motion. It did not escape his obser- 
 vation that this experiment did not represent the movements of the 
 planets with sufficient fidelity, inasmuch as there were two perihelia and 
 two aphelia, the centre of the ellipse being in fact the centre of force, 
 instead of the focus, as in the case of nature. In order to make the 
 parallel more complete, he supposed a gentle wind to blow constantly 
 upon the pendulum in the direction of the major axis of the ellipse. If 
 the representation was still imperfect, it must be admitted that the step 
 here taken was at least in the right direction. Horrocks, in his researches 
 
 * Hooke first gave an account of his experiment at the meeting of the Royal Society, 
 which was held on the 23rd of May, 1666 ( Birch's " History of the Royal Society," vol. ii. , 
 p. 92). It might be supposed that as Horrocks' posthumous works were not published till 
 1 672, Hooke could not have been indebted to them for the original idea of the experiment. 
 It appears, however, that Wallis had completed his task of preparing the writings of Hor- 
 rocks for publication as early as September 21, 1664 (Birch, vol. i., p. 470). The print- 
 ing of the work was deferred by the Council until the president should give his opinion 
 respecting it. The circumstance of its remaining so long in manuscript arose, doubtless, 
 from the impoverished state of the Society's treasury during the early period of its 
 existence. 
 
426 HISTOEY OF PHYSICAL ASTEONOMY. 
 
 on the physical cause of the planetary movements, laboured under the 
 disadvantage of having only accessible to him the erroneous ideas of Kepler 
 on the principles of mechanical science. A remark, however, contained in 
 the letter just cited, will serve to show that he possessed a mind adequate 
 to detect the fallacy of such ideas, and to substitute others more in 
 accordance with nature in their stead. Kepler had supposed the planets 
 to be whirled round in their orbits by the transverse action of magnetic 
 fibres ; but as their revolutions round their axes seemed to him to offer 
 an impediment to this action, he had recourse to the strange supposition 
 of the exterior stratum alone of each planet being endued with a rotatory 
 motion. Horrocks remarked that such a supposition was totally unneces- 
 sary, since the rotatory motion of the planets could not impede their 
 motion of translation, any more than the rotation of a stone thrown with 
 the hand impedes the motion which it has acquired in the direction of the 
 impulse. 
 
 The following passages exhibit a distinct perception of the famous 
 inequality in the mean motions of Jupiter and Saturn arising from their 
 mutual disturbance. It may be remarked that, throughout the whole of 
 the sixteenth century and the first half of the seventeenth century, 
 the mean motion of Jupiter was increasing with great rapidity in virtue 
 of that inequality, while, on the other hand, the mean motion of Saturn 
 was undergoing a corresponding retardation. 
 
 Writing on the 3rd of June, 1637, he mentions that he had at length ob- 
 tained possession of the Rudolphine Tables. A comparison of them with 
 various modern observations convinced him that the mean motion of 
 Jupiter was in reality quicker than Kepler had made it. On the 19th of 
 January, 1638, he makes the same remark in nearly the same terms 
 (JEqualis motus Jovis est notabiliter velocior quam apud Keplerum). On 
 the 25th of July, 1638, he proposes to correct the 'motion of Jupiter by 
 adding 1 30' to the aphelion, and about % to the mean longitude. In a 
 letter dated September 29 of the same year, he states that the observations 
 of Jupiter made in the time of Waltherus agree with the most recent 
 observations in indicating, beyond all doubt, that the mean motion of the 
 planet is more rapid than it appeared to be from the Rudolphine Tables. 
 The quantity of the acceleration seemed to him to amount to I/ in ten 
 years. It was very certain, he added, that from the time of Tycho the 
 mean longitude of the planet was at least 4' or 5' greater than the tables 
 made it. On the 14th of September, 1639, he proposes to add I/ to the 
 mean longitude of Jupiter in the beginning of 1600, and 11' in the begin- 
 ning of 1700, with a proportional quantity in any intermediate period. In 
 order to show how nearly Horrocks arrived at the true acceleration, it may 
 be mentioned that the increments which the mean longitude of Jupiter ac- 
 tually received in the first half of the seventeenth century, during successive 
 periods of ten years, were 1' 22", 1' 20", V 18", l' 15", 1' 12". The time 
 when Horrocks lived was, in fact, exceedingly favourable for detecting the 
 great inequality of Jupiter and Saturn, on account of the rapidity with 
 which it was then developing itself*. In a letter dated July 30, 1640, 
 
 * The truth of this remark will be more apparent when it is stated that from 1800 to 
 1850 the accessions to the mean longitude of Jupiter, arising from the great inequality 
 during successive periods of ten years, were only 10". 8, 17". 0, 22". 9, 28". 5, and 
 34". 1. These results, as well as those of a similar nature in the text, are calculated from 
 the expression for the inequality given by Pontecoulant, ( Theorie Analytique du Systeme 
 du Monde, torn, iii., p. 450), which includes the terms depending on the fifth powers of 
 
HISTOKY OF PHYSICAL ASTKONOMY. 427 
 
 he still adheres to his previous conclusion. He proposes to add 5' to the 
 mean longitude at the beginning of 1640, and 6' at the beginning of 
 1650. Throughout the whole of the current century, the mean motion of 
 the planet seemed to him to be more rapid than it was according to the 
 Kudolphine Tables, the acceleration being equivalent to an increase in the 
 mean longitude of 1' in ten years. " Whether the acceleration will con- 
 tinue or not," says he, " I do not know; but between 1490 and 1590 the 
 mean motion was sensibly more rapid than it is now." He here seems to 
 hint at the possible periodicity of the phenomenon. 
 
 The retardation of Saturn's mean motion did not escape the sagacity 
 of Horrocks, although he does not seem to have retained such a firm hold 
 of the inequality as in the case of the corresponding acceleration of 
 Jupiter's mean motion. On the 3rd of June, 1637, he proposes to 
 subtract 4' from the mean longitude of Saturn at the beginning of 1600. 
 On the 15th of October, 1638, he writes that the observations of Saturn, 
 in the time of Waltherus, indicated the mean motion of the planet to 
 be slower than Kepler had made it in the Rudolphine Tables. On the 
 14th of September, 1639, he again alludes to the irregularity in the mean 
 motion of the planet. "Saturn, "he says, "seems to experience sometimes a 
 singular retardation in its motion. (Videlur Saturnus miram aliquam 
 aliquando habere motus sui retardationem.) He remarks, however, that 
 the phenomenon would occasion him greater annoyance were it not that 
 there was some consolation in being probably the first who discovered 
 it (nisi quod hoc aliquid solatii est, nos, credo, primos esse qui detegimus). 
 He requests Crabtree to watch the phenomenon carefully by making con- 
 stant observations of the planet. With respect to the true correction 
 to be applied to the Rudolphine Tables he was unable to pronounce a 
 positive opinion; "but if we discover anything hereafter," says he, "the 
 retardation of the planet will allow an easy correction of the Ephemerides." 
 
 In a letter dated July 25, 1638, he makes some conjectures relative 
 to the nature and movements of comets. He supposes them to be pro- 
 jected from the sun, and to move with a continually slower velocity as 
 they recede from that body, until at length they become stationary, and 
 then begin to return with accelerated speed, like the sine in the circle, 
 deflecting somewhat in the direction of the sun's rotation. He requests 
 Crabtree to send him Tycho Brahe s observations of comets, contained 
 in his Progymnasmata, in order that he might compare them with his 
 hypothesis. In a letter dated September 29, 1638, he states that the 
 observations of the comets of 1577 and 1590 confirmed his conjecture of 
 comets in general being projected from the sun. He supposes, in accord- 
 ance with Kepler's ideas of a whirling force, that they are subsequently 
 carried round the sun with a motion which is, in all probability, variable*. 
 
 On the 3rd of October, 1640, he announced to Crabtree that he had 
 undertaken the prosecution of a series of observations on the tides, in 
 order that, by the aid of experiment, he might be enabled to arrive at 
 some definite conclusions respecting their real nature. 
 
 the eccentricities and inclinations of the two planets, and also those due to the square of 
 the disturbing force. 
 
 * Wallis, in a letter to the Royal Society dated January 21 , 1664-5, states that Horrocks 
 made the comet to return to the sun in an elliptical figure, or very nearly so. According 
 to this hypothesis he traced the comet of 1577. He requests that the paper relative to 
 this comet, being in Horrocks' own handwriting, be carefully preserved (Birch, Hist. 
 Roy. Soc., vol. ii., p. 11). 
 
428 HISTORY OF PHYSICAL ASTRONOMY 
 
 On the 12th of December, 1640, he' expressed to his friend a strong 
 desire to obtain some of Gascoigne's measurements of the lunar dia- 
 meter*. He also announced to him that his observations of the tides 
 had already revealed to him many interesting particulars. They were 
 withal very regular, although subject to many strange inequalities hitherto 
 remarked by no person. He had only prosecuted his researches three months, 
 but he hoped that, by continuing his observations for a year, he should obtain 
 some valuable results f. In the same letter he entreats his friend to per- 
 severe in his astronomical pursuits, adding, that as soon as his own affairs 
 would permit, he purposed resuming his favourite studies. Alas ! ere an- 
 other month had elapsed, his noble spirit had fled from its mortal tenement. 
 
 It cannot fail to excite the admiration of the reader, that a youth of twenty- 
 two years of age should have exhibited in his researches such sagacity of 
 thought and fertility of invention, such enlightened and judicious views 
 on the various subjects which engaged his attention, and such unwavering 
 confidence in the resources of his own mind. Who can doubt that, if his 
 days had been more numerous, the history of physical science in the 
 seventeenth century would read very differently from what it now does. 
 Justly may it be affirmed, in the language of the illustrious editor of his 
 fragments, " Qiti enim tain paucis annis, auxiliis parvis, tantisgue obsitus 
 difficultatibus tantos progressus facerat ; quid nonfecisset, si Deus hucusque 
 vitam protelavisset ! si necessariis omnibus instructus, doctorum etiam 
 consortio, adjutus fnisset!" 
 
 The utility of the transits of the inferior planets in furnishing an accu- 
 rate method of determining the value of the solar parallax, was first 
 pointed out by James Gregory, the celebrated mathematician, in his 
 treatise entitled " Optica Promote," which was published at London in 
 1063. As the credit due to the original suggestion of this method has 
 been generally ascribed to Halley, it may not be out of place to cite 
 the passage in which Gregory alludes to it. In a scholium to the eighty- 
 seventh problem, the object of which is to determine the parallaxes of two 
 planets by observations of their conjunctions, he makes the following 
 statement: "This problem has a very beautiful application, although 
 perhaps laborious, in observations of Venus or Mercury when they obscure 
 a small portion of the sun ; for by means of such observations the parallax 
 of the sun maybe investigated |. It would be impossible to establish 
 the claims of Gregory to priority of discovery upon a more unequivocal 
 basis than is afforded by this passage. Halley 's attention was first 
 directed to the subject on the occasion of his observation of the transit 
 of Mercury in 1677, that is to say, fourteen years after the publication 
 
 * Gascoigne was the original inventor of the micrometer, as will be shown in the next 
 chapter, and it is to the results obtained by the use of this instrument that Horrocks here 
 alludes. Crabtree had just returned from a visit to Gascoigne in Yorkshire, and one of 
 the principal objects of Horrocks' contemplated visit to his friend was to obtain an account 
 of the very remarkable improvements in practical astronomy which Gascoigne had re- 
 cently effected. See, in the next chapter, an extract of a letter from Crabtree to Hor- 
 rocks, in which there is contained an interesting allusion to the micrometer, which 
 Gascoigne showed Crabtree on the occasion of this visit. 
 
 'f- Horrocks appears to have been the first person who undertook the prosecution of a 
 continuous course of observations of the tides, for the express purpose of obtaining a 
 series of facts which might form the groundwork of a philosophical investigation of the 
 subject. 
 
 J Optica Promota, p. 130. The words in the original are : " Hoc problema pulcher- 
 rimum habet usum, sed forsan laboriosum, in obscrvationibus Veneris vel Mercurii parti- 
 culam solis obscurantis; ex talibus enim solis parallaxis investigari poterit." 
 
HISTORY OF PHYSICAL ASTRONOMY. 429 
 
 of the Optica Promota*. Whatever development the method acquired 
 from him, cannot affect the merits of the original discoverer. Captain 
 Smyth, while vindicating the just claims of Gregory, has truly remarked that 
 Halley needs no borrowed plumes. Even in the present instance it 
 must be admitted, that the ability with which he expounded the pe- 
 culiar advantages attending the determination of the solar parallax by 
 observations of the transits of Venus, the earnestness with which he re- 
 commended the practical application of the method, and the weight of 
 his authority on questions relating to astronomical science, were mainly 
 instrumental in inducing the different governments of Europe to adopt 
 those liberal proceedings for observing the transits of J761 and 1769, 
 which have led to a more accurate knowledge of the dimensions of the 
 solar system than could otherwise be hoped for. 
 
 The physical appearances noticed during the transits of Venus which 
 happened in the last century have given rise to a good deal of speculation, 
 but it must be admitted that the conclusions arrived at upon this point 
 cannot be regarded as altogether satisfactory. The most remarkable of 
 such appearances was that witnessed when the planet was just wholly 
 within the sun's limb. It was found on the occasion of each of the tran- 
 sits of 1761 and 1769, that the interior contact of the planet with the sun 
 did not take place regularly at the ingress, the planet appearing, for some 
 time after it had wholly entered upon the solar disk, to be connected with 
 the sun's limb by a dark ligament. A similar phenomenon was observed 
 at the egress of the planet. It was also found that, even after the planet 
 had wholly separated from the sun's limb, it did not acquire its round form 
 till after the lapse of several seconds. In order that the reader may form 
 a more accurate conception of these phenomena, it may not, perhaps, be 
 unacceptable to cite in detail a few of the observations relating to them. 
 
 Mr. Hirst, who observed the transit of 1761 at Madras, states that "at 
 the total immersion, the planet, instead of appearing truly circular, re- 
 sembled more the form of a bergamot pear, or, as Governor Pigott then 
 expressed it, looked like a nine-pin: yet the preceding limb of Venus 
 was extremely well denned." With respect to the end of the transit he 
 remarked, " that the planet was as black as ink, and the body truly 
 circular, just before the beginning of the egress, yet it was no sooner in 
 contact with the sun's preceding limb, than it assumed the same figure 
 as before at the sun's subsequent limb : the subsequent limb of Venus 
 keeping well denned and truly circular, "f 
 
 A similar appearance was observed by Lalande at Paris, by Bergman 
 at Upsal, and also by several other individuals. 
 
 Dr. Maskelyne, who observed the transit of 1769 at Greenwich, gives 
 the following description of a phenomenon of a similar nature witnessed 
 by him at the ingress of the planet : 
 
 " The irregularity of Venus's circular figure was disturbed towards the 
 place where the internal contact should happen, by the addition of a pro- 
 
 * James Gregory, one of the most eminent mathematicians of the seventeenth century, 
 was born at Aberdeen in 1639, and died at Edinburgh in 1675, at the early age of 
 thirty-six years. He was only twenty-four years old when he published the Optica 
 Promota, which, besides the important remark alluded to in the text, contained also 
 the original explanation of the principle of the reflecting telescope. Halley's earliest 
 allusion to the utility of observations of the transits of the inferior planets in determining 
 the solar parallax, is contained in his Catalogus SteUarum Australium, published in 
 1679. He subsequently returned to the subject in the volumes of the Philosophical 
 Transactions for 1694 and 1716. 
 | Phil. Trans., 1761, p. 396. 
 
430 HISTORY OF PHYSICAL ASTRONOMY. 
 
 tuberance, dark like Venus, and projecting outwards, which occupied a 
 space upon the sun's circumference which bore a considerable proportion 
 to the diameter of Venus. Fifty-two seconds before the thread of light 
 was formed, Venus 's regular circumference (supposed to be continued as 
 it would have been without the protuberance) seemed to be in contact with 
 the sun's circumference, supposed also completed. Accordingly, from 
 this time, Venus's regular circumference (supposed denned in the manner 
 just described) appeared wholly within the sun's circumference, and it 
 seemed, therefore, wonderful that the thread of light should be so long 
 before it appeared, the protuberance appearing in its stead. At length, 
 when a considerable part of the sun's circumference (equal to one-third 
 or one-fourth of the diameter of Venus) remained still obscured by the 
 protuberance, a fine stream of light flowed gently round it from each side, 
 and completed the same in the space of three seconds of time ; and Venus 
 appeared wholly within the sun's lucid circumference. But the protube- 
 rance, though diminished, was not taken away till about twenty seconds more ; 
 when, after being gradually reduced, it disappeared, and Venus's circular 
 jigure was restored"* 
 
 Dr. Bevis states in the account of his observations that " the planet 
 seemed quite entered upon the disk, her upper limb being tangential to 
 that of the sun ; but instead of a thread of light, which he expected im- 
 mediately to appear between them, he perceived Venus to be still con- 
 joined to the sun's limb by a slender kind of tail, nothing near so black 
 as her disk, and shaped like the neck of a Florence flask. The said tail 
 vanished at once ; and^/br a few seconds after, the limb of Venus, to which 
 it had been joined, appeared more prominent than her lower part, somewhat 
 like the lesser end of an egg, but soon resumed its rotundity. "f 
 
 The Rev. Mr. Hirst thus describes the appearance presented during 
 the transit : " The same phenomena of a protuberance which I observed 
 at Madras in 1761, at both internal contacts, I observed again at this last 
 transit. At both times the protuberance of the upper edge of Venus 
 diminished nearly to a point before the thread of light between the con- 
 cave edge of the sun and the concave edge of the planet was perfected, 
 when the protuberance broke off from the upper edge of the sun : but 
 Venus did not assume its circular form till it had descended into the solar 
 disk some distance^. 
 
 Mr. Dunn, who observed the transit at Greenwich, remarks that "he 
 saw the planet held as it were to the sun's limb by a ligament formed of 
 many black cones whose bases stood on the limb of Venus, their vertices 
 pointing to the limb of the sun." 
 
 Mr. Pigott states that Venus, before she separated from the sun, was 
 considerably stretched out towards his limb, which gave the planet nearly 
 the form of a pear ; and even after the separation of the limbs, Venus was 
 twelve or more seconds before she resumed her rotundity "\\ 
 
 With respect to the physical cause of the phenomena above referred to, 
 the most probable hypothesis of their origin is that which attributes them 
 to the influence of irradiation. Lalande first shewed that the dark liga- 
 ment connecting the limbs of the planet and the sun might be satisfacto- 
 rily accounted for upon this principle IT. The most consistent explanation 
 that can be given of the protuberance on the limb of the planet, when it 
 appeared wholly separate from the sun's limb, is that proposed by Prof. 
 
 * Phil. Trans., 1768, p. 358. f Ibid., 1769, p. 190. Ibid., p. 229. 
 
 Ibid., 1770, p. 70. || Ibid., p. 262. f Mem. Acad. des Sciences, 1770, p. 409. 
 
HISTORY OF PHYSICAL ASTRONOMY. 431 
 
 Powell in the analogous case of annular eclipses. The appearance 
 noticed by Mr. Dunn seems to be totally inexplicable, unless it be 
 assimilated to the dark lines witnessed during the annular eclipse of 
 1836, and other similar occurrences. 
 
 It was remarked by several observers of the transits of 1761 and 1769, 
 that both at the ingress and egress, the portion of the limb of the planet 
 that was off the sun, was visible by means of a faint light surrounding it 
 in the form of a ring. La Chappe, who observed the transit of 1761 at 
 Tobolsk, in Siberia, states that the light of the ring was of a very deep 
 yellow near the body of the planet, but that it became more brilliant 
 towards the outer border *. MM. Stromer, Mallet, Bergman, andMelander, 
 who observed the same transit at Upsal, remarked that when three-fourths 
 of the planet's limb had entered upon the sun, the remaining fourth was 
 visible by means of a faint ring which* appeared around itf. A similar 
 phenomenon was observed on the same occasion by Wargentin at Stock- 
 holm, by Planman at Cajainbourg, and in several other instances J. 
 
 Dr. Maskelyne, who observed the ingress of Venus upon the sun's disk 
 at Greenwich on the occasion of the transit of 1769, states that, when the 
 planet was little more than half entered upon the sun, he saw her whole 
 circumference completed, by means of a vivid but narrow and ill-defined 
 border of light, which illuminated that part of her circumference that was 
 off the sun. He adds that it disappeared two or three minutes before the 
 internal contact . A similar phenomenon was witnessed during the same 
 transit, by Wales and Dymond at Hudson's Bay [|, by Pingre and De 
 Fleurieuat Cape Francis in the Island of St. Domingo 11, and by various 
 other observers in different places. 
 
 Several of the observers of the transits of 1617 and 1769 remarked 
 that, when Venus was wholly entered upon the sun, there appeared a faint 
 ring around her limb. Dunn, in his account of the transit of 1769, 
 describes it as a lucid annulus about five or six seconds in breadth, some- 
 what dusky towards the limb of the planet, and at the outer margin tinged 
 a little with blue *#. Mr. Hitchins, alluding to the same phenomenon, 
 states that it was excessively white and faint, and that it ivas brightest 
 towards the body of the planet \\. Nairne asserts that it appeared brighter 
 and whiter than the body of the sun JJ. 
 
 It is worthy of remark that, in general, those individuals who observed a 
 faint light around the part of the limb of Venus that was off the sun, on the 
 occasion of the transits of 1761 and 1769, do not seem to have perceived the 
 complete annulus around the limb of the planet when it was wholly entered 
 upon the sun's disk. On the other hand, most of those observers who 
 witnessed the latter phenomenon do not make any allusion to the former 
 as having been seen by them. The observations of La Chappe, Maskelyne, 
 and several other individuals, are very clear upon this point. It would 
 seem, therefore, that the two phenomena are not of the same nature. W T ith 
 respect to the physical origin of either, no satisfactory explanation has yet 
 been offered. The appearance noticed when the planet was only partially 
 on the sun, has a strong analogy to that alluded to by M. Arago and 
 several other persons in France relative to the visibility of the whole of 
 the moon's limb during the progress of the total eclipse of the sun of 
 
 * Mum. Acad. des Sciences, 1761, p. 363. t Ibid., p. 364. J Ibid. 
 
 Phil. Trans., 1768, p. 357. || Ibid., 1769, p. 482. ^ Ibid., 1770, p. 498. 
 
 ** Ibid., 1770, p. 71. -ft Ibid., 1768, p. 363. \\ Ibid., p. 364. 
 
432 HISTORY OF PHYSICAL ASTRONOMY. 
 
 July 8, 1842. If it be assumed that the atmospheric light diminishes 
 with such rapidity from the sun's limb that the light of the solar atmo- 
 sphere forms an aliquot fraction of it at a very small distance from the limb, 
 it may then be inferred, as in that case,.that the visibility of the planet's 
 limb arises from the obscurity of its surface, when contrasted with the 
 brightness of the ground upon which it appears projected. Such a supposi- 
 tion, however, is by no means probable. The faint ring that was seen by 
 some observers around the planet's limb when it had wholly entered 
 upon the sun's disk, has been supposed to indicate the existence of an 
 atmosphere about the planet, but the various statements respecting its 
 appearance are not sufficiently consistent with each other to warrant 
 such a conclusion, although at the same time ib seems to be justified by 
 other considerations, to which allusion has already been made in a former 
 chapter. 
 
 Sometimes the planets are eclipsed in consequence of the moon passing 
 between them and the earth. The earliest recorded phenomenon of this 
 nature is an occultation of Mars by the moon, which Aristotle makes 
 mention of in one of his works. He states that when the moon was half- 
 full, the planet entered behind the limb on the unenlightened side, and 
 subsequently emerged on the bright side *. Kepler calculated the date 
 of this occultation, and found that it occurred on the night of the 4th of 
 April in the year 357 A.c. f. The rapid and tortuous motion of the moon 
 produces occasional occultations of this nature, but they are not of much 
 importance to the astronomer. It was expected that the circumstances 
 accompanying such occultations'would serve to throw light upon the much- 
 disputed question of the existence of a lunar atmosphere, but no such 
 advantage has hitherto been derived from them. 
 
 The occultation of a star by the moon is a phenomenon which, although 
 of frequent occurrence, never fails to prove interesting. When the dark 
 limb of the moon comes up to the star, the occultation is invariably found 
 to take place instantaneously, whence it is manifest that the apparent 
 magnitude of the star must be excessively small. The effect in such cases 
 is most striking when the whole body of the moon is invisible, as occa- 
 sionally happens when she is totally eclipsed. A phenomenon of this 
 kind was witnessed by Wargentin during the lunar eclipse of May 18, 
 1761, to which allusion has already been made. Previous to the total 
 disappearance of the moon, he perceived a star near her eastern limb, 
 which seemed to be about to undergo occultation. He therefore followed 
 it with great attention until at length, at 10 h 52 m 39 s , when even the 
 faintest trace of the moon had ceased to be visible, it vanished in less than 
 the twinkling of an eye j. 
 
 Occultations of stars by the moon serve to fix the apparent position of 
 the latter body with great accuracy, and in consequence they have proved 
 very serviceable in correcting the elements of her motion. For a similar 
 reason they are of great use in determining the differences of longitude of 
 places on the earth's surface. 
 
 A singular phenomenon of a physical nature is sometimes observed on 
 the occasion of an occultation of a star. When the limb of the moon has 
 come up to the star, the latter appears to advance upon the moon's disk, 
 continuing visible in this manner for several seconds previous to its oc- 
 
 * De Caolo., lib. ii., cap. 12. f Ad. Vitellionem Paralipomena, p. 307. 
 
 \ " Oculi ictu citius" (Phil. Trans., 1761, p. 210). 
 
HISTOBY OF PHYSICAL ASTRONOMY. ' 433 
 
 cultation* . No satisfactory explanation of this strange anomaly has hitherto 
 been advanced by any person. One of the most recent, as well as one of 
 the most specious modes of accounting for its physical origin is due to 
 Prof. Stevelly. According to the hypothesis proposed by him, the phe- 
 nomenon is purely an effect of the diffraction of light. Newton had 
 shewn by experiment that the rays of light which pass very near the 
 edge of a body are bent away from it, so as for a short distance to describe 
 curves which are convex with respect to it. Prof. Stevelly conceives the 
 visible contour of the moon to be such a diffracting edge to the slender 
 beam of light which reaches the eye from a fixed star. Under such cir- 
 cumstances, it is manifest, from the convexity of the course pursued by 
 the beam of light while under the influence of the diffracting force, that 
 its final direction when it enters the eye ought, if produced toward the 
 moon's surface, to fall within her limbf. 
 
 If the above explanation were true, the phenomenon ought to be visible 
 on the occasion of every occultation of a star by the moon. Such, how- 
 ever, is far from being the case. This is a defect which may be said to 
 characterise in a greater or less degree all the explanations that have 
 hitherto been offered relative to a phenomenon, which is manifestly 
 an optical illusion, although its true source is not easy to be discovered. 
 
 Sometimes the planets occult one another in the course of their motion 
 round the sun. Such phenomena, however, are manifestly of very rare 
 occurrence. Kepler states that on the 9th of January, 1591, Msestlin 
 and himself witnessed an occultation of Jupiter by Mars. The red colour 
 of the latter on that occasion plainly indicated that it was the inferior 
 planet \. He also mentions that on the 3rd of October, 1590, Msestlin 
 witnessed an occultation of Mars by Venus. In this case, on the other 
 hand, the white colour of Venus afforded a clear proof that she was the 
 nearer of the two planets to the earth . It is to be borne in mind that 
 these observations were made before the invention of the telescope, so that 
 it is doubtful whether in either of these cases the one planet was actually 
 superposed above the other, for the peculiar colour of the light might 
 arise simply from the predominating influence of the brighter planet ||. 
 
 Sometimes there happen occultations of the fixed stars by the planets. 
 On the 1st of October, 1672, the planet Mars eclipsed a star in the con- 
 stellation Aquarius. Cassini, who was then engaged in researches on the 
 parallax of Mars, had previously resolved to observe this interesting phe- 
 nomenon, but he was prevented by cloudy weather from effecting his ob- 
 ject. Phenomena of a similar nature have occurred in more recent times, 
 but no physical consequences have been deduced from them. 
 
 * See a collection of observations of this nature in a paper by Sir James South on 
 the occultation of 3 Piscium by the moon (Mem. Ast. Soc., vol. iii., p. 303, et seq). 
 
 f Brit. Assoc. Rep., 1845. (Trans, of the Sections, p. 5.) 
 
 J Ad Vitellionem Paralipomena, p. 305. Ibid., p. 305. 
 
 II For an account, by Dr. Bevis, of an occultation of Mercury by Venus, on May 17, 
 1737, see the Philosophical Transactions for 1737, p. 394. On this occasion, the inte- 
 resting phenomenon alluded to by Kepler does not seem to have been remarked by any 
 observer. 
 
 F F 
 
434 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 CHAPTER XVIII. 
 
 Early Methods of observing the Celestial Bodies Instruments of the Greek As- 
 tronomers Accurate Principles of Observation first employed by the Astronomers of 
 
 the Alexandrian School. Improvements effected by Hipparchus. Ptolemy substitutes 
 the Quadrant for the Complete Circle. Arabian Astronomers. The Method by 
 which they indicated the Time of an Observation. Revival of Practical Astronomy in 
 
 Europe Labours of Waltherus. Tycho Brahe. Landgrave of Hesse. Hevelius. 
 
 Close of the Tychonic School of Observation. Observatory of Copenhagen estab- 
 lished. The Pendulum applied to clocks by Huyghens. The Royal Society of 
 London, and the Academy of Sciences of Paris, established. Invention of the Micro- 
 meter. Application of the Telescope to divided instruments Observatories of Paris 
 and Greenwich established. Labours of Roemer. Transit Instrument invented. 
 The use of Circular Instruments for taking Altitudes introduced. Labours of Flam- 
 steed and Halley. Royal Observatory of Paris. Commencement of the era of 
 accurate observation. Bradley. Lacaille. Mayer. Maskelyne. Pond. Airy. 
 Reduction of Planetary and Lunar Observations. Present state of Practical As- 
 tronomy. 
 
 THE history of astronomy does not exhibit a more interesting picture 
 than that which represents the progress of the art of observation, from the 
 rude essays of early ages to the refinement and precision which cha- 
 racterise its present state of advancement. The Chaldeans, to whom the 
 origin of astronomy is usually ascribed, do not seem to have attained any 
 excellence in this important department of the science. Their observa- 
 tions of eclipses of the moon, as cited by Ptolemy in the Syntaxis, are as 
 rude as can possibly be imagined. The time is expressed only in hours, 
 and the quantity eclipsed in terms of the half and quarter of the moon's 
 diameter. Herodotus states that the Greeks were indebted to the Baby- 
 lonians for the pole, the gnomon, and the division of the day into twelve 
 hours. The pole seems to have been a concave hemispherical sun-dial, 
 having a vertical style in the centre, by means of which the interval in- 
 cluded between sunrise and sunset, for each day throughout the year, was 
 divided into twelve equal parts. The construction of such an instrument 
 does not require any acquaintance with the principles of trigonometry or 
 dialling; it merely implies a knowledge of the uniform motion of the 
 celestial sphere. The gnomon, besides being an imperfect instrument for 
 astronomical purposes, is limited in its application. It is probable that, 
 by the use of it, the Chaldeans succeeded in obtaining an approximation to 
 the length of the solar year, but there is not the smallest reason to sup- 
 pose that they employed it in determining any other of the fundamental 
 facts of astronomy. Indeed, they do not seem to have made observations 
 at all for the purpose of forming materials to serve as the groundwork of 
 future reasoning. They simply contented themselves with noting the 
 more remarkable phenomena as they occurred, and hence deducing a few 
 rough conclusions of a general nature. It is manifest that so long as 
 astronomy continued to be cultivated in this manner, it could not attain a 
 high state of perfection. 
 
 The Greek philosophers were too much preoccupied with the idea of 
 arriving at final conclusions on all subjects by the mere force of abstract 
 discussion, to devote their attention to the prosecution of astronomical 
 observations. It would appear, however, that by comparing together the 
 Chaldean records of eclipses, extending over a ]ong succession of ages, 
 some of the earlier of the Greek mathematicians ascertained with con- 
 
HISTORY OF PHYSICAL ASTRONOMY. 435 
 
 siderable accuracy several periods relating to the motion of the moon. The 
 earliest astronomical observation recorded as having been made by the 
 Greeks previous to the establishment of the Alexandrian School, is a deter- 
 mination of the summer solstice by Meton, in the year 430 A.C. The 
 instrument, termed a heliometer, which was used by Meton on this oc- 
 casion, was, in all probability, no other than a modification of the gnomon. 
 The date of this solstice has been chosen for the epoch of the Metonic 
 cycle of nineteen years, which is employed in regulating the occurrence of 
 religious festivals. 
 
 A new era commenced in the history of astronomical observation when 
 Alexandria became the capital of the civilised world. Under the liberal 
 patronage of the Ptolemies a magnificent building was erected, in which 
 were deposited circular instruments for determining the positions of the 
 heavenly bodies, and every facility was given to astronomers for prosecuting 
 a continuous series of observations. Timocharis and Aristillus are the 
 earliest individuals mentioned in connexion with this school. These astro- 
 nomers appear to have flourished about the year 300 A.C. Ptolemy cites 
 several of their observations in the Syntaxis. Among these are the de- 
 clinations of a few of the principal stars. It is evident that such results 
 could not be established without a knowledge of the position of the 
 equator in the celestial sphere. It does not appear that the earlier astro- 
 nomers of the Alexandrian School were acquainted with any method for 
 determining the right ascensions of the stars. At any rate Ptolemy does 
 not cite any observations of this kind as having been made by them. Indeed, 
 there are no grounds for supposing that they knew the exact position of 
 the equinoctial colure upon which the right ascension of a star depends. 
 It is a remarkable fact, however, that Hipparchus was enabled by means 
 of certain eclipses of the moon, observed by Timocharis, to determine the 
 place occupied by the equinox among the stars in the days of that astro- 
 nomer. Thus, Ptolemy states that Hipparchus having compared several 
 eclipses of the moon, observed very accurately by himself, with other more 
 ancient eclipses, observed by Timocharis, found that while the bright star, 
 Spica Virginis, preceded the Autumnal equinox 8 in the time of the last- 
 mentioned astronomer, it preceded the same equinox only 6 in his own 
 time *. No account whatever is given of the process by which these 
 interesting results were arrived at. 
 
 * Syntaxis, lib. vii., cap. ii. With respect to the mode in which Hipparchus determined 
 the place of the equinox by means of his own observations of eclipses of the moon, it was 
 doubtless the same as that which will be presently alluded to in the text. But it is diffi- 
 cult to imagine by what process he was enabled to deduce a similar result from the obser- 
 vations of Timocharis, since there are no grounds for supposing that the latter astronomer 
 possessed an intrument for measuring the difference of the right ascensions of two 
 celestial bodies. It is probable that if a bright star happened to be very near the moon at 
 the time of an eclipse, its position in the direction of the zodiac with respect to that body 
 was roughly determined with the instrument employed in measuring the declinations of 
 the stars, and the result recorded as part of the observation of the eclipse. It is not 
 difficult to conceive that an instrument composed of a circle fixed in the plane 
 of the equator, and another circle of equal magnitude moveable about its poles, 
 might serve for the approximate measurement of the difference of the right ascensions of 
 two celestial bodies situate very near the equator. The earlier astronomers of the Alex- 
 andrian School, in all probability, did not contemplate any definite object in noting the po- 
 sitions of the stars in the vicinity of the moon during the eclipses of that body. Indeed, 
 it would have been impossible to deduce the place of the equinox among the stars from 
 such results, even if they had been accurately determined with the astrolabe ; for the 
 place of the moon, with respect to the equinox, could not have been ascertained without 
 solar tables ; but there is not the smallest reason to suppose that astronomers were ac- 
 
 F F 2 
 
436 HISTOKY OF PHYSICAL ASTEONOMY. 
 
 We owe to Eratosthenes, another of the astronomers who observed at 
 Alexandria, the earliest determination of one of the most important 
 elements of astronomical science. This astronomer is said to have mea- 
 sured the distance between the tropics, and to have found it to be equal 
 to ^j. parts of the circumference of the circle. This gives 23 51' 19".5 
 for the obliquity of the ecliptic a result which exhibits a remarkable agree- 
 ment with that assigned by the theory of gravitation, as the true value of 
 the element, in the age of Eratosthenes. 
 
 It is manifest that* neither the distances of the stars from the equator, 
 nor the obliquity of the ecliptic, could have been determined even roughly 
 without the use of instruments. The information which Ptolemy has 
 supplied upon this subject is exceedingly scanty. In treating of the ob- 
 liquity of the ecliptic, he describes an instrument for determining the 
 meridional altitude of the sun. It was composed of two concentric circles, 
 placed exactly in the plane of the meridian, one of which revolved within 
 the other about their common centre. The inner circle carried two small 
 prisms attached to the opposite extremities of a diameter, and when the 
 sun was on the meridian, it was turned round until the shadow of the 
 upper prism fell exactly upon the lower one. An index, affixed to the 
 latter, then marked upon the graduated limb of the outer circle the 
 meridional altitude of the sun *. It was, in all probability, by means of 
 an instrument of this construction that Eratosthenes determined the 
 altitude of the sun at each of the solstices, and hence deduced the distance 
 between the tropics, the half of which distance gives the obliquity of the 
 ecliptic. 
 
 From the observed altitudes of the sun at the summer and winter solstices, 
 it was easy to infer the position of the equator in the celestial sphere. In 
 order to ascertain the passage of the sun through the equinox, a circular ring 
 of metal was disposed in the plane of the equator, and the shadow of the 
 upper half was watched until it fell upon the inner or concave surface of 
 the lower half. As the shadow did not cover the entire breadth of the 
 surface on which it fell, it is manifest that the instant when the surface was 
 equally illuminated on each side of the shadow, indicated the presence of 
 the sun in the plane of the equator. Ptolemy cites a passage from Hip- 
 parchus, in which that astronomer refers to two circles of this description 
 that were used at Alexandria for observing the passage of the sun through 
 the equinoxes. They were constructed of copper, and were placed in the 
 square portico of the Museum f . 
 
 Ptolemy has given no account of the instrument by means of which 
 the earlier astronomers determined the distances of the stars from 
 the equator. It in all probability resembled, in principle, the astrolabe 
 which Hipparchus employed at a subsequent period in observing the stars, 
 only it was more simple in construction, since the use of it was confined 
 to one measurement relative to each star. In fact, if we suppose a circle 
 to be placed in the plane of the equator, and another circle of equal mag- 
 nitude to be movable around its poles, the distance of each star from the 
 equator would be ascertained by turning the latter circle round until the 
 star appeared in its plane, and then noting the place of the star on its 
 divided limb. 
 
 Whatever credit may be due to the earlier astronomers of the Alex- 
 
 quainted with any method of reducing the motion of the sun to calculation until Hippar- 
 chus undertook his researches on the subject. 
 
 * Syntaxis, lib. i., cap. x. Ibid., lib. Hi., cap. ii. 
 
HISTORY OF PHYSICAL ASTRONOMY. 437 
 
 andrian School for the sound principles of observation which they appear 
 to have practised, as well as for the care with which they determined some 
 elements of fundamental importance, it is to Hipparchus alone that the 
 establishment of astronomy, as a science of calculation based upon ob- 
 served facts, is to be attributed. The mode in which he availed himself 
 of the results of observation, in the execution of this great work, is in the 
 highest degree interesting. One of the most important elements of astro- 
 nomical science is the length of the tropical year. Hitherto it had been 
 supposed to consist exactly of 365^ days. Hipparchus, however, having 
 compared a solstice observed by himself with one observed by Aristarchus 
 147 years earlier, found that the sun arrived in the same place 12 hours 
 sooner than he ought to have done, if the year had consisted exactly of 
 365^ days. He, therefore, concluded that the true length of the year was 
 less than this quantity by -3-^0^ part, and consequently he determined it 
 to be equal to 365 d 5 h 55 m 12 s . This is the earliest example, in the 
 history of astronomy, of the correction of a fundamental fact of the sci- 
 ence by the comparison of two distant observations. The result obtained 
 by Hipparchus on this occasion exceeds the true length of the tropical 
 year by about six minutes ; but the magnitude of the error is not to be 
 wondered at, when the difficulty of determining the exact instant of the 
 solstice is taken into account*. 
 
 Another beautiful example of the simplicity of the means employed by 
 Hipparchus in establishing the basis of his theories, is exhibited in his re- 
 searches on the elements of the solar orbit. Having found that an interval 
 of 94 d 12 h elapsed between the vernal equinox and the summer solstice, 
 while only 93 d 12 h were included between the summer solstice and the 
 autumnal equinox, he from these two facts deduced the eccentricity of the 
 solar orbit, and also the place of the apogee. His mode of deriving the 
 analogous elements of the lunar orbit from three observed eclipses of 
 the moon, is also equally worthy of admiration. 
 
 This illustrious astronomer did not content himself with merely ob- 
 serving the moon on those occasions during which she was eclipsed, and 
 determining her place in the heavens by means of the sun, which was then 
 opposite to her. He also observed her position in other parts of her 
 orbit by means of the astrolabe, an instrument of which he is supposed, 
 with great probability, to have been the original inventor f. Ptolemy 
 
 * The equinoxes admit of more accurate determination than the solstices, but there 
 were no early observations of this kind accessible to Hipparchus. He did not fail, how- 
 ever, to observe several equinoxes with great care, in order that the results might serve as 
 useful materials, at some future period, for the advancement of astronomical science. Pto- 
 lemy, coming 160 years after Hipparchus, might have deduced a further correction to the 
 length of the tropical year, but he has sadly damaged his reputation as an observer by his 
 researches on this subject. Lalande, however, by comparing 9 equinoxes determined by 
 Hipparchus, with the observations of modern astronomers, has obtained, 365 d 5 h 48 48 s 
 for the length of the tropical year; a result which does not perhaps differ one second from 
 the true value. (Mem. Acad. des Sciences, 1782, p. 249.) 
 
 f Certain passages in the works of Pliny and several other ancient writers, concur 
 in supporting this assertion. But, indeed, apart from all positive statements, there is a 
 strong presumption that Hipparchus was the inventor of the astrolabe, since it is almost 
 impossible to conceive that it could be of any service to astronomy previous to his time. 
 Thus, one of the objects of the astrolabe was to determine the longitude of the moon 
 relative to the sun in different parts of her orbit ; but no such observations were made by 
 the earlier astronomers, since they were unacquainted with any theory of the moon's 
 motion, and therefore had no obvious motive for observing that body except in eclipses. 
 Another object of the astrolabe was to determine the difference of the right ascensions 
 
438 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 has given a description of the astrolabe in the beginning of the fifth 
 book of the Syntaxis. It was used for the purpose of determining the 
 latitude of a celestial body, and its longitude relative to another body, 
 with which it was compared, whose absolute longitude was known. Two 
 equal circles, whose planes were perpendicular to each other, were firmly 
 fastened together, and were so disposed that the one represented the 
 celestial ecliptic, and the other the solstitial colure. At the points of the 
 solstitial circle, corresponding to the poles of the ecliptic, there were 
 placed two cylinders, which projected both within and without the circle. 
 To the outer cylinders was adapted a movable circle of latitude, the in- 
 terior of which coincided exactly with the exterior of the solstitial circle. 
 A similarly movable circle was adapted to the inner cylinders, which was 
 so constructed as to be embraced exactly by the concave surface of the 
 solstitial circle. The whole machine was made to turn round the two 
 points in the solstitial colure corresponding to the poles of the equator, 
 and its position was adjusted by directing the axis of revolution to the 
 poles of the celestial equator. 
 
 When it was required to determine the position of a celestial body 
 with this instrument, by means of another body whose position had been 
 already ascertained, the exterior, circle was made to revolve until the latter 
 body appeared in its plane, and the interior circle was similarly directed 
 to the body whose position was to be found. The distance between these 
 two circles, measured upon the ecliptic, then gave the difference of the 
 longitudes of the two bodies, and the distance of the second body from 
 the ecliptic, measured upon the interior circle, gave its latitude *. 
 
 The astrolabe thus constructed served to determine the position of a 
 celestial body by means of its longitude and latitude. It is manifest that, 
 by placing a circle in the plane of the equator, the same object might be 
 accomplished with still greater facility by observing the right ascension 
 and declination of the body Hipparchus must have used the astrolabe in 
 this form in the early part of his career, since it is by means of their right 
 ascensions and declinations that he originally indicated the places of the 
 stars. He was doubtless induced to abandon this practice upon his 
 discovery of the precession of the equinoxes, since an obvious advantage 
 then appeared to result from the designation of the place of a star by its 
 longitude and latitude. 
 
 Ilt does not appear that regular observations of the moon were made by 
 any astronomer previous to Hipparchus. The earlier observers confined 
 themselves to notices of eclipses and occupations, and it was by an exami- 
 nation of records of the former class of phenomena, extending over a long 
 succession of ages, that the Greek mathematicians arrived at those secular 
 periods relative to the moon's mean motion, which Ptolemy has alluded to 
 in the Syntaxis. Hipparchus also, as has been already mentioned, de- 
 duced the elements of the lunar orbit from observations of eclipses, and 
 so long as he confined his researches on the moon's motion to her syzygees, 
 
 or longitudes of two stars. Such observations would have been of no value unless it had 
 been possible, in each case, to ascertain also the absolute place of either of the stars with re- 
 spect to the equinox. This, however, could not be effected without the use of solar tables 
 (at least according to any method known in ancient times), and such were not available to 
 the earlier astronomers of the Alexandrian School, since Hipparchus was the first who 
 established the theory of the sun's apparent motion. 
 
 * The place of the star upon the interior circle of latitude was determined by means 
 of a smaller concentric circle revolving in the same plane, which was furnished with two 
 projecting pinnules diametrically opposite to each other. 
 
HISTORY OF PHYSICAL ASTRONOMY. 439 
 
 he found a satisfactory agreement between the results of theory and those 
 of observation. But when he was enabled by means of the astrolabe to 
 observe the position of the moon in other parts of her orbit, and more 
 especially in the quadratures, he detected a series of discordances between 
 her actual and computed places, which seemed irreconcilable with the 
 theory of her motion as established by him. The true explanation of 
 these anomalies was reserved for Ptolemy ; but it must be borne in mind 
 that Hipparchus first detected their existence, and that he also executed 
 a great number of the observations which served as the basis of Ptolemy's 
 researches on the subject*. 
 
 Hipparchus did not fail to make numerous observations of the planets, 
 which at a subsequent period formed precious materials to Ptolemy in 
 establishing the theory of their movements. But the most remarkable 
 result which crowned the labours of this great astronomer was his dis- 
 covery of the precession of the equinoxes. It was doubtless with the 
 view of enabling posterity to arrive at a more accurate knowledge of this 
 singular phenomenon, that he conceived the grand design of determining 
 the positions of all the stars visible in the firmament, so as to give a 
 faithful representation of the celestial sphere as it appeared in his time. 
 It was necessary for this purpose to determine the exact place of either 
 of the equinoxes among the stars, but a serious obstacle stopd in the way 
 of effecting this object. The position of the equinox in the celestial 
 sphere is determined by the passage of the sun across the equinoctial 
 circle ; but when the sun is above the horizon there are no stars visible 
 whose position might be determined with respect to him, and when the 
 stars have become suitable objects for observation, the sun has already 
 disappeared. This seems to have formed an insuperable impediment to 
 the earlier astronomers in their endeavours to ascertain the absolute right 
 ascension or longitude of a star. Hipparchus devised two distinct modes 
 of obviating this difficulty. One of these was by observations made 
 during eclipses of the moon. Since the angular distance between the 
 sun and moon is exactly 180 on all such occasions, it follows that the 
 place of the moon during an eclipse is directly deducible from that of 
 the sun ; and as the place of the sun with respect to the equinox is known 
 by the solar tables, the place of the moon with respect to the equinox 
 hence becomes known also. It is clear, then, that if the difference of the 
 longitudes or the right ascensions of the moon and a star be determined 
 with the astrolabe during the occurrence of a lunar eclipse, the absolute 
 position of the star with respect to the equinox may hence be ascertained f. 
 
 * It is a curious fact that the inequality here referred to, termed the erection, confounds 
 itself in syzygees with the elliptic inequality or the equation of the centre. Hence it hap- 
 pened that observations confined exclusively to eclipses failed to indicate its existence. 
 Ptolemy, in his preliminary exposition of the inequality, cites two observations, one by 
 Hipparchus and the other by himself, both made when the moon was in the second quadra- 
 ture. The observation of Hipparchus is of so exceptional a nature, that it is impossible 
 not to conclude that it was taken from a great mass of observations, although Ptolemy 
 himself is silent upon this point. In the first place the apsides were in syzygees; secondly, 
 the moon was in quadratures ; thirdly, she was in the nonagesimal, or that point in her 
 diurnal course at which the effect of her parallax took place wholly in latitude. (Syntaxis, 
 lib. v., cap. iii.) With the view of confirming his explanation of the inequality, Ptolemy 
 subsequently cites two additional observations of the moon, both of which are in this case 
 by Hipparchus. (Syntaxis, lib. v., cap. v.) 
 
 f If an eclipse of the moon happened when the sun was in either of the equinoxes, 
 the moon would necessarily be in the opposite equinox, and hence the position of the 
 latter point among the stars might be ascertained without the use of solar tables, by 
 simply measuring the distance, in right ascension, of the moon from any of the neighbour- 
 
440 HISTORY OF PHYSICAL ASTEONOMY. 
 
 This method, however ingenious, laboured under the disadvantage of 
 being practicable only on rare occasions. The other method contrived 
 by Hipparchus for attaining the same end was more general in its appli- 
 cation. When the sun was still above "the horizon, he determined the 
 difference of the longitudes of the sun and moon with the astrolabe, and 
 as soon as the star became visible after sunset, he ascertained, in a similar 
 manner, the difference of the longitudes of the moon and star. It is clear 
 that from these two observations he obtained the difference of the longi- 
 tudes of the sun and star, taking into account the correction due for the 
 motion of the moon during the intermediate interval ; and as the place of 
 the sun with respect to the equinox was known by the solar tables, he 
 hence deduced the absolute longitude of the star. When the longitude 
 of one star was accurately found by this process, the longitude of any 
 other star might be directly derived from it by simultaneous observations 
 of both stars with the astrolabe. It was thus that the genius of Hippar- 
 chus triumphed over a difficulty which long appeared to be insurmount- 
 able, and thereby enabled him to effect with complete success one of the 
 most stupendous undertakings recorded in the annals of science. 
 
 Ptolemy, although the most eminent astronomer of antiquity, after 
 Hipparchus, does not rank high as an observer. It has been already 
 mentioned that his catalogue of the stars has been strongly suspected to 
 be no other than the catalogue of Hipparchus, reduced to his own time by 
 the application to all the longitudes, of what he conceived to be the true 
 quantity of the alteration occasioned by the precession of the equinoxes. 
 An examination of his labours on other subjects of astronomy tends to 
 confirm this impression. He nowhere enters into that minuteness of 
 description which indicates a bond fide observer anxious to persuade his 
 readers of the excellent qualities of his instruments, and of the precautions 
 which he employed to ensure the accuracy of his results. But what is 
 most to be deplored is his suppression of all the ancient observations, 
 including those of Hipparchus, with the exception of the few which 
 squared with his own calculations. The loss of these precious materials 
 has involved many interesting points of the ancient astronomy in impene- 
 trable obscurity. 
 
 An account has been given of the circular instrument employed by the 
 ancient astronomers in determining the meridional altitude of the sun. 
 Ptolemy rejected the complete circle, adopting in its stead a quadrant, 
 which he considered to be preferable. The vertically of the instrument 
 was established by means of the plumb-line. A small cylinder fixed at the 
 centre threw its shadow upon a similar body which moved along the divided 
 limb, and thereby indicated the altitude of the sun *. The Greek astro- 
 nomers appear to have divided their instruments only to every ten minutes. 
 It is remarkable that Ptolemy does not describe any method for placing 
 his instruments in the plane of the meridian. 
 
 Ptolemy's substitution of the quadrant for the complete circle was a 
 
 ing stars. Even if the eclipse occurred a few days before or after the equinox, the place 
 of the sun, and consequently that of the moon, might still be determined within the limits 
 of the errors of the ancient observations, by supposing the sun to revolve uniformly round 
 the earth in 365| days. It is possible that Timocharis may have found in this manner 
 that the star Spica Virginis preceded the autumnal equinox 8 3 in his time, but it is 
 more probable that Hipparchus, who cited this fact as a proof of the precession of the 
 equinoctial points, was in reality the individual who first established its existence by a dis- 
 cussion of the eclipses of the moon observed by Timocharis, and the use of his own solar 
 theory. 
 
 * Syntaxis, lib i. 
 
HISTORY OF PHYSICAL ASTRONOMY. 441 
 
 retrograde step in practical astronomy. This circumstance, however, 
 was generally overlooked by all his successors down to the time of Roemer, 
 who has the merit of being the first to restore the use of the circle in 
 astronomical observations. Indeed, it is only in our own day that the 
 quadrant has been definitively abandoned by astronomers as an essentially 
 imperfect instrument for determining the apparent positions of the celes- 
 tial bodies. 
 
 Although Ptolemy does not seem to have been an observer of the first 
 order, he possesses many claims to the admiration of posterity. Abundant 
 proofs of his sagacity are to be found in his great work, the Mathematica 
 Syntaxis, but his discovery of the inequality in the moon's longitude, termed 
 the evection, by a comparison of his own observations and those of Hip- 
 parchus with the computed places of the moon, would alone entitle him 
 to be ranked with the greatest astronomers of ancient or modern times. 
 
 Very little is known respecting the mode in which time was measured 
 by the ancient astronomers. In the daytime this object seems to have 
 been effected by means of dials. During the absence of the sun they 
 used clepsydras of various sorts, but all such contrivances were found to 
 be very imperfect, on account of the unequal flow of the water. In some 
 instances the time of an observation was indicated by the point of the 
 zodiac which was on the meridian. This method, when practicable, was 
 doubtless preferable to any other with which the ancient astronomers were 
 acquainted. 
 
 The Arabian astronomers do not seem to have effected any essential im- 
 provement in the methods of observation. Their instruments, however, 
 were generally larger and better constructed than those of the Greek astro- 
 nomers, and they appear to have taken greater precaution to ensure the 
 accuracy of their results. The astrolabe, as used by them, was, in some 
 instances, a complicated instrument, since it carried circles representing 
 the equator, the ecliptic, and the other principal circles of the celestial 
 sphere. In this form it acquired the appellation of an armillary sphere. 
 Instruments of a similar construction continued to be used in making 
 observations of the celestial bodies down to the beginning of the seven- 
 
 \teenth century. 
 The Arabians usually indicated the time of an observation by means 
 of the apparent altitude of a star whose position was known. It has 
 been mentioned that Ptolemy has given no account- of the method he 
 employed in tracing a meridian line. The Arabian astronomers effected 
 this object by equal altitudes of the sun when he was east and west of the 
 meridian*. It does not appear that they took into account the effect of 
 the motion of the sun during the interval included between the two ob- 
 servations. 
 
 Upon the revival of science in Europe towards the close of the fifteenth 
 century, the cultivation of astronomy was for some time confined almost 
 exclusively to Germany. Waltherus, a native of Nuremburg, to whom 
 we have already had occasion to allude, may be considered the earliest 
 individual of modern times whose observations have contributed to the 
 advancement of astronomical science. He first introduced the practice of 
 determining the apparent place of a planet by observations of its altitude, 
 and its distance from two stars whose places had been already ascertained. 
 
 * Delambre, Hist. Ast. Moyen Age, p. 129. The astronomers of India appear also 
 to have practised this method by tracing upon the sand a circle around the foot of the 
 gnomon. 
 
449 SISTOEY OF PHYSICAL ASTRONOMY. 
 
 He is also the first astronomer who used clocks moved by weights for the 
 purpose of measuring time. These pieces of mechanism were introduced 
 originally from eastern countries. Pacificus, Archdeacon of Verona, who 
 flourished in the ninth century, was the ftrst European who constructed a 
 clock with wheels. Others were soon fabricated in different countries of 
 Europe, but they were used only in the public edifices of great cities 
 before Waltherus applied them to the purposes of astronomy. 
 
 In consequence of the observations of Waltherus being the earliest of 
 modern times, they were continually used at a subsequent period in recti- 
 fying the elements of astronomical science by comparing them with similar 
 determinations of a more recent date. Lacaille has employed them for 
 this purpose in his researches on the solar theory. This is probably the 
 last important occasion on which the observations of Waltherus will be 
 consulted. In the present day it is found that the modern observations 
 more than compensate by their superior accuracy for the shortness of the 
 time that has elapsed since ^hey were made. 
 
 Copernicus, about the middle of the sixteenth century, had restored the 
 true system of the world, but the epicyclical fabric still remained almost 
 in its original state. To Tycho Brahe is due the immortal honour of 
 having executed the series of observations which led to the discovery of 
 the real nature of the planetary movements. This illustrious individual 
 expended his whole private fortune, amounting to a hundred thousand 
 crowns, upon objects connected with the improvement of practical astro- 
 nomy. His collection of instruments was one of the most magnificent 
 which the world has ever seen. Waltherus, and the earlier astronomers 
 of modern Europe, possessed only wooden appliances for observing the 
 positions of the celestial bodies. The instruments of Tycho Brahe were 
 mainly constructed of metal. They were also larger and more accurately 
 divided than any that had been hitherto applied to the purposes of astro- 
 nomical observation. The ancient astronomers appear to have divided 
 their instruments only to every ten minutes. Some of Tycho Brahe's 
 were actually divided to every minute ; and by employing the method of 
 transversals, which came into use in his time, they were, in some instances, 
 subdivided to every ten seconds *. 
 
 Not only were Tycho Brahe's instruments vastly superior to those 
 hitherto used by astronomers, but his methods of observation were also 
 such as to assure a greater degree of precision to the final results than 
 had been hitherto attained. By taking- into account the effect of refraction, 
 he avoided, to a great extent, a source of error which had vitiated the 
 observations of all preceding astronomers. His method of determining 
 the absolute right ascensions of the stars was also a vast improvement 
 
 * It may be remarked, however, that in his actual observations Tycho Brahe by no means 
 attained the degree of precision contemplated in the construction of some of his instru- 
 ments ; for even although the divisions of the limb had been faultless in any case, the 
 advantage of the instrument in this respect would have been vitiated by the error com- 
 mitted in the pointing of it to any celestial body, an error which it was impossible to avoid 
 so long as observations were made with plain sights. With respect to the method of trans- . 
 versals, or, as it is more commonly termed in England, the diagonal scale, Tycho Brahe 
 mentions (Progymnasmata, p. 671, edit. 1610) that he first became acquainted with it 
 when he was a student, at the university of Leipsic, having obtained a description of it 
 from one of the professors named Homelius, but that he is ignorant of the real author of 
 the invention. Thomas Digges (Alee sen Scales Mathematics, Capitulum JVonum ; Lon- 
 dini, 1573) asserts that it was invented by Richard Chanzler, an English artist famous for 
 his skill in the construction of mathematical instruments, and that it had been long well 
 known in England. 
 
HISTORY OF PHYSICAL ASTRONOMY. 443 
 
 over that employed by the ancient astronomers. It hag been already 
 mentioned that Hipparchus determined the places of the stars with respect 
 to the equinox, by using the moon as an intermediate object of observation 
 between the sun and the stars. This method, however, was very imper- 
 fect, on account of the rapid motion of the moon and the uncertainty that 
 prevailed respecting the exact value of her parallax. Some of Tycho 
 Brahe's contemporaries, among others the Landgrave of Hesse Cassel, 
 sought to determine the absolute place of a star by means of its azimuth 
 and altitude, combined with the time of observation. A serious objection 
 to this method consisted in the difficulty of measuring time with suf- 
 ficient accuracy. Notwithstanding all the efforts of Tycho Brahe and 
 the Landgrave, they were unable to procure clocks that could be relied upon 
 for such a purpose. Tycho has not failed to enumerate the various sources 
 of their irregularity. They were perpetually liable to be affected by 
 changes of temperature and currents of air, even although the precaution 
 was used of keeping them in heated apartments. Again, it was found 
 impossible to construct the teeth of wheels with such regularity as to 
 ensure a perfectly uniform motion ; and hence, even although the daily 
 times of restitution of such clocks should appear equal, by comparing them 
 either with the sun or the stars, they would fail to indicate the interme- 
 diate intervals of time with the same regularity. Finally, the heavy body 
 which occasioned the motion did not act uniformly during its descent, for 
 when it was in the lower part of its course, the weight of the cord by which 
 it was attached tended in some degree to increase its efficacy, however 
 slender the cord might be; and the smallest irregularity could not be 
 overlooked, since an error of four seconds in time was equivalent to one 
 of a minute in space *. 
 
 While pondering on the difficulties of this subject, the happy idea 
 occurred to Tycho Brahe of substituting Venus for the moon, as the inter- 
 mediate object of observation between the sun and the stars. This planet 
 has a much slower motion than the moon, and at the same time has a 
 smaller parallax. It is therefore obviously better adapted than that body 
 for ascertaining an element of fundamental importance, such as the abso- 
 lute right ascension of a star. Before sunset he made simultaneous obser- 
 vations on the sun and the planet, and when the sun disappeared he made 
 similar observations on the planet and the star. In this manner he deter- 
 mined the absolute right ascensions of several of the most brilliant stars, 
 and by means of them he easily obtained the right ascensions of all the 
 others f. It is worthy of remark that Waltherus had already employed 
 Venus for a similar purpose, but this circumstance seems to have totally 
 escaped the notice of Tycho. 
 
 Allusion has been made to the mode of determining the position of a 
 star by means of its altitude and azimuth combined with the time of obser- 
 vation. This method seems to have been practised by the Landgrave of 
 Hesse Cassel, on the occasion of his observations of the new star which 
 appeared in the constellation of Cassiopeia, in the year 1572. Tycho, in 
 his work on the same star, has given the observations of the prince rela- 
 tive to its apparent place in the heavens, extending from Dec. 3, 157'*J, 
 till March 14, 1573 J. These appear to be the earliest observations in 
 which the element of time was employed in determining the right ascen- 
 sion of a star. 
 
 * Progymnasmata, p. 149. t Ibid., p. 491. $ Ibid., p. 152. 
 
444 HISTORY OF PHYSICAL ASTKONOMY. 
 
 It appears from the work of Tycho Brake, above cited, that Thaddeus 
 Hagecius, another contemporary astronomer who wrote upon the new 
 star, advanced a step further than the Landgrave; for he shewed that both 
 the declination and right ascension of ^i star might be determined by 
 observing its altitude on the meridian, and noting the time of observation. 
 Tycho has given, as an example of this method, Hagecius 's determination 
 of the place of the new star. He takes occasion, at the same time, to point 
 out the various defects of the method, and it must be admitted that, in the 
 existing state of practical astronomy, his objections were not without weight. 
 If the time was to be indicated by clocks, it would be impossible, he re- 
 marked, to avoid errors of serious magnitude, as he had already shewn on 
 a former occasion. If the observed altitude of a star was employed for 
 that purpose, the chance of error would be equally great, for neither could 
 the absolute place of the star be ascertained beforehand with sufficient 
 precision, nor could its altitude, corresponding to each observation, be 
 satisfactorily determined. Moreover, when a star is approaching the 
 meridian, its altitude increases very slowly, so that it is exceedingly dif- 
 ficult to assign the precise instant when it is actually upon the meridian. 
 This source of error might be avoided by observing the star near the 
 horizon, where it rises with great rapidity; but, on the other hand, the 
 uncertain effect of refraction at low altitudes would tend to vitiate the 
 observation *. 
 
 Tycho Brahe, for the above reasons, did not deem it safe to employ the 
 element of time in determining the apparent place of a celestial body. 
 In fact, the observations of the Landgrave on the new star, to which 
 allusion has already been made, supplied him with a practical proof of 
 the justness of his views on this subject. In each of these observations 
 the altitude, the azimuth, and the time were different ; but as the posi- 
 tion of the star in the celestial sphere was found to be invariable, it 
 followed, as a necessary consequence, that each combination of these three 
 data ought to assign to the star the same values of declination and right 
 ascension. Tycho calculated these elements by means of the Landgrave's 
 observations ; but he found that although the declinations exhibited a 
 pretty satisfactory agreement with each other, the right ascensions dif- 
 fered, in some instances, to the extent of 2 of space f. This may not be 
 an improper place for a few words on the construction of the clocks of 
 those days. They consisted essentially of a vertical wheel, which was 
 made to revolve with a slow motion by the gradual descent of a weight. 
 The balance was a happy contrivance, devised for the purpose of con- 
 stantly checking by its inertia, the descent of the weight, and thereby 
 rendering the motion of the wheel more uniform. It consisted of a cross- 
 bar, with two weights at its extremities, capable of turning freely in a 
 horizontal direction, upon a vertical axis, which was connected with the 
 wheel by means of two pallets. The distance between the pallets was 
 equal to the diameter of the wheel, and they were so disposed on the 
 vertical axis as to engage alternately the highest and lowest tooth of the 
 wheel. When the highest tooth engaged the upper pallet, the balance 
 was pushed round, and its resistance checked the descent of the weight. 
 As soon as this pallet became freed from the wheel, the lowest tooth 
 engaged the other pallet, and the balance was then pushed in the oppo- 
 site direction. This alternate movement of the balance continually 
 
 * Progymnasmata, p. 523. f Ibid., p. 502. 
 
HISTORY OF PHYSICAL ASTRONOMY. 445 
 
 restrained the descent of the weight, and thereby prevented the 
 acceleration of the motion of the wheel, which would otherwise have 
 necessarily ensued. Clocks upon this principle continued to be fabricated 
 down to the middle of the seventeenth century ; but, notwithstanding all 
 the attention and skill bestowed on their construction, they could not be 
 relied upon for the delicate purposes of astronomy. 
 
 Although Tycho Brahe generally disapproved of employing the element 
 of time in determining the apparent position of a celestial body, he 
 adopted the practice in one or two instances, which it may not be 
 improper to notice. In the first place, he determined the successive 
 positions of the comet of 1577, by means of altitude and azimuth obser- 
 vations. The instrument he used on this occasion was a quadrant 
 revolving in azimuth. He possessed several instruments of this con- 
 struction. The largest had a radius of six feet. It was divided by 
 transversals to every quarter of a minute. The azimuth circle had a 
 diameter of nine feet. The zero point of division was at the extremity 
 of the meridional diameter, the direction of which was determined by 
 observing the greatest eastern and western digressions of the pole 
 stars. 
 
 Another instrument designed by Tycho Brahe, to be used in connexion 
 with the clock, was what he termed the Mural or TycJionic quadrant. It 
 was a large quadrant of copper, placed exactly in the plane of the 
 meridian against a solid wall, to which it was firmly attached. The radius 
 of this instrument was equal to nine feet, and the limb was divided by 
 transversals to every 10". Tycho remarks that by determining the alti- 
 tude of a star with it, and noting the time of observation, the declina- 
 tion and right ascension of the star may be ascertained. He appears, 
 however, to have chiefly used this instrument in making observations of 
 the meridional altitude of the sun, for the purpose of rectifying the 
 elements of the solar theory-!'. 
 
 The Landgrave of Hesse Cassel, whom we have had occasion to allude 
 to in connexion with Tycho Brahe, was a prince no less distinguished by 
 his liberal patronage of astronomical science, than by his actual labours 
 as an observer of the heavens. Unlike most other sovereigns who have 
 affected a disposition to promote the objects of astronomy, he did not 
 content himself with a mere dilettante exhibition of his favours towards 
 the science, but directly contributed towards its advancement by his 
 personal energy and perseverance. It is to be remarked, also, respecting 
 this excellent prince, that he maintained at his own expense some of the 
 most eminent mathematicians and astronomers of his time ; nor should 
 his kindness towards Tycho Brahe be forgotten in considering his claims 
 to the grateful recollection of posterity. 
 
 We shall now briefly allude to the labours of Hevelius, before pro- 
 ceeding to give some account of the modern improvements in practical 
 astronomy. This individual, who was a rich citizen of Dantzic in Prussia, 
 commenced his career as an astronomer in 1630; and throughout a 
 period of nearly fifty years he continued to labour with indefatigable 
 assiduity in making observations of the celestial bodiest. His instru- 
 
 * Astronomise Instauratse Mecanica, No. 4. 
 
 f Hevelius was born in 1611, and died in 1687. Although he observed an eclipse of 
 the sun as early as the year 1630, he did not commence his career of regular observation 
 till 1641. One of his most useful assistants was his wife, who was an expert observer, 
 and was well skilled in drawing. 
 
446 HISTORY OF PHYSICAL ASTRONOMY. 
 
 ments were similar to those of Tycho Brahe ; but they were divided with 
 greater precision, and were more easily managed. The application of the 
 vernier to the measurement of fractional magnitudes, was an improvement 
 of which he did not fail to avail himself. This elegant method of subdi- 
 vision was invented in the year 1631 by Pierre Vernier, a native of 
 Franche Compte*. Hevelius himself devised an ingenious method of 
 effecting the same object by means of a tangent screw, working in the 
 extremity" of the movable radius upon which the pinnules were placed. 
 Knowing the number of revolutions of the screw which were necessary 
 to transport the radius over the interval included between any two con- 
 secutive points of division of the limb, it was hence easy, by counting 
 the revolutions and parts of [a revolution of the screw, in moving the 
 radius from any point on the limb to the nearest point of division, to 
 ascertain the magnitude of the space included between the two points. 
 This must be considered as one of the earliest of those mechanical con- 
 trivances that have been devised for measuring the fractional parts of 
 divided instruments. Hevelius, by refusing to employ the telescope in 
 his observations, was unable to take due advantage of this ingenious 
 method of subdivision; but it was applied with complete success in 
 several instances in the following century. 
 
 In 1679 the observatory of Hevelius was totally consumed by fire. 
 All his instruments and manuscripts, and, with the exception of a few 
 copies, the whole edition of the second part of his great work, the 
 Machina Ccelestis, comprehending the numerous observations which he 
 had made during his long career, unfortunately perished in the flames. 
 The aged astronomer bore this calamity with great fortitude ; and, instead 
 of abandoning himself to despair, he recommenced his labours with 
 renewed energy f. One of the most remarkable of his works is a 
 catalogue of the places of upwards of 1500 stars, which was published a 
 few years after his death. The great ability of Hevelius, as an observer, 
 would have rendered this catalogue a valuable record qf the state of the 
 heavens in his time, if, in making his observations, he had availed him- 
 self of telescopic sights, which came into general use during the latter 
 part of his career. Unfortunately, however, he persevered to the end of 
 his life in rejecting such appliances, adhering to the use of simple pin- 
 nules, under the impression of their affording a more trustworthy indica- 
 tion of the true direction in which a celestial body appears. 
 
 With the labours of Hevelius closes the ancient school of astronomical 
 observation. By constructing instruments of very large size, and em- 
 ploying ingenious methods of subdivision, astronomers had succeeded in 
 determining the apparent position of a celestial body within about \ f of 
 the truth. If the magnitude of the instrument in any instance, however, 
 exceeded a certain limit, it obviously became unmanageable ; and besides, 
 its greater tendency to derangement from its own weight more than coun- 
 terbalanced the advantage gained by enlarging the scale of division. But 
 
 * A method somewhat similar in principle, but more complicated in practice, had 
 been invented by Nonius, a Portuguese mathematician, about the middle of the six- 
 teenth century. Tycho Brahe used it in the early part of his career, but he soon aban- 
 doned it as too troublesome, adopting the method of transversals in its stead. 
 
 f What Hevelius regretted on this occasion more than all his most precious effects 
 were his researches on the planetary motions, and his notes on the stars, which he had 
 been making throughout the long period of his astronomical career. Several years after- 
 wards he assures the reader, in one of his works, that the recollection of their loss never 
 failed to bring tears into his eyes. 
 
HISTORY OF PHYSICAL ASTRONOMY. 447 
 
 apart from these considerations, the difficulty of pointing truly to a celestial 
 body an instrument furnished for that purpose merely with pinnules, pre- 
 sented an insuperable obstacle to the attainment of a high degree of preci- 
 sion in the ascertainment of its apparent position, This was a constant 
 source of error which the astronomer had to contend with in all his 
 operations, whose vitiating influence was essentially beyond the reach 
 either of the ingenuity of the mechanician or the skill of the artist. It 
 is to be remarked, however, in favour of the Tychonic school of observa- 
 tion, that it served effectually to demolish the whole of the ancient fabric 
 of epicycles, and to establish the elliptic theory of the planets upon an 
 incontrovertible basis. This was unquestionably a noble triumph of 
 genius and practical skill ; but in so far as regards the more delicate 
 phenomena of the celestial regions, the methods practised in that school' 
 were utterly powerless. The sublime theory of planetary perturbation 
 would have proved a subject of barren research to Newton and his 
 successors, and those minute movements of the stars, in connexion with 
 which so many brilliant triumphs have been achieved in recent times, 
 would have for ever continued to be involved in impenetrable mystery, 
 unless a complete revolution had been effected in the condition of prac- 
 tical astronomy as it existed about the middle of the seventeenth 
 century. 
 
 The establishment of public observatories in several countries of 
 Europe about the time referred to, could not fail to exercise a direct 
 influence of a favourable character upon the progress of astronomy in all 
 its branches. When it is considered that the various movements of the 
 celestial bodies require for their development a series of cycles of time, 
 many of which are of long duration, it is manifestly indispensable, in order 
 to arrive at an accurate knowledge of the laws of their movements, that 
 the various bodies should be made the objects of continuous observation 
 throughout a long succession of ages. But, on the other hand, it is not 
 less obvious that the limited resources of private individuals are 
 inadequate to a task of such magnitude. Much, indeed, may be effected 
 by genius and perseverance, as in the case of Hipparchus, and several 
 astronomers of modern times ; but, generally speaking, it is only by the 
 steady application of national resources to the observation of the celestial 
 bodies, that a series of facts can be established which shall possess suffi- 
 cient value to form a sure groundwork for the investigation of the laws of 
 their movements. The earliest public observatory, and indeed the only 
 one which history makes mention of as having existed in ancient times, 
 was that which Ptolemy Soter established at Alexandria, and which con- 
 tinued for many centuries to furnish an asylum to the Greek astronomers 
 in the midst of a declining civilisation. The magnificent establishment 
 which Frederick III., of Denmark, assigned to Tycho Brahe, in the 
 island of Huena, for the purpose of enabling him to prosecute his labours 
 more effectually, cannot be called a public observatory, since it was not 
 designed to promote any ulterior object connected with astronomy. But 
 indeed, even in so far as Tycho Brahe himself was concerned, it was soon 
 apparent, from the disgraceful treatment which he experienced in the 
 latter period of his life, that the establishment of Uranibourg was held 
 by a very precarious tenure. It would seem, however, that Christian IV., 
 under whose minority Tycho Brahe was compelled to abandon his native 
 country, felt a disposition to make some reparation for his early indif- 
 ference to the cause of science, by the establishment of a public obser- 
 
448 H1STOKY OF PHYSICAL ASTRONOMY. 
 
 vatory on a permanent basis. Longomontanus, an astronomer of some 
 celebrity, who bad assisted Tycbo in his labours at Uranibourg, was chiefly 
 instrumental in promoting the views of the monarch. The foundation 
 stone of the observatory was laid by Christian IV., on the 7th of July, 
 1637, but it does not appear that the building was completely finished 
 until the year 1656, during the reign of his successor, Frederick IV. 
 The structure was erected in the form of a tower. It was 115 Danish 
 feet in height, and 48 feet in diameter. The observations were made in 
 an apartment at the top of the tower, which was reached by means of a 
 spiral avenue winding gently round the interior of the wall*. We shall 
 presently have occasion to allude more particularly to this observatory, 
 which must be regarded as the earliest of the numerous public institutions 
 for the promotion of practical astronomy that have been established in 
 modern times. 
 
 It has been already mentioned that all contrivances for measuring time 
 by means of clocks composed of a combination of wheels moved by 
 weights, had been found totally inadequate to the delicate purposes of 
 astronomy. Another mode of effecting the same object had been devised 
 by Galileo. Having discovered that the oscillations of a pendulum are 
 isochronous f, it occurred to him that a mechanism might be constructed 
 upon this principle which would serve to indicate the divisions of time 
 with great accuracy ; but although he devoted much attention to the real- 
 isation of this idea, all his efforts to procure a clock that would be practically 
 serviceable proved fruitless. In all such contrivances it was found that 
 the pendulum, when once set in motion, was soon again brought to a state 
 of rest, so that the oscillations could only be maintained by applying to 
 the pendulum a succession of impulses at regular intervals. Huyghens 
 eluded this inconvenience, by substituting the pendulum for the balance 
 in the ancient clocks, so adapting it, that the isochronism of its oscillations 
 regulated the downward motion of the weight. By this admirable con- 
 trivance he combined the advantages of the two methods above referred 
 to, while, at the same time, he eluded their respective defects. The idea 
 of so applying the pendulum to the measurement of time first suggested 
 itself to him in the year 1656, and in the following year he presented to the 
 States General of Holland a clock constructed upon this principle. The 
 invention soon spread abroad throughout Europe, and was hailed with uni- 
 versal applause. Its successful application to the purposes of astronomical 
 observation will be noticed presently. 
 
 The establishment of the Royal Society of London, and of the Academy 
 of Sciences of Paris, exercised a powerful influence on the progress of 
 astronomy, as well as on every branch of physical science. The origin of 
 the Royal Society may be traced to the period of the civil wars in the time 
 of Charles I., when individuals of a contemplative cast of mind sought 
 relief from the prevailing commotion in the calm retreat of scientific dis- 
 cussion. Dr. Wallis states that, about the year 1645, when academical 
 studies were much disturbed at both the universities, several persons 
 inquisitive into natural philosophy, and other parts of human learning, did, 
 
 * Horrebow, in his Basis Astronomies, states that in 1716 Peter the Great of 
 Russia frequently ascended the tower on horseback along this spiral avenue, and that the 
 Empress Catherine occasionally ascended at his side in a four-wheeled chariot, drawn by 
 six horses! 
 
 f They are not exactly isochronous, but for small arcs the times of oscillation may 
 be regarded as equal without committing any sensible error. 
 
HISTORY OF PHYSICAL ASTRONOMY. 449 
 
 by agreement, meet weekly in London on a certain day to treat of such 
 matters. Among the individuals who thus used to assemble together, 
 were Wilkins, Goddard, Wallis, and Samuel Foster, Professor of Astro- 
 nomy in Gresham College. In 1648-9 the attendance at the weekly 
 meetings was considerably reduced by the removal of several members to 
 Oxford, who established a similar association in that city. The original 
 minutes of the Oxford Philosophical Society, dated the 23rd of October, 
 1651, are still preserved in the Ashmolean Museum of that city. The 
 embryo Society of London still continued to hold its meetings, but it 
 seems to have fallen into a very languishing condition until the year 
 1660, when the restoration of Charles II., by holding out the prospect of 
 future tranquillity, had the effect of infusing renewed vigour into its pro- 
 ceedings. The earliest official document of the Society is dated Novem- 
 ber 28, 1660. It was finally incorporated by Koyal Charter on the 15th 
 of July, 1662. The first President was Lord Brouncker, one of the most 
 eminent mathematicians of the age. Among those members who took an 
 active part in promoting the objects of the Society at this period, may be 
 mentioned the President Lord Brouncker, Boyle, Wilkins, Wren, and Sir 
 Robert Moray. A few years after the establishment of the Royal Society 
 upon a permanent basis, a similar association was formed at Paris under 
 the designation of the Royal Academy of Sciences. The first meeting of 
 this celebrated body was held on the 22nd of December, 1666. Some of 
 the earlier members were Roberval, Auzout, Picard, and Richer. A few 
 years later, it was enriched by the accession of Huyghens, Roemer, and 
 Cassini, who were enrolled as members. 
 
 Numerous institutions for promoting the cultivation of science have 
 been established in the different countries of Europe at a later period than 
 that above referred to ; but it is no depreciation of the well-earned repu- 
 tation of many of them to assert that, at no epoch of their history have 
 they in any instance exercised an influence so unequivocally beneficial as 
 that exercised by the Royal Society of London, and the Academy of 
 Sciences of Paris, during the early period of their existence. It is to be 
 borne in mind that the last-mentioned institutions were founded at a time 
 when the inductive philosophy was still engaged in mortal conflict with 
 the scholastic system of Aristotle, and when, consequently, an organized 
 union of the scattered energies of its adherents could not fail to accelerate 
 its final triumph. Practical astronomy participated largely in the advan- 
 tages derived from these institutions. New improvements, both in the 
 construction of instruments and in the methods of observation, were dis- 
 seminated throughout Europe with a rapidity hitherto unknown, andt 
 thereby facilitated in a vast degree the attainment of still further excel- 
 lence. 
 
 The invention of tfye micrometer was one of the earliest of those im- 
 provements which in the seventeenth century had the effect of establishing 
 the methods of astronomical observation upon a totally new basis. The 
 measurement of small angles was found by astronomers, in all ages, to be 
 one of the most difficult objects connected with the practice of observation. 
 Archimedes, in an attempt to determine the apparent magnitude of the 
 sun, was unable to arrive at a result of greater precision than that the 
 apparent diameter was greater than 27', and less than 32'. Coming down 
 to modern times, we have seen that Tycho Brahe was so misled by his. 
 measurements of the apparent diameters of the sun and moon, as to come 
 to the conclusion that a total eclipse of the sun was impossible. Indeed it is 
 
 o a 
 
450 HISTORY OF PHYSICAL ASTRONOMY. 
 
 obvious that a mode of accurately determining the variations in the ap- 
 parent diameters of the sun and moon, could not fail to lead to an improve- 
 ment of the theories of the movements of those bodies. Moreover, the 
 invention of the telescope, by revealing the round figures of the planets, 
 rendered it desirable to devise some means of measuring small angles with 
 a degree of precision conformable to the existing condition of theoretical 
 astronomy. The invention of the micrometer, by means of which this 
 object was effectually accomplished, is originally due to William Gascoigne, 
 a young man who was the friend of Horrocks and Crabtree, and who, like 
 them also, was unfortunately cut off by a premature death in the very 
 outset of his career. It will be desirable, however, to give a previous 
 account of the successive steps by which the same admirable invention 
 was independently effected on the Continent about twenty years after- 
 wards. The person who first suggested the idea of the micrometer in the 
 latter instance was Huyghens. In his Systema Saturnium, which was 
 published in 1659, he remarked that an object placed in the focus of a 
 common astronomical telescope, appears as distinct and as well defined as 
 the image of a remote body. Hence, in order to determine the apparent 
 diameter of a celestial object, he inserted a slip of metal of variable 
 breadth at the focus of the telescope, and observed at what part it exactly 
 covered the object. Applying, then, a finely-pointed compass to the slip of 
 metal, he measured its exact breadth, and, knowing the focal length 
 of the telescope, he hence deduced the apparent magnitude of the 
 object. In this manner he determined the apparent diameters of the 
 principal planets. 
 
 The Marquis Malvasia, in his " Ephemerides," published at Bologna in 
 1662, describes a method of measuring small angles which may be re- 
 garded as the next step in the invention of the micrometer. At the focus 
 of the telescope he placed a net- work of fine silver threads at right angles, 
 which formed by their mutual intersection a number of small squares. In 
 order to determine the mutual distances of the threads that were parallel to 
 each other, he caused a star situate near the equator to traverse a thread 
 perpendicular to their common direction, and counted, by the aid of a pen- 
 dulum clock, the times which it took to pass over the successive intervals* . 
 
 The micrometer of Malvasia was a decided improvement of that of 
 Huyghens. The distances between the threads, when once accurately de- 
 termined, would serve for all future measurements. The method was also 
 more generally applicable than that of Huyghens, since, besides the apparent 
 diameters of the celestial bodies, it might serve to measure the angular 
 distance of two stars that were at the same time in the field of view of the 
 telescope. It laboured, however, under the disadvantage that, if the two 
 stars did not appear exactly on the wires, something was unavoidably left 
 to estimation in the measurement of their mutual distance. Auzout got 
 rid of this defect by substituting for the reticule 'of Malvasia two silk 
 threads, one of which was fixed, while the other was moveable in a direc- 
 tion parallel to it by means of a fine screw. It is evident that, when once 
 the distance traversed by the moveable thread during one revolution of 
 the screw was ascertained with sufficient accuracy, the angular distance 
 between two stars very near to each other might be determined, by causing 
 the moveable thread to traverse the interval between the stars, and noting 
 the number of revolutions and parts of a revolution of the screw which 
 were required to effect this object. 
 
 * Mm. Acad. des Sciences, 1717, p. 78, et seq. 
 
HISTORY OF PHYSICAL ASTBONOMY. 451 
 
 Auzout first announced his improvement of the micrometer in a letter to 
 the Royal Society of London, dated December 28, 1666, which is in- 
 serted in the 21st Number of the Philosophical Transactions. Birch 
 states that, upon this letter being read before the Society, two of the 
 members, Wren and Hooke, took occasion to mention several ways of 
 measuring small angles which were already known in England. These 
 philosophers have nowhere given a detailed description of the micrometers 
 devised by them. Sprat, however, in his "History of the Royal Society," 
 alludes, in a general summary of the labours of the Society, to their 
 construction of telescopes of different lengths, with several contrivances in 
 them for measuring the diameters and parts of the planets*. In another 
 part of the same work, he states that Wren had added many sorts of 
 retes, screws, and other devices to telescopes, for taking small distances 
 and apparent diameters to seconds \. In a work which he published in 
 1665, Hooke proposes to determine the parallax of the moon or any of 
 the planets by observing its distance from the neighbouring stars in two 
 different latitudes, by the aid of a telescope fitted with a rete or divided 
 scale |. It is evident that the micrometrical contrivances of Huyghens, the 
 Marquis Malvasia, and Hooke, were all essentially similar to each other. 
 Indeed, as soon as telescopes composed of two convex lenses began to be 
 commonly used, the invention of such a micrometer as that devised by 
 either of these philosophers was a very obvious step. 
 
 In the 25th Number of the Transactions of the Eoyal Society there is a 
 letter from Richard Townley, of Lancashire, relative to the micrometer of 
 Gascoigne. The date of this letter is March 25, 1667 . " Finding," says 
 he, " in one of the last Philosophical Transactions, how much M. Auzout 
 esteems his invention of dividing a foot into near 30,000 parts, and taking 
 thereby angles to a very great exactness, I am told I shall be looked 
 upon as a great wronger of our nation, should I not let the world know 
 that I have, out of some scattered papers and letters that formerly came 
 to my hands of a gentleman of these parts, one Mr. Gascoigne, found out 
 that, before our late civil wars, he had not only devised an instrument of 
 as great power as Mr. Auzout's, but had also for some years made use of 
 it, not only for taking the diameters of the planets and distances upon 
 land ; but had further endeavoured out of its preciseness to gather many 
 
 certainties in the heavens |j I shall only say of it that it is 
 
 small, not exceeding in weight, nor much in bigness, an ordinary pocket 
 
 * " History of the Royal Society," p. 250, 4to, London, 1667. The account of the 
 scientific labours of the Royal Society, inserted in this work, was compiled from the re- 
 gisters of the Society down to 1665. 
 
 f Ibid., p. 314. 
 
 I Micographia, p. 237, fol., Lond., 1665. Hooke, on a subsequent occasion, described 
 a species of micrometer of a more perfect construction, but he was then acquainted with 
 the contrivances for a similar purpose devised by Gascoigne and Auzout. 
 
 The date of the letter is not mentioned in the number of the Philosophical Trans- 
 actions cited in the text, but the omission is supplied by Birch, who alludes to the letter 
 in his History of the Royal Society (vol. ii. p. 164). This letter, as well as the state- 
 ment respecting it by Birch, has entirely escaped the notice of Delambre, who censures the 
 tardiness of the English astronomers in not bringing forward any account of Gascoigne's 
 micrometer before the 25th of July, 1667. 
 
 II Townley here states that Gascoigne determined the value of the lunar parallax by 
 measuring with his micrometer the apparent diameter of the moon when she was in the 
 horizon, and again when she was on the meridian. He mentions also that he had in his 
 possession the very micrometer that Gascoigne originally used in his observations. 
 
 G G 2 
 
452 HISTORY OF PHYSICAL ASTRONOMY. 
 
 watch, exactly marking above 40,000 divisions in a foot, by the help of 
 two indexes ; the one showing hundreds of divisions, the other divisions 
 of the hundred." Mr. Townley concludes his letter by stating that, if it 
 should be found desirable, the Society .might obtain a more complete 
 description of the instrument. 
 
 Mr. Townley's micrometer was actually produced before the Society at 
 the meeting held on the 25th of July, 1667, and a detailed description 
 of it was subsequently given in No. 29, of the Philosophical Transactions. 
 In principle it exactly resembles the micrometer of Auzout. Two straight 
 edges of metal are made to approach each other at the focus of the telescope 
 by means of a screw, the mechanism being so contrived that the optical 
 axis of the telescope is always situate midway between the two edges. The 
 number of revolutions and parts of a revolution of the screw which are 
 required in order to bring the edges into any determinate position will 
 manifestly indicate the extent of the interval which separates them*. 
 Hooke suggested an improvement of this micrometer by substituting 
 human hairs for the solid edges. 
 
 It appears from the observations of Gascoigne, which are still in exist- 
 ence, that he actually used the micrometer in several delicate measure- 
 ments. Flamsteed, in the first volume of the Historia Celestis, has in- 
 serted a series of celestial observations extending from 1638 to 1643, 
 which were made by Gascoigne and his friend Crabtree, and among these 
 are contained a considerable number of micrometrical measurements by 
 Gascoigne. They consist of a determination of the mutual distances of 
 the Pleiades, a few values of the apparent diameter of the sun, several 
 distances of the moon from the neighbouring stars, and a great number of 
 measurements of the lunar diameter. The results in most instances are 
 given in revolutions and parts of a revolution of the screw. In the forty- 
 eighth volume of the Philosophical Transactions, Dr. Bevis has also given 
 several measurements of the apparent diameters of the planets and the 
 moon, made by Gascoigne with his micrometer. They were extracted by 
 him from a letter written by Gascoigne to Oughtred, the original of which, 
 he stated, was still preserved in the library of the Earl of Macclesfield f. 
 The following comparison instituted by Delambre, between certain mea- 
 surements of the semidiameter of the sun by Gascoigne, and the corre- 
 sponding values in the Connaissance des Temps of the present day, will 
 suffice to convince the reader that the original inventor of the micrometer 
 did not fail to bring his instrument to considerable perfection : 
 
 Gascoigne. Connaissance des Temps. 
 
 October 25, O.S. 16' 11" or 10" 
 October 31, 16 11 
 
 December 2, 16 24 
 
 16' 10" 
 16 11.4 
 16 16.8 
 
 Gascoigne makes the greatest variation of the apparent diameter of 
 
 * Sherburne, in his translation of the Sphere of Manilius (1675), states that Crabtree, 
 
 taking a journey to Yorkshire, in 1639, to see Gascoigne, thus wrote to Horrocks: 
 
 " The first thing Mr. Gascoigne shewed me was a large telescope, amplified and adorned 
 with new inventions of his own, whereby he can take the diameters of the sun or moon, 
 or any small angle in the heavens or upon the earth, most exactly through the glass to a 
 second (see the work cited, p. 92). This is the letter alluded to in the note at the 
 foot of p. 428. 
 
 f Phil. Trans., 1753, p. 190. 
 
HI8TOBY OF PHYSICAL ASTBONOMY. . 453 
 
 the sun to be 35"; according to the Connaissance des Temps it amounts 
 to 32".3 *. 
 
 It appears from the foregoing statements that Gascoigne invented and 
 actually employed the micrometer twenty years before even the original 
 germ of such an instrument had suggested itself to any person on the 
 Continent. At the same time, there is not the smallest reason to suppose 
 that any person out of England had any knowledge of his labours previous 
 to the reinvention of the instrument elsewhere. On this point Delambre 
 makes the following just remark: " II faut remarquer que les observa- 
 tions des deux amis riont ete publiees que 80 ans apres leur date reelle. 
 Ainsi, en accordant a Gascoigne, la premiere idee et meme la premiere execu- 
 tion du micrometre, il est juste de reserver leurs droits aux astronomes qui, 
 sans avoir aucune connaissance des observations Anglaises, ont ete conduits 
 par leur propres reflexions d la meme decouverte." \ 
 
 There can be no doubt that the micrometer of Gascoigne and Auzout is 
 immeasurably superior to any reticule or graduated scale placed in the 
 focus of the telescope, such as was used by Huyghens and the Marquis 
 Malvasia on the Continent, and by Hooke in England. It is right to 
 bear in mind, however, that both Wren and Hevelius had suggested the 
 measurement of small angles, and of the fractional parts of large angles, 
 by means of the revolutions of a screw, although it does not appear 
 that on any occasion they reduced their ideas to practice. 
 
 William Gascoigne, the individual just referred to, was the son of Henry 
 Gascoigne, Esquire, of Middleton, in Yorkshire. While only eighteen 
 years of age he appears to have been actively engaged in observing the 
 celestial bodies, and in advancing the state of optics and practical astro- 
 nomy. He continued to prosecute his labours with remarkable success 
 till the outbreak of the civil wars in 1643, when he joined the cause of 
 Charles I., and fell at the battle of Marston Moor on the 2nd of July, 
 1644, in the twenty-fourth year of his age. To his untimely fate may be 
 applied the language of a distinguished historian in reference to the accom- 
 plished young statesman who, in the previous year, fell at the battle of 
 Newbury, fighting in the same cause : " II mourut, victime d'un temps trop 
 rude pour sa pure et tendre vertu." I Richard Townley states that Gas- 
 coigne had a Treatise on Optics just ready for the press, but that notwith- 
 standing all his efforts he was unable to obtain any trace of it after his 
 death . Sherburne, in his translation of " The Sphere of Manilius," as- 
 serts that Gascoigne was the first person who made a telescope composed 
 of two convex lenses ||. Whether this be true or not, it is very certain, 
 at all events, that he was the first who applied a telescope of such a con- 
 struction, to those purposes for which it is peculiarly designed. 
 
 The application of the telescope to divided instruments, so as to serve 
 in ascertaining the apparent direction of a celestial body, was another of 
 those great improvements which distinguished the progress of practical 
 astronomy in the seventeenth century. The idea of employing the tele- 
 scope in this manner seems to have first suggested itself to Morin, a 
 French astronomer, notorious for his opposition to the Copernican theory 
 of the universe, and his devotion to astrological pursuits. In 1635 he 
 ascertained the interesting fact, that it was possible to see the stars in 
 the daytime by the aid of the telescope, and he sought to avail himself of 
 
 * Hist. Ast. Mod., tome ii., p. 590. t Ibid. 
 
 J Guizot, Histoire de la Revolution d'Angleterre, livre iv. 
 
 Phil. Trans., 1667, p. 457. 
 
 || " The Sphere of Manilius," translated into English, p. 92, fol., London, 1675. 
 
454 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 his discovery in devising a new solution of the problem of the longitude. 
 His method was founded on a comparison of the observed and computed 
 distances of the moon from the stars, but although he succeeded in seeing 
 the stars in the daytime, he in vain sougKt to fix the positions of either the 
 moon or the stars by the aid of the telescope. Indeed, so long as astrono- 
 mers confined themselves to the telescope as originally constructed by 
 Galileo, it was impossible to accomplish such an object, since there was no 
 place of distinct vision at whicb two cross threads could be placed to indi- 
 cate, by their intersection, the invariable position of the optical axis of the 
 instrument. It is a remarkable fact, that the unfortunate Gascoigne was the 
 first person who successfully used the telescope in ascertaining by observa- 
 tion the apparent positions of the celestial bodies. Derham, in a paper 
 which appears in the Philosophical Transactions for the year 1717, has sa- 
 tisfactorily established the claims of Gascoigne upon the evidence of certain 
 letters which passed between him and his friend Crabtree *-. These letters 
 were originally in the possession of Richard Townley, the individual to 
 whom we have already had occasion to allude in connexion with the inven- 
 tion of the micrometer. It may conduce to a clearer understanding of 
 the following extracts from these letters, to bear in mind that the last- 
 mentioned invention affords demonstrative proof that Gascoigne employed, 
 in his astronomical observations, telescopes composed of two convex lenses. 
 
 In a letter to Crabtree, dated January 25, 1640-1, Gascoigne thus 
 writes : " If here (in the focus of the telescope) you place the scale that 
 measures ..... or if here a hair be set that it appear perfectly through 
 the glass ..... you may use it in a quadrant, for the finding of the 
 altitude of the least star visible by the perspective wherein it is. If the 
 night be so dark that the hair, or the pointers of the scale, be not to be 
 seen, I place a candle in a Ian thorn, so as to cast light sufficient into the 
 glass, which I find very helpful when the moon appeareth not, or it is not 
 otherwise light enough." In another letter to Crabtree, dated on Christ- 
 mas eve, 1641, he thus writes : " Mr. Horrocks his theory of the moon 
 I shall be shortly furnished to try, for I am fitting my sextant for all 
 manner of observations, by two perspicills with threads. And also I am 
 consulting my workman about the making of wheels like #, y, 3, E, of 
 diagram 3, to use two glasses like a sector. If I once have my tools in 
 readiness to my desire, I shall use them every night. I have fitted my 
 sextant by the help of the cane, two glasses in it, and a thread, so as to 
 be a pleasant instrument, could wood and a country joiner or workman 
 please me." 
 
 In another letter, the date of which was found by Derham to be worn 
 out, but which was marked as his tenth letter, in Crabtree's own hand- 
 writing, he says : " I have caused a very strong ruler to be exactly made, 
 and intend to fit it with cursors of iron, with glasses in them, and a thread 
 .for my sextant." 
 
 The following extract of a letter from Crabtree to Gascoigne, dated 
 October 30, 1640, will tend still further to establish the same point : 
 " You told me, as I remember, you doubted not in time to be able to make 
 observations to seconds. I cannot but admire it, and yet, by what I saw, 
 believe it ; but long to have some farther hints of your conceit for that 
 purpose. One means, I think, you told me was, by a single glass in a 
 cane, upon the index of your sextant, by which, as I remember, you find 
 the exact point of the sun's rays." In another part of the same letter he 
 
 * Phil. Tran?., 1717, p. 603. 
 
HISTORY OF PHYSICAL ASTRONOMY. 455 
 
 says: " Could I purchase it with travel, or procure it for gold, I would 
 not be without a telescope for observing small angles in the heavens ; 
 nor want the use of your other device of a glass in a cane upon the move- 
 able ruler of your sextant, as I remember, for helping to the exact point 
 of the sun's rays."* 
 
 The perusal of the foregoing extracts cannot leave a shadow of a doubt 
 in the mind of the reader that Gascoigne distinctly perceived the advan- 
 tage of telescopic sights in fixing the position of a celestial body, and that 
 he had actually reduced his ideas to practice, in making observations with 
 the quadrant and the sextant. To him, therefore, must be awarded the 
 credit due to the original invention of this important method of observa- 
 tion. It has been already remarked that the application of the Galilean 
 telescope to that purpose was impracticable. The above-cited extracts 
 from Gascoigne 's letters clearly prove that he had succeeded in fixing the 
 position of the optical axis of his telescope, and in this respect they tend 
 to corroborate the assertion of Sherburne that he was the first who con- 
 structed a telescope composed of two convex lenses. 
 
 The materials which serve to establish the interesting fact that Gas- 
 coigne employed telescopic sights in observing the celestial bodies, were 
 not published until early in the beginning of the eighteenth century, when 
 the same mode of observation had been already known to astronomers for 
 about fifty years. The improvement which he thus effected can only 
 be regarded, therefore, as forming the groundwork of an interesting 
 episode in the history of practical astronomy, rather than as constituting 
 a link in the chain of gradual advancement. In this respect it differs 
 from his invention of the micrometer, which continued after his death 
 to be made use of in the north of England, although it appears to have 
 been unknown for many years both in London and on the Continent. 
 
 The earliest allusion to the use of the telescope in observing the posi- 
 tions of the celestial bodies is contained in Sprat's "History of the 
 Royal Society." In a general exposition of the labours of the Society, to 
 which reference has already been made, he makes the following statement : 
 " They (the Fellows of the Society) have suggested the making of a per- 
 fect survey, map, and tables of all the fixed stars within the zodiac, both 
 visible to the naked eye and discoverable by a six-foot telescope with a 
 large aperture ; towards the observing the apparent places of the planets 
 with a telescope both by sea and land. This has been approved and 
 begun, several of the Fellows having their portions of the heavens allot- 
 ted to them."f 
 
 * The following extracts from the same collection of letters exhibit a beautiful illus- 
 tration of the feeling which ought to reign between persons engaged in scientific pursuits, 
 whether during the period of youthful enthusiasm or that of mature manhood. In a letter 
 to Gascoigne, dated December 8, 1640, Crabtree thus writes: " My friend, Mr. Hor- 
 rocks, professeth that little touch which I gave him of your inventions, hath ravished his 
 mind quite from itself, and left him in an extasie between admiration and amazement. I 
 beseech you, sir, slack not your intentions for the perfecting of your begun wonders. 
 We travel with desire till we hear of your full delivery. You have our votes, our hearts, 
 and our hands should not be wanting if we could further you." In another letter dated 
 December 6, 1641, he thus writes to Gascoigne: " No man that hath written of the 
 diagram (of Hipparchus) understood it fully or described it rightly, but only Kepler and 
 our Horrocks, for whose immature death there is yet scarce a day which I pass without 
 some pang of sorrow." 
 
 + Sprat's "History of the Royal Society," p. 190. The close resemblance of this 
 project to that in which the Berlin Academy of Sciences is engaged in the present day, 
 cannot fail to strike the reader. 
 
456 HISTORY OF PHYSICAL ASTRONOMY. 
 
 In another part of the same work the author states that the Society 
 have made " observations of the fixed stars for the perfecting of astro- 
 nomy by the help of telescopes."* In an account of their optical 
 labours he asserts that they have constructed ~ several excellent tele- 
 scopes of divers lengths of six, twelve, twenty-eight, thirty-six, and sixty 
 feet long, with a convenient apparatus for the managing of them ; and 
 several contrivances in them for measuring the diameters and parts of the 
 planets, and for finding the true position and distances of the sun, fixed 
 stars, and satellites "\ 
 
 In an account of the inventions of Wren (afterwards Sir Chris- 
 topher), one of the Fellows of the Society, Sprat makes the following 
 statement : " He has made two telescopes to open with a joynte like a 
 sector, by which observers may infallibly take a distance to half minutes, 
 and find no difference in the same observation reiterated several 
 times, nor can any warping or luxation of the instrument hinder the truth 
 of it." I 
 
 This seems to be the same instrument as the one mentioned by Hooke 
 in his " Animadversions upon the Machina Celestis of Hevelius," wherein 
 he states in reply to an objection made by Hevelius that telescopic 
 sights had never been applied to large instruments that he had then by 
 him an instrument of Sir Christopher Wren's invention, furnished with 
 two perspective sights of six feet long each, which he made use of for ex- 
 amining the motions of the comet of .1665 . 
 
 It appears that as early as the year 1665, Hooke wrote a letter to 
 Hevelius strongly recommending him to employ telescopic sights in pre- 
 ference to the ordinary pinnules ||. At the meeting of the Royal Society 
 held on the 4th of November, ] 667, there was read a letter from Heve- 
 lius, dated October 21 of the same year, in which he expressed a desire 
 of having one of the longest telescopes made in England pro- 
 vided for him, and of being gratified with a full description, formerly 
 promised him by Mr. Hooke, of the way of applying telescopical sights 
 to sextants. "IT 
 
 It appears from the foregoing statements that at least as early as the 
 year 1665 Wren and Hooke, two of the most distinguished philosophers 
 of the age, had employed telescopic sights in observing the celestial 
 bodies. The earliest observations made by the use of the telescope in 
 this way, of which the details have been actually published, are those of 
 the French astronomer Picard. In the Histoire Celeste of Lemonnier 
 there is an account of observations of the meridional altitude of the sun, 
 made by Picard in the garden of the Eoyal Library of Paris, with a 
 quadrant of nine feet seven inches, and a sextant of six feet, both fur- 
 nished with telescopes. The earliest of these observations is dated 
 October 2, 1667.**. In his treatise on the " Measure of the Earth" the 
 same admirable astronomer has described the different modes of verifica- 
 tion to be employed in using instruments fitted with telescopic sights ff. 
 
 * Sprat's Hist. Roy. Soc., p. 241.' f Ibid., p. 250. $ Ibid., p. 314. 
 
 " Animadversions on the first part of the Machina Celestis," p. 42. London, 4to, 
 1674. 
 
 || Hevelius in the same year replied to Hooke in a letter addressed to the Royal 
 Society, for the contents of which see Hooke's Animadversions, &c., p. 5. 
 
 <f[ Birch, History of the Royal Society, vol. ii. p. 208. 
 
 * Histoire Celeste, p. 11. 
 
 H" See also Anc. Mem. Acad. des Sciences, tome vii., p. 133. 
 
HISTOEY OF PHYSICAL ASTEONOMY. 457 
 
 Hooke, without seeming to be aware of what Picard had done, has also 
 given an account of similar methods of adjustment in his " Animadver- 
 sions upon the Machina Celestis of Hevelius."* 
 
 The establishment of the national observatories of Paris and Green- 
 wich immediately followed the remarkable improvements in practical 
 astronomy above alluded to. The Royal Observatory of Paris was com- 
 menced in 1667, but was not finished before the year 1671. It was a 
 building of great magnificence, designed by Claude Perrault, the famous 
 architect of the Louvre ; but it was constructed without due regard to the 
 purpose for which it was intended. It consisted of a quadrangular pile 
 flanked by two massive towers. NO means were provided in the con- 
 struction of the building for enabling the astronomer to observe the 
 celestial bodies at all altitudes, by means of instruments sheltered under 
 its roof, nor was it possible to repair the omission, on account of the enor- 
 mous thickness of the walls. Dominique Cassini, who had arrived in 
 France in the year 1669, in compliance with an invitation from Louis XIV. 
 to reside in his capital, commenced his labours at the observatory on the 
 14th of September, 1671. It is important to remark, however, that no 
 special duties were assigned to him in connexion with that establishment, 
 nor did he derive any emoluments from the French Government, in con- 
 sideration of his services as an astronomical observer. A liberal pension 
 was, indeed, granted to him upon his arrival in Paris, but this was on ac- 
 count of the sacrifice he had made in leaving his native country to adorn 
 France by his talents f. His superintendence of the Royal Observatory 
 was naturally suggested by the position which he occupied as first astro- 
 nomer of France {, but his duties were altogether discretionary. The 
 other astronomers who had access to the Observatory, occasionally received 
 allowances from the Government for their services, but there was no fixed 
 sum set apart to provide for the annual maintenance of the establish- 
 ment . The consequence of this oversight was, that no definite plan of 
 observation was projected, by an undeviating adherence to which the advan- 
 tages of a national observatory can alone be realised. This circumstance 
 long continued to exercise an injurious influence on the progress of prac- 
 tical astronomy in France. 
 
 The inherent vice in the construction of the Royal Observatory of 
 Paris has been already alluded to. It might be expected that Cassini, 
 who arrived in France when the building was in the course of erection, 
 and in whose opinion upon any subject relating to astronomy the 
 French Government reposed unbounded confidence, would have effectually 
 used his influence in preventing so deplorable a sacrifice of the interests 
 of science to the fancy of the architect. It is true that he did not fail to 
 remonstrate on account of the defective plan of the building, but the 
 modifications proposed by him, shewed that his ideas were not in accord- 
 ance with the existing requirements of practical astronomy. Among the 
 alterations recommended by him, was the construction of an apartment in 
 
 * One of the most remarkable methods of adjustment practised by these astronomers 
 consisted in reversing the instrument so as to determine the error of collimation. It is a 
 curious fact that the Arabian astronomer, Ibyn Jounis had already suggested a similar 
 method of adjustment with respect to the gnomon. Thus, among several modes of veri- 
 fying the perpendicularity of the instrument, he recommends to turn it round and make 
 observations with it in two opposite directions. Delambre, Hist. Ast. Moyen Age, p. 102. 
 
 f Cassini lV.,Memoirespourservir a VHistoire des Sciences, p. 186, 4to, Paris, 1810. 
 
 J First astronomer, at least, in the estimation of the Court of Louis XIV. 
 
 " Memoires pour servir a 1'Histoire des Sciences," p. 186. 
 
458 HISTORY OF PHYSICAL ASTRONOMY. 
 
 which the celestial bodies might be observed from east to west throughout 
 the whole of their diurnal courses *. Such a mode of observation might 
 have been very serviceable for the discovery of satellites, and for the ex- 
 amination of the physical constitution of* the planets, bnt in so far as the 
 determinations of the positions of the celestial bodies was concerned, the 
 tendency of the age was towards observations made exclusively in the 
 plane of the meridian with fixed instruments. The alteration proposed by 
 Cassini was, in fact, such a one as Tycho Brahe would have recommended 
 for the purpose of making ordinary observations of the celestial bodies with 
 his equatorial armillse. Another alteration suggested by him was the 
 admission of the solar light through an aperture, so as to trace upon the 
 floor the daily course of the sun throughout the year. By this con- 
 trivance he contemplated the formation of a vast sun-dial : he also ex- 
 pected to derive from such observations a more accurate knowledge of the 
 variations of refraction. It is not difficult to perceive that such an alter- 
 ation, if it had been carried into effect, would have been in reality a step 
 backwards rather than a positive improvement. The remarkable success 
 which attended Cassini's early efforts of a similar kind at Bologna, seems 
 to have given a bias to his views on practical astronomy, from which he 
 was unable completely to emancipate his mind throughout the whole 
 course of his life. It does not seem to have occurred to him that the use of 
 the telescope and the pendulum, introduced into the practice of observation 
 a degree of delicacy and precision, which left all such clumsy contrivances 
 immeasurably behind. It must be acknowledged, therefore, that notwith- 
 standing the distinguished talents of Cassini, and the many brilliant dis- 
 coveries which he made in celestial physics, the position which he occupied 
 in France at the time of the establishment of the Royal Observatory of 
 Paris, was unfavourable to the advancement of practical astronomy in that 
 country. 
 
 Picard commenced his observations at the Royal Observatory of Paris 
 on the 9th of July, 1673. This admirable astronomer was one of the 
 first to perceive that the improvement effected by Huyghens in the con- 
 struction of clocks completely removed the difficulty experienced by 
 Tycho Brahe and his contemporaries in their attempts to employ the ele- 
 ment of time in astronomical observations. It was now clearly seen that 
 by determining the altitudes of the celestial bodies as they passed the 
 meridian, and noting the times of observation, their declinations and 
 right ascensions Would be obtained with a degree of accuracy commensu- 
 rate to the existing state of theoretical astronomy. The simplicity of this 
 method gave it an incalculable advantage, as soon as it was found to be 
 practicable, over any other that had been hitherto employed for a similar 
 purpose. With the view of carrying it into effect, Picard solicited the 
 establishment of a quadrant in the plane of the meridian, but although 
 he continued to labour several years at the observatory, the object of his 
 request was not accorded to him. Not having such an instrument avail- 
 able to him, he determined the instant of the passage of a celestial body 
 across the meridian, by noting the times at which the body attained 
 the same altitude on each side of that circle f. It is manifest that the 
 
 * " Memoires pour servir a 1'Histoire des Sciences," p. 294. 
 
 f Sometimes the same object was effected by means of observations made with a tele- 
 scope attached to a wall whose face was in the plane of the meridian. This instrument, 
 termed la lunette murale, was also occasionally employed in determining the apparent 
 altitudes of the stars included within a small range of observation. 
 
HISTORY OF PHYSICAL ASTRONOMY. 459 
 
 time equidistant from the two observations, indicated the instant of the 
 passage of the body over the meridian. In applying this method to the sun, 
 Picard did not fail to take into account the correction depending upon the 
 change of declination during the interval included between the two ob- 
 servations. We have seen that this method of observation, which is 
 termed the method of corresponding altitudes, had been already employed 
 by the astronomers of India as well as by the Arabian astronomers, in 
 tracing the direction of a meridian line by means of observations of the 
 sun. It does not appear, however, that they paid any attention to the 
 correction above referred to. The application of the method, however, to 
 the celestial bodies generally, and the necessity of employing a correction 
 in the particular case of the sun, were distinctly pointed out by Thomas 
 Digges in his " Alee seu Scala Mathematics" published at London in 
 1573*. 
 
 Picard 's labours at the Royal Observatory of Paris extend to 1682, in 
 the autumn of which year he died. The name of this astronomer is im- 
 perishably associated with the improvements effected in practical astro- 
 nomy in the seventeenth century. It cannot but be a matter of regret to 
 every person who takes an interest in the progress of astronomical science, 
 that he was not selected to direct the national observatory of his country. 
 Unfortunately his labours were not calculated to attract the attention of 
 that class of persons whose attachment to astronomy is founded solely on 
 the pleasure to be derived from gazing at celestial phenomena. He ap- 
 pears, moreover, to have been a man of a retiring disposition, who de- 
 voted his talents to the cultivation of science for its own sake, regardless 
 alike of the applause of the multitude or the patronage of the great. 
 Hence it happened that although he was, of all the astronomers of his age, 
 perhaps the one most qualified to superintend the duties of an observatory, 
 he was set aside by the government of his own country, and a foreigner 
 appointed over the national observatory, whose labours, indeed, were of a 
 more brilliant character, but were of infinitely less importance to the pro- 
 gress of astronomical science than were those of Picard; It is deplorable 
 to see the interests of a great country thus sacrificed to the caprices of a 
 court. The circumstance may well excite the indignation not merely of 
 Frenchmen, but of every person who is moved by the spectacle of true 
 merit thus contemptuously overlooked, while the individual who exhibits 
 qualities of a more meretricious nature is caressed and favoured. 
 
 La Hire commenced his observations at the Royal Observatory of 
 Paris, in the year 3677. A mural quadrant of 5 feet radius, which Picard 
 had long solicited in vain, was finally adjusted, and permanently fixed in 
 the plane of the meridian on the 25th of April, 1683. La Hire con- 
 tinued to make meridional observations with this instrument for a period 
 of more than thirty years ; but unfortunately none of those later than the 
 year 1 686 have ever been published. 
 
 The establishment of the Royal Observatory of Greenwich was only a few 
 years posterior to that of the similar institution of Paris. The following 
 account of its origin is given by Flamsteed : In 1675, a Frenchman, who 
 styled himself Le Sieur de St. Pierre, represented to the English govern- 
 ment that he was in possession of a method of finding the longitude from 
 
 * The words of Digges are: " .... Non solum per solera orientem aut occi- 
 dentem, seu sub sequalibus altitudinibus deprehensum ( Prosthaphseroesi elapso inter ob- 
 servationes tempore convenient! pro solis rnotu non neglecta), sed etiam per Stellas fixas 
 omnes." ( Supplementa, Capitulum Septimum, Canon Quartus.) 
 
460 HISTOEY OF PHYSICAL ASTEONOMY. 
 
 easy celestial observations, and claimed the reward offered for such a dis- 
 covery. The method which he was desirous of communicating, was 
 founded on a comparison of the observed and calculated distances of the 
 moon from the fixed stars. A committee, consisting of Lord Brouncker, 
 the Bishop of Salisbury, and several other individuals, was appointed to 
 take the subject into consideration. Flamsteed, who, through the influ- 
 ence of his patron Sir Jonas Moore, was nominated one of the members 
 of the committee, was requested to provide the observations which the 
 Frenchman demanded for the purpose of illustrating the practicability of 
 his method. Flamsteed speedily supplied the necessary observations, but 
 he took occasion to remark that, however accurate they might be, the 
 method was still defective, inasmuch as the best astronomical tables some- 
 times erred to the extent of 12' in the moon's place. Moreover, he 
 stated that the method tacitly implied that the places of the fixed stars *in 
 Tycho Brahe's catalogue were absolutely correct, whereas he had found by 
 his own observations that they were generally 5' or 6' in error, and in 
 some instances even more. The commissioners agreed unanimously in 
 the justness of Flamsteed's remarks, and, at the suggestion of Sir Jonas 
 Moore, it was resolved to memorialise the king on the expediency of erect- 
 ing an observatory for the purpose of making observations of the celestial 
 bodies which might serve for the discovery of the longitude, since the 
 solution of that important problem appeared evidently unattainable by any 
 other means *. 
 
 The king gave his cordial assent to the views of the commissioners, 
 and steps were immediately taken to carry them into effect. Flam- 
 steed was appointed Astronomer Royal, with a salary of 100 a year. 
 The warrant of Charles II. for the payment of his salary is dated 
 March 4, 1674-5. He is therein styled " our Astronomical Obser- 
 vator," and it is declared that the duty of his office is " forthwith to 
 apply himself with the most exact care and diligence to the rectifying 
 the tables of the motions of the heavens, and the places of the fixed 
 stars, so as to find out the so much desired longitude of places for 
 the perfecting the art of navigation." The warrant for the building 
 of the Observatory is dated June 2nd, 1675. It modestly announces 
 the royal resolution to build a small observatory in the park at Green- 
 wich "in order to the finding out of the longitude for perfecting navi- 
 gation and astronomy." Sir Christopher Wren is charged to prepare 
 the plan of the building, and to select a proper site for it ; and the Master 
 General of the Ordnance is instructed to advance the funds necessary for 
 its completion, ilpon the condition that the expense of erection do not ex- 
 ceed five hundred pounds f . 
 
 The foundation stone of the observatory was laid on the 10th of August, 
 1675, and the building was finished in less than a year. Flamsteed took 
 up his residence at it on the 10th of July, 1676, and shortly afterwards 
 commenced his duties as an observer. Before proceeding further with the 
 history of this famous observatory, it will be desirable to allude briefly to 
 the important labours of Roemer on the Continent. 
 
 * Baily's Life of Flamsteed, p. 125. 
 
 f Flamsteed states that, besides 500 in money, the king allowed bricks from Tilbury 
 Fort, and some wood, iron, and lead from a gate-house demolished in the Tower; and 
 that he also encouraged them further with a promise of what more would be requisite. 
 According to Mr. Baily, the actual cost of erection amounted to 520 9s. Id. (Baily's 
 Life of Flamsteed, p. 39.) 
 
HISTORY OF PHYSICAL ASTRONOMY. 461 
 
 Olaus Roemer was born at Copenhagen on the 25th of September, 
 1644. When Picard proceeded to Denmark in 1671, for the -purpose of 
 determining the exact position of Uranibourg, the scene of Tycho Brahe's 
 labours, he found Roemer engaged in studying mathematics and astronomy 
 under Erasmus Bartholinus. Having discovered that the young man was 
 possessed of no ordinary talents, the French astronomer employed him as 
 an assistant in his astronomical observations, and, at their conclusion in 
 1672, he brought him along with him into France. In 1675 Roemer 
 communicated to the Academy of Sciences of Paris a memoir, in which 
 he announced his discovery of the gradual propagation of light. This 
 important communication obtained for him a seat in the Academy. He 
 had also apartments assigned to him at the Royal Observatory, where he 
 continued, during his residence in France, tojnake occasional observations 
 of the celestial bodies. In 1681 he returned to Denmark, having been 
 appointed Royal Professor of Mathematics in the University of Copen- 
 hagen. The great reputation which he had already acquired in France, 
 pointed him out as a person eminently qualified to undertake the duties 
 attached to the observatory of that city. The peculiar construction of 
 this edifice has already been briefly alluded to. Roemer did not fail soon 
 to perceive that it could not be advantageously employed for the pur- 
 poses of astronomical observation. In consequence of the instruments 
 being placed at the very top of the building, they were constantly liable to 
 be disturbed in their positions by the violence of tempestuous winds. It 
 was also found to be injurious to the health of the observer to prosecute 
 his labours in so exposed a situation. Roemer, therefore, resolved to 
 obtain the erection of a more suitable observatory in some open district of 
 the country ; but having been unable to realise his views so soon as he 
 desired, he was induced in the meantime to convert his private dwelling- 
 house into a temporary observatory. 
 
 The most remarkable novelty of the Observatorium Domesticum of Roe- 
 mer was the Transit Instrument of which that distinguished astronomer 
 was the inventor*. It was placed so as to make observations with it 
 at a window. In consequence of the interposition of the neighbouring 
 houses, it was impossible to command the view of a very large arc of 
 the meridian. The range of the instrument extended from 20 south 
 declination to 40 north declination. The axis, which was of iron, was 
 five feet long, and an inch and a half thick. Its extremities rested 
 upon iron supports inserted in the sides of the window, and the direc- 
 tion of its position was east and west, so as to allow a telescope attached 
 to it to revolve freely in the plane of the meridian. The telescope was 
 placed near one of the extremities of the axis. In order to obviate 
 . the effects of flexure, the tube of the telescope was composed of two 
 cones attached to each other at their bases. At the focus there were 
 inserted three horrizontal and ten vertical threads, but of the latter only 
 three were used in practice. The illumination of the field of view was 
 effected by means of a lantern placed above the centre of the telescope 
 which threw its light upon a perforated concave speculum inserted a little 
 behind the object-glass, the speculum again reflecting the light along 
 the interior of the tube. In order to admit the passage of the light to 
 the speculum, the upper portion of the tube of the telescope near the 
 object-glass was altogether removed. Towards the other end of the axis 
 was a projecting arm, carrying at its extremity a microscope by means of 
 * Horrebow's Basis Astronomic?., p. 48, 4to. Hafhize, 1735. 
 
462 HISTOBY OF PHYSICAL ASTKONOMY. 
 
 which the declinations of the celestial bodies were read upon a graduated 
 arc fixed opposite to it. The arc, which extended to 75, was divided to 
 every ten minutes. In the common focus of the object-glass and eye- 
 glass of the microscope there were inserted eleven parallel threads, by 
 means of which the interval between two consecutive points of the gradu- 
 ated arc was divided into ten equal parts. The interval between two 
 threads was consequently equal to a minute, and this again, according to 
 Horrebow, the assistant of Roemer, might be subdivided by estimation so as 
 not to commit an error of more than 2 J" or 3" in determining the declina- 
 tion of a celestial body *. The pressure of the telescope and projecting arm 
 upon the axis of the instrument, was counterpoised by a weight tending to 
 pull it upwards at the centre. This contrivance was devised by Roemer 
 some time after the instrument had been in use, in consequence of certain 
 irregularities in the observations, which he could only account for by the 
 flexure of the axis. The error of collimation of the telescope was ascer- 
 tained by reversing the instrument. For this purpose a mark was care- 
 fully observed in the open fields before the instrument was placed in its 
 position. The adjustment of the instrument so as to make the telescope 
 revolve exactly in the plane of the meridian was effected by means of ob- 
 servations of corresponding altitudes of the stars f . Horrebow states 
 that the horizontality of the axis of rotation was carefully ascertained, 
 but he does not mention by what means this object was effected. 
 
 Roemer continued to make observations with this instrument until a 
 suitable observatory was erected for him in the country, when he obtained 
 another of a similar kind but of a more perfect construction. Horrebow, 
 his successor, states that in 1715, he prepared a suitable place for the 
 original instrument in the ancient observatory, and having transported it 
 thither, made many thousand observations with it, which were registered 
 in fourteen folio volumes, when on the 21st of October, 1728, these, 
 as well as all Roemer's observations, and also the others which he himself 
 had made, were destroyed by the fatal conflagration which consumed so 
 large a portion of the city on that occasion J. 
 
 * Roemer's instruments were in general divided in the first instance to every ten mi- 
 nutes, and afterwards subdivided to every minute by means of the microscope, the seconds 
 being estimated as mentioned in the text. From the circumstance of eleven threads 
 being required to divide the space between two consecutive points on the instrument into 
 ten equal parts, Delambre has hastily concluded that the threads performed the function 
 of a vernier, but this is obviously a mistake. 
 
 h Delambre, who can see in Roemer only a person who carried out the ideas of Picard, 
 endeavours, in every possible manner, to diminish the credit due to the Danish astro- 
 nomer for the invention of this invaluable instrument; and, in order to attain his end, he 
 has not scrupled to throw out an insinuation no less at variance with truth than it is un- 
 worthy of his high reputation as an historian of science. Thus, while trying to discover 
 the reasons which induced Roemer to construct his instrument, he expresses himself in 
 
 the following terms: " Peutetre Roemer n'a-t-il ete induit a la faire con- 
 
 struire que pour la raison unique que le mur de sa chambre etait oblique au meridien 
 qu'il ne pouvaity placer un quart de cercle et pas meme la lunette murale de Picard." 
 (Hist. Ast. Mod., tome ii., p. 639.) Now so far from it being true that Roemer fell 
 upon the construction of the transit telescope by mere accident, as Delambre has sug- 
 gested in the foregoing passage, it appears from a letter which the Danish astronomer 
 wrote to Leibnitz in 1700, that as early as the year 1675 he had discovered the peculiar 
 advantages of such an instrument, but was hitherto unable to obtain a suitable building 
 wherein to place it. Thus he commences his description of the instrument in the fol- 
 lowing terms: " De instrumento, cui uni aptum sedificium, jam per 25 annos 
 
 exoptavi, sed nunquam obtinere licuit." (Miscellanea Beroliniensia, tome iii., p. 277.) 
 
 \ Basis Astronomic, p. 55. 
 
HISTORY OF PHYSICAL ASTKONOMY. 463 
 
 Roemer, in his views of practical astronomy, seems to have been far 
 in advance of the age in which he lived. He makes some admirable 
 remarks on this subject, in a letter dated December 15, 1700, addressed 
 by him to Leibnitz, who had solicited his opinion upon the most suitable 
 plan of an observatory. " I differ very widely," says he, " from those 
 who have hitherto decked out observatories more for show than for use, 
 accommodating the instruments to the buildings rather than the buildings 
 to the instruments."* The illustrious Dane, while writing these lines, 
 had doubtless a vivid recollection of the magnificent " Observatoire de 
 parade f" on the banks of the Seine, and of the expedients which Picard 
 and himself were compelled to adopt, while endeavouring to fix a quadrant 
 in the plane of the meridian, in the year 1678 J. The superiority of cir- 
 cular instruments, when compared with the quadrant and sextant, did not 
 escape his sagacity: "I do not concur with others," says he, " in their 
 opinion respecting the construction of instruments, since I consider that 
 the use of the quadrant and sextant should be altogether abandoned, 
 for I would place more confidence in a circle of four feet, than I would in 
 a quadrant of ten feet." He the.n proceeds to describe the plan of an 
 observatory, which he had long desired for himself, and the character 
 of the instruments ,which he designed to employ in it. In both these 
 respects his wishes were fully realised a few years afterwards, as ap- 
 pears from the following description of his Rural Observatory, given by 
 Horrebow : 
 
 " The ' Observatorium Tusculaneum ' of Roemer was built in an open 
 situation upon a gentle eminence, a little to the west of the ancient 
 observatory. It was 17 Danish feet in length, the walls were 5J feet 
 high outside and 6J feet inside. The observations in the meridian 
 were made with an instrument termed the Rota Meridiana, or Meridian 
 circle. It consisted of a circle of 5J feet in diameter, revolving in the 
 plane of the meridian at one of the extremities of a horizontal axis of 
 equal length. A telescope 5 feet long was attached to the eastern face 
 of the circle. The intrument rested upon two solid supports of fir-wood, 
 fitted with bars of metal into which the extremities of the axis were 
 inserted. In order to prevent flexure, the axis was composed of two 
 hollow cones of iron attached at their bases. The focus of the telescope 
 was traversed by seven vertical and three horizontal threads. The divi- 
 sions of the instrument were read by means of two microscopes fixed op- 
 posite the face of the circle at a distance of 10 from each other. The 
 mode of reading off was similar to that practised in the case of the instru- 
 ment already referred to. In order that the instrument might command 
 the whole of the meridian from the northern to the southern horizon, a 
 continuous fissure about 4 inches broad, was formed in the walls and roof 
 of the building, the parts being united by iron bars only in those places 
 where no stars were apparent. 
 
 Roemer did not fail to verify his instrument before commencing his 
 
 * Miscellanea Beroliniensia, tome iii,, p. 277. f M. Arago, Annuaire, 1845. 
 
 \ Horrebow, in his Basis Astronomies, cites a statement of Roemer's to the effect that 
 he, in conjunction with Picard, fixed a mural quadrant in the plane of the meridian, at 
 the Royal Observatory of Paris, in the year 1678. This seems to be contradicted by La 
 Hire, who asserts that the mural quadrant was adjusted permanently in its position only in 
 the year 1683. It is probable that the expedient employed by Picard and Roemer was 
 merely of a temporary nature. 
 
 Miscel. Berol., tome iii., p. 277. 
 
464 HISTORY OF PHYSICAL ASTRONOMY. 
 
 observations with it. The deviation of the optical axis of the telescope 
 from a line perpendicular to the axis of rotation, or in other words, the 
 error of collimation, was ascertained by reversing the instrument. As 
 this mode of verification was troublesome^he subsequently effected the same 
 object by observing two distant marks in the horizon, diametrically opposite 
 to each other. The horizontality of the axis of rotation was ascertained by 
 means of the plumb-line. The adjustment in the plane of the meridian 
 was effected by the aid of observations of Capella and Lyra3, during 
 their passages above and beneath the pole. 
 
 The other instrument employed by Roemer in his Observatory was a 
 telescope revolving in a plane perpendicular to the meridian. It was fur- 
 nished with a system of vertical threads at its focus, similarly to the tele- 
 scope of the meridian circle, being designed to be used in observing the 
 passage of the celestial bodies across the prime vertical *. 
 
 In order to exhibit an illustration of his mode of observing, Roemer drew 
 up a list of the declinations and right ascensions of certain stars, deter- 
 mined by him with the meridian circle on three consecutive nights in the 
 month of October, 1706. This small collection received from him, in 
 
 * It is to be regretted that Delambre, who was so eminently qualified to appreciate the 
 value of the improvements in practical astronomy effected by Roemer, has allowed his 
 mind to be so overruled by preconceived notions as to have been betrayed into a com- 
 plete misrepresentation of the labours of that astronomer on the present occasion. Thus, 
 in his description of the Observatorium Tusculaneum, the following extraordinary pas- 
 sage occurs : " On y voit deux portes, quatre fenetres, un lit, une cheminee, quatre 
 horloges, et deux lunettes, 1'une meridienne, 1'autre, plus petite, qui tournait dans le pre- 
 mier vertical. Mais ce qu'il y a de singulier c'est que de quatre fenetres, deux sont dans 
 la direction de 1'axe de rotation, et qu' une seule tout au plus parait etre dans la direction 
 de la lunette principale ( Planche VI II.), et que la Planche III. destinee principalement a 
 faire connaitre 1'instrument, et qui nous montre Roemer occupe a observer, parait prouver 
 1'impossibilite absolue de diriger la lunette au nord ; et quand tout serait ouvert, et la lunette 
 tournee au nord, on ne concevrait pas mieux comment 1'observateur pourrait passer du cote de 
 1'oculaire." (Hist. Ast. Mod. torn, ii., p. 654). It will be evident to any person who be- 
 stows even a passing glance over the pages of Horrebow's Basis Astronomies, that Delambre, 
 in the foregoing passage, confounds the Observatorium Domesticum fitted up by Roemer in 
 a corner of his house in the year 1690, with the more complete edifice erected by him in 
 1704, which is denominated by Horrebow the Observatorium Tusculaneum. In fact, 
 Plate III. refers to the former of these observatories, and to the original transit instru- 
 ment (termed by Horrebow the Machina Domestica), while, on the other hand, Plate 
 VIII. is intended to represent the Tusculan Observatory with the Rota Meridiana and 
 the prime vertical telescope. It has been mentioned in the text that the observations 
 with the Rota Meridiana, instead of being made at a window barely opposite to the 
 telescope, as Delambre seems oddly enough to imagine, were in reality made through a 
 fissure in the building, situate exactly in the plane of the meridian ; and that so far from 
 its being impossible to direct the telescope towards the north, the extent of the fissure 
 allowed its being directed to any point in the meridian included between the northern 
 and southern horizons. The following words of Horrebow are so explicit upon this 
 point that it seems incredible that they should have escaped the notice of Delambre : . 
 "Ut autem tubo cum machina primaria M (Rota Meridiana) circumvoluto totus meridi- 
 an us ab horizonte australi per zenith usque ad horizontem borealem pateret, parietes 
 sedificii cum tecto acuminate rimam continuam habebant quatuor pollices latam, . ." 
 (Basis Astronomies, p. 141). The following remark of Delambre's in reference to the 
 same subject is, perhaps, still more calculated to excite astonishment than anything that 
 has yet been cited : " Horrebow regrette qu'on n'eut pas lafaculte d'observer les etoiles 
 circumpolaires ; ses planches paraissent demontrer cette impossibility et cependant la 
 polaire ; la tete du Dragon, la Lyre, la tete et la queue du Cygne, deux etoiles de la 
 queue de la Grande Ourse, ont ete observees au dessous comme au dessus du pole." 
 (Hist. Ast. Mod., torn, ii., p. 654). The words in Italics, which are so inserted in the 
 original, with the evident intention of impressing their significance more strongly upon 
 the reader, afford a remarkable illustration of the facility with which a person may be 
 
HISTORY OF PHYSICAL ASTRONOMY. 465 
 
 consequence, the appellation of the Triduum. Unfortunately, it con- 
 tains the only results of his labours that have been preserved, all his other 
 observations having been destroyed during the fire of 1728. In accuracy 
 they are surpassed only in a slight degree by the observations of the pre- 
 sent day. The passages across the meridian are generally observed at the 
 three vertical threads, or wires of the focus, as they are now technically 
 termed. The time is in several instances assigned to fractions of a second. 
 It is no mean tribute to the memory of Roemer, that the observations of 
 the Triduum constitute the earliest collection of facts that have been 
 deemed worthy of being employed as data in the solution of the great 
 problem of modern astronomy the motion of the Solar System in space. 
 
 The Tusculan Observatory was built in the year 1704, and in the month 
 of December of the same year, Roemer commenced his labours in it, 
 which he continued to prosecute till his death in 1710*. Horrebow states 
 that the observations made by Roemer during this period, filled three large 
 folio volumes, and equalled in number those of Tycho Brahe. The ob- 
 servations were continued after the death of Roemer, till the autumn 
 of 1711, when the Observatory, by some unexplained casualty, was de- 
 stroyed f. The instruments, which sustained great injury on this occasion, 
 were transported to the ancient Astronomical Tower, where, with all the 
 observations, except the Triduum of Roemer, a copy of which was safely 
 deposited in the hall of the Academy, they were finally consumed by the 
 dreadful fire of 1728. 
 
 Roemer was the first person who constructed an altitude and azimuth 
 circle. Tycho Brahe and Hevelius had made use of quadrants moveable 
 about a vertical axis, but Roemer did not fail to perceive that such instru- 
 ments were essentially defective. The diameter of the vertical circle of 
 Roemer's instrument was three feet five inches ; the diameter of the azi- 
 muth circle was three feet eight inches. The instrument was chiefly used 
 
 betrayed into error upon any subject, when, instead of carefully examining facts, he 
 allows his mind to be so wholly engrossed by his own favourite ideas as to look for nothing 
 else except what may appear to corroborate them. We venture to assert, that the words 
 above cited are not to be found anywhere in the book which Delambre professes to be 
 analyzing. Indeed, it is obvious that they are utterly inconsistent with Horrebow's de- 
 scription of the Tusculan Observatory, the edifice to which they relate. Delambre him- 
 self has not failed, in the above passage, to remark that the regret expressed by Horrebow 
 is at variance with the fact of several circumpolar stars having been observed by Roemer ; 
 but it seems wholly unaccountable that he was not thereby induced to look more nar- 
 rowly into the subject, so as to discover the origin of this apparent contradiction. It is 
 not difficult to trace the passage in the Basis Astronomic^ which Delambre has so griev- 
 ously misinterpreted (see p. 151 of the work just cited), but it is manifest that only the 
 most unwary explorer of that work, seduced by some mental hallucination, could have 
 been ensnared by such a passage. 
 
 * Delambre remarks, that as the observations which form the basis of Roemer's 
 fragment on the annual parallax of the terrestrial orbit, inserted by Horrebow in 
 his Basis Astronomice, were made by Roemer in the year 1692, they were anterior to the 
 erection of the Tusculan Observatory, and he therefore concludes that we are totally ig- 
 norant of the kind of instrument employed by Roemer in these observations. (Ainsi 
 nous ne savons pas quel instrument il a employe dans ces observations. Hist. Ast. Mod., 
 torn, ii., p. 640.) This is another striking instance of the mistakes into which Delambre 
 has fallen by confounding the Observatorium Domesticum of Roeraer with the Observa- 
 torium Tusculaneum. The observations referred to were, in fact, made at the former of 
 these edifices, (which was fitted up as early as 1690,) with the original transit instrument, or 
 Mac.hina Domestica, already described in the text. 
 
 f* Horrebow simply says " Postea desolatum estobservatorium." From this expression, 
 and also that which follows, " atque instrumenta jam magnis ictibus fracla" it would 
 seem that the building was overthrown by the violence of some dreadful storm. 
 
 H H 
 
466 HISTOET OF PHYSICAL ASTRONOMY. 
 
 in observing corresponding altitudes of the sun and stars, for the purpose 
 of regulating the clock, and adjusting the positions of the meridional in- 
 struments. 
 
 Koemer also constructed an equatorial* instrument, by means of which 
 he was enabled to follow a celestial body throughout the whole of its 
 course above the horizon, and also to measure the differences of the right 
 ascensions and declinations of two stars situate very near to each other. 
 Horrebow states that the object for which Roemer expressly constructed 
 this instrument, was to determine the parallaxes of the planets, by mea- 
 suring their distances from the neighbouring stars at different altitudes 
 above the horizon. We have seen that in 1665 Hooke proposed to effect 
 the same object, by making observations of a similar kind in the meridian 
 under different latitudes. 
 
 There are few individuals, of ancient or modern times, who effected 
 improvements in practical astronomy equal in importance to those due to 
 Roemer. It is a remarkable fact that the Meridian Circle, the Altitude 
 and Azimuth Circle*, and the Transit Telescope, all of which were 
 invented by this astronomer, form the capital instruments of the Central 
 Observatory of Russia, erected recently at Pulkowa, the most magnificent 
 institution that has been established in ancient or modern times for the 
 purposes of astronomical observation. 
 
 Horrebow, who in 1710 succeeded Roemer as Astronomer Royal of Den- 
 mark, has given a detailed account of the catastrophe which resulted in 
 the destruction of the astronomical observations of Roemer, as well as all 
 those made by himself. He had been engaged at his own house on the 
 evening of October 20, 1728, in writing a commentary upon a fragment 
 of Roemer's on the Annual Parallax of the Terrestrial Orbit, which he 
 had a short time previously discovered among the manuscripts of that 
 astronomer, when his attention was aroused by a confused noise of drums 
 and bells, announcing that a serious conflagration had broken out in the 
 city f. As the place where the fire was raging, was at a considerable dis- 
 tance from his own house, he was for some time in hopes that it would be 
 extinguished without occasioning him any inconvenience. The wind, 
 however, having unfortunately shifted about eight o'clock in the evening, 
 the fire now began to approach his own dwelling-house. Presently frag- 
 ments of burning material fell into his court, while other portions, alight- 
 ing on the roof of his house, threatened it with instant danger. There 
 was now no time to be lost. His maid-servants were hastily conducted 
 out of his house, along with eight children, four of whom were in a state 
 of nudity, while the nurse carried in her arms an infant which had been 
 only recently born. His wife and his eldest son, a youth of sixteen years 
 of age, remained with him, and, with other friends, assisted in transport- 
 ing his effects to the Hall of the Academy. This new place of refuge 
 
 * The use of the Vertical Circle of Pulkowa is indeed different from that of Roemer's 
 instrument, being employed mainly in observing the celestial bodies a few minutes before 
 and after their culmination. 
 
 f The mode in which poor Horrebow endeavours to bring the dreadful catastrophe be- 
 fore the mind of the reader is quite dramatic. He supposes himself to be engaged in 
 writing his commentary, and to be interrupted in the midst of his labours (as was really 
 the case) in the following manner : " Namque ex observationibus ab anno 1692 usque ad 
 1702 ipsum beatum authorem parallaxia orbis annui deduxisse ex tota dissertatione, im- 
 primis, 160, clarum est. Sedquid audio ! Tumultus hominwn in plateis cursitantium 
 ct clamantium ! Sonitus fistularum, tympanorum, campanarum, Sfc. Eheu ! incendium 
 ultra modum vires et increments sumens. Die 20 Octob. 1728, hor. 7, vespert. (Basis 
 Astronomic, p. 70. ) 
 
HISTORY OF PHYSICAL ASTRONOMY. 467 
 
 being ere long threatened with conflagration also, Horrebow was compelled 
 to remove his effects to the Astronomical Tower. His wife, worn out 
 with fatigue and anxiety, went in quest of her children, while he, with 
 his eldest son, stationed himself in the Tower, whence he could perceive 
 his house falling a prey to the fury of the flames. About four o'clock in 
 the morning of the 21st of October, the wind having again shifted, the 
 fire began to threaten the Astronomical Tower. By this time the avenue 
 to the superior part of the Tower, where Horrebow had stationed himself, 
 was almost completely blocked up with a multitude of effects which had been 
 deposited for safety by various persons, so as nearly to prevent his descent. 
 The near approach of the fire now suggested the certain conviction that 
 the Tower would speedily become a prey to the flames. The occasion for 
 taking some decisive step was therefore urgent. Some bedding which he 
 had thrown out at a window, was immediately taken away by thieves. He 
 had now to consider only his personal safety. Before leaving his own 
 house he had searched out some manuscripts and a few engravings, which 
 he locked up in a desk, and brought along with him to the Tower. Being 
 anxious to carry away as much of what was really valuable as he possibly 
 could, he was desirous of leaving the desk behind him, but amid so much 
 confusion he lost the key, so that he was unable to obtain access to the 
 manuscripts which he had locked up in it, and he was in consequence re- 
 duced to the necessity of carrying it bodily along with him. This unfor- 
 tunate circumstance prevented him from carrying away other things of 
 greater value. The descent to the bottom of the Tower had now become 
 extremely hazardous. Abandoning, therefore, everything except the desk, 
 he hastened down with it at the risk of his life, and escaped at one of the 
 doors in a state of mind bordering upon complete distraction. Shortly 
 afterwards the Tower was enveloped in flames, and all that was contained 
 in it irrecoverably perished ! 
 
 Horrebow states that he was anxious to record these particulars, 
 lest it should be thought by posterity that the astronomical observations 
 made by Roemer and himself had perished through any fault on his part. 
 Doubtless no one who reads his sad tale will be disposed to harbour such 
 an accusation against him, or to cherish towards him any other feeling 
 than that of deep commiseration for his irreparable misfortune. Notwith- 
 standing the many valuable articles of his own which perished on that 
 occasion, he asserts that there was nothing which he regretted at the 
 time, or which he still continued to regret, except the loss of these obser- 
 vations. He congratulates himself, however, on having rescued from the 
 flames the fragment of Roemer's on the Annual Parallax of the Terres- 
 trial Orbit. 
 
 We now resume the history of the Royal Observatory of Greenwich. 
 Flamsteed, who was appointed Astronomer Royal, was born at Denby, 
 near Derby, on the 19th of August, 1646. His early predilection for 
 astronomy is evinced by an observation of an eclipse of the sun made by 
 him in the year 1662, the record of which appears among his MSS. pre- 
 served at Greenwich. He continued to make observations of celestial 
 phenomena at his native place, till the year 1674, when he was induced by 
 a circumstance, to which allusion has already been made, to transfer his 
 residence to London. When he entered upon his duties at Greenwich, 
 he found that the Government had made no provision to enable him to 
 prosecute his observations, by furnishing the establishment with a collec- 
 tion of suitable instruments. The only appliances which he possessed for 
 
 H H 2 
 
468 HISTORY OF PHYSICAL ASTRONOMY. 
 
 this purpose, were an iron sextant of seven feet radius, and two clocks 
 given him by his kind patron, Sir Jonas Moore, and a quadrant and two 
 telescopes which he brought with him from Derby. The angles were 
 measured with the sextant by the aid of a contrivance which Hooke had 
 suggested in his " Animadversions on the Machina Celestis of Hevelius." 
 A screw working upon the edge of the instrument (which was racked for 
 this purpose) imparted a slow motion to the moveable index, upon the end 
 of which it was fixed, the angles being measm*ed by counting the revolu- 
 tions and parts of a revolution of the screw. The clocks were made by 
 Tompion, the most celebrated artist of the day. The pendulums were 
 thirteen feet long, and made each a single vibration in two seconds of 
 time. The clocks required to be wound up only once in twelve months. 
 The quadrant which Flamsteed brought with him from Derby had a radius 
 of three feet, and was employed by him in regulating his clocks by means 
 of the observed altitudes of the sun or stars *. 
 
 Flamsteed commenced his labours at the Royal Observatory of Green- 
 wich on the 29th of October, 1676. The plan of observation at first 
 pursued by him was the same as that practised by Tycho Brahe and the 
 earlier astronomers. The intermutual distances of the stars were deter- 
 mined by observation, and their positions 'relative to two great circles in 
 the celestial sphere were deduced from these results by trigonometrical 
 calculation. Flamsteed had not long continued his observations, when he 
 found that Hooke's contrivance for measuring angles with the sextant 
 could not be implicitly confided in. He, therefore, drew diagonals upon 
 the limb towards the end of the year 1677, and subsequently ex- 
 pressed each angular distance determined with the instrument not only, as 
 hitherto, in terms of the revolutions and parts of a revolution of the 
 screw, but also in degrees, minutes, and seconds. This practice was 
 found by him to be very useful in checking any inaccurate reading of the 
 observations. 
 
 In order that he might be enabled to deduce useful results from his 
 observations, Flamsteed was desirous of ascertaining the latitude of his ob- 
 servatory, the place of the equinox among the stars, and other points of 
 essential importance; but these objects could not be effected by means of 
 the sextant, which served only to determine the apparent positions of the 
 celestial bodies relative to each other. He perceived that for this purpose 
 a mural quadrant was necessary, and therefore as soon as he entered the 
 observatory he endeavoured to obtain one. Shortly afterwards, Hooke 
 was charged by Sir Jonas Moore, to construct a mural quadrant of ten 
 feet for the observatory ; but the instrument, when completed, was found 
 to be totally unmanageable. Flamsteed, therefore, now began to think 
 how he might take meridional altitudes with his sextant, and he so far 
 succeeded in his object as to be enabled, in 1677, to determine by its aid 
 the latitude of the observatory, which he found to be 51 28' 10". 
 
 Flamsteed now proceeded to correct the elements of the solar theory 
 by means of his own observations. He devised 011 this occasion an inge- 
 nious method for determining the absolute right ascension of the sun. 
 
 * Flamsteed states that he continued to use this quadrant till June, 1678, when he 
 obtained a neater one from the Royal Society, which, however, he was compelled to 
 restore to its owners in the month of October, of the following year. This circumstance 
 induced him to construct a new quadrant of 50 inches radius, fitted with peculiar contri- 
 vances, by means of which he was enabled to ascertain the time from observation within 
 three seconds (Daily's Life of Flamsteed, p. 45.) 
 
HISTORY OF PHYSICAL ASTRONOMY. 469 
 
 He remarked that by observing the meridional altitude of that body near 
 each equinox, two times might be found when he had the same declina- 
 tion ; and by the tables, the intermediate arc described by the sun might 
 be found, half of whose excess above a semicircle (if it were more than 
 one), or half of whose defect (if it were less), would be his true distance 
 from either equinox at those times *. This idea forms the germ of a fun- 
 damental method of great importance which astronomy owes to Flam- 
 steed, and which we shall presently have occasion to allude to more par- 
 ticularly. 
 
 Finding by experience that the sextant was very ill adapted for deter- 
 mining the meridional altitudes of the celestial bodies, and that the 
 Government was not disposed to supply him with a mural arc, Flamsteed 
 resolved to construct an instrument of the latter description at his own 
 expense. This design was carried into effect by him in the year 1681; 
 but the instrument was not fixed in the meridian till 1683. It was 
 of the same radius as the sextant. The arc was made equal to 140 
 in order to allow observations being made of all the stars which passed 
 the meridian between the north pole and the southern horizon. Being 
 very weakly constructed, the instrument was found to have warped when 
 placed in the meridian. Flamsteed, however, was of opinion that with 
 due care it might be usefully employed notwithstanding this defect. Ac- 
 cordingly, during the period included between the years 1683 and 1686- 
 he continued to determine the altitudes of the celestial bodies with it, 
 and in the following year he constructed a small catalogue of stars to serve 
 as points of reference in his future observations, founded upon the results 
 obtained by the aid of this slight arc and the sextant f. 
 
 Having acquired possession of a small property by the death of his 
 father in 1688, and seeing no prospect of being furnished with any instru- 
 ments by the Government, Flamsteed now resolved to construct a strong- 
 mural arc at his own expense. He had already commenced operations for 
 this purpose when, his assistant Stafford dying in the month of May of 
 the year above-mentioned, he engaged in his service the celebrated Abra- 
 ham Sharp I. According to his plan of the instrument, the edge was to 
 
 * Baily's Life of Flamsteed, p. 50. 
 
 + This was a catalogue of 130 stars reduced to the year 1686, which he continued to 
 use in computing from his observations the places of the moon and planets, even for some 
 time after he had commenced his observations with the mural arc in 1689. 
 
 Abraham Sharp was born at Little Horton, near Bradford, in Yorkshire, about the 
 year 1651. After receiving the elements of a sound education at his native place, he was 
 put as an apprentice to a merchant, in Manchester ; but having no natural inclination to- 
 wards commerce, he quitted his situation with his master's consent, and subsequently 
 opened a school in Liverpool, at the same time cultivating an acquaintance with mathe- 
 matics and astronomy. Shortly afterwards he removed to London, where he became 
 known to Flamsteed, who was then about to assume the superintendence of the Royal 
 Observatory of Greenwich. In 1688 he was appointed by Flamsteed to be his assistant/on 
 which occasion he constructed the famous mural arc with which that astronomer made the 
 most valuable part of his observations. Finding that the fatigue of night observation did 
 not suit his weakly constitution, he retired to his native place, where he spent the re- 
 mainder of his days, living upon the proceeds of a small patrimonial estate. Here he 
 erected an observatory, which he fitted up with instruments all of his own construction. 
 He also made his own telescopes, ground his own lenses, and constructed all sorts of tools 
 used by artificers, besides contriving and executing a great variety of ingenious pieces of 
 mechanism. Moreover he is the author of a mathematical work containing a collection 
 of most elaborate tables relating chiefly to logarithms. Although he lived in great re- 
 tirement, he carried on an extensive epistolary correspondence with Newton, Halley, and 
 all the most celebrated mathematicians of his time. In private life he was most exera- 
 
470 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 be racked so as to measure the angles by Hooke's method, while at the 
 same time, as in the case of the sextant, diagonals were to be drawn upon 
 the limb. Sharp, who was at once an ingenious mathematician, an expert 
 calculator, and a skilful mechanic, racked the edge of the limb, prepared 
 the index, and fixed the arc on the wall. Afterwards he divided and en- 
 graved the limb " so exquisitely," says Flamsteed, "as to excite the ad- 
 miration of every beholder." The instrument was not completely ready 
 for use till the month of October, 1689. Fourteen months were occupied 
 in its erection, and the total cost to Flamsteed was no less than one hun- 
 dred and twenty pounds, not one farthing of which was ever refunded to 
 him by the Government. 
 
 The mural arc erected by Flamsteed on this occasion was made equal to 
 140, as in the case of the former instrument of the same description. 
 Its radius was 79 inches in length. The limb was, in the first instance, 
 divided to every 5', and was then subdivided into smaller parts by 
 means of diagonals. For this purpose the fiducial edge of the moveable 
 index, included between the outer and inner arcs of the instrument, was 
 divided into five parts so as to indicate minutes *, and each minute was 
 subdivided into six equal parts, each equal to 10", which again might be 
 bisected by estimation so as to obtain a final subdivision to every 5". 
 
 Before commencing his observations with the mural arc, Flamsteed 
 took the precaution of ascertaining whether the zero point of division had 
 undergone any alteration with respect to the zenith, during the interval 
 that had elapsed since it was marked upon the limb. This was effected by 
 observing certain stars near the zenith, first with the instrument itself 
 attached to the eastern face of the meridian wall, and then observing 
 the same stars with the telescopic index of the instrument transported to 
 the western face of the wall. Half the difference of the zenith distances 
 of each star determined in this manner, gave the corresponding error of 
 collimation of the instrument, and the mean of all the results gave the 
 mean error of collimation. From observations of this kind, Flamsteed 
 found that the zenith distances of those stars which passed the meridian 
 towards the north, were all too great as determined by the instrument. 
 The error on the llth of September, 1689, amounted to 45". In the 
 course of his subsequent observations, he found that the error increased 
 slowly in the same direction every year, a circumstance which he at- 
 tributed to the gradual sinking of the southern extremity of the wall to 
 which the instrument was attached. He did not fail, therefore, to deter- 
 mine from time to time, by means of suitable observations, the amount of 
 deviation arising from this cause. He remarked that the stars in the feet 
 of the constellation Gemini afforded peculiar advantages for this purpose; 
 for being situate near the solstitial colure, they were liable to change very 
 slowly from the retrograde motion of the equinoctial points, and, being at 
 
 plary. He died on the 18th of July, 1742, in the ninety-first year of his age. The 
 delicacy of Sharp's hand for manipulative operations was exquisite. He is generally 
 admitted to be the first person who cut divisions on astronomical instruments with any 
 pretension to accuracy. He is also the first of those remarkable men by the aid of whose 
 mechanical talents the Astronomers of the Royal Observatory of Greenwich were enabled 
 to execute the series of observations which have won for that establishment its unrivalled 
 reputation. 
 
 * The intervals in this case, being the results of a strict mathematical process, were not 
 exactly equal, but the difference between two consecutive divisions could scarcely be con- 
 sidered sensible. 
 
HISTORY OF PHYSICAL ASTRONOMY. 471 
 
 the same time not far removed from the ecliptic, they were subject to only 
 a very small error in the same direction from the parallax of the earth's 
 orbit *. 
 
 Flamsteed's next object was to ascertain the errors produced by the in- 
 strument on the right ascensions of the stars. He remarked that such 
 errors might arise either from the plane of the instrument not being 
 exactly in the meridian, or from the object-glass of the telescope not being 
 properly adjusted in its cell. He proposed to determine by one process 
 the combined effect due to these two causes. This object he accomplished 
 for all altitudes included between the equator and the northern tropic, by 
 comparing the times of the sun's passage over the meridian, as deduced 
 from observations of equal altitudes on each side of that circle, with the 
 corresponding times obtained directly by the aid of the instrument. In this 
 manner he found that at 40 of zenith distance, the transit of a celestial 
 body, when observed with the instrument, took place 33 seconds earlier than 
 the true time. The errors for the parts of the arc, comprised between 
 the tropic and the north pole, and between the equator and the southern 
 horizon, were found by comparing the differences of the right ascensions 
 of several bright stars, derived from observations of their intermutual 
 distances with the sextant, with the corresponding results deduced from 
 observations with the instrument itself. Having thus ascertained the errors 
 of the plane of the instrument at various zenith distances throughout the 
 whole extent of the arc, Flamsteed arranged the results in a table, which 
 he continued to use from the year 1690, in determining by observation 
 the right ascensions of the stars f. 
 
 Flamsteed commenced his course of regular observations with the 
 mural arc on the llth of September, 1689. But before he could deduce 
 any useful results from them, it was necessary for him to determine the 
 latitude of his observatory with greater accuracy than he had hitherto 
 done. From observations of the least and greatest altitudes of circum- 
 polar stars, he finally concluded its true value to be 51 28' 34". He next 
 proceeded to derive from his observations, the obliquity of the ecliptic, 
 and the other fundamental points of astronomical science. His labours 
 on this occasion are distinguished by considerable originality and address. 
 The most important part of them is that which relates to the determina- 
 tion of the absolute right ascension of a celestial object. It has been 
 already mentioned that he succeeded in determining the place of the sun 
 with respect to the solstice, by observing that body at equal altitudes near 
 the equinoxes, and halving the intermediate arc. The magnitude of this arc, 
 however, could only be ascertained by computation, and consequently the 
 accuracy of the result depended in a great degree upon the solar tables. 
 Flamsteed eluded this source of error by a process which enabled him to 
 determine not merely the place of the sun with respect to the equinox, 
 but also the places of the stars relative to the same point. For this purpose 
 the interval between the times of the sun's passage over the meridian and 
 that of a bright star near the equator, was noted by the aid of the pen- 
 dulum clock, on the occasions when the sun attained the same meridional 
 altitude near the two equinoxes. Now since the sun has been continually 
 
 * Historia Caelestis, vol. iii., p. 112. 
 
 f Hist. Csel., vol. iii., p. 133. This table does not appear in the Historia Calestis, 
 but Mr. Daily found it, among the manuscripts of Flamsteed, and has inserted it in his in- 
 teresting collection of memorials respecting the astronomer. (See Life of Flam- 
 steed, p. 374.) 
 
472 HISTORY OF PHYSICAL ASTRONOMY. 
 
 travelling in his orbit, during the period included between the two observa- 
 tions, while on the other hand the position of the star is invariable, it is 
 manifest that the excess of the second of these intervals over the first, 
 when converted into space by supposing very 1 5 equivalent to an hour, 
 will indicate the arc of right ascension described by the sun during the 
 intermediate period. The half of this arc then gives the distance of the 
 sun from the solstice at either observation, 'and since the difference of the 
 right ascensions of the sun and star is known by the clock, the distance 
 of the star from the solstice is also at once ascertained. 
 
 It is obvious that the practice of observing a star in connexion with 
 the sun according to the above method, is attended with a twofold advan- 
 tage. In the first place it serves to determine the right ascension of the 
 sun independently of the solar tables, by affording an accurate measure- 
 ment of the arc described by that body, during the interval of time that 
 elapses between the two observations. Secondly, it leads at the same time 
 to a knowledge of the absolute right ascension of the star. According to 
 every method hitherto practised by astronomers, the ascertainment of the 
 absolute right ascension of the sun was effected by noting the time of his 
 passing through the equinox, and calculating his subsequent motion by 
 the aid of the solar tables. The places of the stars with respect to the 
 equinox were then determined by measuring the distance between the sun 
 and a bright star, employing for this purpose the moon or Venus, as the 
 intermediate object of observation. The method of Flamsteed had the 
 advantage of assigning an easy and direct process by means of which the 
 right ascensions of the sun and star might be simultaneously determined. 
 Moreover, since the altitude of the sun is supposed, according to this 
 method, to be the same at each of the two extreme observations, the final 
 results are not affected by any uncertainty in the values of parallax or re- 
 fraction. They are also, independent of a knowledge of the latitude of 
 the place of observation, an element which entered essentially into all 
 the ancient methods for determining the place of a celestial body with 
 respect to the equinox. 
 
 The absolute right ascension of any one star being accurately deter- 
 mined, the right ascensions of all the others may be readily found by a 
 comparison with the fundamental star. In the year 1690 Flamsteed 
 determined the absolute right ascensions of no less than forty stars by 
 comparing them directly with the sun in the mode above described, and 
 employed the results in establishing a series of points of reference to aid 
 him in his future observations. By his labours on this occasion his name 
 has become imperishably associated with one of the fundamental methods 
 of astronomical science. 
 
 Having established the elements of the solar theory and other points 
 of primary importance, Flamsteed was now enabled to derive from his 
 observations the absolute positions of the celestial bodies. He therefore 
 proceeded to compute the observed positions of the moon and planets, 
 with the view of making the results subservient to the rectification of the 
 theory of their movements. He also commenced the formation of a cata- 
 logue of the fixed stars upon a more extensive scale than any which had 
 been hitherto executed. It must be acknowledged that in the prosecution 
 of these arduous labours, he received very little assistance from the Go- 
 vernment. They had not hitherto furnished the observatory with a single 
 instrument, nor did they allow him even the smallest sum for the occa- 
 sional repair of such instruments as he was actually using. When he 
 
HISTORY OF PHYSICAL ASTRONOMY. 473 
 
 commenced his observations, they assigned to him "a surly labourer" to 
 manage the sextant, but they seemed to imagine that the salary of a hun- 
 dred pounds a year which he received was amply sufficient to ensure his 
 own performance of all the other duties connected with the observatory*. 
 To execute such a task, however, was manifestly impossible. Under 
 these circumstances he was compelled to procure an assistant, by paying 
 him a small salary out of his own pocket. To meet the expenses which 
 the illiberal treatment of the Government thus entailed upon him, he was 
 for some time reduced to the necessity of adding the profession of teacher 
 to his usual avocation. Well might he remark that he earned the salary 
 doled out to him by labour harder than thrashing f. The difficulties of 
 his situation were further aggravated by the possession of a feeble frame 
 of body, and the periodical attacks of a painful malady to which he was 
 constitutionally subject. 
 
 The illustrious Newton was the first person who availed himself of the 
 observations made at the Royal establishment of Greenwich. In the 
 years 1694-5 he obtained from Flamsteed a considerable number of ob- 
 served places of the moon, which proved very serviceable in guiding him 
 to a knowledge of some of the more hidden inequalities in the motion of 
 that body, and thereby affording a seasonable confirmation of the theory of 
 universal gravitation J. 
 
 Notwithstanding the numerous disadvantages against which he had to 
 struggle, Flamsteed continued with unremitting assiduity to labour in the 
 discharge of his duties, and he confidently looked forward to the prospect 
 of being one day enabled to present the results of his observations to the 
 world in a satisfactory form, although he clearly saw that, if left wholly to 
 his own resources, it would be impossible for him to obtain a speedy 
 realisation of his wishes in this respect. Unlike many astronomers, he 
 did not content himself with merely accumulating a mass of observations, 
 leaving to others the task of reducing them to a form which might render 
 them available for any useful purpose. Much of his time was occupied 
 with the formation of his great catalogue of the stars, and with calculating 
 from his observations, the places of the moon and planets ; and it was his 
 desire not to commence the publication of the observations until both these 
 objects were fully accomplished, so as at the same time to be enabled to 
 place within the reach of the public not merely the observations them- 
 selves, but also the results directly deducible from them. 
 
 * The paltry salary which he received was subject to a tax of 10, so that in reality it 
 did not amount to more than .90 a year. Even this pittance, however, seemed to the 
 Government to be more than an adequate remuneration for his labours, for at one time in 
 the early part of his career they annexed to his duties the task of instructing in nautical 
 astronomy two boys of Christ Church Hospital. 
 
 f Baily's Life of Flamsteed, p. 117. 
 
 For the correspondence which took place between Newton and Flamsteed on this 
 occasion, see Baily's Life of Flamsteed, pp. 133-160. 
 
 That Flamsteed seriously contemplated the publication of his observations at some 
 future period, even although he should obtain no assistance from any quarter, is evident 
 from the following passage of a letter dated October 26, 1700, addressed by him to Dr. 
 Smith of Oxford : " Briefly, sir, I am ready to put the observations into the press, as 
 soon as they that are concerned shall afford me assistants to copy them and finish the cal- 
 culations. But if none be afforded, both they and I must sit down contented, till I can 
 finish them with such hands as I have ; when I doubt not but to publish them, as they 
 ought to be, handsomely and in good order, and to satisfy the world, whilst I have been 
 barbarously traduced by base and silly people, that I have spent my time much better 
 than I should have done if, to satisfy them, I had published anything sooner and imper- 
 fect." (Baily's Life of Flamsteed, p. 746.) 
 
474 BDLSTOEY OF PHYSICAL ASTEONOMY. 
 
 While Flamsteed was thus strenuously endeavouring, by his own un- 
 aided efforts, to give a definite shape to his labours, several of his scientific 
 contemporaries began to express a feeling of impatience that the publica- 
 tion of the observations made at the Royal Observatory of Greenwich 
 should be so long delayed. He was induced by this circumstance to draw 
 up an estimate of the extent of the work which he was preparing for the 
 press, and of the plan according to which he was desirous that it should 
 be published *. This estimate was read at a meeting of the Royal 
 Society held on the 15th of November, 1704, and received the unanimous 
 commendation of the members. Prince George of Denmark, the Queen's 
 consort, who was shortly afterwards elected a member of the Society, 
 having been informed of the labours of Flamsteed as announced in this 
 exposition, generously undertook to defray the expense of their publica- 
 tion, and, with a view to this object, a committee, consisting of Newton, 
 Wren, and two or three other individuals, was appointed to inspect the 
 manuscripts. The committee recommended that all the observations 
 should be published, and Flamsteed was instructed forthwith to prepare 
 them for the press. Flamsteed complied with the demands of the com- 
 mittee, surrendering into their hands a copy of his observations, and also 
 a catalogue of the fixed stars which he had deduced from them. As the 
 catalogue was not complete, he merely deposited it with the committee, as 
 a guarantee for his furnishing them on a future occasion with a more 
 perfect copy, expressly stipulating that in the meantime no steps would be 
 taken towards its publication. In the month of May, 1706, the printing 
 of the observations was commenced, but it proceeded very slowly, and was 
 at length interrupted entirely for some time by the death of Prince George 
 of Denmark in 1 708. 
 
 On the 12th of December, 1710, the Queen issued a warrant appoint- 
 ing the President of the Royal Society, and such other members of the 
 Council of the said Society as he should think fit, to be Visitors of the 
 Royal Observatory of Greenwich. They were authorized to demand of 
 the Astronomer Royal to deliver up to them within six months after the 
 close of each successive year, a true and fair copy of his annual observa- 
 tions. They had also full powers to direct him to make such observations 
 as they should deem desirable, and to inspect the instruments from 
 time to time, so that they might be constantly maintained in a proper 
 condition. 
 
 The origin of the Board of Visitors is clearly traceable to the unfortu- 
 nate misunderstanding that prevailed between Flamsteed, on the one 
 hand, and his scientific countrymen generally, on the other. It has con- 
 tinued to exercise its functions to the present day, but at the accession of 
 William IV. a new warrant was issued, according to which its constitution 
 underwent a slight modification f . The salutary influence of such a board 
 
 * It appears from Flamsteed's journal, that he had been only a few years occupied with 
 his duties at Greenwich when persons began to importune him about publishing his ob- 
 servations. " Some people," says he, " to make me uneasy, others out of a sincere 
 desire to see the happy progress of my studies, not understanding amid what hard circum- 
 stances I lived, called hard upon me to print my observations." (Baily's Life of Flam- 
 steed, p. 54.) 
 
 f By virtue of the new warrant, the President of the Royal Society for the time being, 
 and five other Fellows of that Society nominated by him, together with the President of 
 the Royal Astronomical Society for the time being, and five other Fellows of that, Society 
 nominated by him, and the Savilian Professor of Astronomy at Oxford, and the Plumian 
 Professor of Astronomy at Cambridge, are appointed to be Visitors of the Royal Obser- 
 vatory. 
 
HISTOET OF PHYSICAL ASTRONOMY. 475 
 
 of inspection is indisputable, for while on the one hand it serves to pre- 
 vent the application of the resources of the observatory to any unwarrant- 
 able purposes, on the other hand it has the effect of periodically relieving 
 the conscientious astronomer from the responsibility attached to the 
 discharge of his onerous duties, and thereby operates as an encouragement 
 to future exertion. It is gratifying to reflect that during the last hundred 
 years, at least, it is only in the latter respect, that the advantages result- 
 ing from the establishment of the Board of Visitors, have been apparent. 
 
 In the spring of 1711 the printing of Flamsteed's observations was 
 resumed by order of the Queen, and in the following year they were pub- 
 lished in one large folio volume. The preface, which was written by Hal- 
 ley, contained some very ungenerous reflections on Flamsteed. Moreover, 
 the form in which the results of his labours were presented to the world 
 on this occasion was far from being in accordance with his own views. 
 With respect to the stars observed with the mural arc, the places only of 
 those were inserted in the work, which passed the meridian about the 
 same times, and nearly on the same parallels, with the moon and planets. 
 The catalogue of stars was also no other than the avowedly imperfect one 
 which Flamsteed originally deposited with the committee appointed to 
 superintend the printing of the observations in 1704, upon the express 
 condition that it should not be published, but merely that it be retained as 
 a pledge for his subsequent delivery into their hands of a more complete copy. 
 It would appear that the parties charged by the Queen with the publication 
 of the observations, grew impatient at what they conceived to be Flamsteed's 
 tardiness in fulfilling his promise, and adopted the resolution of printing the 
 catalogue in their possession, without his concurrence, or even his know- 
 ledge. This was manifestly an act deserving of severe reprobation. It may 
 be urged, indeed, as an excuse for such an extreme proceeding, that the 
 observations were public property, and that a due regard for the objects 
 contemplated in the establishment of the observatory, suggested the 
 expediency of publishing them within a reasonable period of time ; and, 
 perhaps, according to the strict letter of the law, the act was justifiable 
 upon that ground. But, on the other hand, a more generous allowance 
 ought to have been made for the difficulties of Flamsteed's position, 
 arising mainly from the circumstance of the Government having failed to 
 afford him such support in the prosecution of his arduous labours as he 
 had a right to expect in virtue of the office for which he was held respon- 
 sible. At all events, it looks like a wanton display of harshness on the 
 part of the committee in whose hands the manuscripts of Flamsteed were 
 deposited, to have resorted to their publication without beforehand giving 
 him due notice of their intention *. 
 
 Justly indignant that the results of- his long and toilsome labours 
 should be presented to the world under circumstances so injurious to his 
 personal character, and in a form so little calculated to advance his repu- 
 tation as an astronomer, Flamsteed resolved to publish a complete 
 edition of his observations at his own expense f. He accordingly pro- 
 
 * It is right to state that this charge rests solely upon the authority of Flamsteed. la 
 ail probability the parties misunderstood each other. The whole affair, as disclosed by 
 Mr. Daily's work, is of a very unpleasant nature. 
 
 f There were 400 copies printed of Halley's edition of 1712. In 1715 Flamsteed 
 succeeded in procuring from the Government all the copies that remained in their pos- 
 session, amounting to 300, and immediately committed them to the flames, with the ex- 
 ception of the sheets on which his observations with the sextant were printed. 
 
476 HISTORY OF PHYSICAL ASTKONOMY. 
 
 ceeded to carry his design into effect, with all the energy which the con- 
 sciousness of a just cause, and a laudable desire to set himself right in 
 the eyes of posterity, were capable of inspiring. His constitution, how- 
 ever, already shattered by the incessant* inroads of ill health, and now 
 sinking under the frailties of old age, was inadequate to the complete 
 execution of a task of such magnitude. It was contemplated by him to 
 publish the results of his labours in three volumes ; but he had barely 
 succeeded in completing the second volume when he died, on the 31st of 
 December, 1719. The preparation of tbe third volume for the press, was 
 effected by the voluntary exertions of Crosthwait, his assistant at tbe time 
 of his death, and the famous Abraham Sharp, who had also at one time 
 served him in the same capacity, and had ever since continued his devoted 
 friend*. The whole work was finally published in the year 1725, in 
 three volumes folio, under the title of " Historia Cselestis Britannica," 
 The first volume contains extracts from the observations of Gascoigne and 
 Crabtree from 1638 to 1643, also Flamsteed's own observations at Derby 
 down to 1675, and his subsequent observations at Greenwich with the 
 sextant from 1675 to 1689. It comprehends, moreover, various subsidiary 
 tables to be used in calculation, and also the places of the moon and pla- 
 nets deduced from the observations. The second volume contains the 
 observations made with the mural arc from 1689 to 1719 f. At the end of 
 this volume, also, there is a collection of useful tables, and a list of the 
 places of the moon and planets computed from the observations. The 
 last-mentioned results, as well as the corresponding results in the first 
 volume, exhibit not only the right ascensions and polar distances of the 
 several bodies, but also their longitudes and latitudes. The third volume 
 commences with the Prolegomena, in which Flamsteed takes a rapid 
 survey of the progress of astronomy, concluding with a description of his 
 own instruments and methods of observation. There are next inserted 
 copies of all the catalogues of the fixed stars that had been executed by 
 astronomers previous to the time of Flamsteed. These are succeeded by 
 Flamsteed's own catalogue, which exhibits the right ascensions and polar 
 distances, as well as the longitudes and latitudes of 2935 stars, reduced 
 to the beginning of the year 1689, together with the annual variations in 
 right ascension and polar distance, arising from the regression of the 
 equinoctial points. At the end of the volume there are various subsidiary 
 tables designed for abbreviating the labours of calculation. 
 
 * Sharp resided at this time in Yorkshire. He also assisted Crosthwait in the preparation 
 of the maps of Flamsteed's Atlas, which was published in 1730. The following passage of 
 a letter from Crosthwait to Sharp, dated January 27, 1721-22, reflects so much credit upon 
 all the parties alluded to, that it cannot fa.il to prove acceptable to the reader : " I am much 
 concerned to find, by yours of the 2nd instant, that you had entertained the least suspi- 
 cion of being forgotten or slighted by me, though there had been nothing more for you 
 to do. I can assure you, with the greatest sincerity, that I shall for ever (though I am 
 sure I shall have no share in the profits) retain a grateful remembrance of the generous 
 and kind assistance you have given towards completing Mr. Flamsteed's works, and shall 
 be ready at all times hereafter, so long as life endures, when in my power, to return you 
 gratitude ; and the memory of the ingenuous and disinterested Mr. Sharp will always, 
 by me, be had in the greatest esteem, next to that of my deceased and good friend 
 Mr. Flamsteed." (Baily's Life of Flamsteed,?. 346.) Mrs. Flamsteed died in 1730, 
 without leaving a single farthing either to Crosthwait or Sharp, notwithstanding their dis- 
 interested exertions in her behalf during a period of ten years ! 
 
 f At the top of each page of observations in this volume the error of collimation of 
 the instrument is inserted. 
 
HISTORY OF PHYSICAL ASTRONOMY. 477 
 
 Flamsteed is universally admitted to have been one of the most eminent 
 practical astronomers of the age in which he lived. His merits do not, 
 indeed, appear at first sight so conspicuous as those of some of his illus- 
 trious contemporaries with whom he may be compared, although at the 
 same time they are no less substantial. He does not generally exhibit 
 the enlightened discernment which Picard displays in his researches, nor 
 was he endowed with the fertility of invention by which Roemer was so 
 eminently distinguished ; but in carrying out views of practical utility, 
 with a scrupulous attention to accuracy in the most minute details, in 
 fortitude of resolution under adverse circumstances, and persevering adhe- 
 rence to continuity and regularity of observation throughout along career, 
 he has few rivals in any age or country. Without the possession of these 
 invaluable qualities, the most splendid genius may fail to exercise any 
 durable influence : by means of them Flamsteed was enabled to establish 
 the fundamental points of practical astronomy upon a new basis, and to rear 
 a superstructure which, for many years afterwards, served as a landmark of 
 vast importance to astronomers. In so far as the accuracy of his observa- 
 tions is concerned, his labours must be considered with reference to the 
 times in which he lived, and the difficulties which he had to encounter. 
 When judged according to this equitable standard, they will not suffer from 
 the scrutinies of the candid enquirer. It forms a noble attestation to the 
 merits of Flamsteed in this respect, that his observations are the earliest 
 from which the phenomenon of aberration clearly and unequivocally 
 emerges, its maximum value being assigned by them with a degree of pre- 
 cision almost equal to that deducible from the most trustworthy observa- 
 tions of the present day *. As first Astronomer of the Royal Observatory 
 of Greenwich, he set an example to his successors the beneficial influence 
 of which cannot for a moment be doubted ; nor, while that noble esta- 
 blishment continues to maintain its proud pre-eminence among the insti- 
 tutions devoted to practical astronomy, will the labours of its original 
 Director, prosecuted with such unwearied perseverance throughout a long 
 career, despite the depressing influence of constitutional ill health, and 
 the unrelenting hostility of a powerful faction, cease to be held in respect- 
 ful remembrance by his countrymen. 
 
 Flamsteed \vas succeeded at the Royal Observatory by the celebrated 
 Edmund Halley. This great astronomer was born at London, on the 
 29th of October, 1656, and had already distinguished himself by a bril- 
 liant career of research on various subjects of physical science. It seems 
 somewhat surprising, when we consider that he was now in the 64th 
 year of his age, that he should have undertaken the discharge of duties 
 of so onerous a nature as those attached to the situation of Astronomer 
 Royal. Unlike his predecessor, however, he had the good fortune to 
 possess a robust constitution, and, in reliance upon its vigour, he was 
 desirous of prosecuting a series of observations of the moon, in regard to 
 which he had a special object in view, as will be presently mentioned. 
 
 It has been already mentioned that the instruments used by Flamsteed 
 
 * See page 340 of this work, where the value of aberration deduced by M. Peters 
 from Flamsteed's observations is given. The same astronomer makes the latitude of 
 Greenwich, according to Flamsteed's observations, to be 51 28' 41".9+.0".9. (J^e- 
 cherches sur la Parallaxe des Etoiles Fixes, p. 11.) Mr. Airy, from recent observations, has 
 determined the true value of the latitude to be 51 28' 38".2. (Greenwich Observations 
 1842, p. xliv.) 
 
478 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 were all his own, the Government not having even defrayed the expense 
 of occasionally repairing them. We need not wonder, therefore, that 
 when Halley entered the observatory he found it completely stripped of 
 everything available for the prosecution of celestial observations. The 
 mural arc, the clocks, the telescopes, and, in short, every instrument in 
 the observatory, had been carried away by Flamsteed's executors imme- 
 diately after his death. In consequence of this circumstance, some time 
 elapsed before Halley was enabled to enter upon a regular course of 
 observation. In 1721 he procured a transit instrument, with which he 
 commenced observations of the passages of the celestial bodies over the 
 meridian. This instrument was five feet six inches long, and is stated by 
 Lalande to have been constructed by Hooke. Halley 's first observation 
 with it is dated October 1, 1721. In 1726, a mural quadrant, for the 
 observation of zenith distances as well as differences of right ascension, 
 was at length erected. This instrument was constructed by the cele- 
 brated artist Graham*. It was made of iron, and had a radius of eight 
 feet. The limb was composed of two arcs, upon each of which a different 
 mode of division was executed. The inner arc was divided to every 5', 
 according to the ordinary sexagesimal scale, and was afterwards sub- 
 divided, by means of a vernier, to every 30", which again might be sub- 
 divided, by estimation, to one-fourth of this quantity, or 1\" '. The outer 
 arc was divided, first, into ninety-six parts, and then each of these into 
 sixteen smaller parts, each of which again was subdivided, by means of a 
 vernier, to every 13", and each of these parts might finally be subdivided, 
 by estimation, to 5" or 6". In making observations with the instrument, both 
 modes of reading off were employed, so that the one might serve as a check 
 upon the other ; but in cases of discordance, greater reliance was usually 
 placed on the indications of the outer arc. Halley commenced his obser- 
 vations with this instrument on the 20th of October, 1725. Hencefor- 
 ward he continued to observe not only the transits of the celestial bodies 
 over the meridian, but also their zenith distances. It does not appear, 
 however, that he adopted such an extensive plan of observation as that 
 pursued by his predecessor, Flamsteed. His main object was to procure 
 materials for the improvement of the lunar and planetary tables ; and, for 
 this purpose, he deemed that it would be unnecessary to observe any other 
 stars than those that were situate within the limits of the zodiac. His 
 labours were more especially directed to the observation of the moon. 
 He was stimulated to this object by the large reward which the Govern- 
 ment had offered relative to the longitude, being convinced that the 
 method of lunar distances was better adapted than any other to the 
 solution of that important problem. This subject seems to have so far 
 engrossed his attention as to have caused him in some degree to neglect 
 the ordinary duties of his office. It has been already mentioned that the 
 
 * George Graham was born at Gratwick, in Cumberland, in the year 1675. He was 
 not only the most skilful artist of his time, but was also distinguished by a profound 
 acquaintance with various subjects of natural philosophy. Besides the mural quadrant 
 alluded to in the text, he constructed the famous zenith sector with which Bradley dis- 
 covered the phenomena of aberration and nutation. It was also with a zenith sector 
 executed by the same artist that the French academicians, who measured the length of an 
 arc of the meridian in Lapland, determined the latitudes of their stations. Graham con- 
 tributed various papers to the Philosophical Transactions of the Royal Society, of which 
 he was a member. One of these related to the mercurial compensation pendulum, the 
 invention of which is due to him. He died in 1751, aged 76 years. 
 
HISTORY OF PHYSICAL ASTRONOMY. 479 
 
 Board of Visitors, which was composed of members of the Royal Society, 
 were authorized to demand of the Astronomer Royal, within six months 
 after the lapse of each successive year, "a true and fair copy of the 
 annual observations he had made." At a meeting of the Royal Society, 
 held on the 2nd of March, 1727, Sir Isaac Newton, who was then Pre- 
 sident, took occasion to remark that this regulation had not been recently 
 observed ; and stated at the same time, that, as the continued neglect of 
 it might be attended with detriment to the public interest, he thought it 
 proper to remind the Astronomer Royal of the circumstance of such a 
 regulation being in force. Halley, who was present, replied to Newton 
 by asserting that he had already executed a great number of observations, 
 especially of the moon ; but that on account of the utility of such observa- 
 tions towards ascertaining the longitude, for which a large reward had 
 been offered by the Government, he had hitherto kept them in his own 
 custody, that he might have time to finish the theory he designed to build 
 upon them, before others might take the advantage of reaping the benefit 
 of his labours*. 
 
 Halley died on the 14th of January, 1742, in the 86th year of his age. 
 It appears that for some time previous, he had ceased to attend to the 
 duties of the observatory, a circumstance which is not to be wondered at 
 when his extreme old age is taken into consideration. His last observa- 
 tion is dated December 31, 1739. The only part of the observations 
 made by him at Greenwich that has ever been published, is a collection 
 of observed places of the moon, which are to be found at the end of his 
 Astronomical Tables, which were published in 1749f. These tables were 
 printed off in 1719, with a view to their immediate publication; but their 
 author being in the meantime appointed Astronomer Royal, they were 
 retained by him for his own exclusive advantage, since there was now an 
 increased probability of his bringing the lunar theory to such a state of 
 perfection as would lead to a practical solution of the problem of the 
 longitude. With a view to this object, he had no sooner entered upon 
 his duties at Greenwich, than he commenced instituting a comparison 
 between the places of the moon deduced from his observations, and the 
 corresponding places calculated from the tables. These results were 
 printed off at successive intervals during Halley 's lifetime, and the whole 
 collection was finally published along with his Astronomical Tables, as has 
 been already mentioned. It exhibits a comparison between the observed 
 and calculated places of the moon, extending from 1722 to 1739. The 
 error of the tables in longitude is frequently less than 1', but in some 
 instances it rises to 5' or 6'. In general, it may be said to range between 
 2' and 4'. It does not appear that Halley employed these residual errors 
 in any researches for the purpose of obtaining an improvement of his 
 tables of 1719. 
 
 The original records of Halley 's observations are deposited at Green- 
 wich in four small quarto volumes. Upon the recommendation of Mr. 
 Baily, a manuscript copy of them was taken by the order of the Lords 
 of the Admiralty, and presented to the Astronomical Society, in the year 
 
 * Mem. Ast. Soc., vol. viii., p. 188, cited by Mr. Baily, from the Minute Book of 
 the Royal Society. 
 
 t In the preface to these tables it is stated that they were mainly constructed by 
 Halley, upon the observations of Flamsteed. 
 
480 HISTORY OF PHYSICAL ASTKONOMY. 
 
 1832. Mr. Baily has concluded, from a careful inspection of these ob- 
 servations, that they do not possess sufficient value to render it desirable 
 that they should be printed*. Maskelyne had already intimated to 
 Delambre, that they were hardly preferable to those of Flamsteedf. 
 Halley, indeed, was endowed with a mind of vast compass as well as extra- 
 ordinary sagacity and power; but he seems to have undervalued those 
 habits of minute attention which are indispensable to the attainment of a 
 high degree of excellence in the practice of astronomical observation J. 
 
 The absence of any definite plan of operations in connexion with the 
 Eoyal Observatory of Paris has been already alluded to. The evils 
 arising from this cause did not fail soon to present themselves. The 
 astronomers engaged in prosecuting observations at that establishment, 
 were frequently compelled to discontinue their labours, at the instance of 
 the Government, for the purpose of executing scientific operations in the 
 provinces of France. This circumstance occasioned numerous interrup- 
 tions in the records of the observations, which manifestly tended in a 
 great degree to depreciate their value. Moreover there was an incom- 
 pleteness generally apparent in the observations actually made, arising 
 from the want of a presiding power to direct the labours of the establish- 
 ment. These defects in the constitution of the observatory are described 
 in the following graphic terms, by Cassini IV.: "Chacun venait observer 
 dans les cabinets comme il Ventendait, quand et selon que cela lid plaisait, 
 les astronomes novices pour s'exercer, les academiciens pour leur propre 
 compte. II ny avail ni plan general suivi, ni chef pour diriger ; de Id, ni 
 accord, ni ensemble, ni suite dans les travaux" 
 
 But although the Royal Observatory of Paris failed to attain such a 
 degree of efficiency as was consistent with the flourishing condition of 
 science in France, there was one important department of practical 
 astronomy in which that country took the lead of all other nations. It 
 was in France that -the length of an arc of the meridian was first 
 measured, upon principles so unexceptionable, and with so scrupu- 
 lous a regard to accuracy in all the details of the operation, as to com- 
 mand the confidence of astronomers generally in the result, and to 
 induce Newton to resume the ever memorable investigation which con- 
 ducted him to his grand discovery of the principle of universal gravita- 
 tion. It is to France also that astronomy owes the establishment of the 
 ellipticity of the earth, one of the most conclusive facts that can be 
 adduced in favour of the Newtonian theory. This object was effected by 
 a comparison of geodesical measurements, executed not merely on the 
 soil of France, but also in the arctic regions and under the equator. 
 The operations connected with the establishment of these results ex- 
 tended over nearly three-quarters of a century, and exercised the talents 
 of the most eminent astronomers of France who flourished during that 
 period. The name of Picard is imperishably associated with the origin of 
 
 * See a paper by Mr. Baily on this subject in vol. viii. of the Memoirs of the Astro- 
 nomical Society. 
 
 f Histoire de 1' Astronomic au Dixhuitieme Siecle, p. 134. 
 
 - J It would appear, from the following expression, that Halley did not contemplate the 
 possibility of determining the apparent position of a celestial body within even 10" of the 
 truth: "Utverum fatear, minuta secunda vel etiam dena secunda, instruments quan- 
 tumvis affabre factis certo distinguere vix homini datum est." (Phil. Trans., 1716, 
 p. 456.) 
 
 Memoires pour servir a 1' Histoire des Sciences, etc., p. 191. 
 
HISTORY OF PHYSICAL ASTRONOMY. 481 
 
 these operations which have reflected so much honour on France. Their 
 close was illustrated by the exertions of Lacaille, one of the most distin- 
 guished astronomers of the eighteenth century *. 
 
 In connexion with the Royal Observatory of Paris may be mentioned 
 Louville's application of the micrometer to divided instruments. This 
 was effected by directing the instrument approximatively to the object, 
 and then adjusting it, so that the plumb-line fell exactly upon the nearest 
 point of division. The moveable thread of the micrometer was then 
 brought into exact coincidence with the object, and its distance from the 
 fixed thread, as determined by the revolutions of the screw, gave the 
 fraction of an angle which was to be added to or subtracted from the 
 altitude indicated by the point of division over which the plumb-line 
 passed. Louville first described this mode of applying the micrometer 
 in the "Memoirs of the Academy of Sciences" for 1714f. A sector, 
 furnished with a micrometer of this kind, was shortly afterwards em- 
 ployed by the astronomers engaged in verifying the arc of the meridian 
 that had been measured in France in the seventeenth century. It would 
 appear that a similar application of his instrument did not escape the 
 attention of Gascoigne, the original inventor of the micrometer. Thus, 
 Crabtree, writing to him in a letter dated December 6, 1641, expresses 
 his astonishment that he should be enabled not only to project the 
 diameter of Jupiter into prodigious measures, but also to take distances, 
 altitudes, inclinations, and azimuths without the limb of an instrument, 
 and each to any required number of parts J. 
 
 The difficulty of making accurate observations from the deck of a 
 vessel, arising from the unsteady position of the observer, was found to 
 operate as an insuperable obstacle to the success of any method for find- 
 ing the longitude at sea. This difficulty was entirely removed by the 
 invention of the reflecting quadrant. The germ of this invaluable 
 instrument is to be found in Sprat's " History of the Royal Society." 
 Thus, in an account of the inventions of members of the Society, he 
 alludes to " a new instrument for taking angles by reflection, by which 
 means the eye at the same time sees the two objects, both as touching 
 in the same point, though distant almost to a semicircle, which is of 
 great use for making exact observations at sea." The author of this 
 instrument was Hooke, in whose "Posthumous Works" there is to be 
 found a description of it||; but it does not seem that he attempted to 
 follow out his ingenious idea by a further improvement of the instrument. 
 Newton was the first person who devised the construction of the re- 
 
 * Picard commenced his operations for the measurement of an arc of the meridian in 
 1669. The arc of the meridian in Lapland was measured by Maupertius and his com- 
 panions in 1735-6. The ellipticity of the earth's figure was finally established beyond 
 all doubt by the verification of the French arc of the meridian in 1741. The operations 
 connected with the measurement of the arc in Peru were completed a few years after- 
 wards. 
 
 f Mem. Acad. des Sciences, 1714, p. 73. 
 
 $ Phil. Trans., 1717, p. 609. In 1669 Hooke determined the zenith distances of 
 <y Draconis, by the aid of a micrometrical contrivance similar to that of Louville's, inas- 
 much as the intersection of cross wires of the telescope was not brought into exact coin- 
 cidence with the star ; but in this case the deviations of the star from the optical axis of 
 the telescope were measured by means of a graduated scale. 
 
 History of the Royal Society, p. 246, 4to. Lond., 1667. 
 
 || Hooke's " Posthumous Works," p. 503, folio, Lond., 1705. 
 
 I I 
 
482 HISTORY OF PHYSICAL ASTRONOMY. 
 
 fleeting quadrant, resembling the sextant of the present day. He com- 
 municated an account of it to Halley, who, however, omitted to impart 
 a knowledge of it to the world; but soon after his death, in 1742, a 
 description of the instrument in Newtorl's handwriting was found among 
 his papers*. In the meantime the instrument had been re-invented by- 
 two individuals, independently of each other. The reflecting quadrant 
 of Hadley was first described at a meeting of the Royal Society, held on 
 the 13th of May, 173 If. It was subsequently found that his invention 
 of the instrument could be traced back at least as early as the summer 
 of 1730. The other inventor was Thomas Godfrey, of Philadelphia, in 
 America. He appears to have devised an instrument similar to Hadley 's 
 towards the close of the year 1730. The Royal Society, which took into 
 consideration the claims of the two individuals, decided that both were 
 independent inventors. 
 
 The idea of enlarging Hadley 's reflecting quadrant, or rather octant, 
 so as to measure a distance of 120, was first proposed in 1757, by Cap- 
 tain Campbell, who suggested to the Board of Longitude, that a sextant 
 of large radius, divided by Bird, would serve for making observations at 
 sea, equally well with the reflecting circle as described by Mayer}. The 
 sextant is the form in which the reflecting instrument has since been 
 generally used for nautical purposes. 
 
 Accurate celestial observations being now practicable on board a ship 
 by the use of the sextant, it only remained to construct trustworthy lunar 
 tables, in order to perfect the method of finding the longitude at sea, by 
 means of a comparison between the observed and computed distances of 
 the moon from the neighbouring stars. Many years were not allowed to 
 elapse ere this important object was accomplished, as we shall presently 
 have occasion to mention. 
 
 James Bradley, the third Astronomer Royal of Greenwich, was born at 
 Sherbourn, in Gloucestershire, in the year 1692. In 1711 he entered 
 Baliol College, Oxford, where he completed his education. Having 
 qualified himself for the church, he was presented to a living in the year 
 1719. His predilection for astronomical pursuits, which evinced itself at 
 an early age, was fostered by his uncle, the Rev. James Pound, with whom 
 he resided for several years at Wanstead, in Essex. In 1721 he was 
 appointed to the Savilian chair of astronomy in the University of Oxford, 
 which had then become vacant by the death of Keill. His nomination by 
 the Government, as successor to Halley in the Observatory of Greenwich, 
 is dated February 2, 1742. His reputation as an astronomer was already 
 well established in Europe by observations of a miscellaneous nature, 
 and more especially by his immortal discovery of the Aberration of Light, 
 and at the time of his appointment he was actually engaged in those 
 researches which resulted in his discovery of the Nutation of the Earth's 
 axis. 
 
 Bradley 's first object after his removal to Greenwich was to repair the 
 
 * A drawing and description of the instrument, both taken from Newton's paper, are 
 inserted in the Phil. Trans, for 1742, p. 155. 
 
 I For a description of Hadley's reflecting octant see Phil Trans., 1731, p. 147. An 
 examination of the question relative to the invention of this instrument will be found in 
 the Nautical Magazine, vol. i., p. 351. 
 
 J Bradley's " Miscellaneous Correspondence," P- 89. 
 
HISTORY OF PHYSICAL ASTRONOMY. 483 
 
 instruments, and carefully to adjust their positions. Halley bad confined 
 himself to the use of the mural quadrant soon after its erection in ] 725 *. 
 Bradley, however, resolved to employ both the quadrant and the transit 
 instrument in his observations. The former of these instruments was 
 repaired by Graham, and the latter by Sisson, several important improve- 
 ments being at the same time effected in their construction. Bradley's 
 first observation with the quadrant was made on the 15th of June, 1742. 
 His earliest transit observation is dated the 20th of July in the same 
 year. 
 
 The mode in which Graham's iron quadrant was divided has been 
 already mentioned. Halley generally adopted the nearest reading of the 
 vernier without regard to the fractional parts, but occasionally he marked 
 the half of the interval between two divisions of the vernier. The error 
 of his observations might, consequently, amount from this cause to 5" 
 or 6". Bradley pursued a similar plan of observation till July 18, 1745, 
 when, having applied a new micrometer screw to his instrument, the 
 threads of which were much finer than those of the old one, he employed 
 it to measure the fractional parts of the angles. One revolution of the 
 screw altered the angle upon the instrument 53"; and, consequently, the 
 fifty-third part of a revolution was equivalent to 1". By this application 
 of the micrometer, Bradley was now enabled to make observations to 
 seconds with as great accuracy as he had formerly done to divisions of 
 the vernier f. 
 
 The iron quadrant of Graham continued to be attached to the eastern 
 face of the wall erected for its support in 1725, and was employed both 
 by Halley and Bradley in observing the celestial bodies which passed the 
 meridian to the south of the zenith. Bradley, however, was desirous of 
 extending the plan of his observations, and with a view to this object he 
 presented a memorial to the Government in the year 1749, soliciting 
 another quadrant, by means of which the stars that passed the meridian 
 to the north of the zenith might be observed. The Government, with a 
 promptitude hitherto unusual, at once acceded to his views, and in the 
 following year the observatory was furnished with a magnificent brass 
 quadrant of eight feet radius constructed by Birdj, who now took the 
 place of Graham, as the most skilful divider of instruments in his day. 
 As in the case of the iron quadrant, there were two different modes of 
 division executed upon the limb. By the inner arc the quadrant was 
 
 * This course was imperatively prescribed by the necessities of his situation, for there 
 was only one vertical wire in his transit, and he had no assistant by whose co-operation 
 he might be enabled to make simultaneous observations with two instruments. As soon 
 as Bradley was appointed Astronomer Royal he succeeded in procuring a regular assistant, 
 who was paid by the Government. His first assistant was his nephew, John Bradley, 
 who, according to Lalande, resided in that capacity at the Royal Observatory for a period 
 of fifteen years. 
 
 f Rigaud's Miscellaneous Works, &c., of Bradley, p. Iv. 
 
 J John Bird was born in 1709 ; he was brought up a cloth-weaver in the county of 
 Durham. It is said that his attention was first drawn to the dividing of instruments, by 
 observing the imperfect graduation of a clock dial. Having acquired considerable 
 expertness in his new vocation, he proceeded to London, where he was employed by 
 Graham and other artists of the day. After residing in London for a few years, he com- 
 menced business on his own account, and soon attained an unrivalled reputation as a 
 divider of instruments. In 1767 he received 500 from the Government, on condition 
 that he should divulge his method of graduation. This he did in a work which he pub- 
 lished on the subject. ( The Art of Dividing Instruments, London, 17G7.) He died on 
 the 3 1st of March, 1776. 
 
 II 2 
 
484 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 divided to every 5' ; then the intervals between two consecutive divisions 
 were subdivided by the vernier to every 30", and these were finally sub- 
 divided by the micrometer screw to every 1". By the outer arc the 
 quadrant was divided into ninety-six parts ; then these were subdivided 
 by the vernier into sixteen smaller parts, each equal to 13". 1836; and 
 these were finally subdivided by the micrometer screw to every V. The 
 Government at the same time furnished the observatory with a new 
 transit telescope by Bird, eight feet long, besides an excellent clock by 
 Shelton, and several other instruments of minor importance. They also 
 purchased of Bradley the famous zenith sector with which he discovered 
 the phenomena of aberration and nutation, and appropriated it to the use 
 of the observatory. This noble instrument was designed by Bradley to 
 be henceforward employed in determining the errors of collimation of the 
 quadrants, by making observations with it when its face was turned alter- 
 nately east and west. 
 
 Bradley being now in possession of instruments of unequalled perfec- 
 tion, proceeded to execute a series of preliminary observations for the 
 purpose of ascertaining with greater accuracy the latitude of his observa- 
 tory, the place of the equinox, the quantity and laws of refraction, and 
 other fundamental points of astronomy. In pursuance of this design the 
 brass quadrant was turned towards the north, so as to be employed in 
 making observations of circumpolar stars. These observations were pro- 
 secuted from August 10, 1750, to July 31, 1753. From them Bradley 
 deduced the latitude of the observatory to be 51 28' 38|". He also 
 succeeded by means of them in constructing the elegant rule, so long 
 used by astronomers, for finding the quantity of refraction corresponding 
 to any assigned zenith distance, and any observed readings of the baro- 
 meter and thermometer. He determined the absolute right ascensions 
 of a few of the principal stars, by means of observations made near the 
 equinoxes, according to the method of Flam steed. 
 
 As soon as Bradley had established these fundamental points he re- 
 moved the brass quadrant from the western face of the meridian wall, 
 and permanently attached it to the eastern face, where it was afterwards 
 employed in observing the stars that passed the meridian to the south of 
 the zenith. At the same time the iron quadrant was removed from the 
 eastern face of the wall, and, after being re-divided by Bird, was attached 
 to the western face, for the purpose of making observations with the 
 telescope turned towards the north. Bradley now commenced the series 
 of admirable observations which have formed the groundwork of so much 
 valuable research to future enquirers, and which would have assured to 
 him an immortal reputation, even independently of those great discoveries 
 with which his name is inseparably associated. The sun, moon, and 
 principal stars, and the planets when situate in favourable positions, were 
 regularly observed with the transit instrument and the mural quadrants. 
 Moreover, a multitude of small stars, chiefly those of Flamsteed's cata- 
 logue, were included in the plan of observation. From the year 1750 
 may be dated the commencement of a series of observations which in 
 point of accuracy may bear a comparison with those of modern times. 
 Henceforward the records of Greenwich Observatory embody a collection 
 of materials, which have almost exclusively formed the groundwork of 
 every investigation undertaken in modem times, for the purpose of im- 
 proving the solar, lunar, or planetary tables. 
 
 Bradley, aided by only one assistant, continued with indefatigable assi- 
 
HISTORY OF PHYSICAL ASTRONOMY. 485 
 
 ctuity to prosecute bis labours at tbe Royal Observatory, until at length, 
 in the autumn of 1761, he was compelled by the increasing frailties of 
 old age, to retire from the duties of active life. " Our eye," says his 
 learned biographer, the late Professor Rigaud, " looks into the Greenwich 
 registers with feelings of interest for the traces of that hand which con- 
 veyed so much instruction to mankind, and catches occasionally the sight 
 of it till September 1, 1761, when the sun's transit was the last observa- 
 tion that Bradley ever entered, most probably that he ever made. His 
 existence continued for a few months longer, but his scientific career was 
 closed."* In fact, he shortly afterwards withdrew to Chalford, in Glou- 
 cestershire, where he continued to reside among his wife's relations till 
 his death, which took place on the 13th of July, 1763, having attained 
 the age of 70 years f. 
 
 The registers of Bradley 's observations occupied thirteen folio volumes, 
 and at his death were taken possession of by his executors. In 1767 the 
 Government, under the impression of their being public property, com- 
 menced a law-suit with a view to their recovery, which, however, they 
 abandoned in 1776. As soon as it was ascertained that the Government 
 had relinquished their claim, the manuscripts were transmitted to Lord 
 North, who was then Chancellor of the University of Oxford, to be pre- 
 sented by him to the University. They were finally printed, at the 
 expense of the University, in two folio volumes. The first volume was 
 published in 1798, under the superintendence of Dr. Hornsby. The 
 second volume was prepared for the press by Dr. Robertson, and appeared 
 in 1805. These two volumes contain the observations made by Bradley 
 from 1750 to 1762. The original manuscripts, as well as the registers of 
 the observations made by Bradley, at Greenwich, previous to 1750, are 
 deposited in the Bodleian Library, Oxford. 
 
 The vast mass of observations made by Bradley, which were published 
 in two volumes, as above mentioned }, continued inapplicable to any useful 
 purpose, in consequence of their not being reduced, until, at length, 
 Bessel undertook to execute this task, in so far as regarded the observa- 
 tions of the stars. The results of his labours were published in 1818, 
 at Konigsberg, in one folio volume, entitled, " Fund 'amenta Astronomies 
 pro anno 1755, deducta ex Observationibus viri incomparabilis James 
 Bradley, in specula Astronomica Grenovicensi per annos 1750-1762 
 institutis." In this work Bessel has determined, by a series of elaborate 
 investigations, the quantity and laws of refraction, the maximum value of 
 aberration, and other fundamental points of astronomy, as deducible from 
 Bradley 's observations. He estimates the error in declination of these 
 observations to be generally less than 4", and the error in right ascension 
 less than I" of time. 
 
 The observations made with the zenith sector at Kew and Wanstead, 
 by the intercomparison of which Bradley was conducted to the discovery 
 of aberration, were at one time supposed to be lost; but having been 
 found among the papers of the late Dr. Hornsby, they were published by 
 Professor Rigaud, in 1832, at the expense of the University, of which 
 
 * Bradley's Miscellaneous Works (Memoirs, p. 100). 
 
 j- In 1751 a pension was granted to Bradley by George II., not as an augmentation of 
 salary, but as a gratuitous acknowledgment of his personal merit. 
 Rigaud considers that their number cannot, be less than 60,OCO. 
 
486 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 the immortal author of the discovery forms one of the brightest orna- 
 ments*. 
 
 While Bradley was prosecuting his admirable observations at Green- 
 wich, the Continent was adorned by two astronomers who are justly 
 entitled to be associated in the history of astronomy with their illustrious 
 contemporary. It will be desirable, before proceeding further, to present 
 the reader with a brief notice of their labours. 
 
 Nicholas Louis de Lacaille was born at Eumigny, near Rosoy, in 
 France, on the 15th of March, 1713. He was destined by his parents 
 for the church, but his inclination towards astronomical studies effectually 
 frustrated their design. In 1713 he proceeded to Paris, where he was 
 kindly received by J. Cassini, who assigned to him a situation in the 
 Royal Observatory. In 1738 he was employed, in conjunction with the 
 younger Maraldi, in surveying the western provinces of France. In the 
 two following years he took an active part in the operations connected 
 with the verification of the French arc of the meridian, and it is to his 
 energy and skill that the successful prosecution of that important un- 
 dertaking is mainly to be ascribed. While engaged in these labours he 
 was appointed Professor of Mathematics in the Mazarine College of Paris, 
 whither he retired at their conclusion. A small observatory having been 
 fitted up for his use at the college, he continued to labour there for 
 several years, dividing his time between his professional duties and astro- 
 nomical pursuits. In 1750 he proceeded to the Cape of Good Hope, for 
 the purpose of making observations in the southern hemisphere. During 
 his residence there, he amassed materials for determining the parallaxes 
 of the Moon, Venus, and Mars, and for investigating the laws of refrac- 
 tion. He also measured an arc of the meridian, and the length of the 
 second's pendulum, besides observing ten thousand stars in the southern 
 hemisphere. Upon his return to Europe, in 1752, he established himself 
 in his former place of residence, where he proceeded to deduce a number 
 of important results from his observations. In 1757 he published a 
 fundamental catalogue of stars, forming one of the most valuable contri- 
 butions made to astronomical science during the eighteenth century. In 
 the following year he published his solar tables, the elements of which 
 were determined with such precision as to leave little further to be de- 
 sired. These are the earliest solar tables in which the effects of planetary 
 perturbation are taken into account. He is also the author of a catalogue 
 of about 500 zodiacal stars, which was published after his death. 
 
 The advantages which Lacaille enjoyed in the prosecution of his labours 
 were extremely moderate. He had no assistant to relieve him from a 
 portion of the drudgery incidental to astronomical pursuits, nor were his 
 instruments by any means so perfect as those of some of his contempo- 
 raries. By his talents and perseverance, however, he succeeded in over- 
 coming these difficulties ; but, unfortunately, he fell a victim to incessant 
 application, when he had only attained an age at which the human consti- 
 tution usually retains its full vigour. He died on the 21st of March, 
 1762, in the 49th year of his age. 
 
 When the admirable labours of Lacaille are taken into consideration, it 
 is impossible to repress a feeling of regret that he was not placed in a 
 
 * "Miscellaneous Works and Correspondence of the Rev. James Bradley, D.D., 
 F.R.S.,"4to., Oxford, 1832. 
 
HISTOEY OF PHYSICAL ASTBONOMY. 487 
 
 position wherein he might have been enahled to exercise his talents \vith 
 still greater benefit to astronomical science. Upon this point his dis- 
 tinguished countryman, M. Biot, very naturally makes the following 
 remark : " Quel eclat aurait jete Vastronomie observatrice en France, 
 quelle hauteur aurait-elle pu atteindre, des ce temps-la meme, si un tel 
 liomme avait succcde a Picard et a Roemer, dans un observatoire vraiment 
 royale, cree avec i intelligence de la science, dispose pour ses besoms, et 
 pourvu des instruments propres a Vavancer!"* 
 
 Tobias Mayer was born on the 17th of February, 1723, at Marbach, a 
 town of Wurtemberg, in Germany. His father having died while he was 
 yet young, he was thrown upon his own resources at an earlier age than 
 usual, and was compelled to support himself by teaching mathematics, a 
 knowledge of which he had acquired solely by the perusal of such books 
 as he could occasionally procure. He was only twenty-two years old when 
 he published a treatise on the theory of curve lines. About the same time 
 he began to apply himself with great ardour to the prosecution of astrono- 
 mical inquiries. In 1750 he communicated to the Cosmographical Society 
 of Nuremberg, a paper on the libration of the moon, in which he deter- 
 mined the elements of that curious phenomenon with greater precision 
 than had been hitherto done by any astronomer. This paper is remarkable 
 for containing the earliest example of the method of equations of condi- 
 tion, the use of which has contributed so much to the improvement of 
 modern astronomy. In 1751 he was appointed to the superintendence of 
 the Observatory of Gottingen, having been at the same time nominated to 
 one of the chairs in the University of that city f. The observatory had 
 been recently furnished by George II. of England with a magnificent 
 mural quadrant of six feet radius, constructed by Bird. Mayer proceeded 
 to submit his instrument to a most scrupulous examination, and in the 
 execution of this task he displayed a combination of sagacity and address 
 which would alone suffice to stamp him as an observer of the highest 
 order. He now commenced a course of regular observation, with the 
 view of procuring materials to serve as a groundwork for establishing the 
 fundamental points of astronomy. In 1753 he published new solar and 
 lunar tables. The latter will be for ever memorable, from being the first 
 which afforded a practical solution of the problem of the longitude. The 
 observations employed in their formation consisted chiefly of eclipses of 
 the sun and occultations of the stars. They did not amount to more than 
 200, and yet, with such skill were they discussed by Mayer, that his tables 
 seldom erred so much as lj'. In 1755 he transmitted them to England, 
 where they were compared by Bradley with the Greenwich observations, 
 and were deemed by that astronomer to be so accurate that, in so far as the 
 calculated places of the moon were concerned, they might serve in finding 
 the longitude at sea within half a degree of the truth, and generally much 
 nearer];. In 1756 Mayer communicated a paper to the Royal Society of 
 Gottingen, in which he explained the principle of an instrument, since 
 well known to astronomers as the repeating circle. He continued to pro- 
 secute his astronomical researches with unremitting assiduity, until at 
 length his constitution became impaired from incessant application, and 
 he fell into a languishing illness, of which he expired on the 20th of 
 
 * Journal des Savans, 1847, p. 524. 
 
 f This was the chair of political economy. It does not appear that Mayer delivered 
 
 any lectures upon that subject. 
 
 Mayer's Solar and Lunar Tables, p. cxii. 
 
488 HISTOEY OF PHYSICAL ASTKONOMY. 
 
 February, 1762*. An improved set of lunar tables, which he left 
 behind him at his death, were transmitted to England by his widow, 
 in consideration of which she obtained from the British Government 
 a grant of money amounting to 3000 f.* In 1770, his Theory of the 
 Moon I, which served as the basis of his tables, was published at Lon- 
 don. It is substantially the same as Euler's, but the values of the co- 
 efficients were determined by the aid of his own observations. In the 
 same year there was published, also at London, his improved solar and 
 lunar tables . There is appended to them, a short dissertation entitled 
 Methodus Longitudinum Promota, in which he recommends the method of 
 lunar distances for finding the longitude at sea, and suggests for this 
 purpose the use of a reflecting circle, with the repeating principle applied 
 to it. This work also contains his formula for refraction, embodying the 
 result of his researches on that important subject ||. The two works 
 above mentioned were published at the expense of this country, under the 
 superintendence of the Board of Longitude, the task of editing them 
 being executed by Dr. Maskelyne. In 1775 the first volume of Mayer's 
 " Posthumous Works " was published at Gottingen, which, among other 
 subjects, contained a catalogue of 998 zodiacal stars. The remaining por- 
 tion still exists in manuscript, with the exception of the observations from 
 which the catalogue was formed, which were printed at London, in 1826. 
 
 Mayer has earned for himself an imperishable reputation by his lunar 
 tables. Some astronomers may have achieved results of greater brilliancy, 
 but few have been privileged to contribute so directly by their labours to 
 the well-being of their fellow-men. Even independently of the improve- 
 ment which he effected in this instance, Mayer possesses claims to be 
 ranked with the greatest astronomers of ancient or modern times ; but, as 
 in the case of either of his illustrious contemporaries, Bradley or 
 Lacaille, his labours are not of a nature to be generally appreciated, 
 and therefore his reputation is less widely diffused than that of many an 
 individual whose contributions to science, though more showy, are infinitely 
 less substantial. 
 
 Bradley was succeeded at the Royal Observatory of Greenwich by Dr. 
 Bliss, Savilian Professor of Geometry in the University of Oxford. This 
 astronomer adopted the same plan of observation as that pursued by his 
 predecessor, but his death in 1765 prevented his labours from acquiring 
 any degree of importance in the annals of the observatory. 
 
 Neville Maskelyne, the fifth Astronomer Royal of Greenwich, was born 
 in London in the year 1732. He completed his education at Trinity 
 College, Cambridge, and subsequently qualified himself for entering the 
 church. It is said that his attention was first drawn to the science of 
 
 * It is somewhat singular that, Bradley, Lacaille, and Mayer, the three greatest astrono- 
 mers of the eighteenth century (supposing Halley to have been of the seventeenth), died 
 within a few months of each other. 
 
 t A copy of the resolution of the Board of Longitude, recommending Parliament to 
 grant Mayer's widow the sum of 5000, will be found at page cxxiii. of the Solar and 
 Lunar Tables of that astronomer. It appears from Maskelyne's preface to these Tables 
 that the sum actually awarded by Parliament amounted to 3000. 
 
 Theorise Lunse juxta Systema Newtonianum, &c., 4to., Lond., 1767. Although the 
 title-page of this work bears the date of 1767, it was only published in 1770, as appears 
 from Maskelyne's preface to Mayer's Solar and Lunar Tables., published in the last-men- 
 tioned year. 
 
 " Tabulae Motuum Solis et Lunse, novae et correctae," &c., 4to., Lond., 1770. 
 
 || See page 117 of the work referred to in the text. 
 
HTSTOKY OF PHYSICAL ASTKOXOMY. 489 
 
 astronomy by the great solar eclipse of 1748. He contracted an early 
 intimacy with Bradley, whom he assisted in the computations connected 
 with his researches on refraction. At the recommendation of that astro- 
 nomer, he proceeded to the island of St. Helena, to observe the transit 
 of Venus, in 1761. He commenced his labours at the Observatory of 
 Greenwich on the 7th of May, 1765. His instruments were the same as 
 those used by Bradley and Bliss, but his plan of observation was more 
 limited than that pursued by his predecessors. He confined his attention 
 to the sun, moon, and planets, and a select number of stars. The errors 
 of collimation of his quadrants were determined from time to time by 
 observations of y Draconis, with the zenith sector having its face turned 
 alternately east and west. During the intermediate intervals, the errors 
 were deduced by means of tbe quadrants themselves, from observations of 
 the stars in the feet of the constellation Gemini. We have seen that 
 Flamsteed employed observations of the same stars, for the purpose of 
 determining the error of collimation of his mural arc. In order that he 
 might be enabled to deduce from his observations the absolute right 
 ascensions of the sun, moon, and planets, it was necessary to establish 
 with great precision a definite number of reference points along the con- 
 tour of the zodiac. With this view he selected thirty-six stars situate 
 near the equator, each of which was sufficiently bright to be observed in 
 the daytime, even when not very far removed from the sun. In order to 
 render the observations of these stars available for ulterior purposes, it 
 was necessary to ascertain their places with respect to the equinox. This 
 was effected by comparing one of them, a, Aquila, with each of the re- 
 maining thirty-five, and then comparing Aquilge directly with the sun. 
 The mode of investigation pursued by Maskelyne on this occasion was 
 founded mainly upon Flamsteed's method for determining the absolute 
 right ascension of a star. He continued to observe these stars on every 
 practicable occasion, and employed the results in the formation of a small 
 catalogue which, in point of accuracy, far exceeded anything of the kind 
 hitherto executed. By comparing the observed transits of these standard 
 stars with the corresponding results deduced from the catalogue, it was 
 possible to ascertain the exact error of the clock, and hence to determine 
 the right ascensions of the sun, moon, and planets. 
 
 Maskelyne first introduced the practice of observing a star at the five 
 vertical wires of the telescope. This mode of observation was pursued by 
 him with undeviating regularity throughout his long career. He was also 
 the first who noted the instant of transit in terms of the tenths of a 
 second *. He continued to prosecute his labours without interruption, 
 adhering constantly to the same plan of observation which he had 
 traced out in the beginning of his career till his death, which happened 
 on the 9th of February, 1811, having occupied the situation of Astronomer 
 Royal for a period of forty-six years. 
 
 It is to Maskelyne that the original establishment of the " Nautical 
 Almanac" is due. In 1763 he published a work, entitled " The British 
 
 In noting the passage of a star over the wires in the transit, Bradley in general took 
 the nearest second, except when the interval was perceptible, in which case he marked the 
 observation * or , to indicate that the true time exceeded or fell short of the time recorded. 
 In some cases the time of transit is estimated in terms of the half or third of a second. 
 Maskelyne, in the beginning of his career, divided the second into eight parts. In Sep- 
 tember, 1772, he first commenced the practice of recording the times of transit to tenths 
 of a second. {Miscellaneous Works of Bradley,, p. liv. ) 
 
490 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 Mariner's Guide," in which he pointed out the advantage, for finding the 
 longitude at sea, of calculating beforehand for each year the distances of 
 the moon from the sun, and the principal stars lying near her path, and 
 inserting the results in an annual ephemeris. . This suggestion was 
 approved of by the Government, and he was forthwith appointed to carry 
 it into effect. The "Nautical Almanac" first appeared in 1767. During the 
 remainder of his life Dr. Maskelyne continued to superintend the publi- 
 cation of this ephemeris, which has proved so valuable to the mariner. 
 
 Maskelyne had not long prosecuted his labours at the Observatory of 
 Greenwich, when he succeeded in inducing the Government to print his 
 observations annually. The whole results have been published in four 
 folio volumes. From their uniformity, their continuity, and their general 
 accuracy, they have proved of inestimable value in many important inves- 
 tigations relating to astronomical science. 
 
 It has been already mentioned that Roemer did not fail to perceive the 
 superior advantage of circular instruments in making astronomical obser- 
 vations, when compared with quadrants, or any other sections of a circle, 
 and that, in accordance with this view, he procured the construction of a 
 meridian circle. The example of the Danish astronomer does not seem 
 to have been imitated by any of his contemporaries, nor was the idea of 
 circular instruments revived, until Mayer proposed the construction of 
 the repeating circle. In 1757 a reflecting circular instrument, constructed 
 according to the description which Mayer had transmitted to England 
 along with his lunar tables, was actually employed by Captain Campbell 
 in making observations at sea, but it was speedily replaced by a sextant of 
 twice the radius, as being more easily manageable *. 
 
 Towards the close of the last century the Danish astronomer, Eugge, 
 made observations with an altitude and azimuth circle. The diameter of 
 the vertical circle was four feet f. In 1 789 a vertical circle of five feet in 
 diameter was constructed by Ramsden J for the celebrated astronomer 
 Piazzi, who employed it in determining the decimations of his great cata- 
 logue of stars. Circular instruments of various forms soon afterwards 
 came into general use. 
 
 About the same time that circular instruments were again applied 
 to the purposes of astronomical observation, the method of reading off 
 the angles by means of microscopes fixed in piers opposite to the divi- 
 sions of the limb was also restored. In the present instance, however, an 
 important improvement of Roemer's method was effected, for, instead of 
 subdividing the interval between two consecutive points of division, by 
 means of parallel threads placed in the focus of the microscope, and then 
 estimating the fractional parts of these subdivisions, the exact distance of 
 
 * Mayer's Tables, p. cxi. t Lalande, Astronomic, art. 2333. 
 
 J Jesse Ramsden was born at Salterhebble, near Halifax, Yorkshire, in the year 1735. 
 Having obtained a sound elementary education, including some knowledge of geometry 
 and algebra, he was subsequently apprenticed to a clothworker at Halifax. In 1755 he 
 proceeded to London, where he found employment as a clerk in a warehouse, but having 
 a strong inclination towards scientific pursuits, he bound himself as an apprentice for four 
 years to a mathematical instrument maker. Soon after he completed his engagement, he 
 commenced business on his own account, and eventually attained unrivalled excellence as 
 an artist. Several of the finest astronomical instruments used in the public observatories 
 of Europe towards the close of the eighteenth century were the productions of his ingenuity 
 and skill. He also constructed a great number of achromatic telescopes, and other phi- 
 losophical instruments. He was a Fellow of the Royal Society, and also one of the 
 Foreign Members of the Imperial Academy of St. Petersburg. He died on the 5th of 
 November, 1800. 
 
HISTORY OF PHYSICAL ASTRONOMY. 491 
 
 the index from the nearest point of division was ascertained by means of 
 a micrometer screw. This mode of reading off angles was first proposed 
 by the Due de Chaulnes, in a small work which he published at Paris in 
 the year 1768. Kamsden did not fail to see the advantages of it, and 
 accordingly he applied it to the altitude and azimuth circle which he con- 
 structed for Piazzi. 
 
 Towards the close of his career at Greenwich, Maskelyne began to 
 suspect, from certain irregularities in the declinations of the stars, as 
 determined with Bird's mural quadrant, that the instrument had become 
 defective from long use. This fact having been established beyond doubt 
 by evidence derived from other sources, he represented to the Govern- 
 ment the expediency of replacing it by a circular instrument. This 
 request was acceded to, and a mural circle of six feet in diameter was 
 constructed for the Eoyal Observatory by Troughton*, but it was not 
 actually finished when Maskelyne died. 
 
 John Pond, the successor of Maskelyne at the Royal Observatory of 
 Greenwich, was born in London in the year 1767. At the age of sixteen 
 he was placed at Trinity College, Cambridge. While engaged in prose- 
 cuting his studies there, he displayed an interesting proof of his inclina- 
 tion towards those pursuits which subsequently formed the occupation of 
 his life, by uniting with two of his fellow-students in soliciting Prof. Vince 
 to give a course of lectures on practical astronomy. After leaving Cam- 
 bridge, he proceeded to the Continent, where he continued to travel for 
 some time. Upon his return to England he established his residence at 
 Westbury, in Somersetshire, and devoted his whole attention to practical 
 astronomy. Having procured an altitude and azimuth circle of three feet 
 diameter, constructed by Troughton, he commenced a series of observa- 
 tions with it, and so successfully did he prosecute his labours, that in 1806 
 he was enabled to demonstrate by irrefragable evidence founded upon the 
 results, that the brass quadrant of Greenwich had undergone a change of 
 form since its erection in Bradley 's time f . His earliest observation at 
 Greenwich is dated the llth of January, 1811. In the month of June of 
 the same year the mural circle which Troughton had been charged to 
 construct for the Observatory was ready for use. This magnificent instru- 
 ment demanded a method of observation totally different from that 
 hitherto pursued with the quadrants. In his mode of using it Pond 
 shewed that he possessed talents adequate to the occasion. The observa- 
 tions of a celestial object were now made, not by determining the distance 
 from the zenith agreeably to the practice hitherto pursued with the quad- 
 rants, but by referring the object to the pole as the zero of measurement, 
 
 * Edward Troughton was born in 1753 in the parish of Corney in Cumberlandshire. 
 He was brought up to farming pursuits till he was seventeen years of age, but he then 
 proceeded to London, and acquired instruction as an artist under his brother John. In 
 1782, the two brothers commenced business on their own account, and by their industry 
 and skill soon attained a prosperous condition. Upon the death of his brother, Edward 
 continued to prosecute the business of an artist for many years, and ultimately acquired a 
 European reputation by his excellence as a constructor of astronomical instruments. In 
 1830, be received an honorary gold medal fr-om the King of Denmark. He died on the 
 12th of June, 1835. A marble bust of this distinguished artist adorns the Observatory 
 of Greenwich. He was the last of a succession of English artists, each of whom was 
 without a rival in his day. It is somewhat singular that Sharp, Graham, Bird, Ramsden, 
 and Troughton should have succeeded each other at almost equal intervals ; and still 
 more so, that they should all have been born in a tract of country comprehended within 
 the limits of three adjacent counties of the north of England. 
 
 t Phil. Trans., 1806, p. 420, et seq. 
 
492 HTSTOEY OF PHYSICAL ASTRONOMY. 
 
 the position of the latter being ascertained by observations of circumpolar 
 stars. The instrument, according to this practice, served to determine the 
 polar distance of an object, and therefore the results were totally inde- 
 pendent of the place of observation. The error of the instrument was 
 ascertained by comparing the observed places of certain standard stars 
 with their places as deduced from a fundamental catalogue. The differ- 
 ence between each observed and calculated result gave a corresponding 
 value of the error of the instrument for the day of observation, and the 
 mean of all such differences gave the mean error of the instrument, or, 
 as Pond termed it, the index error. This quantity, being then applied to 
 all the observations, gave the polar distances of the various objects, freed 
 from the effects of instrumental error. In the case of the standard stars, 
 the application of the index error supplied the means of obtaining a cor- 
 rection of their places as assigned by the catalogue, and it is manifest that 
 by frequently repeating the same process the catalogue would be rendered 
 more and more perfect*. This method of observation obviated the neces- 
 sity of employing the plumb-line, the use of which was not, indeed, con- 
 sidered by Troughton in his original design of the instrument; while at 
 the same time it dispensed with an exact knowledge of the latitude of the 
 Observatory f. 
 
 In 1816 the Royal Observatory was enriched by the accession of a new 
 transit instrument ten feet long, constructed by Troughton. Hence- 
 forward the Greenwich determinations, both in polar distance and right 
 ascension, acquired a degree of precision which has hardly been surpassed 
 by the most accurate observations of the present day. 
 
 In the course of his famous controversy with Brinkley on the parallax 
 of the fixed stars, Pond was led to employ occasionally a new method of 
 observation which he subsequently practised with great success. It is essen- 
 tially founded upon the principle of optics that when a ray of light is re- 
 flected from any surface, the angles of incidence and reflexion are equal to 
 each other. In virtue of this principle, it is clear that when a celestial ob- 
 ject is observed with the mural circle by direct vision, and also by reflexion 
 from the surface of a fluid, the half of the angle contained between the 
 two readings of the circle will assign the altitude of the object, and the 
 reading which corresponds to the point of bisection will indicate the 
 horizontal point. Hence, knowing the latitude of the place of observa- 
 tion, the polar distance of the object may at once be determined. Pond 
 first applied this principle by observing the object at one of its transits 
 by direct vision, and then at the next transit by reflexion from the sur- 
 face of a trough of mercury. This method was attended, however, with 
 inconvenience, inasmuch as, in consequence of unfavourable weather, 
 several days might intervene before a complete observation could be 
 obtained. Moreover the result was liable to some degree of uncertainty, 
 arising from the different effects of refraction at the beginning and end 
 of the interval, and from causes tending to produce a slight derange- 
 ment in the adjustment of the different parts of the instrument. Im- 
 pressed with a sense of these defects, Pond contrived a method of observ- 
 
 * The process thus indicated would not free the polar distances of the catalogue of a 
 common error, but Pond shewed how this object might be effected by observations of 
 circumpolar stars. (Phil Trans., 1818, p. 410.) 
 
 t A knowledge of the latitude was necessary for transforming the j.olar distances into 
 altitudes, with a view to compute the effects of parallax and refraction, but it is manifest 
 that, for such a purpose, extreme precision was not required. 
 
HISTORY OF PHYSICAL ASTRONOMY. 493 
 
 ing a celestial object at one transit both by direct and reflected vision, 
 founded upon a combination of simultaneous observations made with two 
 mural circles*. A mural circle by Jones, that had been destined for the 
 Cape of Good Hope, was employed, along with Troughton's circle, in test- 
 ing the practicability of this method. The experiment having been at- 
 tended with complete success, Pond solicited from the Government the 
 permanent use of the second circle, and his request being complied with, 
 he now introduced the method into general practice. 
 
 Pond commenced his regular observations by direct and reflected vision 
 in the month of September, 1825. This method of determining the 
 zenith point continues still to be practised at Greenwich, except in so far 
 as relates to the use of two circles, the present Astronomer Royal having 
 devised a mode of effecting the same object by means of only one circle. 
 
 Pond did not fail to make regular observations of the sun, moon, and prin- 
 cipal stars, but he devoted less attention to the planets than the importance 
 of improving their respective theories demanded. In sidereal astronomy 
 generally, his contribution to the existing stock of knowledge was much 
 more extensive than that of his predecessor. His peculiar methods for 
 eliminating the effects of instrumental error, were founded upon a skilful 
 combination of masses of observations, and he was led in consequence to 
 determine the places of a considerable number of stars. In 1833 he 
 published a catalogue of 1112 stars, which proved a valuable acquisition to 
 the practical astronomer. It is generally admitted to be one of the most 
 accurate productions of the kind that lias ever been given to the world. 
 
 In the autumn of 1835, Pond was compelled by ill health to resign his 
 appointment. The Government manifested a just appreciation of his 
 merits, by bestowing upon him a retiring pension, but he was not destined 
 long to enjoy the fruits of their liberality. He died on the 7th of Sep- 
 tember, 1836, and was buried at Lee in Kent, in the same tomb with 
 Halley. 
 
 George Biddel Airy, Esq., the present Astronomer Royal, commenced 
 his labours at Greenwich as the successor of Pond, on the 2nd of October, 
 1835. He had already earned a distinguished reputation by his re- 
 searches on physical astronomy, and by his directorship of the Observatory 
 of Cambridge, to which he was appointed in the year 1828. During 
 the period of his connexion with the latter establishment, he intro- 
 duced a practice which did not fail to exercise an important influence on 
 the future character of the labour performed at public observatories in 
 this country. It had been hitherto usual for the directors of such estab- 
 lishments, to confine their attention exclusively to observations of the 
 celestial bodies, leaving to others the task of their reduction. Flam- 
 steed, indeed, deserves to be cited as an honourable exception to this re- 
 mark; and with respect to his successors, the circumstance of their 
 having omitted to reduce their observations, must be attributed to the 
 scantiness of the resources which the Government placed at their disposal, 
 rather than to any inattention or apathy on their own part. There can 
 be no doubt, however, that the restriction of their labours to mere obser- 
 vation, tended seriously to frustrate the very object for which public ob- 
 servatories have been established, namely, the attainment of a more 
 accurate knowledge of the movements of the celestial bodies ; for few in- 
 dividuals could muster sufficient courage to undertake the investigation of 
 
 * For a description of this method by Pond, see Mem. Ast. Soc., vol. ii., p. 499, et seq. 
 
494 HISTORY OF PHYSICAL ASTRONOMY. 
 
 any subject relating to astronomical science, when, as a preliminary opera- 
 tion, it was found indispensable to execute an enormous mass of tedious 
 calculations. Indeed it is not to be expected, that any one can take such 
 an interest in the reduction of observations as the person who actually 
 makes them, and hence it is reasonable to presume that he of all others 
 is best qualified for the execution of so laborious a task. Under a strong 
 impression of the imperfect state of all observations that were not imme- 
 diately available for purposes of research, Mr. Airy, as soon as he was 
 appointed director of the Cambridge Observatory, introduced a system of 
 reduction as a normal part of his duties. The volume of results which 
 henceforward issued annually from that establishment, formed a perfect 
 model to the practical astronomer. Not only were the observations regu- 
 larly reduced, but in so far as the planets were concerned, the results were 
 compared in every instance with the corresponding numbers calculated 
 from the most esteemed tables, so that the errors of the latter being thus 
 exhibited in bold relief, served to invite rather than to repel the re- 
 searches of the theoretical enquirer. This admirable system was shortly 
 afterwards introduced at Greenwich. 
 
 Another practice of great utility, which Mr. Airy adopted during his 
 directorship of the Cambridge Observatory, and which he followed up 
 more effectually upon his removal to Greenwich, was that of making 
 regular observations of the planets. This was a department of practical 
 astronomy, which for a long time had been very much neglected at the 
 Royal Observatory. The sun, moon, and principal stars were regularly 
 observed as they passed the meridian ; but, except during opposition, the 
 places of the planets were very rarely determined. Mr. Airy's atten- 
 tion was strongly directed to the expediency of remedying this defect, by 
 the difficulty which he experienced in procuring suitable observations of 
 the planets, while engaged in researches on physical astronomy. The 
 planets are now invariably observed at Greenwich on every practicable 
 occasion, at whatever hour they pass the meridian. 
 
 From the intimate connexion which was found to subsist between the 
 lunar theory and the problem of the longitude, the moon has formed an 
 object of unremitting attention at the Observatory of Greenwich, ever since 
 its establishment in 1675. This constancy of purpose has not failed to 
 produce its due fruits, for it is universally acknowledged that, in so far as 
 observation is concerned, the present advanced state of the lunar theory 
 is almost exclusively attributable to the labours of the Greenwich astro- 
 nomers. It is therefore an object involving in an especial degree the 
 honour of the Royal Observatory, to render the observations of the moon 
 as accurate and as complete as possible. In pursuance of this object Mr. 
 Airy has recently introduced the use of an altitude and azimuth instru- 
 ment at Greenwich, for the purpose of making observations of the moon in 
 any part of her course above the horizon. Two distinct circumstances 
 suggested the expediency of deviating in this respect, from the plan of ob- 
 servation hitherto pursued at the Royal Observatory. In the first place, 
 it frequently happens, from the unfavourable state of the weather, that the 
 moon cannot be seen when she is on the meridian. Secondly, although 
 the heavens should be perfectly serene, it is found to be impossible to 
 discern the moon on the meridian for several days before and after her 
 conjunction with the sun, on account of the overpowering effulgence of 
 the solar rays. It happened from this circumstance that throughout an 
 arc comprehending as much as one-third of her orbit, the moon hitherto 
 
HISTORY OF PHYSICAL ASTRONOMY. 495 
 
 had never been observed at all. The altitude and azimuth instrument, 
 devised by Mr. Airy for remedying this defect, was constructed by the 
 joint exertions of Messrs. Ransome and May, engineers of Ipswich, and 
 Mr. Simms of London, the successor of the celebrated Troughton. Both 
 the vertical and azimuthal circles are 3 feet in diameter. The telescope 
 attached to the instrument is 5 feet long, and is furnished with an object- 
 glass of 3f inches aperture *. The observations with it were commenced 
 on the 16th of May, 1847. In practice it has been found to work admi- 
 rably. Mr. Airy considers the results to be hardly, if at all, inferior to 
 those obtained by the use of the mural circle. The utility of the instru- 
 ment in promoting the object for which it was designed, soon became ap- 
 parent. It has been found that the moon may be observed with it in the 
 morning and the evening, when she is only an hour distant from the sun. 
 The consequence has been, that the number of lunar observations, con- 
 tained in the volume that issues annually from the Greenwich Observa- 
 tory is now about three times greater than it formerly wasf, while, at the 
 same time, the observations with the new instrument, possess this peculiar 
 advantage, that many of them have been made in a part of the moon's 
 orbit, where no observations at all had hitherto been supposed to be prac- 
 ticable J. It is manifest that this circumstance cannot fail to be attended 
 with advantage in contributing towards the further improvement of the 
 lunar theory. 
 
 The complete reduction of the observations of the moon and planets 
 made at Greenwich since the middle of the last century, is a work with 
 which the name of the present Astronomer Royal is imperishably associated. 
 At the meeting of the British Association, held at Cambridge in 1833, Mr. 
 Airy suggested the expediency of effecting a uniform reduction of all the 
 observations of the planets made at Greenwich since 1750, the year when 
 Bradley commenced his observations with the new instruments con- 
 structed by Bird . He proposed, on that occasion, that if the Government 
 should agree to defray the necessary expense, he would undertake gratui- 
 tously to superintend the whole operation. At the instance of the Associa- 
 tion, the Government acceded to this proposal, and the work was forthwith 
 commenced. The results were finally published in 1846, in one large 
 quarto volume. The whole work is divided into five sections. In the 
 first section the errors of the clock are deduced from the observations. 
 In the second the errors of the instrument are similarly investigated. In 
 the third the geocentric places are computed from the observations. In 
 
 * A detailed description of this instrument will be found in the volume of the Green- 
 wich Observations for 1847. 
 
 f During the first year which elapsed after the instrument was in operation, the number 
 of lunar observations made with it amounted to 203. The number of similar observa- 
 tions made on the meridian during the same period was only 111. 
 
 J This must be understood only with respect to the sun. The moon had been 
 observed from the earliest ages in every part of her absolute orbit ; but as the perturba- 
 tions of her motion depend mainly on her angular distance from the sun, it is obviously 
 a matter of primary importance that she should be observed in every part of her course 
 relative to that body. 
 
 Previous to the epoch referred to in the text, astronomers were not in the habit of 
 recording their observations so fully as to admit of their being reduced in the present day 
 with all desirable accuracy. Thus" the indications of the barometer and thermometer had 
 not been hitherto noted by any observer, not even excepting Bradley. Apart, therefore, 
 from all consideration of the superiority of the instruments constructed by Bird, this cir- 
 cumstance alone would render it inexpedient to attempt the reduction of any anterior ob- 
 servations. 
 
496 HISTOEY OF PHYSICAL ASTEONOMY. 
 
 the fourth the corresponding places are calculated from the best existing 
 tables. In the fifth the observed and tabular places are compared to- 
 gether, and the resulting errors exhibited. 
 
 When \ve consider that the observations which form the subject of this 
 immense volume, were made by various individuals, with instruments very 
 different from each other, and by methods totally dissimilar, we may form 
 some conception of the difficulty of eliminating the systematic errors to 
 which they were liable, and assimilating them by legitimate principles so 
 as to exhibit them in the character of one homogeneous collection of 
 results. The execution of this great undertaking renders the Greenwich 
 observations of the planets from 1750 to 1830 immediately available for 
 purposes of theoretical research, leaving in this respect nothing further to 
 be desired. 
 
 The reduction of the Greenwich lunar observations from 1750 to 1830 
 was undertaken at the public expense in consequence of a representation 
 to that effect having been made to the Government by the British Asso- 
 ciation, agreeably to a suggestion of Sir John Lubbock's on the occasion 
 of the meeting of the Association, which was held at Liverpool in 1837. 
 The organization of the plan of reduction, as well as the superintendence 
 of its execution, was in this instance also confided to Mr. Airy. In con- 
 sequence of the multitude of inequalities by which the moon's motion is 
 affected, the undertaking was one of stupendous magnitude. In order to 
 form some idea of the labour expended in its execution, it may be men- 
 tioned that upwards of 8000 places of the moon were deduced from the 
 observations, and compared with the corresponding places calculated from 
 the tables. An extraordinary force of computers was employed for several 
 years at the Eoyal Observatory in these calculations. The results were 
 finally published in the year 1848, in two quarto volumes *. Mr. Airy, 
 who is distinguished no less as a theoretical than as a practical astronomer, 
 has made them the subject of profound discussion, with a view to obtain 
 a more accurate knowledge of the moon's motion, and has announced the 
 conclusions at which he arrived in a paper which appears in the seven- 
 teenth volume of the " Memoirs of the Astronomical Society."! 
 
 Allusion has already been made to Pond's method of determining the 
 zenith distance of a celestial body at one transit by a combination of 
 
 * The calculations connected with this great undertaking were superintended by M-. 
 Hugh Breen, who had the melancholy satisfaction of just living to see its completion. 
 Mr. Airy, who bears honourable testimony to his skill and accuracy, states, at the begin- 
 ning of the first volume of the published results, that after a short illness he expired on 
 the morning of April 1, 1848, only a few hours having elapsed after the last supple- 
 mentary tables had been sent to the press. 
 
 + Allusion has already been made to some of the more important results of these re- 
 searches in a former part of this work. Another very interesting confirmation of them is 
 mentioned by Prof. Hansen, in a letter to the Astronomer Royal, dated June 27, 1850. 
 (Mo. Proc. Ast. Soc., June, 1850.) Mr. Airy had deduced + 1'.721 as the correction 
 of Damoiseau's value of the secular motion of the lunar node. Prof. Hansen, having 
 caused one of his assistants to compute, by the modern tables, the nineteen ancient, eclipses 
 recorded by Ptolemy in the Almagest, found by a comparison of the results with the re- 
 corded observations, that the correction of the same element should be -f- T.643. The 
 close agreement of these two values will appear very remarkable, when the complexity 
 of the moon's motion is taken into account. Professor Hansen states that they both 
 agree as nearly as could be desired, with the corresponding value deduced by him from 
 the theory of gravitation. The result of these different researches completely refutes the 
 statement recently put forth by Prof. Seiffarth of Leipsic, to the effect that the ancient 
 eclipses indicated the necessity of a considerable correction of the motion of the lunar 
 
HISTORY OF PHYSICAL ASTRONOMY. 497 
 
 the results of two mural circles. During Mr. Airy's directorship of the 
 Observatory of Cambridge, he devised a mode of accomplishing the same 
 object by the use of only one circle. This practice was adopted by him 
 at Greenwich, soon after his appointment as Astronomer Royal ; and, as 
 only one mural circle was henceforward necessary for that establishment, 
 the mural circle by Jones was dismounted in the year 1839, and was 
 sent to the Cape of Good Hope, for the use of the Royal Observatory 
 established in that colony. 
 
 In practical astronomy, as in every other department of human know- 
 ledge, circumstances are constantly arising which create the necessity 
 for further improvement. The meridional instruments constructed by 
 Troughton, for the Royal Observatory of Greenwich, were unrivalled 
 specimens of artistic excellence, arid in the hands of Pond and his suc- 
 cessor, served amply to uphold the reputation of that establishment. In 
 recent times, however, it has been found that they are no longer adequate 
 to the exigencies of the present state of astronomical science. The 
 difficulty which has been experienced in observing on the meridian the 
 small planets that have been recently discovered, and also occasionally 
 faint stars, whose positions it is necessary to determine in connexion with 
 extra-meridional observations, has suggested the expediency of replacing 
 the telescope of the mural circle by one of larger aperture*. The mural 
 circle, however, not being adapted for carrying a large telescope, it be- 
 came necessary to devise a different mode of construction ; and as the 
 form of the transit seemed to be most suitable for this purpose, it was 
 proposed that an instrument should be constructed, which should combine 
 the functions of both the mural circle and the transit. The advantage of an 
 instrument capable of assigning with due precision the two elements of the 
 position of a celestial body, must be obvious to every reader. The transit 
 circle devised by Mr. Airy, with a view to the accomplishment of this ob- 
 ject, was constructed by Messrs. Ransome and May, of Ipswich, and Mr. 
 Simms, of London. The circle is 6 feet in diameter. The telescope has 
 an aperture of 8 inches, and a focal length of 11 J feet. The adjustment in 
 azimuth and collimation is effected by means of two collimating telescopes, 
 placed one to the north and the other to the south of the instrument f. 
 
 * The telescope of Troughton's mural circle had an aperture of 4 inches, and a mag- 
 nifying power of 150. 
 
 f It has been already mentioned (see p. 464) that Roemer determined the error of 
 collimation of his transit circle by means of two distinct marks diametrically opposite to 
 each other. In fixing two objects at the exact distance of 180 apart, he employed a 
 telescope of a peculiar construction, termed the ampkioptra, or reciprocal tube, which 
 he contrived for that express purpose (Basis Astronomies, p. 97). It is necessary, when 
 a fixed object is employed directly as a meridian mark, that it be situate at a considerable 
 distance from the telescope, so that the rays of light from it may enter the object glass 
 in sensibly parallel directions, otherwise they will not converge at the focus. The inter- 
 vention of a lens, however, serves to render a near mark equally suitable for this purpose; 
 for since parallel rays of light falling upon the lens converge at its focus, so on the other 
 hand, if an object be placed at the focus of the lens, the rays of light diverging from it 
 will be refracted by the lens, and, emerging in parallel directions, will produce the same 
 effect as if they came from an object at an infinite distance. Hence, if an object be 
 viewed with a common astronomical telescope, through a lens adjusted to it in this man- 
 ner, it will appear quite distinct in the focus of the telescope, at whatever distance it be 
 situate from the observer. This mode of obtaining the advantage of a distant mark, was 
 originally devised in 1785, by Dr. Rittenhouse, an American philosopher ( Trans. Amer. 
 Phil Soc., vol. ii., p. 181). The collimating telescope is an application of the same 
 principle. It consists of a small telescope, having its object glass turned towards the 
 object glass of the telescope to be adjusted. In this case it is clear that the cross wires 
 
498 HISTORY OF PHYSICAL ASTRONOMY. 
 
 The observations are made by direct and reflected vision, in the same 
 way as formerly practised with the mural circle. The instrument has 
 been in constant use since the commencement of the year 1851*. 
 
 Although meridional determinations foum the principal object of atten- 
 tion at Greenwich, observations of a miscellaneous nature are not altoge- 
 ther neglected. In one of the domes of the more ancient part of the 
 building, there is fitted up an equatorial of 5 feet in diameter, which 
 was originally constructed by Ramsden for Sir George Shuckburgh, 
 and which in the year 1811, was presented to the Royal Observa- 
 tory by the Hon. Mr. Jenkinson. This instrument is occasionally used 
 in observing comets. It has recently been employed in determining the 
 distances between Mars and the neighbouring stars, in connexion with 
 the corresponding observations of f the American expedition to Chili f. 
 In the south-eastern dome of the modern part of the observatory, a 
 powerful telescope, mounted equatorial ly, has been in constant use since 
 the year 1838. The object glass, which is by Cauchoix, of Paris, is the 
 munificent gift to the observatory of the Rev. R. Sheepshanks. It has 
 an aperture of 6.7 inches, and a focal length of 8 feet 2 inches. This 
 telescope is fitted with a double-image micrometer, contrived by Mr. 
 Airy. It has been employed in measuring the diameters of the planets, 
 and in determining the distances and angles of position of double stars. 
 An interesting result obtained by the use of this telescope, is the recent 
 determination of the true figure of the planet Saturn, by the Rev. Mr. 
 Main, the chief assistant at the Royal Observatory, 
 
 Besides the equatorials above referred to, there are also detached tele- 
 scopes for the observation of eclipses, occultations, and other phenomena 
 of a similar kind. Among the instruments of this description is a reflect- 
 ing telescope of 10 feet, constructed by Sir William Herschel. 
 
 In Pond's time an instrument termed the zenith tube was constructed 
 by Troughton for the observatory, the object of which was to determine 
 small distances from the zenith. It consisted of a telescope &5 feet long, 
 adjusted to the zenith by the aid of a plumb-line. The small variations 
 in the zenith distance of a star were ascertained by measuring with an 
 internal micrometer, the deviations of the star from the optical axis of 
 the telescope. In practice the use of this instrument was limited to 
 observations of y Draconis, which passes within about % of the zenith of 
 Greenwich. 
 
 The zenith tube was first erected in 1833, and strong hopes were enter- 
 tained that observations with it would lead to a more accurate determina- 
 tion of the constant of aberration, and might also serve to throw light 
 upon several other interesting points of astronomy. These hopes, how- 
 
 in the focus of the former telescope will form a distinct image at the focus of the latter. 
 Hence, if the collimating telescope have a fixed position in the meridian, the transit may 
 be adjusted to it by bringing its cross wires to coincide with the cross wires of the col- 
 Hmator. The principle of the collimating telescope has been applied to various astrono- 
 mical purposes in modern times by Gauss, Bessel, Kater, and others. We have already 
 had occasion to mention a singular mode of using it, by Dr. Robinson, in his researches 
 on Irradiation (see p. 353). 
 
 * One of the peculiarities of this instrument, consists in its being made of as few sepa- 
 rate pieces as possible, so as to obviate the effects of unequal expansion, and to secure 
 more effectually the adjustment of the different parts. For this purpose the material of 
 construction used is cast iron, the pivots of the axis being hardened by the process which 
 engineers term chilling. 
 
 f See at p. 212 a brief allusion to the object of this expedition. 
 
HISTORY OF PHYSICAL ASTRONOMY. 499 
 
 ever, have not been realised. Notwithstanding a great amount of attention 
 and skill bestowed upon it for many years, the results have not been 
 found to exceed in accuracy those obtained by the aid of the mural circle. 
 The Astronomer Royal, in consequence, has recently contrived a new instru- 
 ment, termed the reflex zenith telescope, which appears to be adapted for 
 giving results of great accuracy. The adjustment of this ingenious instru- 
 ment, with respect to the zenith, is effected not by means of the plumb- 
 line, which Mr. Airy considers to have been the main cause of the failure 
 of the former instrument, but by reflexion from a surface of mercury. 
 This instrument is now being constructed, and will soon be ready for use. 
 
 The volume which issues annually from the Greenwich Observatory, 
 exhibits an interesting picture of the activity which reigns in that esta 
 blishment. The sun, moon, and planets, and the stars of the Nautical' 
 Almanac, are observed as they pass the meridian on every practicable 
 occasion. A considerable number of other stars is also observed on the 
 meridian for particular purposes. Then there are the extra-meridional 
 observations with the equatorials, comprehending occasional observations 
 of comets, determinations of the diameters of the planets, and micro- 
 metrical measurements of double stars ; besides observations from time 
 to time of eclipses, occultations, and other such phenomena, with detached 
 telescopes. The observations of the planets for the year are all reduced, 
 and a comparison is instituted between the results thus obtained, and the 
 corresponding results calculated from the most esteemed tables of the 
 several bodies. Not only are the errors in the geocentric longitude and 
 ecliptic polar distance of each planet thus regularly tabulated, but the 
 equations between the errors in geocentric longitude and the heliocentric 
 errors of the earth and planet are also regularly formed. The observa- 
 tions, in fact, are so exhibited as to be immediately available for correcting 
 the elements of the planets, or otherwise perfecting the theory of their 
 movements*. The stars observed during each year are also reduced to 
 their mean places, forming the materials for occasional catalogues, which 
 prove of inestimable value, both as a guide to the practical astronomer 
 and as a groundwork of research to the theorist. The same system of 
 complete reduction is applied to all the other observations. In the case 
 of the occultations of stars by the moon, the results in every instance 
 are employed in forming an equation for the rectification of the lunar 
 theory. So with respect to the occultations and transits of Jupiter's 
 satellites, the times of actual occurrence are compared with the times 
 indicated by the Nautical Almanac, and the errors of the epheineris, 
 or rather of the tables of the satellites, thereby clearly exhibited to 
 the eye. 
 
 It will be obvious to any person who bestows even a passing glance 
 upon the annual volume of the Greenwich Observations, that the office of 
 
 ^ The error in the geocentric longitude of a planet may arise from either of the fol- 
 lowing causes : 1st, an error in the earth's longitude ; 2nd, an error in the radius vector 
 of the earth's orbit ; 3rd, an error in the heliocentric longitude of the planet ; 4th, an error 
 in the radius vector of the planet's orbit. Hence an equation is formed between each 
 error of geocentric longitude and the four errors above mentioned, represented algebrai- 
 cally as unknown quantities. In the annual volume of the Greenwich Observations, the 
 numerical values of the coefficients of the different terms in each equation are regularly 
 calculated, but this is the farthest step that is practicable. The discussion of the equa- 
 tions can only be undertaken, with any hopes of success, when they have accumulated in 
 large numbers, and when the observations to which they relate have extended over a 
 considerable period of time. 
 
 KK 2 
 
500 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Astronomer Royal is no sinecure. One forms, however, a very imperfect 
 idea of the heavy responsibility attached to the directorship of a national 
 observatory, from a mere inspection of the current labours of the establish- 
 ment. The rapid progress of astrouomyin modern times, is constantly 
 suggesting the necessity of modifying in some degree the instruments 
 and methods of observation in actual use, and it is therefore desirable 
 that the individual appointed to such an office should possess a natural 
 aptitude for encountering every fresh difficulty that may occur in the 
 practice of observation, while at the same time he should maintain a 
 vigilant eye over the labours of his contemporaries, so as to avail 
 himself of every really useful improvement that their researches may 
 elicit. It is hardly necessary to remark that sound judgment and 
 strong natural sagacity, combined with a profound knowledge of the 
 various branches of physical science bearing upon practical astronomy, as 
 well as indefatigable energy, are indispensable to the due discharge of 
 such duties. It is universally admitted that the present Astronomer 
 Royal has proved himself to be eminently qualified for his arduous office, 
 and that he has upheld in the most satisfactory manner the ancient repu- 
 tation of the Observatory of Greenwich. Moreover, while he has been 
 actively engaged in the promotion of objects more immediately relating to 
 practical astronomy, he has not failed to contribute to the advancement 
 of astronomical science in general, by researches of a purely theoretical 
 character. It ought to be remarked, also, that in virtue of his office he is 
 frequently called upon by the Government to take an active part in scien- 
 tific operations, which have only a remote connexion with astronomy, but 
 which necessarily demand much careful attention. In all these labours, 
 as well as in the multifarious details connected with the ordinary discharge 
 of his duties, Mr. Airy has uniformly displayed the same consummate 
 ability, the same untiring energy, and the same devotedness to the trust 
 committed to his charge. 
 
 A retrospective view of the history of the Royal Observatory of Green- 
 wich is calculated to excite feelings of agreeable satisfaction with respect 
 to the mode in which that noble institution has fulfilled the end for which 
 it was originally designed. From the circumstance of the observations 
 extending with uninterrupted regularity over a long period of time, and 
 from their undisputed excellence, they have formed almost the exclueive 
 materials by means of which astronomers in modern times have succeeded in 
 bringing the tables of the sun, moon, and planets to their present high state 
 of perfection. The lunar theory, which so intimately concerns the interests 
 of navigation, has been especially indebted for its successive improve- 
 ments to the observations made at Greenwich. It is also mainly by a 
 discussion of Greenwich observations that the constants of precession, 
 and the other uranographical corrections, have been established with such 
 precision in the present day. Delambre has justly remarked, that if by 
 some great revolution the sciences had perished, while this collection of 
 observations alone, with some methods of calculation, had survived the 
 general wreck, there would still remain sufficient materials for recon- 
 structing the whole edifice of astronomical science *. In the present day, 
 when the attention of astronomers is being directed to questions of greater 
 delicacy than any which had hitherto formed the subject of research, the 
 materials annually accumulated at Greenwich have acquired new claims 
 
 * Histoire tie I* Astronomic au Dixhuitieme Siecle, p. 627. 
 
HISTORY OF PHYSICAL ASTKONOMY. 501 
 
 to the consideration of the theorist. It is thus that the recent determi- 
 nations of the places of the stars at that observatory, have served to 
 confirm heyond all doubt the interesting conclusion arrived at by various 
 astronomers in modern times relative to the motion of the solar system in 
 space *. 
 
 In the department of practical astronomy, which relates to the de- 
 termination of the figure of the earth and the promotion of objects con- 
 nected with geographical science, England, although not the first in 
 the field, has in recent times assumed a distinguished position. The 
 geodetical operations which have been carried on in the present cen- 
 tury, both in the British Isles and in India, may fairly challenge compa- 
 rison with the most unexceptionable undertakings of a similar kind that 
 have been executed on the Continent. The Indian arc of the meridian 
 is, moreover, especially remarkable for being the longest that has yet 
 been measured upon the surface of the earth. With respect to those 
 operations which have for their object the determination of the terrestrial 
 ellipticity by means of experiments with the pendulum, it may be asserted 
 with confidence, that no country has achieved so much as Britain has done. 
 The experiments of the lamented Captain Foster, for completeness and 
 delicacy of execution, may be said to leave nothing further to be desired. 
 
 It is impossible, within the limits of this work, to give an account of 
 the numerous establishments that have been founded, in different parts of 
 the British empire, for the promotion of practical astronomy. To the in- 
 fluence of the Astronomical Society is attributable in a great degree the 
 activity which thus generally prevails. This society was founded in the 
 year 1820, and was finally incorporated by Royal Charter in 1830. The 
 first President of the Society was Sir William Herschel. 
 
 In France, practical astronomy continued to make slow progress during 
 the whole of the eighteenth century ; a circumstance mainly attributable 
 to the imperfect organization of the Royal Observatory of Paris. Some 
 brilliant exceptions, indeed, must be made to this remark. We have 
 seen Lacaille, in spite of unfavourable circumstances, raise himself, by 
 the mere force of his talents, to a high position among contemporary as- 
 tronomers. It has been remarked, also, that France took the initiative in 
 those important operations which relate to the determination of the mag- 
 nitude and figure of the earth. In this department of practical astro- 
 nomy, she still continued to maintain her pre-eminence. The measure- 
 ment of the arc of the meridian comprehended between Dunkirk and 
 Barcelona, was one of the most splendid scientific operations of the 
 eighteenth century f . This magnificent undertaking was executed under 
 the joint superintendence of Delambre and Mechain. Delambre, more 
 especially, by his labours on this occasion, proved himself worthy to be as- 
 sociated with Picard, Bouguer, and Lacaille. The main peculiarity of the 
 operation consisted in the observations having been made exclusively with 
 the repeating circle. It has been already mentioned that Mayer first sug- 
 
 * In recent years attention has been devoted at the Greenwich Observatory to the phe- 
 nomena of Meteorology and Magnetism, and the observations relative to these departments 
 of physical science are now published with the same regularity as the astronomical obser- 
 vations. 
 
 f It may be remarked that the object of this operation was, not to determine the figure 
 of the earth, but to obtain an invariable standard of measurement, by adopting as the 
 fundamental linear unit, the ten millionth part of a degree of the meridian. MM. Arago 
 and Biot subsequently extended the arc beyond Barcelona to Formentera, one of the Bale- 
 aric Isles. 
 
502 HISTORY OF PHYSICAL ASTRONOMY. 
 
 gested the principle of repetition as a means of obviating the errors of 
 division in astronomical instruments. The idea of that astronomer was 
 not, however, realised till the year 1787, when it was at length applied 
 successfully by Borda, a French officer of Marine, distinguished by philo- 
 sophical acumen and strong practical talents. 
 
 In the construction of tables of the various planetary bodies, an object 
 of research which may be said to form the connecting link between theo- 
 retical and practical astronomy, the labours of Delambre would suffice to 
 assign to him a high place in the history of astronomy, even although he 
 possessed no other claims to the recollection of posterity. The method of 
 equations of condition, the utility of which Mayer originally exhibited in 
 his admirable researches on the libra tion of the moon, was employed with 
 great success by Delambre, in the year 1785, in correcting the elements 
 of the solar orbit by means of Maskelyne's observations. His tables of 
 the planets Jupiter, Saturn, and Uranus, and of the satellites of Jupiter, 
 which shortly afterwards appeared, as w r ell as his solar tables, which were 
 published at a later period, were all admirable attestations of his perse- 
 verance and skill. He may be said to have been the first who submitted 
 masses of observations to a systematic process of treatment, deducing in 
 this manner, from their totality, an accuracy of result which was unattain- 
 able by a succession of partial operations*. 
 
 About the commencement of the present century, an improvement was 
 effected in the organization of the Royal Observatory of Paris. At the 
 same time, tw r o excellent mural quadrants, one of w 7 hich was constructed 
 by the celebrated Bird, were erected in suitable apartments. Hence- 
 forward the observations assumed a character of regularity and trust- 
 worthiness hitherto unknown, and were destined, in consequence, to prove 
 really serviceable in conducing towards the advancement of theoretical 
 astronomy. In recent times, when the duties of its directorship have been 
 confided to M. Arago, the Royal Observatory of Paris has attained a high 
 degree of efficiency. Observations are now constantly made at that esta- 
 blishment, both by direct and reflected vision, with two mural circles con- 
 structed by French artists of acknowledged eminence f. The brilliant 
 result which M. Le Verrier deduced from his researches on the perturba- 
 tions of Uranus, based to a considerable extent upon data procured from 
 the registers of the Royal Observatory of Paris, was a graceful homage to 
 the illustrious philosopher, at whose suggestion he was induced to under- 
 take an examination of the subject. 
 
 In no country has practical astronomy made more rapid progress during 
 the present century than in Germany. The labours of Bessel and a host 
 of eminent astronomers, afford ample confirmation of the truth of this 
 remark. It must be allowed, also, that in the construction of astronomical 
 instruments, the German artists have attained a degree of excellence 
 which is unsurpassed in any other country of the world. 
 
 Denmark still continues to sustain her ancient reputation by her patron- 
 age of astronomical science. In M. Schumacher, whose recent death has 
 
 * Jean Baptiste Joseph Delambre was born at Amiens, in the year 1749. He died at 
 Paris in 1822. 
 
 f One of the mural circles was executed by Gambey, an artist who appears to have 
 attained a very high degree of excellence in the art' of graduation. According to 
 M. Faye, the probable error of the interval between two consecutive points of division 
 of the circle constructed by him for the Royal Observatory of Paris, is less than (T'108. 
 (Comptes Rendus, tome xxvii., p. 640). Gambey died in 1847. 
 
HISTORY OF PHYSICAL ASTRONOMY. 503 
 
 been so deeply deplored by the astronomical world, practical astronomy, 
 more especially, has lost a supporter whose place it will be difficult to 
 supply. The Astronomische Nachrichten, with which the name of that 
 astronomer is inseparably associated, has, perhaps, contributed more to- 
 wards the improvement of astronomical science, in all its branches, than 
 any similar publication has ever done. This celebrated periodical was 
 established by M. Schumacher at Altona, in the year 1821, and has ever 
 since formed the common medium of intercourse among astronomers over 
 the whole civilised world. Its publication continued to be regularly 
 superintended by him till his death *. 
 
 While England, France, and Germany have been contributing towards 
 the advancement of practical astronomy, Italy has not remained an idle 
 spectator of the scene. There is assuredly no cause of more cheering 
 congratulation, to those who look forward to the regeneration of that noble 
 country, than is afforded by the circumstance that, while trodden in every 
 age under the hoof of the oppressor, she has never, even in the darkest 
 hour of her distress, resigned herself to despair, but has invariably main- 
 tained her high position in the intellectual world, with a constancy of 
 purpose and a brilliancy of success worthy of her deathless renown. 
 While unrivalled in the productions of the imagination, Italy has been 
 always ready to dispute the palm with the most favoured nations in the 
 more severe pursuits relating to the mathematical and physical sciences. 
 In Oriani and Piazzi, as well as many other eminent individuals of modern 
 times, she has afforded abundant evidence that practical astronomers of the 
 first order are not wanting to sustain her reputation. 
 
 The efforts which Russia has made in recent times to acquire a position 
 in the civilised world conformable to the grandeur of her material re- 
 sources, have in no instance been more signally illustrated than in her 
 munificent patronage of astronomical science. The earliest observatory of 
 that country was built at St. Petersburg, in 1725, under the auspices of 
 Peter the Great. Delisle, a French astronomer of considerable experience, 
 was its first director. As in the case of most of the early observatories 
 of Europe, it was built in the form of a high tower, the observations having 
 been made in an apartment at the top of the building. In 1747, this 
 structure was totally consumed by fire, whereupon Delisle returned to 
 France. Shortly afterwards it was rebuilt in its original style, and Hein- 
 sius of Leipsic, an astronomer well known for his observations of the great 
 comet of 1747, was appointed director. The instruments with which the 
 observatory had been hitherto furnished were only of moderate excellence, 
 and consequently the observations could not be expected to possess a high 
 degree of importance. In 1761, however, the Russian Government, with 
 a view to extend the usefulness of the observatory, procured from Eng- 
 land a mural quadrant of eight feet radius, by Bird, who was then in the 
 zenith of his fame, and also a transit instrument of five feet focal length, 
 constructed by the same artist. Grischow, who was then director of the 
 establishment, justly considered that the practice of making the observa- 
 tions in an apartment at the top of the building was unfavourable to the 
 stability of the instruments ; and, moreover, that the situation of the obser- 
 vatory in the heart of a populous city was not by any means desirable. 
 On both these grounds, he suggested that a new observatory should be 
 
 * Heinrich Christian Schumacher was born at Bramstedt, in Holstein, on the 3rd of 
 September, 1780. He died at Altona, on the 28th of December, 1850. The Astrono- 
 mische Nachrichten is now superintended by MM. Petersen and Hansen. 
 
50-4 IJISTOKY OF PHYSICAL ASTKOXOMY. 
 
 built in a more suitable locality, and as this idea was for some time favour- 
 ably entertained by the Academy of Sciences, no immediate steps were 
 taken for mounting the instruments obtained from England. It was not 
 till the year 1798, when the design of erecting a new observatory was 
 temporarily abandoned, that the instruments constructed by Bird were at 
 length adjusted in the meridian in two lateral apartments, situate upon 
 the first floor of the observatory. 
 
 Although Russia had not hitherto contributed greatly to the advance- 
 ment of astronomical science in so far as meridional observations were 
 concerned, it is just to state that, in regard to the important observations 
 connected with the transits of Venus in 1761 and 1769, the Government, 
 as well as the astronomers of that country, took a very distinguished part. 
 Another important object connected with the practice of observation, which 
 exercised the talents of the Russian astronomers towards the close of the 
 last century and the beginning of the present, was the determination of 
 the geographical positions of the principal points comprehended within 
 the vast territories of the empire. The most active in the prosecution 
 of these labours was the well known astronomer Schubert. In 1803, M. 
 Wisniewski*, an astronomer of great merit, was appointed director of the 
 Observatory of St. Petersburg. Although some excellent observations in 
 the meridian were now occasionally made at that establishment f, it was 
 deemed advisable to apply its resources chiefly to observations of comets 
 and other isolated phenomena. In 1827, the idea of a new central obser- 
 vatory began again to be entertained by the Academy, and in 1830 the 
 Emperor at length declared by his minister, that the honour of the country 
 appeared to him to demand the establishment, near the capital, of a new 
 astronomical observatory, conformable to the actual state of science, and 
 capable of contributing to its ulterior advancement. 
 
 The first thing to be done was to fix upon the most appropriate situa- 
 tion for the new observatory. After some deliberation it was at length 
 resolved, at the suggestion of the Emperor, that it should be erected in 
 the vicinity of Pulkowa, a small town situate about ten miles to the south- 
 west of St. Petersburg, upon a gentle eminence commanding an extensive 
 view of the horizon in all directions. The design of the establishment 
 was upon a scale of unprecedented magnificence. The foundation stone 
 of the building was laid on the 21st of June, 1835, and it was finally com- 
 pleted on the 19th of August, 1839. 
 
 * This astronomer seems to have been gifted with a remarkable power of vision. 
 According to M. Struve, he continued to observe the comet of 1807, in the month of 
 March, when all other astronomers had lost sight of it for four weeks. In the case of the 
 great comet of 1811 he gave a still more striking proof of his acuteness of vision. This 
 comet first became visible in the month of March, 1811, and after reappearing on its 
 return from the perihelion, was finally lost sight of on the llth of January, 1812. Bessel, 
 however, suggested that the earth might not improbably overtake the comet, and that the 
 latter might in consequence become visible for the third time, in the month of July or 
 August. Wisniewski actually detected it at Novo-Tcherkask, on the 31st of July, and kept 
 sight of it till the 17th of August. No other European astronomer appears to have per- 
 ceived the comet on this occasion; but it is worthy of remark that it was seen by the 
 Spanish astronomer Ferrer, at Havannah, in the Island of Cuba.(Mem. Ast. Soc., vol. iii., 
 p. 36). It may be mentioned that Ferrer and his companion determined the orbit of 
 this celebrated comet with great accuracy from their own observations, made with a sextant 
 of only seven inches radius, before Bessel or any of the great astronomers of Europe had 
 published any results on the subject. 
 
 f M, Struve states that a series of observations of the newly discovered planets, Ceres 
 and Juno, was made at the St. Petersburg Observatory about this time, which in point of 
 accuracy might bear comparison with those made at any other observatory in Europe. 
 
HISTORY OF PHYSICAL ASTRONOMY. 505 
 
 The task of providing the instruments for the new establishment 
 was confided to M. Struve, the director of the Observatory of Dorpat, so 
 celebrated for his labours on various subjects relating to astronomical 
 science, and more especially for his observations of double stars. The 
 imperial instructions relative to this object were characterised by un- 
 bounded liberality. The principal instruments of the establishment have 
 been constructed by German artists. For meridional observations there 
 are four instruments, two of which have been supplied by Ertel of Munich, 
 and two by Kepsold of Hamburgh. The instruments by Ertel are a ver- 
 tical circle 43 inches in diameter, and a transit instrument of 5.85 inches 
 aperture, and 8 feet 6 inches focal length : those by Repsold are a meri- 
 dian circle 48 inches in diameter, and a prime vertical telescope of 6.25 
 inches aperture and 91 inches focal length. For extra-meridional obser- 
 vations, the observatory is furnished with a magnificent equatorial tele- 
 scope by Merz and Mahler of Munich, the object glass of which has a free 
 aperture of 14.93 inches, and a focal length of 22.55 feet. Moreover, it 
 contains several clocks constructed by the most esteemed artists of Ger- 
 many and England, as well as an ample collection of other instruments, 
 both astronomical and physical, destined for various purposes connected 
 with the practice of observation. In short, the Observatory of Pulkowa 
 may be regarded as one of the most complete in existence, of those insti- 
 tutions that have been founded for promoting the advancement of astro- 
 nomical science. The expense attending the erection of the building, and 
 its subsequent equipment, amounted in round numbers to 600,000 roubles 
 of silver*. 
 
 The illustrious Struve has been appointed first director of the Obser- 
 vatory of Pulkowa. An ample staff of assistants, several of whom enjoy a 
 European reputation, is allowed him for carrying on effectually the labours 
 of the establishment. The sum allotted from the imperial treasury for its 
 annual maintenance is no less than 62,200 roubles f. 
 
 M. Struve commenced his labours at the Observatory of Pulkowa in the 
 month of September, 1839. The main object to which he has proposed 
 to devote the resources of the establishment, is the advancement of side- 
 real astronomy. Results of great importance relative to precession, 
 aberration, and other kindred subjects, have already been deduced from 
 the observations J . 
 
 In the United States of America, practical astronomy has recently been 
 making rapid progress. A central observatory has been established at 
 Washington, which is placed under the direction of Lieut. Maury. The 
 expedition to Chili, undertaken with a view to determine the solar paral- 
 lax by means of simultaneous observations of Venus and Mars, bears 
 honourable testimony to the enlightened views and liberality of the 
 American Government. Besides the national observatory above alluded 
 to, there are similar institutions, upon a smaller[scale, established in several 
 of the states of the Union. Of these, the most celebrated is the observa- 
 tory of Harvard University, Cambridge, Massachusetts, which boasts of one 
 of the largest and most perfect refracting telescopes in the world. The 
 discovery of the eighth satellite of Saturn, and the establishment of various 
 facts of a highly interesting nature, relative to the physical constitution 
 
 * 100,000. t 10,366 13s. 4d. 
 
 J M. Struve has given a complete description of the Observatory of Pulkowa in a mag- 
 nificent work entitled, " Description de 1'Observatoire Astronomique Central de Pul- 
 kowa, par F. G. W. Struve," 2 vols. fol., St. Petersburg, 1845. 
 
506 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of the celestial bodies, have resulted from the labours of Mr. Bond, the di- 
 rector of the observatory, achieved by the use of this powerful instrument. 
 One of the inventions which do most honour to the Americans, consists 
 in the application of electro-magnetism to 1 geographical and astronomical 
 purposes. As early as the year 1844, the instantaneous transmission of 
 time by the electric telegraph, was employed in determining the difference 
 of the longitudes of Washington and Baltimore. The same method has 
 since been practised for ascertaining the relative longitudes of various 
 other transatlantic cities. Recently, attempts have been made, with 
 complete success, to record transit observations of the celestial bodies, by 
 means of the electro-magnetic principle. As soon as the star is seen 
 bisected by the wire of the telescope, a slight pressure of the ringer com- 
 pletes or breaks the galvanic circuit, and the effect is instantaneously 
 transmitted, by the intervention of a magnet, upon a recording surface, 
 to which a uniform motion is given by a peculiar mechanism. This in- 
 genious . contrivance for fixing the precise instant of a phenomenon, by 
 calling into exercise the sense of touch to aid that of vision, promises, 
 at no distant period, to supplant the usual mode of recording by the 
 combined application of the eye and the ear*. We may remark, in con- 
 cluding this chapter, that it ought to be borne in mind also, as an 
 earnest of what may be expected from the future exertions of our trans- 
 atlantic brethren, that to an American philosopher Practical Astronomy is 
 indebted for the beautiful invention of the collhnating telescope. 
 
 CHAPTER XIX. 
 
 Catalogues of the Fixed Stars. Their importance as forming the Groundwork of Astro- 
 nomical Science. Earlier Catalogues. Ptolemy. Ulugh Beigh. Tycho Brahe. 
 
 Halley Hevelius. Flamsteed. Modern Catalogues Bradley Lacaille Mayer. 
 
 Maskelyne. Publication of the Histoire Celeste of Lalande. Piazzi. Groom- 
 bridge. Zone Catalogues of Stars. Bessel. Argelander Sautini. Catalogue of 
 
 the Astronomical Society. Catalogues of Southern Stars Fallows. Brisbane. 
 
 Johnson. Henderson. Standard Catalogues of Stars. Catalogue of the British As- 
 sociation. Recent Standard Catalogues. 
 
 CATALOGUES of the fixed stars, considered as contributions to Astronomical 
 Science, possess an importance arising from two distinct causes. In the 
 first place, an accurate catalogue of such objects furnishes a series of 
 points of reference by means of which the positions of the various bodies 
 composing the planetary system may be determined from observation, and 
 the laws of their motions investigated. Secondly, it constitutes the 
 groundwork of stellar astronomy. A comparison of catalogues constructed 
 at different dates, enables the astronomer to ascertain the proper motions of 
 the stars, and to arrive at conclusions respecting the changes which may be 
 taking place in the physical constitution of the sidereal heavens. More- 
 
 * It would appear that several individuals in the United States are entitled to share in 
 the merit of this ingenious invention, among whom may be more especially mentioned 
 Mr. Bond, Mr. Sears Walker, Prof. Mitchell, and Dr. Locke. It has been stated in the 
 text, that the instant of transit may be noted, either by completing the galvanic circuit, 
 supposing that in the ordinary state of the apparatus the current of electricity is inter- 
 rupted, or by making the electricity to flow in a continual current, and then suddenly 
 breaking the circuit. Both of these methods have been practised in America. At the 
 meeting of the Astronomical Society held on the 9th of May, 1851, there was exhibited 
 
HISTORY OF PHYSICAL ASTRONOMY. 507 
 
 over, it is by such a comparison alone, that he can discover whether there 
 exist any real grounds for believing that the whole solar system is affected 
 with a motion of translation in space. 
 
 The first individual who constructed a catalogue of the stars was 
 Hipparchus, who may be considered as the true founder of Astronomical 
 Science. It is said by Pliny, that he was induced to enter upon this 
 undertaking, by the sudden apparition of a new star in his time. Be this 
 as it may, it is certain that he actually determined by observation, the 
 longitudes and latitudes of upwards of a thousand stars, and arranged the 
 results in a catalogue. The earliest production of this kind now extant, 
 is the catalogue inserted by Ptolemy in the Syntaxis. It contains the 
 longitudes and latitudes of J028 stars, arranged in 48 constellations. 
 The epoch is the first year of the reign of the emperor Antoninus, which 
 corresponds to the year 138 A.D. It has been suspected, on very probable 
 grounds, that this catalogue is nothing more nor less than the catalogue of 
 Hipparchus, transported to the time of its reputed author, by applying to 
 the longitudes of all the stars a common additive quantity for the sup- 
 posed effect of precession during the intermediate period. 
 
 The next catalogue of stars, in the order of time, is that of the Tartar 
 prince, Ulugh Beigh. This individual, who was a grandson of the re- 
 nowned Tamerlane, established an observatory at Samarcand, the capital 
 of his father's dominions, and devoted himself with great ardour to astro- 
 nomical pursuits. Having found that the positions of the stars, as 
 assigned by Ptolemy in his catalogue, were in many instances considerably 
 erroneous, he formed the resolution of constructing a new catalogue, 
 founded exclusively upon his own observations. This design was actually 
 realised by him. The number of stars in the catalogue of this prince is 
 1019, being only nine less than the number contained in Ptolemy's 
 catalogue. The epoch is the year 1437 A.D. The mode of arrangement 
 is the same as that employed by Ptolemy. Ulugh Beigh was treache- 
 rously slain by his son in the year 1449, shortly after his accession to the 
 throne of his father. 
 
 The next catalogue recorded in the annals of astronomy, is that of the 
 illustrious Tycho Brahe. It originally appeared in the work of that 
 astronomer, entitled Astronomic Instaurata Progymnasmata, which was 
 first published in the year 1602. The number of stars is 777. The 
 epoch is 1600 A.D. From the labour and skill employed by Tycho Brahe 
 in its construction, this catalogue was vastly more accurate than any other 
 that had been hitherto executed. Kepler subsequently enlarged it from 
 Tycho Brahe's observations to 1005 stars, and published it in the year 
 1627, at the end of the Rudolphine Tables. 
 
 Halley's Catalogue of Southern Stars was the next in succession after 
 
 a contrivance for recording transits by electro-magnetism, which had been used for some 
 time at the Cambridge Observatory, U. S. In this apparatus, the signal was made by 
 interrupting the galvanic circuit, the recording paper upon which the magnet acted being 
 applied closely upon a cylinder, to which a uniform motion was given by a mechanism 
 devised at Cambridge, termed the spring governor. Mr. Airy proposes to introduce the 
 mode of recording transits by electro-magnetism at the Royal Observatory, where the 
 necessity of transmitting time from the meridian transit clock to the altitude and azimuth 
 instrument (the observations with which are made by noting the transit of the object over 
 a system of horizontal and vertical wires) renders such a method peculiarly desirable. It 
 would seem that the Astronomer Royal contemplates applying the principle so that the 
 instant of transit shall be indicated by completing the galvanic circuit, and that he purposes 
 giving a uniform motion to the recording cylindrical surface by means of a centrifugal 
 pendulum. 
 
508 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Tycho Brake's. The observations which form the basis of this catalogue 
 were made at St. Helena, during the years 1676-7-8. The number of 
 stars is 341. The epoch is 1677. Besides the circumstance of its relating 
 exclusively to stars in the southern hemisfmere, this catalogue is further 
 remarkable for being the first that was constructed from observations 
 made by the use of telescopic sights. Although not so accurate as was 
 desirable, even for the astronomy of his time, Halley did not on any 
 subsequent occasion attempt its improvement. It was submitted, however, 
 to a careful revisal by Abraham Sharp, and was inserted in its amended 
 form in the third volume of the Historia Celestis of Flamsteed. 
 
 The catalogue of Hevelius appeared in a posthumous work published in 
 1690*. It contained 1564 stars. The epoch is 1660. Inconsequence 
 of the pertinacity with which its author adhered to the use of simple 
 pinnules in making observations of the celestial bodies, this catalogue has 
 not been attended with so much advantage to astronomical science as 
 might have been expected from the labour bestowed upon its construction. 
 
 All the above-mentioned catalogues, after being subjected to a careful 
 revisal by the late Mr. Baily, were then reprinted; and, in their improved 
 state, they now form the thirteenth volume of the "Memoirs of the 
 Astronomical Society." 
 
 It has been already mentioned that Flamsteed's " British Catalogue" 
 was published in 1725, in the third volume of the " Historia Celestis" 
 Mr. Baily executed a scrupulous revisal of this catalogue also, adding to 
 it several hundred stars, which he extracted from Flamsteed's original 
 observations. In this form it was republished by him in 1835, at the end 
 of his "Account of the Life and Correspondence of Flamsteed," a work 
 to which we have repeatedly had occasion to allude. 
 
 No catalogue of stars was constructed from Bradley 's observations 
 during the lifetime of that great astronomer. In the Nautical Almanac 
 for 1773, there finally appeared a catalogue of 389 principal stars, ex- 
 tracted by Mason from the records of the observations made by him at 
 Greenwich. This catalogue was subsequently inserted by Dr. Hornsby in 
 the first volume of Bradley 's Observations, which was published at Oxford 
 in 1798. Allusion has been made to Bessel's Fundamenta Astronomia, 
 which he published in 1818, containing a catalogue of stars constructed 
 from the totality of the observations made by Bradley between the 
 years 1750 and 1762. The number of stars in this catalogue is 3112. 
 The epoch is January 1, 1750. 
 
 The illustrious Lacaille is the author of three catalogues of stars. 
 The first of these was published in 1757, in his Fundamenta Astronomic. 
 It contains the places of 398 stars. The epoch is January 1, 1750. The 
 place of the equinox was determined by Flamsteed's method, from obser- 
 vations of a Lyra and Sirius, in connexion with corresponding observa- 
 tions of the sun. This may be considered as the first catalogue which, in 
 point of accuracy, can bear a comparison with those of modern construc- 
 tion. In consequence of its having become exceedingly rare, the late 
 Francis Baily undertook a careful revisal of it, and procured its insertion 
 in the fifth volume of the " Memoirs of the Astronomical Society." 
 
 The second catalogue of Lacaille's is founded on observations of 
 southern stars made by him during his residence at the Cape of Good 
 Hope. Of these observations, comprehending the places of nearly ten 
 
 * Prodromus Astronomies, Gedan, 1690. 
 
HISTOKY OF PHYSICAL ASTRONOMY. 509 
 
 thousand stars, a partial catalogue only was formed by the author, con- 
 taining the reduced places of 1942 stars*. The remaining mass con- 
 tinued in their original condition, until at length, in 1838, the British 
 Association, at the suggestion of Mr. Baily, undertook the reduction of 
 the whole of the observations according to a uniform system. The com- 
 putations were executed under the superintendence of the late Professor 
 Henderson, of Edinburgh. The number of stars is 9766. The epoch is 
 January 1, 1750. The catalogue was printed in 1845, at the expense of 
 the Government. 
 
 Lacaille's third catalogue is one of 515 zodiacal stars, which was pub- 
 lished in 1763 as a posthumous work. He contemplated that this 
 catalogue should contain the places of 800 stars ; but he was prevented 
 by death from realising his design. The observations upon which it is 
 based were reduced, shortly after his death, by his personal friend Baily ; 
 who does not seem, however, to have executed his task with the scrupulous 
 regard to accuracy which a work of so much importance demanded. The 
 epoch of this catalogue is the year 1765. 
 
 Mayer is the author of a catalogue of 998 zodiacal stars, which appeared 
 in a volume of posthumous works, published at Gottingen, in 1775. 
 Through the influence of Francis Baily, the original observations were 
 brought from Gottingen to this country, and were published in 1826 at 
 the expense of the Board of Longitude. The same individual having 
 carefully revised the catalogue, by collating it with the original observa- 
 tions, procured its insertion in the fourth volume of the " Memoirs of 
 the Astronomical Society." 
 
 Maskelyne's fundamental catalogue of 36 stars, published by him, 
 originally in the Greenwich Observations, was by far the most accurate 
 production of the kind that had been hitherto given to the world. This 
 small collection long continued to be an indispensable guide to the 
 practical astronomer. 
 
 Observations of circumpolar stars present a peculiar interest, on account 
 of their utility in researches on refraction and various other subjects of 
 astronomical science. In 1800 the Rev. Francis Wollaston published a 
 small catalogue of such stars in a work entitled " Fasciculus Astronomicus." 
 Towards the close of the last century, a vast number of observations of 
 stars were made at the Ecole Militaire of Paris, by D'Agelet and Michael 
 Lefran9ais Lalande, nephew of the celebrated astronomer of that name. 
 The observations were made in zones. It was contemplated in this 
 manner to determine .the positions of all the stars in the northern 
 hemisphere down to the ninth magnitude. They were published in 
 1801, in a volume entitled " Histoire Celeste Frai^aise," but they were 
 unreduced, and therefore they were, in point of fact, inaccessible to the 
 astronomer. Partial reductions of these observations were shortly after- 
 wards made; but the great mass remained for many years in their 
 original condition. In 1825, Schumacher published tables for facilitating 
 the reduction of the stars contained in the Histoire Celeste, computed 
 according to a plan suggested by Bessel. In 1837, the British Associa- 
 tion agreed to defray the expense of the reduction of all the observations, 
 at the suggestion of Francis Baily, who undertook the superintendence of 
 the whole operation. The Government, as in the case of Lacaille's 
 observations of southern stars, agreed to defray the expense of printing. 
 
 * All the observations, including the partial catalogue, were published after Lacaille's 
 death, in a work entitled Ccelum Austrate Stelliferum 4to., Paris, 1763. 
 
510 HISTORY OF PHYSICAL ASTRONOMY. 
 
 This great catalogue contains the places of 47,390 stars, reduced to the 
 beginning of the year 1800. Although the results are not distinguished 
 by a high degree of accuracy, they have proved eminently useful as points 
 of reference in extra-meridional observations, and have served to throw 
 light upon several interesting points of astronomical science. 
 
 In 1803 Piazzi published, at Palermo, his first catalogue of 6748 stars. 
 The fundamental points used in its construction were the thirty-six stars of 
 Maskelyne's catalogue. As some doubt seemed to rest upon the accuracy 
 of the right ascensions of these stars, the illustrious Italian resolved to 
 establish his results solely upon his own observations, and, in accordance 
 with this view, he formed a preliminary standard catalogue of 120 prin- 
 cipal stars, which he published in 1807. These formed the basis of his 
 more extensive catalogue of 764C stars, which appeared in 1814*. This 
 great work is justly considered to be one of the most important that has 
 ever been executed by a single individual. Every star was observed 
 several times, and a mean of all the results taken as the final place of 
 the starf. Moreover, the table of refractions employed by Piazzi in re- 
 ducing the stars to their mean places, was deduced by him exclusively 
 from his own observations. The epoch of the catalogue is the beginning 
 of the year 1800. From the circumstance of its being at once so ex- 
 tensive, so accurate, and so independent in its construction, this catalogue 
 has formed the groundwork of much valuable research to the theorist, 
 while at the same time it has proved an inestimable boon to the practical 
 astronomer J. 
 
 In 1806 De Zach published a catalogue containing the places of 1830 
 zodiacal stars, founded on observations made by him at the observatory of 
 Seeberg in Saxe Gotha. 
 
 * " Prsecipuarum Stellarum Inerrantium Positiones Mediae, ineunte seculo xix". 
 Quarto, Panormi, 1814. The observations employed in the formation of this catalogue 
 were made by Piazzi, at the Observatory of Palermo, between the years 1792 and 1813, 
 with the famous altitude and azimuth instrument constructed for him by Ramsden. 
 
 f- According to Captain Smyth, each star was observed from five or six to ten or 
 twenty, or even occasionally to a greater number of times. The same author states that 
 the whole number of observations amounted to nearly 1 50,000. ( Cycle of Celestial 
 Objects, vol. i., p. 433.) 
 
 Joseph Piazzi was born on the 16th of July, 1746, at Ponte in the Valteline, a dis- 
 trict of Northern Italy, which then formed part of the Helvetic Confederation. In early 
 life, he became a member of the monastic order of Theatines. As soon as he had 
 qualified himself for holy orders, he was appointed to teach philosophy in a convent of 
 Genoa, but having incurred the displeasure of the theological party by too free an 
 expression of his opinions, he shortly afterwards resigned his situation. Having now de- 
 voted his attention more especially to the exact sciences, towards which he always evinced 
 a strong inclination, he was appointed Professor of Mathematics at Malta, and subse- 
 quently at Rome. In 1780, he was appointed Professor of Mathematics in the Academy 
 of Palermo. Shortly afterwards Ferdinand IV., King of Naples, having founded an 
 observatory at that city, Piazzi was appointed director of the establishment. Having 
 visited France and England, in order to extend his knowledge of practical astronomy, he 
 returned to Palermo, bringing with him a collection of astronomical instruments from the 
 latter country, and commenced his labours at the new observatory in 1792. He now 
 proceeded to carry into effect his resolution of executing a great catalogue of stars, an 
 undertaking which may be said to have formed the principal object of his life. Captain 
 Smyth, who was a personal friend of the celebrated astronomer, referring to this great 
 work, says of its author : " I cannot forget his emphatic expression on putting a final 
 correction to the last proof sheet in 1814. 'Now,' said he, ' my astronomical day 
 is closed.'" (Cycle of Celestial Objects, vol. i., p. 433.) Piazzi died on the 22nd of 
 July, 1826. By his will he bequeathed his library and instruments to the Observatory of 
 Palermo, and an annuity to be employed in educating young men who showed an incli- 
 nation towards astronomical pursuits. 
 
HISTORY OF PHYSICAL ASTRONOMY. 511 
 
 A remarkable instance of devotion to this department of astronomical 
 science is exhibited in the case of Stephen Groombridge. In 1806, this 
 individual commenced observations of all the stars, down to the eighth 
 magnitude, situate within 50 of the North pole, and finally completed 
 his task in the year 1816. These observations were made with a transit 
 circle constructed by Troughton. During the period included between 
 the years 1816 and 1827, he was engaged in reducing his observations, 
 but, before he succeeded in bringing his labours to a close, he was com- 
 pelled by the weak state of his health to desist from his undertaking. The 
 task of completing the reductions was executed at the expense of the Govern- 
 ment, under the superintendence of Mr. Airy, and a catalogue embodying 
 the results was finally published in 1838. It exhibits the mean places 
 of 4243 circumpolar stars reduced to the year 1810. This is universally 
 admitted to be one of the most valuable contributions to practical astro- 
 nomy made during the nineteenth century. 
 
 The astronomical career of the illustrious Bessel was distinguished by 
 a remarkable series of sidereal observations. In 1821 he commenced 
 observations of all the stars, down to the ninth magnitude, comprehended 
 between the parallels of 15 south declination and 45 north declination. 
 These observations were made in zones with a meridian circle byKeichen- 
 bach, the right ascension and declination of each star being determined 
 at a single observation. This great undertaking was completed in 1833. 
 The number of observations amounted to about 75,000. By means of 
 subsidiary tables appended to them, it was easy to perform their reduction 
 in any particular instance ; but still it was desirable that they should be 
 exhibited in a completely reduced form. This task was executed by 
 Professor Weisse, of Cracow, for all the stars situate within the region 
 extending 15 on each side of the equator, and a catalogue of the results 
 was published in 1846, at the expense of the Academy of Sciences of St. 
 Petersburg. The number of stars in this valuable catalogue is 31,895, 
 reduced to the year 1825. The preface to it is written by M. Struve. 
 Professor Weisse is at present engaged in completing the reduction of 
 the remaining zones of Bessel's observations. Argelander has followed 
 up Bessel's undertaking by a similar observation in zones of all the stars 
 included between 45 and 80 of north declination. These observations 
 were commenced in 1841, and were finished in 1844. The number of 
 stars is about 22,000, arranged in 204 zones. Tables are appended to 
 facilitate their reduction. 
 
 It ought to be mentioned that, previous to the publication of Weisse's 
 catalogue, a similar catalogue of stars, although less extensive, had been 
 published by Sig. Santini, of Padua, founded upon his own observations. 
 The number of stars in this catalogue is 1677, comprehended between the 
 equator and 10 of north declination. The observations were made during 
 the years 1838-39-40. The epoch is January 1, 1840. The object of 
 this catalogue was to establish a series of reference points which might 
 be useful in extra-meridional observations of new planets or comets. For 
 this purpose the catalogue was so planned that, on each parallel of decli- 
 nation, some well-determined star should be found at every eight or ten 
 minutes of time. The catalogue is inserted in the twelfth volume of the 
 " Memoirs of the Astronomical Society." 
 
 In 1827 the Astronomical Society of London rendered an important 
 service to practical astronomy, by the publication of a general catalogue 
 
512 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of stars, founded upon the most celebrated catalogues that have been 
 executed since the middle of the eighteenth century. This catalogue con- 
 tains the places of 2881 stars, reduced upon a uniform system to the 1st 
 of January, 1830. In addition to the mean place of each star, the con- 
 stants for computing its apparent place, according to Bessel's method, are 
 also inserted in the catalogue. The introductory explanation is by 
 Francis Baily, to whom was assigned the important task of selecting the 
 most trustworthy values of the uranographical corrections. The calcula- 
 tions were executed under the superintendence of Lieut. Stratford. 
 
 Hitherto the stars in the southern hemisphere had been almost entirely 
 neglected by astronomers since the time of Lacaille. With the view of 
 remedying this defect, the Government, in 1820, established an observatory 
 at the Cape of Good Hope, appointing the Rev. F. Fallows to be its 
 director. In the Philosophical Transactions for 1824 there is inserted 
 a small catalogue by that astronomer, containing the mean places of nearly 
 all the principal stars between the zenith of the Cape of Good Hope 
 and the South Pole. 
 
 When Sir Thomas Brisbane was appointed Governor of New South 
 Wales in 1821, he erected an observatory at Paramatta, which he furnished 
 with excellent instruments. In the same noble spirit of disinterested 
 liberality, he employed, at his own expense, two qualified assistants, 
 Messrs. Riimker and Dunlop, to aid him in his astronomical labours. 
 In 1832 M. Riimker published, at Hamburg, a small catalogue of 
 stars observed in the southern hemisphere, designed as preliminary 
 to one of greater extent. In 1835 Sir Thomas Brisbane published 
 a catalogue of 7385 stars, chiefly in the southern hemisphere, founded 
 also upon observations made at his establishment at Paramatta. M. 
 Riimker is at present engaged in constructing from the same collection 
 of observations a catalogue of 12,000 stars. 
 
 In 1830 an observatory was erected, at St. Helena, and Lieut. John- 
 son, a talented officer who happened to be on duty on the island, was 
 appointed its director. Two years only elapsed, when a stock of obser- 
 vations was amassed, which served for the formation of an admirable 
 catalogue of 006 principal stars in the southern hemisphere. This cata- 
 logue was published in 1835, at the expense of the East India Com- 
 pany. 
 
 In 1844 Taylor's catalogue of 11,015 stars, founded on observations 
 made at Madras during the years 1822-43, was published at the expense 
 of the East India Company. This catalogue includes upwards of three 
 thousand stars situate in the southern hemisphere, observed with especial 
 reference to the same stars in Sir Thomas Brisbane's catalogue. 
 
 In the tenth volume of the " Memoirs of the Astronomical Society," there 
 are inserted the mean declinations of 172 principal stars in the southern 
 hemisphere, reduced by the late Professor Henderson of Edinburgh, from 
 his own observations at the Cape of Good Hope. In vol. xv. he has 
 given the mean right ascensions of the same stars. While on the sub- 
 ject of the southern stars, it may be mentioned, that the observations made 
 by Fallows at the Cape of Good Hope, during the years 1829-30-31, 
 have been recently reduced under the superintendence of Mr. Airy, and 
 that from the results, a catalogue has been constructed, containing the 
 mean places of 425 stars, situate chiefly in the southern hemisphere. 
 
 The only catalogues of stars distinguished by a high degree of accuracy 
 
HISTORY OF PHYSICAL ASTRONOMY. 51-3 
 
 which were accessible to astronomers in the year 1830, were those of 
 Bradley and Piazzi. It was desirable, however, for purposes of research, 
 as well as for facilitating the practice of observation, that a new catalogue 
 of equal accuracy should be constructed from recent observations. In 
 1833, Pond, the Astronomer Ro} 7 al, contributed towards supplying this 
 desideratum by the publication of a catalogue containing the mean places 
 of 1J12 stars reduced to the beginning of the year 1830. In 1835, 
 M. Argelander published a catalogue of 560 stars founded on observations 
 made by him at Abo. The epoch is the same as that of Pond's catalogue. 
 In the eleventh volume of the " Memoirs* of the Astronomical Society," 
 there is inserted a catalogue of 726 stars, formed by Mr. Airy from observa- 
 tions made by him at the Observatory of Cambridge during the interval 
 included between the years 1828 and 1835. The epoch in this case also 
 is January 1, 1830. In the Greenwich Observations for 1842, the same 
 distinguished astronomer has published a catalogue of 1439 stars, founded 
 on observations made at the Pioyal Observatory, between the years 1836 
 and 1841 inclusive. The epoch of reduction is January 1, 1840. 
 
 The publication of the catalogue of the Astronomical Society, in 1827, 
 suggested the desirableness of re-observing the stars whose places were 
 therein given, for the purpose of throwing light upon the question of their 
 proper motions. In the tenth volume of the " Memoirs of the Astrono- 
 mical Society " there is inserted a catalogue of the right ascensions of 1318 
 stars, determined by Mr. (now Lord) Wrottesley at a private observatory 
 which he fitted up at Blackheath, the right ascension of each star being com- 
 pared with the corresponding right ascension of the Astronomical Society's 
 catalogue*. A similar catalogue of the right ascensions of 1248 stars 
 has been recently formed by Lieut. Gilliss, of the United States Navy. 
 It may be mentioned, that one of the objects proposed by the American 
 expedition to Chili, of which that excellent astronomer has been appointed 
 the superintendent, is the formation of a catalogue of all the stars down 
 to the eighth magnitude, situate within 60 of the South Pole. 
 
 The great utility of the catalogue published by the Astronomical Society, 
 suggested to astronomers the expediency of forming a more extensive cata- 
 logue upon the same plan, but accompanied with some improvements in 
 the details. At the meeting of the British Association which was 
 held at Liverpool in 1837, it was agreed to defray the expense of 
 constructing such a catalogue. The superintendence of the operation 
 was undertaken by Mr. Baily ; but that individual, whose unparalleled 
 exertions in this department of astronomical science will not fail to 
 excite the gratitude and admiration of all future astronomers, had not 
 the satisfaction to witness its completion, having died on the 30th of Au- 
 gust, 1844, only a few months before the catalogue was ready for pub- 
 lication. The British Association appointed a committee consisting of 
 Dr. Robinson, Lieut. Stratford, and Prof. Challis, to superintend the re- 
 maining part of the operation, and the catalogue was finally published in 
 1845. The preface is by Mr. Baily. The materials of its construction are 
 derived from all the trustworthy catalogues that have been executed since 
 the time of Bradley. The number of stars is 8377. The epoch of reduc- 
 tion is January 1, 1850. This catalogue is distinguished from the catalogue 
 
 * Lord Wrottesley is at present engaged in prosecuting a series of observations with a 
 view to the formation of a similar catalogue, which he purposes to compare with that of 
 the British Association. 
 
 L L 
 
514 HISTOP.Y OF PHYSICAL ASTRONOMY. 
 
 of the Astronomical Society in two important particulars. In the first place, 
 the secular variation of precession, both in right ascension and declination, 
 is given for each star. Secondly, the proper motions of the stars are 
 assigned with as great a degree of nearness to the truth, as the existing state 
 of sidereal astronomy allowed. This catalogue has proved of vast ser- 
 vice to astronomers in every part of the civilised world. 
 
 An important catalogue has recently issued from the Greenwich Obser- 
 vatory, founded on observations made during the twelve years commencing 
 with 1836, and ending with 1847. On account of the increasing im- 
 portance of the subject of the proper motions of the stars, it has been 
 deemed expedient to employ two epochs in the formation of this catalogue. 
 The observations made during the first six years, are reduced to the first 
 of January, 1840; the epoch of the remaining observations is the com- 
 mencement of 1845. The number of stars in the catalogue is 2156. 
 One peculiarity of this catalogue consists in the constants of reduction 
 being computed according to the modification of Bessel's method, which 
 Mr. Airy had shortly before suggested. 
 
 Allusion has been made to Mr. Johnson's catalogue of southern stars. 
 This distinguished astronomer, who was appointed Director of the Rad- 
 cliffe Observatory, Oxford, upon the death of Prof. Rigaud in 1838, 
 has been engaged for several years in re-observing the circumpolar stars 
 of Groombridge's catalogue. This great undertaking is now all but 
 completed. The number of stars observed will exceed the number in 
 Groombridge's catalogue by about 2000. The epoch of reduction is the 
 beginning of 1845. A comparison of this catalogue with Groombridge's 
 cannot fail to lead to results of great importance. 
 
 In addition to the catalogues of stars alluded to in the foregoing pages, 
 accurate catalogues of a select number of stars have been formed at every 
 observatory, both in this country and on the Continent, where meridional 
 observations form the chief object of attention. Apart from the special 
 utility of these catalogues in so far as the practice of observation is con- 
 cerned, they have in many instances been employed in some of the most 
 delicate researches of modern astronomy*. 
 
 CHAPTER XX. 
 
 Early Notions of the Telescope. Invention of the Telescope in Holland. Galileo 
 constructs a Telescope. Kepler proposes the Telescope composed of Two Convex 
 Lenses. This Instrument first applied to Astronomical Purposes by Gascoigne. 
 Telescopic Observations of Huyghens and Cassini Reflecting Telescope proposed 
 by Gregory. Newton executes a Reflecting Telescope. Efforts of his Successors to 
 construct these Instruments. Invention of the Achromatic Telescope by Dollond. 
 Reflecting Telescopes executed by Herschel. Modern Improvements in the Re- 
 fracting Telescope. Improvements in the Construction of Reflecting Telescopes.. 
 Lassell Lord Rosse. 
 
 THE telescope is justly considered to be one of the noblest inventions 
 which the annals of human ingenuity can boast of. By its means the 
 
 * It may be stated in illustration of this remark, that a small catalogue of stars which 
 Bessel constructed from his own observations at Konigsberg, was employed by him in 
 combination with the observations of Bradley and Piazzi, in his celebrated investigation 
 of the quantity and laws of Precession. Again, M. Otto St.ru ve has availed himself of a 
 small catalogue of stars founded on observations made at Dorpat, in his recent researches 
 on the same subject, in connexion with the great problem of the Motion of the Solar 
 System in space. 
 
HISTOKY OF PHYSICAL ASTRONOMY. 515 
 
 distant regions of space have been unveiled, and views of the material 
 universe have been obtained, surpassing in splendour the most dazzling 
 pictures of the imagination. Its penetrating power has revealed to us 
 the astonishing fact, that far beyond the visible confines of the starry fir- 
 mament, there exist countless myriads of suns and systems of suns, each 
 of these glorious luminaries being in all probability the centre of a 
 numerous cortege of revolving worlds. Nor has its influence been less 
 apparent in conducting the mind to juster ideas respecting the system of 
 which our own planet forms a part. The sun, which the ancient philo- 
 sophers supposed to be merely a resplendent orb composed of a pure and 
 immaculate substance, exhibits, when viewed with the telescope, unequi- 
 vocal traces of a complex organization, accompanied with continual fluc- 
 tuations in its physical condition, suggesting the sublime idea of its being 
 the abode of innumerable objects of creative wisdom and beneficence. 
 The planets, whose structure seemed to be equally mysterious with their 
 movements, have been transformed from so many insignificant specks of 
 light to an assemblage of magnificent worlds, presenting numerous points 
 of analogy to the earth, and affording thereby irrefragable evidence in 
 favour of the Pythagorean system of the universe. Even the loftier 
 researches of physical astronomy are, to a great extent, dependent on the 
 revelations of the telescope. Many of the beautiful conclusions that 
 have been deduced from the theory of gravitation would fail to excite any 
 interest in the mind of the enquirer, and the geometer would be deprived 
 of some of his noblest triumphs, if the telescope were not available to 
 trace their real counterpart in the heavens. 
 
 The deep interest associated with the revelations of the telescope has 
 called forth a variety of speculations respecting the probable epoch to 
 which its origin may be referred. Some persons have pretended to dis- 
 cover in the writings of the ancient philosophers, indubitable proof that 
 the telescope is not a modern invention. Thus it has been asserted that 
 Democritus, who announced that the Milky Way is composed of a vast 
 multitude of stars, could only have been led to form such an opinion by 
 an actual examination of the heavens with the telescope. We are not 
 warranted, however, in drawing so important a conclusion from a casual 
 remark, however sagacious, any more than we should be justified in 
 inferring that Seneca was in possession of the discoveries of Newton, 
 because he predicted that comets would one day be found to revolve in 
 periodic orbits. The same consideration applies to various other pas- 
 sages cited from the Greek and Latin writers, upon the strength of 
 which attempts have been made to assign a high antiquity to the 
 telescope. 
 
 When 'we come down to modern times, we find the invention of the 
 telescope claimed for a still greater number of persons who flourished 
 anterior to the epoch to which its origin is usually referred. Among- 
 these there is no individual who appears to have made so near an approach 
 to the invention as our celebrated countryman, Roger Bacon. In the 
 following passage, extracted from his Opus Majus, he describes the phe- 
 nomena depending on the refraction of light by lenses with so much 
 truth, that we should almost feel justified in ascribing to him some share 
 in the invention both of the telescope and microscope. " Greater things than 
 these may be performed by refracted vision. For it is easy to understand by 
 the canons above mentioned that the greatest things may appear exceeding 
 small, and the contrary. For we can give such figures to transparent 
 
 LL 2 
 
516 HISTORY OF PHYSICAL ASTRONOMY. 
 
 bodies, and dispose them in such order with respect to the eye and the 
 objects, that the rays shall be refracted and bent towards any place we 
 please ; so that we shall see the object near at hand, or at a distance 
 under any angle we please. And thus from an incredible distance we 
 may read the smallest letters, and may number the smallest particles of 
 dust and sand, by reason of the greatness of the angle under which we 
 may see them ; and on the contrary, we may not be able to see the 
 greatest bodies close to us, by reason of the smallness of the angle under 
 which they may appear ; for distance does not affect this kind of vision, 
 except by accident, but the magnitude of the angle does so. And thus a 
 boy may appear to be a giant, and a man as big as a mountain, for as 
 much as we may see the man under as great an angle as the mountain, and 
 as near as we please ; and thus a small army may appear a very great one, 
 and though very far off, yet very near to us, and the contrary. Thus also, 
 the sun, moon, and stars may be made to descend hither in appearance, 
 and to be visible over the heads of our enemies, and many things of the like 
 sort, which persons unacquainted with such things would refuse to believe." * 
 
 The following passage, extracted from the preface, written by Thomas 
 Digges, to the second edition of the Pantometria of his father, Leonard 
 Digges, would also seem to imply that telescopes were not unknown in Eng- 
 land previous to the seventeenth century ; " My father, by his continue!! 
 painfull practices, assisted by demonstrations mathematical, was able, and 
 sundrie times hath, by proportional glasses, duly situate in convenient 
 angles, not only discovered things farre off, read letters, numbered pieces 
 of money, with the very coyne and superscription thereof, cast by some of 
 his freends of purpose upon downs in the open fields, but also seven miles 
 off declared what hath been doone in private places." Some remarkable 
 passages to the same effect are to be found in Dee's preface to the edition 
 of Euclid, published by him in 1570. 
 
 There are also two Italian philosophers who deserve to be mentioned 
 in connection with the invention of the telescope. Battlsta Porta, in his 
 Magia Naturalis, originally published in 1561, remarks that by combining 
 together convex and concave lenses, objects may be seen enlarged. He 
 then proceeds to describe an instrument capable of being constructed upon 
 this principle, but his language is so utterly obscure as to defy interpre- 
 tation. Again, Antonio de Dominis, Archbishop of Spalatro, in a post- 
 humous work entitled De Hadiis Visus dc., which was published in 
 1611, traces very clearly the progress of rays in passing through convex 
 and concave lenses, and remarks that by placing one of each kind at a 
 certain distance apart, the direct and refracted rays will not interfere with 
 each other. He adds that the proper distance between the two lenses 
 must be found by experiment, and that the effect of their adjustment will 
 be to magnify objects by increasing the angle under which they are seen. 
 It is to be borne in mind, that this work was published at a time when 
 the invention of the telescope was already notorious throughout Europe. 
 Bartolo, the editor of the work, states, however, in the preface, that the 
 manuscripts communicated to him by the author had been written twenty 
 years previously, and that he received full authority from him to publish 
 them with the addition of one or two chapters. 
 
 Notwithstanding the plausible statements contained in the various 
 passages above cited, there does not exist clear proof that the specula- 
 
 * Opus Majus, Pars Tertia, caput iv.,p. 357. Lond., 1733. 
 
HISTORY OF PHYSICAL ASTBONOMY. 517 
 
 tions of any of the individuals alluded to, conduced to practical results, 
 and therefore we cannot be justified in awarding to either of them the 
 honour associated with the invention of the telescope. 
 
 It has long been generally admitted that telescopes were first made iii 
 Holland, about the beginning of the seventeenth century ; but the question 
 with respect to the real author of the invention has, until very recently, 
 been involved in much obscurity. Three persons have been generally 
 mentioned as possessing distinct claims to this much-contested honour. 
 These are, Henry Lipperhey and Zacharias Jansen, spectacle makers in 
 the town of Middleburg, and James Metius of Alkmaer, a son of the 
 mathematician of that name, celebrated for having been the first who 
 expressed the relation between the diameter and the circumference of 
 a circle by the numbers 113 and 355. 
 
 Descartes, in his treatise on Dioptrics, published in the year 1637, 
 thus alludes to the origin of the telescope : " It is now about thirty 
 years since a person named James Metius, who never studied at all, 
 although his father and brother were both professors of mathematics, but 
 who took pleasure in constructing mirrors and burning glasses, of which 
 he had many of various forms in his possession, thought of looking 
 through two lenses, one convex and the other concave. These happened 
 on one occasion to be situated at the proper distance for magnifying 
 objects, whereupon he applied them to the ends of a tube, and in this 
 manner he constructed the first telescope." 
 
 Schyrlaeus de Eheita, the Capucin friar, gives another account of the 
 invention, in a work published a few years later*. He states that 
 telescopes; were first made by Lipperhey, whom he calls Lippensum, and 
 he refers the date of the invention to the year 1609. Lipperhey, hap- 
 pening to place a concave before a convex glass, discovered by accident 
 that the weathercock of a neighbouring church and other objects appeared 
 nearer and larger. Having fitted the glasses in a tube, he placed the 
 instrument in lifs shop, and amused his customers by showing- them the 
 magnified image of the weathercock. The Marquis of Spinola, who was 
 then at the Hague, bought the instrument, and presented it to the Arch- 
 duke Albert of Austria, by whom the great utility of the invention was 
 first made known to the world. 
 
 During the early part of the seventeenth century numerous con- 
 flicting accounts circulated throughout Europe relative to the -origin of 
 the invention, which was in all cases alleged to be due to accident. It 
 is singular that so much uncertainty should have prevailed respecting an 
 event of so recent a date. In 1655, Pierre Borel, physician to the French 
 king, published a work at the Hague f, professing to contain authentic 
 particulars relative to this much-disputed question. He had taken con- 
 siderable pains to collect all the evidence which might throw any light 
 upon the matter, and he was warmly seconded in this object by William 
 Boreel, the Dutch envoy at the Court of France. He searched out five 
 individuals who were personally acquainted with the reputed inventors of 
 the telescope, and induced them to make public declarations on the sub- 
 ject of the invention before the magistrates of Middleburg. The work 
 above referred to contains the details of the examination of those persons, 
 together with a letter of William Boreel's relative to the same subject. Two 
 cf the witnesses deposed in favour of Jansen, but they differ in the dates they 
 
 * Oculus Enoch et Elise, Antverpise, 1645. 
 
 f De vcro Telescopii Inventore, Hag., 4to, 1655. 
 
518 HISTORY OF PHYSICAL ASTRONOMY. 
 
 assign to the invention, one of them, his son, fixing it in the year 1590 ; 
 while the other witness, his sister, brings it down to 1611 or 1619. The 
 other three witnesses declared that Lipperhey was the original inventor, 
 one of them asserting that he made telescopes before the year 1605, while 
 the other two fix the invention in the year 1609 or 1610. The deposi- 
 tions of these persons are so imperfect and contradictory, that little or no 
 reliance can be placed on them. 
 
 The testimony of Boreel is more deserving of attention. He men- 
 tions, in his letter, that he knew Zacharias Jansen personally, and had 
 often heard that he and his father were the real inventors of the micro- 
 scope. When he was in England, in the year 1619, he saw in the hands 
 of Cornelius Drebbel, his friend, the very microscope which had been 
 given by them to the Archduke Albert of Austria. Boreel then con- 
 tinues : " But long after, in 1610, after much research, these individuals 
 invented, in Middleburg, the long sidereal telescope with which we gaze 
 at the moon and planets, and presented one of them to Prince Maurice, 
 who deemed it prudent to conceal the invention in order to make use of 
 it in military operations. While rumours were abroad regarding the 
 invention, a stranger came to Middleburg, and having asked for a 
 spectacle maker, was shown by mistake into Lipperhey 's shop. From the 
 questions put by the stranger, Lipperhey, being a shrewd man, was 
 enabled to detect the construction of the instrument, and having suc- 
 ceeded by this means in making telescopes, he was generally considered 
 the real inventor of them. However, the mistake was soon discovered, 
 for Drebbel, upon his return to Holland, proceeded with Adrian Metius 
 to Jansen's shop, and purchased telescopes of him." 
 
 It follows, then, from Boreel's letter, that Jansen invented, first the 
 microscope, and, after the lapse of several years, the telescope. This 
 account tends in some degree to reconcile the conflicting statements of 
 the two witnesses who deposed in favour of that individual : but indeed 
 the whole evidence contained in Boreel's book is of so meagre and un- 
 satisfactory a character, as to leave the- question relative to the actual 
 inventor of the telescope, still open to dispute. 
 
 In the first volume of the "Journal of the Royal Institution," published 
 in 1831, there appeared an interesting communication from Dr. Moll, of 
 Utrecht, relating to the invention of the telescope. The materials of this 
 paper are due to the researches of Van Swinden, who had ! succeeded in 
 discovering some authentic records, which serve to remove much of the 
 obscurity that has hitherto prevailed respecting the real author of the 
 invention. 
 
 In the library of the University of Leyden there exists, among the 
 manuscripts of Huyghens, an original copy of a petition sent to the 
 States General by Jacob Andrianzoon, the person whom Descartes calls 
 James Metius. This petition is dated October 17, 1608. The object of 
 it is to obtain the exclusive right of selling an instrument he had in- 
 vented, by means of which distant bodies appeared larger and more 
 distinct. He declares that the idea of the instrument occurred to him 
 accidentally, while he was engaged in making other experiments ; that he 
 afterwards bestowed much attention on the subject, and had succeeded so 
 far in bringing the invention to maturity, as to make objects appear as 
 visible and distinct by his instrument, as could be done with the one which 
 had been lately offered to the States by a citizen and spectacle maker of Mid- 
 dleburg. Metius was exhorted to bring his instrument to greater perfec- 
 tion, when his petition for a privilege would be taken into consideration. 
 
HISTORY OF PHYSICAL ASTRONOMY. 519 
 
 Among the Acts of the States General preserved in the Government 
 Archives at the Hague, Van Swinden found some interesting documents 
 relative to the spectacle maker of Middleburg, alluded to in the petition 
 of Metius. On the 2nd of October, 1608, the Assembly of the States 
 took into consideration the petition of John Lipperhey, spectacle maker, 
 a native of Wesel, and an inhabitant of Middleburg, inventor of an in- 
 strument for seeing at a distance. A committee was appointed to confer 
 with Lipperhey, for the purpose of ascertaining whether it might not be 
 possible to improve the instrument so as to enable one to look through it 
 with both eyes. On the 4th of the same month it was resolved that certain 
 of the members should test the instrument of Lipperhey, by observing 
 with it from the turret of Prince Maurice's mansion. "It was further 
 resolved, that if the perspective should be found useful, an engagement 
 should be entered into with the inventor, to execute three such instruments 
 of rock crystal, and that he should be enjoined not to divulge the invention 
 to anybody. On the 6th of the same month, the Assembly agreed to give 
 Lipperhey 900 florins for such an instrument. On the 15th of December 
 they examined the instrument invented by Lipperhey to see with both 
 eyes, and approved of it ; but as many others had a knowledge of this 
 new invention to see at a distance, they did not deem it expedient to 
 grant him an exclusive privilege to execute such instruments. How- 
 ever, they gave him orders to execute, for the use of the Government, 
 two other instruments to see with both eyes, allowing him the same 
 remuneration for his services as in the first instance. 
 
 The evidence afforded by the documents found among the manuscripts 
 of Huyghens, restores to James Metius his right to the invention of the 
 telescope, which had not been taken notice of in Borel's book, and was 
 probably allowed, in consequence, to fall into oblivion. It would seem 
 also, from the same document, that the telescopes of Metius could bear a 
 comparison in point of efficiency with those constructed about the same 
 time by another individual. However, as this statement rests entirely 
 upon his own authority, and as he does not appear to have given the 
 benefit of his invention to the world, we cannot consider his labours to be 
 entitled to much consideration. The other documents prove that Lip- 
 perhey was in possession of the invention as early as October, 1608, 
 and therefore that he could not have been indebted for his views on the 
 subject to Jansen, who, according to William Boreel's letter, succeeded 
 in constructing telescopes only in the year 1610. No mention of Jansen 
 could be found in any of the State Records, and as his right to the 
 original invention of the telescope is set aside by the authentic documents 
 in favour of Lipperhey, there only remains to be claimed for him the 
 invention of the microscope, upon the evidence set forth in Borel's book. 
 We may conclude, then, that Lipperhey was the person who originally 
 executed telescopes, and also that he was the first who made them known 
 to the world ; and, therefore, upon these grounds he possesses a just 
 claim to the honour associated with the invention. 
 
 It is quite clear that Lipperhey must have been no common artizan, from 
 his adapting his invention so readily to the views of the Assembly of the 
 States General. The worthy individuals composing that Assembly were 
 by no means satisfied with an instrument that was destined to penetrate 
 into the immensity of space, and reveal the existence of unnumbered 
 worlds, unless it was so executed as to enable them to see through it with 
 both eyes. We have seen that a telescope of this construction was 
 actually supplied to them by Lipperhey, and that upon its being sub- 
 
520 HISTORY OF PHYSICAL ASTRONOMY. 
 
 mitted to trial, it was cordially approved of by the Committee of their 
 Highnesses. It appears, then, that this ingenious individual was the first 
 person who executed the binoculuts, an instrument the invention of which 
 has been usually ascribed to De Rheita. Lipperhey doubtless fell upon 
 the construction of the telescope by combining together lenses in various 
 ways, as we may easily conceive that an optician might be induced to do. 
 Attempts have been made to depreciate the merit of the Dutch inventor, 
 on the ground that his discovery was made by chance. There exists, 
 indeed, no reason to suppose that he was acquainted with the principles, 
 whether mathematical or physical, upon which the construction of the 
 telescope depends, or that he was indebted to a knowledge of those prin- 
 ciples for the admirable result at which he arrived ; but how few original 
 discoveries or inventions, either in the arts or sciences, have been achieved 
 by the aid of purely theoretical considerations; and, on the contrary, 
 how many have been suggested to their authors by circumstances appa- 
 rently unconnected with the object of their researches, and, therefore, to 
 a certain extent, fortuitous ! But, in fact, this circumstance of accidental 
 discovery is no other than the result of that sagacious observation which 
 distinguishes one man from a multitude of others, and enables him to 
 select from the multitude of objects that claim his attention such relations 
 as possess a character of generality that renders them subservient in 
 extending the conquests of the human mind over the material world. 
 Theory serves to develope principles that have been already established by 
 induction, and in this manner acts the part of a valuable guide to the 
 discovery of derivative truths ; but in attempting to penetrate the secrets 
 of nature, or in devising new combinations of principles with a view to 
 the attainment of any specific end, the mind must rely mainly on its own 
 innate sagacity. 
 
 Galileo has related the circumstances under which he first became 
 acquainted with the invention of the telescope, and has also given an account 
 of his early efforts to construct one of these instruments. Happening to 
 be in Venice in the month of May, 1609*, he learned in that city that a 
 Belgian had invented a perspective instrument, by means of which dis- 
 tant objects appeared nearer and larger. This report, which was soon 
 confirmed by a letter he received from Paris, excited an intense interest 
 in his mind, and upon his return to Padua he began to ponder upon the 
 probable mode by which such an effect could be produced. He dis 
 covered, upon the very night of his arrival, that the enlargement of the 
 object depended upon the doctrine of refraction, and on the following day 
 he made his first attempt to execute an instrument upon this principle. 
 Having procured a leaden tube, he fitted in one of its extremities a plano- 
 convex lens, and in the other a plano-concave one, and, having applied his 
 eye to the concave lens, he was delighted to perceive objects pretty much 
 magnified. They appeared to be three times nearer and nine times 
 larger. He immediately gave intimation of his success to his friends in 
 Venice, with whom he had been conversing on the subject the previous 
 day. Having succeeded a few days afterwards in making a better in- 
 strument, he joyfully proceeded to Venice, taking it with him. The 
 perspective of the Paduan philosopher soon became an object of universal 
 admiration in Venice. In order to afford the senators of the republic a 
 practical proof of its efficiency, Galileo accompanied them to the more 
 
 * This is inferred from the expression " mensibus abhinc decem fere," used by him 
 in the Sidereus Nuncius, the dedication of which is dated March, 1610. 
 
HISTORY OF PHYSICAL ASTRONOMY. 521 
 
 elevated parts of the city, whence, by looking through it, they surveyed 
 the various objects of the surrounding landscape with inexpressible sur- 
 prise and delight. During the whole period of his residence at Venice, 
 which extended to a month, he was besieged from morning to night by 
 crowds of the inhabitants, all eager to have a peep through the won- 
 derful glass. He had not yet divulged the secret of his invention, but, 
 with his wonted liberality, he now communicated it to the public, and, at 
 the suggestion of one of his friends, he presented the instrument itself 
 to the Doge Leonardi Deodati, who accepted it from him, sitting in full 
 council. He accompanied it with a paper, in which he gave an explana- 
 tion of its construction, and of the important purposes to which it might 
 be applied both on land and at sea. The Senate indicated their appre- 
 ciation of this novel compliment which Galileo paid to the chief magis- 
 trate, by increasing his salary as lecturer in the University of Padua to 1000 
 florins, and appointing him to his office for life. 
 
 Galileo's object now was to construct a telescope'of superior magnifying 
 power. This he found to be a task of very difficult accomplishment, for 
 the art of grinding and polishing lenses was then in its infancy. We have 
 seen that at his first trial the instrument made objects appear three times 
 nearer and nine times larger ; in other words, it amplified three times in 
 linear dimensions, and nine times in superficies. Soon afterwards he made 
 another instrument which magnified sixty times in surface ; and finally, 
 sparing neither application nor expense, he succeeded in executing an in- 
 strument of such excellence as to represent objects almost 1000 times 
 larger, and above 30 times nearer, than they appeared to be by the natural 
 power of the eye *. 
 
 He points out a simple method of determining by experiment the 
 magnifying pow r er of the instrument. " Place," says he, " upon a wall at a 
 certain distance, two disks, one of which you will observe with the 
 telescope and the other with the naked eye. If the disk seen through 
 the telescope appear equal to the external one, the magnifying power 
 of the instrument' is in the proportion of the two disks. If they do not 
 appear equal, the external disk must be enlarged or diminished until this 
 result takes place, and then the magnifying power will be, as already 
 mentioned, in the proportion of the two disks." 
 
 Galileo's best telescopes did not magnify more than thirty-two or thirty- 
 three times. Previous to the invention of achromatic object-glasses, this 
 was the highest magnifying power that was attainable with telescopes of 
 the form of construction employed by him and his contemporaries. The 
 triumphs of genius are signally illustrated in the multitude of beautiful 
 discoveries which Galileo achieved by the aid of his little perspective. 
 Whatever claims other individuals ; J may possess to the original invention 
 of the telescope, the merit of applying it to the great purposes of phy- 
 sical science must be awarded, with acclamation, to the illustrious 
 philosopher of Italy. 
 
 The telescopic discoveries of Galileo exercised such a withering 
 influence upon the ancient philosophy, that many of its adherents, in the 
 height of their mortification, took refuge in absolute incredulity, and, with 
 absurd pertinacity, refused to assure themselves, by actual inspection, of 
 the reality of the phenomena thus revealed for the first time to mortal 
 eyes. " Oh ! my dear Kepler," says Galileo, in one of his letters to that 
 
 * Opere di Galileo, tome ii., pp. 5 et 267. 
 
522 HISTORY OF PHYSICAL ASTRONOMY. 
 
 astronomer, " how I wish that we could have one hearty laugh together ! 
 Here, at Padua, is the principal professor of philosophy, whom I have 
 repeatedly and earnestly requested to look at the moon and planets 
 through my glass, which he pertinaciously refuses to do. Why are you 
 not here ? What shouts of laughter we should have at this glorious 
 folly, and to hear the professor of philosophy in Pisa labouring before the 
 Grand Duke with logical arguments, as with magical incantations, to 
 charm the new planets out of the sky !" 
 
 Galileo can hardly be considered an independent inventor of the 
 telescope. Admitting that he obtained no other account of the Dutch 
 invention, than that a spectacle maker had succeeded in executing 
 a perspective instrument by means of which distant objects appeared 
 nearer, still the fact of his having received such a hint deprives his 
 labours in a great degree of the character of originality. When once a 
 problem is known to be resolvable, the difficulties which it involves may then 
 be overcome with comparative ease by a strong concentration of the mental 
 powers upon it. But, in justice to the original inventor, and the country 
 which gave him birth, it is but right to mention, that more than one of 
 the Dutch instruments had found their way into Italy about the time 
 when Galileo was led to construct his first telescope. Sirturus, writing 
 in 1618, makes the following statement: "A Frenchman proceeded to 
 Milan in the month of May, 1 609, and offered a telescope for sale to the 
 Count di Fuentes."* Again, in a fetter from Padua, dated August 31, 
 1609, Lorenzo Pignoria announces to Paolo Gualdo that Galileo had 
 been, appointed lecturer at Padua for life on account of a perspective, 
 like the one which was sent from Flanders to Cardinal Borghese. " We 
 have seen some here," adds the writer, " and truly they succeed well."f 
 
 We dismiss, as an unfounded calumny, the assertion of Fuccarius, that 
 Galileo had actually seen one of the Dutch telescopes, nor can we even 
 admit, in the face of his own words to the contrary J, that he received 
 any hint relative to the peculiarity of their construction; but the noto- 
 riety of the invention, as confirmed by the preceding extracts, could not 
 fail to have operated as a powerful incentive to his efforts. 
 
 Some writers have been disposed to think that the Dutch telescope was 
 constructed upon a different principle from Galileo's instrument. Pro- 
 ceeding upon the tradition of its having been originally exhibited as an 
 amusing toy, by producing an inverted image of a weathercock, they 
 have hence inferred that it was composed of two convex lenses, like the 
 modern astronomical telescope. This conclusion, if true, would certainly 
 go far to enhance Galileo's merit, but it rests on so narrow a foundation 
 as to be totally inadmissible, being suggested solely by the vague tradition 
 just mentioned. On the other hand, Descartes and De Rheita positively 
 
 * Sirturus de Telescopic, Franc., 1618. 
 
 f " Di nuovo non abbiamo altro se non la reincidenza di S. Serenita, e ricondotti di 
 Lettori, fra' quali il Sig. Galileo ha buscato 1000 fiorini in vita, e si dice col benefizio 
 d'un occhiale simile a quello, che di Fiandra fu mandate al Card. Borghese. Se ne 
 sono veduti di qua. e veramente fanno buona riuscita." (Lettere d'Uomini Illustri, 
 p. 112, Venez., 1744. 
 
 i The following are the terms in which he alludes to the information he received 
 respecting the Dutch invention on the occasion of his visit to Venice, as mentioned in 
 the text: " Giunsero nuove, che al Sig. Conte Maurizio era stato presentato da un 
 Olandese un occhiale, col quale le cose lontane si vedevano cosi perfettamente, come 
 se fussero state molto vicine, ne piii. fu aggiunto." (Opere di Gal., Edit. Pad., 1744, 
 torn. ii. p. 267.) 
 
HISTORY OF PHYSICAL ASTRONOMY. 523 
 
 assert that the Dutch instrument was formed by a combination of a convex 
 with a concave lens. The account of the invention as given by the latter 
 of these two writers is the more worthy of confidence, inasmuch as he 
 associates it with the story of the weathercock, but, of course, makes no 
 allusion to an inverted image. Again, we find Lorenzo Pignoria writing 
 to his friend, that Galileo had received a thousand florins annually for 
 life, on account of a perspective like the one which had been sent from 
 Flanders ; but it is very obvious that if the Dutch telescopes had ex- 
 hibited objects inverted, he would have expressed himself in different 
 language. 
 
 The Dutch telescopes were, doubtless, much less powerful than those 
 of Galileo, but this is not to be wondered at, when we consider the con- 
 summate skill of the latter in matters relating to practical science, and 
 the remarkable success which generally attended his experimental efforts. 
 Still, we are by no means disposed to believe that they were such mean 
 productions of art as they have been frequently represented to be. We 
 have seen that the States General agreed to give 900 florins to Lipperhey 
 for his instrument. The amount of remuneration tends to impress us 
 with a favourable opinion of the instrument given in exchange, for, as 
 Dr. Moll justly remarks, the Dutch people cannot be charged with a 
 readiness to throw away their money upon a trifling toy, which possessed 
 no other claim to recommendation than its novelty. It is true that the 
 inventor was prohibited from making any telescopes except those ordered 
 by the States General, and the latter would naturally consider themselves 
 bound, on this account, to remunerate him more liberally for his labours 
 than they would otherwise feel disposed to do. This prohibition, however, 
 tends to confirm our belief of the value they set upon his telescopes. 
 They refused him an exclusive privilege to make and sell them, on the 
 alleged grounds that others were already in possession of the invention, 
 but they reasonably believed that the instruments of the inventor would 
 be superior to any others constructed, and they accordingly resolved to 
 secure to themselves the monopoly of his skill. That the invention had 
 already transpired, and that a restriction, such as we have mentioned, had 
 been imposed upon the inventor, is clearly proved by the following ex- 
 tract from the correspondence of the celebrated president, Jeannin, who 
 had been sent to Holland by his sovereign, Henry IV., to negotiate a 
 truce between Spain and the States General. On the 28th of December, 
 ] 608, only a few days after the States General had refused the object of 
 Lipperhey 's petition, Jeannin thus writes to Henry's minister, the famous 
 Sully: " The bearer of this letter is a soldier from Sedan, who belongs 
 to the Prince's company, and who is held very ingenious in many inven- 
 tions and artifices of war. He has also made, a few days ago, an instru- 
 ment, in imitation of that which has been made by a spectacle maker of 
 Middleburg, to see at a distance. He will show it to you, and make you 
 some for your sight ; I requested the original inventor to make me two, 
 one for the king, and one for you ; but the States prohibited him from 
 making any but for themselves. They have, however, given orders to 
 execute some for me, that I may send them to you, which I will not fail 
 to do as soon as I receive them."* It is quite clear, from the foregoing 
 passage, that the States General contemplated making use of the instru- 
 
 * " Lettres et Negotiations du President de Jeannin," fol., Paris, 1656 (cited by Dr. 
 Moll). 
 
524 HISTORY OF PHYSICAL ASTRONOMY. 
 
 ment of Lipperhey in military reconnaissances ; and their formal approval 
 of it already referred to, when taken in connexion with this circumstance, 
 implies that it possessed a considerable magnifying power. 
 
 We have seen how quickly the Dutch telescopes passed into France 
 and* Italy. If we are to believe the German astronomer, Simon Marius, 
 he commenced astronomical observations in the year 1609, with a telescope 
 which he procured from Holland. Telescopes were also imported into 
 England soon after their invention. The late Professor Rigaud found, by 
 an inspection of the manuscripts of Harriot, the celebrated mathema- 
 tician, that even as early as July, 1609, he had been making observations 
 of celestial phenomena with one of these instruments. This fact tends 
 very much to disprove the assertion that the telescopes originally made in 
 Holland were totally unfit for scientific purposes, for it can hardly be 
 doubted that the one which Harriot used was obtained from that country. 
 On the 6th of July, 1610, Sir Christopher Heyden thus writes to 
 Camden, the famous antiquarian : " I have read Galilasus, and, to be 
 short, do concur with him in opinion, for his reasons are demonstrative ; 
 and, of my own experience, with one of our ordinary trunks I have told 
 eleven stars in the Pleiades, whereas no age ever remembers above seven, 
 and one of them, as Virgil testifieth, not always to be seen."* There 
 can be no doubt that the expression *' one of our ordinary trunks " 
 refers to the Dutch telescopes which were in common use in England, as 
 distinguished from the superior tefescopes of Galileo recently imported 
 from Italy. 
 
 In a letter dated Tra'venti in Caermarthenshire, Feb. 6, 1610, Sir 
 William Lower thus writes to Harriot : " I have received the perspective 
 cylinder that you promised me, and am sorrie that my man gave you not 
 more warning, that I might have also the two or three more that you 
 mentioned to chuse for me. Henceforward he shall have orders to attend 
 you better, and to defray the charge of this and others, for he confesseth 
 to me that he forgot to pay the workman. 
 
 " According as you wished, I have observed the moone in all his changes. 
 In the new manifest-lie I discover the earthshine a little before the di- 
 chotomie ; that spot which represents unto me the man in the moone 
 (but without a head) is first to be seene. A little after, neare the brimme of 
 the gibbous parts towards the upper corner appeare luminous parts like 
 starres ; much brighter than the rest; and the whole brimme along looks like 
 unto the description of coasts in the Dutch books of vo}^ages. In the full 
 she appeares like a tart that my cooke made me last weeke ; here a vaine of 
 bright stuffe, and there of darke, and so confusedlie all over. I must 
 confesse I can see none of this without my cylinder ; yet an ingenious 
 younge man that accompanies me here often, and loves you, and these 
 studies much, sees manie of these things, even without the helpe of the 
 instrument, but with it sees them most plainlie I mean the young Mr. 
 Protheroe." * 
 
 We have deemed it proper to dwell at some length upon the early 
 history of the Dutch telescopes, because those instruments have been 
 thrown into unmerited oblivion by the splendour of Galileo's discoveries. 
 We cannot reasonably avoid the conclusion, when the subject is taken 
 into complete consideration, that, even although the last-mentioned philo- 
 sopher had never lived, the Dutch telescopes would have been gradually 
 
 * Supplement to Bradley's Miscellaneous Works, p. 27. f Ibid., p. 42. 
 
HISTORY OF PHYSICAL ASTRONOMY. 525 
 
 perfected in their construction, and would have been eventually applied 
 with success to the great purposes of physical science. The merits of 
 the original inventor of the telescope cannot affect the reputation of 
 the illustrious Italian, who owed his brilliant discoveries in celestial 
 physics much less to his good fortune in executing a telescope, than to his 
 sagacity as an interpreter of nature. 
 
 Kepler first explained the construction of the telescope formed by a 
 combination of two convex lenses, in his treatise on Dioptrics, which was 
 published in 1611. Possessing no aptitude for observation, however, he 
 did not attempt to reduce his ideas to practice. Scheiner appears to have 
 been the first, person who actually executed a telescope upon the principle 
 suggested by Kepler. In his Rosa Ursina, which was published in 1630, 
 he states 'that, thirteen years previously, he made observations in- the 
 presence of the Archduke Maximilian, with a telescope composed of t\vo 
 convex lenses. The Galilean telescope, however, still continued to be pre- 
 ferred, 011 account of the superior distinctness of the image which it formed. 
 
 The first person who appears to have discovered the peculiar value of 
 the telescope recommended by Kepler, and who applied it to the purposes 
 of astronomical observation, was Gascoigne. This highly-gifted young 
 man did not fail to perceive that it possessed an immense advantage over 
 the Galilean telescope, in affording a situation within the tube where any 
 object being placed might be viewed as distinctly as a celestial object. 
 This circumstance suggested to his inventive mind the use of telescopic 
 sights in astronomical observations, and the application of the micrometer 
 to the telescope. The micrometrical measures of that astronomer, pre- 
 served by Flanisteed in the first volume of the Historia Celestis, may be 
 considered as the earliest collection of facts that have been established 
 by the use of the Keplerian telescope. In this respect they possess an 
 interest analogous to that associated with the early discoveries of Galileo 
 relative to the 2^ysical constitution of the celestial bodies. 
 
 It was not until about the middle of the seventeenth century, that tele- 
 scopes composed of two convex lenses came to be generally employed in 
 astronomical observations. The use of such telescopes, however, was 
 then suggested, not on account of the advantage which Gascoigne found 
 them to possess, but because they afforded a much larger field of view 
 than could be obtained by means of the Galilean telescope. The first 
 person who distinguished himself by his labours in connexion with the 
 Keplerian, or astronomical, telescope was Huyghens. This distinguished 
 philosopher attained great excellence in the grinding and polishing of 
 lenses, and succeeded in constructing telescopes far superior to any 
 hitherto executed. In the year 1655 he discovered a satellite revolving 
 round Saturn in sixteen days, by the aid of a telescope 12 feet long, 
 and by prosecuting observations of the planet with the same instrument, 
 lie was shortly afterwards enabled to establish the real nature of the 
 appendage with which it is furnished. 
 
 As the definition of objects was very imperfect in telescopes of this 
 construction, it was found to be indispensable in every instance wherein 
 a high magnifying power was required, to increase the focal length of the 
 object-glass to an immense extent. Huyghens states that he and his 
 brother made object-glasses of 170 and 210 feet focal length I These 
 glasses were used without tubes. Huyghens devised mechanical combi- 
 nations of great ingenuity, by means of which they could be directed with 
 facility towards any object in the visible heavens. From the circumstance 
 
526 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 of their being used without tubes, these contrivances were termed aerial 
 telescopes. Huyghens presented one having a focal length of 123 feet to 
 the Royal Society of London. This philosopher effected a capital im- 
 provement in the construction of telescopes by the invention of an eye- 
 piece consisting of a combination of lenses which, by their respective 
 refractions, served to correct the effects of spherical aberration. 
 
 While Huyghens was engaged in these labours, the art of executing 
 telescopes was attaining a high !degree of excellence in Italy. Eustachio 
 Divini at Rome, and Campani at Bologna, more especially signalised 
 themselves in this department of practical optics. It was with telescopes 
 executed by the latter that Cassini made the multitude of interesting dis- 
 coveries in the heavens which have rendered the name of that astronomer 
 so deservedly celebrated. The object-glasses had, in some instances, 
 focal lengths of 90, and even 130, feet. Cassini was enabled, like Huy- 
 ghens, to make use of such glasses without tubes. 
 
 Telescopes of great length were constructed in most other countries of 
 Europe during the seventeenth century, especially in France and England. 
 Auzout is said to have made a telescope of 300 feet focal length. It does 
 not appear, however, that he actually employed such an instrument in 
 astronomical observations. In England the construction of telescopes 
 seems to have attained considerable perfection at a comparatively early 
 period. Among the instruments with which the observatory of Copenhagen 
 was furnished, on the occasion of its original establishment in 1656, was a 
 telescope magnifying 100 times, which Longomontanus brought with him 
 from England in the year 1642. The telescopes of Sir Paul Neile, as well 
 as those of Reeves and Cox, are said to have been equal to the best tele- 
 scopes executed at the same time in any country of Europe. It speaks 
 very much in favour of the English telescopes made during the latter 
 part of the seventeenth century, that with one of such instruments, of 38 
 feet focal length, William Ball of Mainhead, in Devonshire, having ob- 
 served Saturn on the 13th October, 1665, perceived that the ring around 
 the planet was double *. This observation was made ten years before 
 Cassini remarked a similar appearance on the ring. It appears that 
 Bradley occasionally employed telescopes of great length, in the early part 
 of his career. On the 27th of December, 1722, while he was residing 
 at Wanstead with Pound, his uncle, he measured the diameter of Venus 
 with a telescope, or rather object-glass, of 212^ feet focal length f. 
 
 Notwithstanding the vast amount of labour and skill bestowed upon 
 the construction of refracting telescopes, it was still found that the images 
 formed in these instruments were by no means so well denned as was 
 necessary for delicate observations. This circumstance was attributed to 
 the spherical aberration of the lenses, but, although the indistinctness no 
 doubt partly arose from that cause, it was mainly due to the influence of 
 a physical principle which had not yet been discovered. When, to the 
 imperfect formation of the image, the inconvenience attending the use of 
 telescopes of enormous focal length was taken into account, it obviously 
 became desirable to devise a different mode of construction. In 1663, 
 James Gregory published his Optica Promota, in which he explained the 
 construction of the reflecting telescope which has since been called by his 
 name. He proposed that the rays of light from a remote object should 
 
 * Phil. Trans. 1666, p. 153. 
 
 + Bradley's Miscellaneous Works, p. 354. 
 
HISTORY OF PHYSICAL ASTRONOMY. 527 
 
 be received by a concave parabolic speculum, and, after forming by re- 
 flexion an image of the object at the focus, should hence diverge and fall 
 upon a smaller concave speculum of an elliptic figure having the same 
 focus as the larger one. The rays would now be reflected by the elliptic 
 speculum, so as to form a second image of the object near the anterior 
 surface of the larger, or parabolic, speculum ; and this image might finally 
 be viewed by the observer through an eye-lens placed behind the latter 
 speculum, which was to be perforated for that purpose. Gregory expected 
 that, by substituting the principle of the reflexion of light for that of re- 
 fraction, so as to get rid of the effect of spherical aberration, the image 
 of the object would be rendered much more distinct. When he was in 
 London, about the year 1664, he employed an optician to execute a tele- 
 scope for him according to the above design, but the attempt to give 
 a true parabolic figure to the larger speculum proved a failure ; and, 
 although he subsequently tried to effect the same object by means of a 
 spherical speculum, yet, in this instance also, the result was so unsatis- 
 factory that he seems to have been discouraged from prosecuting the matter 
 further. 
 
 It appears that, before the publication of the Optica Promota, Mer- 
 senne had already suggested the idea of a reflecting telescope. This 
 he did originally in a letter to Descartes written about the year 1639 *, 
 and, afterwards, in his Catoptrics, which was published in 1651 . Descartes 
 offered several objections to Mersenne's proposal, and no attempt was 
 made to carry it into effect. It has been said, by Fontenelle, that Father 
 Zucci was acquainted with the reflecting telescope as early as 1618. 
 Indeed, Montucla has justly remarked, that as soon as it was known that 
 the image of an object might be formed in the focus of a concave mirror, 
 the idea of applying the principle of reflexion to the construction of tele- 
 scopes (after the invention of refracting telescopes) was a very obvious 
 suggestion. It is impossible to ascertain whether Gregory was indebted 
 to any previous writer for the hint of the reflecting telescope, or not ; but, 
 at any rate, it must be allowed that he was the first person who gave a 
 complete explanation of the construction of such a telescope. Moreover, 
 he has the merit of having suggested a form of the instrument which has 
 been in use ever since, and which, as far as ordinary purposes are con- 
 cerned, has been found more convenient in practice than any other that 
 has subsequently been devised. 
 
 The first person who actually executed a reflecting telescope was New- 
 ton. As soon as that philosopher discovered the unequal refrangibility of 
 light, about the year 1666, it occurred to him that any further improve- 
 ment of the refracting telescope was impossible, and he was led, in con- 
 sequence, to consider the application of the principle of reflexion to the 
 same object. Finding that for the different rays of the prism, the angle 
 of reflexion was in each case equal to the angle of incidence, he per- 
 ceived that, by means of this property of light, optical instruments might 
 be brought to any degree of perfection, provided a substance could be 
 found which reflected a sufficient quantity of light, while at the same time 
 it was capable of being highly polished, and of receiving a true parabolic 
 figure. But the difficulties which stood in the way of accomplishing the 
 fulfilment of these conditions, were very great; nay, they almost seemed 
 to him to be insuperable, when he recollected, that every irregularity in a 
 reflecting surface would make the rays deviate five or six times more out 
 
 * " Leltrcs de Descartes," torn, ii., Nos. 29, 32. 8vo, Paris, 1659. 
 
528 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of their due course than in a refracting telescope *. While his mind was 
 occupied with these reflections, he was compelled, by the prevalence of 
 the plague, to quit Cambridge, and more than two years elapsed before he 
 again turned his attention to the subject.. Having now reflected upon the 
 construction of Gregory's instrument, he came to the conclusion that it 
 would be preferable to place the eye-glass in the middle of the tube. Ac- 
 cordingly, having succeeded, after much trouble, in discovering a substance 
 that, was adapted for the formation of the larger speculum, and having also 
 devised a delicate mode of polishing the surface, he actually executed a tele- 
 scope upon this principle. He wisely abstained from attempting to make 
 the speculum truly parabolic, on account of the extreme difficulty of the 
 operation, contenting himself with giving it the figure of a segment of a 
 sphere. With this instrument he could see the satellites of Jupiter and the 
 horns of Venus ; but the latter were not very distinct, nor could they be 
 perceived at all without some nicety of adjustment. Encouraged by the 
 success of his efforts, he made a second telescope, which proved to be 
 still better than the former one. The focal length of .the speculum was 
 6 ; V inches, and that of the eye-glass (which was a plano-convex lens, with 
 the flat side turned towards the eye) was Jth of an inch ; the magnifying 
 power of the instrument was therefore 38. 
 
 In the month of December, 1671, Newton transmitted to London the 
 second reflecting telescope executed by him, in order that it might be 
 submitted to the inspection of the Royal Society. At the meeting of the 
 Society, held on the llth of January, 1072, it was announced that Mr. 
 Newton's instrument had been examined by the President, Sir Robert 
 Moray, Sir Paul Neile, Dr. Wren, and Mr. Hooke, and that it had re- 
 ceived their unanimous commendation. The Society at the same time 
 resolved, that in order to secure the right of the inventor, a description of 
 the instrument should be sent to Huyghens, who was then residing at 
 Paris f. Huyghens communicated an account of it to the Academy of 
 Sciences, and in consequence it soon became generally known upon the 
 Continent t- 
 
 * Phil. Tran., 1672, p. 3080. 
 
 T" Birch, Hist. Roy. Soc. , vol. in. p. 1. The same telescope was afterwards presented 
 to the Royal Society. This interesting relic of the immortal philosopher is still to be 
 seen at the apartments of the Society in Somerset House. 
 
 $ Huyghens addressed a letter to the Academy of Sciences, in which he gives a de- 
 scription of Newton's reflecting telescope, and enumerates its peculiar advantages. The 
 following passage, extracted from this letter, is worthy of notice. " Je compte pour un 
 troisieme avantage, que par la reflexion du miroir de metal, il ne se perd point de rayons, 
 comme aux verres qui en reflechissent une quantite notable, par chacune de leurs sur- 
 faces, et en interceptent encore une partie par 1'obscurite de leur matiere." (Mem. 
 Acad. des Sciences, tome x., p. 506.) M. Arago cites this passage as a proof that 
 Huyghens was not aware of any light being lost in the course of its reflexion from a 
 metallic surface, and he naturally expresses his astonishment that the Dutch philosopher 
 should have been unacquainted with so obvious a principle of physics. (Annuaire, 1842, p. 
 293.) It would appear, however, from the following passage of a letter addressed by 
 Huyghens to the Royal Society in answer to their communication respecting Newton's 
 telescope, that the case cannot be made out so clearly against him: "Again, by the 
 racer reflexion of the metallic speculum, there are not so many rays lost as in glasses, 
 which reflect a considerable quantity by each of their surfaces, and besides intercept many 
 of them by the obscurity of their matter." (Phil. Trans., 1672, p. 4008.) Whether 
 Huyghens had corrected his mistake in the latter of the two passages just cited, or 
 whether his views on the subject have been misrepresented in one or other of the two pas- 
 sages, we leave our readers to decide. The communication inserted in the Memoirs of 
 the Academy of Sciences, bears no date. The letter to the Royal Society is dated Feb. 
 10, 1672. ' 
 
HISTORY OF PHYSICAL ASTRONOMY. 529 
 
 In 1673 Cassegrain, a Frenchman, devised a new form of the reflect- 
 ing telescope. It differed from the Gregorian telescope in the small mirror 
 being convex, and in its being placed so as to intercept the rays before 
 they came to a focus. This telescope is more convenient than the Gre- 
 gorian, inasmuch as it is shorter, cceteris paribus, by twice the focal length 
 of the small mirror. Ramsden remarked, that the effect of spherical 
 aberration was also less than in the Gregorian telescope *, and more 
 recently, Captain Kater shewed, by a series of experiments, that it was 
 greatly superior in point of light and distinctness to any telescope of the 
 latter construction, possessing an equal aperture f. Notwithstanding these 
 alleged advantages, this form of the reflecting telescope has been com- 
 paratively seldom used since its invention. As has been already hinted 
 at, the Newtonian telescope exhibits objects not in their true direction, 
 but at right angles to it. Hooke was the first person who executed a 
 telescope, the observations with which were made by viewing the object 
 directly. This he effected in 1674, by perforating the centre of the larger 
 speculum agreeably to the suggestion of Gregory J. 
 
 Although both Newton and Hooke shewed that the construction of 
 reflecting telescopes was perfectly practicable, it does not seem that for a 
 long time any further attempts were made to execute such instruments ; 
 at all events no progress was made in bringing them to perfection. The 
 first person who succeeded in accomplishing this object was Hadley, the 
 individual whom we have had occasion to allude to, as one of the inde- 
 pendent inventors of the reflecting octant. In 1723 he presented to the 
 Royal Society a reflecting telescope of the Newtonian form, which he 
 executed with his own hands. The diameter of the speculum was 
 6 inches, and its focal length was 5 feet 3 inches. Pound and Bradley, 
 having compared it with the refracting telescope of 123 feet focal 
 length, which Huyghens had presented to the Society, found that it 
 bore as high a magnifying power as that instrument, and exhibited ob- 
 jects equally distinct though not quite so bright. Notwithstanding its in- 
 feriority in the latter respect, they were enabled to perceive with it all 
 the phenomena which they had hitherto discovered with the Huygenian 
 telescope, such as the transits of Jupiter's satellites ; their shadows upon 
 the disk of the planet; the Hack list on Saturn's ring; and the edge 
 of his shadow upon the ring. On several occasions they succeeded in 
 seeing with it the five satellites of Saturn . Reflecting telescopes 
 were executed by Hawksbee, about the time that Hadley was prosecuting 
 his labours with such success. This individual made a telescope of 
 3 1 feet focal length, which proved to be even more perfect than any of 
 Hadley 's. About the same time Bradley and Molyneux, having been 
 instructed by Hadley in the grinding and polishing of metallic specula, 
 began to turn their attention to the construction of reflecting tele- 
 scopes. After much trouble, they finally succeeded in executing several 
 telescopes of considerable magnitude. One of these had a focal length 
 of 8 feet||. 
 
 Hitherto the execution of reflecting telescopes was confined exclusively 
 to persons engaged in scientific pursuits, whence it may naturally be 
 
 * Phil. Trans., 1779, p. 427- 
 
 t Phil. Trans., 1813, p. 206 ; 1814, p. 231. 
 
 Birch, Hist. Roy. Soc., vol. iii., p. 122. 
 
 Phil. Trans., 1723, p. 382. 
 
 || Smith's Optics, Book III., chap. 1. 
 
 M M 
 
530 HISTORY OF PHYSICAL ASTRONOMY. 
 
 presumed that the number of such instruments actually made continued 
 to be very limited. Molyneux, however, having acquainted Scarlett and 
 Hearne, two London opticians, with the mode of grinding and polishing 
 specula, these individuals commenced jnaking reflecting telescopes for 
 sale ; and, in consequence, this class of instruments soon afterwards came 
 into general use*. 
 
 The next person who distinguished himself by his skill in the con- 
 struction of reflecting telescopes, was James Short, of Edinburgh. In 
 1732, when he was only twenty-two years of age, this individual turned 
 his attention to the polishing of specula, in which he soon attained an 
 unrivalled degree of excellence. He also discovered a method of giving 
 them a true parabolic figure, which had not hitherto been done by any 
 person. In his first attempts he confined himself to glass specula, which 
 were made to reflect the light by covering them behind with quicksilver. 
 James Gregory had recommended the use of glass for reflectors, on the 
 ground of its absorbing less light than metal, and being at the same 
 time less liable to tarnish f. With one of Short's glass reflectors, which 
 had a focal length of only 1 5 inches, Maclaurin asserts that it was pos- 
 sible to read in the Philosophical Transactions at a distance of 280 feet f . 
 Finding that in such telescopes the light was fainter than in those in 
 which the speculum was composed of metal, Short abandoned the use of 
 glass, and confined himself in future to metallic reflectors. The tele- 
 scopes of the latter description made by him appear to have been exqui- 
 site specimens of skill. Maclaurin states, that having compared some of 
 them with instruments of much greater focal length, made by London 
 artists, he found the former to be far superior in respect of brightness, 
 distinctness, and magnifying power. With a metallic reflecting telescope 
 of Short's, which had a focal length of only 15 inches, it was possible to 
 read distinctly in the Philosophical 'Transactions at a distance of 500 feet, 
 and to see the five satellites of Saturn all at the same time. In 1742 
 Short removed to London, where he continued to prosecute his former 
 vocation with great success till his death, in 1708. One of the last 
 instruments executed by him was a large reflecting telescope, which his 
 brother Thomas mounted equatorially for the observatory of Edinburgh, 
 and for which he was offered 1200 guineas by the King of Denmark. 
 The telescopes of Short were all of the Gregorian construction. 
 
 It has been already mentioned, that as soon as Newton discovered the 
 
 * Smith's Optics, Book III. chap. 1. 
 
 f Newton in his Optics (1704) states that, about five or six years previously, he tried 
 to make a reflecting telescope 4 feet in length, that would magnify 150 times, the 
 speculum of which was of glass, and that he satisfied himself that there wanted nothing 
 but a good artist to bring the design to perfection. He recommends glass specula in 
 preference to metal, as being more easily polished, less liable to tarnish, and at the same 
 time capable of reflecting more light. ( Optics, part i. prop, vii.) Smith has inferred 
 from the passages of Newton's work just cited that " the method of making reflecting 
 telescopes with glass speculums, quicksilvered over," was first recommended by that phi- 
 losopher. (System of Optics, Remarks, No. 489.) This, however, is a mistake. The 
 person who first recommended glass specula for telescopes, was James Gregory, as has 
 been mentioned in the text. Gregory made this suggestion in a letter to Collins, dated 
 St. Andrew's, March 7, 1673, pointing out at the same time the peculiar advantages of 
 glass specula, and requesting that his views on the subject might be communicated to 
 Newton. The letter of Gregory was read at the meeting of the Royal Society, held 
 on the 26th of March, 1673, and it was ordered, that it should be communicated to 
 Newton as the person most concerned in it. (Birch, Hist. Roy. Soc., vol. iii., p. 79.) 
 
 | Smith's Optics (Remarks, No, 489). 
 
HISTOBY OF PHYSICAL ASTKONOMY. 531 
 
 unequal refrangibility of light, he perceived that the existence of that 
 principle offered a serious obstacle to any further improvement of the 
 refracting telescope. This great philosopher did not fail to make expe- 
 riments on the passage of a ray of light through several contiguous media, 
 in order to ascertain whether the different refractions might not correct 
 each other, so that the emergent ray, while deflected from its original course, 
 might still be free of colour. The results of his labours on this occasion 
 served, however, to convince him that no such compensation could be 
 effected. He found, in fact, that when the ray emerged in a direction 
 parallel to its original course, it was invariably white; but when it 
 emerged obliquely with respect to the direction of incidence, it became 
 gradually tinged with different colours in passing from the place of emer- 
 gence *. Having satisfied himself in this manner that no combination 
 of substances could be devised which would be capable of refracting the 
 rays of light so as to produce a colourless image of an object, he seems to 
 have despaired of improving the refracting telescope by any other means 
 than that of increasing the focal length of the object-glass. 
 
 It was reserved for Dollond f to shew that the views which guided 
 Newton in arriving at this conclusion were erroneous, and to apply the 
 true principle of physics to the construction of refracting telescopes free 
 of colour. This highly-gifted individual, although moving in a humble 
 sphere of life, had devoted much attention to mathematical and physical 
 pursuits. He seems to have been originally led to consider the subject of 
 the dispersion of light by the researches of Euler. In 1747 that distin- 
 guished mathematician communicated a memoir to the Berlin Academy of 
 Sciences, in which he attempted to shew that, by a combination of different 
 substances, it would be possible to construct object-glasses for telescopes, 
 in which the effects arising both from spherical aberration and the unequal 
 refrangibility of light would be completely corrected. He remarked that 
 the different humours of the human eye refracted the rays of light, so as 
 to produce a perfectly-distinct image of an object, and he argued by ana- 
 logy, that a similar effect would be produced by the object-glass of a 
 telescope, provided a suitable combination of substances was employed in 
 its construction. Proceeding upon a certain hypothetic law of the dis- 
 persion of light, he accordingly devised a combination of hollow spherical 
 lenses, enclosing water within their concave surfaces, which, he asserted, 
 
 * Optics, Book II. Part I. Exper. viii. Newton states that he made this experiment 
 with a prism glass and one of water, so adapting the two prisms that they refracted the light 
 equally in opposite directions. In such a case, although the rays of light emerged paral- 
 lel to the direction of incidence, they ought also to have been coloured, as Dollond, upon 
 repeating the experiment in the following century, actually found them to be ; but New- 
 ton asserts that he found the emergent, rays to be white. Sir David Brevvster states that 
 the mistake of Newton arose from his having mixed a little sugar of lead with the water, 
 in order to increase its refractive power, and that the high dispersive power of the ingre- 
 dient caused the residuum of uncorrected colour to disappear (Life uf Newton, p. 58). 
 The same statement is made by Sir John Herschel, in his Treatise on Light, in the 
 Encyclopedia Metropolitans . Neither of the two distinguished philosophers just cited 
 has acquainted his readers with the source whence this explanation of Newton's mistake 
 has been derived. Newton himself makes no mention of his having added any ingre- 
 dient to the water in the part of his work above referred to, where he alludes to the 
 experiment. 
 
 f John Dollond was born at Spitalfields, in London, in the year 1706. He was de- 
 scended from French ancestors, who were compelled to quit Normandy upon the revo- 
 cation of the edict of Nantes, by Louis XIV. In early life he worked at the loom, but 
 in 1752 he joined his son as an optician. He died in 1761, having been struck with 
 apoplexy, while engaged in an intense study of Clairaut's Theory of the Moon. 
 
 M M 2 
 
532 HISTORY OF PHYSICAL ASTRONOMY. 
 
 would form an object-glass for a telescope, capable of producing an image 
 free of colour. 
 
 In the Philosophical Transactions for 1753, Dollond pointed out that 
 the law of dispersion assumed by Eulerwas inconsistent with the conclu- 
 sion immediately deducible from the experiments of Newton on the sub- 
 ject, and therefore he maintained that the result of his researches could 
 not be entitled to any confidence. Soon afterwards, however, Klingen- 
 stierna, an eminent Swedish philosopher, succeeded in demonstrating that 
 the result of Newton's experiment was at variance with certain acknow- 
 ledged phenomena of refraction, and upon this ground he justly asserted 
 that it could not be received as the true law of nature. 
 
 Dollond, who was endowed with the true spirit of philosophical enquiry, 
 now resolved to satisfy his mind upon the subject by actual experiment. 
 With this view he formed a prismatic vessel of water, the sides of which 
 were composed of plate-glass, and inserted into it a glass prism, so that 
 the water and glass refracted the rays of light in opposite directions. 
 When the angles of the two prisms were so adjusted that the emergent 
 ray was parallel to the incident ray,- he found that the emergent ray was 
 tinged with different colours, a result directly contrary to that which New- 
 ton obtained in a similar instance. Pursuing his experiment, Dollond 
 found that when the angles of the two prisms bore a certain relation to 
 each other, the rays of light emerged free of colour, while at the same 
 time they were deflected from their original course. It appeared, then, 
 that although the refractions of the rays in passing through the two 
 prisms were uncompensated, their divergences were completely corrected, 
 and the unavoidable conclusion therefore was, that the dispersion of the 
 rays of light did not depend simply on the mean angle of refraction, as 
 Newton had supposed, but that it was also influenced to a certain extent 
 by the nature of the refracting substance. 
 
 It now occurred to Dollond that a similar effect might be produced by 
 combining together prisms of glass of different qualities. By a series of 
 experiments he discovered that of the various kinds of glass, crown-glass 
 produced the least dispersion of the rays, and flint-glass the greatest. 
 He moreover found, that if a prism of flint-glass, and one of crown-glass, 
 were so combined as to refract the rays of light in opposite directions, 
 and if the angles of the two prisms were so related to each other that the 
 refraction produced by the flint-glass was to that produced by the crown- 
 glass as two to three, the dispersion of the rays would be completely cor- 
 rected, and they would emerge from the compound refracting substance at 
 an angle inclined to their original course. 
 
 The step to the construction of an object-glass for a telescope which 
 would produce an image free of colour was now obvious. Dollond per- 
 ceived that this might be effected by combining a convex lens of crown- 
 glass with a concave lens of flint-glass, the focal distances of the two lenses 
 being in the proportion of their dispersive powers. He therefore con- 
 structed object-glasses upon this principle, which were found to produce 
 the effect contemplated, and thus he was enabled to execute telescopes, 
 in which the indistinctness arising from the unequal refrangibility of light 
 was completely obviated *. The term achromatic, which has been aptly 
 applied to such telescopes, was originally suggested by Dr. Bevis. 
 
 * For an account of Dollond's experiments relating to the dispersion of light, see Phil. 
 Trans., 1758, p. 733, et seq. 
 
HISTORY OP PHYSICAL ASTRONOMY. 533 
 
 Although Dollond is entitled to the credit of having executed achro- 
 matic telescopes by the aid of his own researches on the dispersion of 
 light, there is reason to believe that he was not the first individual who 
 accomplished that object. It appears, in fact, that as early as the year 
 1729, Chester More Hall, a gentleman residing in Essex, having reflected 
 upon the circumstance that the different humours of the eye so refract 
 the rays of light as to produce images free of colour, was led to consider 
 the possibility of combining together different substances, so as to form 
 object-glasses for telescopes which would produce a similar effect. After 
 devoting some time to the enquiry, he found that by combining together 
 different kinds of glass, the effect of the unequal refrangibility of light 
 was corrected; and, in 1733, he succeeded in executing telescopes which 
 exhibited objects quite free of colour. One of these instruments, although 
 its focal length was no more than 20 inches, bore an aperture of 2J 
 inches. More, who was living in independent circumstances, and who 
 appears to have been nowise anxious about his reputation, did not take 
 any trouble in communicating his invention to the world *. It has been 
 insinuated that Dollond had seen one of More's telescopes, and that he 
 was indebted to this circumstance for his construction of the achromatic 
 object-glass ; but the statement does not rest upon any solid foundation, 
 and therefore it can only be regarded as an unfounded calumny. 
 
 The achromatic telescopes of Dollond soon became known throughout 
 the whole civilised world, and were universally adopted by astronomers as 
 affording an incontestable advantage over the ancient refracting telescopes. 
 In one respect, however, they laboured under a defect which very much 
 restricted the range of their efficiency. This consisted in the impossibi- 
 lity of obtaining pieces of pure flint-glass of sufficient magnitude to serve 
 for telescopes of large aperture. It happened, from this circumstance, that 
 no astronomical discoveries of importance resulted from the invention of 
 the achromatic telescope. Huyghens and Cassini, by their combined ex- 
 ertions in the preceding century, seemed to have so thoroughly scrutinized 
 the celestial regions, as to leave little or nothing to be gleaned by their 
 successors, until instruments should be constructed capable of penetrating 
 still further into the bosom of space. This remark is applicable to re- 
 flecting as well as refracting telescopes; for it is to be borne in mind, that 
 not a single discovery had yet been made in the heavens by the use of a 
 telescope constructed upon the principle of reflexion. 
 
 At length the discoveries of Herschel introduced a new era in the history 
 of celestial physics. This highly-gifted individual, while occupying the 
 humble situation of organist of the Octagon Chapel, Bath, to which he was 
 appointed in the year 1766, was in the habit of devoting his leisure hours 
 to the study of mathematics, and various branches of physical science, 
 more especially optics and astronomy. Happening, on one occasion, to 
 obtain the temporary use of a 2-feet Gregorian reflector, he was so 
 transported with the celestial wonders which it revealed to him, that he 
 conceived a passionate desire to procure a similar instrument for himself, 
 and he instructed a friend in London to purchase one for him. The price 
 
 * This account is taken from the Gentleman's Magazine for 1790, Part II., p. 890. 
 The author states, that in a trial at Westminster Hall, about the patent for making achro- 
 matic telescopes, Mr. Hall was allowed to be the inventor; but Lord Mansfield ob- 
 served, that " it was not the person who locked his invention in his scrutoire that 
 ought to profit for such invention, but he who brought it forth for the benefit of the 
 public." 
 
534 HISTORY OF PHYSICAL ASTRONOMY. 
 
 demanded by the optician proving too great for his slender means, he re- 
 solved, with the true instinct of genius, to rely upon his own personal 
 resources for attaining the object of his wish; and after a course of perse- 
 vering efforts, he at length, m the year 1774, enjoyed the satisfaction of 
 surveying the heavens with a 5-feet Newtonian reflector, which he con- 
 structed with his own hands. This was speedily followed by other 
 reflectors of 7-feet, 10-feet, and even 20-feet focal length, all of which 
 were exquisite specimens of artistic skill. 
 
 Armed with such powerful instruments, Herschel now proceeded to 
 explore the heavens with all the enthusiasm which genius, stimulated by 
 success, is capable of inspiring. He soon convinced astronomers that he 
 was no ordinary amateur, who had betaken himself to the observation of 
 celestial phenomena, by the high magnifying powers which he employed, 
 amounting to 2000, 3000, and even in some instances to 6500. These 
 numbers far surpassed the magnifying powers hitherto employed in tele- 
 scopic observations. In 1781 his perseverance was rewarded by the dis- 
 covery of the planet Uranus. Soon afterwards, George III. having bestowed 
 upon him a liberal pension, he abandoned his original vocation, and hence- 
 forth devoted himself exclusively to astronomical pursuits. Having re- 
 moved from Bath, he established himself first at Datchet, in the neighbour- 
 hood of Windsor, and subsequently at Slough, where he continued during 
 the remainder of his life to prosecute a career of astronomical discovery, 
 which has few parallels in any age or country. The telescopes which 
 Herschel employed in the early part of his astronomical observations, 
 were all of the Newtonian construction. In 1780, however, he laid aside 
 the small mirror, and adopted the form of construction which he dis- 
 tinguished by the appellation of the front view. By giving a slight incli- 
 nation to the speculum, so as to throw the image a little to one side of the 
 tube, it was possible to view the latter directly with an eye-glass. By 
 this contrivance the light usually absorbed by the small mirror was 
 saved, and the illumination of the image increased in a corresponding 
 degree. In such a telescope it is obvious that the observer looks at 
 the image with his back turned towards the object. Herschel applied 
 this form of construction to all the instruments which he subsequently 
 employed in his astronomical observations. His discovery of two satel- 
 lites around Uranus was a result which speedily followed its adoption. 
 It is right to mention that a similar form of construction had been already 
 proposed by Lemaire, a Frenchman, as early as the year 1732. 
 
 In 1789 Herschel surpassed all his former efforts as a practical opti- 
 cian by the completion of a telescope of 40-feet focal length and 4-feet 
 aperture. This gigantic instrument was no sooner turned towards the 
 heavens than it revealed to him the existence of two satellites around 
 Saturn which had hitherto escaped the scrutinies of astronomers. It is 
 impossible, within a moderate compass, to give even a simple enumera- 
 tion of the multitude of brilliant discoveries in celestial physics which 
 rewarded the labours of this great astronomer. It may be remarked, 
 however, that admirable as were the immediate results of his telescopic 
 observations, they would have failed to secure to him the exalted place 
 which is now universally assigned to him in the history of astronomical dis- 
 covery, if he had not at the same time been endowed with a mind of rare 
 originality and power, combined with a strong turn for speculation. 
 
 For many years after the invention of the achromatic telescope, the ma- 
 nufacture of flint-glass continued to be confined to England, which 
 
HISTORY OF PHYSICAL ASTRONOMY. 585 
 
 country, in consequence, enjoyed an exclusive privilege in the construc- 
 tion of instruments of this description. At length Guinand, a humble 
 mechanic of Brenetz, a small village in the Canton of Neuf'chatel, Swit- 
 zerland, having turned his attention to the manufacture of flint-glass 
 towards the close of the eighteenth centuiy, succeeded, after a long course 
 of persevering efforts, in producing masses of that substance perfectly free 
 of stria?, and therefore adapted for the construction of object-glasses of 
 telescopes. Frauenhofer*, the Bavarian optician, having been made 
 acquainted with the wonderful success of Guinand, resolved to take ad- 
 vantage of the circumstance, and with a view to this object he induced 
 the Swiss artizan to remove to Munich, in the year 1805. This eminent 
 individual, who was no less remarkable for sagacity in philosophical 
 enquiries than for skill as an artist, possessed peculiar qualifications for 
 profiting by the instructions of Guinand, and he soon succeeded in attain- 
 ing unexampled excellence in the construction of achromatic object- 
 glasses. Telescopes were now executed by Frauenhofer, the apertures of 
 which far exceeded anything hitherto known since the discovery of achro- 
 matism. It was with one of these instruments, having an aperture of 
 9.9 inches, and a focal length of 13^ feet, that M. Struve made the 
 series of micrometrical measurements of double stars at Dorpat, between 
 the years 1824 and 1837, which have rendered the name of that astro- 
 nomer so deservedly famous. With another of them, having an aperture 
 of 12 inches, and a focal length of 18 feet, M. Lamont, of Munich, 
 made those interesting observations of the satellites of Uranus, to which 
 allusion has been made in one of the preceding chapters. Frauenhofer 
 was contemplating the execution of object-glasses of still greater mag- 
 nitude than either of those above-mentioned, when his brilliant career 
 was unfortunately brought to a close by a premature death. His succes- 
 sors, MM. Merz and Mahler, have succeeded in effectually realising his 
 views. Among the clicf-d'ceuvres of these artists may be cited the famous 
 refractors of Pulkowa and Cambridge, U.S., to both of which instru- 
 ments allusion has already been made in the foregoing part of this work. 
 Guinand remained at Munich from 1805 till 1814, in which year he 
 finally returned to his native country. A few years afterwards he was 
 visited by Lerebours, an eminent French optician, who purchased of him 
 all the flint-glass in his possession. Subsequently he also supplied Can- 
 choix, another artist of Paris, with portions of the same valuable substance. 
 The French opticians skilfully worked the material into object-glasses, 
 and in this manner refracting telescopes came to be constructed in France, 
 rivalling the most finished productions of the Munich artists. England, 
 which continued long to be the exclusive seat of the manufacture of 
 achromatic telescopes, had the mortification of finally seeing both Ger- 
 many and France completely outstrip her in this branch of practical 
 optics. This result she owed to the short-sighted policy of the Govern- 
 ment, which had placed an exorbitant duty on the manufacture of flint- 
 glass. The removal of this pernicious impost a few years since, has 
 given a new impulse to the art, and already results have been achieved 
 which seemed to indicate that before a long period shall have elapsed, 
 refracting telescopes will be executed in this country, rivalling the most 
 
 * Joseph Frauenhofer was born in the year 1787, at Straubing, in Bavaria. Besides 
 having attained unrivalled eminence in his professional vocation, he achieved many 
 important discoveries in physical optics. He died in 1826, while yet in the prime of 
 life ; but he left behind him an immortal reputation. 
 
536 HISTORY OF PHYSICAL ASTRONOMY. 
 
 powerful instruments of the same kind which have emanated from the 
 workshops on the Continent *. 
 
 While the refracting telescope has been rendered vastly more efficient 
 in modern times, the reflecting telescope has received a corresponding 
 degree of improvement. During the present century several very large 
 telescopes were constructed upon this principle by the late Mr. Ramage, 
 of Aberdeen, an individual of considerable originality, who possessed a 
 remarkable aptitude for mechanical inventions. The perfection of these 
 instruments does not seem, however, to have been commensurate with 
 their magnitude, for they have been employed only to a very limited 
 extent in astronomical observations. In more recent times, Mr. Lassell, 
 of Liverpool, has especially distinguished himself by his skill in the 
 construction of reflecting telescopes. With a Newtonian reflector of 2-feet 
 aperture, which he executed with his own hands, he has discovered the 
 single satellite of Neptune, and the eighth satellite of Saturn ; while, at 
 the same time, he has been enabled by its use, to make several very 
 interesting physical observations of the planetary bodies. In the con- 
 struction of reflecting telescopes the Earl of Rosse has attained a degree 
 of excellence which far surpasses all previous efforts of the kind. It is 
 impossible here to give any account of the multitude of admirable con- 
 trivances by means of which that distinguished nobleman has succeeded 
 in bringing his telescopes to so high a state of perfection. It must suf- 
 fice to state, that in 1840, he completed a Newtonian reflector of 3 feet 
 aperture, which he subsequently employed in astronomical observations. 
 Phenomena of a highly-interesting nature were soon disclosed by the use 
 of this powerful instrument. Several nebulre, hitherto observed as such 
 in the most powerful telescopes, were resolved into clusters of stars, while 
 others exhibited forms totally different from those which had been hitherto 
 assigned to them. In 1845 Lord Rosse gave to the world a still more 
 striking proof of his practical talents, and his devotion to astronomical 
 science, by the construction of a reflecting telescope of 6-feet aperture, 
 and 54-feet focal length ! This magnificent instrument, by far the most 
 powerful which the genius of man has hitherto executed for the purpose 
 of exploring the grand phenomena of the heavens has already, in the hands 
 of its noble owner, done valuable service to astronomy, by the light which 
 it has thrown upon the structure of the nebular part of the uni verse f. 
 
 The brilliant success which has attended Lord Rosse's efforts to 
 construct reflecting telescopes, has suggested to several eminent sci- 
 entific men of the present day the expediency of transporting a powerful 
 instrument of this description to the southern hemisphere, for the pur- 
 
 * At the meeting of the British Association, held in the month of July of the present 
 year (1851), at Ipswich, the Astronomer Royal, in his opening address as President of 
 the Association, stated that Mr. Simms had completed the flint-glass for an achromatic 
 object-glass of 13 inches in diameter, and that he was engaged in executing one of 16 
 inches. He also mentioned that Mr. Ross was attempting to make an object-glass of 
 2 feet in diameter ! It is to be hoped that these glasses may turn out to be remarkable 
 for quality as well as size. 
 
 I Dr. Robinson, in a brief account of Lord Rosse's optical labours, delivered at the 
 meeting of the British Association, held at Cork in 1843, has remarked that " between the 
 spherical and parabolic figures, the extreme difference is so slight, even in the telescope 
 of 6-feet aperture, that if the two surfaces touched at their vertex, the distance at the 
 edge would not amount to the 17i ,gg,th of an inch, a space which few can measure, 
 and none without the microscope." This statement may give the reader some idea of 
 the exquisite delicacy of the opeiatioa necessary for giving the speculum its true para- 
 bolic figure. 
 
HISTORY OF PHYSICAL ASTRONOMY. 537 
 
 pose of employing it in physical observations of the celestial bodies. At 
 the meeting of the British Association, which was held at Edinburgh in 
 1850, it was agreed to memorialise the Government upon the advantages 
 which would accrue to astronomical science from the practical adoption of 
 such a scheme. It is to be hoped that, ere long, steps will be taken 
 towards its complete realisation. 
 
 CHAPTER XXL 
 
 Origin of Stellar Astronomy. Physical Changes observed in the Starry Regions.. 
 Disappearance of Stars from the Heavens New Stars. Stars of Variable Lustre. 
 Photometric Researches on the Stars Attempts to Determine their Apparent Dia- 
 meters. Space-penetrating Power of Telescopes. Applied to ascertain the relative 
 Distances of the Stars. Absolute Distances of the Stars determined by Photo- 
 metric Principles. Parallax of the Fixed Stars. Early Researches on the Subject 
 
 Modern Researches. Bessel. Henderson. Struve. Peters. Proper Motions of 
 
 the Stars Motion of the Solar System in Space. Double Stars. Discovery of their 
 
 Physical Connexion by Sir William Herschel. Methods for determining the Elements 
 of their Orbits. Nebulae. Speculations of Sir William Herschel. Modern Re- 
 searches on the Subject Sir John Herschel. The Earl of Rosse. Early Specula- 
 tions on the Milky Way. Theory of Wright Observations of Sir William Herschel. 
 
 Speculations of that Astronomer on the breaking up of the Milky Way. Re- 
 searches of Struve on the Distribution of the Stars in Space. Gauges of Sir John 
 Herschel in the Southern Hemisphere. Speculations of M. Struve on the Extinction 
 of Light in its Passage through Space. 
 
 THE aspect of the starry firmament furnishes one of the most glorious 
 spectacles which nature displays throughout the entire range of her widely- 
 diversified empire. The multitude of luminaries with which the blue 
 vault of heaven appears bespangled, the endless variety of lustre which 
 they exhibit, the striking configurations which they form, and the calm 
 regularity with which they pursue their nocturnal courses all conspire 
 together in awakening a feeling of adoration in the most listless spectator, 
 while at the same time they are eminently calculated to excite the 
 enquiries of the more rational observer of physical phenomena. Attention 
 could not long have been directed to the appearance of the starry heavens, 
 before it was discovered that, except in a few instances, the entire multi- 
 tude of luminaries constantly maintained the same relative position. 
 Hence they received the appellation of Fixed Stars, an expression, how- 
 ever, which is now found to be inaccurate, since the researches of modern 
 astronomers have served to demonstrate that many of the stars are affected 
 by very minute movements, while at the same time it can hardly be 
 doubted that they are all subject to a similar influence. 
 
 During the early period of astronomical science, the fixed stars were 
 observed merely 011 account of their utility in forming reference points, by 
 means of which the apparent positions of the planetary bodies might be 
 determined with greater accuracy, and the laws of their movements hence 
 ascertained. Indeed, the Ptolemaic astronomy, by making the whole 
 sphere of the stars perform a complete revolution round the earth once 
 in every twenty-four hours, assigned to those luminaries a very subordi- 
 nate place in the physical universe. When the immortal Copernicus 
 restored the true system of the world, the stars assumed their just dignity 
 as vast bodies placed at an immeasurable distance from the earth ; but 
 it seemed hopeless ever to arrive at any knowledge respecting their 
 physical constitution. At length the invention of the telescope, about 
 
538 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the beginning of the seventeenth century, by removing the veil which had 
 so long concealed those remote orbs from the scrutinies of the human 
 mind, gave an unexpected impulse to researches of this nature. From 
 the epoch of Galileo's brilliant discoveries in the celestial regions, may 
 be said to date the origin of Stellar Astronomy, a branch of enquiry which 
 has ever since attracted more or less attention, and which, in recent times 
 especially, has excited an intense degree of interest. 
 
 That the stars are so many suns shining by their own light, is an 
 opinion which seems to have been entertained by some of the ancient 
 philosophers. This view of their nature came to be universally adopted 
 upon the establishment of the true system of the world by Copernicus, 
 since it was considered to be improbable in the highest degree, that bodies 
 shining by reflected light would be visible at the earth, when at the same 
 time their distance was so immense, that they did not exhibit any sensible 
 change of position even when viewed at the opposite extremities of a 
 diameter of the terrestrial orbit. 
 
 The number of stars visible to the naked eye, is found to amount only 
 to a few thousands ; for although at first sight they seem to be innume- 
 rable, yet a closer scrutiny of the heavens soon serves to convince the 
 observer that he has been labouring under a delusion in this respect. 
 But what the unaided organ of vision merely suggests to the imagina- 
 tion, without affording any substantial grounds of belief in its existence, 
 an examination of the starry heavens with the telescope has proved to be 
 a reality. Multitudes of stars are then perceived, which were invisible to 
 the naked eye. The number also thus disclosed to view, continually 
 augments with each successive increase of the optical power of the in- 
 strument, until the imagination is at length absolutely overwhelmed with 
 the countless myriads of suns, and systems of suns, which are found to 
 people the immensity of space. 
 
 The ancient philosophers supposed the celestial bodies to be essentially 
 incorruptible and eternal, and hence maintained that they were not sub- 
 ject to physical changes, as in the case of bodies at the surface of the 
 earth. The progress of astronomical science, however, has served amply 
 to demonstrate that those brilliant orbs are not exempt from the great 
 law of mutation, to which all the other objects of the created universe 
 appear to be liable. Exclusively of the evidence afforded by the observa- 
 tions of astronomers on the physical constitution of the sun, there are 
 various stellar phenomena of a highly-interesting nature, which concur in 
 establishing this important fact, A brief allusion to some of them may 
 not perhaps be unacceptable to the reader. 
 
 In some instances, stars which have shone for ages in the firmament, 
 have ceased to be visible. A comparison of catalogues of the stars con- 
 structed for different epochs, would indeed seem to indicate that a great 
 number of such objects that were formerly visible in the celestial 
 sphere, have totally vanished ; but it is probable that in most of these 
 cases the discordance is attributable to the imperfection of the earlier 
 observations of astronomers. Stars, however, have been mentioned by 
 Montanari*, Maraldif, and Sir William Herschel J, respecting whose ex- 
 tinction there hardly exist grounds for entertaining any reasonable 
 doubt. 
 
 * Phil. Trans., 1671, p. 2202. f Mem. Acad. des Sciences, 1709, p. 40. 
 
 J Phil. Trans., 1792, p. 20. 
 
HISTORY OF PHYSICAL ASTRONOMY. 539 
 
 Various new stars are recorded in history, which after having shone 
 with great splendour for a short time, then gradually faded away until 
 they ceased to be visible. Thus Pliny asserts, that the appearance of a 
 new star in the time of Hipparchus, about the year 180 A.D., was the 
 occasion of inducing that astronomer to construct his famous catalogue 
 of the stars. A new star is said to have appeared in the reign of the 
 Emperor Honorius, about the year 390 A.D. ; also one in the reign of the 
 Emperor Otho, about the year 945 ; and again a phenomenon of a similar 
 nature in the year 1 264. 
 
 * In the year 1572, there appeared a splendid new star in the constel- 
 lation of Cassiopeia, which is memorable for being the earliest of such 
 phenomena respecting which any authentic particulars have been recorded 
 by astronomers. This star was observed by Tycho Brahe, who, in a long 
 work, written expressly on the subject, has given a detailed account of 
 the various circumstances connected with its appearance ; including a 
 critical discussion of the speculations of his contemporaries on its pro- 
 bable origin. It was first seen by him on the evening of the llth of 
 November, 1572. It then surpassed in lustre the brightest of the fixed 
 stars, and was even more brilliant than the planet Jupiter, although 
 then in opposition and near perihelion. It almost rivalled Venus, 
 and, like that planet, w r as seen by some persons even in the daytime. 
 During the remaining part of November, it continued to shine with 
 undimiriished lustre ; but it subsequently began to decline, and it gra- 
 dually grew fainter, until at length, in the month of March, 1574, it 
 ceased to be visible. The colour of this extraordinary object underwent a 
 succession of changes during the period of its appearance. When it first 
 became visible, it shone with a bright white light, like Venus or Jupiter. 
 It then acquired a yellowish tinge; afterwards became ruddy, like Mars 
 or Aldebaran ; and finally exhibited a leaden hue, like the planet Saturn *. 
 Tycho Brahe supposed it to be generated from the ethereal substance of 
 which he imagined the Milky Way to be composed, and to have been 
 afterwards dissipated by the light of the sun and the other stars, or to 
 have dissolved spontaneously from some internal cause f. A more modern 
 hypothesis has referred the origin of the phenomenon to some vast com- 
 bustion, an explanation which receives some degree of support from the 
 gradual change of colour which the light of the star exhibited. 
 
 A few years after the close of the sixteenth century, another splendid 
 new star burst forth in the constellation of Serpentarius. In this instance 
 the phenomenon was witnessed by many eminent astronomers, including 
 Kepler, who wrote an interesting dissertation on the subject of its appear- 
 ance J. It was first seen by that astronomer on the 17th of October, 
 1604. It surpassed in brightness the stars of the first magnitude, as 
 well as the planets Mars, Saturn, and Jupiter, all of which were in its 
 vicinity. Like the star of 1572, it began to decline soon after its appear- 
 ance, and finally ceased to be visible between October, 1605, and February, 
 1606. Kepler was of opinion that it was generated from an ethereal 
 substance, not confined exclusively to the region of the Milky Way, as 
 Tycho Brahe had supposed in the case of the star of 1572, but pervading 
 all space. In connexion with this explanation of the origin of the star, 
 he remarked, that the luminous ring observed around the dark body of 
 
 * Progymnasmata, p. 297. + Ibid., p. 795. 
 
 J " De Stella Nova in Pede Serpentarii," 4to, Pragce, 1606. 
 
540 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the moon at Naples during the total eclipse of the sun which happened 
 in the year 1605, was occasioned by the existence of such a substance 
 around the sun *. 
 
 The new stars of 1472 and 1604, are memorable in the history of 
 astronomy, for the extraordinary splendour with which they suddenly 
 burst forth upon the world. Several phenomena of a similar nature have 
 subsequently been observed, but they have not exhibited such remarkable 
 features as the stars just mentioned. 
 
 A comparison of the writings of the ancient astronomers with the 
 results of actual observation, would seem to indicate that some stars have 
 undergone a permanent change of brightness. Besides these, however, 
 there are several stars which have been recognized in modern times to be 
 subject to periodic variations of lustre, completing the cycle of their 
 phases in comparatively short intervals of time. The most celebrated of 
 these is the star in the neck of the Whale, which Bayer has marked in 
 his charts with the Greek letter omicron, and which, in consequence of 
 the singular changes exhibited by it, was termed Mir a CetL This star 
 was first seen by David Fabricius, on the 13th of August, 1596 f ; and as 
 it disappeared in the following October, it was considered by Kepler and 
 the other astronomers of the time to have been a new star, like the one 
 of 1572. It was first recognised as variable by Phocylides, a Dutch 
 philosopher, who commenced his observations of it in the year 1638J. 
 Bouillaud, by a comparison of all the observations included between the 
 years 1638 and 1667, ascertained that its variations are periodic, and that 
 it passes through the course of its phases in about 333 da} r s. The 
 more accurate researches of modern astronomers make the period 
 to be 331 d 15 h 7 m . This star is generally invisible to the naked eye 
 for about five months. It then gradually increases until it attains the 
 brightness of a star of the second magnitude ; and after remaining 
 in this state for about fifteen days, it begins to decline in brightness, 
 diminishing nearly at the same rate as that at which it had formerly 
 increased. 
 
 A great number of stars have been recognised by modern astronomers 
 to be subject to variations of brightness similar to those remarked in 
 the case of o Ceti. One of the most interesting of these is the bright 
 star in the head of Medusa, termed Algol or |3 Persei. Montanari, and 
 afterwards Maraldi, found that it was subject to singular fluctuations of 
 brightness ; but no attempt was made to ascertain either the period or law 
 of variation, until Goodricke commenced his observations of the star in 
 the year 1782. By continuing for some time to watch its successive 
 phases of brightness, that acute observer found that, after resembling a 
 star of the second magnitude, for about two days thirteen hours and 
 three quarters, it descended in the short space of three hours and a half 
 to the fourth magnitude, and then in an equal interval of time regained 
 its former brightness, thus completing the cycle of its variations in 
 about two days twenty hours and three quarters ||. By a subsequent 
 comparison of an observation of the star by Flamsteed, who in the year 
 
 * Kepler, De Stella Nova, cap. xxiii. p. 115. 
 + Ibid., cap. xxii., p. 112. 
 
 I Hevelius, Historiola Mirce Stellas, p. 147, fol, Gedan, 1662. 
 
 The researches of Bouillaud on the subject appeared in a small tract, entitled "Ad 
 Astronomos mo nita duo," Paris, 1667. 
 || Phil. Trans., 1783, p. 474, et seq. 
 
HISTORY OF PHYSICAL ASTRONOMY. 541 
 
 1696 noted it as a star of the third magnitude, \vith a corresponding ob- 
 servation of his own, he determined the period more accurately to be 
 2 d 20 h 48 m 66 s *. 
 
 Another interesting star, the discovery of whose variability is due to 
 Goodricke, is @ Lyrce. It was first recognised by him as subject to changes 
 of brightness in the year 1784. He was originally induced to fix the 
 period of variation at 6 d 9 h ; but after continuing his observations for 
 some time, he found that, although the course of the phases very nearly 
 agreed with this period, an exact compensation of brightness did not take 
 place in less than 13 d 19 h , there being in reality two maxima and two 
 minima. When it attains its maximum brightness, it is equal to a star of 
 the third magnitude. At one of its minima, it appears between the 
 fourth and fifth magnitude, and at the other between the third and 
 fourth f. These interesting particulars have been fully confirmed by the 
 recent researches of M. Argelander. 
 
 It may be remarked respecting variable stars, that in passing through 
 their successive phases, they are subject to sensible irregularities, which 
 have not hitherto been reduced to fixed laws. In general they 
 do not always attain the same maximum brightness, their fluc- 
 tuations being in some cases very considerable. Thus, according to 
 Argelander, the variable star in Corona Borealis, which Pigott dis- 
 covered in 1795, exhibits on some occasions such feeble changes of 
 brightness, that it is almost impossible to distinguish the maxima from 
 the minima by the naked eye ; but after it has completed several of its 
 cycles in this manner, its fluctuations all at once become so considerable, 
 that in some instances it totally disappears. It has been found, 
 moreover, that the light of variable stars does not increase and di- 
 minish symmetrically on each side of the maximum, nor are the succes- 
 sive intervals between the maxima exactly equal to each other. 
 
 Several persons have endeavoured to account for the phenomena of 
 variable stars, but no satisfactory view of the subject has yet been 
 arrived at by any enquirer. Bouillaud sought to account for the variations 
 of o Ceti, by attributing to the star a rotation round a fixed axis, 
 and supposing the greater part of its surface to be obscure. According 
 to Maupertius, some stars, by whirling rapidly round their axes, became 
 flattened to such an extent as to resemble millstones : they were, more- 
 over, liable to periodic perturbations from the action of opaque bodies 
 revolving round them. Hence, \vhen one of such stars presented its 
 flattened surface to the earth, it shone with its maximum brightness, 
 and when seen edgewise, its lustre was manifestly a minimum. Good- 
 ricke suggested that the variations of Algol might perhaps arise from the 
 periodic transit of an opaque planet revolving round the star. Pigott 
 assimilated the phenomena of variable stars to the solar spots, and this 
 view of the subject is beyond doubt the most satisfactory that has yet 
 been advanced. 
 
 The Photometry of the stars, although forming one of the most im- 
 portant subjects of Stellar Astronomy, has hitherto remained in a very 
 imperfect condition. The usual mode of designating the brightness of 
 the stars by arranging them according to different magnitudes, is both 
 vague in theory and contradictory in practice. It is vague, inasmuch as 
 the place of a star in the scale of magnitudes conveys no definite idea of 
 
 * Phil. Trans., 1784, p. 289. f Phil. Trans., 1785, p. 153, et scq. 
 
542 HISTORY OF PHYSICAL ASTRONOMY. 
 
 the quantity of light emitted by it relative to any other star whose place 
 is assigned in the scale ; and it is contradictory, inasmuch as in number- 
 less instances the same star has a different magnitude assigned to it by 
 different authorities. Bailly proposed ^to amend the system of stellar 
 nomenclature by determining the brightness of each star upon strict photo- 
 metrical principles. To this end he suggested that all the stars should 
 be observed with the same telescope, and that in every instance the aper- 
 ture should be diminished until the star just ceased to be visible *. It is 
 obvious that the light usually emitted by any star to the earth would then 
 be inversely proportional to the corresponding aperture. This mode of 
 determining the relative brightness of the stars is unexceptionable in 
 point of theory, but practical difficulties have hitherto stood in the way of 
 its adoption as the basis of a new system of nomenclature. 
 
 Sir William Herschel rejected the system of magnitudes altogether, as 
 unworthy of any reliance, and determined the relative brightness of a great 
 number of stars visible to the naked eye, by comparing each star with the 
 other stars in its vicinity, and noting those which were sensibly equal to 
 it in lustre, or differed from it only in a very small degree. The results 
 of his labours on this occasion form a valuable record for ascertaining at 
 some future epoch whether any of the stars to which they refer have 
 undergone a variation of lustre f . 
 
 More recently Sir John Herschel has employed a similar method in 
 connecting a great number of stars distributed over both hemispheres in 
 one unbroken chain of relative brightness, and has also succeeded in 
 adapting the results to the conventional system of magnitudes so as to 
 represent the brightness of the various stars according to the usual 
 nomenclature, but in a vastly-improved condition as respects accuracy of 
 detail. The same distinguished astronomer has moreover determined, by 
 a series of photometrical experiments, the quantity of light actually 
 emitted by each star relative to a certain standard star considered as 
 the unit of light, and has instituted a comparison between the results 
 and the corresponding magnitudes of the stars. The conclusion to which 
 he was conducted by his researches on this occasion, is at once curious 
 and instructive. It appeared that if the conventional magnitudes of the 
 stars as rectified by him, were all increased by the common fraction 0-414, 
 the squares of the resulting magnitudes would then be inversely pro- 
 portional to the corresponding photometric numbers, representing the 
 light of the stars as determined by experiment. Now this is precisely 
 the relation that would subsist between the distances of the stars from the 
 earth, and their respective photometric intensities, on the probable sup- 
 position that they all yield the same quantity of light at the same distance. 
 It follows, therefore, that the ordinary nomenclature of magnitudes, when 
 sufficiently amended, represents pretty nearly the order of the distances 
 of the stars, and would even rigorously do so, provided the magnitudes 
 were augmented by the common fraction above mentioned {. An example 
 will illustrate this curious conclusion more clearly. The bright star a 
 Centauri being assumed as the standard unit in the scale of conventional 
 magnitudes, the star Antares, according to Sir John Herschel, will be 
 represented in the same scale by 1-6. Now if the distance of Centauri 
 
 * Mem. Acad. des Sciences, 177 1, p. 580. 
 
 t See Phil. Trans., 1790, 1797, 1799. 
 
 $ Results of Ast, Observ., &c., p. 304, et seq. 
 
HISTORY OF PHYSICAL ASTHONOMY. 543 
 
 from the earth be at the same time assumed as the unit of distance, it 
 would follow from the photometric experiments of the astronomer just 
 mentioned, that the distance of Antares, as deducible from the quantity of 
 light which it emits, would he represented by 2'014, which is equal to 
 1*6 -f- -414. Consequently, if the nomenclature of the stars was so mo- 
 dified that the magnitude of Antares, as it stood in the old scale, was 
 increased by '414, the resulting magnitude would then afford an accu- 
 rate representation of the relative distance of the star; and the same 
 may be said of all the other stars whose conventional magnitudes have 
 been rectified by Sir John Herschel *. 
 
 Hooke appears to have been the first person who considered the mode 
 in which the visibility of the stars depends upon the telescope. In his 
 Micographia he remarks that the number of stars visible in a telescope 
 will increase with the enlargement of the aperture, for, by uniting a great 
 number of rays into one point, many stars, which from their faintness 
 would otherwise be invisible, are thereby brought into view, and rendered 
 conspicuousf. In 1717, J. Cassini alluded to the same subject in a com- 
 munication to the Academy of Sciences, on the parallax of Sirius. He 
 remarked that the stars of the sixth magnitude are six times more remote 
 than those of the first, and hence he concluded, that with a telescope 
 magnifying 200 times, it would be possible to perceive stars that were 
 1200 times more remote than those of the first magnitude J. The visi- 
 bility of the stars is here made to depend wholly upon the magnifying 
 power of the telescope. That some obscure connexion really does exist 
 between the two principles appears evident from the observations of sub- 
 sequent astronomers , but it has been no less unequivocally established 
 that the visibility of the stars mainly depends upon the magnitude of the 
 aperture. 
 
 Lambert, in his " Cosmological Letters," accounts for the power of the 
 telescope to render small stars visible by the superior precision of the 
 image which it forms, when compared with that formed by the naked eye. 
 He makes no allusion whatever to the magnitude of the aperture, but he 
 expressly asserts that the visibility is independent of the magnifying 
 power. Michell, in the year 1767, took a more correct view of the sub- 
 ject, making the visibility to depend on the magnitude of the aperture. 
 Assuming the diameter of the pupil of the eye to be equal to one-third of 
 an inch, and roughly estimating the quantity of light lost in passing 
 through the telescope, he was enabled to compare the distance of the 
 
 * The researches of Sir John Herschel do not extend to stars lower than those of the 
 fourth magnitude. It would appear from a recent, paper by Mr. Dawes (Mo. Proc. Ast. 
 Soc., June, 1851), that the nomenclature of telescopic stars, as indicated by the obser- 
 vations of Lalande, Bessel, and Argelander, is based upon a different principle. 
 
 f See the work cited, p. 241. 
 
 t Mem. Acad. des Sciences, 1717, p. 2CO. 
 
 Thus Sir William Herschel, in one of his earlier communications to the Royal So- 
 ciety, cites several instances of stars which could not be seen with a magnifying- power of 
 227, but which became distinctly visible when a power of 460 was applied (Phil. Trans., 
 1782, p. 92). Mr. Dawes has recently remarked that the aperture necessary to render 
 the stars steadily visible to him in a telescope magnifying sixteen times, is less than the 
 pupil of his eye, being only '15 inch in diameter, whereas he estimates that of the 
 pupil of his eye at "25 inch (Mb. Pro. Ast. Soc., June, 1851). Now in such a case 
 it might be expected that the aperture of the telescope would be greater than the pupil 
 of the eye, in order that a compensation might be effected for the light necessarily lost 
 in telescopic observation. Is not this apparent anomaly due to the influence of the mag- 
 nifying power, which, under certain circumstances, is favourable to the visibility of the 
 object, as in the instances above alluded to? 
 
544 HISTORY OF PHYSICAL ASTRONOMY. 
 
 faintest stars seen in a telescope of given aperture, with the distance of 
 those barely visible to the naked eye *. 
 
 The subject of the visibility of the stars has been fully considered by 
 Sir William Herschel, in an admirable paper which appears in one of the 
 volumes of the Philosophical Transactions}. By a series of photometrical 
 experiments, he determined the quantity of light lost in telescopes of dif- 
 ferent forms of construction. Assuming, moreover, that the pupil of the 
 eye was equal to two-tenths of an inch in diameter, he compared the dis- 
 tance at which a star would be barely visible in a telescope of given aper- 
 ture with the distance of the smallest stars visible to the naked eye, con- 
 sidered as the linear unit. The former of these distances was termed by 
 him the space-penetrating power of the telescope. Herschel, in accord- 
 ance with these principles, determined the space-penetrating powers of 
 various telescopes, differing either in construction or aperture, which he 
 employed in his observations. 
 
 Since the brightness of a star seen in a telescope depends upon the 
 magnitude of the aperture, it follows, that by gradually diminishing the 
 latter, the image of a star may be reduced to any degree of faintness we 
 please. Hence, if two stars of unequal brightness be observed with two 
 telescopes exactly similar in all respects, and if the aperture of the tele- 
 scope directed to the brighter star be reduced until both stars appear of 
 the same brightness, it is manifest that the absolute quantity of light 
 emitted by each star to the earth, will be in the inverse ratio of the aper- 
 ture of the telescope through which it is thus seen. Now, knowing the 
 relative quantities of light emitted by the two stars, their relative dis- 
 tances may be readily determined, supposing, as before, that both stars 
 possess the same degree of intrinsic brightness. Sir William Herschel 
 applied these principles to the determination of the relative distances of 
 the stars J and clusters of stars visible in his powerful telescopes. It is 
 impossible within the limits to which we are confined, to give any account 
 of the sublime results to which he was conducted by his labours on this 
 occasion. 
 
 The question with respect to the absolute distance of the stars from the 
 earth, is one which has excited a high degree of interest among astrono- 
 mers ever since the re-establishment of the true system of the world by 
 Copernicus. This might be ascertained in any case by a simple and direct 
 process, if the star exhibited a change of position depending on the mo- 
 tion of the earth in her orbit, but such a parallactic displacement was long 
 found to be insensible. Another mode of effecting the same object was 
 founded upon a knowledge of the apparent diameter of the star. Assum- 
 ing the star to be equal in absolute magnitude to the sun, it is clear that 
 the distance of the sun from the earth would be to the distance of the star 
 from the same body, as the apparent diameter of the star to the apparent 
 diameter of the sun. This mode of determining the distance of a star 
 was less satisfactory than that founded upon a knowledge of its parallax, 
 seeing that it involved an arbitrary assumption with respect to the mag-, 
 nitude of the star ; but still it was exceedingly desirable to arrive at some 
 probable conclusion upon the subject. It was soon found, however, that 
 the measurement of the apparent diameter of a star was an object of as 
 great delicacy as the detection of its parallax. The earlier astronomers, 
 indeed, supposed that the principal stars possessed an apparent magnitude 
 
 * Phil. Trans., 1767, p. 234, ct seq. f Ibid., 1800, p. 49, et seq. 
 
 Ibid., 1817, p. 302, ct seq. Ibid., 1818, p. 429, ct seq. 
 
HISTORY OF PHYSICAL ASTRONOMY. 545 
 
 of 2' or 3' * ; but the telescope shewed this to be to a great extent an illu- 
 sion, produced by the false light surrounding the star. Galileo attempted, 
 by a very ingenious method, to get rid of the effects of irradiation in 
 measuring the apparent diameter of Lyra3, and he so far succeeded in 
 his object as to assign to the star an apparent diameter of only 5"|. This 
 was undoubtedly a much nearer approximation to the truth than any esti- 
 mate that had been hitherto formed of the apparent magnitude of a star. 
 
 Horrocks first remarked a phenomenon -which furnishes a striking 
 proof of the extreme smallness of the apparent diameters of the stars. 
 In company with his friend Crab tree, he witnessed an occultation of the 
 Pleiades by the moon, on the evening of the 39th of March, 1687. As 
 soon as the stars approached in succession the dark limb of the moon, 
 they were in each instance observed to vanish instantaneously]:. Horrocks 
 justly asserted, that if the whole of the light in each case had emanated 
 directly from the body of the star, the latter ought to have disappeared by 
 sensible gradations. He therefore concluded that the apparent diameters 
 of the stars are mere points which are not capable of measurement. 
 
 Hevelius, by diminishing the aperture of his telescope, succeeded in 
 giving a round planetary appearance to the stars, and he determined the 
 apparent diameters of the resulting disks by comparing them in succes- 
 sion with Mercury, whose apparent diameter he had previously ascer- 
 tained from observations of its transit across the sun's disk. In this 
 manner he found the apparent diameter of Sirius to be 6" 21'"; that of 
 Procyon, 4" 58"', &c., &c. . In 1717, J. Cassini observed Sirius with a 
 telescope, the aperture of which he had similarly reduced, and by com- 
 paring the round disk thus formed with the planet Jupiter, he concluded 
 that the apparent diameter of the star did not exceed 5"(|. Both He- 
 velius and Cassini erred in supposing that the round appearance of stars 
 seen in telescopes with reduced apertures was real. The phenomenon is, 
 in fact, a spurious image produced by the diffraction of the light in passing 
 the contour of the aperture. 
 
 Halley did not fail to express his suspicion that the apparent diameter 
 ascribed by J. Cassini to Sirius was an optical fallacy, occasioned by the 
 great contraction of the aperture of the object-glass IF. From the instan- 
 taneous disappearance of stars on the occasion of their occultation by the 
 moon, he concluded, as Horrocks had already done, that the apparent 
 diameters of the stars is excessively small. He considered that the appa- 
 rent diameters of Spica Virginis and Aldebaran were in both cases less 
 than 1". Michell supposed that the diameter of Sirius was even less than 
 0".08. We thus see that the progress of research on the subject tended 
 invariably to assign a less and less apparent diameter to the stars. 
 
 * Tycho Brahe estimated the apparent diameters of the stars of the first magnitude at 
 2' ; those of the second at 1^' ; those of the third at l T y ; those of the fourth at f ; those 
 of the fifth at ' ; and those of the sixth at '. (Progymnasmata, p. 482.) 
 
 >t* Opere de Galileo, tome iv., p. 259. 
 
 $ " Venus in Sole Visa," p. 139. The merit of having originally deduced from this 
 phenomenon a proof of the extreme smallness of the apparent diameters of the stars has 
 been erroneously ascribed by some writers to Halley, upon the strength of a remark made 
 by that philosopher, in 1718, relative to the same subject. (Phil. Trans., 1718, p. 853.) 
 
 " Mercurius in Sole Visus," p. 92. Hevelius states on this occasion that he saw Sirius 
 with the naked eye, on the morning of October 2, 1661, when the sun had already 
 ascended above the horizon. 
 
 || Mem. Acad. des Sciences, 1717, p. 258. 
 
 t Phil. Trans., 1720, p. 3. 
 
 N N 
 
546 HISTORY OF PHYSICAL ASTRONOMY. 
 
 Sir William Herschel devoted considerable attention to the subject of 
 the apparent diameters of the stars, but he was unable to effect any mea- 
 surement on which he could rely with sufficient confidence. As might be 
 expected, he made the real apparent magnitudes of the stars to be less 
 than any other astronomer had hitherto determined them to be from 
 observation. On the 22nd of October, 1781, he observed the bright star a 
 Lyr, with a power of 6450, and, having measured the apparent diameter 
 with the micrometer, he found it amount to 0".3553 *. It may not be un- 
 interesting to compare the absolute magnitude which this result would 
 assign to the star, with the absolute magnitude of the sun. To this end it 
 may be remarked that the parallax of . Lyrse, as determined in recent times 
 by M. Struve, amounts to 0".261. Its distance from the earth exceeds, 
 therefore, the radius of the terrestrial orbit in the proportion of 790,283 
 to 1. Hence, if we suppose the sun to be transported to this distance, 
 his apparent diameter (estimated at the mean value of 32') would be 
 diminished in the same proportion, and would therefore be equal only 
 to 0".0024. Now the apparent diameter of a Lyrse, as determined by 
 Herschel, exceeds this quantity in the proportion of 148 to 1. It follows, 
 therefore, either that the result obtained by Herschel on this occasion 
 differs widely from the true value, or that a Lyras vastly exceeds the sun 
 in absolute magnitude. It can hardly be doubted that the physical 
 anomaly which here presents itself, is mainly due to an erroneous determi- 
 nation of the apparent diameter of the star. Indeed, as has been already 
 remarked, Herschel does not appear to have reposed any confidence in 
 such measurements, being of opinion that the round appearance of the 
 stars, even when seen in the most perfect telescopes, was almost wholly 
 spurious. 
 
 When the stars are observed with telescopes of great optical perfection, 
 furnished with high magnifying powers, they are generally found to 
 exhibit a well-defined planetary appearance, even although the aperture 
 should not be reduced. There is also visible around the disk of the star 
 an alternate succession of dark and bright rings of uniform breadth. It 
 has been already mentioned that the round disk is a spurious pheno- 
 menon, occasioned by the diffraction of light. The rings have also been 
 satisfactorily explained by the same principle. It is important to remark, 
 that these phenomena would be produced in greatest perfection if the star 
 was merely a physical point of light. Mr. Airy, by a mathematical inves- 
 tigation, has rigorously accounted for the appearance of the disk and sur- 
 rounding rings, upon the principle of the mutual interference of the rays 
 of light, and has also explained a part of the phenomenon which had 
 hitherto seemed very obscure, namely, the dependence of the magnitude 
 of the disk on the intensity of the light of the star f . 
 
 The parallax of the fixed stars having been found for a long time to be 
 insensible, attempts were made to determine their distances from the 
 earth by photometrical principles. Assuming the stars to be equal to the 
 sun, both in magnitude and intrinsic splendour, it is clear, since light 
 diminishes in the inverse ratio of the square of the distance, that the 
 light of the sun will be to the light of any of the stars, as the square of 
 the distance of the star from the earth to the square of the distance of 
 the sun. Hence, if the quantity of light sent to us by the star be 
 determined relatively to the light of the sun, its distance from the earth 
 
 * Phil. Trans., 1782, p. 147. f Camb. Phil. Trans., vol. v., p. 283. 
 
HISTORY OF PHYSICAL ASTRONOMY. 547 
 
 may be ascertained by a simple process of arithmetic. James Gregory 
 appears to Lave first suggested this mode of determining the distance of 
 a star from the earth.- Huyghens, by applying it to Sirius, found that 
 the distance of that star from the earth exceeded the distance of the 
 sun 28,000 times. The same method subsequently attracted the atten- 
 tion of various astronomers, among whom may be mentioned Chesaux, 
 Lnmbert, Michell, and Olbers, who all agree in assigning to the stars of 
 the first magnitude a parallax less than 0".5, as the result of its application. 
 
 Wollaston found that the light of Sirius appeared equal to that of the 
 sun when reflected from the surface of a sphere -y^th of an inch in 
 diameter, and seen at the distance of 210 feet. Supposing the half of 
 the solar light to be lost during reflexion, he hence concluded that the 
 light of the sun was to that of the star as 20,000 millions to one. 
 Hence, if we assume the star to be equal in magnitude and intrinsic 
 splendour to the sun, this result would imply that the distance of the star 
 from the earth is 141,421 times greater than the distance of the sun, 
 whence its parallax would amount to 1".8*. It has been ascertained, 
 however, from the observations of astronomers, that the parallax of 
 Sirius is in reality less than half a second. The conclusion therefore 
 is, that in magnitude the star greatly surpasses the sun. 
 
 Wollaston found by a similar method, that the light of the sun was 
 to the light of Lyrse, as 180 thousand millions to one, and consequently 
 that the light of a Lyrae was only one-ninth of that of Sirius. This would 
 imply that Lyraa was three times more distant than Sirius, and that its 
 parallax was therefore only 0".6. Even this, however, considerably ex- 
 ceeds the true value as recently determined by M. Struve. 
 
 It has been already mentioned, that the attempts of the earlier astro- 
 nomers to detect an annual variation in the apparent places of the stars, 
 depending on the motion of the earth in her orbit, was not attended with 
 any success. Copernicus attributed the absence of all sensible indication 
 of 'parallax to the immense distance of the stars compared with the radius 
 of the terrestrial orbit. Tycho Brahe, although possessing instruments of 
 much more perfect construction than any hitherto employed for the pur- 
 poses of astronomical observation, was unable to detect the slightest trace 
 of an annual displacement in any of the stars. On the other hand, he 
 estimated the stars of the first magnitude to have an apparent diameter 
 of about 2' or 3'. He asserted, therefore, that if the earth really moved 
 round the sun, it would necessarily follow that the stars of the first 
 magnitude exceeded in dimensions the whole amplitude of the terrestrial 
 orbit, a conclusion, which appeared to him to be palpably absurd, and fatal 
 to the Copernican theory of the universe. 
 
 Galileo suggested a mode of investigating the parallax of the fixed 
 stars, which has received more than one successful application in recent 
 times. He remarked, that in those instances wherein two stars of un- 
 equal magnitudes are apparently very near to each other, it may be 
 presumed that the smaller of the two stars, appears so only from its 
 being more distant, and therefore that its parallax may be considered as 
 insensible relative to the parallax of the larger star. He imagined, 
 therefore, that by continuing to observe the position of the larger star 
 with respect to the smaller, throughout the course of the year, the 
 parallax of the larger star might be detected f. This method obviously 
 
 * Phil. Trans., 1829, p. 19, et seq. + Opere di Galileo, tome iv., p. 272. 
 
 N N 2 
 
548 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 afforded a more favourable chance of detecting the parallax of a fixed 
 star, than that founded on observations of the absolute position of the 
 star in the celestial sphere. It does not appear that Galileo attempted 
 on any occasion to reduce it to practice. 
 
 Hooke first employed the telescope in observations for the purpose of 
 detecting the annual parallax of the fixed stars. In order to avoid the 
 eifects of refraction, he confined his observations to the star y Draconis, 
 which passes near the zenith of Gresham College, London, where his 
 observatory was established. From four observed zenith distances of the 
 stars, as determined by him in the months of July, August, and October 
 of the year 1669, with a zenith sector 36 feet long, he concluded that 
 the star had an annual parallax, amounting to somewhere between 27" 
 and 30"*. It is to be remarked, however, that Picard, a few years after- 
 wards, observed the altitude of Lyrse at both solstices, but was unable 
 to detect the slightest trace of parallax f. 
 
 Previous to the discovery of the Aberration of Light, the displacement 
 due to that principle exhibited itself in the observations of several 
 astronomers, who, in some instances, were induced erroneously to at- 
 tribute it to the effects of parallax. In all probability the variations in 
 the apparent place of y Draconis, observed by Hooke, proceeded from 
 this cause. This was certainly the case with respect to Flamsteed, who, 
 from a series of observations of the zenith distance of the polar star, 
 made by him at Greenwich with the mural arc, between the years 1689 
 and 1697, concluded that the star possessed an annual parallax equal 
 to at least 40" {. J. Cassini shortly afterwards remarked, with justness, 
 that the displacement indicated by the observations of Flamsteed, was 
 incompatible with the supposition of its being produced by parallax . 
 It has been already mentioned, that the variations in the position of 
 the pole star, detected by Flamsteed on this occasion, were, in reality, 
 the results of aberration, the maximum value of which is cleducible 
 with an astonishing degree of accuracy from the observations of that 
 astronomer 1|. It may be mentioned, that, about the same time, Wallis 
 suggested observations of the greatest azimuth, east or west of a circum- 
 polar star, as favourable for the detection of parallax, since the effect of 
 refraction would thereby be completely avoided^". It does not appear that 
 any astronomer attempted to reduce this method to practice. 
 
 Horrebow states that, in the years 1 692-3, Roemer remarked a series 
 of irregularities in the declinations of the stars, which could not be 
 accounted for either by parallax or refraction, but which he suspected 
 to arise from a variation in the position of the terrestrial axis, the theory 
 of which he hoped to assign on some future occasion**. It cannot 
 udmit of any doubt that the anomalies observed by that distinguished 
 astronomer were attributable to the effects of aberration which hitherto 
 continued to be unaccounted for. Dismissing the declinations as not suffi- 
 ciently trustworthy in so delicate an enquiry, Roemer attempted to deduce 
 the parallax of the fixed stars from observations of their right ascensions. 
 By a series of observations of Sirius and Lyra, made at different 
 seasons of the year, he found that the aggregate of the parallaxes of the 
 two stars produced an annual variation in the difference of their right 
 
 * " Attempts to Prove the Motion of the Earth," p. 7. 
 
 f Lemonnier, Hist. Celeste, p. 252. \ Wallis's " Opera Mathematica,"tom. iii.,p. 705. 
 Mem. Acad. des Sciences, 1699, p. 177. || See chapter xiv. 
 
 f Phil. Trans., 1693, p. 844. ** Basis Astronomise, p. 66. 
 
HISTOEY OF PHYSICAL ASTRONOMY. 549 
 
 ascensions, amounting to somewhere between l m and lj m . It has been 
 proved by the observations of subsequent astronomers, that such a dis- 
 placement could not have arisen from the effects of parallax. The same 
 may be said respecting a series of results which Horrebow deduced at a 
 subsequent period from the observations of Ptoemer, and which he 
 published with great confidence, as affording incontestable evidence of the 
 motion of the earth, in his work entitled " Copernicus Triumphans." 
 
 It has been already mentioned, that, in an attempt to establish the 
 existence of a sensible parallax in y Draconis, Bradley was conducted 
 to his immortal discovery of the aberration of light. This important 
 result put an end to the anomalous irregularities which continued to 
 affect the observations of astronomers, ever since they became sufficiently 
 accurate to render sensible the displacement arising from that cause. It 
 was now evident that the parallax of the fixed stars was in all cases 
 vastly smaller than it had hitherto been supposed to be. Bradley was of 
 opinion that if the parallax of y Draconis had amounted even to I", his 
 observations with the zenith sector could not fail to have detected its 
 existence *. 
 
 Allusion has been made to the method proposed by Galileo for deter- 
 mining the parallax of a star. The invention of the micrometer, about 
 the middle of the seventeenth century, tended very much to enhance the 
 practical utility of that method. It was probably this circumstance 
 which induced James Gregory to recommend its application in a letter- 
 to Collins, the Secretary of the Koyal Society, dated June 24, 1673 f. 
 Gregory does not seem to have been aware that Galileo had already 
 suggested the same method. Huyghens appears to have been the person 
 who first reduced it to practice. He mentions, in one of his works, that 
 he in vain attempted to detect any traces of an annual change in the 
 relative position of the two stars composing the middle star in the tail of 
 the Great Bearj (f Ursa Majoris). In the following century Dr. Long 
 endeavoured to detect a similar variation in the relative positions of 
 several double stars, but all his efforts were fruitless . It is . to be 
 remarked, with respect to the stars upon which he made his observations, 
 that the component objects in each case were nearly equal in apparent 
 magnitude, whence it might be presumed that they were equally distant 
 from the earth. The absence of an indication of change in their relative 
 positions did not, therefore, necessarily imply the non-existence of a sen- 
 sible parallax. 
 
 The parallax of the fixed stars was one of the earliest subjects which 
 engaged the attention of Sir William Herschel||. He did not fail to 
 perceive the many peculiar advantages which the method of Galileo 
 offered, and, with a view to its practical application, he selected a great 
 number of double stars, which, in consequence of the inequality of the 
 component members, in every case appeared to be well adapted for that 
 purpose. His labours on this occasion are memorable in the history of 
 astronomy, on account of their having been instrumental in enabling him 
 to establish the existence of a physical connexion between the bodies com- 
 posing Double Stars. 
 
 About the beginning of the present century, the celebrated Piazzi 
 endeavoured to ascertain the parallax of some of the principal stars by 
 means of their declinations, as observed with the famous altitude and 
 
 * Phil. Trans., 1728, p. 637. f Birch, Hist. Roy. Soc., vol iii. p. 225. 
 
 J Cosraotheoros, p. 134. Astronomy, vol. i., p. 322, Camb. 1742 
 
 || Phil. Trans., 1792, p. 82, et seq. 
 
550 HISTORY OF PHYSICAL ASTRONOMY. 
 
 azimuth instrument of Ramsden. From such data he determined the 
 parallax of Sirius to be 4", and that of Procyoii to be 8". The researches 
 of subsequent astronomers have not confirmed these results ; indeed, 
 there was very little confidence reposed in them even at the time of 
 their first announcement. The same may be said respecting the contem- 
 poraneous labours of Calandrelli, the countryman of Piazzi, who, from 
 observations of . Lyree at Rome, deduced a parallax of 3". 9. 
 
 A few years afterwards Dr. Brinkley undertook a series of observa- 
 tions of several of the principal stars, with the view of detecting the 
 existence of a sensible parallax in some of them. His researches were 
 founded on the declinations of the stars, as determined by him at the 
 Observatory of Dublin, with a magnificent altitude and azimuth circle, 
 eight feet in diameter, designed by Ramsden, and partially executed by 
 that famous artist. The results at which he finally arrived seemed to 
 indicate that some of the principal stars really possessed a parallax 
 amounting to a few seconds of space, but their accuracy was disputed 
 by Pond, the Astronomer Royal, who was unable to deduce analogous 
 results from the observations with the mural circle, recently erected at 
 Greenwich. A controversy thereupon arose between the two astronomers, 
 which was maintained for several years with great vigour and ability on 
 both sides, but which finally terminated, leaving the question at issue still 
 undecided. It is now well ascertained that Pond was right in his conclu- 
 sions, but it must be admitted, on the other hand, that the anomalous 
 results obtained by his opponent have not been satisfactorily accounted 
 for. This celebrated controversy, if it did not lead to the object originally 
 contemplated by Brinkley, was not unproductive of advantages of great 
 importance, in so far as the ultimate accomplishment of that object was 
 concerned ; since it had the effect of placing in a vastly clearer light than 
 hitherto, the influence of the various disturbing causes which go to com- 
 plicate the observations of astronomers, and which completely efface the 
 delicate variations arising from the parallax of the fixed stars, unless 
 rigorously taken into account*. 
 
 During the interval included between the years 1818 and 1821, M. 
 Struve made a series of observations of circumpolar stars at Dorpat, 
 with the view of detecting a sensible parallax in some of them. His 
 method consisted in observing the stars by pairs, selecting those which 
 were nearly opposite in right ascension, so that the superior passage of 
 one of the stars took place almost simultaneously with the inferior pas- 
 sage of the other ; and the evidence of parallax was sought for, by com- 
 paring the differences of the right ascensions of the two stars as determined 
 at various times throughout the year. The researches of M. Struve 
 seemed to indicate the existence of a sensible parallax in several in- 
 stances, but the results were in all cases so insignificant, and consequently 
 the probability was so much the stronger of their being produced by 
 disturbing causes, whose influence had not been taken into account, that, 
 notwithstanding the acknowledged reputation of the astronomer to whom 
 they were due, they did not generally command the confidence of the 
 scientific world. 
 
 In the year 1835 M. Struve commenced a series of observations with 
 the view of detecting the parallax of the bright star a Lyras. The 
 method pursued by him on this occasion, consisted in measuring with 
 
 * See, on the subject of this controversy, the Philosophical Transactions for 1810- 
 17-18-21-23-24; also vols. xii. and xiv. of the Transactions of the Royal Irish 
 Academy. 
 
HISTORY OF PHYSICAL ASTKONOMY. 551 
 
 a micrometer the distance between the star and another very small star, 
 situate about 43" from it, repeating the operation at different seasons 
 throughout the year. The result of this enquiry went to assign a parallax 
 of 0".261 to the brighter of the two stars. 
 
 Shortly afterwards, the existence of an annual variation of sensible 
 amount in the apparent position of a star, depending on the motion of 
 the earth in her orbit, was established beyond all doubt, in two instances, 
 by the independent labours of two contemporary astronomers. The stars, 
 whose absolute distances have been thus ascertained, are 61 Cygni and 
 . Centauri, the parallax of the former having been determined by Bessel, 
 and that of the latter by the late Professor Henderson, of Edinburgh. It 
 is impossible, within the limits to which we are confined, to do anything 
 else than merely bestow a passing glance on the important researches 
 of these astronomers on this occasion. 
 
 The star 61 Cygui, besides being double, is remarkable for an unusually 
 large proper motion. It appears, in fact, from the observations of astro- 
 nomers, to be transported through space with an annual motion of rather 
 more than 5" of arc. This circumstance induced Bessel to suspect that 
 its parallax must be very considerable, and he resolved accordingly to 
 ascertain its amount. He chose for this purpose two very small stars, 
 one at the distance of ll'.S from the centre of the line joining the two 
 component members of 61 Cygni, and the other at the distance of V.! 
 from the same point ; and the establishment of the parallax of the star 
 depended on the detection of an annual variation of these distances, as 
 determined by observation at different seasons of the year. The distances 
 were ascertained by means of a magnificent heliometer, which Fraun- 
 hofer, of Munich, had recently executed for the Observatory of Ko'nigs- 
 berg, and which, from the principle of its construction, was eminently 
 adapted for micrometric measurements on so large a scale. The observa- 
 tions were commenced in the month of October, 1837, and were continued 
 till March, 1840. By a subsequent discussion of them, in which every 
 imaginable cause of disturbance was taken into careful consideration, and 
 its effect rigorously calculated, Bessel arrived at the final conclusion that 
 the parallax of the star amounts to O r/ .3483. This result has received a 
 complete confirmation from the recent researches of M. Peters, who, from 
 a series of zenith distances of the star, determined at the Observatory of 
 Pulkowa during the years 1842-3, has found its parallax to be equal to 
 (T.349. 
 
 It has been mentioned, that the other astronomer who succeeded in 
 establishing by unequivocal evidence the existence of a sensible parallax 
 in one of the fixed stars, was the late Professor Henderson, of Edinburgh. 
 The double star, a Centauri, which was the object of his researches on 
 that occasion, is one of the brightest sidereal objects in the southern he- 
 misphere. His investigation was founded on the zenith distances of the 
 star as observed by himself at the Cape of Good Hope, with a mural 
 circle, during the years 1832-3. These observations were made with the 
 view of establishing the mean declination of the star. It was only from 
 a consideration of the large proper motion of the star, which amounts 
 annually to 3". 6 of arc, that he was, induced several years afterwards to 
 institute an enquiry into its parallax. The result at which he arrived 
 confirmed his previous suspicion, the star having been found by him to 
 have a parallax of 1".16. The researches of Mr. Maclear, the successor 
 of Henderson at the Cape of Good Hope, have completely verified the 
 
552 HISTOKY OF PHYSICAL ASTKONOMY. 
 
 existence of a sensible parallax in the star, the final result obtained by him 
 being only a small fraction less than that deduced by Henderson. From 
 observations made at the Cape, during the years 1839-40, Mr. Maclear de- 
 termined the parallax of the star to be 0'.9128, and from still more recent 
 observations, extending down to 1848, he has found it to be 0".9187. The 
 latter may be considered as the definitive value of the parallax of the star. 
 
 The parallax of a Centauri, as determined by the researches of Mr. 
 Maclear, assigns to the star a distance from the earth which may be said 
 to amount, in round numbers, to 20 billions of miles. The successive 
 propagation of light supplies the only means of forming anything like an 
 adequate conception of this immense distance. Now light traverses space 
 at the rate of 192,000 miles in a second of time, and consequently the 
 distance traversed in a year would extend to 6.059 billions of miles. 
 Hence it follows, that notwithstanding the amazing velocity of this agent, 
 it would require about three years and a quarter to pass from a Centauri 
 to the earth. The distance of 61 Cygni is about 60 billions of miles'; 
 consequently the light of that star does not reach the earth in less than 
 ten years after its emission ! 
 
 Knowing the parallaxes of 61 Cygni and a Centauri, and also their 
 apparent proper motions, it is hence easy to deduce the absolute amount 
 of space through which each of these stars is transported in the course of a 
 year. Thus, in the case of 61 Cygni, which has an annual proper motion 
 of about 5", since the radius of the terrestrial orbit subtends only an angle 
 of // .348 when viewed at the distance of the star, it follows, that the 
 space through which the star is annually transported in virtue of its 
 proper motion, exceeds the radius of the terrestrial orbit in the proportion 
 of 5" to O r/ .348. Now the radius of the terrestrial orbit may be esti- 
 mated, in round numbers, at 95 millions of miles. Hence it may be ascer- 
 tained, by a simple process of arithmetic, that the star, 61 Cygni, whose 
 proper motion can only be established by observations of the most delicate 
 kind, and which in consequence was long regarded as a fixed star, is 
 continually transported through space at the annual rate of 1 333 millions 
 of miles ! In the same way it may be shewn, that the linear space 
 through which a Centauri is transported in the course of a year, amounts 
 to no less than 371 millions of miles. It is manifest, from these 
 numbers, that the epithet, fixed, can no longer be regarded as an appro- 
 priate designation of any class of the celestial bodies. 
 
 Allusion has been made to M. Struve's investigation of the parallax of 
 a Lyra3. The more recent researches of M. Peters, tend to prove that 
 the star has a sensible parallax, although the result is considerably less 
 than the parallax previously assigned to the star by M. Struve. As- 
 suming the latter to be the true value, as being determined by a more 
 trustworthy method than that founded on observations of the zenith 
 distance of the star, which formed the groundwork of M. Peters' re- 
 searches, we may, by combining it with the light of the star as ascertained 
 by the experiments of Wollaston, arrive at an evaluation of the absolute 
 magnitude of the star. To this end it may be remarked that the parallax 
 0".261, arrived at by M. Struve, supposes the distance of a Lyr from 
 the earth to exceed the distance of the sun from the earth in the propor- 
 tion of about 800,000 to 1. Now if the sun was transported to this distance, 
 it would follow, from the diminution of light according to the reciprocal 
 of the square of the distance, that the actual light of the sun would ex- 
 ceed the light he would then emit, in the proportion of 640,000 millions 
 
HISTORY OF PHYSICAL ASTRONOMY. 553 
 
 to 1. But Wollaston found that the actual light of the sun exceeded the 
 light of a Lyrse, only in the proportion of 180,000 millions to 1. It 
 follows, therefore, that the light of a Lyres would exceed that of the sun 
 placed at the same distance, in the proportion of 64 to 18, or, in other 
 words, the light of a Lyras is equal to that afforded by 3.5 suns. 
 
 In addition to the parallaxes of 61 Cygni and * Lyrae, M. Peters has in- 
 vestigated those of several other stars. The groundwork of his researches 
 in all these instances consisted of a series of apparent zenith distances 
 of the stars determined at the Observatory of Pulkowa, with the great 
 vertical circle by Ertel, during the years 1842-3. The results have been 
 employed by him in establishing the mean value of the parallax of a star 
 of the second magnitude, which he finds to amount to // .116. Hence it 
 may be readily inferred that the light from one of such stars would not 
 reach the earth in less than 28 years. Combining the result at which 
 he had arrived relative to the mean parallax of a star of the second mag- 
 nitude, with the relative distances of the stars of successive magnitudes, 
 as determined by M. Struve, in his Etudes d "Astronomic Stellaire, M. 
 Peters was enabled to estimate the parallaxes of the stars of the various 
 orders, from the stars of the first magnitude down to the smallest stars 
 visible in the 20-feet reflecting telescope of Herschel. In this manner 
 he found that the distance of the smallest stars visible to the naked eye 
 is such, that the light emitted by them does not reach the earth in less 
 than 138 years. He also found that the light from one of the smallest 
 stars visible in the 20-feet reflecting telescope of Herschel, occupied 
 3541 years in traversing the distance between the star and the earth ! 
 These results can of course only be regarded as provisional, until obser- 
 vations of sufficient delicacy be amassed, which shall form the groundwork 
 of a more rigorous investigation of the subject ; but, being founded upon 
 principles which present a strict accordance with analogy, they cannot fail 
 to prove highly interesting and suggestive to the reflecting mind. 
 
 Although it was long generally supposed that the stars are absolutely 
 immoveable with respect to each other, there were occasionally indi- 
 viduals of an original turn of mind who refused their assent to a prin- 
 ciple which formed so striking an anomaly to all the other arrangements 
 of nature, and who ventured to suggest the probability of a motion of the 
 stars, inter se, before the observations of astronomers acquired a suf- 
 ficient degree of precision to indicate even the slightest trace of its 
 real existence. Among these may be mentioned Jordano Bruno, an 
 Italian philosopher of the sixteenth century, whose abjuration of the 
 Komish faith, and vigorous exposure of the fallacies of the Aristotelian 
 physics, the adherents of which were closely leagued with the Church in 
 repressing all rational enquiry, unfortunately led to the forfeiture of his 
 life. This daring, although somewhat eccentric individual, believed that 
 the stars are all equal to the sun in magnitude and splendour; and that 
 the universe is peopled with an innumerable multitude of such bodies. 
 He maintained that we are not warranted in supposing that they are all 
 fixed with respect to each other* since their distance from the earth is so 
 immense, that it would be difficult to estimate their motions ; and he 
 remarked, that it could only be decided after a long course of observation, 
 whether the stars revolved round each other, or what other motions they 
 might have*. Hooke, whose genius threw a gleam of light on every 
 
 * Jordano Bruno was born about the middle of the sixteenth century, at Nole, in 
 the kingdom of Naples. In early life he entered the order of Dominicans ; but having 
 
554 HISTORY OF PHYSICAL ASTRONOMY. 
 
 subject of physics which engaged his attention, did not fail to perceive 
 the improbability of the stars being absolutely fixed with respect to each 
 other, and he suggested that not only these bodies, but the whole solar 
 system might be in a state of continual notion*. 
 
 The first person who suspected, from observation, that the stars have a 
 proper motion, was the celebrated Edmund Halley. His remarks on the 
 subject are contained in a paper which is inserted in the Philosophical 
 Transactions for 1718. By comparing the observations of the earlier 
 astronomers of the Alexandrian school with those of more recent times, 
 he was led to conjecture that the stars Aldebaran, Arcturus, and Sirius 
 were advancing slowly towards the south. In 1738 J. Cassini commu- 
 nicated a memoir on the same subject to the Academy of Sciences, which 
 served to confirm the justness of Halley 's surmise. By comparing the 
 observations of Arcturus made by Richer, at Cayenne, in 1672, with 
 similar observations executed in his own time at Paris, he found that the 
 latitude of the star had undergone a sensible change during the included 
 interval. It was still uncertain, however, whether this proceeded from a 
 displacement of the ecliptic, or from an actual change in the position of 
 the star. J. Cassini demonstrated, by the most conclusive evidence, that 
 the phenomenon was attributable to the latter cause. He found, in fact, 
 that while Arcturus had shifted to the extent of 5' in latitude since the 
 time of Tycho Brahe, the star *> Bootes, situate in its vicinity, did not 
 exhibit any sensible displacement. Now the change of latitude ought to 
 have been sensibly the same for both stars if it had arisen from a dis- 
 placement of the ecliptic. It was therefore manifestly due to an altera- 
 tion in the position of Arcturus with respect to the other stars f. 
 
 Bradley, in the paper containing the account of his discovery of the 
 nutation of the earth's axis, inserted in the Philosophical Transactions for 
 1748, has remarked, that the apparent motions of the stars may arise 
 either from a motion of the solar system in space, or from a real change 
 in the positions of the stars themselves ; but he considered that many 
 ages would elapse before it would be possible to arrive at a definitive con- 
 clusion on the subject. 
 
 The motion of the solar system in space formed part of the cosmical 
 system of Thomas Wright, propounded by him in his " Theory of the 
 
 become disgusted with the corrupt morals of his brother monks, he soon afterwards 
 retired from the cloister. About the year 1580 he repaired to Geneva, where he abjured 
 the Romish faith, and embraced the doctrines of Calvin. It does not appear, however, 
 that he was a steadfast adherent to the principles of his new creed. From Geneva he 
 passed into France, and afterwards visited England and Germany. During his residence 
 in these countries he distinguished himself by the originality of his ideas on different 
 subjects of philosophy, and by his merciless exposure of the absurdities of the school- 
 men. Being naturally desirous of revisiting his native country, he proceeded to Venice 
 in 1598 ; but he had no sooner arrived in that city than he was arrested, and sent as a 
 prisoner to Rome. Here he was detained for two years in the dungeons of the Inqui- 
 sition, without being brought to trial. At length, on the 9th of February, 1600, he was 
 condemned to die the death of a heretic and infidel. It is said, that when his sentence 
 was read to him, he replied to his judges in the following terms : " This sentence, pro- 
 nounced in the name of a God of mercy, terrifies you more than it does me." In pur- 
 suance of the sentence, the unfortunate man was carried to the place of execution on 
 the 17th of the same month, and forthwith committed to the flames. There is reason to 
 suspect that, as in the more lenient case of Galileo, the baffled Aristotelians had some 
 complicity with the Romish Church in the perpetration of this atrocious crime. Jordano 
 Bruno was the author of a great number of works on philosophy, all of which display 
 great boldness and originality of thought. 
 
 * Posthumous Works, p. 506. 
 
 f Mem. Acad. des Sciences, 1738, p. 337. 
 
HISTORY OF PHYSICAL ASTRONOMY. 555 
 
 Universe," published in 1750*. He supposes that the sun, with his 
 cortege of planets, as well as all the stars of the firmament, are in 
 continual motion. We shall have again occasion to refer to the specula- 
 tions of this individual. 
 
 Mayer was the first astronomer who endeavoured to deduce some defi- 
 nite result from an examination of the proper motions of the stars. 
 His researches on the subject are contained in a memoir which he com- 
 municated to the Academy of Sciences of Gottingen, in 1760, and which 
 was subsequently inserted in vol. i. of his " Opera Inedita" published 
 in 1771. They were based upon the proper motions of 80 stars, deter- 
 mined by a comparison of the observations of Roemer, in 1706, with 
 corresponding observations of his own and Lacaille's, in 1750 and 1756. 
 He remarked, that if the solar system was advancing towards any deter- 
 minate part of the celestial sphere, it would necessarily follow that the 
 stars in that region would appear to be gradually approaching together, 
 whereas in the opposite region they would seem to be withdrawing more 
 and more apart from each other. He arrived, however, at the conclusion 
 that the observed proper motions of the stars did not afford evidence of 
 the solar system being transported through space towards any particular 
 region of the heavens. 
 
 In 1783 Herschel examined the same subject, and arrived at a conclu- 
 sion diametrically opposed to that of Mayer. His investigation was 
 founded, in the first instance, upon the proper motions of seven principal 
 stars, as determined by Maskelyne. These data seemed to indicate that 
 the solar system was advancing towards a point in the constellation of 
 Hercules, corresponding to about 257 of right ascension. An examina- 
 tion of the proper motions of several of the stars contained in Mayer's 
 list tended to confirm this opinion. He arrived at the final conclusion, 
 that by taking a point somewhat to the north of the star x Herculis, 
 the observed proper motions would be reconciled to a great extent with 
 the hypothesis of a motion of the solar system in that direction. The 
 point thus assigned by him was situate in 257 of right ascension and 25 
 north declination f. 
 
 The same year which produced the researches of Herschel on the 
 motion of the solar system in space, was also distinguished by a similar 
 investigation on the part of Prevost. By a discussion of Mayer's proper 
 motions, he found that the solar system was advancing towards a point 
 situate in 230 of right ascension and 25 north declination. 
 
 The subject of the motion of the solar system in space was subse- 
 quently considered by Klugel in the Berlin Ephemeris for 1789. His 
 researches were founded on the proper motions contained in Mayer's list. 
 He found that the apex of the solar motion was situate in 260 of right 
 ascension and 27 north declination. This result presented a very satis- 
 factory agreement with that obtained by Herschel. 
 
 In 1805 Sir W. Herschel communicated to the Royal Society a second 
 paper on the motion of the solar system. His researches on this occa- 
 sion were based upon Maskelyne's catalogue of the proper motions of 36 
 stars published in 1790. He obtained for the solar apex a position whose 
 right ascension was 245 52' 30" and north declination 49 38'. This 
 result differed considerably from that to which his previous researches had 
 conducted him. 
 
 * " An Original Theory, or New Hypothesis of the Universe, founded upon the Laws 
 of Nature, &c., by Thomas Wright, of Durham." 4to, London, 1750. 
 f Phil. Trans., 1783, p. 247, et seq. 
 
556 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 Biot, in the additions to his Astronomic Physique, published in 1812, 
 has considered the subject of the motion of the solar system in space. 
 An investigation, based on the proper motions of several stars, as deter- 
 mined by a comparison of the observations of Bradley and Mayer with 
 those of Maskelyne and Piazzi, induced him to conclude that there did 
 not exist sufficient grounds for believing that the solar system is advanc- 
 ing towards any determinate point of the heavens. The same conclusion 
 was arrived at in the year 1818 by Bessel, who examined the subject in 
 the Fundamenta Astronomies, the groundwork of his researches consisting 
 of the proper motions of a considerable number of stars, determined by a 
 comparison of the observations of Bradley with those of Piazzi. 
 
 No enquirer seems to have attempted to verify or disprove the assertion 
 of Bessel until Argelander was induced to direct his attention to the sub- 
 ject. The researches of that distinguished astronomer were published in 
 the year 1837, in vol. iii. of the " Memoires Presentes par Divers Savans," 
 of the Academy of St. Petersburg. They were based upon the proper 
 motions of 390 stars, determined by a comparison of the observations of 
 Bradley with those executed by himself at Abo. The result at which he 
 arrived was favourable to the supposition of the motion of the solar system 
 in space. The following are the co-ordinates of the point towards which 
 he found it to be advancing, referred to the mean equinox of 1792: 
 
 Right Ascension. Declination North. 
 
 259 47'.6 32 29 / .5. 
 
 This result, deduced by a method founded upon some of the most refined 
 principles of mathematical investigation, presents a remarkable agree- 
 ment with the rough determination of Herschel in 1783. 
 
 The next person who undertook to investigate the subject of the solar 
 motion was Lundahl. His researches were based upon the proper motions 
 of about 150 stars, determined by a comparison of the observations of 
 Bradley with those of Pond. He obtained, for the apex of the solar 
 motion, the following co-ordinates, reduced to the mean equinox of 1792 : 
 
 Right Ascension. Declination North. 
 
 252 24'.4 14 26'. 1. 
 
 This result presents a considerable discordance with most of those hitherto 
 deduced. 
 
 M. Otto Struve soon afterwards undertook the investigation of this 
 interesting subject. His researches were based on the proper motions of 
 about 400 stars, determined by a comparison of their places, as observed 
 by Bradley, with those deduced from the observations of M. Struve at 
 Dorpat. The following are the co-ordinates he obtained for the apex of 
 solar motion, reduced to the beginning of the year 1790 : 
 Right Ascension. Declination North. 
 
 261 23'.1 37 35'.7. 
 
 By combining this result with the corresponding results arrived at by 
 Argelander and Lundahl, M. Otto Struve determined the co-ordinates of 
 the point in the celestial sphere, towards which the sun is advancing 
 to be : 
 
 Right Ascension. Declination North. 
 
 259 9'.4 34 36'.5 
 
 for the epoch of 1792. 
 
HISTORY OF PHYSICAL ASTRONOMY. 557 
 
 This may be considered as the definitive position of the apex of solar 
 motion, deducible from the proper motions of stars in the northern hemi- 
 sphere, as hitherto determined. A remarkable confirmation of its accu- 
 racy has been recently afforded by the researches of Mr. Galloway on the 
 same subject, founded on the observations of stars in the southern hemi- 
 sphere *. The data which formed the groundwork of Mr. Galloway's 
 investigation, consisted of the proper motions of 81 stars, determined by 
 a comparison of their places, as assigned by Lacaille, about the middle of 
 the eighteenth century, with those deducible from the modern observa- 
 tions of Johnson and Henderson. The following are the values of the 
 co-ordinates which he obtained for the apex of solar motion, the epoch of 
 the mean equinox being the beginning of 1790 : 
 
 Right Ascension. Declination North. 
 
 259 46'.2 32 29'.6. 
 
 Mr. Main, of the Royal Observatory, Greenwich, has recently commu- 
 nicated to the Astronomical Society a paper on the proper motions of 
 875 stars, which may be considered as establishing, beyond all doubt, the 
 general accuracy of the various investigations above referred to f. 
 
 The researches of M. Otto Struve have conducted him to a deter- 
 mination of the actual velocity with which the solar system is being trans- 
 ported through space. Having found that the space traversed by the sun 
 in a year would subtend an arc equal to 0".3392, if viewed at the mean 
 distance of stars of the first magnitude, and having, moreover, ascer- 
 tained that the mean parallax of the stars of the latter class amounted to 
 0".209, he was enabled hence to conclude that the space through which 
 the solar system annually moves, exceeds the radius of the terrestrial 
 orbit in the proportion of 0".3392 to 0".209. In this manner he found 
 that the absolute space traversed by the solar system in the course of a 
 year amounts to 1.623 radii of the terrestrial orbit, which is equivalent to 
 154 millions of miles. Comparing this result with the corresponding 
 results obtained for 61 Cygni, and a Centauri, we have 
 
 The sun . . . . .154 millions of miles. 
 Centauri . . . .371 ,, ,, 
 
 61 Cygni 1333 
 
 These numbers are fairly comparable with each other, and are very 
 interesting on account of the analogy which they exhibit as existing 
 between the sun and the stars. 
 
 The elder Struve has thus summed up the results to which the three 
 astronomers, MM. Argelander, O. Struve, and Peters have been conducted 
 by their researches in stellar astronomy: " The motion of the solar 
 system in space is directed to a point in the celestial sphere, situate on the 
 right line, which joins the two stars of the third magnitude, w and ^ Her- 
 culis, at a quarter of the apparent distance between these stars, measured 
 from TT Her cults. The velocity of this motion is such, that the sun, with 
 the whole cortege of bodies depending on him, advances annually in the 
 direction indicated, through a space equal to 1.623 radii of the terrestrial 
 orbit, or 154 millions of miles "\ 
 
 Although the recent researches of astronomers have thus fully esta- 
 blished that the sun, and his attendant planets, are at present advancing 
 
 * Phil. Trans., 1847, p. 79, et seq. 
 
 f Mem. Ast. Soc., vol. xix., p. 121, et seq. 
 
 J " Etudes d'Astronomie Stellaire," p. 108. 
 
558 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 towards a determinate point in the heavens, it would be inconsistent with 
 analogy to suppose that the motion will always be directed towards the 
 same point. From a consideration of all the other celestial movements 
 that have been hitherto recognised by Astronomers, it is impossible to 
 avoid the conclusion that the path traced out by the sun is in reality cur- 
 vilinear. But, indeed, motion in a right line would be utterly incom- 
 patible with the principle of gravitation, as established by Newton, between 
 the different parts of the material universe. It can hardly be doubted, 
 therefore, that the apex of solar motion is slowly shifting its position in 
 the celestial sphere, and that it will eventually exhibit a sensible displace- 
 ment. It is not improbable that by thus tracing out the path of the solar 
 apex in the heavens, the actual path of the sun in absolute space may be 
 one day determined. This would, indeed, be a magnificent triumph of 
 inductive science ; but a countless series of ages may, perhaps, elapse 
 before its achievement will be realised. 
 
 Guided, also, by the analogy of the planets and satellites revolving 
 round their respective primaries, several enquirers into the cosmical struc- 
 ture of the heavens have come to the conclusion, that the whole solar 
 system is revolving round some central body. This principle formed part 
 of the system of Wright, as expounded in his remarkable work on the 
 " Theory of the Universe," to which allusion has already been made. It 
 was also" maintained by his successors, Kant, Lambert, and Michell. Sir 
 William Herschel has cautiously abstained from expressing a decided 
 opinion upon this point. In more recent times M. Madler has made the 
 hypothesis of a central sun the groundwork of some very remarkable 
 speculations. His final conclusion is, that the Pleiades may be regarded 
 as the central group of the stars composing the system of the milky way, 
 and that the bright star of that group, Alcyone, is the central body, round 
 which they are all revolving. It is manifest that all such speculations 
 are far in advance of practical astronomy, and therefore they must be 
 regarded as premature, however probable may be the suppositions on 
 which they are based, or however skilfully they may be connected with 
 the actual observations of astronomers. 
 
 When astronomical observations came to be made with telescopes pos- 
 sessing a considerable degree of optical power, it was found that several 
 stars, which to the naked eye appeared single, consisted in reality of two 
 stars, so very near to each other that they severally failed to produce an 
 impression of their individuality upon the unaided organ of vision. As 
 early as the middle of the seventeenth century, Riccioli remarked that 
 the star in the middle of the tail of the Great Bear (f Ursse Majoris), 
 when observed with the telescope, was found to exhibit the appearance of 
 two distinct stars in close juxtaposition*. A few years afterwards a 
 similar remark was made by Hooke with respect to the double star y 
 Arietisf. Several other stars, such as Geminorum or Castor, y Vir- 
 ginis, &c., were also found to be double, about the beginning of the seven- 
 teenth century. The star Orionis, in the middle of the great nebula, 
 discovered by Huyghens in 1656, even presented the appearance of three 
 distinct stars in close proximity to each other. 
 
 Occasional discoveries of double stars continued to be made throughout 
 the eighteenth century ; but these objects cannot be said to have excited 
 
 * Almag. Nov., torn, i., part i., p. 422. 
 
 f " Attempt to prove the Motion of the Earth," p. 7 (1674). 
 
HISTORY OF PHYSICAL ASTEONOMY. 559 
 
 a general interest among astronomers until Sir William Herschel directed 
 his attention to them. In the year 1779, that illustrious astronomer 
 undertook an extensive examination of the heavens with a view to the 
 discovery of double stars, hoping that he might be enabled in some in- 
 stances to establish an annual change in the relative positions of the two 
 component members, which might indicate the existence of a sensible 
 parallax. In 1782 he exhibited the first fruits of his labours by commu- 
 nicating to the Royal Society a paper containing the places of 269 double 
 stars, together with the distances of the component members, and also 
 their angles of position corresponding to a given epoch. Of the stars 
 contained in this catalogue there were 227 which had not hitherto been 
 recognized as double by any observer*. In 1785 Herschel commu- 
 nicated to the Royal Society a second catalogue of double stars, containing 
 434 more of such interesting objects f. 
 
 Michell appears to have been the first person who suggested that the 
 close proximity of the constituent members of double stars was owing 
 to some physical connexion existing between them. In a remarkable 
 paper, which he communicated to the Royal Society, he presented this 
 view of the subject in a very strong light, by an application of the doc- 
 trine of probabilities to the theory of the distribution of the stars in the 
 celestial sphere J. In a subsequent communication, which appears in the 
 Philosojyhical Transactions for 1784, he expressed his firm conviction that 
 the double and triple stars discovered by Herschel were so many systems 
 of stars, so near to each other as to be liable to be affected by their 
 mutual gravitation ; and he considered it as not unlikely that the periods 
 of the revolutions of some of these about their principals might some 
 time or other be discovered . 
 
 If double stars formed in reality independent systems, maintained 
 .under the influence of the principle of gravitation, it would follow as a 
 necessary consequence, that the constituent members of edch system 
 would be subject to a constant change of relative position from their revo- 
 lution round their common centre of gravity. It is worthy of remark, 
 however, that there is another fact connected with double stars which, 
 when established by observation, affords equally unequivocal evidence of 
 the physical connexion of the constituent members. If among those 
 double stars which have a sensible proper motion, it be found in any 
 instance that both stars are transported with the same apparent ve- 
 locity, we have just grounds for believing that a physical relation exists 
 between them. Such a fact had been noticed towards the close of the 
 eighteenth century, but, strange to say, the astronomer who directed at- 
 tention to it, did not perceive the legitimate conclusion which was deducible 
 from it. The bright star Castor, besides being double, is, moreover, re- 
 markable for a sensible proper motion, which amounts to about O'Mo of 
 space every year. Now, Dr. Hornsby remarked, in the year 1798, that 
 notwithstanding the large proper motion of this star, the mutual distance 
 of the two constituent members did not seem to have undergone any 
 change during a period of twenty years embraced by his observations. 
 The only conclusion which he drew from this remarkable fact was, that 
 both stars were moving with the same velocity and in the same direction ||. 
 
 * Phil. Trans., 1782, p. 112, et seq. f Ib5d., 1785, p. 40, et seq. 
 
 J Ibid., 1767, p. 234, et seq. Ibid., 1784, p. 36, et seq. 
 
 || "Bradley's Observations," vol. i., Preface, p. xxiii., Oxford, 1798. 
 
560 HISTOEY OF PHYSICAL ASTRONOMY. 
 
 The glory of establishing the physical theory of Double Stars upon 
 the solid basis of observation and sound reasoning was reserved for Sir 
 William Herschel. The results of his researches on this occasion are 
 contained in two papers communicated by him to the Royal Society, 
 which are inserted in the Philosophical Transactions of that body for the 
 years 1803 and 1804*. By a comparison of his earlier observations of 
 a great number of double stars, with corresponding observations made 
 after an interval of about twenty years had elapsed, he found that in 
 many instances the relative positions of the constituent bodies had 
 undergone a sensible change. He demonstrated by incontrovertible rea- 
 soning, that all those double stars, which afforded evidence of such a 
 change of relative position in the constituent members, formed so many 
 independent systems of bodies revolving under the influence of their 
 mutual attraction around their common centre of gravity. He even car- 
 ried his researches so far as to assign the periods of revolution of several 
 of these Binary Systems. Thus to Castor he assigned a period of 342 
 years, to Serpentis, a period of 375 years, and to y Leonis, a period 
 of 1 200 years. These numbers were of course assigned merely as rough 
 approximations to the true periods of revolution. 
 
 The last contribution of Sir William Herschel, on the subject of 
 Double Stars, was a paper which he communicated to the Astronomical 
 Society upon the occasion of its establishment in the year 1820. It con- 
 tains the places of 145 double stars, with their distances and angles of 
 position at certain epochs. The observations which form the groundwork 
 of this catalogue appear to have been all anterior to the year 1802. 
 
 In 1824 fresh interest was awakened in the subject of Double Stars by 
 the communication of a paper to the Royal Society on the part of Sir 
 John Herschel and Sir James South, containing the results of their joint 
 labours in this field of enquiry. This paper contained micrometrical 
 measures of 380 double and triple stars, carefully observed with a 7-feet 
 equatorial. A comparison of these measures with the earlier obser- 
 vations of Sir William Herschel, afforded in many instances an interest- 
 ing confirmation of the result arrived at by that astronomer relative to 
 the physical connexion of the constituent members of double stars. One 
 of the objects composing the double star, j Corona, had accomplished a 
 complete circuit round its primary, and was already well advanced in a 
 second revolution. The star T Serpentarii, which Sir William Herschel 
 in his first catalogue communicated to the Royal Society had stated to be 
 double, no longer exhibited the slightest trace of duplicity one of the 
 constituent stars having been now exactly projected upon the other in 
 virtue of its relative motion. On the other hand, Orionis, which Sir 
 William Herschel had marked as a single star, was now recognised to be 
 double even in telescopes of moderate power f. 
 
 In 1826 Sir James South communicated to the Royal Society a paper 
 containing micrometrical measures of 458 double stars executed solely 
 by himself. The results of Sir John Herschel's subsequent labours in 
 the same field, exclusive of his more recent observations in the southern 
 hemisphere, are contained in a series of papers communicated by him at 
 different times to the Astronomical Society. The stars whose duplicity 
 was recognised by him on this occasion, amount in number to 3347, being 
 
 * Phil. Trans., 1803, p. 339, et seq. ; 1804, p. 353, et seq. 
 f Annuaire, 1834. 
 
HISTOBY OF PHYSICAL ASTRONOMY. 661 
 
 such as he happened to meet with, while engaged in an extensive survey 
 of the nebular contents of the heavens with a 20-feet reflector. The 
 original observations were transmitted to the Society in six successive 
 catalogues ; but as they were considered by their author to be subordinate 
 to the main object of his labours, they did not possess any pretension to 
 extreme accuracy. He, however, communicated to the Society two papers 
 containing micrometrical measures of a considerable number of double 
 stars, carefully determined with a 7-feet equatorial*. 
 
 No astronomer of the present day has contributed in so high a degree 
 to the advancement of the subject of Double Stars as the illustrious M. 
 Struve. His labours in this interesting field of astronomical enquiry 
 were commenced in the year 1813, upon his being appointed Director of 
 the Observatory of Dorpat. He continued to prosecute them with more or 
 less assiduity till the year 1824 1, when, having obtained possession of a 
 magnificent refractor of 9.9 inches aperture, executed by Fraunhofer, he 
 conceived the design of examining with it all the stars down to the 
 eighth magnitude, situate between the north pole and 15 of south decli- 
 nation. This design was followed up by him with admirable perseverance 
 during many years J. In 1837, he finally published the results of his 
 labours in a large folio volume . It contains micrometrical measures of 
 the distances and angles of position as well as the approximate places of 
 3112 double stars, as determined between the years 1824 and 1836, 
 besides the results of his earlier labours on the same subject, extending 
 from 1813 to 1824. 
 
 While M. Struve was engaged in his extensive micrometric measure- 
 ments of double stars, an important advance was made in the theory of 
 the movements of bodies of this class. The growing evidence of a 
 physical connexion between the constituent members of double stars, 
 which was afforded in many instances by a comparison of the more recent 
 with the earlier observations of astronomers, suggested the possibility of 
 deducing from observation the elements of the elliptic orbit, in which it 
 was presumed that the one star revolved around the other. Researches 
 undertaken with a view to effect this object were attended with complete 
 success. To M. Savary is due the honour of having first demonstrated 
 that the elements of the orbit of a double star might be derived from a 
 determinate number of the observed distances and angles of position of 
 the star. In the Connaissance des Temps for 1830, he has explained a 
 method invented by him for the attainment of this end, and has exhibited 
 a proof of its practical utility by employing it in calculating the elements 
 of the orbit of the double star f Ursae Majoris. M. Encke shortly after- 
 wards assigned a method of his own, by means of which he computed the 
 
 * Mem. Ast. Soc., vols. v., viii. 
 
 f In 1822, he published a catalogue of 795 double stars which had passed under his 
 examination since the commencement of his labours at Dorpat. 
 
 J In 1827, he published a catalogue of about 3000 double stars, which he detected 
 during the first two years of his labours, with the great refractor. In the course 
 of his survey on that occasion he examined no fewer than 120,000 stars! The objects 
 of this catalogue were chiefly those of which he published the micrometric measures in 
 1837. 
 
 " Stellarum Duplicium, &c., Mensurse Micrometricoe per magnum Fraunhoferi 
 tubum, 1824-37, specula Dorpatensi institutes; adjecta, Synopsis Observationum de 
 Stellis Compositis, 1814-24, per minora instrumental folio, Petrop, 1837. In 1845, M. 
 Struve published a catalogue of 514 double and multiple stars discovered at Pulkowa 
 with the great refractor of 14.9 inches aperture. 
 
 
 
562 HISTORY OF PHYSICAL ASTEONOMY. 
 
 elements of the orbit of the double star 70 Ophiuchi. A third method, 
 totally different from either of the two others just mentioned, was in- 
 vented about the same time by Sir John Herschel *. 
 
 The elements of a considerable number of double stars have been cal- 
 culated by one or other of the methods above referred to, and an elliptic 
 orbit has thus, in each instance, been deduced, in the focus of which the 
 primary star is supposed to be situate. The place of the revolving star 
 has then been computed in a great many different positions of its orbit, 
 upon the supposition that the motion is regulated by a force tending con 
 stantly to the focus, and the results have been compared with the cor- 
 responding places assigned by observation. The observed and computed 
 places of the star have thus been found in general to agree within the 
 limits assigned by the probable errors of observation. We are therefore 
 warranted in concluding that the principle of gravitation, as announced 
 by Newton, extends to systems of bodies placed at an almost inconceivable 
 distance from the earth, and that by its controlling agency those systems 
 are perpetually upheld. This may be justly asserted to be one of the 
 most sublime truths which Astronomical Science has hitherto disclosed to 
 the researches of the human mind. 
 
 No mention has hitherto been made of observations of double stars in 
 the southern hemisphere. A considerable stock of such observations has, 
 however, been already amassed. In 1828, Mr. Dunlop communicated to 
 the Astronomical Society a catalogue of 253 double stars observed by 
 him at Paramatta, in New South Wales. When Sir John Herschel was 
 engaged at the Cape of G-ood Hope, in examining the nebulae of the 
 southern hemisphere with his 20 -feet reflector, he did not fail to 'make 
 observations of such double stars as he happened to meet with. The 
 number of such objects which he thus detected in the course of his 
 sweeps amounted to 2095. Accurate micrometrical measures were also 
 made by him with his 7-feet equatorial. 
 
 With respect to those stars which have been discovered by astronomers 
 to be double, many are doubtless merely optically so, their apparent 
 proximity arising from the circumstance of their being situate nearly in 
 the same line of vision. It is only in those cases wherein a change in 
 the relative position of the two stars has been established by a comparison 
 of observations made at different times, that we are enabled definitively 
 to infer the existence of a physical connexion. It is to be remarked, 
 however, that the lapse of time is constantly unfolding indications of 
 such changes, and is thereby leading to a continual increase of the 
 number of stars recognised as physically double. Stellar objects of this 
 class have been distinguished from stars that are merely optically double 
 by the appellation of Binary Systems. 
 
 The subject of Double Stars has engaged the attention of several astro- 
 nomers of recent times, besides those to whose labours allusion has just 
 been made. In this country, Captain Smyth, R.N., and the Rev. Mr. 
 Dawes, have especially distinguished themselves by their exquisite obser- 
 vations connected with this department of sidereal astronomy. The 
 Bedford Catalogue, executed by Capt. Smyth, and inserted in vol. ii. of 
 his " Cycle of Celestial Objects," contains the results of observations of 
 the most interesting double and multiple stars, of which the primaries 
 are in Piazzi's catalogue. It comprises 580 double stars, 20 binary 
 
 * Mem. Ast, Soc., vol. v. 
 
HISTORY OF PHYSICAL ASTRONOMY, 563 
 
 systems, and 80 triple and multiple stars *. The micrometric measures 
 of these objects were executed by Capt. Smyth, at a private observatory 
 which he erected at Bedford. This is one of several instances in which 
 we have had occasion to allude to the labours of officers in the naval and 
 military service of this country, who have adorned their profession by an 
 enthusiastic devotion to scientific pursuits. The results of Mr. Dawes' 
 micrometric measurements of double stars are contained in several import- 
 ant papers communicated by him on various occasions to the Astronomical 
 Society, and subsequently inserted in the " Memoirs " of that body. 
 
 Among the astronomers of the Continent who, besides the elder Struve, 
 have occupied themselves with observations of double stars, the illustrious 
 Bessel is entitled to the first place. In the present day, M. Madler has 
 acquired just distinction by his labours in this interesting branch of astro- 
 nomy. The theory of the subject has recently received some important 
 elucidations from the researches of M. Yvon Villarceau, of Paris. 
 
 We now proceed to notice briefly the history of the NebulaB of the 
 celestial regions. Ptolemy has inserted five stars in his catalogue, which, 
 on account of their hazy aspect, he distinguished by the appellation of 
 Cloudy Stars. When these objects were examined with the telescope, they 
 were found, in each instance, to consist of a cluster of stars situate so 
 near to each other, that they failed to produce an impression of their dis- 
 tinct existence upon the naked eye. In the year 1612, however, Simon 
 Marius, the German astronomer, discovered a nebulous object, which 
 appeared to be of a totally different nature from any of those hitherto 
 discovered. To the naked eye, indeed, it presented a dull nebulous 
 aspect, like the other objects of the same class ; but when examined with 
 the telescope, it did not exhibit any indications of a sidereal structure. 
 There were merely visible some faint rays of light, increasing in bright- 
 ness towards the centre. The nucleus consisted of a dim light, fading 
 away insensibly on all sides. Marius compared its appearance to that 
 presented by the flame of a candle shining at night through a transparent 
 hornf. In 1656, Huyghens discovered another nebula of this class in 
 the middle of the sword of Orion. It struck its distinguished discoverer 
 with amazement, as something totally different in its nature from those 
 sidereal aggregations of which nebulous objects had hitherto been found 
 to consist. The aspect of the heavens around this nebulous light was 
 intensely black, a circumstance which suggested to Huyghens the idea of 
 the phenomenon being occasioned by looking through an aperture in the 
 heavens into a luminous region beyond \. 
 
 In the year 1714, Halley communicated a short paper to the Royal 
 Society, in which he gave an account of the various nebulse with which he 
 was acquainted as having been hitherto recognised by astronomers!. In 
 number they amounted only to six. Two of these were the nebulae above 
 mentioned. Another was situate between the head and bow of Sagit- 
 tarius ; according to Halley it was discovered by Abraham Ihle in 1665. 
 
 * The Bedford Catalogue also comprises monographs of 170 nebulae and clusters, 
 which Capt. Smyth had selected for observation from Messier's Catalogue, and from the 
 papers of the two Herschels. The " Cycle of Celestial Objects " was published in two 
 volumes in 1844, and is justly esteemed to be one of the most instructive and delightful 
 works on astronomy in our language. 
 
 *t* Simon Marius has given an account of his discovery of this nebula in the preface to 
 his " Munclus Jovialis," published in 1612. 
 
 J Opera Varia, torn, ii., p. 54Q(Systema Saturnium). 
 
 Phil. Trans., 1714, p. 390, et seq. 
 
 O 2 
 
564 HISTORY OF PHYSICAL ASTRONOMY. 
 
 A fourth was in the constellation Centaurus, and was marked by Bayer 
 with the Greek letter u ; it was discovered by Halley at St. Helena, in 
 1677, while engaged in observing the stars of the southern hemisphere. 
 A fifth preceded the right foot of Antinous ; it was discovered by Kirch 
 in 1681. The sixth was discovered by Halley in 1714; it was situate in 
 the right line joining the stars u and { of the constellation Hercules. 
 Halley was of opinion that the light of these objects came from an 
 extraordinary distance. He supposed it to be occasioned by a lucid 
 medium diffused throughout the ether, and shining with its own proper 
 lustre. 
 
 If Halley had consulted the observations of Hevelius, he would have 
 been enabled to assign a more ample list of iiebula3 than that contained 
 in his paper to the Royal Society. In the Philosophical Transactions for 
 1733, Derham has enumerated sixteen nebula?, in addition to those con- 
 tained in Halley 's paper, which he extracted from the observations of the 
 astronomer just cited. 
 
 An important contribution to the existing stock of nebulae was made 
 by Lacaille. In 1755, that distinguished astronomer communicated to 
 the Academy of Sciences a catalogue of 42 nebula? in the southern 
 hemisphere, observed by him during his residence at the Cape of Good 
 Hope*. They were divided by him into three distinct classes, each of 
 which contained an equal number of objects. The first class contained 
 all those nebula? which failed to afford any indications of a sidereal struc- 
 ture. They were assimilated by Lacaille to small patches of the Milky 
 Way. The objects of the second class were nebulous only in appearance, 
 consisting in reality of so many congeries of stars, whose close proximity 
 rendered them individually imperceptible to the naked eye. The objects 
 of the third class were stars surrounded by a nebulous substance. He sup- 
 posed that the latter were identical in structure with the nebula? of the first 
 class, and that the appearance of stars in the midst of them was merely 
 accidental, arising in each case from the circumstance of the nebula and 
 the star being both projected on the same region of the heavens. 
 
 Messier was the next astronomer who by his observations contributed 
 to the enlargement of the number of recognised nebula?. His first col- 
 lection of these objects was published in the Memoirs of the Academy of 
 Sciences for 1771. This list contained 45 nebula? and clusters of stars. 
 It was subsequently inserted, with successive additions, in the volumes 
 of the Connaissance des Temps for 1783 and L784, the number of objects 
 in the last instance amounting to 103. Messier did not pronounce any 
 opinion respecting the nature or physical constitution of the nebulae ; 
 but, with the view of arriving at some conclusion on this subject, he 
 recommended to future astronomers to make careful observations of them, 
 in order to ascertain whether they exhibited any indications of a change 
 of form or structure. 
 
 It appears from the foregoing brief notice of the nebula? discovered by 
 astronomers previous to the time of Sir William Herschel, that their 
 number did not altogether amount to one hundred and fifty. In 1786, it 
 received a notable accession from the labours of that distinguished astro- 
 nomer, who communicated to the Royal Society a catalogue of 1 000 new 
 nebula? and clusters of stars f. In 1789, he communicated to the same 
 
 * Mem. Acad. des Sciences, 1755, p. 194, etseq. 
 f Phil. Trans., 1786, p. 457, et seq. 
 
HISTORY OF PHYSICAL ASTRONOMY. 565 
 
 Society a second catalogue, containing 1000 additional nebulae* and 
 clusters, and in 1802, a third catalogue, which included 500 more of 
 similar objects f. The nebulas and clusters in each of these catalogues 
 were distributed by Herschel into eight different classes ; but this mode 
 of arrangement had reference to the convenience of the astronomer who 
 might be desirous of re-examining the objects, rather than to any pecu- 
 liarities of physical structure. In the paper containing his third cata- 
 logue, he has enumerated the various objects of which he considered the 
 fabric of the material universe to be composed. They are distributed by 
 him into twelve different classes. A brief notice of each of these in 
 succession may serve to acquaint the reader, in some degree, with the 
 ideas entertained by Herschel on the construction of the material uni- 
 verse. 
 
 I. Insulated Stars. Under this class, Herschel comprehended all those 
 stars which do not afford any indication of being resolvable into two or 
 more constituent objects. Among the stars of this class are included 
 Arcturus, Capella, Sirius, Canopus, and the Sun. He supposed each of 
 these stars to be sufficiently insulated in space, not to be sensibly affected 
 by the attraction of the other bodies of the universe. They appeared to 
 him, 011 this account, to be peculiarly adapted for constituting the centres 
 of planetary systems. He was, in fact, inclined to suspect that the stars 
 which appear in clusters, are unattended by revolving bodies ; but that 
 each star forms a magnificent world by itself, fulfilling all the purposes 
 of a planetary body J. 
 
 II. Binary Stars. These are systems composed in each case of two 
 stars revolving around their common centre of gravity. 
 
 III. Triple and Multiple Stars. These are systems of a more com- 
 plicated structure than those just mentioned ; but like them are resolvable 
 into a determinate number of constituent bodies. 
 
 IV. Clustering Collections and the Milky Way. Herschel was of 
 opinion that in many instances the stars by their mutual attraction 
 are gradually forming into clusters. The Milky Way, in many parts, 
 appeared to him to afford unequivocal indications of such a clustering ten- 
 dency. We shall presently have occasion to allude to his remarkable 
 speculations on the structure of the Milky Way. 
 
 V. Groups of Stars. Under this class, Herschel comprehended all 
 those collections of stars which do not exhibit any regularity of outline, 
 nor superior condensation in any particular part : at the same time they 
 appear sufficiently insulated from the stars around them, to justify the 
 conclusion that they formed so many separate systems . 
 
 VI. Clusters of Stars. These were justly considered by Herschel to 
 be the most magnificent objects of the heavens ||. They are round in 
 
 * Phil. Trans., 1789, p. 212, et seq. f Ibid., 1802, p. 477, et seq. 
 
 J Ibid., 1795, p. 69. 
 
 One of the most interesting objects of this class is the group in the southern 
 hemisphere, surrounding the star x Crucis. According to Sir John Herschel it occupies 
 an area of about l-48th part of a square degree, and consists of about 110 stars, from 
 the seventh magnitude downwards, eight of the more conspicuous of which are coloured 
 with various shades of red, green, and blue, so as to give to the whole the appearance of 
 a rich piece of jewellery. (Results of Ast. Obs., &c., pp. 17, 102 ; Outlines of Astro- 
 nomy, p. 597. ) 
 
 || Sir John Herschel, the highest living authority on Nebulae, states that by far the 
 most remarkable object of this class in the heavens, is the globular cluster w Centauri 
 
566 HTSTOEY OF PHYSICAL ASTRONOMY. 
 
 form, and are gradually more condensed towards the centre. These facts 
 clearly point out the existence of an attractive force, binding the con- 
 stituent bodies together, so as to form an independent system*. 
 
 VII. Nebulas. These were suspected by Herschel to be so many col- 
 lections of stars, reducible to one or other of the three classes last men- 
 tioned, the nebulous aspect assumed by them being merely an illusion 
 arising from the impossibility of discerning the stars individually, in con- 
 sequence of the immense distance at which they are placed. Herschel 
 calculated that the light from one of the faint nebulae seen in his 40-feet 
 telescope, must have occupied about two millions of years in its passage 
 to the earth, although traversing space at the rate of 192,000 miles in a 
 second ! Well might the illustrious astronomer remark, that the tele-* 
 scope had the power of penetrating into time as well as into space. 
 
 VIII. Stellar Nebulae. These were supposed by Herschel to be in all 
 probability clusters of stars whose light, on account of their immense dis- 
 tance, is collected so closely into one point, that the only evidence remain- 
 ing of their resolvability into discrete bodies, consists in the appearance 
 of burs. 
 
 IX. Milky Nebulosity. According to Herschel, the phenomena of this 
 class were of two distinct kinds. One of these was nebulous only in 
 appearance, consisting in reality of so many systems of clustering collec- 
 tions of stars contiguous to each other, like the series of clustering col- 
 lections of which he had found the Milky Way to be composed. The 
 other species of objects consisted of those whose structure was purely 
 nebulous. One of the most remarkable of such objects was the great 
 nebula of Orion, which Huyghens had discovered in 1656. From a com- 
 parison of his earlier with his more recent observations of this nebula, 
 Herschel concluded that during the intermediate period it had undergone 
 a sensible change of aspect, a circumstance which appeared to him clearly 
 to indicate that its structure was not sidereal. 
 
 X. Nebulous Stars. These are stars surrounded by a pale nebulous 
 atmosphere. Herschel had, in a former communication to the Royal 
 Society, directed the attention of astronomers to these remarkable objects |. 
 The star, in each case, appeared to be situate exactly in the centre of the 
 nebulosity, whence it was evident that they were connected together by 
 some physical relation. The question with respect to the real nature of 
 these objects, was supposed by Herschel to be involved in great obscurity. 
 
 in the southern hemisphere. To the naked eye it appears like a dim coraetic object, equal 
 in brightness to a star of between the fourth and fifth magnitudes. Viewed in a powerful 
 telescope it resembles a globe of fully 20' in diameter, very gradually increasing in bright- 
 ness to the centre, and composed of innumerable stars of the thirteenth and fifteenth mag- 
 nitudes. (Results of Ast. Obs., &c., pp. 21, 104; Outlines of Astronomy, p. 595.) 
 This is the object alluded to in the text, as having been discovered by Halley in J677, 
 under the impression .of its being a nebula. The globular cluster between w and 
 Herculis, which was also first observed by Halley as a nebula in the year 1714, is the most 
 magnificent in the northern hemisphere. Sir William Herschel estimates the number of 
 stars contained in it to amount to as many as 14,000! (Phil. Trans., 1806, p. 230.) 
 
 * If the stars were regularly distributed in a globular cluster, this circumstance alone 
 would manifestly cause the cluster to appear more condensed towards the centre. It 
 appears, however, that in many cases the condensation of the cluster is greater than that 
 which would arise from a uniform distribution of the stars. The obvious inference is, 
 that the cluster forms an independent system, the constituent bodies of which, under the 
 influence of their mutual attraction, have a tendency to congregate towards the centre. 
 
 t Phil. Trans., 1791, p. 71, et seq. 
 
HISTORY OF PHYSICAL ASTRONOMY. 567 
 
 If the nebulosity consisted of stars so remote as to put on a milky 
 appearance, it necessarily followed that the central body, which usually 
 resembled a star of the seventh or eighth magnitude, must possess enor- 
 mous dimensions. If, on the other hand, the central body be supposed 
 not to exceed the ordinary size of the stars, how small, argued Herschel, 
 must be the remaining stars of the system, and how inconceivably great 
 must be their compression to produce the observed nebulosity. Instead 
 of adopting either of these hypotheses, Herschel was inclined to believe 
 that the phenomenon arose from a star of the ordinary magnitude being 
 involved in a shining fluid of a nature totally unknown. 
 
 XI. Planetary Nebulae. These are nebulae of a pale uniform aspect, 
 and of a perfectly round form. Like the objects of the preceding 
 class, they appeared to Herschel to be of a very mysterious nature. If 
 they were admitted to be suns, it would be difficult to account for the 
 faiutness of their light. On the other hand, the supposition of their 
 being sidereal aggregations was at variance with their uniform structure. 
 
 XII. Planetary Nebulae with Centres. The objects of this class were 
 suspected by Herschel to form the connecting link between nebulous 
 stars and planetary iiebulaB. This view of their nature suggested to him 
 a conclusion which he subsequently developed at greater length. " If," 
 says he, " we might suppose that a gradual condensation of the nebu- 
 losity about a nebulous star could take place, this would be one of them, 
 in a very advanced state of compression."* 
 
 In the year 1811, Herschel communicated to the Royal Society a 
 paper in which he gave an exposition of his famous hypothesis of the 
 transformation of nebulae into stars f. Assuming a self-luminous sub- 
 stance of a highly-attenuated nature to be distributed through the 
 celestial regions, he endeavoured to show that, by the mutual attraction 
 of its constituent parts, it would have a tendency to form itself into 
 distinct aggregations of nebulous matter, which in each case w r ould 
 gradually condense, from the continued action of the attractive forces, 
 until the resulting mass finally acquired the consistency of a solid body 
 and became a star. In those instances wherein the collection of nebulous 
 matter was very extensive, subordinate centres of attraction could not fail 
 to be established, around which the adjacent particles would arrange 
 themselves, and thus the whole mass would in process of time be trans- 
 formed into a determinate number of discrete bodies, which would ulti- 
 mately assume the condition of a cluster of stars. Herschel pointed 
 out various circumstances which appeared to him to afford just grounds 
 for believing that such a nebulous substance existed independently in 
 space. He maintained that the phenomena of nebulous stars, and the 
 changes observable in the great nebula of Orion, could not be satisfac- 
 torily accounted for by any other hypothesis. Admitting, then, the 
 existence of a nebulous substance, he concluded, from the extensive indi- 
 cations of milky nebulosity which he encountered in the course of his 
 observations, that it was distributed in great abundance throughout the 
 celestial regions. The vast collection of nebula which he had observed, 
 of every variety of structure, and in every stage of condensation, were 
 employed by him with admirable address in illustrating the modus ope- 
 randi of his hypothesis. The planetary nebulae, whose nature had for- 
 merly appeared to him to be totally inexplicable, were now reasonably 
 
 * Phil. Trans., 1802, p. 502. f Ibid., 1811, p. 269, et seq. 
 
568 HISTORY OF PHYSICAL ASTRONOMY. 
 
 supposed to be nebulae which had finally assumed the consistency of a solid 
 body, so that the aspect exhibited by them in the telescope thenceforward 
 necessarily failed to afford any indication of their internal structure. 
 
 Notwithstanding the ingenuity of illustration and incontestable force 
 of reasoning by which Herschel sought to establish this bold hypothesis, it 
 has not received that confirmation from the labours of subsequent enquirers 
 which is so remarkable in the case of many of the other speculations of 
 that great astronomer. It is now generally admitted, that the changes 
 which at one time were supposed to be taking place in some nebulae were 
 altogether illusive, having been suggested partly by erroneous delinea- 
 tions of the objects as they actually appeared in the telescope, and partly 
 by the different aspect which they necessarily assumed when viewed in 
 telescopes possessing different degrees of optical power. Moreover, the 
 phenomena denominated Nebulous Stars which seemed to Herschel to be 
 incapable of any satisfactory explanation, except by adopting the hypothesis 
 of a self-luminous fluid when examined with the powerful telescopes of 
 Lord Rosse, have been found to exhibit an aspect totally different from 
 that which appeared to Herschel so enigmatical. In fact, the greater the 
 optical power of the telescope with which the heavens are surveyed, the 
 more strongly do the results tend to produce the impression that all nebulas 
 are in reality vast aggregations of stars, which assume a nebulous aspect 
 only because the telescope with which they are observed in each instance 
 is not sufficiently powerful to resolve them into their constituent parts, 
 and thereby disclose their real nature*. 
 
 The only nebulae visible exclusively in the southern hemisphere, with 
 which astronomers hitherto were acquainted, were those discovered by 
 Halley and Lacaille, to which allusion has already been made. In 1828, 
 the number of such objects was considerably augmented by the late Mr. 
 Dunlop, who in that year communicated to the Royal Society a catalogue 
 containing 629 nebulae and clusters observed by him at Paramatta, 
 in New South Wales. From the small optical power possessed by his 
 telescope, which was a Newtonian reflector of nine inches aperture, and 
 doubtless, also, in some degree from his inexperience in such observations, 
 this catalogue by no means afforded a faithful representation of the objects 
 to which it related. 
 
 In 1833, Sir John Herschel communicated to the Royal Society a paper 
 containing the results of an examination of the nebulae in the northern 
 hemisphere, undertaken in the year 1825, with a twenty-feet reflector, 
 and prosecuted during the course of the following eight years. This 
 catalogue contained 2306 nebulas and clusters. Of these about 500 were 
 new : the remaining objects had been already discovered by his father. 
 It would be out of place here to attempt to give a detailed account of 
 this magnificent production, which is destined to form one of the great 
 landmarks of sidereal astronomy. 
 
 In 1847, the distinguished astronomer just referred to, published his 
 " Results of Astronomical Observations made at the Cape of Good Hope," 
 
 * It may be mentioned, in connexion with this remark, that the great nebula of Orion 
 has finally begun to exhibit indications of resolvability, upon being observed with the 
 6-feet reflector of Lord Rosse, and with the powerful refractor of Cambridge, U. S. 
 The same may be said respecting an examination of the nebula of Andromeda, by the 
 aid of the latter telescope. For magnificent delineations of these two nebulas, as 
 observed at Cambridge, by Mr. Bond, the Director of the Observatory, and Mr. G. P. 
 Bond, his son, see Mem. of the Amer. Acad. of Arts and Sciences, New Series, 
 vol. iii. 
 
HISTORY OF PHYSICAL ASTRONOMY. 569 
 
 which, among other objects of importance, contained a catalogue of 1708 
 nebulae and clusters in the southern hemisphere. The observations 
 which form the groundwork of this catalogue were made by Sir John 
 Herschel at the Cape of Good Hope, between the years 1834 and 1838, 
 with an instrument of the same optical power as that employed by his 
 illustrious father and himself in their respective examinations of the 
 nebulae of the northern hemisphere. This great catalogue, in conjunction 
 with the one of 1833, by the same astronomer, may be said to afford an 
 accurate representation of all the nebula in the celestial sphere, which 
 are visible in a reflecting telescope of 18 inches' aperture. From the 
 unrivalled powers of description by which the author of these catalogues 
 is distinguished, the monographs which they contain have imparted to 
 them an interest extending far beyond the mere circle of strictly scientific 
 enquirers, who see in them mainly the solid groundwork of ulterior 
 researches of high importance in stellar astronomy. 
 
 The most recent contribution to the subject of nebul has been fur- 
 nished by Lord Rosse, who in the year 1850 communicated to the Royal 
 Society a paper containing the results of a re-examination of several of 
 the nebula3 comprised in Sir John Herschel's catalogue of 1833*. These 
 observations were made with the reflecting telescope of three-feet aper- 
 ture, originally executed by Lord Rosse, but chiefly with the more power- 
 ful instrument of six-feet aperture subsequently constructed by him. 
 New phenomena of a highly interesting nature have been revealed in the 
 course of these observations. Many nebulas, which had hitherto resisted 
 all attempts to resolve them with instruments of inferior power, were 
 now found to consist wholly of stars. Others exhibited peculiarities of 
 structure totally unexpected. Among these there are several which have 
 been found to exhibit unequivocal indications of a spiral arrangement. 
 One of the most remarkable objects of this class is the nebula marked 
 No. 51 in Messier's catalogue. This nebula has a smaller one in its 
 immediate vicinity. Messier describes the two objects as a double 
 nebula without stars. The powerful telescopes of Sir William Herschel 
 disclosed the existence of a new feature in its structure of a very inte- 
 resting kind. He has represented the object as a bright round nebula, 
 surrounded by a halo or glory at a distance from it, and accompanied by 
 a companion. Sir John Herschel discovered that the south following 
 half of the ring was divided into two parts, producing an appearance 
 bearing some resemblance to the bifurcation of the Milky Way. This 
 circumstance suggested the probability of the nebula being a vast sidereal 
 system, identical in structure with that to which it offered so striking an 
 analogy. The telescopes of Lord Rosse have served to destroy this 
 interesting surmise, by showing the nebula to be of a totally different 
 structure from that which it exhibited in instruments of inferior power. 
 It has been found to be in fact composed of a series of spiral convo- 
 lutions, arranged with remarkable regularity. A connexion has also 
 been traced by means of these spirals between the nebula and its com- 
 panion. The number of nebulae in which Lord Rosse had already detected 
 unequivocal indications of a spiral structure, amounted to fourteen. 
 
 The remarkable class of objects termed Planetary Nebulae, when viewed 
 in the 6-feet reflector of the distinguished astronomer just alluded to, 
 have failed to exhibit that uniform aspect which had proved such a stum- 
 bling-block to Herschel in his attempts to explain their structure. Five 
 
 * Phil. Trans., 1850, p. 499, et seq. 
 
670 HISTORY OF PHYSICAL ASTRONOMY. 
 
 nebulae, which previous astronomers had represented as possessing a 
 round uniform disk, were found by Lord Rosse to exhibit unequivocal 
 indications of an annular structure. Nebulae of this description are 
 extremely rare in the heavens. Only pur of such objects had hitherto 
 been recognised by astronomers, two in the northern and two in the 
 southern hemisphere. 
 
 The class of objects comprehended under the designation of Nebulous 
 Stars, whose appearance Sir William Herschel was unable to account for, 
 except by assuming the existence of a shining fluid existing independ- 
 ently in space, have also exhibited, in the telescopes of the distinguished 
 nobleman just referred to, an aspect which entirely obviates the necessity 
 of having recourse to such an hypothesis. One of the most interesting 
 objects of this class is the nebulous star marked No. 450 in Sir John 
 Herschel's catalogue of 1833. The star-like point of this object, when 
 viewed in the 6-feet reflector, is seen to be placed in the centre of a 
 nebulous nucleus, and beyond there appears a nebulous ring completely 
 separated from the latter. Another nebulous star, i Orionis, has been 
 found to exhibit a somewhat analogous aspect. The pale nebulous light 
 surrounding the star is found to contain a dark cavity, not exactly sym- 
 metrical with respect to the star. 
 
 Of the other nebulas examined by Lord Rosse, one of the most inte- 
 resting is the one marked No. 2098 in Sir John Herschel's northern 
 catalogue. This object has been found to exhibit CIIISCB, indicating, in 
 all probability, a nebulous ring seen edgeways. This phenomenon appears 
 to afford a valuable experimentum crucis in deciding the question relative 
 to the structure of those nebulas which exhibit an annular aspect. It 
 is not difficult to see that such an appearance might be produced either 
 by a real ring or by a hollow spherical shell of nebulous light. In the 
 latter case, however, it would always exhibit a perfectly round appear- 
 ance ; whereas, in the former, there is only one position of the ring 
 in which it would appear round. In every other position it would appear 
 more or less elliptical, and when its plane passed through the earth, it 
 would resemble two opposite ans<z attached to the central object, provided 
 there was one. Now, since observation has, in one instance at least, dis- 
 closed indications of such ansa, and thereby afforded unequivocal evi- 
 dence of the actual existence of a ring composed either of stars or of 
 a nebulous substance, we may reasonably conclude that the annular 
 appearance exhibited by several other nebulas is occasioned by a similar 
 cause, and not by a hollow sphere of nebulous light. We are also 
 warranted by the same consideration in supposing that those elliptical 
 nebulas which exhibit dark chinks are in reality nebulous rings of more 
 or less regular structure, seen obliquely with respect to the line of vision, 
 and not hollow elliptical shells of nebulous light. 
 
 Sir John Herschel has remarked, in the paper containing his catalogue 
 of nebulas visible in the northern hemisphere, that further discoveries of 
 such objects can only be expected to result from the use of telescopes pos- 
 sessing a higher degree of optical power than a reflector of eighteen 
 inches' aperture, the instrument with which all the nebulas hitherto known 
 to exist were mainly discovered. The observations of Lord Rosse are 
 plainly destined to be instrumental in realising this expectation. Although 
 no direct search for new nebulas has yet been undertaken by his lord- 
 ship, several objects of this class, which it was impossible to discern in 
 instruments of inferior power, have been incidentally revealed by the im- 
 mense light of the 6-feet reflector. It is thus evident that, with a greater 
 
HISTOKY OF PHYSICAL ASTRONOMY. 571 
 
 increase of optical power, new. accessions will be constantly made to the 
 visible extent of the universe. 
 
 The results which Lord Rosse has already achieved by means of his 
 powerful telescopes, clearly point out the course which must be pursued 
 in order to acquire some degree of knowledge respecting the nature and 
 constitution of those magnificent systems of sidereal bodies which have 
 been found to pervade the immensity of space. In the first place, it is 
 manifest that a careful delineation of the different parts of each system 
 forms an indispensable preliminary to any progress in this branch of 
 enquiry. It is only by a subsequent comparison, instituted between 
 nebula of every observable variety of form, that any knowledge can be 
 obtained respecting the real structure of those wonderful systems. 
 Among them there are, doubtless, systems of different orders, as we find 
 exemplified to a limited extent in the solar system, but among those of 
 the same order we have just grounds for suspecting that a kindred form 
 of structure prevails. It is probable that such systems are viewed in 
 every variety of position relative to the earth, and hence we may reason- 
 ably expect that, by an extensive collation of their apparent forms, it will 
 be possible to arrive at some definite conclusions respecting their actual 
 configuration in space. Formidable as the problem relative to the struc- 
 ture of these systems may appear when considered from this point of view, 
 its difficulties are vastly enhanced by the internal changes which are con- 
 stantly taking place in each system. It must be borne in mind that, 
 although the various bodies of which each system is composed are doubt- 
 less linked together by intimate physical relations, the condition which 
 thus subsists is one of dynamical stability rather than statical equilibrium. 
 In fact, we are amply justified, both by reason and analogy, in supposing 
 that the constituent bodies of every system are revolving in curvilinear 
 orbits under the influence of their mutual gravitation. It is manifest 
 that from this cause each system will be liable, in process of time, to 
 undergo a modification of form. Hence it follows, that not only will 
 systems of the same order exhibit different external forms when com- 
 pared with each other, but even the same system will vary from time 
 to time relatively to itself. That the eccentric position of the observer, 
 and the displacements arising from the internal movements of its con- 
 stituent bodies, may cause a system to appear very complicated, while at 
 the same time its various parts are adjusted in the most perfect harmony, 
 is evident, from a consideration not only of the planetary system itself, but 
 also of those miniature systems of which it is mainly composed. What 
 more admirable arrangements can the imagination conceive than those 
 which pervade the system of Jupiter's satellites, and yet when this exqui- 
 site mechanism is casually viewed through a telescope, what can be more 
 devoid of symmetry than the configurations of its different parts? 
 
 It is manifest, from the foregoing considerations, that, in order to acquire 
 just ideas respecting the construction of those vast systems of worlds which 
 the telescope has shown to be distributed throughout the immensity of 
 space, an assiduous course of observation and research, prosecuted through- 
 out a long succession of ages, is absolutely indispensable. The investi- 
 gation of the dynamical laws by which those systems are governed and 
 their stability is assured, must be regarded as an ulterior object. It is 
 only in the case of the more simple systems, the relative movements of 
 whose constituent bodies admit of being readily deduced from observation, 
 that the dynamical conditions of the system can form a feasible subject 
 
572 HISTORY OF PHYSICAL ASTRONOMY. 
 
 of research. To attempt to discover the mechanical structure of more 
 complicated systems, before observations were amassed capable of forming 
 a sure groundwork of research, would be manifestly a hopeless under- 
 taking. All speculations directed to thi end must therefore be regarded 
 as premature, in the present state of sidereal astronomy*. 
 
 The remarkable Zone of light termed the Milky Way, which is seen 
 encircling the starry heavens, has in all ages excited the admiration of 
 mankind, and stimulated the enquiries of the contemplative observer of 
 nature. It would serve no useful purpose to refer here to the erroneous 
 opinions entertained by various ancient philosophers respecting the nature 
 of this luminous circle. Aristotle supposed it to be composed of a sub- 
 stance occupying an intermediate position between the terrestrial atmo- 
 sphere and the region of the stars. In no part of his great work has 
 Ptolemy expressed an opinion respecting the nature of the Milky Way. 
 It is a remarkable fact, however, that Democritus hit upon the true ex- 
 planation of its aspect. According to Plutarch, he maintained that it 
 was composed of a multitude of small stars, so very near to each other, 
 that their light became blended together so as to produce the appearance 
 of a luminous zonef. A similar opinion respecting the Milky Way is 
 expressed by Manilius, in his poem on the sphere t. 
 
 Copernicus has cautiously abstained from any allusion to the Milky 
 Way, in his immortal work wherein he expounds the true system of the 
 universe. Tycho Brahe supposed it to be formed of a nebulous sub- 
 stance, as is evident from his speculations on the origin of the new star 
 which appeared in the year 1572. A similar view of its structure was 
 implied in Kepler's speculations on the origin of the new star of 1604 ||. 
 
 The invention of the telescope, about the beginning of the seventeenth 
 century, had the effect of conducting astronomers to a more accurate 
 knowledge respecting the constitution of the Milky Way than had hitherto 
 prevailed. When Galileo first explored the heavens with his telescope, 
 he discovered everywhere, to his unspeakable admiration, a multitude of 
 stars which were too faint to be perceived with the naked eye. The 
 aspect of the Milky Way was found by him to arise wholly from its being 
 composed of a vast collection of small stars in close proximity to one 
 another. In the Sidereus Nuncius, a small work containing the first 
 announcement of his telescopic discoveries in the heavens, he congratu- 
 lates himself on having put an end to the ancient controversy respecting 
 the Milky Way, by actually exhibiting its structure to the senses IF. 
 Thenceforward it has been generally admitted, that the Milky Way is, in 
 fact, no other than a vast assemblage of stars too small to be individually 
 visible. 
 
 * Among those who have partially laboured on the subject of nebulse, no one exhi- 
 bited such high qualifications for cultivating so delicate a branch of stellar astronomy as 
 Ebenezer Porter Mason, a young American of great promise, who unfortunately died in 
 the year 1840, at the early age of twenty-one years. An important paper, containing the 
 results of his observations of some remarkable nebulae, is inserted in vol. vii. of the 
 Transactions of the American Philosophical Society. There is a very interesting ac- 
 count, of the life and writings of this true son of genius, written by Professor Olmsted, 
 of Yale College, Connecticut. (12mo, New York, 1842.) 
 j- De Placit. lib. iii., cap. i. 
 
 J " An major densa stellarum turba corona 
 
 Contexit fiammas, et crasso lumine candet, 
 Et fulgorenitet collate clarior orbis." Lib. i., cap. ix. 
 
 Progymnasmata, p. 795. || " De Stella Nova," cap. xxiii., p. 115. 
 
 fl Opere di Galileo, tome ii., p. 4. 
 
HISTOBY OF PHYSICAL ASTRONOMY. 573 
 
 Although the nature of the Milky Way was now well understood, 
 no attempt was made for a long time to investigate the particulars of 
 its structure, and to connect its appearance with the distribution of the 
 stars throughout the other parts of the visible heavens. This important 
 object was at length accomplished by Thomas Wright, in his " Theory of 
 the Universe," a work to which we have already had occasion to allude. 
 The author has given an exposition of his theory in nine letters addressed 
 to a friend. Alluding to the current opinion respecting the Milky Way, 
 that it is composed entirely of stars, he asserts that this view of its 
 nature was supported by his own observations with a reflector of one foot 
 focal length. The following statement embraces the more important 
 points of his theory. 
 
 If we judge of the Milky Way by phenomena only, we must conclude 
 it to be a vast ring of stars, scattered promiscuously round the celestial 
 regions in the direction of a perfect circle. This view of its structure, 
 however, does not accord with the aplanatic position and irregular distri- 
 bution of multitudes of other stars of the same nature, dispersed through- 
 out the celestial regions. It is not consistent with the harmony which 
 pervades all the other arrangements of nature, that one portion of the 
 stars should be disposed with the most perfect regularity, while all the 
 others were scattered about in the utmost confusion, without any regard 
 to symmetry. It is more probable that the whole visible creation of 
 stars forms one vast system, the parts of which are adjusted with the most 
 perfect harmony, and that its incongruous aspect is due to the eccentric 
 position in which it is viewed, and to the motions of the constituent 
 bodies relatively to each other. When we reflect upon the various con- 
 figurations of the planets, and the changes which they perpetually 
 undergo, we may be assured that nothing but a like eccentric position of 
 the stars could occasion such confusion among bodies otherwise so regular. 
 In like manner we may conclude that, as the planetary system, if viewed 
 from the sun, would appear perfectly symmetrical, so there may be some 
 place in the universe where the arrangement and motions of the stars 
 may appear most beautiful. 
 
 If we suppose the sun to be plunged in a vast stratum of stars, of 
 inconsiderable thickness compared with its dimensions in other respects, 
 it is not difficult to see that the actual appearance of the heavens may be 
 reconciled with a harmonious arrangement of the constituent bodies of 
 such a system, relative to some common centre, provided it be admitted, 
 at the same time, that the stars have all a proper motion. In such a 
 system it is manifest that the distribution of the stars would appear more 
 irregular the farther the place of the spectator was removed from the 
 centre of the stratum towards either of the sides. It is also evident that 
 the stars would appear to be distributed in least abundance in the oppo- 
 site directions of the thickness of the stratum, the visual line being 
 shortest in either of those directions, and that the number of visible 
 stars would increase as the stratum was viewed through a greater depth, 
 until at length, from the continual crowding of the stars behind each 
 other, it would ultimately assume the appearance of a zone of light. 
 According to this hypothesis, then, the whole of the visible stars, including 
 the sun, form part of the system of the Milky Way, their irregular dis- 
 tribution being occasioned by the eccentric position of the sun, combined 
 with their own proper motions. 
 
 There are, in all probability, various systems resembling the Milky Way; 
 but it is not unreasonable to suppose, that there may be systems of stars 
 
574 HISTOBY OF PHYSICAL ASTRONOMY. 
 
 differing as much in the order and distribution of their constituent bodies 
 as the zones of Jupiter do from the rings of Saturn. We may, in fact, 
 suppose that some systems of stars move in perfect spheres, at different 
 inclinations and in different directions ; 'while others, again, may revolve, 
 like the primary planets, in a general zone, or more probably in the 
 manner of Saturn's ring; nay, perhaps, ring within ring, to a third or 
 fourth order *. 
 
 In propounding his theory of the Milky Way, of which the foregoing 
 is a brief sketch, Wright does not recognise the existence of systems of 
 stars subordinate to that great system. He, indeed, asserts, that those 
 cloudy spots which are resolvable into stars, might be explained by the 
 principles which he laid down, but he does not formally assign to them a 
 place in his theory. In the concluding letter, however, he appears to 
 admit the existence of a multitude of sidereal systems within the boun- 
 daries of the visible universe, subordinate, of course, to the great system 
 of the Milky Way. We also find, in the same letter, an interesting ex- 
 pression of his opinion respecting those nebulae which had hitherto proved 
 irresolvable even in the best telescopes. Taking into consideration the 
 multitude of sidereal systems included within the confines of the visible 
 universe, it appeared to him not improbable that the immensity of space 
 is occupied by an endless succession of systems, analogous in their struc- 
 ture to the great system (the Milky Way) of which the visible universe is 
 composed. " That this, in all probability, may be the real case," says he, 
 " is in some degree made evident by the many cloudy spots, just perceiv- 
 able by us, as far without our starry regions, in which, although visibly 
 luminous spaces, no one star or particular constituent body can possibly 
 be distinguished ; those, in all likelihood, may be external creation, bor- 
 dering upon the known one, too remote for even our telescopes to reach" \ 
 
 The speculations of Wright on the Milky Way are so consistent with 
 sound philosophy and the results of observation, that they cannot fail to 
 obtain the sanction of every person who submits them to a careful exami- 
 nation. At the time of their original promulgation, however, the atten- 
 tion of mathematicians had become deeply engrossed with the develop- 
 ment of the theory of gravitation, while astronomers, on the other hand, 
 were impressed with the necessity of introducing a corresponding degree 
 of refinement into their observations, and establishing with the utmost 
 possible accuracy the elements of the planetary movements. It hap- 
 pened, from this cause, that only individuals of the same speculative 
 turn of mind as Wright himself were induced to adopt his theory as the 
 basis of further enquiry. Such was the case with respect to Kant, the 
 celebrated German metaphysician, who, in the year 1755, published a work 
 containing an exposition of his views respecting the cosmical arrangement 
 of the celestial bodies. In the introduction to this work, he acknowledges 
 that the germ of his ideas on the distribution of the stars was suggested 
 to him by the speculations of Wright on the subject. His system, 
 indeed, does not materially differ from that of the English philosopher. 
 A system bearing a close affinity to either, was also propounded a few 
 years afterwards, by Lambert, in his " Cosmologies,! Letters."! 
 
 The physical constitution of the Milky Way, and its connexion with 
 
 * It is impossible not to be struck with the connexion subsisting between these saga- 
 cious remarks, and the phenomena which Lord Rosse has recently succeeded in disclosing 
 by means of his powerful telescopes. 
 
 f- Theory of the Universe, p. 83. 
 
 J Lambert has aptly denominated the Milky Way the Ecliptic of the Fixed Stars. 
 
HISTORY OF PHYSICAL ASTEONOMY. 575 
 
 the arrangement of the stars constituting the visible universe, formed a 
 subject of too great importance in stellar astronomy not to have engaged 
 the attention of Sir William Herschel. The results of his early labours 
 relative to this branch of enquiry are contained in two papers inserted in 
 the volumes of the Philosophical Transactions for 1784 and 1785. His 
 theory agrees in the main with that of Wright and the other enquirers 
 above alluded to ; but in this, as in every other instance of his specula- 
 tions, he produced a strong conviction of their reality in men's minds, by 
 establishing a close connexion between them and the results of actual 
 observation. His powerful telescopes enabled him to penetrate far more 
 deeply into the structure of this wonderful zone than had been hitherto 
 possible, when, to his admiration, he found it to consist, in every part of 
 its visible course, of an innumerable multitude of small stars*. On one 
 occasion he found that in the short interval of one-quarter of an hour 
 no fewer than 116,000 stars had passed through the field of view of his 
 telescope f. On another occasion he found that in forty-one minutes of 
 time as many as 258,000 stars had passed in review before him { ! 
 
 It would be inconsistent with the object of this work, to enter into 
 a detailed account of the researches of Herschel on the Constitution of 
 the Milky Way. A remarkable method devised by him for ascertaining 
 the configuration in space of this great sidereal system, consisted in ex- 
 amining the heavens at different distances from the Galactic circle, and 
 numbering the stars visible in the field of view of his telescope. Assuming 
 that the stars are uniformly distributed throughout space, and that the 
 telescope suffices to penetrate to the utmost limits of the sidereal stratum 
 constituting the Milky Way, it is manifest that the number of stars visible 
 in the field of view of the telescope would increase with the length of the 
 visual line, and would thereby afford an indication of the distance from 
 the observer to the exterior surface of the Milky Way. Hence, by com- 
 paring together the lengths of the various lines found in this manner, and 
 taking into consideration their respective distances from the Galactic 
 circle, the actual configuration in space of the Milky Way may be ascer- 
 tained. Such is a brief outline of the celebrated method of gauging the 
 heavens, which Herschel practised to a vast extent in the early period of 
 his researches on the constitution of the Milky Way. 
 
 Although Herschel assumed as one of the fundamental points of his 
 theory of the Milky Way, that the stars are distributed uniformly 
 throughout space, he had recourse to this principle, not from a conviction 
 of its being absolutely true, but because, while there was a probability of 
 its constituting a tolerable approximation to the actual state of nature, it 
 at the same time had the advantage of affording a convenient basis of 
 calculation. Even as early as the year 1785, he remarked that in many 
 
 * Phil. Trans., 1784, p. 438. f Ibid., 1785, p. 244. { Ibid., 1795, p. 70. 
 
 These observations were made by Herschel with the 20-feet reflector, the field of 
 view of which was 15' in diameter. In some instances the number of stars in the field 
 of view did not exceed a few units. On one occasion, indeed, Herschel was enabled to 
 count only three stars in four successive gauges. The paucity of stars in the field of 
 view was of course mainly observable in those parts of the heavens which were at a con- 
 siderable distance from the Milky Way. As the gauges approached the Galactic circle 
 the number of stars rapidly increased, amounting in many instances to between 400 and 
 500, and on one occasion running as high as 588. A list of these gauges, with the 
 elements of their respective positions, is given by Herschel in his paper inserted in the 
 Philosophical Transactions for 1785. They amount in number to between three and 
 four thousand. 
 
576 HISTORY OF PHYSICAL ASTRONOMY. 
 
 parts of the Milky Way the stars exhibited indications of a tendency to 
 collect together into separate clusters *. It was this circumstance which 
 induced him to assert that some parts of our sidereal system seemed to 
 have suffered more from the ravages of -time than other parts f. In con- 
 firmation of this statement, he remarked that in the constellation Scor- 
 pio there existed an absolutely dark space, about 4 broad, in which not 
 a single star was visible ; while on the other hand the object marked No. 
 80 in Messier's catalogue, one of the richest and most compressed clusters 
 of stars in the heavens, was situate close upon its western border J. 
 
 In his paper of 1802, Herschel again referred to the manifest evidence 
 of a tendency of the stars in the Milky Way to form themselves into 
 distinct sidereal aggregations. In all those instances wherein small 
 spaces of a milky aspect in a state of isolation were discernible, he 
 found that the brightness was invariably greatest in the middle, and 
 least around the borders ; and since he had shown, by means of his 
 powerful telescopes, that the peculiar aspect of the Milky Way arose 
 entirely from the presence of a multitude of small stars in close prox- 
 imity to each other, this gradation of brightness clearly indicated that the 
 stars of each distinct group were clustering towards a common centre. 
 A striking example of the tendency of the stars to collect together into 
 separate systems was cited by him in the paper just referred to. He 
 remarked that in the interval between @ and y Cygni, including a space 
 of about 5, the stars seemed to be clustering towards opposite regions 
 of the heavens. By a computation, based upon the number of stars 
 contained in the field of view of bis telescope when directed towards 
 different parts of this space, he found that it contained at least 331,000 
 stars. Hence, admitting that the stars were really clustering in equal 
 numbers towards opposite regions of the heavens, as observation seemed 
 to warrant, he concluded that each of such clusters contained at least 
 165,000 stars ! 
 
 In a paper which he communicated to the Royal Society in the year 
 1814, Herschel again alluded to the tendency of the stars constituting 
 the Milky Way to arrange themselves into separate systems. He also 
 took into consideration the consequence which must inevitably ensue from 
 the continued operation of such a clustering process [|. By a series of. 
 careful observations he found that the clusters of various kinds were 
 much more numerous within the Milky Way and the regions bordering 
 upon it, than they were in the more distant regions of the heavens 
 with respect to the Galactic circle. He considered that under the 
 influence of the mutual attraction of the stars this clustering process 
 would continue until it would ultimately result in the complete breaking 
 up of the Milky Way, and the formation of a number of sidereal systems 
 totally distinct from one another. The grandeur of this conclusion was 
 worthy of the genius of Herschel ; but it may be urged against its 
 admission that we have no reason to suppose that the various parts of 
 the Milky Way are not already in a condition of dynamical stability, and 
 that the clustering patches of light by which it is distinguished through- 
 out its visible course, are not in reality'so many sidereal systems, existing 
 independently of one another, but subordinate to the great system of 
 which they apparently form a part. 
 
 * Phil. Trans., 1785, p. 255. f Ibid., p. 256. 
 
 \ Ibid. Ibid., 1802, p. 495. || Ibid., 1814, p. 248 et seq. 
 
HISTORY OF PHYSICAL ASTRONOMY. 577 
 
 Although the hypothesis of a uniform distribution of the stars in space, 
 combined with their arrangement, in the form of a vast stratum of incon- 
 siderable thickness, accounts for the general appearance of the starry 
 heavens, still it is not improbable that the gradual increase in the num- 
 ber of stars visible upon approaching the Milky Way, may arise, in some 
 degree at least, from a real condensation of them towards the plane of 
 the Galactic circle. This point can only be decided by taking into account, 
 in conjunction with the number of stars visible in the field of view of 
 the telescope, their relative distances as indicated by their apparent mag- 
 nitudes. If we suppose the observations to be limited to stars of a cer- 
 tain magnitude, and to include all those of superior brightness, which 
 are presumed, in consequence, to be nearer to the earth, the question will 
 then be reduced to the investigation of the law of distribution of the stars, 
 comprehended within a sphere whose radius corresponds to the apparent 
 magnitude of the extreme stars. Now, if in such a case the stars appear 
 more numerous upon approaching the Milky Way, it is manifest, from 
 this circumstance alone, that they must increase in density towards the 
 plane of the Galactic circle. Moreover it is evident that, for two such 
 spheres of different radii, the maximum number of stars would bear to 
 the minimum a much higher ratio in the case of the larger sphere than 
 it would do in that of the smaller, provided there was a real condensa- 
 tion of the stars. The work recently published by M. Struve, entitled 
 11 Etudes cT Astronomic Stellaire" contains some remarkable speculations 
 on the constitution of the Milky Way, which bear directly upon this 
 question. By a skilful discussion of the gauges of Herschel, and the 
 catalogues of modern astronomers, chiefly those of Bessel and Arge- 
 lander, he has ascertained that the stars of the visible universe are not 
 uniformly distributed throughout space, but that they are gradually more 
 condensed towards the plane of the Milky Way. He moreover has suc- 
 ceeded, by means of empirical formulae, in representing the law of appa- 
 rent condensation with remarkable fidelity. Our limited space prevents 
 us from giving a detailed account of his interesting researches on this oc- 
 casion. 
 
 During Sir John Herschel's residence at the Cape of Good Hope, he 
 executed an extensive series of observations, with the view of discovering 
 whether the distribution of the stars in the southern hemisphere cor- 
 responded with the results of Sir William Herschel's similar labours, 
 prosecuted mainly on the opposite side of the Galactic circle. In order 
 that the observations might admit of comparison with those of his father, 
 they were made according to the same method, and with a telescope of 
 the same optical power. They embraced a region of the celestial sphere 
 extending from the south pole of the Galactic circle to a distance of 150, ' 
 measured upon a great circle passing through it. The whole number of 
 stars counted in the telescope amounted to 68,948, which were included 
 within 2299 fields of view *. The results were found to present a remark- 
 able agreement with those deduced by M. Struve from the gauges of Sir 
 William Herschel. It would appear from them, that the southern hemi- 
 sphere is somewhat richer in stars than the northern. This would in- 
 dicate that our system is not situate exactly in the plane of the Galactic 
 circle, but is displaced a little towards the north. The apparent position 
 of the Milky Way presents an interesting accordance with this conclu- 
 
 * Results of Ast. Obs., &c., p. 380. 
 
 P P 
 
578 HISTORY OF PHYSICAL ASTRONOMY. 
 
 sion ; for it lias been found that its mean course does not coincide 
 exactly with a great circle of the sphere, but with a parallel distant 
 about 92 from the Galactic north pole*. 
 
 By a computation based on the gaugae in both hemispheres relative to 
 the Galactic circle, Sir John Herschel found that the whole number of 
 stars visible in a reflecting telescope of 18 inches aperture amounts to about 
 five millions and a half f. It may be remarked in connexion with this 
 fact, that the whole number of stars visible to the naked eye in both 
 hemispheres does not exceed six thousand, even in the case of persons of 
 the most acute vision}. 
 
 We shall conclude our labours with a brief account of the speculations 
 of astronomers on the subject of the Extinction of Light in its passage 
 through space. We have seen that, even as early as the sixteenth century, 
 Jordano Bruno ventured to assert that the universe is peopled with an 
 infinite number of suns. As soon as the telescope disclosed the actual 
 existence of innumerable stars invisible to the naked eye, the doctrine of 
 an infinity of worlds presented itself with greater plausibility to minds 
 imbued with a natural propensity towards speculation. In a short paper 
 inserted in the Philosophical Transactions for 1720, Halley has considered 
 the effect which would be produced upon the aspect of the heavens if the 
 universe was peopled with an infinite number of shining bodies . The re- 
 sult of his enquiry was not unfavourable to that hypothesis. He remarked 
 that the light of the stars diminishes at a more rapid rate than the interval 
 included between them does, the law of diminution being represented in 
 the one case by the reciprocal of the square of the distance, and in the 
 other simply by the reciprocal of the distance. He moreover added, that 
 when the stars are very remote they vanish, even in the most powerful tele- 
 scopes. Upon these grounds he concluded that, even if the number of 
 bodies was infinite, the heavens could not exhibit a uniformly illuminated 
 aspect from their combined lustre. 
 
 Plausible as the reasoning of Halley undoubtedly is, it cannot be 
 regarded as satisfactory when submitted to close examination. Chesaux, 
 the Swiss astronomer, to whom allusion has already been made on more 
 than one occasion, arrived! at a different conclusion. He asserted that 
 the light of an infinite number of shining bodies would cause the heavens 
 to appear everywhere equally illuminated with the sun, and upon this 
 ground he maintained that we must either abandon the supposition of 
 infinity, or admit that light is gradually extinguished in its passage 
 through the celestial regions. A similar view of the subject was enter- 
 tained by Olbers, the celebrated German astronomer. M. Struve, in his 
 "Etudes d'Astronomie Stellaire," has given an account of some interesting 
 speculations on this subject, which were suggested to him by his researches 
 on the law of the distribution of the stars constituting the visible universe. 
 He considers that positive evidence in favour of the extinction of light 
 is afforded by the circumstance that the space-penetrating power of a 
 telescope, when computed according to the usual principles, far exceeds 
 
 * Struve, Etudes d' Astronomic Stellaire, p. 61. 
 
 f Results of Ast. Obs., &c., p. 381. The precise number of stars assigned by his 
 computations is 5,331,572. He considers, however, that the number really visible in 
 the telescope is much greater, as in many parts of the Milky Way the stars appeared so 
 crowded as to defy counting. 
 
 \ Struve, Etudes d' Astronomic Stellaire, p. 2. 
 
 Phil. Trans., 1720, p. 22. 
 
HISTORY OF PHYSICAL ASTRONOMY. 579 
 
 its value as indicated by actual observation. Thus, according to the 
 usual theory, M. Struve found that the space-penetrating power of the 
 20-feet reflecting telescope of Herschel was 74.83, the linear unit being 
 the distance of the smallest stars visible to the naked eye. On the 
 other hand, he found by a computation based upon the law of con- 
 densation of the stars, which he had deduced from the observations of 
 Herschel and other astronomers, that the radius of a sphere embracing 
 the smallest stars visible in the 20-feet reflecting telescope of Herschel, 
 does not exceed 25.672 of the same units. It would appear, therefore, 
 that the telescope does not in reality penetrate into space beyond the third 
 part of the distance assigned by theory. M. Struve maintains that the 
 inconsisteuce between theory and observation which is thus found to pre- 
 vail, can only be accounted for by supposing that the light of the stars is 
 gradually extinguished in its passage through the celestial regions. 
 Adopting this hypothesis, he proceeds to investigate the results deducible 
 from it, assuming as a fundamental principle that the light is enfeebled 
 in geometrical progression as the space traversed by it increases in arith- 
 metical progression. By strict computation he found that the theory 
 which usually assigns the space-penetrating power of the telescope might 
 be reconciled with observation, by supposing that the light of the stars 
 was enfeebled to the extent of T ^ T th of its intensity in its passage through 
 a space equal to the distance of a star of the first magnitude. 
 
 The extinction of light occasions a diminution in the brightness of all 
 the stars that are visible, either to the naked eye or in the telescope. M. 
 Struve found, that for the smallest stars visible to the naked eye, the 
 diminution of brightness is equal to -j-^ths of the whole quantity. For 
 stars of the ninth magnitude the diminution of brightness amounts to 
 j^gths, and for the smallest stars visible in the 20-feet reflecting tele- 
 scope of Plerschel the diminution of brightness is no less than -^ths of 
 the whole quantity. 
 
 The effect of the extinction of light upon the space-penetrating power 
 of telescopes is equally remarkable. The 20-feet reflector of Herschel, 
 which M. Struve calculated to have a penetrating power of 813.9, abstrac- 
 tion being made of the extinction of light, was found by him to have a 
 power of only 250.7, when the influence of that principle was taken into 
 account. In like manner he found that the space-penetrating power of 
 the 40-feet reflecting telescope of the same astronomer was reduced from 
 2080.3 to 368.5, in consequence of the extinction of light. It is manifest 
 that, if these results be admitted as true, the distances assigned by Her- 
 schel to the celestial bodies, must necessarily undergo a corresponding 
 diminution. 
 
 If light really diminishes in geometrical progression relative to the 
 space through which it is transmitted, it is evident that, beyond a deter- 
 minate distance, the light of a star can produce no sensible effect to an 
 observer at the earth, and therefore the apparent illumination of the 
 general ground of the heavens will depend wholly on the light of the 
 stars included within that limit. This circumstance has suggested to M. 
 Struve some curious calculations relative to the effect contributed by the 
 different classes of stars towards the brightness of the heavens, as observ- 
 able in the region of the Milky Way, and in the direction of the poles 
 of the Galactic circle. The following are some of the more interesting 
 conclusions at which he arrived : 
 
 1st. The stars situate beyond the reach of tho 20-feet reflecting tele- 
 
 p p 3 
 
580 HISTOKY OF PHYSICAL ASTRONOMY. 
 
 scope of Herscliel, do not contribute more than 12 per cent, to the bright- 
 ness of the Milky Way. 
 
 2nd. If the effect produced by the stars visible to the naked eye be 
 abstracted, the illumination of the groutid of the heavens in the middle 
 of the Milky Way will be expressed by 0.92007, the total illumination 
 being represented by unity. 
 
 3rd. The total illumination of the heavens, in the direction of the poles 
 of the Galactic circle, is only T - ~jths of what it is in the middle of the 
 Milky Way. 
 
 4th. When the combined lustre of stars of distinct classes is con- 
 sidered, the ratio of the illumination in the Milky Way to that in the 
 direction of its poles, gradually increases as the stars are more remote. 
 
 5th. If we exclude from consideration the stars visible to the naked 
 eye, the brightness of the heavens in the direction of the poles of the 
 Galactic circle, is only one-sixth of the brightness of the Milky Way. 
 
 It must be admitted that the hypothesis of the extinction of light, from 
 which M. Struve has deduced the foregoing interesting conclusions, can- 
 not be considered as a principle of physics, the reality of which has been 
 established beyond all doubt upon the solid basis of observation. It has 
 been mentioned, that his reason for adopting this principle was founded 
 on the circumstance of the space-penetrating power of the telescope 
 having been discovered by him to be in reality much less than what 
 theory indicated it to be. The question may be considered under the 
 following aspect : In the Milky Way the average number of stars visible 
 in the field of view of the 20-feet reflecting telescope of Herschel, was found 
 by M. Struve to be 122, and the distance of the smallest of such stars, as 
 deducible from his researches on the law of the density of the stars, was 
 determined by him to be 25.672 units. Hence, if the density of the 
 stars in the direction of the plane of the Milky Way was uniform, as M. 
 Struve in his researches assumed it to be, the number of stars visible in 
 the telescope at the distance of 74.83 units, ought to be 3021. Now, 
 the space-penetrating power of the telescope, as computed upon the ordi- 
 nary principles, was found by M. Struve to be represented by 74.83 units. 
 The conclusion would, therefore, appear to be unavoidable ; either that 
 the density of the stars diminishes towards the limits of the Milky Way, 
 or that the light of the stars is gradually extinguished in its passage 
 through the celestial regions to the earth. With respect to the question 
 of a diminution of density, it is to be remarked that, since the incon- 
 sistency between theory and observation, above referred to, is presumed to 
 manifest itself in every part of the contour of the Milky Way, it cannot 
 be considered as available in explaining that inconsistency, unless the sun 
 be supposed to be situate near the centre of the great sidereal disk, con- 
 stituting the Milky Way. M. Struve, however, contends that we have no 
 knowledge of the limits of the Milky Way that to us it is absolutely 
 unfathomable, and consequently that there does not exist any probability 
 of the sun being situate near the centre of the Galactic circle. Upon 
 these grounds, therefore, he maintains that the explanation of the incon- 
 sistency, by a diminution in the density of the sidereal stratum, in the 
 direction of its principal plane, is inadmissible, in ipso limine. 
 
 The assertion of M. Struve with respect to the absolute unfathom- 
 ability of the Milky Way, appears to be founded on certain observations 
 cited by Sir William Herschel in the course of his sidereal researches ; 
 but, with all due deference to the authority of the illustrious astronomer of 
 
HISTOBY OF PHYSICAL ASTROKOMY. 581 
 
 Pulkowa, we are inclined to believe that he has not apprehended the real 
 drift of the language used by Herschel on those occasions to which he 
 refers. It appears to us evident, from the tenor of Sir William Herschel's 
 remarks on the Milky Way, scattered through his various papers, that he 
 considered it to be a vast sidereal system of definite dimensions, and, 
 generally speaking, of ascertainable limits. In his important paper on 
 the subject, inserted in the Philosophical Transactions for 1785, he has 
 remarked, that even in those cases wherein the gauges were very high, 
 the stars were neither so small nor so crowded, as they must have been 
 on the supposition of a much farther continuance of them, and when cer- 
 tainly a milky nebulous appearance must have come on *. On a sub- 
 sequent occasion, indeed, he cited some observations of the Milky Way, 
 from which it appeared that, notwithstanding the application of higher 
 and higher degrees of optical power, there still remained traces of nebu- 
 losity in the telescope, indicating that the limits of the stratum had not 
 been reached. It is important to remark, however, that the object he had 
 in view in citing these observations, was not for the purpose of showing 
 that the Milky Way was unfathomable even in those parts to which his 
 observations referred, and to which such an expression, in a certain sense, 
 was fairly applicable ; but to demonstrate that the nebulosity in the tele- 
 scope was not of an ambiguous nature that, in fact, it was attributable 
 to the circumstance of its consisting of stars too remote to be distinctly 
 visible by any optical aid that was available, and not to its being in reality 
 composed of nebulous matter f . 
 
 A more serious objection urged by M. Struve against the hypothesis of 
 a diminution of the density of the stars in the plane of the Milky Way, 
 is founded on the circumstance that an examination of the gauges of 
 Herschel conducts to the same law of condensation in a direction per- 
 pendicular to that plane, with the law which he found, from the obser- 
 vations of Bradley and Argelander, to prevail in the immediate vicinity 
 of the sun, as far as the stars of the eighth and ninth magnitudes. By 
 his researches on the gauges of Herschel, he found that, at a distance 
 from the plane of the Milky Way equal to the radius of a sphere com- 
 prehending the stars of the seventh magnitude, the density of the stars 
 was equal to 0.41365, the mean density in the Milky Way being repre- 
 sented by unity. His examination of the zones of Bessel gave him 
 0.40525 for the density at the same distance. In like manner he found 
 that, at a distance from the Milky Way equal to the radius of a sphere 
 embracing the stars of the eighth magnitude, the density of the stars, as 
 deducible from the gauges of Herschel, was represented by 0.31083; 
 while, again, the zones of Bessel made the density at the same distance 
 equal to 0.28410 J. The near agreement of the results for both classes 
 of stars must, indeed, be regarded as very remarkable, especially when 
 we take into consideration the very different sources from which they 
 were in each case derived. It may be remarked, however, that the obser- 
 vations from which these results were derived, however trustworthy they 
 may be in point of accuracy, can hardly be allowed to constitute a suf- 
 ficiently ample basis for establishing beyond doubt so extensive a conclu- 
 
 * Phil. Trans., 1 785, p. 247. 
 
 f Herschel cites six of such observations in a paper inserted in the Philosophical Trans- 
 actions for 1817 (pp. 325, 26, 27), and four additional observations of the same nature 
 in a paper published in the following year (Phil. Trans., 1818, p. 463). 
 
 Etudes d' Astronomic Stellaire, p. 77. 
 
582 HISTORY OF PHYSICAL ASTRONOMY. 
 
 sion as that relative to the law of the distribution of the stars. Moreover, 
 the results of Sir John Herschel's gauges in the southern hemisphere 
 would seem to indicate, that for the sjars in the vicinity of the sun a 
 different law of density prevails from that deduced by M. Struve*. 
 On the other hand, the hypothesis of a gradual diminution of the den- 
 sity of the stars in the plane of the Milky Way, as well as in a direction 
 perpendicular to that plane, is not only consonant to sound philosophy, 
 but is also strongly suggested by analogy from observations of the arrange- 
 ments prevailing throughout the other systems of the sidereal universe. 
 
 The other alternative suggested by M. Struve, as an explanation of the 
 inconsistency between theory and observation, which he encountered in 
 the course of his researches ; namely, the hypothesis of a gradual extinc- 
 tion of light in its passage through the celestial regions, has been objected 
 to on very strong grounds by Sir John Herschel. If such an hypothesis 
 were true, we might reasonably presume that, in consequence of the light 
 being everywhere extinguished at the same distance, the Milky Way 
 would present a uniform aspect throughout its course. As, however, 
 observations of the actual aspect of the Milky Way do not accord with 
 this conclusion, the hypothesis from which it is deduced is manifestly 
 inadmissible. 
 
 It is very evident, that in the present state of sidereal astronomy the 
 interesting question proposed by M. Struve, and discussed with so much 
 ability by that astronomer, does not admit of a definitive solution. To 
 attain this end it will be desirable to institute an extensive series of obser- 
 vations relative to the apparent distribution of the stars, both in the 
 Milky Way arid in a variety of other positions, with respect to the plane 
 of the Galactic circle, employing at the same time telescopes of different 
 apertures. By such means alone can we reasonably hope to arrive at 
 reliable conclusions relative to the constitution of the great sidereal 
 system, which presents itself to our observation under the aspect of the 
 Milky Way, and of which the sun, as well as the greater number of the 
 stars visible even in the most powerful telescopes, may be regarded in all 
 probability as so many of the constituent bodies. 
 
 * See the table of apparent densities for stars of different magnitudes, which Sir John 
 Herschel has given at page 382 of his Results of Astronomical Observations at the Cape 
 of Good Hope, $-c. 
 
APPENDIX. 
 
 i. 
 
 ILLUSTKATIONS OF PLANETARY PERTURBATION. 
 
 IT is not intended here to attempt a detailed exposition of the principles 
 of Planetary Perturbation. The object of the following remarks is 
 mainly to elucidate the peculiar features of perturbation which characterise 
 the mutual action of two revolving bodies, the mean motion of one of 
 which around the central body is almost exactly double the mean motion 
 of the other. Several examples of this mode of perturbation occur in 
 Physical Astronomy, one of the most interesting of which relates to 
 the mutual action of Uranus and Neptune ; and it is chiefly with the view 
 of exhibiting its influence in the theory of these planets that the series of 
 illustrative notes, which we now submit to the attention of the reader, 
 have been drawn up. 
 
 (1 .) Let us suppose a body to receive an impulse in free space, and to be 
 subjected at every instant to the action of a force tending to a fixed point s. 
 
 Let P represent the initial 
 position of the body, and let 
 us first suppose it to be pro- 
 jected in the direction FT, so 
 that the angle s P T is obtuse. 
 If it was not acted upon after- 
 wards by any force, it would 
 advance along p T with a uni- 
 form velocity depending on 
 the intensity of the impulse ; 
 and the angle contained be- 
 tween the radius vector and 
 the line PT, representing the 
 direction of motion, would con- 
 tinually increase. The central 
 force at s, however, by its in- 
 cessant action, prevents the 
 
 body from moving in the same direction during any assignable interval of 
 time, however short ; so that while the body would have described the 
 small space p Q with the velocity due to the impulse, it is in reality con- 
 strained to move in the curvilinear arc PR; and the angle contained 
 between the direction of motion and the radius vector, instead of being 
 equal to SQT, is now equal only to SRX. It appears, therefore, that the 
 central force tends to make the angle contained between the direction of 
 motion and the radius vector less than it would be, if the body had pro- 
 ceeded in the direction of the impulse. The same remark evidently 
 applies to the case in which the body is impelled in the opposite direction 
 p T', making an acute angle with the radius vector. 
 
584 APPENDIX. 
 
 (2.) Since the central force acts obliquely at p, with respect to the direc- 
 tion of motion, it does not draw the body with its whole intensity out of the 
 line P T. If we resolve it into two directions, one of which is parallel to 
 the tangent p T, and the other perpendicular to that line, it will at once 
 be seen, that only the force which acts in the latter direction is effective 
 in pulling the body into the orbit. The intensity of this force is to that 
 of the whole central force as the perpendicular upon the tangent to the 
 radius vector, or as s Y to s P. The remaining element of the force acts 
 in the direction of the tangent T T', and tends to retard or accelerate the 
 body, according as it is proceeding towards T or T', its intensity being to 
 that of the whole force as p Y to s P. 
 
 (3.) It appears, then, that when a body is compelled to revolve in a curvi- 
 linear orbit, by the action of a force directed constantly to a fixed point, its 
 motion is continually retarded as it recedes to a greater distance from the 
 centre of force ; while, on the other hand, when the body is approaching 
 the centre of force, its motion is continually accelerated. It may be shewn, 
 by a strict investigation founded on dynamical principles, that the motion 
 of a body, when maintained under such circumstances, is so regulated, 
 that the areas swept over by the radius vector are proportional to the 
 times in which the corresponding curvilinear spaces are described by the 
 body. This celebrated theorem was first discovered by Kepler, who found 
 it to be applicable to the elliptic movements of the planets ; and it was 
 subsequently demonstrated by Newton to be true in every case of curvi- 
 linear motion depending on the action of a central force. (Principia, 
 lib. i., prop, i.) 
 
 (4.) Although the central force at s tends to make the angle contained 
 between the direction of motion and the radius vector less than it would 
 have been if the body had been allowed to proceed in the direction of the 
 impulse, it does not necessarily follow that the same angle, when con- 
 sidered solely with reference to the orbit in which the body revolves, will 
 actually undergo a diminution of magnitude. Thus, although the angle snx 
 representing the new inclination of the path of the body to the radius vec- 
 tor, is less than s Q T, it is not necessarily less than the angle s p T, repre- 
 senting the angle of inclination at p. In fact the angle contained between 
 the line representing the direction of motion and the radius vector, or the 
 tangential angle, as we shall hereafter for the sake of brevity denominate 
 it, may continually increase or continually diminish, or it may even con- 
 stantly retain the same magnitude ; the question of its variation at any 
 given point depending on the circumstances which determine the motion 
 of the body at that point ; namely, the relative values of the radius 
 vector, the tangential angle, the velocity, and the force. It is manifest 
 that if the deflection of motion at any point be exactly equal to the 
 angular displacement of the radius vector, the tangential angle will not 
 vary ; if it be greater than the displacement of the radius vector, the 
 tangential angle will diminish ; if less, the same angle will increase. 
 
 (5.) It may be demonstrated that if the velocity of a body revolving in 
 a curvilinear orbit under the influence of a force tending to a fixed point, 
 be less than that of a body revolving at the same distance in a circular 
 orbit under the influence of a force of equal intensity, directed to the 
 centre of the circle, the tangential angle will diminish ; but if the velocity 
 be greater than that in a circle under similar circumstances, the tangential 
 angle will increase. 
 
 (6.) If the velocity of the body at any given point be exactly equal to 
 
APPENDIX. 585 
 
 that in the circle at the same distance, the tangential angle will neither 
 increase nor diminish at that point ; and, therefore, it may be regarded as 
 invariable for an infinitely short space of time. If this relation hold 
 good for every point of the orbit, the tangential angle will always retain 
 the same magnitude. The circle is a particular example of the orbit 
 described under such circumstances; the force being supposed to be 
 directed continually to the centre of the circle. In this case the tan- 
 gential angle is always equal to a right angle. The orbit generally cor- 
 responding to any constant value of the tangential angle, is represented 
 by a curve termed the equiangular spiral. Newton has demonstrated 
 (Principia, lib. i., prop, ix.), that the force required to maintain a body 
 revolving in such a spiral, varies inversely as the cube of the distance. 
 
 (7.) Since the circumstances which determine the motion of a body in 
 a circle are, the relative values of the distance, velocity, and force, it is 
 clear that the invariability of the tangential angle, in any case of curvi- 
 linear motion maintained by a central force, will be independent of 
 the actual magnitude of the tangential angle at the point under con- 
 sideration. 
 
 (8.) We have seen that if the motion of a body be supposed to be free, 
 after it has received an impulse in any direction, the angle contained 
 between the direction of motion and the radius vector will continually 
 increase. Hence if the angle of projection be acute, there is a point 
 in the subsequent path of the body at which the direction of motion is 
 perpendicular to the radius vector. In the case of curvilinear motion, it 
 is manifest that if the tangential angle at any point be acute, it would 
 gradually increase so as to become equal to a right angle, provided the 
 body was allowed to proceed in the direction of the tangent. Thus, if the 
 body revolving at p was allowed to proceed in the direction p T', uninfluenced 
 by any force, the motion would be perpendicular to the radius vector ; or, 
 in other words, the tangential angle would be equal to a right angle, when 
 the body arrived at Y. Beyond this point the tangential angle would 
 continually increase, approaching nearer than any assignable limit to two 
 right angles. It follows, therefore, that when the tangential angle is 
 acute, the body is naturally approaching an apse ; and, since the central 
 force generally tends to diminish the tangential angle, its effect in such a 
 case is manifestly to retard the arrival of the body at the apse. It is 
 clear also, that the more intense the central force is, the more influential 
 will it be in producing such an effect. 
 
 (9.) When the tangential angle is obtuse, the body, if free to move in 
 the direction of the impulse, would continually recede from the position 
 in which the direction of motion is perpendicular to the radius vector. 
 The central force, however, by tending to diminish the tangential angle, 
 manifestly retards the recess from perpendicularity ; and if the deflective 
 influence of the force so far prevail over the natural tendency of the body 
 to persevere in the same direction as to occasion an actual diminution of 
 the tangential angle, the latter may be reduced to such an extent as to 
 become ultimately equal to a right angle. In such a case it is manifest 
 that the more intense the force is, the sooner will the perpendicularity of 
 the motion with respect to the radius vector be effected. It has been 
 remarked that the contrary is true when the tangential angle is acute ; or, 
 in other words, when the body is approaching an apse, independently 
 of the action of any force. 
 
 (10.) Let us now consider the motion of a body which is compelled to 
 
586 
 
 APPENDIX. 
 
 revolve in an elliptic orbit by the action of a force directed continually to 
 one of the foci. Let A B c D represent the extremities of the axes of 
 the ellipse, and let the force tend to the focus s. Let us suppose the 
 
 body t6 have been originally at the 
 upper apse A, and to have received an 
 impulse in the direction AT at right 
 angles, to CA. If no force afterwards 
 acted upon the body, it would have pro- 
 ceeded with a uniform motion along the 
 tangent AT, and the angle contained 
 between the direction of motion and 
 the radius vector would have continually 
 increased. The influence of the force 
 at s, however, is such that while the 
 planet would have described the small 
 space AQ in virtue of the impulse, it 
 is in reality constrained to move in 
 the curvilinear arc A R. The amount of deflection also is more than that 
 which would be required in order to maintain the perpendicularity of the 
 motion with respect to the radius vector ; for the new tangential angle 
 SRX is not only less than the obtuse angle SQT, but is even less than 
 the right angle SAT, representing the angle of projection. From A to B 
 the deflection of motion is more than adequate to compensate for the 
 angular shifting of the radius vector, and the tangential angle in conse- 
 quence diminishes. The momentary decrement of the angle, however, 
 continually diminishes also from A, and finally vanishes altogether when 
 the planet arrives at B. At this point of the orbit, the deflection of 
 motion exactly compensates for the angular shifting of the radius vector, 
 and the tangential angle remains for an instant invariable. As the planet 
 revolves from B, the angular shifting of the radius vector, now very rapid, 
 from the continued acceleration of the planet, exceeds the corresponding 
 deflection of motion ; and the tangential angle gradually opens out, 
 becoming again equal to a right angle at c, when the radius vector has 
 swept over an arc of 180 from A. At this point, therefore, the direction 
 of motion represented by the tangent CY, is exactly opposite to the direc- 
 tion of the original impulse. As the planet revolves from c to D, the 
 momentary deflection of motion is still inadequate to compensate for the 
 angular displacement of the radius vector, and the tangential angle con- 
 tinues to open out. The momentary increment of the angle, however, 
 which increased from nothing at B, until it attained its maximum at c, 
 has since been continually diminishing, and finally vanishes when the 
 planet arrives at D. At this point the deflection of motion again exactly 
 compensates for the angular displacement of the radius vector, and the 
 tangential angle for an instant neither increases nor diminishes. As the 
 planet revolves from D, the deflection of motion is now more than ade- 
 quate to compensate for the angular shifting of the radius vector ; and, as 
 a necessary consequence, the tangential angle diminishes, becoming once 
 more equal to a right angle when the planet has returned to its original 
 position A. The momentary decrement of the angle increases from nothing 
 at D, until it attains its maximum at A ; from which point it continually 
 diminishes, and finally vanishes at B, as has been already stated. 
 
 (11.) It appears, then, that when the planet is revolving from mean 
 distance to mean distance through the lower apse, the deflection of motion 
 
APPENDIX. 587 
 
 occasioned at each successive instant by the action of the central force, is 
 inadequate to compensate for the angular shifting of the radius vector, 
 and the tangential angle in consequence continually enlarges; but, on 
 the other hand, when the body is revolving from mean distance to mean 
 distance through the upper apse, the deflection of motion is more than 
 adequate to compensate for the angular shifting of the radius vector, and 
 the tangential angle in consequence continually diminishes. Hence the 
 tangential angle attains its greatest contraction when the planet in the 
 course of descending to the lower apse has arrived at the mean distance, 
 and it has opened out to its greatest extent when, in the course of ascend- 
 ing to the upper apse, the planet has again receded as far as the mean 
 distance. In the former case it will be represented by SBV, and in the 
 latter by its supplement SDZ. Moreover, the enlargement of the tan- 
 gential angle is most rapid when the planet is passing through the lower 
 apse, and its diminution most rapid at the upper apse; while again, 
 in each of the positions of mean distance, it remains for an instant in- 
 variable. 
 
 (12.) It has been stated (6), that if, in any case of a body revolving in 
 a curvilinear orbit, under the influence of a force tending continually to a 
 fixed point, the deflection of motion caused by the force at any assigned 
 point, should exactly compensate for the angular displacement of the 
 radius vector, so that the tangential angle should remain for an instant 
 invariable, the velocity at that point is equal to the velocity in a circle at 
 the same distance. Now, since in the foregoing case the tangential angle 
 remains for an instant invariable when the planet is at the mean distance, 
 we may conclude that the velocity is then equal to the velocity in a circle 
 at the same distance. This theorem was originally deduced by Newton 
 from his investigation of the laws of elliptic motion maintained by 
 the action of a force tending to the focus (Principia, lib. i., prop, xvi., 
 cor. 4.). 
 
 (13.) Let us now suppose a planet to be revolving in an elliptic orbit, 
 and to be disturbed by a small force acting for a short space of time in 
 the direction of the radius vector. Let us assume the eccentricity of the 
 orbit to be so inconsiderable that the radius vector does not deviate sen- 
 sibly from a perpendicular to the planet's motion. In such a case the 
 disturbing force tends wholly to increase or diminish the tangential angle 
 according as it acts outwards or inwards with respect to the central force. 
 Let us suppose it to act inwards so as to diminish the tangential angle, 
 and let us first consider the case in which it disturbs the planet a little 
 after the passage of the perihelion. Since the tangential angle is in the 
 
 course of opening out, the action of the 
 disturbing force will make it equal to the 
 tangential angle at Q, a point less advanced 
 in the orbit. Now when the planet is in 
 the vicinity of either apse, its distance 
 from the focus varies very slowly, and the 
 same is true respecting the velocity and 
 the force. Hence the circumstances which 
 determine the path of the planet at p and Q may be regarded as identical. 
 The new orbit of the planet may therefore be represented by supposing 
 the line of apsides of the original ellipse to have revolved in the direc- 
 tion of the planet's motion through an angle equal to P s Q. In other 
 
588 APPENDIX. 
 
 words, the effect of the disturbing force is to make the line of apsides to 
 progress. 
 
 (14.) It is manifest that the increment of the tangential angle in pass- 
 ing from Q to P is equal to the excess of 'the angular displacement of the 
 radius vector over the absolute deflection of motion corresponding to the 
 arc included between the same two points. Hence the diminution of the 
 tangential angle at P due to the disturbing force is less than the angle 
 p s Q representing the progression of the apsides, by the absolute deflec- 
 tion of the motion of the planet in passing from Q to p. 
 
 (15.) Let us now suppose that p has revolved to a sufficient distance 
 from the perihelion to occasion a sensible difference in the circumstances 
 of motion at p and Q. We have seen (11) that the effect of this differ- 
 ence is such as to make the tangential angle open out more slowly at p 
 than at Q. Hence it is evident, that if we trace back the motion of the 
 planet in the new orbit from P, the place of the perihelion will be reached 
 later than if the motion had been similarly traced back from Q, the place 
 of the corresponding tangential angle in the original orbit. The line of 
 apsides in this case will therefore have advanced through an angle ASA' 
 (see the figure on the preceding page), which will be somewhat less than 
 the angle p s Q. It is manifest also, from the circumstance of the velocity 
 and force at P being less than the velocity and force at Q, that the motion 
 of the planet at the lower apse will now be slower than it was in the 
 original orbit ; and since the area momentarily described by the radius vec- 
 tor is not altered by the disturbing force, it follows that the perihlion dis- 
 tance of the planet will be greater than it formerly was. Now 7 , the mean 
 distance being independent of the disturbing force (inasmuch as its direct 
 effect is supposed to be confined to an alteration of the tangential angle), 
 it is a necessary consequence of the perihelion distance being greater that 
 the aphelion distance should be less. It is manifest, therefore, that be- 
 sides causing a progression of the apsides, the disturbing force tends to 
 diminish the eccentricity as the planet revolves from the perihelion. 
 
 (16.) It is easy to perceive, from geometrical considerations, that the 
 eccentricity is diminished by the disturbing force, for unless the perihe- 
 lion distance of the ne\v ellipse was somewhat greater than that of the 
 undisturbed ellipse, it would be impossible for the two orbits to intersect 
 each other in p, so that the planet should subsequently move within its 
 original path a condition necessarily implied by the diminution of the 
 tangential angle at that point. 
 
 (17.) Let us now suppose that the planet while receding from the sun 
 has arrived at the mean distance, and let the disturbing force act, At 
 
 this point the momentary variation 
 of the tangential angle vanishes. 
 Now, it has been remarked (7) that 
 the fulfilment of this condition is in- 
 dependent of the actual magnitude 
 of the tangential angle ; it will there- 
 fore still hold good in the present 
 case, notwithstanding the diminution 
 of the tangential angle occasioned by 
 the action of the disturbing force. But the point at which the momentary 
 variation of the tangential angle vanishes, is that at which the same angle 
 is a maximum or a minimum, and in an elliptic orbit is one of the points 
 
APPENDIX. 589 
 
 of mean distance. Hence it follows that in the new, as well as in the 
 undisturbed ellipse, the planet is at the mean distance. Let p denote the 
 place of the planet, p T the tangent of the undisturbed orbit, and p tf the 
 tangent of the new orbit. Now, since in an ellipse the tangent at either 
 extremity of the minor axis is parallel to the major axis, the position of 
 the latter will be determined by drawing A' s B' parallel to p T 7 . The line 
 of apsides has therefore progressed through an angle equal to the amount 
 of deflection occasioned by the disturbing force. 
 
 (18.) The eccentricity of the new ellipse will be determined by the 
 angle s p T', representing the maximum value of the tangential angle. 
 The greater this angle is the more eccentric is the ellipse. In the present 
 case this angle is less than it was in the undisturbed orbit. Hence it 
 appears that the eccentricity is diminished by the action of the disturbing 
 force. 
 
 (19.) Let the planet now be moving towards the aphelion, and, when it 
 has arrived at p, let it be disturbed by a small force tending to increase 
 the central force at s. Since the tangential angle is now in the course of 
 
 contracting, the immediate effect of the 
 disturbing force will be to make it equal 
 to the tangential angle at Q, a point more 
 advanced in the orbit ; and since the dis- 
 tance, velocity, and force maybe supposed 
 to be equal at p and Q,'in consequence of the 
 vicinity of the planet to the apse, the cir- 
 cumstances which determine its path may 
 be regarded as identical at those points. 
 Hence, the new orbit of the planet may 
 
 be represented by supposing the major axis of the original ellipse to 
 have revolved through an angle equal to p s Q, in a direction contrary to 
 that of the planet's motion; in other words, the line of apsides has 
 regressed. 
 
 (20.) In the foregoing case it has been assumed that the circumstances 
 of motion at p and Q are identical. Let us suppose, however, that while 
 the planet is moving towards the aphelion, its distance from the apse at 
 the instant when the disturbing force acts, is sufficiently great to occasion 
 a sensible difference in the circumstances of motion at p and Q. Since 
 the tangential angle is closing more slowly at p than at Q (1.1) the planet 
 will be somewhat longer of arriving at the apse in the new orbit than if it 
 had started in the original orbit from Q. Hence it is obvious that the 
 line of apsides will have revolved through an angle B s B' (see the above 
 figure), somewhat less than the angle p s Q. In this case, then, the regres- 
 sion of the apsides is less considerable than that which results when the 
 planet is in the immediate vicinity of the apse. Again, since the velocity 
 at P is presumed to be sensibly greater than that at Q, while at the same 
 time the motion of the planet in either case is almost perpendicular to 
 the radius vector, it is clear that the velocity of the planet at the aphelion 
 will now be quicker than it was in the original orbit. The eccentricity 
 has therefore been diminished by the disturbing force. This, indeed, is 
 readily perceived from the mode in which the two ellipses intersect each 
 other ; for the aphelion distance of the new orbit is manifestly less than 
 that of the original orbit. 
 
 (21.) It will be found, by reasoning precisely similar to that employed 
 above, that when the planet is revolving from the aphelion to the perihe- 
 
590 APPENDIX. 
 
 lion, the line of apsides will regress if the disturbing force should act 
 after the passage of the aphelion, but will progress if it should act at the 
 mean distance or before the passage of the perihelion ; while again, the 
 eccentricity in each of these three cases will be increased by the disturbing 
 force. 
 
 (22.) We have seen that if the disturbing force should act when the 
 planet is at the perihelion, the effect is then thrown wholly upon the 
 apsides, which rapidly progress ; that at the mean distance the apsides 
 also progress, (though with less rapidity, the effect now being thrown 
 partly upon the apsides and partly on the eccentricity) ; but that 
 if the disturbing force acts when the planet arrives at the aphelion, 
 the effect is again thrown wholly upon the apsides, which, however, in this 
 case regress. Hence it is obvious, that there must be some intermediate 
 point of the orbit between the mean distance and the aphelion at which 
 the disturbing force produces no effect on the position of the line of 
 apsides. Similarly, it is manifest that there must exist some point between 
 the aphelion and the subsequent point of mean distance, at which the 
 line of apsides does not undergo any change of position from the action of 
 the disturbing force. It may be found by a simple investigation, to which 
 we shall presently allude more particularly, that the two points in ques- 
 tion are the extremities F G of the ordinate passing through H the upper 
 focus of the ellipse. In fact, as the planet revolves 
 from F to G through A, the line of apsides every- 
 where progresses from the action of the disturbing 
 force, the amount of progression increasing from 
 nothing at F until it attains its maximum at A, and 
 subsequently diminishing until it vanishes again at 
 G. Similarly, from G to F through B, the line of 
 apsides everywhere regresses from the same cause, 
 the amount of regression being greatest at A, and 
 diminishing in either direction towards F and G. 
 
 (23.) We have seen that if, when the planet 
 is revolving from the lower to the upper apse, the 
 disturbing force act a little after the passage of the 
 perihelion, at the mean distance, or a little before the passage of the 
 aphelion, the eccentricity is in each case diminished ; but that, on the 
 other hand, when the planet is revolving from the upper to the lower 
 apse, the eccentricity in each of the corresponding cases is increased by 
 the action of the disturbing force. Generally it may be shewn, that from 
 A to B through G the eccentricity is everywhere diminished by the action 
 of the disturbing force, the amount of diminution increasing from nothing 
 at A until it attains its maximum at G, and subsequently diminishing until 
 it vanishes at B ; and on the other hand, that from B to A through F the 
 eccentricity is everywhere increased by the action of the disturbing force, 
 the amount of increase being greatest at F, and diminishing from that 
 point towards A and B. Thus it appears, that when the variation in the 
 position of the apsides is greatest, the variation of the eccentricity is least, 
 and vice versa. 
 
 (24.) If we suppose the disturbing force to act in the direction of the 
 radius vector so as to diminish the central force at s, it will be found, in a 
 similar manner, that the effect both upon the eccentricity and the apsides 
 will now be precisely the reverse of that produced when the disturbing 
 force acts inwards. In this case the eccentricity will increase from A to 
 
APPENDIX. 591 
 
 B through G, and will diminish from B to A through F ; and on the other 
 hand, the apsides will regress from F to G through A, and will progress 
 from G to F through B. The points where the variations of both elements 
 attain their maximum values, and also those at which they severally 
 vanish, will be the same as in the former case. 
 
 (25.) Let us now consider the effect of a small disturbing force acting 
 in a direction perpendicular to the radius vector. In all such cases the 
 eccentricity of the orbit is supposed to be so inconsiderable, that the dis- 
 turbing force may be regarded as acting in the direction of the tangent, 
 and consequently as tending wholly either to accelerate or retard the 
 motion of the planet. Let us suppose, then, that it tends to increase the 
 velocity of the planet, and first let it act when the planet is at the 
 perihelion. The velocity being now increased, the central force will have 
 less control over the planet, and the latter in consequence taking a wider 
 sweep, will now recede, farther at the mean distance. It is manifest, also, 
 since the tangential angle continually enlarges from the perihelion to the 
 mean distance, that it will now open out to a greater extent than it for- 
 merly did. Now, the greater the maximum value of the tangential angle, 
 the more eccentric is the orbit. Hence the effect of the disturbing force 
 is to increase the mean distance, and also the eccentricity. It is manifest 
 that the position of the line of apsides cannot suffer any alteration from 
 the action of such a force. 
 
 (26.) Let us now suppose the disturbing force to act at the aphelion. 
 Since the velocity is increased, the central force will be less effective 
 in deflecting the motion of the planet, and the latter in consequence 
 taking a wider circuit, will not approach so near the centre of force at 
 the mean distance as it formerly did. Moreover it is manifest, since the 
 diminution of the tangential angle continues from the aphelion to the 
 mean distance, that when it attains its minimum value, it will be less 
 acute than it formerly was. Hence the effect of the disturbing force in 
 this case is, to increase the mean distance, and to diminish the eccen- 
 tricity. 
 
 (27.) It is manifest that the conclusions above deduced are equally 
 applicable if we suppose the disturbing force to act at a little distance on 
 each side of the apse, whether the latter refer to the perihelion or the 
 aphelion, for the circumstances which determine the path of the planet 
 are then almost the same as if the disturbing force had acted exactly at 
 the apse. 
 
 (28.) Let us suppose the planet to be revolving from the lower to the 
 upper apse, and let the disturbing force act when it has arrived at the 
 
 mean distance E. At this point the 
 deflection of motion in the undis- 
 turbed orbit exactly compensates for 
 the angular displacement of the radius 
 vector, and the tangential angle in 
 consequence remains for an instant 
 invariable. The velocity of the planet, 
 however, being now increased by the 
 action of the disturbing force, the 
 momentary deflection of motion will 
 be diminished, and therefore the tan- 
 gential angle will still continue to open out. Let E' be the point at which 
 the momentary deflection of motion in the new orbit is equal to the cor- 
 
593 APPENDIX. 
 
 responding change of direction of the radius vector, and let E' T' be a 
 tangent to the orbit at that point. Then, since the angle s E' T' is greater 
 than s E T, it follows that the eccentricity is increased by the disturbing 
 force. It is evident, however, that the Increase of that element is very 
 small, for the planet is in the most favourable position for the retardation 
 of its motion by the central force, and consequently the deflection of 
 motion is speedily brought to an equality with the angular displacement 
 of the radius vector. The position of the major axis of the new orbit will 
 be determined by drawing A' B' parallel to E' T', whence it is evident that 
 the line of apsides has progressed. It may be shewn, in a similar manner, 
 that when the planet is revolving from the upper to the lower apse, the 
 effect of the disturbing force at the mean distance is, to diminish the 
 eccentricity, and to make the line of apsides regress. In every point of 
 the orbit, the mean distance is obviously increased by the action of the 
 disturbing force. 
 
 (29.) Since the eccentricity is increased at E and diminished at B by the 
 action of the disturbing force, it is evident that there is some intermediate 
 point at which the disturbing force produces no effect upon that element. 
 For a similar reason, there must be some point between B and the follow- 
 ing point of mean distance at which the eccentricity does not undergo anv 
 change from the action of the disturbing force. These neutral points are 
 found by strict investigation to be F G, the extremities of the ordinate pass- 
 ing through the upper focus of the ellipse. (See the figure at page 590). 
 
 (30.) Generally it may be shewn, that from F to G through A, the eccen- 
 tricity is everywhere increased by the action of the disturbing force, the 
 variation increasing from nothing at F until it attains its maximum at A, 
 and subsequently diminishing by equal degrees until it vanishes at G. 
 On the other hand, from G to F through B, the eccentricity is every- 
 where diminished by the action of the disturbing force, the variation 
 being a maximum at B, from which point it diminishes towards F and G. 
 
 (31.) With respect to the line of apsides, it has been found to progress 
 if the planet, while revolving from the perihelion to the aphelion, should 
 be at the mean distance when the disturbing force acts, and to regress, 
 if the planet, in the course of revolving from aphelion to perihelion, 
 should have arrived at the corresponding point of the orbit; while, again, 
 at either apse it does not undergo any change of position. Generally it 
 may be shewn, that from A to B through G, the line of apsides progresses, 
 and that from B to A through F, it regresses, the variation attaining its 
 maximum values at F and G, and vanishing at A and B. Thus it appears, 
 that in passing from a disturbing force acting in the direction of the 
 radius vector, to one acting at right angles to that direction, an inter- 
 change takes place between the points of maxima and minima of the 
 variations of the eccentricity and the apse. 
 
 (32.) If the disturbing force act in a direction contrary to that of the 
 planet's motion so as to diminish the velocity, the effects produced upon 
 the eccentricity and the line of apsides will be precisely the reverse of 
 those abovementioned. The eccentricity will increase from A to B 
 through G, and will diminish from B to A through F ; while again the line 
 of apsides will regress from F to G through A, and will progress from G to 
 F through B. Moreover the points at which the variations attain their 
 maximum values, and also those at which they vanish, will be the same 
 as in the case wherein the disturbing force tends to increase the velocity 
 of the planet. 
 
APPENDIX. 593 
 
 (33.) The variation induced in the position of the line of apsides by a dis- 
 turbing force of given intensity is greater, as the eccentricity of the orbit is 
 less. The truth of this proposition will appear manifest on a very slight 
 consideration of the subject. It is easily seen that a variation in the posi- 
 tion of the line of apsides is tantamount to a variation of the tangential 
 angle in any point of the orbit. Now the variation of the tangential angle 
 is slower as the eccentricity is less, the difference between its least and 
 greatest values continually diminishing, until at length, when the orbit 
 becomes a circle, the difference vanishes altogether, and the tangential 
 angle is constantly of the same magnitude. The same is obviously true 
 if the difference refer to any two values of the tangential angle compre- 
 hended within the extreme values. Hence it follows that the displace- 
 ment of the line of apsides which will be required in order to adapt the 
 orbit to a given alteration in the magnitude of the tangential angle due to 
 a disturbing force of given intensity at any point, will be greater as the 
 eccentricity of the orbit is less. 
 
 (34.) Since the tangential angle varies to a greater extent as the disturb- 
 ing force is more intense, we may therefore infer conversely, that in order 
 to induce an alteration of given magnitude in the position of the line of 
 apsides, the intensity of the disturbing force must be greater as the orbit 
 is more eccentric. 
 
 (35.) Hitherto we have supposed the disturbing force to act for a short 
 space of time and then to cease. If its action be constantly kept up as in 
 overy case of planetary perturbation, the alteration effected in any of the 
 .elements of the orbit during a given interval of time, may be ascertained 
 by investigating the change for each successive instant, and then sum- 
 ming up the results. It is easy by means of the foregoing principles to 
 determine the character of the effect produced in any such case, although 
 its exact amount can only be ascertained by a process of computation 
 based on the principles of the infinitesimal calculus. 
 
 (36.) Mr. Airy has shewn (Gravitation, notes to Arts. 50 and 65), that 
 by a slight modification of the figure given by Newton in Prop. XVII. of 
 the first book of the Principia, the effects produced on the eccentricity 
 and the position of the line of apsides by a force acting either in the di- 
 rection of the radius vector, or along the tangent of the orbit, may be 
 clearly exhibited to the eye. Sir John Herschel has actually employed 
 this mode of expounding the variations of the elements in question in his 
 recently-published Outlines of Astronomy. The simplicity and elegance 
 of the investigation will amply justify its insertion here. 
 
 (37.) First let us suppose the disturbing force to act in the direction of 
 the radius vector, so as to increase the attractive force at s. We have 
 
 seen that the direct effect of such a force is 
 to diminish the tangential angle. Let it act 
 at P, and let the tangent T T' at that point be 
 deflected in consequence, so as now to occupy 
 the position x x'. Draw P H' so that the 
 angle H' P x' shall be equal to s P x, the new 
 value of the tangential angle. From P, set off 
 p H r equal to PH. Bisect s H' in c'. Then is s c' 
 the new eccentricity of the orbit, and A'S H'B' 
 the new position of the line of apsides. For, 
 by the property of the ellipse, the two lines 
 drawn from any given point of it to the foci make equal angles with the 
 
 Q Q 
 
594 
 
 APPENDIX. 
 
 tangent. Hence the upper focus of the new ellipse must be somewhere 
 in the line p a'. Again, by another property of the ellipse, the sum of the 
 same two lines is equal to the major axis. Hence s and H' will represent 
 the foci of an ellipse whose tangential angle at p is equal to s p x, and 
 whose major axis is equal to that of the undisturbed orbit. But by the 
 principles of dynamics, the major axis of the ellipse is not altered by 
 the disturbing force. Hence the truth of the proposition is manifest. 
 By varying the position of p, and supposing the disturbing force as 
 tending either to increase or diminish the attractive force at s, the 
 different results referred to in (22), (23), and (24) may be very easily 
 deduced. 
 
 (38.) Next let the disturbing force act in the direction of the tangent, 
 so as to retard or accelerate the velocity of the planet. Let it he sup- 
 posed to increase the velocity and let p be the point at which it acts. In 
 
 this case the tangential angle at P is not 
 affected by the disturbing force, but the major 
 axis of the ellipse is increased by its action. 
 Produce p H so that H H' may represent the 
 increment of the major axis occasioned by the 
 disturbing force. Join s H', and bisect the 
 line s H in c'. Then will s c' represent the 
 new eccentricity of the orbit, and A' s H' B' 
 the new position of the line of apsides. The 
 truth of this proposition is so obvious as to 
 render any formal demonstration of it super- 
 fluous. The various theorems announced in (30), (31), and 32) are easily 
 deducible from it. 
 
 ii. 
 
 APPLICATION OF THE FOBEGOING PEINCIPLES TO CEKTAIN CASES OF ACTUAL 
 
 PEETUEBATION. 
 
 (39). Let us suppose two comparatively small hodies to be revolving in 
 circular orbits situate in the same plane, round a large central body s, and let 
 the mean motion of the interior revolving body be almost exactly double the 
 mean motion of the exterior one. Let us assume also, for facility of explana- 
 tion, that the exterior body maintains a fixed position at p, while the interior 
 
 body performs an entire revolution around 
 s. Join s p by a straight line, cutting the 
 orbit of the interior body in A and D. 
 Then DAP will represent the line of 
 conjunction of the two bodies. Now in 
 those cases of the solar system where- 
 in the mean motion of one revolving 
 body is almost exactly double the mean 
 motion of the other, the effects produced 
 by the mutual perturbation of the two 
 bodies are sensible only near conjunc- 
 tion. Let us suppose that in one of 
 
 such cases the disturbing influence of the exterior body first becomes sen- 
 sible when the interior body has arrived at B, a position somewhat less ad- 
 vanced than the line of conjunction. It may be easily shewn that the disturb- 
 
APPENDIX. 595 
 
 ing force of the exterior body will then be resolvable into two distinct forces, 
 one of which acts in the direction of the radius vector, and the other in the di- 
 rection of a tangent to the orbit. The former of these forces acts outwards 
 throughout the whole of the arc B A c, and consequently tends to diminish 
 the attractive force of the central body s. With respect to the force which 
 acts in the direction of the tangent, or the tangential force as it may be 
 called, it tends to accelerate the interior body while revolving from B to A, 
 and to retard it by like degrees while revolving from A to c. 
 
 (40.) The disturbing influence exercised by the interior body upon the 
 exterior one, is also sensible only near conjunction. In this case the 
 force resolved in the direction of the radius vector of the disturbed body 
 acts inwards, and consequently tends to increase the attractive force of 
 the central body. The tangential force tends to retard the exterior 
 body before conjunction and to accelerate it by like degrees after con- 
 junction. 
 
 (41.) If we suppose the orbits to be slightly eccentric, as when the 
 question refers to the mutual action of the celestial bodies, the character 
 of the disturbing forces will be the same as above described. It is mani- 
 fest that in such a case the disturbing body will occasion a continual 
 change in the elements of the disturbed body during the time of its 
 influence being sensible. Let us suppose, for example, that the orbit 
 A c D B, of the interior body, is slightly eccentric. It is manifest that 
 when the body is revolving from c to B through D, the elements of its 
 orbit will not undergo any material alteration, because the action of 
 the disturbing body over that portion of the orbit is so feeble that it 
 may be neglected without occasioning any sensible error. As it revolves 
 from B to c, however, the elements of the orbit will continually vary from 
 the action of the disturbing force, and when it has arrived in the latter 
 position, it will proceed to revolve in a new elliptic orbit, the difference 
 between the elements of which and those of the orbit in which it was 
 revolving previous to its arrival in B, will generally differ for each sy- 
 nodic revolution. It is manifest, from what has been already said in the 
 foregoing pages, that the variations thus induced in the elements of the 
 orbit of the disturbed body, will depend mainly on the position of the line 
 of apsides of the orbit of each body with respect to the line of conjunction. 
 
 (42.) Let us now consider more particularly the perturbations produced 
 in those cases of the planetary system wherein the mean motions of the 
 two revolving bodies are actually characterised by the relation above men- 
 tioned. One very striking instance of such a relation occurs among the 
 primary bodies of the system. The mean motion of Uranus is almost 
 exactly double that of Neptune. A similar relation holds good between 
 the first and second, and the second and third satellites of Jupiter ; and 
 also between the first and third, and the second and fourth satellites of 
 Saturn (counting outwards from the planet). We shall first consider 
 the mutual action of Uranus and Neptune. 
 
 (43.) According to the most recent researches of astronomers, the period 
 of Uranus is 84.014 years, and that of Neptune, 164.6181 years. Hence 
 when Uranus has completed two revolutions, Neptune will have completed 
 one revolution, and will also have advanced in a second revolution over 
 an arc corresponding to 3.4099 years. It is manifest, therefore, that if 
 the two planets be supposed to have been originally in conjunction, Uranus 
 after completing two revolutions, will require to advance a little beyond 
 the -point of starting, before it can overtake Neptune so as to come again 
 
 QQ 2 
 
596 APPENDIX. 
 
 into conjunction with that planet. It may be easily shown that Uranus 
 will require to advance through an arc equal to 15 15', before it again 
 comes up with Neptune. The same is true with respect to the third 
 conjunction of the planets, and thus it fe evident that the line of conjunc- 
 tion on each of such occasions will advance through an arc equal to 15 15' 
 in the direction of the motions of the two planets. 
 
 (44.) It has been remarked (41), that the alteration induced in the 
 elements of either planet on the occasion of its conjunction with the 
 disturbing planet, will depend upon the position of the line of apsides 
 of the orbit of each planet with respect to the line of conjunction. Let 
 us consider the effect which Neptune tends to produce on the eccen- 
 tricity and the longitude of the perihelion of Uranus. If the line of 
 apsides of the disturbed planet be oblique with respect to the line of 
 conjunction, it is manifest that the variation of the eccentricity cannot 
 effect a complete compensation, and therefore a change will ultimately be 
 produced in the value of that element, which will be maintained until 
 the planet again arrives within the sphere of the disturbing force on 
 the occasion of approaching the next conjunction. It is easy to see, 
 therefore, that in such a case the eccentricity of the orbit would undergo 
 an alteration at each successive conjunction. Let us suppose, however, 
 that the eccentricity constantly retains the same value (which is actually 
 true in so far as regards that part of the eccentricity which is essentially 
 co-existent with the disturbing force, and which is the only part we are 
 here considering), and let us enquire into the circumstances under which 
 this condition of permanence can be maintained. Now it appears from (24), 
 (30), and (32), that if the line of apsides coincide with the line of conjunction, 
 the eccentricity will not undergo any change from the action either of the 
 radial or the tangential force. It is manifest, however, that this coin- 
 cidence can only be maintained by a progressive motion of the line of 
 apsides, equal to that of the line of conjunction. Now if the perihelion 
 of the planet be turned towards the disturbing body, it follows, from (24), 
 that the line of apsides will regress, and therefore, instead of constantly 
 coinciding with the line of conjunction, it will immediately commence to 
 deviate from that line by receding in the opposite direction. But if the 
 aphelion of the planet be turned towards the disturbing body, the line of 
 apsides will then progress (24), from the action of the disturbing forces ; 
 and, by duly adjusting the eccentricity, the progression may be made 
 exactly equal to the progression of the line of conjunction. In this case, 
 then, the variation of the eccentricity occasioned by the disturbing force 
 will effect a complete compensation at each conjunction, leaving the 
 eccentricity of the undisturbed portion of the orbit unaltered, while at the 
 same time the line of apsides will advance regularly in the direction of 
 the planet's motion with an angular velocity equal to that of the line of 
 conjunction, or at the rate of 15 15' in each synodic revolution of the two 
 planets. 
 
 (45.) The eccentricity above referred to, may be considered as an 
 inequality of a perturbative character, inasmuch as the necessity for its 
 existence depends wholly on the action of the disturbing force. It is 
 right to bear in mind, however, that its maintenance is mainly due to the 
 central force. The direct effect of the disturbing force is, merely to pro- 
 duce a slight variation of the eccentricity (which, however, effects a com- 
 plete compensation at each conjunction), and to cause a constant progres- 
 sion of the line of apsides. 
 
APPENDIX. 597 
 
 (46.) The more nearly the mean motions of the two planets are com- 
 mensurable, the less will be the angle through which the line of apsides 
 will have to advance during each synodic revolution of the two planets, 
 and consequently the greater will be the eccentricity depending upon 
 the disturbing force. 
 
 (47.) The progressive movement of the line of apsides is mainly due 
 to the part of the disturbing force which acts in the direction of the 
 radius vector. For, in the first place, the tangential force vanishes alto- 
 gether at the point of conjunction, where the disturbing force is most 
 intense ; and, in the second place, its influence in altering the position of 
 the apsides is very feeble near conjunction (where alone the disturbing 
 force is sensible), since, by (31), its effect vanishes at the aphelion, which, 
 in this case, always coincides with the point of conjunction. On the other 
 hand, the radial force is not only most intense at conjunction, but is also 
 most effective (24) at the same point*. 
 
 (48.) If we had considered the perturbation of Neptune by Uranus, 
 it would readily appear, by (22), that it is the perihelion of the disturbed 
 orbit which, in this case, would require to be turned towards the point of 
 conjunction, in order that the line of apsides might progress ; and it is 
 manifest that, by a due adjustment of the eccentricity, the amount of ad- 
 vance during each synodic revolution might be rendered exactly equal to 
 the advance of the line of conjunction. Thus the eccentricity would con- 
 stantly retain the same value, while the line of apsides would regularly 
 progress, coinciding always with the line of conjunction. 
 
 (49.) With a view to illustrate the foregoing remarks, we insert the 
 principal terms of the mutual perturbations of both planets, exclusive of 
 those arising from independent eccentricity, the influence of which we 
 are not at present considering. In calculating these terms, a mean dis- 
 tance equal to 19.18239 has been assigned to Uranus. The mean dis- 
 
 * If we exclude from consideration the tangential force, as incapable of exercising any 
 influence upon the character of the perturbative effect, it is easy to see that the disturb- 
 ing force, by acting outwards in the direction of the radius vector, tends continually to 
 twist round the line of apsides in the direction of the planet's motion. First, let the 
 planet be advancing towards conjunction. In this case the tangential angle is obtuse, 
 and the planet is naturally receding from the position in which the radius vector is per- 
 pendicular to the tangent ; but the deflective influence of the central force is so powerful, 
 that the tangential angle is actually contracting, and is again rapidly approaching to a 
 right angle. Hence the disturbing force, by weakening the influence of the central body, 
 diminishes the deflection of the orbit, and thereby retards the perpendicularity of the 
 tangent with respect to the radius vector. It is manifest, therefore, that the planet will 
 require to revolve through an angle of somewhat more than 180 from the perihelion before 
 it arrives at the aphelion, or, in other words, the line of apsides will have progressed. With 
 respect to the influence of the disturbing force after the passage of the aphelion, it is to be 
 remarked, that if the central force were diminished in due proportion throughout the whole 
 semi-ellipse, extending from the aphelion to the perihelion, the position of the line of 
 apsides would not undergo any change. It is evident, therefore, that the character of 
 the effect produced after the passage of the aphelion (whether progression or regression) 
 will be the same as if the central force was increased a little before the arrival of the planet 
 in the perihelion. Now when the planet is approaching the perihelion, the tangential 
 angle is rapidly opening out, from the natural tendency of the body to persevere in the 
 same direction ; and the efficacy of the central force consists in opposing its enlargement, 
 and thereby retarding the arrival of the planet at the apse. It is evident, therefore, that 
 the effect of an increase of the central force will be to retard, in a still greater degree, the 
 arrival of the planet in such a position. It appears, then, that the action of Neptune upon 
 Uranus causes the line of apsides to progress both before and after conjunction. It may 
 be shewn, in a similar way, that the action of Uranus upon Neptune will cause the line of 
 apsides of the disturbed orbit to progress at each conjunction. 
 
598 APPENDIX. 
 
 tance of Neptune has been assumed equal to 30.0363, agreeably to the 
 researches of Mr. Walker of Washington, U. S. The mass of each 
 planet is supposed to be equal to -g^^o, the sun's mass being repre- 
 sented by unity. The angle <p denotes the excess of the mean longi- 
 tude of Uranus above that of Neptune. 
 
 PEETUEBATION OF TBUE LONGITUDE. 
 
 Neptune disturbing Uranus. Uranus disturbing Neptune. 
 
 &! = - 33".537 sin <p J, a = + 252".836 sin q> 
 
 815.596 sin 2p 10.648 sin 2$ 
 + 13.943 sin 3p 3.094 sin 3p 
 + 3.146 sin 4p 0.665 sin 4?) 
 + 1.055 sin 5p 0.261 sin 6<p 
 + 0.433 sin 6?) 0.115 sin 6<p 
 
 PEETUEBATION OF EADIUS YECTOE. 
 
 Neptune disturbing Uranus. Uranus disturbing Neptune. 
 
 Jn = + 0.00085 cos <p Sr 3 = 0.01635 cos (p 
 
 + 0.03738 cos 2p + 0.00119 cos 2p 
 
 0.00083 cos 3p + 0.00028 cos 3p 
 
 0.00021 cos 4<p + 0.00010 cos 4p 
 
 0.00008 cos 5?) + 0.00004 cos 5? 
 
 0.00003 cos 6?) 4- 0.00002 cos 6p 
 
 (50.) The enormous magnitude of one of the terms in each of these 
 four columns relatively to the others cannot fail to strike the reader. It 
 is to be remarked also, that while in the case of Neptune disturbing 
 Uranus, the preponderating term is the second in the column, both when 
 the perturbation of longitude and that of the radius vector are considered, 
 on the other hand, in the case of Uranus disturbing Neptune, it is the 
 first term in each column which is the preponderating one. Finally, the 
 sign of the preponderating term in the column representing the action 
 of Neptune upon the longitude of Uranus is negative, while that of the 
 corresponding term in the column which represents the action of Uranus 
 upon the longitude of Neptune is positive ; and the contrary holds good 
 when the question refers to the perturbation of the radius vector. All 
 these points may be easily explained by reference to the principles which 
 govern the mutual action of the two planets. 
 
 (51.) First let us consider the predominant term in the perturbation of 
 the longitude of Uranus by the action of Neptune. It has been stated that 
 g> denotes the excess of the mean longitude of Uranus over the mean 
 longitude of Neptune. Hence, if during a synodic revolution we reckon 
 the longitudes from the point of conjunction we have <p = nf nj, and 
 
 2 (p (2 n^ 2 w a ) t = ( 7?i (2 n z n^ J t, n lt n z denoting the 
 
 mean annual motions of Uranus and Neptune. Now n 2 = 7872".77, and 
 consequently 2 ?i 2 = 15745".54. Again, n t 15425".64. Hence 
 2 n. 2 n l = 319 // .90, which is a very small quantity relatively to 
 
 n l or w a , and therefore 2 $ = f n t (2 n 2 n ^ J t = n L t very nearly. 
 
 We have, therefore, 815 // .596 sin2<? = 815.596 sin njplus a small quan- 
 tity of variable value. Now 8 15". 5 96 sin n v t represents the principal term 
 
APPENDIX. 599 
 
 of the equation of the centre in an ellipse whose eccentricity is equal to 
 0.001 97, and, since the sign of the term is negative, it necessarily follows 
 that the aphelion is turned towards the point of conjunction. 
 
 (52.) It appears, then, that if we refer the motion of the planet to 
 the line of conjunction, the predominant term of the perturbation in 
 longitude becomes confounded with the principal inequality of an ellipse 
 whose aphelion coincides with the point of conjunction. The same con- 
 clusion is obviously deducible from an examination of the corresponding 
 term in the perturbation of the radius vector. 
 
 (53.) Let us now consider the predominant term in the column re- 
 presenting the action of Uranus upon the longitude of Neptune. In this 
 
 case <p = n$ n.,t = (n l n 2 ) t ( n 2 (2 n 2 n^ j =n 2 t 
 
 nearly, and consequently 252".836 sin <p = 252".836 sin nj plus 
 a small quantity of variable value. Now 252". 836 sin n.J represents 
 the principal term of the equation of the centre in an ellipse whose 
 eccentricity is equal to 0.0006. Hence arises an elliptic inequality ana- 
 logous to that produced by the action of Neptune upon Uranus, the only 
 difference being, that in this case it is the perihelion which is turned 
 to the point of conjunction, a circumstance implied by the positive sign of 
 the inequality. It is manifest that the corresponding term in the pertur- 
 bation of the radius vector is consistent with this conclusion. 
 
 (54.) It appears, then, that the predominant term in the perturbation 
 of the longitude of each planet represents the equation of the centre 
 in an ellipse, in the focus of which the sun is placed. It is manifest, 
 therefore, that the inequality is maintained during each synodic re- 
 volution by the action of the central force, being perturbative only in 
 so far as the line of apsides is continually twisted round in the direction 
 of the planet's motion. The remaining terms of perturbation in each case 
 may be considered as representing the effects more directly due to the 
 disturbing force. 
 
 (55.) The mean motions of the two planets being very nearly commen- 
 surable, it is manifest that a slight change effected in the value of either, 
 would exercise a very considerable influence on the displacement of the 
 line of conjunction, and consequently would affect, in an equal degree, 
 the progression of the line of apsides. Now the eccentricity thus depending 
 on perturbation must always be adjusted to tbe motion of the apsides, 
 increasing as that diminishes, and vice versa. When the motion of the 
 apsides is very slow, a slight diminution of its value occasions an enor- 
 mous increase of the eccentricity. Now, in the present case, the more 
 nearly the mean motion of the interior planet approaches to twice the 
 mean motion of the exterior one, the slower will be the motion of the 
 points of conjunction, and, consequently, so will be that of the line of 
 apsides. Hence it is manifest, that the eccentricities of the two planets 
 will increase indefinitely as their mean motions satisfy with greater accu- 
 racy the relation just mentioned. This relation corresponds to a mean 
 distance of Neptune equal to 30.4507, the radius of the terrestrial orbit 
 being assumed equal to unity. 
 
 (56.) When the mutual action of the planets is viewed through the 
 medium of analysis, this principle exhibits itself in the form of the co- 
 efficient of the predominant term, which has for a divisor the square of 
 (2n 2 n { ). It is manifest, that when this quantity is very small, a slight 
 
600 APPENDIX. 
 
 change in the mean motion of either planet will occasion an enormous 
 alteration in the value of the coefficient, which is divided by the square of 
 the same quantity. 
 
 (57.) The remaining terms of the perturbation vary only in a degree 
 commensurate with the change which may be effected in the mean motion 
 of either planet. This circumstance arises from their being mainly 
 dependent on the direct action of the disturbing force, the intensity of 
 which cannot be expected to undergo a considerable change in conse- 
 quence of a slight alteration in the relative values of the mean distances 
 of the two bodies. 
 
 (58.) We have hitherto supposed that neither the orbit of Uranus nor 
 that of Neptune possesses any eccentricity except what arises from their 
 mutual action. In reality, however, both orbits are slightly eccentric, 
 independently of the effects of perturbation. In consequence of this 
 circumstance, the mutual distance of the two planets will vary at each 
 successive conjunction ; whence it is manifest that the intensity of their 
 disturbing forces will undergo a corresponding variation. Now, in con- 
 sequence of the near commensurability of the mean motions of the two 
 planets, the line of conjunction shifts with extreme slowness, its displace- 
 ment during a synodic revolution amounting only to 15 15'. The dura- 
 tion of a synodic revolution is 171.6 years ; whence it follows that the line 
 of conjunction will not accomplish a complete revolution before the lapse 
 of 4051 years. During this period the disturbing forces of the two 
 planets will be constantly varying in intensity, returning only at its close 
 to their original values. 
 
 (59). It is easy to see that this variation of the intensity of the disturbing 
 forces of the two planets will occasion corresponding variations in the 
 elements of both orbits, requiring an equal lapse of time to effect a com- 
 plete compensation. Hence the mean distance, eccentricity, and longitude 
 of the perihelion of either planet, will be subject to an excessively slow 
 variation, which in each case will pass through the cycle of its values in a 
 period of 4051 years. The variation of the mean distance will pro- 
 duce a corresponding variation in the mean motion of each planet, and 
 hence will originate an inequality in the mean longitude analogous to the 
 long inequality of Jupiter and Saturn, and several others to which we- 
 have had occasion to allude in the course of this work. 
 
 (60.) The circumstances which determine the long inequality of Uranus 
 and Neptune are less favourable to its magnitude than those which deter- 
 mine the analogous inequality in the longitudes of Jupiter and Saturn, 
 inasmuch as the masses, eccentricities, and inclinations of the disturbing 
 planets are less in the former case than in the latter. In one respect, 
 however, the magnitude of the inequality is liable to be much greater in 
 the case of Uranus and Neptune than in that of Jupiter and Saturn, or 
 any other two planets yet discovered, whose mean motions are nearly 
 commensurable. In the case of Jupiter and Saturn, every three conjunc- 
 tions take place in different parts of the orbit, and it is merely the minute 
 quantity which remains outstanding after every such triple conjunction, 
 that is allowed to accumulate upon the longitude. With respect to the 
 long inequality of the Earth and Venus, the accession to the mean longi- 
 tude is only what remains uncompensated after every fifth conjunction of 
 the two planets. On the other hand, in the case of the long inequality of 
 Uranus and Neptune, every two successive conjunctions occur in the same 
 part of the orbit, the interval included between them being merely the 
 
APPENDIX. 601 
 
 small displacement arising from the absence of perfect commensurability 
 in the mean motions of the two planets. In consequence of this circum- 
 stance, it happens that the whole effect produced by the disturbing planet 
 at each successive conjunction is accumulated upon the mean longitude. 
 
 (61.) A similar conclusion is suggested by the analytical view of the 
 subject. In the case of Jupiter and Saturn, the inequality is mainly 
 represented by a class of terms, which are only of the third order of mag- 
 nitude with respect to the eccentricities and inclinations of the two 
 planets. The long inequality of the Earth and Venus depends upon a 
 series of terms, the most considerable of which are only of the fifth order 
 of magnitude with respect to the eccentricities and the inclinations. On 
 the other hand, the long inequality of Uranus and Neptune is mainly con- 
 tained among a class of terms which are as high as the first order of 
 magnitude relatively to the same elements. 
 
 (62.) The more nearly the mean motion of Uranus approaches to 
 double the mean motion of Neptune, the more slowly will the line of con- 
 junction of the two planets advance, and consequently the longer will the 
 inequality in the mean longitude continue to vary in the same direction. 
 Hence it is manifest, that the maximum value of the inequality will 
 increase as the mean motions of the two planets are more nearly com- 
 mensurable. 
 
 (63.) It appears from the foregoing consideration, that the more perfect 
 commensurability of the mean motions of the two planets tends to 
 promote the ultimate magnitude of the long inequality, by prolonging the 
 time during which it continues to accumulate upon the mean longitude. 
 We have seen that the elliptic inequality depending upon perturbation 
 increases also with the more perfect commensurability of the mean 
 motions of the two planets, in consequence of the slower motion of the 
 line of conjunction hence resulting, which creates the necessity of a 
 greater amount of eccentricity, so as to oppose an adequate resistance to 
 the disturbing force, in its tendency to twist round the line of apsides 
 which must always advance at the same rate as the line of conjunction. 
 In the former case the inequality results from the direct action of the dis- 
 turbing planet at each successive conjunction, and depends, for its ultimate 
 magnitude, on the length of time during which the effects thus produced 
 are allowed to accumulate upon the mean longitude. In the latter case 
 the inequality arises from the powerful agency of the central force, and is 
 developed in a single synodic revolution. 
 
 (64.) It has been stated that the system of Jupiter's satellites presents 
 two instances in which the mean motion of one of the disturbing bodies is 
 almost exactly double the mean motion of the other. In effect, the first 
 satellite performs a sidereal revolution in l d 18 h 27 m 34 s , and the second 
 satellite in 3 d 13 h 13 m 42 s . Hence two revolutions of the first satellite 
 will be completed in 3 d 12 11 56 m 8 s , an interval of time which falls short 
 of one period of the second satellite by only 1 7 m 34 s . In consequence of 
 this circumstance, the line of conjunction of the two satellites shifts with 
 extreme slowness, regressing through an arc of little more than 2, at the 
 close of each synodic revolution. Hence arises in the motion of each satel- 
 lite a large elliptic inequality of a perturbative character, resembling that 
 produced by the mutual action of Uranus and Neptune, with this interest- 
 ing distinction that as the line of conjunction now regresses, it is the 
 lower apse of the interior body and the upper apse of the exterior one which 
 will require to be turned constantly to the point of conjunction, in order 
 
602 APPENDIX. 
 
 that the line of apsides of the orbit of either body may always coincide with 
 the line of conjunction. 
 
 (65.) The third satellite of Jupiter accomplishes a sidereal revolution 
 in 7 d 3 h 42 m 32*. Now two periods of the second satellite are equal to 
 7 d 2 h 27 m 24 s , which differs from one period of the third by only l h 15 m 
 8 s . This case, then, is clearly analogous to that of the first and second 
 satellites. In fact it is easy to infer, from the remarkable relation between 
 the mean motions of the three interior satellites mentioned at page 92, 
 that the mean motion of the second satellite exceeds twice the mean 
 motion of the third by a quantity which is exactly equal to the excess of 
 the mean motion of the first satellite over twice the mean motion of the 
 second. The line of conjunction of the second and third satellite will 
 therefore regress at the same rate as the line of conjunction of the first 
 and second, and hence will arise a large inequality in the motion of each 
 satellite, resembling the one mentioned in the foregoing article. The 
 motion of the second satellite is thus affected by two elliptic inequalities 
 of a perturbative character, depending upon the combined action of the 
 first and third satellites, and in consequence of the remarkable relation 
 which subsists between the mean longitudes of the three interior satellites, 
 the two inequalities are thoroughly confounded together, so as to assume 
 the complexion of only one great inequality (see p. 89). 
 
 (66.) Astronomers have been unable to discover the slightest trace of 
 independent eccentricity in the orbit of the first satellite of Jupiter. With 
 respect to the orbits of the second and third satellites, the independent 
 eccentricity is in either case exceedingly small. In consequence of this 
 circumstance, no sensible evidence has been derived from observation, of 
 the existence of a long inequality in the mean longitude of any of the 
 satellites, depending on the near commensurability of their mean 
 motions. 
 
 (67.) Some of our readers may perhaps find it difficult to reconcile the 
 foregoing remark with the fact of Bradley 's discovery of a great inequality 
 in the three interior satellites, the period of which he found to extend to 
 437 days, which vastly exceeds the duration of a synodic revolution of 
 either of the satellites. It is to be borne in mind, however, that the ex- 
 istence of this inequality was indicated solely by observations of eclipses . 
 of the satellites. Now, in the case of an elliptic inequality of a perturba- 
 tive character, depending on the mutual action of any two of the satellites, 
 it will manifestly pass through the cycle of its values when the two satel- 
 lites return to the same position with respect to the line of conjunction. 
 If, however, the inequality be considered solely with reference to its 
 influence upon the times of the eclipses of the satellites, it will not in 
 either case effect a compensation during the period comprised between 
 two successive oppositions of the satellite with respect to Jupiter ; for 
 while the line of conjunction of the satellites has regressed, in virtue of 
 the relation between their mean motions, the planet whose position, rela- 
 tively to the sun, determines the time of the eclipse, has revolved in the 
 opposite direction, and it is manifest that a complete restoration of the 
 inequality cannot be established until the satellites have returned to the 
 same position with respect to the line of conjunction, and the axis of 
 Jupiter's shadow. Hence the long inequality discovered by Bradley is 
 rather apparent than real, being merely the consequence of adopting a 
 restrictive view of the mode in which the elliptical perturbation affects the 
 motions of the satellites. 
 
APPENDIX. 603 
 
 (68.) The spheroidal figure of Jupiter exercises a considerable influence 
 on the motions of the satellites, and thereby occasions their observed 
 perturbations to be materially different from those which would be pro- 
 duced by their mutual action. The reader will find a complete exposition 
 of the theory of this interesting system in Mr. Airy's treatise on 
 Gravitation. 
 
 (69.) Two remarkable instances of commensurability similar to those 
 already noticed in the foregoing pages, are suggested by a comparison of 
 the mean motions of Saturn's satellites. According to Sir John Herschel 
 (Outlines of Astronomy, Appendix], the innermost satellite (Mimas) ac- 
 complishes a sidereal revolution round the planet in O d 22 h 37 m 22 S .9, 
 and the third satellite (Tethys) in l d 21 h 18 m 25 S .7. Hence Mimas 
 completes two revolutions in l d &l h 14 m 45 s . 8 ; an interval of time which 
 falls short of one period of Tethys by only 3 ra 39 S .9. Hence it is easy 
 to infer that the line of conjunction of the two satellites regresses with 
 excessive slowness ; the displacement during a synodic revolution amounts 
 in effect only to 58'. It is manifest that, in consequence of this 
 circumstance, an elliptic inequality of a perturbative character will be 
 developed in the motion of each satellite, exactly resembling the elliptic 
 inequalities depending on the mutual action of the first and second and 
 on the second and third satellites of Jupiter. Again, the second satellite 
 of Saturn (Enceladus) effects a complete sidereal revolution in l d 8 h 53 m 
 6 S .7, and the fourth satellite (Dione) in 2 d 17 h 41 m 8 8 .9. Hence two 
 periods of Enceladus amount to 2 d 17 h 46 m 13 s . 4, an interval of time 
 which exceeds one period of Dione by 5 m 4 S .5. The line of conjunction 
 of the two satellites will, therefore, advance in the direction of their 
 orbitual motion at the rate of 55' in each synodic revolution. In this 
 case, then, the elliptical inequality in the motion of each satellite de- 
 pending on their mutual perturbation, will resemble the inequality of the 
 same nature occasioned by the mutual action of Uranus and Neptune. 
 
 (70.) In consequence of the excessive slowness with which the line of 
 conjunction shifts in each of the foregoing cases, it might be expected 
 that a very large amount of eccentricity depending on perturbation would 
 be developed in the orbit of each satellite. The theory of the motions of 
 these bodies is, however, still in a very imperfect condition ; a circum- 
 stance arising from the difficulty of making accurate observations of their 
 positions. Moreover, it is probable that, as in the case of Jupiter and his 
 attendants, the spheroidal figure of the central body modifies in a con- 
 siderable degree the perturbations which would otherwise ensue from their 
 mutual action. 
 
 III. 
 
 EEMAEKS ON CEKTAIN CIKCUMSTANCES CONNECTED WITH THE DISCOVEKT 
 OF THE PLANET NEPTUNE. 
 
 (71.) Allusion has been made (p. 902) to the remarkable discordance 
 which presented itself between the elements of Neptune as determined by 
 actual observations of the planet after its discovery, and the correspond- 
 ing results which Adams and Le Verrier had previously obtained by a 
 theoretical investigation of the observed irregularities of Uranus. It was 
 soon found, however, that this circumstance did not affect the accuracy 
 
604 APPENDIX. 
 
 of the solutions of the inverse problem of perturbation due to these 
 distinguished geometers, or detract from the merit of their researches in so 
 far as the main object of them was concerned ; namely, the ascertainment 
 of the position of the disturbing body with a view to its physical discovery. 
 
 (72.) No difficulty can be experienced in arriving at the conclusion, that 
 elements widely different from the true values might serve to indicate 
 the position of the disturbing body with sufficient accuracy, provided 
 the following two facts be borne in mind: first, that the action of 
 Neptune upon Uranus is sensible only near conjunction ; secondly, that 
 during the interval embracing the observations of Uranus which formed 
 the groundwork of the investigations of both Adams and Le Verrier, there 
 happened only one conjunction of the two planets. Thus the disturbing 
 influence which Neptune exercises upon Uranus is sensible only for about 
 twenty years before, and about an equal interval after, conjunction. Again, 
 the last conjunction happened in the year 1822, and, as the period of a 
 synodic revolution of the two planets is 171.6 years, it follows that the 
 previous (mean) conjunction happened in the year 1650. Now the earliest 
 observation of Uranus is one by Flamsteed in the year 1690, at which 
 epoch the action of Neptune was, therefore, quite insensible. 
 
 (73.) It is manifest from the foregoing considerations, that the question 
 relative to the discovery of the disturbing planet was resolvable by 
 means of any elements which might be capable of representing the 
 intensity and direction of the disturbing force on the occasion of the last 
 conjunction in 1822. Now, when it is borne in mind that the mean distance, 
 the eccentricity, the longitude of the perihelion, and the mass of the dis- 
 turbing body may be varied at pleasure, it is not difficult to see that this 
 object may be effected by means of a variety of sets of elements all very 
 different 'from the real elements of the planet. Thus if the mean dis- 
 tance be assumed too great, the error arising in consequence may be 
 obviated by increasing the eccentricity in a corresponding degree, and 
 placing the perihelion so as to coincide nearly with the point of conjunc- 
 tion. Moreover, if it should happen that the intensity of the disturbing 
 force is represented with a less degree of accuracy than its direction by 
 such an adjustment of the elements of the orbits, this defect might be 
 remedied by assigning a suitable value to the mass of the disturbing body.. 
 It is by such an adjustment of the elements of the disturbing planet, that 
 Le Verrier and Adams succeeded in indicating its actual position with 
 such remarkable precision, as may be easily seen by comparing their 
 elements with those subsequently deduced from actual observation. It 
 is not difficult to conceive that if a mean distance less than that of the 
 true value had been assumed, the direction of the disturbing force might 
 have been represented by increasing the eccentricity and turning the 
 aphelion to the point of conjunction. 
 
 (74.) If the observations of Uranus, upon which the researches of 
 Le Verrier and Adams were based, had embraced more than one conjunc- 
 tion of that planet with Neptune, the elements of the hypothetical planet 
 would manifestly have been confined within narrower limits. It is pro- 
 bable that the difficulty which both of these geometers experienced in 
 accounting for Flamsteed's observation of 1690, arose from the circum- 
 stance of the planets of their respective theories being capable of occa- 
 sioning considerable disturbance in the motion of Uranus at an epoch 
 when the action of Neptune was totally insensible. This view of the 
 subject is still further strengthened by the fact that the American 
 
APPENDIX. 605 
 
 astronomers, by applying to the elliptic motion of Uranus the perturba- 
 tions produced by Neptune as represented by the formula of analysis, have 
 succeeded in satisfying the observation of 1 690 with almost perfect accuracy, 
 the outstanding error being less than 1". The question appears to admit of 
 a definitive solution by adopting the following mode of procedure : Since 
 the action of Neptune upon Uranus continued insensible from 1670 to 
 1800, it necessarily follows that the motion of Uranus, after subducting 
 from it the effects produced by the disturbing action of the other planets, 
 was purely elliptic during the whole of the interval of time included 
 between these two epochs. Hence it is obvious, that if the elements of 
 Uranus be deduced from a sufficient number of observations made within 
 the included interval, the motion of the planet, when calculated from 
 such elements, ought to satisfy the totality of the observations, extending 
 from 1690, the year of Flamsteed's earliest observation, down to 1800, 
 or even a few years later. 
 
 (75.) The elements of Neptune being considerably different from those 
 of the hypothetical planets of Le Verrier and Adams, and its mean motion 
 being nearly commensurable with the mean motion of Uranus, the theory 
 of its action upon the latter planet presents a wide discordance, when com- 
 pared with the theory of either of the geometers just mentioned. It 
 is to be borne in mind, however, that this circumstance is immaterial, 
 when the question relates merely to the perturbations produced in the 
 motion of Uranus, on the occasion of one conjunction with Neptune. 
 Prof. Peirce, however, took a different view of the subject. He con- 
 tended, on the ground of the discordance above referred to, that Neptune 
 was not the planet designated by geometry, and that, in fact, its discoveiy 
 must be regarded as a happy accident. " The solutions of Adams and 
 Le Verrier," says he, " are perfectly correct for the assumption to which 
 they are limited, and must be classed with the boldest and most brilliant 
 attempts at analytical investigation, richly entitling their authors to all 
 the eclat which has been lavished upon them on account of the singular 
 success with which they are thought to have been crowned. But their 
 investigations are nevertheless wholly inapplicable to the theory of the 
 mutual perturbations of Uranus and Neptune. The successive periods 
 of conjunction and opposition, occurring at intervals of eighty-four years, 
 that is, in about the time of a revolution of Uranus, this planet is always 
 at the same part of its orbit when it is most affected by the action of 
 Neptune. The action of Neptune consequently assumes a fixed, perma- 
 nent undisturbed character, so that it can hardly be recognised as pertur- 
 bation by the practical observer. It is far otherwise with the ordinary 
 class of perturbations, where the place of greatest disturbance varies from 
 point to point of the orbit : thus the place of greatest disturbance, in 
 the case of the theoretical planet, would not have remained stationary, 
 but have varied 80 upon the orbit of Uranus at each successive conjunc- 
 tion and opposition ; so that the disturbance could not in this case be 
 disguised to any great extent under the fixed laws of ordinary elliptic 
 motion. In the case of Neptune, its action on Uranus is to be detected 
 in the comparatively small differences between its character and that of 
 an elliptic motion, and the difference between the influence at opposition 
 and that at conjunction."* 
 
 (76.) The assertion of Prof. Peirce that the investigations of Adams and 
 Le Verrier are inapplicable to the theory of the mutual action of Uranus 
 * Proc. Arner. Acad. of Arts and Sciences, vol. i., p. 341. 
 
06 APPENDIX. 
 
 and Neptune is perfectly just. But it seems surprising that so excellent 
 a mathematician should contest upon this ground the claim of geometry to 
 the discovery of the planet Neptune. What matters it, although the succes- 
 sive conjunctions of Uranus with the hypothetical planet shift to the extent 
 of 80, while in the case of the real planet the line of conjunction continues 
 immoveable (or rather undergoes only a slight displacement), when there 
 are only the perturbations produced at one conjunction to satisfy by the 
 action of the disturbing body ? for the perturbations produced by Neptune 
 during opposition may be excluded from consideration as wholly insen- 
 sible. 
 
 (77.) If indeed it be true, as Prof. Peirce remarks, that the perturbations 
 produced by Neptune upon Uranus, in so far as its action during one 
 synodic revolution is concerned, assume to a great extent an elliptic 
 character in consequence of the near commensurability of the mean mo- 
 tions of the two planets, it might then be fairly questioned whether it 
 would be practicable, in any case whatever, to deduce by a legitimate process 
 the position of the disturbing body from data so minute as the outstanding 
 deviations from elliptic motion must necessarily be. This conclusion, 
 however, can only be arrived at by losing sight of the true character of 
 the ellipticity depending on perturbation. In the case of the mutual 
 action of Uranus and Neptune, it arises from the mean motion of the 
 former planet being a small fraction less than twice the mean motion of 
 the latter. According to Walker's researches the mean distance of Nep- 
 tune is 30.0363. Now if it was equal to 30.4507, the mean motion of 
 Uranus would be exactly equal to twice the mean motion of Neptune. 
 Hence it follows that, by increasing the mean distance of Neptune so as 
 to make it approach indefinitely near to 30.4507, the ellipticity depending 
 on perturbation may be increased without limit, the mass of the disturbing 
 body and all other circumstances remaining the same. It would be absurd 
 to suppose that the slight change in the distance of the disturbing body 
 could produce such an effect. In reality, however, this circumstance tends 
 to weaken the intensity of the disturbing force, since the mutual distance 
 of the two planets in conjunction obviously increases as the mean distance 
 of the exterior planet increases. Nor can the indefinite increase of the 
 inequality be explained by the principle of the disturbing force acting . 
 during a longer period of time as the mean motions of the two planets 
 approach more nearly to perfect commensurability, since the inequality in 
 all cases passes through the cycle of its values in the course of a synodic 
 revolution of the two planets. The conclusion is therefore unavoidable, 
 that the maintenance of the inequality is entirely due to the central force, 
 as has indeed been already shown by an examination of the mode in which 
 the forces operate. 
 
 (78.) This point, then, being once established, we must look elsewhere 
 for the effects of the disturbing force. If the orbits of both planets 
 were independently circular, these effects would consist in a uniform 
 displacement of the zero points of the inequality above referred to, and a 
 slight disturbance of its maximum value (without, however, inducing any 
 permanent change) on the occasion of each conjunction. Since the orbits 
 of both Neptune and Uranus possess an independent eccentricity, the 
 effects actually produced by the disturbing body at each conjunction, will 
 admit of being represented by a variation of the perihelion arid the eccen- 
 tricity, the magnitude of which, in either case, will generally differ for 
 each successive conjunction. Now in the case of the last conjunction of 
 
APPENDIX. 607 
 
 Uranus and Neptune, the disturbing force of the latter planet was repre- 
 sented very nearly, both in intensity and direction, by the disturbing force 
 of either of the hypothetical planets of Adams and Le Verrier. Hence, 
 as like causes produce like effects, we are warranted in concluding that 
 the irregularities which either of the hypothetical planets would have 
 been capable of producing on that occasion are exactly commensurate in 
 magnitude with those actually produced by the planet Neptune, and there- 
 fore afford an equal hold to the geometer for investigating the position of 
 the disturbing body. In fact, it will appear obvious on the slightest con- 
 sideration of the subject, that the mere circumstance of the near commen- 
 surability of the mean motions of Uranus and Neptune cannot exercise 
 any influence upon the magnitude of the perturbations produced at one 
 conjunction of the two planets. The ellipticity which accompanies such a 
 relation of the mean motions, has its magnitude adjusted so as to form 
 an opposing obstacle of adequate inertia, if we may use the expression, 
 to the disturbing force, by preventing the line of apsides from revolving at 
 a more rapid rate than that at which the line of (mean) conjunction re- 
 volves, but, in so far as its own existence is concerned, it is maintained 
 solely by the action of the central force. 
 
 (79.) Prof. Peirce has exhibited a comparison between the numerical values 
 of the perturbations of Uranus, as computed in the one case by himself 
 from an analytical investigation of the action of Neptune, and in the 
 other case by Mr. Adams, from a similar investigation of the action of his 
 second hypothetical planet. The enormous discordance between the results 
 derived from these two distinct sources, appears to Prof. Peirce to consti- 
 tute a sufficient refutation of what he considers the fallacious notion " that 
 the less distance of Neptune than the planet of geometry is compensated 
 by its smaller mass, so that its action upon Uranus is the same with that 
 which was predicted."* He remarks that the difference of the pertur- 
 bations produced by the two planets is just balanced by the difference 
 due to the corrections of the elements of Uranus, so that the corre- 
 sponding effects upon the longitude of that planet are equal in both 
 theories. 
 
 (80.) We may reply, with reference to this mode of viewing the subject, 
 that the formulae of analysis do not furnish a direct criterion of the disturb- 
 ing action of a planet during one synodic revolution. It must be borne in 
 mind, that all those terms which are not absolutely elliptical (or, in other 
 words, which do not rigorously satisfy the differential equation of the 
 second order relative to elliptic motion) are contained in these formula, 
 even although they may be to a great extent due to the central force. 
 Such is the case with respect to the great elliptic inequality in the per- 
 turbations of Uranus and Neptune depending on the near commensura- 
 bility of their mean motions. Again, there are terms representing in- 
 equalities of long duration which hardly undergo any sensible deviation 
 from ellipticity during one synodic revolution. In effect, the analytical 
 theory of the action of a planet supplies a fund of terms adequate to 
 meet the requirements of the ever-shifting position of the line of con- 
 junction with respect to the orbits of the disturbing and disturbed planets, 
 throughout indefinite ages, both past and future. Now the action of the 
 planet during a short interval of time is embedded in these terms, so that 
 it is impossible to estimate its magnitude by the numerical values of the 
 terms corresponding to the same interval. This object can only be 
 * Proc. Amer. Acad. of Arts and Sciences, vol. i., p. 341. 
 
608 APPENDIX. 
 
 effected by eliminating from the numerical results all the portion which 
 sensibly coincides with elliptic motion during the period of time under 
 consideration. If both planets revolved in circular orbits, the amount of 
 perturbation thus extinguishable from .the analytical formula would be 
 the same in each synodic revolution; but when the orbits possess any 
 independent eccentricity, it will generally be different. It will at once 
 appear, from a bare inspection of the numerical results given by Mr. 
 Adams at the close of his memoir*, that by far the greater portion of the 
 perturbations of a planet as represented by the formula? of analysis, 
 coincides sensibly with elliptic motion during a synodic revolution of the 
 two planets. Now, since the action of Neptune upon Uranus was in- 
 sensible from 1670 to 1800, the planet must have revolved during the 
 whole of the included interval of time in an elliptic orbit, the elements of 
 which resulted from the action of the disturbing body on the occasion of 
 the previous conjunction in 1650. Hence it follows, that the numerical 
 values of the perturbations for the same period of time, as derived from 
 the analytical formulae, admit of being represented by corrections to the 
 elliptic elements of the planet's motion ; and it is manifest that their 
 subsequent deviations from the results of such corrections will indicate 
 the action of the disturbing body on the occasion of the conjunction of 
 the two planets in 1822. If the perturbations produced by the hypo- 
 thetical planets of Le Verrier and Adams were treated in the same way, 
 the direct action of the disturbing body would similarly emerge in each 
 case from the ellipticity in which it is embedded, and it is manifest that 
 the results thus obtained would coincide, or very nearly so, with those 
 relative to the direct action of Neptune. 
 
 (81.) It has been stated, in the account of the discovery of the planet Nep- 
 tune (Chap. XII.), that Le Verrier, besides determining the precise posi- 
 tion of the disturbing body, assigned at the same time the limits of 
 longitude within which it was probably confined, and also the limits of 
 the elements of its orbit. In this part of his investigation he attributed 
 a large probable error to the observations, distinguishing them accord- 
 ing to the degree of confidence to which he considered them to be en- 
 titled on the score of accuracy. The error of Flamsteed's observation of 
 1690, was estimated by him to be 25". The subsequent observations of 
 the planet down to the epoch of its discovery in 1781, were supposed to 
 be erroneous, in some cases to 15"; in others to only 10". The modern 
 observations of the planet, extending from 1781 to 1845, were all esti- 
 mated to have a probable error of 5". It must be acknowledged that the 
 conclusions at which he arrived, relative to the limits of the elements of 
 the disturbing body, have not been subsequently borne out by the results 
 deduced from actual observations of the planet Neptune. Thus he found 
 that the mean distance of the disturbing body could not be greater than 
 37.90 nor less than 35.04. Now we have seen that the most probable 
 value of the mean distance of the planet Neptune is 30.0363. This 
 large discordance between theory and observation cannot be removed by 
 attributing to the observations of Uranus a larger probable error than that 
 which Le Verrier assigned to them ; since it appears that the action of Nep- 
 tune accounts for the irregularities of that planet to a degree of accuracy 
 which obviates the necessity of supposing the observations to be erroneous, 
 even to so great an extent as Le Verrier estimated them to be. The following 
 
 * Nautical Almanac, 1851, p. 289 (Appendix). 
 
APPENDIX. 
 
 609 
 
 table, constructed by Prof. Peirce, exhibits an interesting view of the 
 residual errors in the longitude of Uranus, corresponding to four distinct 
 theories of the planet. The numbers in the second column are the 
 results of Le Verrier's attempt to account for the irregularities of the 
 planet without supposing it to be influenced by any foreign cause of dis- 
 turbance. The third and fourth columns contain the errors of the theories 
 of Le Verrier and Adams, founded on the assumption of the existence of 
 a disturbing planet. The fifth column exhibits the residuaL errors of the 
 planet after taking into account the action of Neptune as calculated by 
 Prof. Peirce, from the elements of Walker. The mass of Neptune 
 employed in these calculations was deduced by Prof. Peirce from Bond's 
 observations of the satellite discovered by Lassell. The results due to 
 Le Verrier inserted in the second and third columns, represent the excess 
 of theory over observation. The same is true with respect to the numbers 
 in the fourth column containing the results of Adams's theory; but, in 
 consequence of this circumstance, their signs are contrary to those of the 
 same numbers in Peirce's table. Prof. Peirce does not state whether the 
 numbers in the fifth column represent the excesses of theory above obser- 
 vation, or those of observation above theory ; but this point is immaterial 
 in so far as our present purpose is concerned. 
 
 RESIDUAL DIFFERENCES BETWEEN THE THEORETICAL AND OBSERVED 
 LONGITUDES OF URANUS. 
 
 Date. 
 
 Without any ex- 
 ternal planet. 
 
 By Le Verrier's 
 theory of a dis- 
 turbing planet 
 mass = g3 L 5 . 
 
 By Adams's 
 theory (Hyp. II.) 
 mass of disturbing 
 planet = ^g. 
 
 By Peirce's 
 theory of the 
 planet Neptune 
 mass = Tg ^ 5 . 
 
 1845 
 
 + 6".5 
 
 - 0".S 
 
 
 - 0".9 
 
 1840 
 
 + 0.7 
 
 + 2.2 
 
 - 1.3 
 
 1.1 
 
 1835 
 
 - 4.5 
 
 - 0.8 
 
 + 1.2 
 
 + 2.0 
 
 1829 
 
 7.8 
 
 2.2 
 
 2.0 
 
 + 0.8 
 
 1824 
 
 - 7.6 
 
 5.4 
 
 1.7 
 
 - 2.0 
 
 1819 
 
 + 38 
 
 + 0.4 
 
 + 2.2 
 
 + 1.0 
 
 1813 
 
 + 4.5 
 
 - 0.9 
 
 + 1.0 
 
 - 0.3 
 
 1808 
 
 + 3.8 
 
 + 0.8 
 
 0.0 
 
 0.4 
 
 1803 
 
 - 3.4 
 
 + 0.8 
 
 1.6 
 
 + 0.8 
 
 1797 
 
 - 6.7 
 
 1.0 
 
 + 0.5 
 
 + 0.3 
 
 1792. 
 
 - 7.8 
 
 + 0.3 
 
 + 1.1 
 
 + 0.3 
 
 1787 
 
 + 2.0 
 
 1.2 
 
 + 0.2 
 
 0.5 
 
 1782 
 
 + 20.5 
 
 + 2.3 
 
 0.0 
 
 - 3.0 
 
 1769 
 
 + 123.3 
 
 + 3.7 
 
 1.8 
 
 6.0 
 
 1756 
 
 + 230.9 
 
 4.0 
 
 + 4.0 
 
 4- 4.0 
 
 1715 
 
 + 279.6 
 
 + 5.5 
 
 + 6.6 
 
 + 8.7 
 
 1690 
 
 + 289.0 
 
 19.9 
 
 - 50.0 
 
 + 0.8 
 
 (82.) Le Verrier has attempted to defend the conclusions at which he ar- 
 rived relative to the limits of the mean distance of the hypothetical planet 
 upon the ground that he assigned too small a probable error to the obser- 
 vations. " When the calculation of the limits of the mean distance," says he, 
 "is resumed with other probable errors of observation than 5", it will 
 readily be seen that the interval included between these limits by no 
 
 R R 
 
610 APPENDIX. 
 
 means varies proportionally to the uncertainty of the data. It varies much 
 more rapidly. Thus while for a probable error of 5" in the data, we find 
 2.86 for the interval between the limits of the mean distance, this interval 
 so diminishes with the probable error, that when the latter is reduced to 
 half this quantity we no longer find any value of the mean distance which 
 can satisfy the question. And on the contrary, when the probable error 
 of the modern observations is extended beyond 5", the inferior and 
 superior limits of the mean distance will be found to vary with rapidity, 
 and to leave the greatest latitude in the choice of that auxiliary." * 
 These remarks are not borne out by the results contained in the foregoing 
 table. The action of the planet Neptune accounts for the irregularities 
 of Uranus, without even supposing so large an error as 5" in the modern 
 observations, and yet its mean distance is 30.0363, which is far below 
 Le Verrier's inferior limit of the mean distance. The modern observa- 
 tions of Uranus are satisfied to within 3" by the action of Neptune, 
 whereas Le Verrier found that if the probable error of these observations 
 was reduced to 2". 5, there is no mean distance of the hypothetical planet 
 which could satisfy the observations. The trifling difference between 
 3" and 2". 5 can hardly serve to account for the discrepancy which here 
 presents itself between the results of Le Verrier's theoretical researches, 
 and those relative to the perturbations actually produced by Neptune. 
 
 It is manifest, without pursuing the subject any further, that the limits 
 assigned by Le Verrier to the mean distance of the hypothetical planet, 
 are at direct variance with the mean distance of Neptune, as deduced 
 from actual observation. Nor is it a matter of any importance, whether 
 the elements employed in calculating the action of Neptune do or do not 
 represent the true orbit of that planet. It is sufficient that an orbit can 
 be assigned, the mean distance of which lies far below the inferior limit 
 assigned by Le Verrier, in which if a planet of a given mass be supposed 
 to revolve, its action will be capable of completely accounting for the 
 irregularities of Uranus. 
 
 (83.) The question then arises, where are we to look for the origin of this 
 discordance between theory and observation ? In order to arrive at some 
 conclusion upon this point, it is necessary to direct attention to the method 
 of investigation by which Le Verrier deduced his final results respecting 
 the hypothetical planet. The groundwork of these results consisted of 
 thirty- three equations of condition. Le Verrier concluded from his pre- 
 vious researches that , the ratio of the mean distance of Uranus to 
 a' 
 
 that of the hypothetical planet, must be very nearly equal to .51, and that 
 e, its mean longitude at the beginning of the year 1800, must be con- 
 tained somewhere between 234 and 270. He, therefore, in his final in- 
 vestigation assumed = 5l + 02y, and e = 252 + 18, y being a 
 
 quantity which he imagined would not differ much from unity, while was 
 supposed by him to lie somewhere between + 1 and 1. Besides 
 these quantities each of the equations contained other seven unknown 
 quantities, namely, the corrections of the four elements of Uranus, and 
 the eccentricity, longitude of perihelion, and mass of the disturbing 
 planet. The corrections y and enter into the equations in a very com- 
 
 * Comptes Rendus, tome xxvii., p. 330. 
 
APPENDIX. 611 
 
 plicated manner ; but if we suppose these quantities to be known, the 
 equations assume a linear form, and the values of the remaining quantities 
 may be obtained without any serious difficulty. Le Verrier proposed to 
 give the equations a linear form by employing particular values of y and 
 , assuming such values as he expected would not be very distant from 
 the real values. For this purpose he selected six particular sets of 
 values, namely, (7 = 1, = 0), (y = 0, = 1), (y = 0, = 0), 
 ( y = 0, = 1), (7 = 1, = 1), (y = 1, = 0); and, sub- 
 stituting these successively in the thirty-three equations of con- 
 dition, he obtained six distinct groups of equations involving the 
 remaining seven unknown quantities. These equations being all 
 linear, he at once derived from them the particular values of six of the 
 unknown quantities, and finally, by substitution, he obtained six sets 
 of equations corresponding to the particular values of y and , which in- 
 volved only one unknown quantity, namely, the mass of the disturbing 
 planet. These equations would be the particular forms assumed by the 
 original equations of condition, if the six unknown quantities referred to 
 had been in the first instance eliminated from them, and then each par- 
 ticular set of values had been substituted for y and . Le Verrier proposed, 
 therefore, to construct the general equations involving y, , andm' by means 
 of the six sets of particular equations involving m f alone. He assumed, 
 moreover, that the general form of the equation might be represented by 
 an algebraic function of the second degree with respect to y and . 
 From these equations he deduced the most accurate values of y, , and mf. 
 In this manner he found y = 1.029,= 0.65, andm' = 1.072, the mass 
 of the sun being supposed equal to 10,000. The limiting values of these 
 quantities were determined by a discussion of the equations, founded on the 
 supposition of the various observations being erroneous to the extent already 
 mentioned. The most accurate value of y assigned 36.1539 as the mean 
 distance of the hypothetical planet, and the discussion of limits gave 
 37.90 and 35.04 for the extreme values of that element. 
 
 (84.) Prof. Peirce has suggested, that the circumstance of the mean 
 distance of Neptune not being comprehended within the limits assigned 
 by Le Verrier to the mean distance of the hypothetical planet, may have 
 arisen from an oversight on the part of the latter, in not having taken 
 into account the peculiar character of the perturbations which would be 
 produced if there existed a relation of perfect commensurability between 
 the mean motions of the disturbing and disturbed planets. " An im- 
 portant change, indeed, in the character of the perturbations," says he, 
 " takes place near the distance 35.3 ; so that the continuous law by which 
 such inferences are justified is abruptly broken at this point, and it was 
 hence an oversight in M. Le Verrier to extend his inner limit to the 
 distance 35. A planet at the distance 35.3 would revolve about the sun 
 in 210 years, which is exactly two and a half times the period of the 
 revolution of Uranus. Now, if the times of revolution of two planets 
 were exactly as 2 to 5, the effects of their mutual influence would be 
 peculiar and complicated, and even a near approach to this ratio gives 
 rise to those remarkable irregularities of motion which are exhibited in 
 Jupiter and Saturn, and which greatly perplexed geometers until they 
 were traced to their origin by Laplace. This distance of 35.3, then, is 
 a complete barrier to any logical deduction, and the investigations with 
 regard to the outer space cannot be extended to the interior." * 
 * Proc. Amer. Acad., vol. i., p. 66. 
 
 R E 2 
 
612 APPENDIX. 
 
 (85.) Plausible as these remarks may at first sight appear to be, we 
 venture to assert, with all due respect to Prof. Peirce, that they will be 
 found, upon an attentive examination of the subject, to have no essential 
 connection with the point at issue. It must be borne in mind that the 
 question under consideration, as it suggested itself to Le Verrier, was 
 this within what limits may the mean distance of the hypothetical 
 planet vary, so that a determinate number of observations of Uranus 
 included between the years 1690 and 1845 may be satisfied by the dis- 
 turbing action of the planet within certain assignable limits of error ? 
 Now, the consequences resulting from a near approach to commen- 
 surability in the mean motions of the two planets can only be developed 
 in the course of many synodic revolutions. As to an exact commen- 
 surability of the mean motions, it will be found, on a very slight con- 
 sideration of the subject, to be incompatible with the mutual action of 
 the two planets ; but at all events, it is manifest that such a condition 
 cannot exercise any peculiar influence on the perturbations of either 
 planet during a short interval of time. Hence it follows, that whether 
 the mean motions of the disturbing and disturbed planets be to each 
 other exactly as 2 to 5, or whether they be very nearly in this ratio, 
 the effects produced by their mutual action must be sensibly the same 
 during the limited period of time over which the observations extend. 
 We may remark further, that innumerable instances of commensurability 
 may be suggested between the limits assigned by Le Verrier, besides 
 the relation alluded to in the foregoing passage by Prof. Peirce, 
 and that the inequality arising from a near approach to such a relation 
 in any case, may be rendered theoretically as great as we please by bring- 
 ing the mean motions sufficiently near to the condition of perfect com- 
 mensurability. It is manifest, however, that the contingent occurrence 
 of any such relation between the mean motions of the two planets, is 
 entirely foreign to the question under examination, which merely relates 
 to the direct action of Neptune during the interval comprised between 
 they ears 1690 and 1845, a period of time embracing less than one synodic 
 revolution of the two planets. 
 
 (86.) But it may be asserted, in support of the argument of Prof. 
 Peirce, that, although the influence of an exact commensurability of the 
 mean motions of the two planets, or of a near approach to that relation., 
 is unimportant, in so far as the mutual action of the two bodies during a 
 short interval of time is concerned, still Le Verrier, by deducing the 
 limits of the mean distance of the hypothetical planet from analytical for- 
 mula involving the mean motions of the two planets as arbitrary constants, 
 without taking into consideration the discontinuity occasioned by the passage 
 of any of the terms of the formula through infinity in consequence of a 
 relation of commensurability between the mean motions, committed an error 
 of reasoning, which could not fail to vitiate his results. To this it may be 
 replied, that the formulae which Le Verrier used as the groundwork of his re- 
 searches do not contain the terms involving the relation between the mean 
 motions alluded to by Prof. Peirce. But, in point of fact, the method em- 
 ployed by Le Verrier in his final researches on the hypothetical planet is 
 totally independent of any relation of commensurability whatever. The 
 action of the disturbing body is computed for a certain number of values 
 of the mean distance, and a general equation * of the second degree, in- 
 volving the true correction of that element, is then constructed from 
 
 * In this and in every subsequent instance in which the word equation is used, the 
 
APPENDIX. 613 
 
 the particular results by interpolation. It is manifest that, by such a 
 method, he gets rid of the embarrassment which might be occasioned by 
 the passage through infinity arising from a relation of perfect commen- 
 surability in the mean motions of the two planets; so that any objection to 
 his reasoning founded upon that ground, cannot be admitted to possess 
 any weight. Indeed any attempt to determine the limiting values of the 
 elements of the disturbing planet by the general formula of perturbation, 
 would seem to be utterly impracticable in the present state of analysis. 
 
 (87.) The question, however, still remains for solution how are we 
 to account for the circumstance of the mean distance of Neptune not 
 being included within the limits assigned by Le Verrier to the mean 
 distance of the hypothetical planet ? It appears to me that the discord- 
 ance is attributable partly to Le Verrier having arbitrarily assumed the 
 form of the general expression involving y and ?, and partly to his having 
 fixed the particular values of these corrections too near each other. If, 
 indeed, we could be assured beforehand of the whereabouts of the most accu- 
 rate values of y and , it plainly follows that the general equations involving 
 these quantities would be most faithfully represented by an algebraic function 
 of the second degree, provided that, in the construction of the latter, such 
 particular values had been employed as were at no great distance from the 
 approximate values. That Le Verrier was under the impression of the 
 most accurate values of y and being included within the limits of the 
 interpolated values, is evident from the following words used by him : 
 "Dans la solution a laquelle nous arriverons en definitive, y sera a tres 
 peu pres egal a 1, et 6 sera compris entre et ] ; en sorte que les 
 valeurs particulieres desfonctions calculees pour les divers etats des variables 
 que nous venons d'indiquer, assurent, dans les environs de la solution qui 
 convient au problems t ^exactitude de la marche des expressions algebriques 
 approchees auxquelles nous parviendrons."* 
 
 (88.) Now if we assume as the elements of the planet Neptune those de- 
 duced from observation by Walker, we shall obtain y = 6.432, 6 = 1.493. 
 It will be seen, however, that these values are very far removed from 
 those particular values by means of which Le Verrier constructed the 
 general equations involving y, 6, and m f . Since it appears, then, that 
 the interval between the limits of the mean distance vastly exceeds the 
 corresponding interval deducible from the researches of Le Verrier, it 
 may fairly be questioned whether an algebraic function of the second 
 degree, constructed from particular values of y and , widely distant from 
 the real values, is capable of representing with sufficient fidelity the form 
 of the general equations involving y, , and m f , such as they would result 
 after the elimination of the other unknown quantities. If we could be 
 assured that any values of y and included within the limits of the par- 
 ticular values employed by Le Verrier in his researches were capable of 
 satisfying the observations of Uranus with tolerable precision, it might 
 then be expected that the equations of the second degree, constructed by 
 that geometer, would assign values of y and differing only in a slight 
 degree from the approximate values. This would follow as an obvious 
 consequence of the vicinity of the particular values of y and to the 
 approximate values, combined with the absence of any rapid variation of 
 the algebraic function representing the equations. Now Le Verrier found, 
 
 terms are supposed to be all ranged on one side so as to constitute an algebraic function 
 equal to zero, and it is to such a function that the expression is considered to apply. 
 * " Recherches sur les Mouvemens de la Planete Herschel," p. 198. 
 
614 APPENDIX. 
 
 by his previous researches, that the observations would be very nearly 
 satisfied by supposing y = 0, = 0. It might, therefore, be inferred 
 that the equations would assign to y and values of inconsiderable magni- 
 tude, which would probably satisfy the* observations to a still greater 
 degree of accuracy. But if the algebraic function of the second degree, 
 involving y, , and m', did not represent with sufficient fidelity the equations 
 resulting from the elimination of the other unknown quantities of the 
 problem, it would manifestly follow that any values of y and , considerably 
 removed from the particular values by means of which Le Verrier con- 
 structed the algebraic equations, would fail, in a corresponding degree, to 
 satisfy these equations, even although such values should satisfy the ob- 
 servations of the planet as well as any others. 
 
 (89.) According to this viewof the subject, the extreme values of the mean 
 distance resulting from Le Verrier 's researches ought to be considered as 
 indicating, not the limits within which the observations of Uranus might 
 be satisfied, by attributing to each of them a probable error of a certain 
 magnitude, but those within which an algebraic function of the second 
 degree, involving y, , and w', constructed from certain particular values 
 of the two former quantities, is capable of representing the equations re- 
 sulting from the elimination of the other unknown quantities of the 
 problem. Admitting this to be true, it would follow that if Le Verrier 
 had assumed 30.0363 as his approximate mean distance, and constructed 
 his equations by means of a series of particular values of y and , cor- 
 responding to mean distances in the immediate vicinity of the approximate 
 value, he would have obtained for the latter merely a slight correction, 
 while 'at the same time he would have deduced limiting values which 
 would have totally excluded the results of his actual researches. 
 
 (90.) The conclusion definitively suggested by the foregoing remarks is, 
 that Le Verrier's theory of limits is rather specious than real, in so far as 
 it relates to the possibility of representing the observations of Uranus 
 within a certain range of mean distance upon the supposition of 
 each of them containing a probable error of a certain magnitude. 
 It is not pretended, however, that these remarks involve the true 
 explanation of the remarkable discordance which prevails between the 
 results of Le Verrier's researches and those deducible from observa- 
 tions of the planet Neptune. They are merely put forth with the view of 
 indicating a probable mode of accounting for the discordance, in the 
 absence of a thorough investigation of the subject. Until this be accom- 
 plished there is full warrant for suspecting the legitimacy of the method 
 by which Le Verrier arrived at his results. This is a point, however, of 
 very trivial importance, which does not in the remotest degree affect the 
 merits of that illustrious geometer, in so far as his theoretical discovery 
 of the planet Neptune is concerned. 
 
 (9L) We shall conclude with a few remarks on a recent publica- 
 tion entitled " Report to tlie Smithsonian Institution on the History of the 
 Discovery of Neptune," * 
 
 The author of this Report, Mr. Gould, of Cambridge, U.S., while 
 giving full credit to both Le Verrier and Adams for the accuracy of their 
 respective solutions of the inverse problem of perturbation, stoutly main- 
 tains the opinion expressed by his countryman, Prof. Peirce, to the effect 
 that the remarkable connexion which was found to subsist between the 
 
 * Published at Washington, 1850. 
 
APPENDIX. 615 
 
 theoretical researches of these geometers and the actual position of the 
 planet Neptune, must be regarded as wholly fortuitous. Let us examine 
 some of the arguments which he adduces in support of this peculiar view 
 of the subject. 
 
 (92.) It has been stated (p. 185) that Mr. Adams, in his final communi- 
 cation to the Astronomer Royal, remarked that the observations of Uranus 
 would in all probability be satisfied best by adopting for the hypothetical 
 planet a mean distance equal to 83.6. He was led to entertain this opinion 
 by a comparison of the errors of his theory for the three oppositions of Uranus 
 in 1843-44-45, resulting from the two hypotheses of the mean distance 
 which he bad already employed in his researches. It is manifest, when 
 this inference is viewed in connexion with his previous results, that 
 Adams had renounced all faith in even an approximation to Bode's law 
 of the distances of the planets, and that the current of his researches was 
 rapidly conducting him to a mean distance of the hypothetical planet 
 agreeing with the actual mean distance of the planet Neptune. Mr. 
 Gould seeks to depreciate the merit of this sagacious conclusion by con- 
 tending that a mean distance equal to 33.6 would give erroneous results. 
 "Le Verrier," says he, " has shewn that the assumption of even 35 as 
 the mean distance would lead to intolerable discordances. Peirce has 
 further proved that an important change in the character of the perturba- 
 tions takes place near the distance 35.3. It is therefore evident that no 
 claims can be based upon the rough inference alluded to." 
 
 It has been mentioned that Peirce objected to the reasoning by 
 which Le Verrier established the inferior limit of the mean distance of the 
 hypothetical planet (35.04), on the ground of the continuity of the investi- 
 gation being broken at the distance 35.3 by the commensurability of the 
 mean motions of the two planets. It is plain, therefore, that the pro- 
 positions announced by these two geometers are mutually incompatible ; 
 and yet Mr. Gould adduces them as confirmatory of each other ! We 
 have already had occasion to remark that there do not exist grounds for 
 supposing that either of them is entitled to any confidence. 
 
 (98.) Mr. G ould admits that Le Verrier may be considered the discoverer 
 of the planet Neptune, in so far as he proved not only that it was impossible 
 to represent the motions of Uranus without the assumption of some un- 
 known disturbing body, but that the perturbations were of that analytical 
 form which belongs to an exterior planet. 
 
 Now it appears to me, that the latter assertion is at direct variance with 
 the actual state of the question. Le Verrier demonstrated, by his re- 
 searches, that the perturbations were such as would be produced by the 
 direct action of an exterior planet during the interval of time over which 
 the observations extended ; but, with respect to the analytical form of these 
 perturbations, it depended on the elements of the disturbing planet, which 
 were beyond the scope of investigation, and in fact turned out to be 
 entirely different from those deduced by Le Verrier. 
 
 (94.) Mr. Gould further remarks that Le Verrier omitted the considera- 
 tion of the terms depending on a near approach to commensurability ; but 
 that this, although certainly a defect, cannot be considered as an error in 
 the theory, since within the limits where he had reason to suppose that 
 the orbit was situated, these terms are almost uniformly negligible. 
 
 With reference to this point it may be remarked, that the irregularities 
 in the motion of Uranus depended on the direct action of Neptune during 
 the period of last conjunction, and not on the analytical theory of that 
 
616 APPENDIX. 
 
 planet, which involves all the consequences liable to be developed in the 
 lapse of indefinite ages. Hence it is manifest that the absence of any re- 
 semblance between the theory of the hypothetical planet of Le Verrier 
 and that of the planet Neptune, cannot Hbe considered as affecting in the 
 slightest degree the merit of Le Verrier's researches, in so far as they had 
 for their object the discovery of the disturbing body. Even in the case of 
 Neptune, the terms to which Mr. Gould alludes do not exercise any 
 sensible influence on the action of the planet between the years 1690 
 and 1845. 
 
 (95.) With reference to the same geometer Mr. Gould makes the following 
 statement : " His laborious and elegant researches have been crowned 
 with brilliant success, and M. Le Verrier himself rewarded by the con- 
 sciousness of having been the immediate occasion of the discovery of 
 Neptune. And although the agreement of Neptunes direction at the 
 time of the discovery with the direction of the theoretical planet was but 
 accidental, it almost seems as though the heavens strove to show themselves 
 propitious, so happy was the accident, so wonderful the coincidence" * 
 
 (96.) Leaving the above passage to the reader's own reflections, we proceed 
 to notice one or two other statements of Mr. Gould's. Referring to the 
 assertion of Sir John Herschel, in his " Outlines of Astronomy," that the 
 longitude and radius vector of the hypothetical planet, whether of Adams 
 or Le Verrier, very nearly coincided with the longitude and radius vector 
 of Neptune during the period of its action being sensible, Mr. Gould 
 remarks: "But surely it cannot be considered as an analogy between 
 the two orbits, that the perihelion of the one was so near the aphelion of 
 the other." 
 
 The analogy between the two orbits, demanded by the question relative 
 to the disturbing body, was confined solely to a pretty close coincidence 
 of the paths of the hypothetical and real planets during the period of the 
 disturbing force being sensible. Even in this case it was a near agreement 
 of the longitudes, rather than of the distances, which was required by the 
 conditions of the problem. With respect to the absolute identity of the 
 two orbits, the establishment of such a condition was an object of no im- 
 portance in so far as the discovery of the disturbing body was concerned. 
 Sir John Herschel, in the work to which Mr. Gould refers so far from 
 attempting to demonstrate any resemblance between the elements of Nep- 
 tune on the one hand, and those of the hypothetical planet of either 
 Le Verrier or Adams on the other on the contrary, utterly repudiates 
 the existence of any necessary connexion between such an analogy and 
 the question relative to the discovery of the disturbing body. But, apart 
 from all consideration of this circumstance, it seems surprising that Mr. 
 Gould should urge such an objection to the identity of the two orbits as 
 that above cited, when it is born^ in mind that in the one case the orbit 
 is very eccentric, and in the other case is almost circular. 
 
 (97.) Mr. Gould concludes his Report with a remark the object of which 
 is to reconcile the conflicting results of observation and theory. " The 
 combined labours of Le Verrier and Peirce," says he, " have incontro- 
 vertibly proved that, by reducing the limits of error assumed for the 
 modern observations to 3", there can be but two possible solutions of the 
 problem. There are two different mean distances of least possible error, 
 one of which is 36, and the other 30. The one is included within the 
 
 * Report, p. 51. 
 
APPENDIX. 
 
 617 
 
 theory and limits of Le Verrier, and corresponds with Adams's solution ; 
 the other is the orbit of Neptune." * 
 
 With respect to the existence of two mean distances of least possible 
 error, with an interval included between them, any mean distance corre- 
 sponding to which is incapable of satisfying the observations with sufficient 
 accuracy, it seems to be in the highest degree improbable. This will be 
 readily seen by reference to the theoretical researches of Le Verrier and 
 Adams. The elements of the first and second planet of Adams, and 
 those which Le Verrier deduced from his final investigation, exhibit a 
 successive diminution of the mean distance. Now, in each of these three 
 cases, the mean distance was greater than the true value ; but this defect 
 was- remedied by increasing the eccentricity in a corresponding degree, and 
 placing the perihelion near the point of conjunction of Neptune and Uranus. 
 By this means the distances of the disturbing body were rendered in each 
 case very nearly equal to the true distances in the part of the orbit where 
 considerable precision was indispensable ; and the effect of the error in 
 the mean distance was thrown upon the opposite portion of the orbit 
 extending on each side of the aphelion, where it was incapable of exer- 
 cising any influence. The following table will exhibit this view of the 
 subject in a clearer light : 
 
 Hypothetical Planet. 
 
 Mean 
 Distance. 
 
 Perihelion 
 Distance. 
 
 Aphelion 
 Distance. 
 
 Longitude of 
 Perihelion. 
 
 Adams, Hyp. I. 
 
 38.400 
 
 32.216 
 
 44.584 
 
 315 57' 
 
 Hyp. II. . 
 
 37.478 
 
 32.958 
 
 41.998 
 
 299 11 
 
 Le Verrier . . . 
 
 36.154 
 
 32.264 
 
 40.044 
 
 284 45 
 
 It appears from these results, that the perihelion distance is almost the 
 same for each of the three planets, and that the longitude of the perihelion 
 does not in any case differ materially from the longitude of Uranus and 
 Neptune (273) on the occasion of their last conjunction, about the begin- 
 ning of the year 1822. On the other hand, the aphelion distance varies 
 nearly at a rate corresponding with the variation of the mean distance. 
 Now if we suppose the mean distance of the hypothetical planet to be 
 diminished below the value assigned by Le Verrier, so as to approach 
 nearer the mean distance of Neptune, have we not strong reason to believe 
 that, by similarly throwing the effect of the change mainly upon the 
 aphelion distance, where it would be altogether uninfluential, the observa- 
 tions of Uranus would be satisfied with the same degree of precision as 
 in the foregoing cases? Indeed it seems very probable that this object 
 might be accomplished by employing any mean distance within a range 
 extending considerably both above and below the mean distance of Nep- 
 tune, the perihelion being turned towards the point of conjunction when 
 the mean distance was greater, and the aphelion being turned towards the 
 same point when the mean distance was less, than the true value. 
 
 (98.) We may recapitulate the conclusions suggested by the discovery of 
 the planet Neptune in the following terms : Two contemporary geometers, 
 
 * Report, p. 55. 
 
618 APPENDIX. 
 
 Mr. Adams in England, and M. Le Verrier in France, undertook about 
 the same time to investigate the irregularities of Uranus upon the suppo- 
 sition of their being produced by the action of an exterior planet, and, in- 
 dependently of each other, arrived at a ve*ry approximate determination of 
 the position of the disturbing body. Upon this ground, therefore, they are 
 severally entitled to the honour associated with the theoretical discovery 
 of the planet Neptune. With respect to Le Vender's researches on 
 the limits of the orbit of the disturbing body, they have not been 
 borne out by the results of actual observations ; but this circumstance, 
 attributable in all probability to the intricacy of the subject and 
 the imperfect state of analysis, does not in the slightest degree impugn his 
 claims to the great discovery just mentioned. The American astronomers 
 and mathematicians have more especially distinguished themselves by their 
 labours in connexion with the planet Neptune, since the epoch of its phy- 
 sical discovery. The results that have been deduced from Bond's observa- 
 tions of the satellite of Neptune and the mathematical researches of 
 Walker and Peirce, unquestionably exhibit a degree of consistency with 
 the actual observations of Uranus and Neptune which has not been paral- 
 leled by any similar efforts on this side of the Atlantic, while at the same 
 time they tend to throw much interesting light on the theory of both 
 planets. The peculiar views which Prof. Peirce was led to entertain, 
 respecting the researches of the distinguished geometers to whom the 
 theoretical discovery of Neptune is due, may perhaps be attributed to his 
 having devoted his attention too exclusively to the analytical formulae re- 
 presenting the action of the planets, without taking into sufficient con- 
 sideration the mode in which the disturbing forces directly operate. These 
 views were announced by Prof. Peirce in a spirit of candour and mode- 
 ration highly honourable to his character as a philosopher. They are be- 
 yond all doubt erroneous, but the trifling inadvertence into which he was 
 thus betrayed does not detract from the merit of his more substantial 
 labours in connexion with the theory of Uranus and Neptune. 
 
 IV. 
 
 REMARKS ON THE LUNAR INEQUALITY TERMED THE EVECTION. 
 
 One of the most remarkable instances of perturbation which occurs 
 in the solar system is the inequality in the moon's longitude termed the 
 evection. So long as the moon was observed merely in eclipses, this in- 
 equality continued to escape the notice of astronomers. When Hippar- 
 chus, however, after having constructed the astrolabe, succeeded in deter- 
 mining the position of the moon in quadratures, he found that the results 
 could not be generally reconciled with the existing theory of her 
 motion. That great astronomer, having no similar observations of the 
 moon, anterior to his own accessible to him, was unable to arrive at a defi- 
 nitive conclusion respecting the anomaly ; but he formally pointed out its 
 existence, and executed a series of valuable observations with the view of 
 aiding future astronomers in their researches on the subject. It is well 
 known that the discovery of the law of this famous inequality is due to 
 Ptolemy. The account which he has given of the inequality as it pre- 
 sented itself to his observations *, would seem to imply a law of variation 
 * Syntaxis, lib. v., cap. ii. 
 
APPENDIX. 619 
 
 materially different from that suggested by the term representing the same 
 inequality in the modern theory of the moon's motion. He states that 
 the observed places of the moon in quadratures, whether those recorded 
 by Hipparchus or those actually determined by himself, were found in 
 some instances to agree very well with the computed places ; in other in- 
 stances to differ considerably, being sometimes in excess and at other times 
 in defect. By attentively pursuing the inequality through its various 
 phases, he found that it was generally insensible in sizygees. It also 
 vanished in the quadratures when the moon was in the apogee or perigee 
 of her epicycle (in other words, when the line of apsides was in quadra- 
 tures) ; but it increased from those points towards the mean points of the 
 orbit where it was greatest (in other words, it increased as the line of 
 apsides revolved from the quadratures to the sizygees). Moreover, when 
 the first anomaly (the equation of the centre) was subtractive, the observed 
 place of the moon was in defect, in consequence of the new inequality ; 
 and when the first anomaly was additive, the observed place was in advance 
 of the computed place, from the same cause. 
 
 It appeared, then, that while the inequality vanished in sizygees, its 
 effect in quadratures was invariably to augment the equation of the centre, 
 unless the line of apsides was in quadratures, when it vanished altogether 
 Ptolemy, from observations of the moon in sizygees, had determined the 
 maximum value of the equation of the centre to be 5 1'*. Inconsequence 
 of the new inequality, its value, as indicated by observations in quadratures, 
 generally exceeded 5 1', increasing from that value to 7 40' as the line 
 of apsides revolved from quadratures to sizygees. Hence it followed that 
 the maximum effect of the new inequality amounted to 2 39'. 
 
 In modern astronomy the inequality in the moon's longitude, depending 
 on the combined effects of the equation of the centre and the evection, 
 is represented thus : 
 
 3v = + 6 18' sin A + 1 20' sin (3 (<)_ A), 
 
 where A represents the mean anomaly of the moon, <[ the mean longitude 
 of the moon, and the mean longitude of the sun. 
 
 Nothing can at first sight appear more different than the ancient and 
 modern modes of representing the two inequalities. With respect to the 
 equation of the centre, its magnitude is materially different in the two 
 cases. The evection, however, differs not merely in absolute magnitude, 
 but also in the law of its variation. According to Ptolemy the zero points 
 of the inequality were fixed, in position, being constantly situate in the 
 sizygees, while its maximum value was variable. On the other hand, it is 
 manifest, from the second term of the above equation, that the zero points 
 of the modern inequality are variable in position relatively to the line 
 of sizygees, but that its absolute magnitude is constant. 
 
 * Ptolemy determined the ratio of the epicycle of the lunar orbit to the deferent, or, 
 in other words, the maximum value of the equation of the centre, from three eclipses 
 of the moon observed at Babylon, about 700 years before the Christian era, and also 
 from three similar eclipses observed by himself. In both cases he found the ratio to be as 
 5W to 60, which gives 5 3 1' for the equation of the centre (Syntaxis, lib. iv.). Delambre, 
 having computed the equation of the centre by the modern analytical formulae, found that 
 the three Chaldean eclipses assigned 4 59' 16" as its value, and that the three eclipses of 
 Ptolemy made it equal to 4 59' 42". The close agreement of these results affords a 
 strong presumption, that the two sets of eclipses employed by Ptolemy in his calculations 
 were selected on account of their mutual consistency, from a vast mass of similar ob- 
 servations in his possession. 
 
620 
 
 APPENDIX. 
 
 Notwithstanding the striking points of dif- 
 ference referred to in the foregoing remark, the 
 effects produced by the combination of the two 
 constituent inequalities are identical in t>oth 
 cases as respects the law of variation, and are 
 also nearly so in respect of absolute magni- 
 tude. This may be easily shewn in the follow- 
 ing manner. Let A c represent the line of 
 sizygees, B D the line of quadratures, E F the 
 line of apsides, M the place of the moon 
 in her orbit. 
 
 Let A T E = $, ATM= ([0=9. 
 Hence A = E T M = <. 
 
 2 ( - 0) - A = 2 - (9 - <) = + <. 
 Therefore lv = 6 18' sin A + 1 20' sin (2 (d ) - A), 
 
 = 6 18' sin (0 0) 4- 1 20' sin (9 + <), 
 = 4 58' sin (0 <j>) + 1 20' sin (9 </>) + 1 20' sin (9 + <), 
 = 4 58' sin A + 2 40' cos < sin 0. 
 
 The first of these terms is manifestly the equation of the centre as de- 
 duced by Ptolemy from observations of the moon in sizygees. The second 
 term also represents the evection as it exhibited itself to that astronomer. 
 Thus let us suppose the moon to be in either of the sizygees. In such a 
 case 0=0, or 180, and consequently the second term vanishes. 
 Hence > = 4 58' sin A. 
 
 Again, if the moon be in quadratures, we have = 90, and therefore 
 h = 4 58' sin A + 2 40' cos < 
 = 4 58' cos $ + 2 40' cos <#>, 
 = 7 38' cos <j>. 
 
 In this case, then, the two inequalities conspire together. The effect 
 is obviously a maximum, when <jb = 0, or 180. We have then 
 
 S v = 7 38'. 
 
 These conclusions agree with Ptolemy's description, subject to a 
 slight difference in the numerical values. Indeed the precision with 
 which that astronomer determined the combined effects of the two ine- 
 qualities in sizygees and quadratures, is one of the most astonishing 
 circumstances connected with the ancient astronomy. 
 
 Since the evection as represented by Ptolemy has always the same sign 
 in the quadratures as the equation of the centre, it is manifestly positive 
 when the moon is revolving from conjunction to opposition, and negative 
 throughout the remaining half of the orbit, or vice versa ; according as the 
 perigee is situate in the first and fourth, or in the second and third 
 quadrants of the lunar orbit, counting from the point of conjunction in 
 the direction of the moon's motion. 
 
 In order to determine the zero points of the evection as represented by 
 modern astronomers, we have 
 
 sin (0 + </>) = ; 
 
 .-. 9 = <, or J80 <. 
 
 Hence it is manifest that by drawing G H, making with A c the same angle 
 which E F makes with it, the extremities G, H, will indicate the zero points 
 of the inequality. 
 
 It has been stated (p. 424) that Horrocks first explained the evection 
 upon the Keplerian principles of astronomy, by supposing the eccentricity 
 
APPENDIX. 621 
 
 of the lunar orbit to be variable, and attributing a libratory motion to the 
 line of apsides. Allusion has also been made to the difficulty experi- 
 enced for some time in computing, by the theory of gravitation, the motion 
 of the lunar apogee, upon which the inequality to a great extent depends. 
 It is worthy of remark that in the original edition of the " Principia," pub- 
 lished in 1687, Newton states* that he computed the motion of the 
 lunar apogee in sizygees and quadratures, and also the mean motion. He 
 asserts that he found the daily progression in sizygees to be 23', the daily 
 regression in quadratures to be 16^', and the mean annual motion to be 
 40. He remarks that these results do not accord exactly with the tables, 
 a circumstance which he thinks may be attributable to the errors of the 
 observations. The calculations being very intricate and embarrassed with 
 approximations, and the results not possessing all the accuracy that was 
 desirable, he refrained from publishing the details of his researches on the 
 subject. (Computationes autem, ut nimis perplexas et approximationibus 
 impeditas, neque satis accuratas, apponere non lubet.) 
 
 The results which Newton obtained on this occasion cannot by any 
 means be considered very inaccurate, when the intricacy of the subject and 
 the imperfect state of analysis in his time are taken into account. They 
 give 11 2 1/ for the monthly progression of the apogee in sizygees, and 
 8 V for the monthly regression in quadratures. The modern tables of 
 the moon assign, in round numbers, 1 1 and 9 as the corresponding values of 
 the motion of the apogee. Newton found the mean annual progression of 
 the apogee to be 40 ; the modern tables of the moon make it 40 40' 32". 
 
 Newton appears to have been so dissatisfied with his researches on this 
 subject, in all probability from the circumstance of the results not pre- 
 senting a more complete accordance with those deducible from observa- - 
 tion, that he suppressed all allusion to them in the second edition of the 
 " Principia," published in 1713, under the superintendence of Cotes. What- 
 ever may have been the method of investigation employed by him on this 
 occasion, it was manifestly one which was capable of grappling with the 
 main difficulties of the question. It is not improbable that a careful in- 
 spection of those manuscripts of Newton, which are still in existence, might 
 serve to throw some light on this interesting point. 
 
 V. 
 
 NOTE EESPECTING HORROCKS. 
 
 At page 421 I have hazarded the conjecture that it was duties of a 
 religious nature which called away Horrocks so peremptorily, while en- 
 gaged in looking out for the transit of Venus on the 24th of November, 
 1639. This is confirmed by a note which the late Prof. Bigaud dis- 
 covered in one of Hearne's Memorandum Books preserved in the 
 Bodleian Library, Oxford, from which it appears that Horrocks was a 
 hard-working curate at Hoole, subsisting upon a wretched pittance 
 (Eigaud's Correspondence of Eminent Men of the Seventeenth Century, 
 vol. ii. p. 112). It appears also, from one of Flamsteed's letters to 
 Collins, contained in the same work, that Crabtree's death occurred in 
 the year 1652, and not shortly after that of Horrocks, as Wallis erroneously 
 stated in the dedicatory epistle to Lord Brouncker, inserted at the com- 
 mencement of the *' Opera Posthuma " of the latter. 
 * Principia, lib. iii. prop, xxxv., scholium. 
 
622 APPENDIX. 
 
 VI. 
 
 ACCOUNT OF SOME RECENT RESULTS OF ASTRONOM[CAL OBSERVATION. 
 
 Two instances of a total eclipse of the sun have recently furnished 
 opportunities of observing the circumstances usually attending these phe- 
 nomena. The first of these eclipses happened on the 8th of August, 
 
 1850. It was visible only in the Pacific Ocean. An account of the 
 phenomenon as observed by M. Kutczycki at Honolulu, the chief town of 
 the Sandwich Isles, appeared in the Comptes liendus for the 21st of April, 
 
 1851. The second eclipse happened on the 28th of July, 1851. Being 
 visible in the northern countries of Europe, it was observed by a great 
 number of astronomers. Two important facts were satisfactorily estab 
 lished by the observations of these eclipses. In the first place, the reddish 
 protuberances usually visible on such occasions, appeared in some instances 
 to be isolated from the moon's limb. Secondly, those protuberances that 
 were visible towards the point of immersion, were seen gradually to diminish 
 as if concealed by the passage of the moon over the solar disk ; while, on 
 the other hand, those towards the point of emersion appeared to en- 
 large as if gradually disclosed to view by the same cause. Both these 
 facts tend to support the opinion that the protuberances are solar phe- 
 nomena. A serious difficulty attending the explanation of their physical 
 cause, consists in the material difference of aspect which they exhibit to 
 spectators distant from each other by only a very short interval. 
 
 Five more planets revolving between the orbits of Mars and Jupiter, 
 have been discovered in addition to those referred to in the body of this 
 work (see p. 240). Three of these bodies were discovered in the year 
 1850. The first (Parthenope) was discovered by De Gasparis on the llth 
 of May; the second (Victoria), by Hind on the 13th of September; and 
 the third (Egeria), by De Gasparis on the 2nd of November. The re- 
 maining two planets were discovered in the course of the year 1851. The 
 first of these (Irene) was discovered by Hind oYi the 19th of May, 1851. 
 By a singular coincidence, De Gasparis also independently discovered this 
 planet on the 23rd of the same month. The second planet (Eunomia) 
 was discovered by De Gasparis on the 29th of July. Parthenope revolves 
 round the sun in 1401 days, Victoria in 1303 days, Egeria in 1496 days, 
 Irene in 1510 days, and Eunomia in 1424 days. These numbers, of 
 course, can only be regarded as provisional. The total number of asteroids 
 now discovered amounts to fifteen. It is not improbable that hundreds of 
 these minute bodies may be revolving in the same region. 
 
 On the 4th of December, 1850, intelligence reached this country that 
 on the 15th of the previous month, Mr. Bond, Director of the Observatory 
 of Cambridge, U. S., had discovered a new ring round Saturn, interior to 
 the bright rings already known to exist. It soon turned out that the same 
 phenomenon had been observed in England by Mr. Dawes on the 29th of 
 November, before he received any intimation of Mr. Bond's discovery. 
 The most surprising circumstance, however, connected with the phe- 
 nomenon is, that it was actually observed as early as the year 1838, by 
 Dr. Galle of Berlin ; although no further notice seems to have been taken 
 of it till the announcement of its rediscovery as above mentioned. The 
 ring now forms an interesting object of observation to astronomers armed 
 with powerful telescopes. In brightness it is very much inferior to the 
 outer rings. Its breadth is equal to about two-fifths of the interval in- 
 cluded between the bright rings and the body of the planet. It would 
 
APPENDIX. 623 
 
 appear from most of the observations that it is not a distinct appendage of 
 the planet, but simply a continuation of the inner bright ring. 
 
 On the 24th of October, 1851, Mr. Lassell discovered two new satellites 
 revolving round Uranus. He has subsequently succeeded in seeing them 
 with his powerful reflector, on every occasion on which he looked for them. 
 He finds that the observations may be pretty well satisfied by supposing 
 the period of the inner satellite to be 2.506 days, and that of the outer 
 satellite to be 4.150 days. It appears, therefore, that they are interior to 
 the two bright satellites discovered by Sir William Herschel in 1787. 
 From the diagram of their positions inserted in the Monthly Proceedings 
 of the Astronomical Society for November, 1851, they appear, like the 
 other satellites, to revolve in orbits nearly perpendicular to the plane of the 
 ecliptic. 
 
 It has been mentioned (p. 139) that a comet discovered by M. Faye, in the 
 year 1843, was found to revolve in an elliptic orbit, and that its perturba- 
 tiona for the ensuing revolution were calculated by Le Verrier, who 
 arrived at the conclusion that its passage through the perihelion would 
 take place on the 2nd of April, 1851. It is a gratifying fact that the 
 comet has actually returned at the appointed time. It was first seen by 
 Prof. Challis, with the Northumberland refractor, on the 28th of 
 November, 1850. The observations of its apparent position have been 
 found to present a remarkable agreement with the corresponding results 
 derivable from the calculations of M. Le Verrier. 
 
 Allusion has been made at page 243 to the discovery of a small ultra- 
 zodiacal planet (Metis) at the observatory of E. Cooper, Esq., of Markree, 
 in the north of Ireland. An achievement of vastly greater importance has 
 since emanated from that observatory in the shape of a catalogue of 14,888 
 stars near the ecliptic, the places of which, in general, are not to be 
 found in any catalogues hitherto published. This catalogue was constructed 
 from observations made in the years 1848, 1849, and 1850, and was pub- 
 lished in 1851, the expense of printing^ having been defrayed by the Go- 
 vernment, upon the recommendation of the Royal Society. A second 
 catalogue, destined to contain the places of about 12,000 additional stars, 
 observed in the year 1851, is in the course of preparation at the same 
 observatory. Mr. Cooper and his active assistant, Mr. Graham, are also 
 engaged in executing a series of celestial maps upon a magnificent scale. 
 Each map has a range of 8 both in right ascension and in declination. 
 The scale is four times larger than that of the Berlin maps. It is con- 
 templated to insert in these maps all the stars within their range which 
 have either been observed at Markree, or have been already published in 
 other catalogues. The epoch of reduction is 1850.0. The advantages 
 which cannot fail to accrue to astronomical science from the construction 
 of these maps is incalculable. It must be acknowledged that the labours 
 at Markree Observatory exhibit a loftiness of aim as well as a unity of 
 design, and a spirit of skilful perseverance, which not only serves effec- 
 tually to remove that establishment from the category of mere amateur 
 observatories, but entitles it to an honourable place in the highest class 
 of those institutions that have been founded for the promotion of astro- 
 nomical science. 
 
 In concluding this note it may be stated, that the Astronomer Royal 
 has now (February, 1852) completed the arrangements at the Royal 
 Observatory for recording transits of stars by means of an electro-magnetic 
 apparatus. The accuracy of this method may be relied on to the twentieth 
 
624 APPENDIX. 
 
 of a second of time. It is contemplated, in connexion -with this improve- 
 ment, to transmit Greenwich time, by means of the electric telegraph, to 
 all the most important places in the kingdom. The realisation of this 
 project will constitute a boon of inestimable value to the outports, by 
 affording on all occasions a reliable standard for the regulation of chro- 
 nometers. The successful construction of the submarine telegraph 
 between Dover and Calais will also enable the Royal Observatory to 
 record transits simultaneously with the Royal Observatory of Paris and 
 other similar establishments on the Continent, by which means their 
 respective longitudes relatively to each other may be more accurately 
 ascertained. The immense importance of this object must be obvious 
 to any person who possesses an ordinary acquaintance with astronomical 
 science. 
 
 VII. 
 
 COPY OF THE NOTE OF THE OBSERVATION OF y DRACONIS, made by 
 Bradley, at Kew, with the zenith sector of Molyneux, on the 2 1st of 
 December, 1725 ; the discordance of which with the results of previous 
 observations, revealed to him the first glimpse of his immortal discovery 
 of the Aberration of Light. 
 
 It has been mentioned at page 337 that the original note of the obser- 
 vation, of which the subjoined words are an exact copy, was found a few 
 years since by Prof. Rigaud, among the manuscripts of Bradley, written 
 upon a loose piece of paper. 
 
 Dec 21 st Tuesday 5 h 40' sider time 
 
 Adjusted y e mark to y e Plumb line 
 
 & then y e Index stood at 8 
 
 5 h 48' 22" y e star entred 
 
 49 52J Star at y e Cross 
 
 51 24 Star went out 
 
 could 
 As soon as I let go y e course 
 
 A 
 screw I perceived y e star too 
 
 much to y e right hand & 
 
 so it continued till it passed 
 
 y e Cross thread and within a quarter 
 
 was 
 of a minute after it had passed 
 
 graduat 
 I turned y e fine screw till I saw 
 
 A 
 
 y e light of y e star perfectly 
 
 bissected and after y e obser 
 
 vation I found y e index 
 
 at 11 j, so that by this 
 
 observation y e 
 
 mark is about 3"f 
 
 too much south 
 
 but adjusting 
 
 y e mark and plumb line 
 
 I found y e index at 8. 
 
INDEX. 
 
 ABERRATION of Light discovered by Brad- 
 ley, 338; various determinations of its 
 maximum value, 340. 
 
 Adams Researches on the theory of Uranus, 
 168; transmits his results to the Astro- 
 nomer Royal, 173 ; they furnish the earliest 
 indication of the Trans-Uranian planet, ib. ; 
 second series of results obtained by him, 
 185; announcement of his researches by Sir 
 John Herschel, 194. 
 
 Airy Researches on the lunar theory, 120; 
 discovers the long inequality in the Earth 
 and Venus, 127; determines the mass of 
 Mars, 129; researches on the mass of Ju- 
 piter, 130 ; determines the ellipticity of the 
 Earth, 145; measures an arc of longitude 
 in the British Isles, 150 ; demonstrates the 
 existence of errors in the tabular radius 
 vector of Uranus, 167; receives from 
 Adams the results of his researches on the 
 existence of an exterior planet, 173; his 
 reply to Adams, 174; correspondence with 
 Le Verrier on the theory of Uranus, 184; 
 reply of the latter, ib. ; proposes a search 
 for the planet, ib. ; announces to Le Ver- 
 rier the results arrived at by Adams, 194 ; 
 communicates an historical statement re- 
 specting the discovery of the Trans-Ura- 
 nian planet, 196; detects two new ine- 
 qualities in the motion of the moon, 206; 
 determination of the lunar parallax, 229; 
 modification of Bessel's method for facilitat- 
 ing the reduction of observations, 345 ; suc- 
 ceeds Pond at the Observatory of Green- 
 wich, 493; reduction of the Lunar and 
 Planetary Observations, 495; introduces 
 the use of an altitude and azimuth instru- 
 ment at the Greenwich Observatory, ib. ; 
 transit circle, 497; reflex zenith telescope, 
 499; Cambridge Catalogue of Stars, 513; 
 first Greenwich Catalogue, ib. ; second 
 Greenwich Catalogue, 514; physical ex- 
 planation of the disksand rings of stars, 54 6. 
 
 Al Batani discovers the motion of the aphe- 
 lion of the terrestrial orbit, 97. 
 
 Altitude and Azimuth Instrument first used 
 by Roemer, 465. 
 
 Apian first suggests the use of coloured 
 glasses in observations of the sun, 227; re- 
 marks that the tails of comets are turned 
 opposite to the sun, 297. 
 
 Arago Remarks respecting the discovery of 
 the planet beyond Uranus, 196; observes 
 occultations of small stars by the moon, 
 230; phenomeon witnessed by him on 
 those occasions, 231 ; experiments on the 
 light of comets, 313; account of the solar 
 eclipse of 1842, 368. 
 
 Arcs of the Meridian Measurement of the 
 arc between Gottingen and Altona, 144; 
 arc of India, 145; arc measured by La- 
 caille at the Cape of Good Hope, 147; la- 
 bours of Maclear, 148; arc measured in 
 the British Isles, 149. 
 
 Argelander Zone observations of stars, 511 ; 
 executes a catalogue of stars, 513; re- 
 searches on stars having a variable bright- 
 ness, 541 ; researches on the motion of the 
 solar system in space, 556. 
 
 Atmosphere, terrestrial Researches on the 
 oscillations of the, 163. 
 
 Attraction Ideas of Copernicus on the sub- 
 ject of, 15; Gilbert, 16; Kepler, 17; 
 Galileo, 19; Borelli, 20; researches of 
 Newton, 20-40; experiments of Bouguer, 
 158; Schehallien experiment, ib. 
 
 Auzout his remark respecting a twilight in 
 the moon, 232; invents the micrometer, 
 450. 
 
 Bacon, Roger Ideas of the telescope, 517. 
 
 Baily Researches on the influence of the air 
 in pendulum experiments, 156 ; determines 
 the mean density of the earth, 159; phe- 
 nomena observed during the annular 
 eclipse of 1836, 409; labours connected 
 with star catalogues, 508-13. 
 
 Bailly explains the origin of the libratory 
 motion of the nodes of the second satellite 
 of Jupiter, 86; researches on the physi- 
 cal theory of the satellites, 88; determines 
 the magnitude of Jupiter's satellites, 250. 
 
 Ball discovers the duplicity of Saturn's 
 ring before the same phenomenon was re- 
 marked by Cassini, 526. 
 
 Battista Porta Ideas of the telescope, 518. 
 
 Bernouilli his researches on the tides, 71. 
 
 Bessel his researches on the mass of 
 Saturn, 131; experiments on the attrac- 
 tion of different bodies, 133 ; researches on 
 the satellites of Saturn, 142; investigates 
 the ellipticity of the earth, 145; method 
 S S 
 
626 
 
 INDEX. 
 
 
 for determining the length of the seconds' 
 pendulum, 155; investigates the influence 
 of the resistance of the air on the rate of 
 oscillation, ib. ; directs his attention to 
 the irregularities of Uranus, 167; re- 
 searches on the elements of Saturn's ring, 
 259; determines the period of the comet 
 of 1811, 289; observations on the nucleus 
 of Halley's comet, 294 ; opinion respect- 
 ing the tails of comets, 311; researches 
 on the quantity and laws of precession, 
 320; researches on refraction, 335; 
 method for facilitating the reduction of 
 observations, A84^ zone observations of 
 stars, 511; determines the parallax of 
 61 Cygni, 551 ; researches on the motion 
 of the solar system in space, 556. 
 
 Bianchini Researches on the rotation of 
 Venus, 234. 
 
 Biot Experiments with the pendulum, 153 ; 
 value of the terrestrial ellipticity hence 
 deduced by him, 1 53 ; researches on the 
 motion of the solar system in space, 556. 
 
 Bode Explanation of the solar spots, 222. 
 
 Bond Physical observations of Saturn's 
 ring, 265; discovers the eighth satellite of 
 Saturn, 271. 
 
 Borel Account of the invention of the 
 telescope, 517. 
 
 Borelli his ideas of circular motion, 20 ; 
 surmise respecting the orbits of comets, 102. 
 
 Bouguer Researches on atmospheric refrac- 
 tion, 328. 
 
 Bouillaud determines the period of the 
 variable star Mira Ceti, 540 ; opinion re- 
 specting the cause of its variable bright- 
 ness, 541. 
 
 Bouvard his determination of the mass of 
 Jupiter, 130 ; publishes tables of Jupiter 
 and Saturn, 131 ; determines the mass of 
 Uranus, 132 ; calculates tables of Uranus, 
 165; finds it impossible to reconcile the 
 ancient with the modern observations, ib. ; 
 suspects the existence of an exterior planet, 
 ib. 
 
 Bouvard, E. calculates tables of Uranus, 
 174; finds it impossible to reconcile them 
 with all the observations of the planet, 175. 
 
 Bradley Researches on the satellites of Ju- 
 piter, 81 ; first introduces the equation of 
 light into the tables of these bodies, ib. ; 
 discovers the great inequality of the three 
 interior satellites, and suggests its physical 
 cause, 82 ; discovers that the orbit of the 
 fourth satellite is eccentric, ib.; researches 
 on refraction, 329 ; discovers the aberra- 
 tion of light, 338 ; discovers the nutation 
 of the earth's axis, 341; accounts of his 
 labours at the Observatory of Greenwich, 
 483; remark respecting the parallax of 
 the fixed stars, 549; remark relative to 
 the motion of the solar system in space, 
 554. 
 
 Brahe, Tycho overthrows the theory of 
 solid orbs, 15; demonstrates that comets 
 
 are situate beyond the moon's orbit, 102; 
 supposes them to move in circular orbits, 
 ib. ; views respecting the tails of comets, 
 308 ; first employs refraction in correct- 
 ing, astronomical observations, 321 ; in- 
 vents the mural quadrant, 445 ; observes 
 the new star which appeared in the year 
 1572, 539; opinion respecting its origin, 
 ib. ; estimate of the apparent diameters of 
 the stars, 547. 
 
 Brewster his opinion respecting the solar 
 spots, 227. 
 
 Brinkley Researches on refraction, 332; 
 researches on the parallax of the fixed 
 stars, 550. 
 
 Burchardt calculates the terms of the long 
 inequality of Jupiter and Saturn, depend- 
 ing on the fifth powers of the eccentricities 
 and inclinations, 129 ; calculates the ele- 
 ments of Halley's comet for 1759, 137; 
 calculates the lunar parallax by means of 
 the formulae of Laplace, 228. 
 
 Burg calculates tables of the moon, 118; 
 discovers irregularities in the moon's epoch, 
 ib. ; attempts to represent them by an 
 empiric equation, 119. 
 
 Campani attains great excellence in the 
 construction of refracting telescopes, 526. 
 
 Capocci Researches on the comet of 1843, 
 290. 
 
 Carlini Researches on the lunar theory, 
 119; experiments with the pendulum for 
 the purpose of determining the mean den- 
 sity of the earth, 160. 
 
 Cassini, J. D. Discovers the coincidence of 
 the nodes of the moon's orbit with those 
 of the moon's equator, 73 ; publishes tables 
 of Jupiter's satellites at Bologna, 80; re- 
 jects the equation of light, ib. ; method for 
 determining the solar parallax, 211; 
 value of that element assigned by him, 
 212; remarks respecting the solar spots, 
 219 ; executes a chart of the moon's sur- 
 face, 230 ; observes an occultation of 
 Jupiter by the moon, 231 ; researches on 
 the physical constitution of Venus, 234 ; 
 discovers that she has a rotatory motion, 
 ib.f determines the period of rotation, 
 ib.; observations on the physical constitu- 
 tion of Mars, 236 ; discovers that it revolves 
 on an axis, ib. ; determines the time of rota- 
 tion, ib. ; researches on the rotation of 
 Jupiter, 244; theory of the belts of Ju- 
 piter, 248; discovers the duplicity of 
 Saturn's ring, 260; physical observations 
 of the ring, 263 ; discovers four satellites 
 of Saturn, 268 ; variable brightness of the 
 fifth satellite, 271; hypothesis of atmo- 
 spheric refraction, 322; appointed Director 
 of the Royal Observatory of Paris, 457. 
 
 Cassini, J. his remarks on the rotation of 
 Venus, 234; views respecting the visi- 
 bility of the stars, 543 ; attempts to de- 
 termine the apparent diameter of Sirius, 
 
INDEX. 
 
 627 
 
 545; researches on the proper motions of 
 the stars, 554. 
 
 C'assini, IV. Remark respecting the Obser- 
 vatory of Paris, 480. 
 
 Cassegrain devises a new form of the re- 
 flecting telescope, 529. 
 
 Catalogues of Stars Catalogues of various 
 astronomers, 507-15. 
 
 Challis institutes a search for the planet 
 indicated by the theoretical researches of 
 Adams, 185; secures two positions of the 
 planet anterior to its actual discovery, 193. 
 
 Clairaut solves the problem of three bodies, 
 44 ; researches on the lunar theory, ib. ; 
 fails to account for the motion of the lunar 
 apogee, 45 ; revises his solution and obtains 
 the true result, 46 ; researches on the figure 
 of the earth, 67; theorem on the variation 
 of gravity at the earth's surface, 68; cal- 
 culates the perturbations of Halley's comet, 
 104. 
 
 Comets Tycho Brahe demonstrates that 
 comets are situate beyond the moon's or- 
 bit, 102; opinions respecting their orbits, 
 ib. ; Lagrange's method for calculating 
 their perturbations, 105; methods devised 
 for the determination of their orbits, 133; 
 comets of 1807, 134; comet of 1680, 
 289; supposed to move in an elliptic 
 orbit, ib. ; various determinations of its 
 periodic time, ib.; comet of 1264, 290; 
 comet of 1811, ib.; comet of Brorsen, ib.; 
 comet of 1843, ib. ; various determinations 
 of the orbit of this comet, 291 ; general 
 aspect of comets, 293 ; comets without 
 either nucleus or tail, ib.; translucency 
 of cometic matter, ib.; envelope surround- 
 ing the heads of comets, 294 ; proved to be 
 hollow, ib.; dimension of the envelope, 
 295; nucleus of comets, ib.; supposed in 
 some instances to be solid, 296; attempts 
 to determine its magnitude, ib.; structure 
 of the tail, ib. ; its direction generally 
 opposite to that of the sun, ib.; lateral 
 deviation of the extremity of the tail, 297 ; 
 direction of the tail first remarked in 
 Europe by Apian, ib. ; the same fact 
 previously noticed by the Chinese, ib. ; 
 comets \vith several tails, ib. ; comets with 
 tails of great length, ib.; the absolute 
 dimensions of the tail are in many in- 
 stances immense, 298 ; phenomena usually 
 exhibited by comets during their passage 
 of the perihelion, ib.; variation of volume 
 depending on their position relative to 
 the sun, 301 ; great heat to which some 
 comets are subjected on their passage of 
 the perihelion,^.; dissolution of comets, 
 302; development of the tail, ib. ; varia- 
 tions in the length of the tails of some 
 comets, 303 ; examples of very conspi- 
 cuous comets, 304 ; various opinions 
 with respect to the durability of comets, 
 306; variation of volume, 307; different 
 explanations of this fact, ib. ; hypotheses 
 
 respecting the tails of comets, 308; light 
 of comets, 312; by some enquirers sup- 
 posed to be self-luminous, ib. ; by others 
 they are held to shine only by reflected 
 light, ib. ; experiments of M, Arago, 313 ; 
 hypothesis of Laplace with respect to the 
 heat suffered by comets, 314 ; their mass 
 must be very inconsiderable, ib. ; ultimate 
 end for which comets are destined, 315. 
 
 Comet of Biela demonstrated by Gambart 
 and Clausen to revolve in an elliptic 
 orbit, 135; its perturbations calculated 
 by Damoiseau, ib.; apparition in 1846, 
 136; divides into two parts, ib. 
 
 Comet of Encke demonstrated to revolve 
 in an elliptic orbit, 134 ; tends to confirm 
 the hypothesis of a resisting medium, 135. 
 
 Comet of Faye discovered by Faye in 
 1843, 139; its orbit shown to be elliptic, 
 ib.; its perturbations calculated by Le 
 Verrier, ib. 
 
 Comet of De Vico Discovery of the, 141; 
 shown to revolve in an elliptic orbit, ib. 
 
 Comet of Halley its return first predicted 
 by Halley, 103; first seen in 1759 by 
 Palitzch, 104; passage of the perihelion 
 in 1835, 136 ; various determinations of 
 its elements for 1759, ib. ; its perturba- 
 tions calculated by various geometers, 
 137; ancient observation of, by the 
 Chinese, 288; physical observations of 
 Sir John Herschel, 301. 
 
 Comet of Lexell First shown by Lexell to 
 revolve in an elliptic orbit, 105; thrown 
 out of its orbit by the disturbing action of 
 Jupiter, ib. ; suspected by Valz to be 
 identical with Faye's comet, 139; this 
 opinion shewn by Le Verrier to be 
 erroneous, 140. 
 
 Copernicus his ideas on the attraction of 
 matter, 15. 
 
 Crabtree observes the transit of Venus in 
 1639, 421. 
 
 D'Alembert solves the problem of three 
 bodies, 44; computes the lunar perturba- 
 tions, ib. ; researches on the attraction of 
 ellipsoids, 69. 
 
 Damoiseau Researches on the lunar theory, 
 119; calculates the perturbations of 
 Biela's comet, 136; researches on Hal- 
 ley's comet, 137; his evaluation of the 
 lunar parallax, 228. 
 
 Dawes determines the ellipticity of Mer- 
 cury, 233; observations on Saturn's ring, 
 265. 
 
 Day, Sidereal Invariability of the, demon- 
 strated by Poisson, 161; confirmed by 
 ancient eclipses, ib. 
 
 De Dominis Notions of the telescope, 518. 
 
 De Grasparis discovers the planet Hygeia 
 P 243. (See Appendix.) 
 
 Delambre calculates tables of Jupiter's sa- 
 tellites, 96; tables of Jupiter and Saturn, 
 142; calculates tables of Uranus, 165. 
 
 So O 
 o A 
 
628 INDEX. 
 
 Delisle Hypothesis respecting the lumi- 
 nous ring seen during solar eclipses, 386. 
 
 De Rheita Account of the origin of the 
 telescope, 517. 
 
 De Vico determines the time of rotation of 
 Venus, 234. 
 
 Descartes opinion respecting the irradiation 
 of light, 351 ; account of the origin of the 
 telescope, 517. 
 
 Diffraction of Light discovered by Grimaldi, 
 345 ; researches of Newton on the sub- 
 ject, ib. 
 
 Dollond Researches on the dispersion of 
 light, 531 ; controversy with Euler on the 
 subject, ib.} discovers the principle of 
 achromatism, 532; constructs achromatic 
 telescopes, ib. 
 
 Dorfel proves that the comet of 1680 
 moved in a parabolic orbit, 102. 
 
 Dunthorne Researches on the secular in- 
 equality in the meanmotion of the moon, 60. 
 
 Du Sejour his researches on the subject of 
 a lunar atmosphere, 232 ; explanation of 
 the origin of Saturn's ring, 267. 
 
 Earth Researches of Newton on the figure 
 of the, 37; perturbations of the, computed 
 by Clairaut, 50 ; figure of the, investigated 
 by Huyghens, 66 ; researches of Maclaurin 
 on the same subject, 67 ; researches of Clai- 
 raut, ib.; his theorem relative to the varia- 
 tion of gravity at the surface of the, 68 ; 
 motion of the aphelion of the, discovered, 
 97; its perturbations investigated by La- 
 place, 127; long inequality discovered by 
 Airy, 128 ; determinations of the ellipticity, 
 145, 146; determinations of the mean 
 density, 159. 
 
 Eclipses of the Sun, Total rareness of their 
 occurrence, 361 ; circumstances upon which 
 they depend,362; ancient records of, 363- 
 364 ; modern records,365-7 ; account of the 
 eclipse of 1842, 367-71; change of colour 
 exhibited by the sky during the obscura- 
 tion, 372; darkness during the totality, 
 374 ; sudden transition from day to night, 
 375 ; luminous ring seen around the moon, 
 376; recorded observations of this pheno- 
 menon, ib.; appearance of the ring du- 
 ring the eclipse of 1842,381-5; explana- 
 tions of the nature and physical cause of 
 the ring, 386-90; luminous protuberances 
 observed during the totality, 390-393; 
 reddish streak of light observed around 
 the moon's limb immediately before and 
 after the total obscuration, 396; conclusions 
 suggested respecting the physical constitu- 
 tion of the sun, 400; aspect presented by 
 the moon, 401; coruscations of light ob- 
 served, 403; undulatory movements ob- 
 served before and after the total obscuration, 
 404; beads of light observed, 406-10; 
 explanations of their physical cause, 411. 
 
 Eclipses of the Sun, Annular earliest re- 
 cords of, 371; modern records, 372; lu- 
 
 minous appearance observed around the 
 moon's limb, 397; aspect of the moon 
 during the eclipse of 1836,401; beads of 
 light seen at the exterior and interior con- 
 tacts, 407 ; explanations of their physical 
 cause, 411. 
 Eclipses, Lunar Phenomenaobserved during 
 
 the occurrence of, 412. 
 Ecliptic various determinations of the obli- 
 quity of the, 98; its diminution explained 
 by the theory of gravitation, 98 ; influence 
 of its displacement on the length of the 
 tropical year, 99 ; its variation affected by 
 the secular displacement of the equator, 
 100. 
 
 Ellipsoids, Attraction of Researches of Mac- 
 laurin, 67; D'Alembert, 69; theory of 
 the attraction of spheroids of small eccen- 
 tricity, ib. 
 
 Encke determines the mass of Mercury, 
 125; researches on the mass of Jupiter, 
 130; demonstrates that the comet which 
 bears his name revolves in an elliptic orbit, 
 134; speculations on a resisting"medium, 
 ib. 
 Equinox, place of the Method of Flamsteed 
 
 for determining it, 471. 
 Eratosthenes determines the obliquity of 
 
 the ecliptic, 436. 
 
 Euler solves the problem of three bodies, 
 44; researches on the lunar theory, ib., 
 46 ; researches on the long inequality of 
 Jupiter and Saturn, 48; invents the me- 
 thod of the variation of elements, 49 ; 
 investigates the secular inequalities of the 
 planets, 51 ; fruitless attempt to account, 
 by the theory of gravitation, for the secu- 
 lar inequality in the mean motion of the 
 moon, 61; investigates the theory of the 
 tides, 71; researches on the physical 
 theory of Jupiter's satellites, 88 ; researches 
 on the dispersion of light, 531. 
 Everest measures an arc of the meridian in 
 India, 146; remarks respecting the arc of 
 the meridian measured by Lacaille at the 
 Cape of Good Hope, 147. 
 
 Fabricius, David observes the variable star 
 Mira Ceti, 540. 
 
 Fabricius, John discovers the solar spots, 
 213; his mode of observing them, 227. 
 
 Faye discovers the comet which bears his 
 name, 139. 
 
 Ferrer observes the solar eclipse of 1806, 
 367 ; researches on the existence of a lunar 
 atmosphere, 386. 
 
 Flamsteed appointed director of the Royal 
 Observatory, Greenwich, 460 ; account of 
 his labours, 467477; attempts to deter- 
 mine the parallax of the polar star, 548. 
 
 Fontana first observes spots on the surface 
 of Mars, 235. 
 
 Foster Experiments with the pendulum 
 for the purpose of determining the ellipti- 
 city of the earth, 156. 
 
INDEX. 
 
 629 
 
 I/ 
 
 Frauenhofer Excellence attained by, in the 
 construction of refracting telescopes, 535. 
 
 Galileo discovers the diurnal libration of 
 the moon, 72 ; discovers the satellites of 
 Jupiter, 76 ; deduces the rotatory motion 
 of the sun from observations of the solar 
 spots, 216 ; determines the period of rota- 
 tion, ib. ; his mode of observing the solar 
 spots, 228; discovery of mountains on 
 the moon's surface, 229 ; phases of Venus, 
 233; inexplicable appearance of Saturn, 
 251 ; researches on irradiation, 347 ; exe- 
 cutes a refracting telescope, 520 ; method 
 for ascertaining the magnifying power of 
 telescopes, 521 ; first applies the telescope 
 to the purposes of physical science, ib.', 
 attempt to determine the apparent dia- 
 meter of a. Lyrae, 545; method for deter- 
 mining the parallax of the fixed stars, 
 547. 
 
 Galle discovers the planet exterior to Ura- 
 nus, 192. 
 
 Galloway Researches on the motion of the 
 solar system in space, 557. 
 
 Gambart demonstrates that the comet of 
 Biela revolves in an elliptic orbit, 135. 
 
 Gascoigne first invents the micrometer, 
 450; micrometrical results due to him, 
 452 ; first employs telescopic sights in 
 astronomical observations, 454. 
 
 Gassendi Researches on irradiation, 347 ; 
 observes the transit of Mercury in 1631, 
 415. 
 
 Gilbert his ideas of attraction, 16. 
 
 Gilliss appointed to determine the solar 
 parallax, 213; catalogue of stars, 513. 
 
 Goodricke Researches on variable stars, 
 540. 
 
 Gravitation, theory of established by New- 
 ton in all its generality, 26 ; slowness of 
 its early progress, 41. 
 
 Gregory, James first points out the utility 
 of transits of the inferior planets in deter- 
 mining the value of the solar parallax, 
 428 ; explains the principle of the reflect- 
 ing telescope, 526 ; method for deter- 
 mining the parallax of the fixed stars, 
 547. 
 
 Groombridge executes a catalogue of stars, 
 511. 
 
 Hadley invents the reflecting octant, 482; 
 attains great excellence in the construc- 
 tion of reflecting telescopes, 529. 
 
 Halley encourages Newton in his researches 
 on the theory of gravitation, 27 ; suspects 
 the physical cause of the long inequality 
 of Jupiter and Saturn, 48 ; discovers the 
 secular inequality in the moon's mean 
 motion, 60; researches on Newton's theory 
 of comets, 102; predicts the return of the 
 comet which bears his name, 103 ; deter- 
 mines the period of the great comet of 
 1680, 289; remark relative to the solar 
 
 eclipse of 1715, 372 ; succeeds Flam- 
 steed at the Observatory of Greenwich, 
 477; opinion respecting the apparent dia- 
 meters of the stars, 545; first discovers 
 the proper motions of the stars, 554. 
 
 Hansen his researches on the planetary 
 perturbations, 113; accounts by the 
 theory of gravitation for the irregularities 
 in the moon's epoch, 120 ; accounts for 
 two new inequalities in the moon's motion, 
 206. 
 
 Harding discovers Juno, 240 ; observa- 
 tions of Saturn's ring, 264. 
 
 Harriot observes the solar spots, 215. 
 
 Hencke discovers the planet Astrea, 242; 
 Hebe, ib. 
 
 Henderson Researches on the value of the 
 solar parallax, 212; investigation of the 
 lunar parallax, 228; determines the pa- 
 rallax of the double star a, Centauri, 551. 
 
 Herschel, Sir John observes Halley's comet 
 after the passage of the perihelion in 
 1835, 138; researches on the satellites of 
 Saturn, 142 ; explanation of the physical 
 cause of the solar spots, 225; reobserves 
 two of the satellites of Uranus, 285; re- 
 searches on their motions, ib. ; observa- 
 tion indicative of the transparency of 
 comets, 294; the nucleus of a comet ap- 
 pears to be merely a vaporous substance, 
 ib.; observations on the physical aspect of 
 Halley's comet after the passage of the 
 perihelion in 1835, 299; variation of the 
 volume of the comet assigned, 301 ; re- 
 mark on the great heat to which comets 
 are subject on their passage of the perihe- 
 lion, 302 ; explains the variation of volume 
 which comets undergo, 307 ; researches on 
 the relative brightness of the stars, 542; 
 researches on double stars, 560; observa- 
 tions of nebulae, 568; star gauges in the 
 southern hemisphere, 577. 
 
 Herschel, Sir William determines the rela- 
 tive quantity of light emitted by the dif- 
 ferent parts of solar spots, 217; measures 
 their size, 218; remarks their rapid changes, 
 ib. ; explanation of the penumbrse, 223 ; 
 hypothesis of the generation of the spots, 
 ib.' } determines the altitude of the lunar 
 mountains, 229; determines the time of 
 rotation of Mars, 236; assigns the ellip- 
 ticity of that planet, ib.', explains the ap- 
 pearance of white spots at the poles, 237; 
 researches on the rotation of Jupiter, 245; 
 velocity of the spots on the planet's disk, 
 247; opinion respecting their nature, ib.; 
 explanation of the belts of Jupiter, 248 ; 
 physical observations of the satellites of 
 Jupiter, 249; determines the equality be- 
 tween the periods of rotation and revolu- 
 tion in the case of all the satellites, ib. ; 
 determines the absolute magnitude of the 
 second satellite, and the relative magni- 
 tudes of all the four, 250 ; observes the 
 bands of Saturn, 251 ; deduces from them 
 
630 
 
 INDEX. 
 
 the rotation of the planet on an axis, 251 ; 
 determines the time of rotation, ib. ; dis- 
 covers that the figure of the planet is 
 spheroidal, 252; determines the ellipticity, 
 ib. ; observes an irregularity in the figure 
 of the planet, 253 ; discovers phenomena 
 indicative of an atmosphere, ib.; pheno- 
 mena observed about the polar regions, 
 254; demonstrates the duplicity of the 
 ring, 260; proves the thickness of the 
 ring to be inconsiderable, 261 ; discovers 
 the rotatory motion of the ring, 262 ; de- 
 termines the time of rotation, ib. ; physical 
 observations of the ring, 263; suspects it 
 to be encompassed by an atmosphere, 264; 
 perceives the unenlightened side of the 
 ring, 265; explanation of its visibility, 
 266; discovers two satellites of Saturn, 
 270; observations on the variable bright- 
 ness of the fifth satellite, 272; discovers 
 the planet Uranus, 272-274 ; determines 
 its magnitude, 275; discovers two satel- 
 lites revolving round Uranus, 279; de- 
 monstrates that their orbits are nearly 
 perpendicular to the ecliptic, and that 
 their motion is retrograde, 282 ; discovers 
 four additional satellites, ib. ; observations 
 on the physical constitution of the two 
 old satellites, 284; observation illustra- 
 tive of the transparency of comets, 293 ; 
 researches on the comet of 1811, 294; re- 
 searches on the light of comets, 312; 
 opinion on the purpose which they serve 
 in the economy of the physical universe, 
 315; experiment illustrative of irradiation, 
 352; attains great excellence in the con- 
 struction of reflecting telescopes, 533; re- 
 searches on the relative brightness of the 
 stars, 542; space-penetrating power of 
 telescopes, 544; applies it to determine 
 the relative distances of stars and clusters 
 of stars, ib.; attempts to determine the 
 apparent magnitudes of the stars, 546; 
 researches on the parallax of the stars, 549; 
 researches on the motion of the solar sys- 
 tem in space, 555; observations of double 
 stars, 559 ; establishes their physical 
 theory, 560; observations of nebula?, 565 ; 
 nebular hypothesis, 567; structure of the 
 Milky Way, 575; star gauges, ib. ; 
 speculations on the breaking up of the 
 Milky Way, 576. 
 
 Hevelius discovers the libration of the moon 
 in longitude, 72; surmises that comets 
 move in parabolas, 102 ; constructs charts 
 of the moon's surface, 229; observes a 
 transit of Mercury, 417; constructs a 
 catalogue of stars, 508; attempts to deter- 
 mine the apparent diameters of the stars, 
 545. 
 
 Hind Discovery of Iris, 243 ; Flora, ib. ; 
 
 researches on the identity of the comets of 
 
 1264 and 1556, 290. (See Appendix.) 
 
 Hipparchus discovers the precession of the 
 
 equinoxes, 318; determines the place of 
 
 the equinox among the stars, 435 ; estab- 
 lishes the solar and lunar theories, 436; 
 invents the astrolabe, 438 ; the first who 
 executes a catalogue of stars, 507. 
 
 j his correspondence with Newton 
 relative to the path of a projectile, 22; 
 contests Newton's claim to the discovery 
 of the law of gravitation, 29; discovers 
 the rotation of Mars, 236; his estimation 
 of the time of rotation, ib. ; discovers the 
 rotation of Jupiter, 244 ; suggests the first 
 notion of the reflecting quadrant, 481; 
 first executes a Gregorian telescope, 529; 
 points out the principle upon which the 
 visibility of stars depends, 543; attempts 
 to determine the parallax of the stars, 548; 
 suggests the probability of a proper motion 
 of the stars, 553. 
 Horrebow Account of the destruction of 
 
 the Copenhagen Observatory, 466. 
 Horrocks observes the transit of Venus in 
 1639, 421; account of his life, 422; col- 
 lection of his manuscripts by the Royal 
 Society, 424; brief notice of his posthu- 
 mous fragments, 424-428; attributes the 
 motion of the lun;ir apsides to the disturb- 
 ing force of the sun, 425; devises the ex- 
 periment of the circular pendulum with a 
 view to illustrate the action of a central 
 force, ib. ; obtains a glimpse of the long 
 inequality of Jupiter and Saturn, 426; 
 surmise respecting the movements of 
 comets, 427; undertakes researches on 
 the tides, ib.; remark respecting the ap- 
 parent diameters of the stars, 545. 
 Hussey suspects the existence of a planet 
 
 beyond Uranus, 166. 
 
 Hu3 r ghens refuses to admit the attraction 
 of the constituent particles of matter, 42 ; 
 his researches on the figure of the earth, 
 66 ; discovers the true form of Saturn's 
 appendage, 257; determines the magni- 
 tude and position of the ring, 258; dis- 
 covers a satellite of Saturn, 267; applies 
 the pendulum to clocks, 448; method 
 devised by him for measuring small angles, 
 450; attains great excellence in the con- 
 struction of telescopes, 525 ; determina- 
 tion of the parallax of Sirius by photo- 
 metric principles, 547; discovers the 
 nebula of Orion, 563. 
 
 Invariable Plane of the Solar System 
 existence of the, demonstrated by Laplace, 
 101. 
 
 Irradiation of Light first remarked as a 
 general principle by Kepler, 346; re- 
 searches of Galileo on the subject, 347; 
 Gassendi, 351; Descartes, ib. ; illustra- 
 tive experiment by Sir William Herschel, 
 352; researches of Dr Robinson, 353; 
 Plateau, 355; Powell, 356. 
 
 Ivory Theorem relative to the attraction of 
 ellipsoids, 143; researches on the theory 
 of refraction, 333. 
 
INDEX. 
 
 631 
 
 Johnson executes a catalogue of southern 
 stars, 512; observations of circumpolar 
 stars in the northern hemisphere, 541. 
 
 Jupiter long inequality in the mean mo- 
 tion, 47; its physical cause first suspected 
 by Halley, 48; researches of Euler, ib.; 
 Lagrange, 50, 58; Lambert, 57; Laplace 
 finally accounts for it by the theory of 
 gravitation, 59 ; various determinations of 
 the mass of the planet, 130; belts on 
 his surface, 243; when discovered, 244; 
 rotation of the planet on an axis sus- 
 pected by Hooke, ib. ; established beyond j 
 doubt by Cassini, ib.; researches of Sir 
 William Herschel on the subject, 245 ; 
 researches of Airy, ib. ; ellipticity dis- 
 covered, ib. ; determined by Pound, ib. ; 
 Struve, ib. ; near agreement between the 
 observed ellipticity and the theoretical 
 determination of Laplace, ib.; observa- 
 tions of his belts, 246; explanations of 
 their nature, 248. 
 
 Jupiter, Satellites of discovered by Galileo, 
 76 ; tables of Hodierna, 79; Borelli, ib. ; 
 tables of Cassini, 80 ; tables of Bradley, 81 ; 
 equation of light first introduced into 
 their theory by that astronomer, ib. ; his 
 discovery of the inequality in the three 
 interior satellites, 83 ; researches of New- 
 ton on their physical theory, 88; disturb- 
 ing influence of the spheroidal figure of 
 Jupiter first remarked by Euler, ib.; 
 effects thus produced first pointed out by 
 Walmsley, ib. ; subjected to rigorous inves- 
 tigation by Euler, ib.; their perturbations 
 investigated by Bailly, ib.; researches of 
 Lagrange, 90; relation between the mean 
 longitudes and the mean motions of the 
 three interior satellites discovered by La- 
 place, 92; libration of the three interior 
 satellites, ib. ; researches of Laplace on the 
 theory of the satellites, 93 ; invariable plane 
 of reference discovered by him, 94; masses 
 assigned to the satellites by him, 96; 
 elements determined by Delambre, ib. ; 
 maximum value of aberration deduced 
 from the eclipses of the satellites, ib. ; 
 shadows and transits of the satellites ob- 
 served by Cassini, 248 ; physical observa- 
 tions by Maraldi, ib.; conclusion deducible 
 from them, 249 ; the times of rotation and 
 revolution of each satellite shown to be 
 equal, ib.; various determinations of the 
 magnitudes of the satellites,^. Sat. II.,its 
 inclination demonstrated by Maraldi I. to 
 be variable, 81 ; period of this inequality de- 
 termined by Wargentin, 85; libratory mo- 
 tion of the nodes discovered by Maraldi 
 II., 86; explained by Bailly, ib.; deter- 
 mination of its mass by that geometer, 89. 
 Sat. III., Maraldi II. discoversits inclina- 
 tion to be variable, 82 ; its eccentricity dis- 
 covered by him, 84; suspected by Wargentin 
 to be variable, ib. ; period of the inequality 
 in the inclination determined by Maraldi 
 
 II., 86; its mass determined by Bailly, 89. 
 Sat. IV., its orbit suspected by Bradley 
 to be eccentric, 82; eccentricity established 
 by Maraldi II., ib.; the nodes discovered 
 to have a direct motion on the plane of 
 Jupiter's orbit, 85; explanation of this 
 apparent anomaly by Lalande, ib. ; incli- 
 nation shown to be variable, 86. 
 
 Kater Mode of determining the length of 
 the seconds' pendulum, 153. 
 
 Kepler his ideas of an attractive force, 17; 
 surmises that comets move in straight 
 lines, 102; opinion respecting the tails 
 of comets, 309; researches on refraction, 
 321 ; researches on irradiation, 347; opi- 
 nion respecting the luminous ring seen 
 during solar eclipses, 385 ; predicts transits 
 of Mercury and Yenus, 415; first explains 
 the principle of the refracting telescope, 
 525; observes the new star of 1604, 539 ; 
 opinion respecting its origin, ib. 
 
 Kramp Researches on the mathematical 
 theory of refraction, 330. 
 
 Lacaille measures an arc of the meridian 
 at the Cape of Good Hope, 147 ; deter- 
 mines the solar parallax, 212; lunar 
 parallax, 228 ; researches on refraction, 
 330 ; account of-his labours in practical 
 astronomy, 486 ; observations of nebulae 
 in the southern hemisphere, 564. 
 
 Lagrange devises a new solution of the 
 problem of three bodies, which he applies 
 to the investigation of the long inequality 
 of Jupiter and Saturn, 50 ; demonstrates 
 the invariability of the mean distances of 
 the planets, 52 ; investigates the secular 
 variations of the other elements, ib. ; se- 
 cond investigation of the long inequality 
 of Jupiter and Saturn, 58 ; researches on 
 the secular inequality in the mean motion 
 of the moon, 61 ; researches on the at- 
 traction of ellipsoids, 69 ; libration of 
 the moon, 74 ; investigates the perturba- 
 tions of Jupiter's satellites, 90 ; computes 
 the diminution of the ecliptic by the 
 theory of gravitation, 98 ; his method for 
 calculating the perturbations of comets, 
 105 ; his researches on the variations of 
 the elements of the planetary orbits, 110 : 
 invents the theory of the variation of 
 arbitrary constants, 111 ; researches on 
 the origin of the ultra-zodiacal planets, 
 241. 
 
 La Hire his explanation of the solar spots, 
 219; hypothesis respecting the luminous 
 ring seen during solar eclipses, 386. 
 
 Lalande his researches on the libration of 
 the moon, 73; objections urged by him 
 against Wilson's theory of the solar spots, 
 222. 
 
 Lambert Researches on the long inequality 
 of Jupiter and Saturn, 57 ; remark re- 
 specting the visibility of the stars, 543 ; 
 
632 
 
 INDEX. 
 
 adopts the hypothesis of a central sun, 
 558 ; views respecting the structure of the 
 Milky Way, 574. 
 
 Lamont Researches on the satellites of 
 Uranus, 285. 
 
 Laplace his opinion respecting the Prin- 
 cipia, 33 ; his researches on the mean 
 notions of the planets, 51 ; investigates 
 the secular variations of the planetary 
 elements, 52; his theorems relative to the 
 stability of the planetary system, 55; ex- 
 plains by the theory of gravitation the 
 long inequality of Jupiter and Saturn, 59 ; 
 discovers the physical origin of the secular 
 inequality in the moon's mean motion and 
 computes its amount, 62 ; investigates 
 the secular inequalities of the perigee and 
 nodes of the lunar orbit, 64 ; computes the 
 lunar inequalities depending on the sphe- 
 roidal figure of the earth, 65 ; investi- 
 gates the inequality in the moon's longi- 
 tude depending on the solar parallax, ib. ; 
 discovers inequalities in the moon's mo- 
 tion, depending on the spheroidal figure 
 of the earth, ib. ; determines the lunar 
 inequality in longitude involving the solar 
 parallax, ib. ; theory of the attraction of 
 spheroids, 69 ; demonstrates the stability 
 of the ocean, 71 ; researches on the tides, 
 ib. ; investigates the disturbing influence 
 of the ocean on the earth's axis, ib. ; re- 
 searches on the stability of Saturn's rings, 
 76 ; investigates the perturbations of Ju- 
 piter's satellites, 91 ; researches on the 
 diminution of the obliquity of the ecliptic, 
 99 ; comparison of his formula with an 
 ancient Chinese observation, ib. ; investi- 
 gates the secular variation of the tropical 
 year, ib. ; discovery of an invariable plane 
 in the solar system, 101 ; publication of 
 the Mecanique Celeste, 108 ; researches 
 on the variations of the elements of the 
 planetary orbits, 111 ; suggestion respect- 
 ing the cause of the irregularities in 
 the moon's epoch, 119; determines the 
 mass of the moon, 122 ; researches 
 on the mean temperature of the earth, 
 162; oscillations of the atmosphere, ib. ; 
 first calculates the elliptical elements of 
 Uranus, 275 ; hypothesis relative to the 
 heat of comets, 314 ; researches on the 
 theory of refraction, 331. 
 
 Lassell discovers the eighth satellite of Sa- 
 turn, 271 ; reobserves one of the satellites 
 of Uranus, 286; discovers a satellite re- 
 volving around Neptune, ib. ; effects im- 
 provements in the construction of reflect- 
 ing telescopes, 536; discovers two satel- 
 lites of Uranus, Appendix. 
 
 Le Verrier his researches on the inclina- 
 tions of the planetary orbits, 116; in- 
 vestigates the secular variations of the 
 planetary elements, 117 ; investigates the 
 theory of Mercury, 125; calculates the 
 long inequality of Pallas, 132 ; researches 
 
 on the perturbations of Faye's comet, 139 ; 
 researches on the identity of the comets 
 of Lexell and Faye, 140; proves them to 
 be distinct bodies, 141 ; researches on the 
 identity of the comets of 1585 and 1843, 
 ib. ; investigates the theory of Uranus, 
 175 ; fails to account for the observed ir- 
 regularities of the planet, 177 ; investigates 
 them upon the hypothesis of a disturbing 
 planet, 178; first results which he ob- 
 tained, 183; second investigation of the 
 subject, 187; final results deduced by 
 him, 188 ; remarks on the physical aspect 
 of the disturbing planet, 190. 
 
 Lexell shews that the comet which bears his 
 name revolved in an elliptic orbit, 105; 
 his explanation of its disappearance, ib. ; 
 first suspects Uranus to be a planet, 274 ; 
 determines its apparent diameter, 275. 
 
 Light Researches of Struve on the ex- 
 tinction of, in its passage through space, 
 577. 
 
 Lipperhey proved to be the original in- 
 ventor of the telescope, 519. 
 
 Longitude Arc of, measured in the British 
 Isles, 150. 
 
 Louville applies the micrometer to divided 
 instruments, 481. 
 
 Lubbock Researches on the lunar theory, 
 120. 
 
 Lunar Mountains first discovered by Gali- 
 leo, 229 ; various determinations of their 
 altitudes, ib. 
 
 Maclaurin his researches on the equili- 
 brium of ellipsoids, 67 ; investigates the 
 subject of the tides, 71. 
 
 Maclear observes Halley's comet after the 
 passage of the perihelion in 1835, 138; 
 geodesical operations at the Cape of Good 
 Hope, 148; researches on the parallax of 
 a. Centauri, ib. 
 
 Madler Surmise respecting the possibility 
 of discovering a planet beyond Uranus, 
 167; executes, in conjunction with Beer, 
 a chart of the moon's surface, 230 ; de- 
 termines the ellipticity of Uranus, 278 ; 
 speculations on the existence of a central 
 sun, 558. 
 
 Main demonstrates the elliptical figure of 
 Saturn, 266 ; researches on the proper 
 motions of the stars, 557. 
 
 Mairan Hypothesis of Saturn's ring, 267. 
 
 Maraldi I. his researches on Jupiter's satel- 
 lites, 80 ; rejects the equation of light, 
 81 ; discovers that the inclination of the 
 second satellite is variable, ib. ; deter- 
 mines the time of rotation of Mars, 236 ; 
 physical observations of the satellites of 
 Jupiter, 248; observations of Saturn's 
 ring, 263. 
 
 Maraldi II. Piesearches on the motions of 
 Jupiter's satellites, 83 ; discovers that the 
 inclination of the third satellite is variable, 
 ib.; establishes the eccentricity of the 
 
INDEX. 
 
 033 
 
 fourth satellite, ib. ; first rejects and sub- 
 sequently admits the equation of light, ib.; 
 remarks that the nodes of the fourth sa- 
 tellite have a direct motion on the plane 
 of Jupiter's orbit, 85; discovers the libra- 
 tory motion of the nodes of the second 
 satellite, 86; investigates the inclination 
 of the third satellite, ib. ; determines the 
 magnitudes of Jupiter's satellites, 250. 
 
 Mars various determinations of his mass, 
 129 ; spots on his surface, 235 ; their first 
 discovery, ib.; they indicate a rotatory 
 motion of the planet, 236; period of rota- 
 tion determined, ib. ; appearance of bright 
 spots at the poles, 237; physical explana- 
 tion of these phenomena, ib. 
 
 Maskelyne Experiment of, to determine 
 the attraction of Schehallien, 158; phe- 
 nomena observed by him during the tran- 
 sit of Venus in 1769, 429; appointed di- 
 rector of Greenwich Observatory, 488. 
 
 Maupertius Explanation of the origin of 
 Saturn's ring, 267; hypothesis respecting 
 the variability of the light of stars, 541. 
 
 Mayer calculates lunar tables,4 6 ; researches 
 on thelibrationof the moon, 73; researches 
 on refraction, 330; account of his labours 
 in practical astronomy, 487; suggests the 
 use of the repeating circle, 488 ; researches 
 on the proper motions of the stars, 555. 
 
 Mecanique Celeste publication of the, 108. 
 
 Mercury Researches of Le Verrier on the 
 theory of, 125; various determinations of 
 its mass, ib. ; difficulty experienced in 
 making researches on its physical constitu- 
 tion, 233; mountains upon its surface, ib. ; 
 is surrounded by an atmosphere of con- 
 siderable extent, ib. ; is slightly spheroidal, 
 ib. ; its ellipticity determined by Dawes, ib. 
 
 Mercury, transits of Transit predicted by 
 Kepler, 415; observed by Gassendi; ac- 
 counts of various transits, 417; pheno- 
 menon observed during the transit of 1753 ; 
 physical appearances noticed during seve- 
 ral other transits, 418. 
 
 Meridian Circle invented by Roemer, 461. 
 
 Mersenne suggests the principle of the re- 
 flecting telescope, 527. 
 
 Messier Observations of Saturn's ring, 264 ; 
 remark on the discovery of Uranus, 277 ; 
 observations of nebulae. 
 
 Metius proved to be one of the inventors 
 of the telescope, 519. 
 
 Michell first points out the principle upon 
 which the visibility of the stars mainly 
 depends, 543 ; applies it to the determina- 
 tion of the relative brightness of the stars, 
 ib. ; estimate of the apparent diameter of 
 Sirius, ib.; adopts the hypothesis of a 
 central sun, 558; views on the physical 
 theory of double stars, 559. 
 
 Micrometer first invented by Gascoigne, 
 450 ; contrivance devised by Huyghens, 
 ib. ; Malvasia, ib. ; Auzout, ib. ; Hooke, 
 451; Wren, ib. 
 
 Milky Way Early notions of the, 572; 
 theory of Wright, 573; researches of Sir 
 W. Herschel, 575; method of gauging the 
 heavens devised by him, ib.; speculations 
 on the breaking up of the, 576; researches 
 of Struve on the physical structure of the, 
 577; gauges of Sir J. Herschel iu the 
 southern hemisphere, ib. 
 
 Moll Communication relative to the inven- 
 tion of the telescope, 518. 
 
 Montanari first discovers that the star ft 
 Persei is variable, 540. 
 
 Moon Newton's researches on the theory of 
 the, 36; motion of the apogee erroneously 
 computed by him, 37 ; researches of 
 Euler,44; Clairaut,45; D'Alembert, ib.; 
 motion of the apogee reconciled with the 
 theory of gravitation, 46; secular inequa- 
 lity in the mean motion, discovered by 
 Halley, 60; researches of Dunthorn on the 
 subject, ib. ; fruitless attempts of geometers 
 to account for it by the theory of gravita- 
 tion, 61; finally traced to its origin by 
 Laplace, 62; secular inequalities of the 
 perigee and nodes, 64; perturbations de- 
 pending on the spheroidal figure of the 
 earth, 65 ; inequality in longitude involv- 
 ing the solar parallax, 65 ; irregularities 
 in the epoch discovered, 118; suspected 
 to arise from some long inequality, 119; 
 represented by an empiric equation, ib. ; 
 researches on the lunar theory by Damoi- 
 seau, 119 ; researches of Plana and Carlini 
 on the same subject, ib. ; Lubbock, 120; 
 Poisson, 120; irregularities in the epoch 
 accounted for by Hansen, 121 ; mass de- 
 termined by Newton, 122; determination 
 of the same element by Laplace, ib. ; two 
 new inequalities detected by Airy, 206 ; 
 accounted for by Hansen, ib. ; charts of 
 her surface constructed by different per- 
 sons, 229 ; existence of a lunar atmo- 
 sphere, 230; controversy on the subject, ib. 
 
 Moon, Libration of Diurnal libration dis- 
 covered by Galileo, 72; libration in longi- 
 tude discovered, ib. ; researches of Cassini, 
 73 ; Mayer, ib. ; Lalande, ib. ; physical 
 libration pointed out by Newton, 74; re- 
 searches of Lagrange, ib.; Poisson, 142; 
 Nicollet, 143. 
 
 Motion of the Solar System in space Re- 
 searches on the, 555-557. 
 
 Mural Circle first used at the Observatory 
 of Greenwich, 491. 
 
 Mural Quadrant invented by Tycho Brahc, 
 445. 
 
 Nebulee Early observations of, 563; obser- 
 vations of Sir W. Herschel, 564 ; nebular 
 hypothesis, 567; observations of Dunlop, 
 568 ; Sir John Herschel, ib. ; Lord Rosse, 
 569. 
 
 Neptune discovered by Dr. Galle, 192; 
 discordance between the observed and 
 theoretical elements, 202 ; explanation of 
 
634 
 
 INDEX. 
 
 this discordance, 203; comparison of the 
 theoretical and observed places of the 
 planet, ib. ; observed by Lalandein 1790, 
 204 ; remarks on the character of its per- 
 turbations, 205; evaluations of its mass, 
 ib. ; discovery of a satellite revolving 
 around it, ib. 
 
 Neptune, Satellite of discovered by Lassell, 
 286; determination of its periodic time, 
 287. 
 
 Newton his early notions of an attractive 
 force, 21 ; attempts to compute the gravity 
 of the moon to the earth, ib. ; fails to 
 obtain the true result, 22; resumes the 
 subject on a future occasion, ib. ; discovers 
 the law of attraction in an ellipse when 
 the force tends to the focus, 23 ; resumes 
 the consideration of the action of the earth 
 upon the moon, 24; employs in his re- 
 searches Picard's measurement of an 
 arc of the meridian, ib.; discovers the 
 law of gravitation, 25 ; considers the 
 mutual attraction of the particles of mat- 
 ter, ib. ; determines the attraction of 
 spherical bodies, ib. ; establishes the 
 principle of gravitation in its utmost 
 generality, 26 ; explains by its agency all 
 the grand phenomena of the celestial 
 motions, ib. ; stimulated in his researches 
 by Halley, 27; publication of the Priu- 
 cipia, 28 ; his intellectual character con- 
 sidered, 33 ; his partiality towards the 
 ancient geometry, 36; researches on the 
 lunar theory, ib. ; imperfect computation of 
 the motion of the lunar apogee, 37; re- 
 searches on the figure of the earth, ib. ; de- 
 monstrates the law of the variation of gra- 
 vity in different latitudes, 38 ; investigates 
 the problem of the precession of the equi- 
 noxes, ib.; compensates by his great sagacity 
 for the imperfection of his methods, 39; 
 points out the solar nutation, 69 ; explains 
 the libration of the moon in longitude, 
 73 ; his researches on the physical theory 
 of Jupiter's satellites, 88 ; method for de- 
 termining the orbit of a comet, 1 33 ; re- 
 searches on the theory of the pendulum, 
 152; surmise respecting the mean density 
 of the earth, 160; opinion respecting the 
 tails of comets, 309 ; researches on atmo- 
 spheric refraction, 323; correspondence 
 with Flamsteed on this subject, 324; in- 
 vestigates the mathematical theory of re- 
 fraction on various suppositions with re- 
 spect to the constitution of the atmosphere, 
 325, 326 ; researches on the diffraction of 
 light, 345 ; invents the reflecting octant, 
 482 ; executes the first reflecting telescope, 
 527 ; researches on the dispersion of light, 
 531 ; despairs of effecting any further im- 
 provement in the construction of refract- 
 ing telescopes, ib. 
 
 Nicolai determines the value of Jupiter's 
 mass, 130 ; his opinion respecting the force 
 of gravitation, 133. 
 
 Nicollet Researches on the libration of the 
 
 moon, 143. 
 Nutation the effect depending on the action 
 
 of the sun pointed out by Newton, 69; 
 
 lunar effect discovered by Bradley, 341; 
 
 determinations of its maximum value, 342. 
 
 Observatories Observatory of Copenhagen 
 established, 447; Paris, 457; Greenwich, 
 459; Pulkowa, 503. 
 
 Ocean stability of the, demonstrated, 71 ; 
 its influence on the motion of the earth's 
 axis, ib. 
 
 Olbers discovers Pallas, 239; Vesta, 241; 
 his speculations respecting the origin of 
 the ultra-zodiacal planets, 240. 
 
 Parallax, Lunar different determinations of 
 its value, 228. 
 
 Parallax, Solar Laplace computes the value 
 of the, by the theory of gravitation, 65; 
 various determinations of its value, 211. 
 
 Parallax of the Stars Tycho Brahe finds it 
 to be insensible, 547; method proposed 
 by Galileo, ib. ; observations of Hooke, 
 548; Flamsteed, ib. ; Roemer, ib.; re- 
 searches of Brinkley, 550; his results 
 controverted by Pond, ib. ; researches of 
 Struve, ib. ; Bessel, 551 ; Henderson, ib.; 
 Peters, ib. 
 
 Pendulum theory of the, 151 ; applied to 
 determine the ellipticity of the earth, 153; 
 imperfect reduction to a vacuum, 155; 
 researches of Bessel on this subject, ih. ; 
 Bail\ r ,156 ; applied to clocks by Huyghens, 
 448; 
 
 Peters determines the maximum value of 
 aberration, 340 ; researches on the parallax 
 of the fixed stars, 553. 
 
 Piazzi discovers the planet Ceres, 238 ; 
 executes a fundamental catalogue of stars, 
 510; attempts to determine the parallax 
 of the fixed stars, 549. 
 
 Picard determines the inclination of Saturn's 
 ring, 258; suspects that the temperature 
 of the atmosphere exercises an influence 
 upon the quantity of refraction, 323 ; one 
 of the first astronomers who employed 
 telescopic sights, 458; method of cor- 
 responding altitudes, 459 ; finds the paral- 
 lax of Lyrae to be insensible, 548. 
 
 Pierce calculates the perturbations of Nep- 
 tune, 205; researches on the comet of 
 1843,292. 
 
 Plana Researches on the lunar theory, 
 119; researches on the long inequality of 
 Jupiter and Saturn, 130; determination 
 of the lunar parallax, 228. 
 
 Planetary System Secular variations of 
 the planetary elements, 51 ; researches of 
 Euler on the subject, ib. ; Lagrange, 52; 
 Laplace, ib. ; invariability of the mean 
 distances demonstrated by Lagrange, ib. ; 
 theorems of Laplace relative to the sta- 
 bility of the eccentricities and the inclina- 
 
INDEX. 
 
 635 
 
 tions, 55; Poisson's researches on the 
 variation of the mean distance, 109; 
 theory of the variation of elements, 110; 
 researches on the secular variations of the 
 inclinations, 116. 
 
 Planets, Ultra-zodiacal researches on their 
 perturbations, 132; circumstances con- 
 nected with their discovery, 238 ; dis- 
 covery of Ceres, 239 ; Pallas, ib. ; Juno, 
 240 ; Vesta, 241 ; speculations of Gibers 
 on their origin, 240 ; researches of La- 
 grange on the subject, 241 ; discovery of 
 Astrea, 242 ; Hebe, ib. ; Iris, 243 ; Flora, 
 ib.; Metis, ib.; Hygem,ib. (See Appendix.} 
 
 Plantamour Researches on Biela's comet, 
 136. 
 
 Plateau Researches on the irradiation of 
 light, 355. 
 
 Plutarch Statement respecting the luminous 
 ring seen during total eclipses of the sun, 
 377. 
 
 Pond succeeds Maskelyne at the Obser- 
 vatory of Greenwich, 491 ; introduces the 
 practice of observing with two mural 
 circles, 493; controversy with Brinkley 
 on the parallax of the fixed stars, 550. 
 
 Pontecoulant calculates the perturbations 
 of Halley's comet, 137. 
 
 Poisson his researches on the variations of 
 the mean distances of the planets, 109; 
 developes the method of the variation of 
 arbitrary constants, 112 ; researches on the 
 lunar theory, 120; investigates the phy- 
 sical libra tion of the moon, 142 ; researches 
 on the motion of the earth's axis, 160. 
 
 Pound calculates ecliptic tables in time of 
 the first satellite of Jupiter, 81 ; measures 
 the dimensions of Saturn's ring, 260. 
 
 Powell Researches on the irradiation of 
 light, 356 ; explanation of the luminous 
 ring seen during total eclipses of the 
 sun, 387 ; theory of the beads and 
 threads observed during annular eclipses, 
 411 ; explanation of a phenomenon seen 
 during the transit of Mercury, 418. 
 
 Precession of the Equinoxes Researches on 
 its quantitative value, 318 ; erroneous de- 
 termination of the annual value by Pto- 
 lemy, ib. ; conclusion hence deduced, ib. ; 
 its quantity determined by the Arabian 
 astronomers, 319; modern evaluations, 
 ib.; researches of I3essel, 320; Otto 
 Struve, ib. 
 
 Prime Vertical Telescope first employed 
 by Roemer, 464. 
 
 Principia Publication of the, 28; synopsis 
 of its contents, 32. 
 
 Problem of Three Bodies Solutions of the, 
 obtained by various geometers, 44, 47. 
 
 Ptolemy estimates the value of the solar 
 parallax, 211 ; his erroneous evaluation 
 of the quantity of precession, 318; first 
 points out the effects of atmospheric re- 
 fraction, 321 ; describes the instruments 
 used by the Greek astronomers, 436. 
 
 Reflecting Octant first invented by Newton, 
 482; reinvented by Hadley and Godfrey, 
 ib. 
 
 Refraction, atmospheric its influence on 
 the apparent position of a celestial body 
 first recognised by Ptolemy, 321 ; first 
 applied as a uranographical correction by 
 Tycho Brahe, ib. ; table calculated by 
 Kepler, ib. ; law of refraction discovered 
 by Snell, ib. ; researches of Cassini, ib. ; 
 influence of temperature remarked by 
 Picard, 323 ; researches of Newton, ib. ; 
 mathematical theory of, investigated by 
 Taylor, 327 ; researches of Bouguer, 328 ; 
 Simpson, ib. ; influence of the pressure of 
 the atmosphere pointed out by Halley, 
 329 ; researches of Bradley, ib. ; Mayer, 
 330 ; Lacaille, ib. ; improvements in the 
 theory of, effected by Kramp, ib. ; re- 
 searches of Laplace, 331 ; Brinkley, 332 ; 
 Ivory, 333 ; researches of modern astro- 
 nomers on the subject, 335 ; Bessel, ib. 
 
 Repeating Circle principle of the, sug- 
 gested by Mayer, 488. 
 
 Right Ascension of a Star how deter- 
 mined by Tycho Brahe, 443; method of 
 Flamsteed for effecting the same object, 
 472. 
 
 Robinson Researches on the Irradiation of 
 Light, 353. 
 
 Roemer invents the transit instrument, 
 461 ; perceives the superior advantages of 
 instruments composed of complete circles, 
 463 ; invents the meridian circle, ib. ; 
 prime vertical telescope, 464; methods of 
 adjustment practised by him, 464; con- 
 structs an altitude and azimuth circle, 
 465; equatorial instrument, 466; at- 
 tempts to determine the parallax of the 
 fixed stars, 548. 
 
 Rosse, Earl of attains unrivalled excellence 
 in the construction of reflecting telescopes, 
 536; observations of nebulae, 569. 
 
 Rumker observes the comet of Encke at 
 Paramatta, 134; catalogue of stars, 512. 
 
 Saturn long inequality of, 47; accounted 
 for by Laplace upon the principles of the 
 theory of gravitation, 59 ; determination 
 of its mass by Newton, 131; modern 
 evaluations of the same element, ib. ; 
 bands on his disk discovered, 251; they 
 indicate a rotatory motion, ib. ; time of 
 rotation determined, ib. ; discovered to be 
 spheroidal, 252; value of the ellipticity 
 determined, ib. ; irregularity in the figure 
 of, suspected by Herschel, ib. ; figure de- 
 monstrated by Bessel to be truly elliptical, 
 253; surrounded by an atmosphere, ib.; 
 appearances observed about the polar re- 
 gions of, 254. 
 
 Saturn, Rings of their condition of equi- 
 librium investigated by Laplace, 76; 
 early observations of Galileo, 254; im- 
 perfect attempts to ascertain its real 
 
636 
 
 INDEX. 
 
 nature, 255; annular form established by 
 Huyghens, ib.; its position determined, 
 258; discovered to be double, 259; sus- 
 picion of many divisions on the, 260; 
 its magnitude determined, ib. ; its thick- 
 ness inconsiderable, 261 ; discovery of 
 its rotatory motion, 262; time of rota- 
 tion determined, ib. ; physical observa- 
 tions of the ring, 263; not bounded by 
 parallel planes, 264; encompassed by an 
 atmosphere, ib.; visibility of the unen- 
 lightened side, 265; hypothesis of the ' 
 physical origin of the, 267. (See Appendix?) 
 
 Saturn, Satellites of Researches of Bessel, 
 142; satellites discovered by Huyghens, 
 267; discovery of four satellites by 
 Cassini, 268, 269; discovery of two new 
 satellites by Herschel; an eighth satellite 
 discovered simultaneously by Lassell and 
 Bond, 271; variable brightness of the 
 fifth satellite, ib.; conclusion hence de- 
 duced, 272. 
 
 Schemer observes the solar spots, 214; 
 controversy with Galileo respecting their 
 real nature, 214 ; first remarked that the 
 nucleus and penumbras are separated 
 by a well-defined boundary, ib. ; deter- 
 mines the time of the sun's rotation, ib.; 
 employs coloured glass in observations of 
 the sun, 228; constructs charts of the 
 moon's surface, 229 ; first who executed a 
 refracting telescope, 525. 
 
 Schroeter discovers a twilight in the moon, 
 233; his researches on the physical consti- 
 tution of Mercury, 233; determines the 
 time of rotation of Venus, 234 ; maintains 
 that high mountains exist on the surface 
 of Venus, 235; discovers that Venus is 
 surrounded by an atmosphere, ib. ; deter- 
 mines the magnitude of Jupiter's satel- 
 lites, 250; observations of Saturn's ring, ' 
 262. 
 
 Simpson computes the motion of the lunar 
 apogee, 46; researches on the theory of 
 refraction, 328. 
 
 Solar Spots observed by several persons, 
 213; their motions on the sun's disk, 
 215; conclusion hence derived, ib.; de- 
 tailed description of their appearance, 217; 
 relative quantities of light emitted by the 
 different parts of which they are com- 
 posed, ib. ; their mode of formation, ib. ; 
 some are destitute of penumbrae, ib. ; pe- 
 numbrae without a nucleus, ib. ; great 
 magnitude of the spots, 218 ; rapid changes 
 which they undergo, ib. ; constantly ob- 
 served near the solar equator, ib.; solar 
 faculaa, ib.; first seen by Galileo, ib.; 
 their immense extent, 219; they are gene- 
 rally brightest on the sun's limb, ib.; 
 their invariable appearance in the region 
 of the spots, ib. ; discovery of luculi, ib. ; 
 seen over the entire disk of the sun, ib.; 
 various explanations of the real nature of 
 the spots, ib. ; Schemer, ib. ; La Hire, ib. ; 
 
 Derham, 220; theory of Dr. Wilson, ib. ; 
 objections urged against it, 221 ; theory 
 of Bode, ib. ; Sir W. Herschel, 223 ; Sir 
 J. Herschel, 225; how observed by various 
 astronomers, 227. 
 
 Snell discovers the law of refraction, 321. 
 
 South Observations of double stars, 560. 
 
 Stars Immense multitude of the, 538; 
 stars which have disappeared from the 
 heavens, ib.; new stars, 539; variable 
 stars, 540; researches on the relative 
 brightness of the stars, 542; principles 
 upon which their visibility depends, 543; 
 various attempts to determine their ap- 
 parent diameters, 544 ; researches on their 
 parallax, 546; their proper motions dis- 
 covered, 553. 
 
 Stars, Double early observations of, 558; 
 observations of Sir William Herschel, 
 559 ; speculations of Mtchell on the theory 
 of, ib.; remark of Dr. Jlornsby, ib.; phy- 
 sical theory of, first established upon ob- 
 servation by Sir William Herschel, 56Qj 
 recent researches of astronomers on The 
 subject, 560-563. 
 
 Struve, F. W. G. Determines the magni- 
 tudes of Jupiter's satellites, 250; assigns 
 the dimensions of Saturn's ring, 260; 
 discovers the ring to be eccentric, 262; 
 determines the maximum value of aber- 
 ration, 340; appointed director of the 
 Observatory of Pulkowa, 505; researches 
 on the parallax of the fixed stars, 550; 
 determines the parallax of a Lyne, 551 ; 
 observations of double stars, 561; re- 
 searches on the physical constitution of 
 the Milky Way, 577; speculations on the 
 extinction of light in its passage through 
 space, 578. 
 
 Struve, Otto Researches on the mass, of 
 Neptune, 287 ; investigates the quantity 
 and laws of precession, 320; researches 
 on the motion of the solar system in space, 
 556. 
 
 Taylor, Brooke investigates the mathema- 
 tical theory of refraction, 327. 
 
 Telescope early notions of, 515; Bacon, 
 ib.; Digges, 516; Battista Porta, ib. ; De 
 Dominis, ib. ; first executed in Holland, 
 517; various accounts of its origin, ib.; 
 researches of Van Swinden on the subject, 
 518; Galileo constructs a telescope, 520; 
 his mode of ascertaining the magnifying 
 power, 521 ; he was not an independent 
 inventor, 522 ; remarks upon the Dutch 
 telescopes, 523 ; telescopes introduced into 
 England, 524; refracting telescope ex- 
 plained by Kepler, 525; first executed by 
 Scheiner, ib.; first employed in astro- 
 nomical observations by Gascoigne, ib. ; 
 improvements in its construction, ib. ; 
 Huyghens, ib.; Campani, 526; Auzout, 
 ib.; reflecting telescope, ib.; first exe- 
 cuted by Newton, 527 ; improvements in 
 
INDEX. 
 
 G57 
 
 its construction, 529 ; views of Newton 
 on chromatic aberration, 531 ; he pro- 
 nounces any further improvement of the 
 refracting telescope to be desperate, ib. ; 
 researches of Dollond on the dispersion of 
 light, ib. ; constructs achromatic telescopes, 
 532 ; instruments of this description pre- 
 viously executed by More, 533 ; reflecting 
 telescopes of Herschel, ib. ; improve- 
 ments in the construction of refracting 
 telescopes, 535; Guinand, ib.; Frauen- 
 hofer, ib.' } Reflecting telescopes, 536; 
 Lord Rosse, ib. 
 
 Telescopic Sights first employed by Gas- 
 coigne, 454. 
 
 Tides shewn by Newton to be a necessary 
 consequence of the principle of gravita- 
 tion, 26; researches of Euler, 71; Mac- 
 laurin, ib.', Bernoulli, ib. ; Laplace, ib.', 
 researches of Whewell, 162. 
 
 Transit Instrument invented by Roemer, 
 461. 
 
 Transit Observations recorded in America 
 by means of electro-magnetism, 506. 
 
 Transversals, Method of invented, 442. 
 
 Uranus early observations of, 164; tables 
 calculated by Delambre, 165; irregula- 
 rities in the longitude of the planet, ib. ', 
 tables of Bouvard, ib.; impossibility of 
 reconciling the modern with the ancient 
 observations, ib. ; the existence of an 
 exterior planet suspected, ib. ; radius 
 vector shewn to be erroneous, 167; the 
 irregularities attract the attention of Bes- 
 sel, ib. ; researches of Adams on the same 
 subject, 168 ; inverse problem of pertur- 
 bation, 169; results obtained by Adams, 
 173 ; new tables calculated by Eugene 
 Bouvard, 174 ; they fail to account for 
 the irregularities of the planet, 175; 
 theory of the planet investigated by Le 
 Verrier, 175 ; the results obtained by 
 him are found to be incompatible with 
 the observations of the planet, 177; the 
 researches of Le Verrier on the hypothesis 
 of a disturbing planet, 178; first results 
 which he obtained, 183 ; search for the 
 new planet undertaken by Prof. Challis, 
 185 ; second investigation of Le Verrier, 
 187; final results obtained by him, 188 ; 
 they are transmitted to the astronomers 
 of Berlin, 191 : discovery of the exterior 
 planet by Dr. Galle, 192; account of 
 Prof. Challis' search for the planet, ib. ; 
 his observations had effectually secured 
 it, 193; reflections on the comparative 
 merits of the two geometers who assigned 
 the position of the exterior planet, 197; 
 discovered by Herschel, 272 ; first sup- 
 
 posed to be a comet, 273; difficulties 
 experienced in determining its orbit, ib.; 
 discovered to be a planet, 274 ; its appa- 
 rent diameter measured, 275 ; elements 
 of its orbit determined, 277; suspected 
 to be spheroidal, ib.; determination of its 
 ellipticity by Madler, 278 ; suspected to 
 be encompassed by a ring, ib. 
 Uranus, Satellites of Discovery of two 
 satellites by Herschel, 279 ; the elements 
 of their orbits determined, 280 ; orbits 
 found to be almost perpendicular to the 
 ecliptic, 282; their motion found to be 
 retrograde, ib. ; discovery of four ad- 
 ditional satellites, ib. ; physical observa- 
 tions of the, 284 ; researches of Sir John 
 Herschel, 285 ; Lamont, ib. ; observations 
 of Lassell, 286; Otto Struve, ib. (See 
 Appendix.} 
 
 Valz Speculations of, on the identity of 
 the comets of Lexell and Faye, 139 ; 
 suspects the existence of a planet beyond 
 Uranus, 166. 
 
 Variation of Elements Method of the, in- 
 vented by Euler, 49. 
 
 Venus Perturbations of, investigated by 
 Laplace, 126 ; long inequality discovered 
 by Airy, 127; mass of determined by 
 various enquirers, ib. ; her phases dis- 
 covered by Galileo, 233 ; her rotation 
 round a fixed axis discovered, 234 ; vari- 
 ous determinations of the time of rota- 
 tion, 234, 235 ; mountains on her surface, 
 ib. ; atmosphere surrounding her, ib. 
 
 Venus, Transits of Transit predicted by 
 Kepler, 415; transit of, 1639, observed 
 by Horrocks and Crabtree, 421 ; physical 
 appearances noticed during the transits of 
 1761 and 1769, 429. 
 
 Vernier Invention of the, 446, 
 
 Wallis prepares the writings of Horrocks 
 
 for publication, 423 ; suggests a method 
 
 for determining the parallax of the fixed 
 
 stars, 548. 
 Wargentin his researches on the motions 
 
 of Jupiter's satellites, 83; observes the 
 
 lunar eclipse of 1761, 413. 
 Whewell Researches on the tides, 162. 
 Wilson, Dr. his theory of the solar spots,220. 
 Wollaston experimental researches on the 
 
 light of the stars, 547. 
 Wright adopts the hypothesis of a central 
 
 sun, 558; theory of the Milky Way, 573. 
 Wrottesley executes a catalogue of stars, 
 
 513. 
 
 Zach, De calculates tables of aberration and 
 nutation, 343. 
 
ADDITIONS AND CORRECTIONS. 
 
 PAGE vi, line 2 from top, for Ferdinand, read Frederick. 
 20, line 34 from top, /or into, read in. 
 51, line 43 from top, for has read have. 
 70, line 21 from top, for that, read twice that. 
 70, line 9 from bottom, for 10", read 18". 
 81, line 1 from bottom, after Sciences read 1707. 
 
 81, line 9 from bottom, for Pond, read Pound ; read also similarly pp. 84, 130. 
 
 82, line 4 from top. Bradley's tables of Jupiter's satellites, although not published 
 till 1749, were printed off in 1719. His discovery of aberration did not occur 
 till a few years afterwards. This circumstance accounts for the erroneous value 
 which he assigned to the equation of light in his tables. 
 
 119, line 20 from top, for third, read first. 
 
 122, line 9 from bottom, for September read June. 
 
 150, line 2 from bottom, for 62 s read 52 s . 
 
 172, line 34 from top, for 1846 read 1845. 
 
 188, line 6 from bottom, for ^ m read g^. 
 
 197, line 1 from top, /or 1850 read 1851. 
 
 212, line 13 from top. The utility of the transits of the inferior planets for deter- 
 mining the solar parallax was first announced by James Gregory, (p. 428.) 
 Halley merely pointed out the peculiar advantages which the transits of Venus 
 offered for this purpose. 
 
 217 lines 4 and 5 from top, for pole read axis. 
 
 253, line 17 from top, for ,fo read -fa. 
 
 415, line 1 from top, /or Vitellionem read Vitellion. 
 
 512, line 27 from top. The stars of M. Rumker's great catalogue have been 
 observed at Hamburgh : they are consequently visible in the northern hemis- 
 phere. 
 
 542, line 3 from bottom, for 1.6 read 1.2. 
 
 543, line 2 from top, for 2.014, which is equal to 1.6 -f 414, read 1.614, which 
 is equal to 1.2 + 414. 
 
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