IMAGE EVALUATION TEST TARGET (MT-S) 1.0 I.I ■so |28 1^ 2.0 m III— 11'''^ ''^ ^ 6" ► Hiotographic Sciences CorpQration 23 V»ST MAIN STRMT WIBSTIR.N.Y. 145*0 (716)S7a-4S0:t CIHM/ICMH Microfiche Series. CIHIVI/ICIVIH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques fk Technical and Bibliographic Notas/Notes tachniquas at bibtiographiquaa to Tha Inttituta hat attamptad to obtain tha baat original copy availabia for filming. Faaturaa of thia copy which may ba bibiiographicaliy uniqua, which may aitar any of tha imagaa in tha raproduction, or which may significantly changa tha usual mathod of filming, ara chackad balow. □ Colourad covars/ Couvartura da coulaur □ Covars damagad/ Couvartura andommag^a □ Covars restorad and/or laminatad/ Couvartura rastaurta at/ou pallicul6a D Covar title missing/ Le titre de couvertura manque I — I Coloured maps/ Cartes gdographiquas en couleur □ Coloured inic (i.e. other than blue or biacit)/ Encre de uouleur (i.e. autre que bleue ou noke) □ Coloured plates and/or illustrations/ Planches at/ou illustrations en couleur □ Bound with other material/ Reli6 avac d'autres documents Q- D Tight binding may cause shadows or distortion along interior margin/ La reliure serrde peut causer de I'ombra ou da la distortion le long de la marge int^rieure Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut que cartainas pages blanches ajcutias lors d'une restauration apparaissant dans la texte, main, lorsque cela Atait possible, ces pages n'ont pas tftti film^as. Additional comments:/ Commentairas supplAmentaires: PLATE ENGRAVINGS VERY FINE. PLATES MAY FILM LIGHT. L'Institut a microfilm* la mailleur exemplaira qu'il lui a AtA possible de se procurer. Les details da cat exemplaira qui sont paut-Atre uniques du point de vue bibliographiqua, qui peuvent modifier une image reproduite, ou qui peuvent exiger une modification dans la mAthode normale de filmage sont indlquAs ci-dessous. I I Coloured pages/ Pages de couleur Pages damaged/ Pages endommagias Pages restored and/oi Pages restaur^as at/ou peliicul^es Pages discoloured, stained or foxei Pages d^color^es, tachet6es ou piqu6es Pages detached/ Pages d4tach6es Showthroughy Transparence Quality of prir Quality in6gale de I'impression Includes supplementary materic Comprend du material suppiimantaira Only edition available/ Seule Edition disponible r~~| Pages damaged/ I I Pages restored and/or laminated/ [7^ Pages discoloured, stained or foxed/ I I Pages detached/ r^K Showthrough/ [~n Quality of print varies/ I I includes supplementary material/ I — I Only edition available/ 0- Pages wholly or partially obscured by errata slips, tissues, etc., have been refllmed to ensure the best possible image/ Les pages totalament ou partlellement obscurcies par un feulllet d'errata, une pelure, etc., ont 6t6 filmtes A nouveau da fafon h obtenir la meilleure image possible. pc of fii Oi be th sU ot fir si( or Th sh Til wl Ml dil ei. be rig rei mt □ This item is filmed at tha reduction ratio checked below/ Ca document est film* au taux da reduction indiquA ci-dassous. 10X 14X 18X 22X 26X 30X T I J 12X 16X 20X 2«X 2BX 32.: The copy filmed here ha* been reproduced thanks to the generosity of: Thomai FiiTiar Rare Boole Library, University oi Toronto Library L'exempiaire fiimt fut reproduit grice i la g^nArositt de: Thomas Fisher Raie Book Library, University of Toronto Library The images appearing here are the best quality possible considering the condition and legibility of the original copy and in keeping with the filming contract specifications. Original copies in printed paper covers are filmed beginning with the front cover and ending on the last page with a printed or illustrated impres- sion, or the back cover when appropriate. All other original copies are filmed beginning on the first page with a printed or illustrated Impres- sion, and ending on the last page with a printed or illustrated impression. The last recorded frame on each microfiche shall contain the symbol —^(meaning "CON- TINUED"), or the symbol y (meaning "END"), whichever applies. Les images suivantes ont 6t6 reproduites avec le plus grand soln, compte tenu de la condition et de la nettet6 de rexemplaire film6, et en conformity avec lei; conditions du contrat de f ilmage. Les exemplalres originaux dont la couverture en papier est imprimte sont fiimto en commen9ant par le premier plat et en terminant soit par la dernlAre page qui comports une empreinte d'impression ou d'illustration, soit par le second plat, salon le cas. Tous les autres exemplalres originaux sont filmte en commenpant par la premiere page qui comporte une empreinte d'impression ou d'illustration et en terminant par la dernldre page qui comporte une telle empreinte. Jn des symboles suivants apparaftra sur la derniftre image de cheque microfiche, selon le cas: le symbols — ► signifie "A SUIVRE", le symbols V signifie "FIN". Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be er.dreiy included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc., peuvent Atre filmto A des taux da reduction diffirents. Lorsque le document est trop grand pour Atre reproduit en un seul clich6, 11 est filmA A partir de Tangle sup6rieur gauche, de gauche A droite, et de haut en bas, en prenant le nombre d'images n6cessaire. Les diagrammes suivants illustrent la m^thode. 1 2 3 1 2 3 4 5 6 PUTE XI. TIIK NOK CIKCUMPOLA TIIK NOKTH OIKCUMPOLAll STARS {Fr^m Diek't Anlroaomi/, ■J •.;.■ i iVf-: iA i m ITie position of (lie Planetary Axis relative to that of the Primary. (a.) Parallel, (h.) Transverse, {d.') Perpetidicular . (a ) The general arrangement of the axia in the planets belonging to the solar Bystem. M") The exceptional arrangement in the case of the planet Uranos. i (3.) CEJ^TRIFUGAL FORCE 4- GRAVITATIOjY' THIO O.RY or THE STELLAR UjYIVERSE. AM) The Mixed Doctrine of PARALLAX AND ABERRATION. BY JOHN HARRIS. ■--•.:' X PRINTED BY THE LOVELL PRINTING AND PUBLISHING 00 St. Nicholas Street; May. 1875. i73'f ^ 0- r t.z INDEX 'Aoa Chap. I. — The Solau System and the general ARRANGEMENT OP THE SiDEREAL UNIVERSE. (1.) The present state of Astronomical Science 9 Horizontal System of Astronomy 11 (2.) Stellar Systems having their axes of revo- lution perpendicular to that of the Solar System 13 (3). The planets Uranus and Neptune, and the question of a neighbouring Stellar system . 15 (4.) Masses of aggregated matter and their rela- tion to the laws of the material universe. . 23 (5.) The relative distances of the visible stars.. 27 Chap. II. — The Present mixed doctrine op Parallax and Aberration. (G.) Theory of Parallax 30 (7.) Theory of Aberration 48 (8.) A direct method of obtaining parallax of the distant stara 68 8 INDEX. Chap. UI. — The AuEiuarioN-ot-LiGnT Tue- OKY KXAMINEl). * (0 ) The conditions and requisitions of the theory 70 (10.) Practienl Jipplication of the theory 72 (11.) The nature of Light as assumed by the theory (Immaterial Matter) 7-5 (12.) Aberration a dynamical theory 77 Note a. The dynamical theory not in har- mony with the laws of motion (13.) Distrust in the gift of sight required by the Aberration theory 80 Note b. A further dynamical test of the theory 82 Note c. The continuous radiation of light and heat into space. . . A. e., radiation to waste. . . .required by the theory 83 (14.) Direct heliocentric methods of obtaining parallax of the distant stars 85 I INDEX OF PLATEH. Ploto 11. Illustrating tho Circumpolar Stara... [ pjg"Q"\' Page Pinto 12. Illustrating... Tho Equinoctial and Ecliptic. 88 " 13. ^* Early Systems of Astronomy. 10 " 14.) „ • ( Tho Theory of tho Stellar Uni- " 16. J ( verso 22 t. in „ J The Theory of Cometary '^^' I Orbits 24 i Tho position of tho Axis of") planetary bodies in ro- ^Jf"^"!; lacioii to their primary.... ) Plato I « f Uranus considered m a Solar Pig. 6. 1 I Planet 20 Plato 1 t< J Practical application of tho Pig. 11. j,^ \ Aberration Theory 74 Plato I .. f Method of obtaining helio- V Fio- 12 f "i centric parallax of the dis- *= ) (tant stars 86 ^pfff 13 } " Aberration and Parallax 78 Plato 6. Fig. 10 belong f The Solar System and the ing to Part Second. ( Polo Star 12 i>i„+^ 1 v A V ( Tho deviations of Uranus Plato 1. Fig. 4. From \ ^^^^ ^^^ supposed Solar Herschel 8 Astronomy, j Orbit 92 on h.i'i •If .£1 -ai'l ;j .• I •'M''* M!'i 0) CHAPTER I. The Solar System and the General Arrangemmis qf the Sidereal Universe. INTKODUCTOKY OBSERVATIONS. (1) The present state of Astronomical Science. If we go back to that epoch in human education which may be termed the childliood or early age of astronomical science and make comparison, we find the general apprehension of the relation existing between the particular stellar system to whicli we as terrestrial beings belong, and the sidereal universe, to be, at the present time, in some important respects, much more distinct and based in a more considerable degree upon a natural foundation of I'eality and certainty, but, in other respects, also very important, we find the ground occu- pied by doctrines not wholly consistent with those gener- alizations of experience and fact to which they pertain, and by theories some of which are as artificial and unreal in character as any, perhaps, of those taught at the earlier period. it is ifue the fact has been now long known that the eun and not the earth occupies the centre of the solar «ystem ; much precise and accurate knowledge lias been B INTRODUCTORT OBSERVATIONS. ! obtained as to the dynamical relations of the various- members thereof to each other ; much has been done in ascertaining and permanently recording the relative posi- tions of the more distant celestial bodies ; much progress has been made in the formal and rigorous (mathematical) application of the sciences of force and motion (Mechan- ics), of magnitude and form (Geometry), and of number and quantity (Algebra), to the observed phenomena of astronomy ; great improvements have been effected in the instruments which enable or aid the astronomer to correctly observe those phenomena, and experience has made evident the importance of systematic observations by trained and practised observers to ensure correctness and accuracy in the general record of the observed facts belonging distinctively to astronomical science. Notwithstanding, however, the great advance whicb has undoubtedly been made in these particulars, the pre- sent state of the astronomical department of general science may be considered an intermediate station be- tween the old (artificial) system and a new (natural) system rather than as constituting in itself a complete, coherent, and intelligible system. Such as it is, it may, for reasons which we shall immediately proceed to explain, be distinguished by the appellation of. . ' the horizontal system.' It may be described as consisting in part of an imperfect natural system — i. e., of a sound system based on reality and fact, and in part of the old artificial system which, although nominally and formally discarded, still retains its hold on a not inconsiderable portion of that domain of which it formerly held exclu- sive possession. I'Laii 13 ./ . r V yfvfliuni Mobile Sniurn «• juptter ^V(lr.s ' . Sun. \ \ \ \ N. ^: - / ,. -^ ,'/../' '-v 'i;\\«' tvr^''-^*^:.^;r.^^^«'i .9,,,.^^ .lupiter MCl-s * * \ ■Ad' \ ■^ Frcrrt T/if Sysiern o/' Tyrho Brnhp .11). 1580. f.ncyc. Itritanniia. BW "-^1 The Horimiidl System of Askommt}. Hipparclms, of Rhodes (140 years b. c), is, perliaps, entitled to rank as the last, as well as one of the greatest of the astronomers belonging to the older civilization ; for T'tolemy (a. d. 130) was more a recorder of the progress already made and a connecting link between ancient and modern astronomy than himself an original observer or discoverer. Now the ancient system, of which Hipparchus was the most advanced exponent, represented the various celestial bodies as revolving in concentric circles, within which the earth, already posited obliquely with the axis Inclined to that of the sun, occupied the actual centre ; See Plate 13. Amongst the later of the ancient mathematicians Plato, in particular,is supposed to have suggested the theoretical representation of the planetary orbits by circles in the same piano, and, the resalt appearing to harmonize well with the observed phenom>^na, the inference appears to have been at once adopted that the dynamical orbit of each planet or moving star, must be an undeviating hori- zontal plane, and this inference seems to have included the assumption that one uniform horizontal plane was common to all the planets of the solar (or terrestrial) system. * * Whether la aaclent astronomy any inference was arrived at as to the obliquity ot the orbits of other planets, or as to the perpendicularity or incli- nation of their respective axes, does not appear ; but in modern astronomy, even to the present time, the doctrine of the inclined axis leo ves it open to the astronomical student to suppose all the planetary orbits to bo confined to the one uniform horizontal plane of the ecliptic, (as shown in iig. 23 R, belonging to the preceding part of this series), the axis of the planet hav ing, in each case, its own especial and distinctive inclination. It is true the practical astronomer, at the present time, would, if he CDrefuUy con- 12 HORIZONTAL SYSTEM OP ASTRONOMY. So proiuineiit a pheiiomouon as the undulating path of the sun in the heavens during its annual revolution could scarcely fail, however, to attract the notice and attention of astronomers at an earlier age than the com- paratively advanced epoch of PVito and Ilipparchus ; we find it recorded, accordingly, that Tliales, of Miletus ((i'lO years b. c.)j the lounder of the Ionian school, either discovered for himself or obtained information * that the equatorial plane of the earth is cut obliquely by the ecliptic ; but tiie assumption that the earth's axis of rota- tion was inclined to the axis of the sun appears to have been proposed and accepted as a satisfactory explanation at a very early date, and the prejudice that an oblique position of the earth combined witli a revolution in a horizontal plane was equivalent to an oblique orbit f having established itself as a postulate or a (supposed) demonstrated theorem of astronomical science as then tauglit, became inlierited and accepted as a part of modern astronomy, without suspicion. aidercd the case without prejudice, at once know that such cannot be the actual arrangement, for, if it were true, eclipse, occultation, or transit would necessarily take place each time of conjunction between a planet revolving in ihc outer circle and an inferior planet; but, on the other hand, there is the obvious obliquity of the sun's apparent path as seen from the earth, and if that can be accounted for by supposing an inclined position of the earth revolving in a horizontal orbit, it is evident that the same explanation would apply to the case of each other planet supposed to revolve in a hori- zontal orbit. * It is recorded that Thales, as Plato and others of the Greek astro- nomers subsequently did, travelled into Egypt expressly to obtain inform- ation from the Egyptian priests on scientific subjects. t Observe that if the case were confined to the earth and sun only, and the position of the sun's axis be considered indeterminate or optional by the theorist, the obliquely posited earth and horizontal orbit would actually be equivalent to the oblique terilestrial orbit. . , \ r iM ■'■»; itiiig path revolution lotice and I the com- rchu8 ; we hjtus (040 ol, either ion * that cly by the ds of rota- irs to have xplanation in obhque ution in a lie orbit f supposed) JO as then of modern cannot be the transit would met revolving hand, there is the earth, and n of the earth le explanation olve in a hori- ■M ■ Greek astro- >btain iuform- sun only, and )r optional by nrould actually • '."!*■ • * 1 ■ *•/! ' • 4 'i • . .^' . » » ' • »•/•.■• • ' ,'• < ,' * ".''*' • ■ 1 . • V t **''.' • f • • / » , •! * » ' <' ' . ' » ' ' . ' * 1. •' •.•;.* • * • ••»[«• • '" i" ' I • .*■!■••• • • 1. ' y '^ r ■ 1 ► . , * '■. * .■:;*.■ « • ' ♦ • .^*| . . - • < ' ■ 1 * 1 , - ',",* ' » ''. • • • ♦«• 1 *i*' < M • , ;-i ' ,1 ♦ • •'<^^^. '^..p. ' oil. ' .\* ^■^ >• ♦ ^ % . #*^ ■'^i^. v..^ /r '>-^. '^/^>-... \ -#' / % flA rv (2.) Stellar systems having their axes of revolution perpendicular to that of the solar system. The effect of a stellar system having its orbitnl plane perpendicular, or inclined at some considerable angle to the orbital plane of the solar system, does not seem: to have been made the subject of especial study by astron- omers. In our Fig. 10 (PI. 6^, illustrating the pole star and the solar system, the distance of the pole star from the sun as represented is less than twice the distance which the planet Uranus (if represented) would be from the sun. Therefore, if we suppose, for the purpose of illustra- tion, the pole star to be the centre of gravitation of a system, having its central axis directly perpendicular to that of our solar system, and of which the orbit of one of the planets was about equal in diameter to the orbit of the planet Neptune, it is evident that tiie planet so circumstanced would approach more or less closely to our sun. In looking at such a rciiresentation as that shown at Fig. 10, and on a merely superficial con- sideration of the case, it would seem that such a vertical motion of a body at right angles to the path in which the earth is moving, if seen from the earth, could not be mis- taken for or confounded with a motion in the same or nearly in the same plane as that of the earth's revolution, A closer and more attentive consideration of the actual conditions, however, will show that it might not be vcrv difficult to fall into such an error. The planet would have descended, so to speak, more or less nearly to the horizontal pLne before the light from our sun rendered it visible to an observer on the earth, it would th m appear to approach the sun from or in an almost horizon- tal plane ; and, if instead of the directly vertical, we sub- 14 STELLAR SYSTEMS. stitute the supposition of a plane apparently deviating very considerably from the vertical, we shall then have a case wherein the compounded motions would be very likely to perplex and mislead an observer whose point of view was upon the earth ; and such would be almost certainly the result, if tiie observer viewed the moving body with a prejudice or foregone conclusion that the body was revolving around our own sun in a plane either horizon- tal or not deviating very mach from a horizontal plane. Let us consider some of the conditions under which a planet, belonging to a system having its axis perpendicular to a vertical plane passing through its centre and through the centre of the sun, would present itself to a terrestrial observer. In the first place, since the motion of the stran- ger planet would be at right angles to that of the earth, the actual orbital motion of the earth would in appearance be transferred to the planet, and would become an addition to the actual motion of the planet, thereby converting the vertical into an apparently oblique motion. If the stranger planet was of considerable size and approached sufficiently near to any of the planetary members of the solar system, it would perturb or cause a deviation in their orbital motion. If attended by satellites or moons, these would have an apparently oblique motion of revo- lution around their central planet in tlie opposite direc- tion to the orbital motion of tiie earth. It is evident that — so long as the two systems retained the same relative positions, and the distance between the sun and the star remained the aa.h:?t — the stranger planet would periodi- cally return in its orbit of revolution around its own centre of gravitation to the same relative place ; and hence, particularly if the distance was very great, and ,!.. iii i STELLAR 8T8TEMS. IB iiting very ave a case ery likely t of view certainly )ody with body was r horizon- tal plane. ' which a pendicular d through terrestrial the stran- earth, the jarance be n addition ion verting 11. If the pproached lers of the viation in or moons, 11 of revo- •site direc- ident that le relative d the star d periodi- i its own lace ; and great, and observations required the medium of a powerful tele- scope, the stranger planet might be very easily mistaken for an additional member of the solar system. Enter- taining the not improbable supposition that other stellar systems may be so arranged as to have their planes of revolution vertical to, or differing considerably from, that of the solar system ; and that some of the members of one or more of these stellar systems may be, or become by the aid of very powerful telescopes, visible from the earth, let us consider the case of the two most distant planets which are now supposed to belong to the solar system. In doing so it will be most satisfactory to take the least distant of the two, as being the best observed and of which the apparent motion, for some considerable time past, has been recorded. (3.) The planets Uranus and Neptune, and the question of a neighbouring Stellar system. The Planet Uranus. — Subsequently to the discovery of this planet by Sir Wm. Herschel in 17SI, it was found that observations of it had been recorded by preceding astron- omers, and that its progress could be thereby traced back, witii some degree of certainty, to the earliest period of such observations. This having been done, the result showed that the actual orbital path, through which the planet had (appeared to have) moved, differed greatly from the theoretical path which, considered as a member of the solar system, it should have followed. By attri- buting possible error to the earlier observations, and by theoretical suppositions of more or less ingenuity, the discrepancies were greatly reduced, and the motion of the planet was thus made to seemingly harmonize with that of the solar system until the year 1805, from which 16 THE PLANET URANUS. time till the year 1822 the departure of the planet from its supposed orbit became so marked as to suggest a search for some sufficient cause of such apparently un- accountable disturbance. The result of this search was the discovery of the planet Neptune. There can be no question as to the result being highly creditable to the perseverance and industry of those concerned in the in- vestigation ; but as to the precise nature of the result in a scientific sense, there is a great diversity of opinion — some considering it a great astronomical and mathe- matical achievement, because the planet was found in consequence of and very near to the actual place indi- cated by the calculation ; but by others, viewed as being to a certain extent a merely fortuitous coincidence (a lucky chance), because wlien discovered and actually observed, the elements of the real planet were found to differ greatly (enormously) from those which had been assigned to it as the result of the hypothetical computation. The accompanjring diagram, Fig. 4 (PL 1), copied from HerscheVs Outlines of Astronomy, shows the discrepancy between the theoretical and ob- served path of the planet Uranus from the year 1690 to about 1845. (See the Appendix.) The actual discovery of the planet Neptune having confirmed and apparently verified the conclusion that the motion of Uranus, in its departure from its sup- posed orbit, was to some extent effected by such source of local gravitating influence («?> was perturbed by Nep- tune's attraction), seems to have occasioned a forgetful- ness on the part of astronomers as to the previous lesser but yet very considerable discrepancy which had been partially reconciled by the ingenious but somewhat ''^ii THE PLANET URANUS. IT net from iuggest a jntly un- irch was an be no le to the n the in- le result opinion d mathe- found in ace indi- as being idence (a actually re found hich had jothetical Fig. 4 stronomy^ I and ob- r 1690 to le having si on that its sup- ch source i by Nep- forgetful- ous lesser bad been omewhat '4! violent suppositions already mentioned. If, however, this partially reconciled discrepancy were the only remaining cause of doubt, it would not have been sur- prising that astronomers should, under the circumstances, consider the case, for the time, as satisfactorily explain- ed, and rest satisfied accordingly ; but there is another known (observed) circumstance belonging to this planet Uranus, so remarkable from its exceptional character as to forcibly suggest itself as an independent reason for the exercise of great caution in admitting the newly discovered planet (Uranus) to be a member of the solar system. The circumstance is that "the orbits of these satellites (the satellites of Uranus) offer remarkable and indeed quite unexpected and unexampled peculiarities. Contrary to the unbroken analogy of the whole planetary system — whether of primaries or secondaries — the planes of their orbits are nearly perpendicular to the ecliptic, being inclined no less than 78° 38' to that plane, and in these ^orbits their motions are retrograde; that is to say, their positions, when projected on the ecliptic, instead of advancing from west to east round the centre of thf-ir primary, as is the case with every other planet and satellite, move in the opposite direction. Their orbits are nearly or quite circular,and they do not appear to have any sensible, or, at least, any rapid motion of nodes, or to have undergone any material clmnge of inclination, in the course, at least, of half a revolution of their primary round the sun. When the earth is in the plane of their orbits, or nearly so, their apparent paths are straight lines or very elongated ellipses, in which case they become invisible, their feeble light being effaced by the superior light of the planet, long before they come u]> 18 THE PLANET URANUS. to its disc. So that the observations of any eclipses or occultation they may undergo is quite out of the question with our present telescopes." {HerscheVs Outlines of Astro- nomy'). The observed facts hei'ein recorded, if the suppo- sition that the planet Uranus belongs to the solar system is retained,appears even more remarkable and extraordinary, when the circumstances of the case are submitted to a particular examination ; because the fact of the satellites or moons revolving around the planet in a plane perpendi- cular to the plane of the solar system, almost necessitates the inference that the planet itself must rotate on an axis parallel to the plane of the solar system, and thus, on the supposition that Uranus is a solar planet, we have a departure from what may be called the plan of the sys- tem, considerably greater than at first sight appears. Is mechanical science sufficiently advanced as yet to decide, by reference to experimental demonstration (i. e., by the record of reliable and unobjectionable experiment), whether such arranorement would be mechanical)' admissible ; that is to say, whether, according to the laws governing mechanical forces, such arrangement would have the necessary quality of stability ? The arrangement would admit of three forms ; namely, the horizontal axis, on which the revolving planet rotates, might have (1) a position at right angles to a Tertical plane joining the planet and the (centre of gra- vitation) central body of the system ; or, (2) it might be situated obliquely to such a plane ; or, (3) one extremity of the axis might point directly towards the central body. Such three forms of the arrangement are indicated in Fig. 6. (Note. The axis of the central body of the system, supposing it to rotate, is understood to be per- THE PLANET URANUS. 19 pendicular to the nodal plane of the planet's revolution.) We do not think the case can be authoritatively decided by reference to experiment, but we do not hesitate to express a strong opinion that neither of the forms of the arrangement vi^ould be permanently stable ; the axis of rotation of the planet, in such a case, v^^ould more or less gradually assume a vertical position ; that is to say, it would become perpendicular to the sun's equatorial plane. If, however, we admit the assumption that the planet Uranus belongs to the solar system, we then have the form of the arrangement defined by the observed fact as recorded by Herschel* to be similar to that of (1) in the *This is manifestly included in the statement of the (observation) already quoted. Owing to the great distance of Uranus from the sun, the line of vision from the earth, in any relative positions the moons can occupy, will be very nearly the same as if the planet was viewed from the sun : consequently the recorded observation necessitates the inference of the planet being posited as shown at (1) in the figure. 20 URANU8 AND NEPTUNE. : ti I figure — namely, with the axis of the planet at right angles to a vertical plane joining the planet and the sun. The difficulty as to admitting the assumption is increased by taking into consideration the moons or satellites of the planet, as shown at (d) in Fig. 6 (PI. 2) ; the angular orbi- tal velocity of each moon would be greater than that of the planet when inside the orbital circle, and less when outside the planet's path ; the difference would be very small, but there would necessarily be a continual and active tendency of the moons towards the horizontal plane of revolution. Now if we take the assumption that the, planet Uranus belongs to a stellar system having its plane perpendicular to that of the solar system, the same very important and interesting fact observed and recorded by Ilerschel (quoted at page 17), v/ill also serve to indicate, if not to define, the relative position of the central body of the neighbouring system, viz. thes^^r, to that of our sun ; because it is at once evident that the plane of the planet's Mhit must coincide (or nearly so) with a vertical plane joining the central star and the sun ; for if it does not, let it be supposed that the plane of the planet's revolution is at right angles to the vertical plane joining the star and the sun; then, observation would show the planet's moons revolving as at (6) Fig. 6 (PI. 2), whereas the fact is recorded to be as at (a) in the same figure ;* and similarly the supposition of more than a slight deviation (j. e., a moderate degree of obliquity) from the plane join- • The meaning inteuded, as to the relative positions, may be defined by stating that the vertical plane j.)ining the sun and star coincides with the equatorial plane of the srar. !-ti»'. I'hilr Fill (I Vnnin^ coiia'nh'rrd oh n Sohir l*hinfl. h) / / '\ >." ^ \ V "j #" / / / ""^^ \ /' X \ "- v .^ X 4-.-^- /-;X'U\>,^ :\^ W"' -\>w-/^ / / fci J UKANU8 AND NEPTUNE. n ing the star and the stm, may be at once negatived. The question is therefore reduced to (!) wliether the place of the star is vertically above or beneatli the polar axis of the sun ; or, (2) whether it is above or below the equatorial plane of the sun ; or (3) whether the place of the star is in the equatorial plane of the sun. The (1) case it is not necessary to consider, as such a supposition is clearly inadmissible ; but to decide astronomically be- tween the (2) and (3) — that is, whether the place of the star is above, below, or in the equatorial plane of the sun — will probably require further careful observation of the planet. The observations already recorded seem, how- ever, to support the supposition that the place is consi- derably above the equatorial plane of the sun, as shown in the illustrations, plates 14 and 15 ; the conclusion that such is the true locality of the star will be somewhat strengthened by including the circumstances at present ascertained of the still more recently discovered and less known planet Neptune. Taking the assumption that Uranus belongs to a neigh- bouring stellar system, the probability is at once sug- gested that Neptune is another member of the same sys- tem and at a less distance from the central body.* The few observations as yet recorded of this planet cannot be * On the assumption that Uranus and Neptune belong to the solar system, the orbital distance between Mercury and Neptune should be, according to Eode's law, twice that between Mercury and Uranus. It is now estimated from observation, only to exceed the latter by a little more than half the distance. ' i ' m I "■■ 22 URANUS AND NEPTUNE. considered, on account of the great distance of the planet and difficulties of observing it, as very reliable ; two moons are reported, of which one has " an orbit " — ac- cording to Mr. Otto Struve — " inclined to the ecliptic at the considerable angle of 35° ; but whether, as in the case of the satellites of Uranus, the direction of its motion be retrograde, it is not possible to say until it shall have been longer observed." Now, an angle of 35° differs considerably from perpendicularity; but, even if admitting the coiTectness of the observation, we must remember it was made on an assumption (prejudice) that the earth and the planet were in the same or nearly in the same plane ; whereas, if we assume Neptune to belong to the neighbouring stellar system, that planet would probably be considerably above the plane of the earth's orbit, and consequently (as before shown, with regard to the solar spots, in Part Second) an erroneous inference as to the obliquity of the satellites' plane of revolution would be occasioned. See the accompanying figure (Fig. 1), where the lower body E may be considered to represent the earth. Fig. 1. i /•/u/f I i- Til K Til Mom' O V TIIK STMLLAR IWIVKHSK. The 'S' II IIS ./.t/.if heiutf ronsiiirn't/ VrrlhnI »\ii Safuim Enrfh S vn Earth K. -/// Earth i! i. If • Tllh: THEORY OF TIIK STIi:LLAIi rNlVERSE. 77//" fS'u/i's .ir/.f /'ci/tf/ consu/erff/ Vriiu-iii yf%^. // /V ' /' / ^ @- X •^ tr. N^ / ^ N ^ ^ v^ "4 l-^, I I \lf^Utfl EaHk S un Earth Sfi/t(,-rt T/ranus .Vf/jiiine iTrnrm^ i |i .; J T y Ha/r 15 '1' i i I^ 'Y II E ( ) I^ Y THE STELI.An rNIVf^RSE I'ritu/ mnsulvn'il Horcovlal ^•!^^^ ■*^^' % (§'--- ^/:^ ^// ♦»♦- :;ii G. // i» Hff/r 15 Til f: theory O V rilJ'] STt:LI,AI[ UN [VERSE. Tin' -Sim's Arh I'rhu/ ronnuh'n'd Honzovtal ^- /i ^:i€ii m ® ^ r/i ferh'cal aaris '■9*- V 4 / ® ' MATTER AND MATERIAL LAWS. 23 Summing up the consideration of the cas<}, we conclude (1) that the planets Uranus and Nepttmt are not solar planets belonging to cur system, but that they are stellar planets belonging to a neighbouring system which has its axis of revolution perpendicular to that of the solnr system ; (2) that the (central) star round which those planets revolve is very probably above the equatorial plane of our sun j and (3) that the distance of the star from the sun may be roughly estimated (by adding the distance of the planet Saturn to that of Uranus, 890 + 1800 = 8690 million miles) at about 3000 million miles. (See Plates 14 and 15.) Note. — The following apparently weighty or fatal olijec- tios to the opinion expressed above — that the planets Uranu-s and Neptune belong not to the solar but to a neighbouring steiiPT system — is very likely to suggest itself at once . — The planet Uranus has been for a considerable time, nearly a century, directly uuder astronomical observation, and occasional notices of its having been previously observed,^ and mistaken for a star, are on record. Now if evidence- can be shown that the planet has been observed at succes- sive places in its (alleged) solar orbit, and, so to speak, tracked throughout its orbit; or if, having been seen atone extremity of its supposed solar orbit, it has been subse- quently observed at the opposite extremity, then the opinion stated by us cannot certainly be upheld. It is therefore to bo understood that the strong and confident ■ f \ S( 24 nOMETAUY OUBIT8. opinion Ktiited inc-liidos tlie opinion on our part that no such oviiloneo of an nctnal Kolar orltit can bo shown* (4,) Masses (if agtjreyntcd maffcr uvil tlirir relation to the laws of the material uniccrsc. The nssuinption that masses of matter, revolving around centres of gravitating influence in the iieighbouriioofl of, but not belonging to the solar system, may approach sufficiently near to be visible from the earth, will perhaps enable us to understand and give a reasonable explana- tion of some of those observed facts of astronomy, which at present occupy the position of mechanical eflects ap- parently governed and regulated by laws unknown to or unrecognized by mechanical science. We allude more par- ticularly to those very various bodies at present group- ed and classed together under the name comet. Plate ] from the (Encyc. Britannica) is an example of the illus- trationo given at the present time in astronomical works, of the supposed orbital revolution of a comet around the sun. In some cases the orbital path is considered to be an ellipse of extreme eccentricity ; in other cases, a'para- bola ; or, a hyperbola. The objection to this teaching seems to have been overlooked that it is inadmissible in a scientific sense, because contrary to the law of gravi- tation ; a law which is recognized both by astronomical * Considered as solar planets, theory assigns 84 years as the period of Uranus, and about 165 years as that of Neptune. uch n to uiid lof, >ach baps « na- il ich i ap- ;o or par- oup- e IG Uus- Drks, i the ►e an para- !hing tie in ravi- nical iod of I'LATH (i. Fimn the Emyv. JJritln. COMETARY ORBITS. ||| and mechnnicul science. In Fig. 2, the body C, to the north-east of the sun, isinovingwlth an increasing velocity in the direction BD. The gravitating influence of the sun is supposed, at this place in the cornet's orbit, to exceed the centrifugal force, causing it to gravitate towards and Fio. 2. approach the sun. Since the approach is very considerable in extent and rapid, so is the increase in the velocity pro- portionately great, and when the comet has arrived (i.e., supposed to have arrived) at its perihelion P, it is moving with enormous velocity past the sun in the direction DE ; for a certain short distance, it proceeds in a curve not differing very much from the arc of a circle, but then, notwithstanding that it is supposed to be comparatively 26 COMET ART ORBITS. very near the sun and under the influence of an enor- mous attractive force, it suddenly ceases altogether to obey this force, and proceeds in the direction EF, as shown in the figure, without any further regard to the central gravitating influence. If the body is material and subject to the known laws governing matter when moving from B towards D, and if, even after passing its perihelion, it still retains its material i ature and re- cognizes the influence of gravitation until beyond E, how is it to be admitted that its subjection to the laws of matter can be suddenly abrogated! We cannot admit a supposition that any material mass, having once become subject to the sun as the central gravitating influence governing its motion, and thus belonging to the solar system, can suddenly throw off" its allegi- ance and withdraw from the sun's controlling power into • space, or to visit some other system in a similarly capri- cious manner. If we assume the body (comet) to have an'ived at the place (P) shown in the figure, nearest the sun (without troubling ourselves to explain how it got there), and to be moving past the sun with such very great velocity that the centrifugal force developed is more than sufficient to counterbalance the enormous attractive force of the sun, at so short a distance ; then the inference will be sound that the comet must recede from the sun ; and further, the distance to which the comet will recede will be proportional to the excess in the centrifugal force over the gravitative force when nearest to the sun, as explained and demonstrated in Part First of this Series ; but even in such case the recession could only take place in an orbit with a continually increasing radial distance from the sun, as shown in Fig. 3, and the path of the DISTANCE OF THE VISIBLE STARS. 21 TecediDg body would have the form of a spiral curve continually increasing outwards from the sun as its centre. Fio. 3. (5) The relative distance of the visible stars. Previously to explaining the real character of the cometary motions, it will be proper to examine the ques- tion as to the relative distances of the visible stars. In Plate 6 (Fig. 10), the illustration plainly shows, that assuming the pole star, for instance, to be at a much less distance than is attributed to it by astronomers at tlie present time, the orbital movement of the earth would not suffice to much alter tlie apparently relative place of the star. To an observer viewing it from the earth, it would appear almost directly over the pole — in whatever part of the orbit the earth's place might be at the time of the observation. And further, it will be found that if the assumed distance of the star be again diminished, and taken at (let us say) one half the dis- |:1 2S DISTANCES OF THE VISIBLE STARS. taiice shown in that illustration, the difference to the- terrestrial observer would still be difficult to detect with- out some object having a relatively fixed position to com- pare with ; for example (assuming the axes of the earth and sun to be both perpendicular to the plane of revolu- tion), if the star was directly over the pole of the sun, it would be extremely difficult, even if the distance of the star was very much less than is supposed, to detect any difference ; by careful and precise determination of the celestial sphere, however, and by comparison with a num- ber of the (so called) fixed stars, a point could be found which would be relatively motionless and around which the earth's pole star would appear to revolve in a small circle — the direction of the earth's actual revolution be- ing reversed in that of the apparent revolution of the star ; and this effect would still be essentially the same even if the distance was very great, and indeed so long as the star remained visible ; only that, tlie greater the distance of the star from the earth, the less would be the diameter of the circle in which the earth's pole star would appear to revolve around the point representing the pole of the celestial sphere ; and if the distance was extremely great, so would the apparent circle of revolu- tion be very small. The apparent motion or change in the apparent position of the pole star, since it would result from a change in the observer's actual position, would be astronomically termed the effect of " parallax ;"* • Parallax may be either geocentric or heliocentric ; in the one, the diameter, or pnrt of the diameter, of the earth ; iu the other, the diameter or part of the diameter of the orbital circle of the earth's revolution, is the measured base of the triangle. The general expression " parallax " is well' defined, in Lardner's Astronom;;, as " the apparent displacement of any ob'ect seen at a distance, due to a change of position (place) cf the observer." DISTANCES OF THE VISIBLE STARS. 29 and as the distance of the earth from the sun is (approxi- mately) known and therefore tlie diameter of the earth's orbit, the distance of the star from the sun (or earth) could be thus measured by parallax. . . Have the distances of the various stars been thus ascertained by parallax ? The question will be answered by the following extracts from the Astronomical Record. Note. — We will here again remind the reader that by the perpendicular axis theory such a parallax of the earth's polar-zenith (pole-star) can be only attainable by observations n' ie when the earth is passing or repass- ing the sun's equatorial plar ; if the observations be made at other times, the parallactic effect of the horizontal movement would be entirely masited or much interfered with by the effect of the vertical movement. And, Again, should it appear that the earth is subject, as we have supposed, to a vibration on a horizontal axis transverse to a line joining the earth and sun this would constitute an independent interfering cause unless the observations were made at the nodal plane when the earth's position is strictly perpc idicular (11. Hi HI 'Vil [-( e:zi * CHAPTER II. V The present mixed doctrine of Parallax and Aberration, (6) Theory OF Parallax. HerscheVs Outlines of Astronomy. (800.) " The diameter of the eailu haa served us for the base of a triangle, in the trigonometrical survey of our sys- tem (art. 274), by which to calculate the distance of the sun ; but the extreme minuteness of the sun's parallax (art. 275) is so delicate, that nothing but the fortunate combi- nation of favourable circumstances afforded by the transits of Venus (art. 479) could render its results even tolerably worthy of reliance. But the earth's diameter is too small a base for direct triangulation to the verge even of our own system (art. 626), and we are, therefore, obliged to substi- tute the annual parallax for the diurnal, or, which comes to the same thing, to ground our calculation on the relative velocities of the earth and planets in their orbits (art. 486), when we would push our triangulation to that extent. It might be naturally enough expected that by this enlarge- ment of our base to the vast diameter of the earth's orbit, the next step in our survey (art. 275) would be made at a great advantage ; — that our change of station, from side to side of it, would produce a considerable and easily measur- able amount of annual parallax in the stars, and that by its means we should come to a knowledge of their distance. But, after exhausting every refinement of observation, astronomers were, up to a very late period, unable to come to any positive and coincident conclusion upon this head ; and the amount of such parallax, even for the nearest fixed star examined with the requisite attention, remained mixed up with and coneealed among the errors incidental to all astronomical determinations. The nature of these errors JELIOCENTRIO PARALLAX. 31 " has been explained in the earlier part of this work, and we need not remind the reader of the difficulties which must necessarily attend the attempt to disentangle an element not exceeding a few tenths of a second, or at most a whole second, from the host of uncertainties entailed on the results of observations by. them : none of them individually, per- haps, of great magnitude, but embarrassing by their number and fluctuating amount. Nevertheless, by successive refine- ments in instrument-making, and by constantly progressive approximation to the exact knowledge of the Urano- graphical corrections, that assurance had been obtained, even in the earlier years of the present century, viz., that no star visible in northern latitudes, to which attention had been directed, manifested an amount of parallax exceeding a single second of arc. It is worth w^^'le to pause for a moment to consider what conclusions would follow from the admission of a parallax to this amount." (801.) " Radius is to the sine of 1" as 206265 to 1. In this proportion then at least must the distance of the fixed stars from the sun exceed that of the sun from the earth. Again, the latter distance, as we have already seen (art. 357), exceeds the earth's radius in the proportion of 23984 to 1. Taking, therefore, the earth's radius for unity, a parallax of 1" supposes a distance of 4947059760, or nearly five thousand millions of such units ; and lastly, to descend to ordinary standards, since the earth's radius may be taken at 4000 of our miles, we find 19788239040000, or about twenty billions of miles for our resulting distance." (802.) " In such numbers the imagination is lost. The only mode we have of conceiving such intervals at all is by the time which it would require for light to traverse them. (See note §, at the end of this chapter, for a more familiar illustration.) Light, as we know (art. 545), travels at the rate of a semidiameter of the earth's orbit in S"- I'd'- '6. It would, therefore, occupy 206205 times this interval, or 32 HELIOCENTRIC PARALLAX. "3 yonra and 83 days, to traverse the distance in question. Now, as this is an inferior limit whicli it is already ascer- tained that even the brightest and therefore i)robably the nearest stars excoed, what are we to allow for the distance of those innumei'able stars of the smaller magnitudes which the telescope discloses to us ! What for the dimensions of the galaxy in whose remoter regions, as wo have seen, the united lustre of myriads of stars is perceptible only in pow- erful telescopes as a feeble nebulous gleam 1" (803.) " The space-penetrating power of a telescope, or the comparative distance to which a given star would require to bo removed in order that it may appear of the same brightness in the telescope as before to the naked oyo, may be calculated from the aperture of the telescope com- pared with that of the pupil of the eye, and froi;>. 5ts reflect- ing or transmiting power, i.e. the proportion of the incident light it conveys to the observer's eye. Thus it has been computed that the space-penetrating power of such a reflec- tor as that used in the star-gauges above referred to is expressed by the number *75. A star, then, of the sixth magnitude removed to 75 times the distance would still be perceptible as a star with that instrument, and admitting such a star to have 100th part of the light of a standard star of the first magnitude, it will follow that such a stand- ard star, if removed to 750 times its distance, would excite in the eye, when viewed through the gauging telescope, the same impression as a star of the sixth magnitude does to the naked eye. Among the infinite multitude of such stars in the remoter regions of the galaxy, it is but fair to con- clude that innumerable individuals, equal in intrinsic bright- ness to those which immediately surround us, must exist. The light of such stars, then, must have occupied uj^wards of 2000 years in travelling over the distance which sepa- rates them i'rora our own system. It follows, then, that when we observe the places and note the ajjoearances of HELIOCENTRIC PARALLAX. 33 <' such stars, we are only reading their history of two thousand years anterior date, thus wonderfully recorded. We cannot escape this conclusion but by adopting as an aU-^rnative an intrinsic inferiority of light in all the smaller stars of the galaxy. We shall be better able to estimate the probability of this alternative when we have made acquaintance with other sidereal systems whose existence the telescope dis- closes to vis, and whose analogy will satisf}- us that the view of tl.e subject here taken is in perfect harmony with the general tenor of astronomical facts."' (SOi.) " Hitherto we have spoken of a parallax of 1" as a mere limit below which that of any star j'et examined assuredly, or at least very probably falls, and it is not with- out a ceitain convenience to regard this amount of parallax 418 a sort of unit of reference, which, connected in Iho reader's recollection with a parallactic unit of distance from our system of 20 billions of miles, and with a H^ ^-ears' journey of light, may save him the trouble of such calcu- lations, and ourselves the necessity of covering our pages with such enormous numbers, when speaking of stars whose parallax has actually been ascertained with some approach to certainty, either by direct meridian observation or by more refined and delicate methods. These we shall proceed to explain, after first pointing out the theoretical peculiar- ities which enable us to separate and disentangle its etiects from those of the Urano-graphical corrections, and from •others causes of error which, being periodical in their nature add greatly to the difficulty of the subject. The effects of precession and proper motion (see art. 852), which are uni- formly progressive from year to year, and that of nutation which runs through its period in nineteen year^, it is obvious enough, separatej^themselves at once by these > pi'esent purpose, we may suppose circular. The star will therefore appear to describe each year about its mean place regaixled as fixed, and in virtue of parallax alone, a minute ellipse, the section of this cone by the surface of the celes- tial sphere, perpendicular to the visual ray. But there is * " In the actual state of astronomy and photology, this necessity can hardly be considered as still existing, and it is desirable, therefore, that the practice of astronomers of introducing an unknown correction for the con- stan^f aberration into their equatians of condition for the determination of pWallaz, should be disused, since it actually tends to introduce error into the fiaal result." PARALLAX AND ABERRATION. 35- " also another way in which the same fact may be repre- sented. The apparent orbit of the star about its mean place^ as a centre, will be precisely that which it would appear to describe if seen from the sun, supposing it really revolved about that place in a circle exactly equal to the earth's annual orbit, in a plane parallel tc» the ecliptic. This is evident fi-om the equality and parallelism of the lines and directions concerned. Now, the effect of aberration (disre- garding the slight variation of the earth's velocity in different parts of its orbit) is precisely similar in law, and differs only in amount, and in its bearing reference to a direction llO" different in longitude. Suppose, in order to fix our ideas, the maximum of parallax to be 1" and that of aberration 20-5", and let AB, ab, bo two circles ima^^ined to be described separately, as above, by the star about its mean place S, in virtue of these two causes respectively, St being a line parallel to that of the line of equinoxes. Then if, in virtue of pr-rallnx alone, the star would bo found at a, in the smaller orbit, it would, in virtue of aberration alone, be found at A in the larger, the angle, a S A, being a right angle. Drawing then A C equal and parallel to S a, and joining S C, it will, in virtue of both simultaneously, bo found in C — i. e. in the circumference of a circle whose radius is SC, and at a point in that circle in advance of A ,! 36 PARALLAX AND ABERRATION. " the nborrational place, by tho angle ASC. Now, since SA : AC : ; 20-6 ; 1, wo find, for tho angle ASC, 2° 47' 35"; and for the length of the radius SC, of the circle represent- ing tho compound motion 20".524. The difference (0".024) between this and SC, the radius of the aberration circle, is quite imperceptible, and even supposing a quantity so minute to be capable of detection by a prolonged series of ooservations, it would remain a question whether it were produced by parallax or by a specific difference of aberration from the general average 20".5 in the star itself. It is, therefore, to the difference of 2° 48' between the angular situation of tho displaced star in this hypothetical orbit, i, e. in tho arguments (as they ai'O called) of the joint correction (ySC) and that of abberration alone (ySA), that we have to look for the resolution of the problem of parallax. Tho reader may easily figure to himself tho delicacy of an enquiry which turns wholly (even when stripped of all its other difficulties) on the p'eme determination of a quantity of this nature, and of such very moderate magnitude." The form of the figure illustrating the case defines the relative position which the observer's station is supposed to occupy, for, because A.B., a.h. are circles described by the star about its mean place S., a line passing through the star and through the earth must be perpen- dicular to the plane of the circles in every direction, or in other words, it must be a transverse axis to the circles passing perpendicularly through their common centre. Now parallax is an effect consequent ujwn an alteration in the observer's position, and parallax of the fixed stars is an effect consequent upon the constantly progres.sive change of the earth's place in its orbit. The parallactic circle of the star's apparent movement in the heavens is the representation, the inverted reflection, of the earth's actual movement in its orbital revolution. There- PARALLAX AND ABERRATION. 37 fore the parallactic displacement of the star through the semi-diameter of the circle, from Stoals consequent upon the (completed) motion ot the earth through its second semi-orbit in the opposite direction, viz : correspondent to the semi-diameter SJ. For if a be the extreme east of the star's parallactic circle, it is tlie iipparent place of the star observed from the earth wlicn at the western extremity of its orbit, and tlie stir's apparent motion from S. to «. is the gradually increasing effect of the eartli's motion from the central place of its orbit to the extreme west thereof. Aberration is an (hypothetical) effect consequent upon the motion of tlie person whose eye receives the light from the object, and aberration of the hxed stars is a (supposed) apparent effect conse- quent upon the actual motion of the eartli in its orbit. The supposed aberrational circle of the star's apparent motion in the heavens is a representation or reflection of the vdocity and I'he direction of the earth's orbital motion. Therefore the aberrational displacement of the star consequent upon the earth's orbital motion in the direction D. S. will be in the opposite direction, viz: from A. towards the west (i- e. the opposite direction to A. c.) For the aberrational displacement of the star to take effect in the direction S. A, the earth's orbital motion must evidently be in the direction opposite thereto, viz : in the direction A. S. or A.B. / but oi-bital motion of the earth in such direction cannot cause paral- lactic displacement in the direction S. a, nor yet in the direction a. S, bocause the displacement belonging to parallax as well as the supposed displacement due to aberration must be parallel to the motion or altera- tion in relative position of the observer's station, upon 38 I'AHAI-l.AX AND AUEURATION. wliich «'.ich is dnpeiuUMit and of which both • are coiisiMii.ents. W»? are, thoreforf, quite iitsable to accept the state- ment, here made and deiiiied by illustration, of an a)t|>arent theoretical motion by the star, compounded of an aberrational effect at right angles to the effect of parallax. In order that the reader may be able to fairly consider the evidence in this and other cases, we will presently give as fully and completely as our limits per- mit. Sir John Herschel's own statement and definition of the doctrine of aberration. If aberration be indeed a reality, if it be anything more than a chimera of the imagination, some intelligible reason consistent with the theory to whioli it belongs can be shown why aberrational displacement should take effect in a direction at right angles to that of the dis- placement due to parallax. Assuming, for a moment, the aberrational eflfect to be a reality in its application to the case here illustrated, that effect must be so related to that of parallax that the one is a deduction from the other, because when the one causes, or tends to cause, an effect in the one direction, the other causes, or tends to cause, an effect in the con- trary direction, so that if the respective effects of the two causes should be exactly equal, the one must neu- tralize the other, and no apparent displacement of the star would take place. The characteristic difference between the two effects is. that of parallax is consequent upon a completed movement from one place to another more or less distant from the first : in the case of the earth's orbital motion it is progressive from any given place in the orbit as a PARALLAX AND ABRHRATION. 89 starting point until the fintirc diiimetcr of the orbit lias Iteen completed. The qiuintity of oppurciit eflecton the stiir, for any given distunce moved through by the enrth, is dependent upon the diHtnnce of the stur ; the result is ntly constructed instrument of tlie same description mad', in the years 1839 and 1S40, have fully loiitirmed the reality of the parallax indicated b}- Professor Henderson's observations, though with a slight iliniinution ill tU condud^jd amount, which comes out equal to 0"-9128 or alxMit jytlis of a second ; Irujht stars in its immediate uei(/hboiirk^x/d being unaffected by a similar periodical dis- placement, and tlius affording satisfactory proof that the dis- jdacement indicated in the case of the star in question is )iot merely a result of annual variations of temperature. As it is im^wssible at present to answer for so minute a quantity as that by which this result differs from an exact second, wo may consider the distance of this star as. approximately 48 PARALLAX OF THE STARS. "expressed by the parallactic unit of distance referred 1o irt art. 804." (808.) " A short time previous to the publication of this important result, the detection of a sensible and measurable amount of parallax in the star No. 61 Cygni of Flamsteed's Catalogue of Stars, was announced by the celebrated astron- omer of Konigsberg, the late M. Bessel. This is a small and inconspicuous star, hardl}' exceeding the sixth magni- tude, but which had been pointed out for especial obser- vation by the remarkable circumstance of its being affected by a proper motion (sec art. 852), i.e. a regular and contin- ually progressive annual displacement among the sur- rounding stars to the extent of more than 5" per annum, a quantity so very much exceeding the average of similar minute annual displacements which many other stars exhibit, as to lead to a suspicion of its being actually nearer to our system. It is not a little remarkable that a similar presumption of proximity exists also in the case of a Cen- tauri, whose unusually large proper motion of nearly 4" per annum is stated by Profess'>r Henderson to have been the motive which induced him to subject his observations of that star to that severe discussion which led to the detection of its parallax. M. Besscl's observations of tJl Cygni were commenced in August, 1837, immediately on the establish- ment at the Kiinigsberg observatory of a magnificent heli- ometer, the workmanship of the celebrated optician Fraun- hofer, of Munich, an instrument especially fitted for the system of observation adopted ; which, being totally dif- ferent from that of direct nu-ridional observation, more refimed in its conception, and suscejitible of far greater accuracy in its practical application, we must now explain." (809.) "Parallax, i»ro])er motion, and specific aberration (denoting by the latter piirasc that pai't ol the aberration of u star's light which may be supposed to ari'^e from its indi- vidual peculiarities, and which we have every reufcou to PARALLAX OF STARS OPTICALLY DOrBLE. 43 " believe, at all events, an exceedingly minute fraction of the \7hole), are the only uranographieal corrections which do not necessarily affect alike the apparent places of two stars situated in, or very nearly in, the same visual line. Sup- posing, then, two stars at an immense distance, the one behind the other, but otherwise so situated as to appear very nearly along the same vi.-ual line, they will constitute what is called a star optically double, to distinguish it from a star physically double, of which more hereafter. Aber- ration (that which is common to all stars), precession, nutation, nay, even refraction, and instrumental causes of apparent displacement, will affect them alike, or so very nearly alike (if the minute difference of their apparent places be taken into account), as to admit of the difference being neglected, or very accurately allowed for, by an easy calculation. If then, instead of attempting to determine by observation the place of the nearer of two very unequal stars ■ (which will probably be the larger) by direct observation of its right ascension and polar distance, we content ourselves with referring its place to that of its remoter and smaller companion by differential observation, i.e. by measuring only its difference of situation from the latter, we are at once relieved of the necessity of making these corrections, and from all uncertainty as to their influence on the result. And for the very same reason, errors of adjustment (art. 736), of graduation, and a host of instrumental errors, which would, fur this delicate purpose, fatally affect the absolute determination of either star's piaeo, are harmless when only the ditfei*ence of their places, each equally affected by .such causes, is required to bo known." (810.) "Throwing aside, therefore, the consideration of all these errors and corrections, and tlisregai-iling for the present the minute efl'ect of aberration and the uniformly ])rogre8sive effect of proper motion, let us trace the effect of the difforenccs of the parallaxes of two stars thus juxta- ^' I 44 PARALLAX OP STARS OPTICALLY DOUBLE. i " posed, or thoir apparent relative distance and position at various seasons of the year. Now, the parallax being inversely as the distance, the dimensions of the small ellipses appai'cntlj' described (art. 805) by each star on the concave surface of the heavens by parallactic displacement will differ — the nearer star describing the larger ellipse. But both stars lying verj' nearly in the same direction from the sun, these ellipses will be similar and similarly situated. Suppose S and s to bo the positions of the two stars as seen from the sun, and let ABCD, abed, be their parallactic ellipses; then, since they will ■ be at all times similarly situ- ated in the^o ellipses, when the one etar is seen at A, the other will be seen at a. When the earth has made a quarter of a ^ revolution in its orbit, their apparent places will be 36 ; ^ when another, quarter, Cc ; and when another, Dd. If then, Ave measure carefully, with mi- crometers atlapted for the purj^oscs, their apparent situation with respect to each other, at different times of the year, we should perceive a periodical change, both in the direction of the line joining them, and in the distance between their centres, For the lines A't, and Cc, cannot be parallel, nor the lines B6, and Dd, equal, unless the ellii)ses bo of equal dimensions, i.e. unless the two stars have the same parallax, or are equidistant from the earth." In examining the case here illustrated we are in u3ubt as to the latitudinal place of the star represented in the figure and with respect to which no information appears to be given. It must be remembered that Herschei assigns to the earth an orbit horizontal to the axis of the PARALLAX OF STARS OPTICALLY DOUBLE. 45 celestial sphere; consequently, it seems to us that a paral- lactic ellipse, having its major axis perpendicular to the station of the terrestrial observer, as shown in the figure, could be only obtained by positing the celestial sphere horizontally. Let us suppose the double star under exami- nation to be Polaris with a companion star actually at a much greater distance but apparently in close proximity. We then have Herschel's figure modified as in fig. ^ . . because the sum of the annual parallactic movements (displacements) of the two stars would be circles reflect- ing the orbital revolution of the earth, the greater circle belonging to the nearer star, the lesser to the more dis- tant.* Now, if we suppose the star to be equatorial, or nearly so, we shall have the figure modified as shown at C. . . that is, the two stars would appear to shift their position almost linearly, having a reciprocating move- ment to and fro annually, in the same line, or in an extremely elongated ellipse. Again, if we suppose the double star to be located intermediately between the celestial pole and equator, we then have an ellipse such as shown oX B. I : \ '<: * From this figure it may be readily understood that the phenomenon of a revolving double star may be occasioned by the greater parallactic dis-. placement of tlie nearer of two polf.r str.rs which are nearly in the same u PARALLAX OF DOCBLE STARS. i i "We have given reasons in the preceding part of this work why the earth's orbit should be considered to be compounded of vertical motion as well as of horizontal ; adopting this theory (of the earth's perpendicular axis) we shall then have the parallactic effect on the equatorial star, illustrated by the fig. B instead of by the fig. C, and in the case of the intermediately located star the ellipse of the fig. B would be converted into an ellipse similar to that of Herschel's figure, but placed horizon- tally instead of upright.* The quotation from HerschcVs Outlines of Astronomy continued. (811.) "Now, micrometers, properly mounted, enable us to measure very exactly both the distance between two objects which can bo seen together in the same field of a telescope, and the position oi the line joining them with respect to the horizon, or the meridian, or any other deter- minate direction in the heavens. The double image micro- meter, and especially the heliometer (art. 200, 2U1), is peculiarly adapted for this purpo^se. The images of the two stars formed side by side, or in the same line prolonged, however momentarily displaced by temporary refraction or instrumental tremor, move together, preserving their rela- tive situation, the judgment of which is in no way disturbed by such irregular movements. The heliometer also, taking visual line from the earth. That one of the two, which is much the nearer, appearing to revolve ecrdntricallj once in the year around the more distant. • The reader will understand the theoretical representation ot the case belonging toeach of the respective localities will be thus modified by the parallactic effect due to the vertical motion of the earth through 4'" (or 4S°) equalling about 74 million miles, and, therefore, not very much less than one half the horizontal diameter of the orbit. PARALLAX OF STARS OPTICALLY DOUBLE. 47 ;his be tal; [xis) )rial C, the lipse Izon- in a greater range than ordinary micrometers, enables us to •compare one large star with more than one adjacent small one, and to select such of the latter among many near it, as shall be most favourably situated for the detection of any motion of the large one, not participated in by its neighbour." (812.) " The star examined by Bessel has two such neigh- ' hours both very minute, and therefore, probably, very dis- tant, most favourably situated, the one (s) at a distance of 7' 42", the other (s') at 11' 46" from the large star, and so ■ situated, that their directions from that star make nearly a right angle with each other. The effect of parallax, there- fore, would necessarily cause the two distances (Ss, and Ss') to vary so as to attain their maximum and minimum values alternately at throe-monthly intervals, and this is what was actually observed to take place, the one distance being always most rapidly on the increase or decrease when the other was stationary (the uniform effect of proper motion being understood, of course, to be always duly accounted for). This alternation, though so small in amount as to indicate, as a final result, a parallax, or rather a difference of parallaxes between the large and small stars, of hardly more than one-third of a second, was maintained with such regularity as to leave no room for reasonable doubt as to its cause ; and having been confirmed by the further continu- ance of these observations, and quite recently by the •exact coincidence between the result thus obtained and that deduced by M. Peters from observations of the same star at the observatory of Pulkova, is considered on all hands a? fully established. The parallax of this star, finally resulting from Bessel's observation, is 0".348, so that its distance from our system is very nearly three parallactic units (art. 804)." (813.) " The bright star a Lyrse has also near it, at only 43" distance (and, therefore, within reach of the parallel Tvire or ordinary double-image micrometer), a very minute I 48 PARALLAX OF STARS OPTICALLY DOUBLE. star which has been subjected, since 1835, to a severe and assiduous scrutiny by M. Struve, on the same principle of differential observation. He has thus established the exist- ence of a measurable amount of parallax in the large star, loss indeed thar that of 61 Cygni (being only about J of a second), but yet sufficient (such was the do\icacy of his measurements) to justify this excellent observer in an- nouncing the result as at least highly probable, on the strength of only five nights' observation, in 18.35 and 1836. This probability, the continuation of the measures to the- end of 1838 and the corroborative, though not, in this case, precisely coincident result of Mr. Peters' investigations, have converted into a certainty. M. Struve has the merit of being the first to bring into practical application this method of observation, which, though proposed for the purpose, and its groat advantages pointed out by Sir William Herschel so early as 1781, remained long unproductive of any result, owing partly to the imperfection of micrometers for the measurement of distance, and partly to a reason which we shall presently have occasion to refer to." (814.) " If the component individuals S, s (fig. art. 810) bo (as is often the case) very close to each other, the paral- lactic variation of their anyle of position, or the extreme angle iLcluded between the lines Aa, Cc, may be very con- siderable, even for a small amount ofdifferenco of parallaxes between the large and small stars. For instance, in the case of two adjacent stars 15" asunder, and otherwise favourably situated for observation, an annual fluctuation to and fro in the apparent direction of their line of junc- tion to the extent of half a degree (a quantity which could not escape notice in the means of numerous and careful measurements), would correspond to a difference of parallax of only J of a second. A difference of 1" between two stars apparently situated at b" distance might cause an oscillatioit THEORY OF ABERRATION. 49 in that line to the extent of no less than 11°, and if nearer, one proportionally still greater. This mode of observation has been applied to a vonsideruble number of stars by Lord Wrottesley, and with such aa amount of success, as to make its further application desirable. (Phil. Trans., 1851.)" f (816.) "Che following are some of the principal fixed stars to which parallax has been, up to the present time, more or less probably assigned : a Centauri 0".976 (Henderson, con-'d by Peters.) 61 Cygni 0".348 (Bessel.) 21258 Laland... 0".260 (Kriiger.) 1U\5-G Oeltzen. 0".247 (Kriiger.) * a Lym 0".155 (W. Struvo, corr. by O. Struve.) Sirius 0".150 (Henderson, corr. by Pctern.) lO.pOphinchi 0".16 (Kruger.) Ursoe Majoris... 0".133 (Peters.) Arcturus 0".127 do Polaris 0".067 do Capella 0".046 do • Qy. 0'.255 (see art. 813). Although the extreme minuteness of the last four of these results deprives them of much numerical reliance, it is at least certain that the parallaxes by no means follow the order of magnitudes ; and this is farther shown by the fact that a Cygni, one of M. Peters' stars, shows absolutely no indication of any measurable parallax whatever." (7.) The Theory of Aberration. , Let us now examine the " theory of aberration, to which (as shown by the foregoing quotation) so great an importance is attached by astronomers. t See Note on last page (page 89.) < ■ \ .i 60 TnEORT or aberration. We will first take the explai)atiori given by Dr. LarJner. Handbook of Astronomy. (2440.) " Aherradon of Zljf//^— Assuming, tl\pn, the velo- city of light, and th.it the earth is in motion in an orbit round the sun with a velocity of about 19 miles per second, which must be its speed if it move at all, as will hereafter . /pear, an effect would be produced upon the apparent placcHofall celestial objects, by the combination of these two motions which we shall now explain. " It has been statod that tli« apparent direction of a visible object is in the direction from which the visual ray enters the eye. Now, this diroetion will depend on the actual direction of the ray if the eye which receives it be quiescent; but if the eye bo in motion, the same effect is produced upon the organ of sense, as if the ray, besides the motion which is proper to it, had another motion equal and contrary to that of the eye. Thus, if light moving from the north to the south with a velocity of 192,000 miles per second, be struck by an eyo moving from west to oast with the same velocity, the effect produced by the light upon the organ will be the same as if the eye, being at rest, were struck by the light having a motion compounded of two equal motions, one from north to south, and the other from east to west. The direction of this compound effect would, by the principles of the composition of motion (176), be equivalent to a motion from the direction of the north-east. The object from which the light comes would, therefore, be apparently displaced, and would be seen at a point beyond that which it really occupies in the direction in which the eye of the observer is moved. This displacement itt called accordingly the aberration of lioht. THBORT OP ABERRATION. It fr. Mo- Jit Id, for ^nt Jse " This may bo mada Htill more evident by the following mode of illustration. Let (Fig, 717) l>o the oijject from ^> Q which light comt's in the direction Ooe". Lot fi \ i he tho place of the eye of the observer when the \ \ light is at 0, and let the eye bo upposod to \ j move from e to e", in tho same time that tho \ i light moves from o to e". Lot a straight tube \ \ be imagined to bo directed from tho oyo at<^, to \ i the light at o, so that the light shall bo in tho • ; centre of its opening, while the tube moves with > i the eyo from o etooV, maintaining constantly .'' the same direction, and remaining parallel to itself: the light in moving from o to e" will pass along it>< axis, and will arrive af e" when tho oyo arrives at iliat point. Now it is evident that in this case tho direction in which the object would be visible would be tho direction of tho axis of • the tuV>o, so that, instead of appearing in tho direction ' -vhich is its true direction, it •would appear in the direci.. >0', advanceJ from o. in dircc- tioiiof tho motion e e", with which the i)l>*orvcr is aifected, "The motion of light being at the rate of 192,000 miles per second, and that of tho earth (if it move at all) at tho rate of 19 miles por second (both those velocities will bo ostablishod hereafter), it follows that the proportion of o e" to e e" must bo 192,00o to 19, or 10,000 to 1. " The angle of aberration OoO' will vary with the obliquity of tho direction e e" of tho observer's motion to that of tho visual ray o e". In all cases the ratio of o e" to e e" will bo 10,000 to 1. If tho direction of the earth's motion be at right angles to tho direction o e" of the object 0, we shall have (2294) tho aberration a = '^^^ « 20".42. If the angle o e" e be oblique, it will be necessary to reduce e e" to its component at right angles to o e", which is done by multi- plying it by the trigonomotriciii sine of the obliquity oe" e of I it « 52 THEORY OV ABERRATION. " tho direction of tho object to that of the earth's motion. If thJH obliquity bo exprossoil by 0, wo hHrII hnvo for tho uliorrations in gcnornl a = 20". 42 x »in. 0, Acconling to this, the attorrntion would bo groutoiitt when tho direction of tho earth'H motion \n at right angles to that of tho object, and would docrottHO as tho angle docroaHOs, being nothing when tho object in iseon in tho direction in which tho earth is moving, or in exactly tho controry direction. " Tho phonomuiia may alsso bo imagined by considering that the earth, in revolving round tho sun, constantly chango.s tho direction of its motion ; that direction making a complete revolution with tho earth, it follows that tho ctfect produced upon tho ai»parent place of a distant object would be the name if that object really revolved onco a year roun it is evident that the ball would, throughout its whole do- 54 THEORY OP ABERRATION. " scent, be foutul in the axis of the tube ; and a spectator referring to the tube the motion of the ball, and carrietl along with the former unconscious of its motion, would fancy that the ball had been moving in the inclined direc- tion KS of the tube's axis." (330 ) . " Our eyes and telescopes are such tubes. In whatever manner we consider light, wiiether as an advanc- ing wave in a motionless ether, or a shower of atoms travers- ing space (provided that m both cases we regard it as absolutely incapable of suffering resistance or corporeal obstruction from the particles of tran-ipnrent media traversed by it*), if in the interval between the rays traversing the object glass of the one or the cornea of the other (at xohich moment they acquire that convergence which directs them to a certain point in fixed space), and their arrival at their locus, the cross wires of the one or the retina of the other be slipped aside, the point of convergence (which remains unchanged) will no longer correspond to the intersection of the wires or the central point of our visual area. The object then will appear displaced ; and the amount of the displaoe- ment is abirration." (331.) " The earth is moving through space with a velocity of about 19 miles per second, in an elliptic path round the sun, and is therefore changing the direction of its motion at every instant. Light travels with a velocity of 192,000 miles per second, which, although much greater than that of the earth, is yet not infinitely so. Time is occupied by * " Tliis conditiun is indispensable. Without it we fall into all those difficulties which .M. Doppler has so well pointed out in his paper on Aberration. If light itself, or the luminlferous ether, be corporeal, the condition insisted on amounts to a formal surrender ol the dogma, eitl.or of the extension or of the impenetrability of mat- ter; at least in the sense iu which those terms have been hitherto used by metaphysicians. At the poin'. to which science is arrived, probably few will be found disposed to mention either the one or tha olhor." THEORY OF ABERRATION. 5» "it in traversing any space, and in tliat time the earth de- BcribeB a space which is to the former an 19 to 192,000, or as the tangent of 20",5 to radius. Suppose now APS, to represent a ray of light from a -star at A, and let the tube PQ bo that of a telescope so inclined foi-wai-d that the focus formed by its object glass shall be received upon its cross wire, it is evident from what has been said, that the incli- nation of the tube must bo such as to make PS: SQ:: velocity of light: velocity of the earth : : 1 : tan. 20".6; and, therefore, the angle SPQ, or PSll, by which the axis of the telescope must deviate from tiie true direction of the staiv, must Iie20".5." (332.) "A similar reasoning will hold good when the direction of the earth's motion is not perpendicular to the visual ray. If SB be the true direction of the visual ray. and AC tlie position in which the telescope requires to be held in the apparent direction, we mu;erration, then is to distort the aspect of the heavens, causing all the stars to crowd, as it were, directly towards that point in the heavens which is the vanishing jioint of all lines parallel to that in TIIEOUV or ABERRATION. " which tlic earth is for tlio momont moving. As the earth jiiovos round the sun in the ph»no of the ecliptic, this j)oint must lie in that phme, 90° in advance of the earth's longi- tude, or 90** behind the sun's, and shifts, of course, contin- ually, describing the circumference of the ecliptic in a year. It in easy to demonstrate that the oft'ect on each particular star will be to make it apparently describe n small ellipse in the heavens, having for its centre the point in which the star would bo seen if the earth were at rest." (3;{4.) " Aberration, then, aflbcts the apparent right as- censions and declinations of al! the stars, and that by quan- tities easily calculable. The formulae most convenient for that purpose, and which, sj-slematicall}' embracing at the same time the corrections for precession and nutation, enable the observer, with the utmost readiness, to disen- cumber his observations of right ascension and declination of their influence, have been constructed by Professor Hcssel, and tabulated in the a))])cndix to the first volume ol" the Transactions of the Astronomical Society, where they will be found accompanied with an extensive catalogue of the places, for 1830, of the princij)al fixed stars, one of the most useful and best arranged works of the kind which has ever appeared." ^ (335.) " When the bod}' from which the visual ray ema- nates is itself in motion, an ett'ect arises which is not, ])ro- jterly speaking, aberration, though ic is usually treated under that head in astronomical books, and indeed confounded with it, to the production of some confusion in the mind of the student. The effect in question (which is independent of any theoretical views respecting the nature of light) may be exi)lained as f(;llows. The ray by which wo see any object is not that which it emits at the moment we look at it, but that which it did emit some time before, viz., the time occupied by light in traversing the interval which weparatcs it from us. The aberration of such a bo ly then THEORY OP ABERRATION. 67 " arising fromtho earth's velocity must l)o applied as a cor- rection, not to the lino joining the earth's place at the moment of observation witli that occupied by the body at the same rroment, but at thut antecedent instant when the ray quittel it. Hence it is easy to derive the rule given by an*' .omical writers for the case of a moving object. Fiom ihc hnoun hues of its motion and the earth's calculate Its apparent or relative anyu/ar motion In the time taken by Uyhtto traverse its distance from the earth. This is the total amount of its apparent misplacement. Its ert'cet is to dis- place the body observed in a direction contrary to its apj)a- rent motion in the heavoris. And it is a compound of aggrogaie etlect coiiHisting of two parts, one of which is the aborration, projicrly so called, resulting from the compo- sition of the earth's motion with that of light; the other being what is not inaptly termed the equation of Hylit, being the allowance to be made for the time occupied by th« light in traversing a variable Hjjaco." The hist section brings in a division of the subject not immediately under consideration, but it is given here to complete the explanation byHerschel, and also as belong- ing to the general theory of (the so-cuUed) aberration of light. The explanation and illustration by Lardner are included in those of llerschel; it will, therefore, suflice to take the latter here for preliminary consideration. The defmition of the meaning is by inference from ana- logy, and the first illustration is that of the shower of rain. The simple statement of fact, herein made, appeals to the experience of every individual, and, as it is not at onc«; contradicted by that experience, it may be termed plausible; but upon more careful consideration, it will appear, in respect to the application to be made and the m THEORT OF ABERRATION. ;i inference intended to be drawn from it, that the statement is not supported by fact. It is true that if a person runs rapidly in a shower of rain, a drop of the water may come in contact with his face, which would not have done so had he stood still ; but it is suiely evident that the angle at which the drop of water descended (or tlie angle at which it rains) cannot have been altered by the person's running, and this is the question at issue. A drop of rain win occupy a certain time in descending through a spuco equal to the distance from the upper part of a man's forehead to his chin ; and if, during the time of that de- scent, a man running brings his face in contact with the drop, the effect is of the same kind as if the drop had been suspended at that height from the ground at which it comes in contact with his face. The additional sup- position of the wind increasing the effect is, in regard to the rain only, not open to the same objection, because therein would be an actual cause operating to alter (increase or decrease) the angularity of the rain's descent ; the effect of the wind's force would combine with that of the force of gravitation, and result in a compound effect ; but in regard to the analogy, the supposition is entirely false and inapplicable, because there are no grounds for supposing that wind can divert or affect a ruy of light ; on the contrary, it is quite established that the fact is the reverse : the most violent hurricane dues not cause a ray of light to deviate in tlie slightest degree from its direction o'" ?.\>:{\r of incidence. The illustratiun ( f th<* incMni .< tube, as shown, is not altogether incorrect, u ic &h an »tn lioty it is very imperfect and objectionable ; iu ! a i r.n explanation, very likely to mislead the student. Takiiig the same figure, we will THSORT OF ABERRATION. s» apply it, in the first instance, as follows (supposing the inclined tube to be left out of the figure) : £SF represents a plane moving horizontally with a certain velocity in the direction EF. At P, in the perpendicular line APS, is a ball falling vertically from A, towards S ; the propor- Fig. 6. Oa o.. T a -Oc -*«« tional velocity of the moving plane EF to that of the falling ball is such, that a place on the plane will move from Q to S, in the same time that the ball falls, from P to S ; consequently, the boll P will fall upon the place Q. At the same time the place S will have moved towards F, and when P (the ball) arrives at S (or Q), S will have arrived at T ; ST being equal to QS. The interposition of the tube, in fact, alters nothing ; but it apparently com- plicates the otherwise simple case — which is, that the ball falls vertically and strikes the plane at right angles to its position and motion : just the same as if the plane had remained at rest, and the ball had been allowed to fall from a place at the same height vertically over Q. The analogy of the falling ball to light emitted from a luminous body is very imperfect, because, whereas the ball can only fall vertically or in some one angular direc- tion, the rays of light from the luminous body are emit- i. 60 TIIEORr OF ABERRATION. ted, in every angular direction, in radiant lines from the body as a centre. The conditions of the case are, there- fore, essentially different from tliose of a ball falling ver- tically ; whatever distance is assumed for A (supposing it a star), rays of light from it will be continuuUy arriv- ing at the earth in angular directions, depciident upon its situation relatively to tlie place upon wliich tiie ray h incident, and whenever the earth, moving in tlie direction EF, arrives at Q, it will evidently nuu!t rav of light which have just arrived from the star.* By the illustration, the ball falls vertically upon the moving plane ; now, su[>|»osing the ball is made to descend at a detinite angle, as, for instance, through the tube PQ, it would strike or conw in contact witli tlie plane at its angle of descent {i.e. PQS), not, however, at the place Q ; for, supposing the plane to be in nmtion, and Q to have been at the base of the tube when the ball commenced to descend, Q during the descent will have moved to S, and another place on the moving plane will receive the ball ; but this does not alter the angle of incidence of the ball or of the light. The correctness of this theory (aberration of liglit) may be tested by the illustration of the method (>f determining the Sim's parallax (as given in IlcrscloTs Astronomy, Fig. art. 3oo). We will suppose the earth to be moving in its orbit in the direction of the arrows; the effect of the aberration of light (if real) would be, as explained in the preceding (juotations, to shift the apparent place of the sun from S to (some place) T. Conseipiently, if the • We nre hero adopting, for the nionicu*, the Inngimgc of the theory, in order to meet the argument on its own ground : in u strictly scicntilic sense the ex{>ression is objectioniible. -,-ji .*sicioi!i . HELIOCENTRIC PARALLAX. dl zeniths of the places of observation were determined independently of the sun's apparent place, the effect would be to give a different parallax for the two places ; that of BTC being greater than ATC ; but the zeniths of the two places of observation must be determined independently of the observed place of the sun, for otherwise there could be no parallax ; the effect must be therefore to increase the actual parallax — i.e. the total apparent displacement — by the distortion due to F!g. 7. aberration. Now the parallax obtained by this geocen- tric method is 8" 6 ; and the supposed displacement attri- buted to aberration is 2()".5. If now, leaving the case for particular examination in the next cha[)ter, we discard for the moment the sup- posed aberration of light as altogether imaginary ; and, then, we assume those observed effects which have been attributed by astronomers to aberration of light to be really the effects of parallax, can we thus (from the total amount of parallax) obtain an approximate meas- r 62 HILIOOXNTRIO PARALLAX. ure of the distance of the visible stars? The quotation already given from Herschel's work shows that the efforts of astronomers to obtain even such approximate measurement .have been entirely un- successful. These attempts were made by heliocentric or annual parallax, in which the distance of the earth from the sun serves for the base line of the triangle. But this heliocentric parallax (as a trigonometrical pro- cess) differs essentially from the geocentric ; nor is it anywhere explained how the apparently great, if not insurmountable, difficulty of thus directly obtaining the parallax of a star, even if the distance was less than the distance of the sun, has been over- come. It is evident that knowledge as to the dis- tance of a body is obtained in the geocentric method by the two observations from places, at a definite and known distance from each other on the earth, being made at the same time ; but to obtain parallax by the heliocentric method, it is impossible for two observers to be stationed at different and distant places in the earth's orbit at the same time, and therefore the method differs assentially from the geocentric. It is true an observation can he made from the earth at' one extremity, or at any place in the orbit, and subsequently a second observation can be made from the opposite extremity or from some other dis- tant place in the orbit ; and the two observations may be compared ; but does it follow, or is it to be expected that the same result as by the geocentric method, or, indeed, that any (reliable) result can be in this manner obtained I If some of the stars moved with a known velocity, and others were comparatively motionless, it is not difficult to understand that observations of them HBLIOCBNTRIO PARALLAX. would have a diffiirentiaJ value from which further know- ledge might be obtained. But as all the stars are rela- tively (iilnioat> motionless, it doo!« not immediately ap- pear wherv the standard of cumpurison is to be found, or whoHtM* th« diflTeivinlHl iinsflo to Uv obtained wpon which to btt«r \\w ('(Mnpntiition. Theiippiirent motion of all the gta»"»* V HVjpposing tho distanct' tliem aM to be very great) |i necessarily nearly tlie same. An ennentially distinct basis .'or the (^unputatiou has, therefore, to be sought, and may be found in observing the relative positions of the sun and the stiir to that of the earth when the eartb is at some di'tinito place in its orbit, as for example, the central ploc» eqnidly distant from twc definite extre- mities of the orbit; and then when the earth has arnved at a distant part of the orbit, observing tiie alteration in the relative angidar position of the earth and sun, and the earth and star, respectively. In this manner the h#'lio-centric parallax of the star may be obtained ; and, a? we will presently show, by a modification of the same method two definite compara- tive angles may be obtained proport'onal to each other in the same ratio as the distance of the star from the sun is to the distance of the earth from the sun. Since the last is a known quantity, the distance of the star may be thus measured. The collective parallactic result of the earth's pro- gressive change of position throughout a complete revo- lution known by the tenn annual parallax is thus described by Dr. Lardner: — Lardner's Handbook of Astronomy : (2442.) " Annual parallax. — If the earth he admitted to movo annually round the sun, as a stationary centre in a u HELIOCENTRIC PARALLAX. circle whoso diamotor muHt liavo the vast magnitude of 209 millions of milcH, nil obHorvera placed upon the earth, seeing distant objects from points of view so extremely distant one from the other as nrr opposite extremities of the same diameter of such a circle, must necessarily, as might bo supposed, see those objects in very ditforent directions. " To comprehend the effect which - might be expected to be produced upon the apparent place of a distant object by such a motion, lot E E E E (fig. 718) represent the earth's annual course round the sun as scon in per- spective, and let bo any distant ob- ject visible from the oarlh. The ex- tremity E of the line EO, which is the visual direction of the object, being carried with the earth round the circle E E E E \\\\\ annually describe a cone of which the base is the path of tho earth, and the vertex is tho place of the object 0. While the earth moves round the c\vc\o E E, tho lino of visual direction would, therefore, have a cor- responding motion, and tho apparent place of tho object would be succes- sively changed with the change of di- rection of this line. If the object bo i\ imagined to be projected by the 03-0 upon tho firmament, it would trace upon it a path 0' 0" o"\ which would Fig. L. 718. bo circular or elliptical, according to the direction of the object. When the eailh is at Ey the object would be seen at 0; and when tho earth is at J?, it would be seen at 0". The extent of this ai)parent displacement of HBLIOCINTRIC PARALLAX. 6& m I bo " tho object would be mooHurud by the angle E £, which the (liamotor E Js! of the eorth'H path or orbit would subtuml at tho object 0. It haH boon Htuted that, in general, tho appa- rent dirtplacenient of a distant viBiblo object, produced by any change in tho utation from which it \n viewud, ia cnllod parallax. That which in produced by tho change of position duo to the diurnal motion of the earth being called diurnal parallax, the corres]ionding diaplacement duo to the annual motion of tho earth in called annual parallax." The general conclusion come to is the same as that expressed in the r|uotation previously given from Iler- schel's work : namely, that no parallax of any of the stars has be';n obtained in this way. On careful examination, however, it will appear that all the parallax observations in recent times have been rnude with a foregone conclu- sion that no parallax wos attainable ; or that, if any was attainable, it must necessarily be an extremely small amount, not exceeding, at the utmost, the sine of 1". The consequence seems to have been that any quantity of parallax obtained exceeding this 1" has been set down to aberration of light, or to error. The Encyclopedia Britannica — art. Astronomy: " Suppose, for oxam])le, wo observe a star situated in the plane of the odiptic. When tho earth is at that point of its orbit, between tho sun and the star, where the tangent to the orbit is perpendicular to the visual ray (which, on account that tho star has no sensible parallax, alwaj's main- tains a paralhtl direction), the apparent place of tho star will be 20".4 to the westward of the true place ; so that it will appear to have an oscillatory motion on tho ecliptic, the rang© of which is 40".8, and the period exactly a year. Half way between these two points, the tangent of the orbit IMAGE EVALUATION TEST TARGET (MT-3) w % .«v -;lf* e foregoing quotftion from Herschel's Outlines ? The observer first looiis towards Alpha. Since he is moving directly * Evidently he could not observe these stars all \t the same time of the day, although he could do so at dififbrent times of the same day. It is meant that he determine the longitude of each star successively, when the earth is at or near the place indicated. V ABERBATION-OP-LiaHT THEORY. 73 towards that star, there is, by the theory, no aberration, and he sees it in its actual place at a. He next observes lieta. . . .Since the earth's motion (of about 19 miles a second) is at right angles to a line joining that star and the sun, tlie aberration is, according to the theory, here effective to the fullest extent; and, instead of seeing Beta at a', he sees it at c'. He next turns to Cramma. . . .And since he is moving directly away frpm that star, he sees it in its true place at a". Lastly, he looks at the star Delta,. . . .here again aberration is fully effective, and he sees Delta not at a'", but at h'". We now suppose the earth to. have proceeded to the northern extremity of its orbit, at n ; and the astronomer repeats his observations of the four stars successively. By the theory of aberra- tion (Ilerschel's foregoing explanation) he will find that each one of the four stars has moved to another place ; for he is now passing Alpha at right angles to a line joining that star and the sun, and therefore, by the theo- ry, he sees Alpha at h. And he is moving directly towards Beta, which he now sees in its true place at a' . Similarly Gamma has moved its apparent place from a", to c", and Delta has retired to its true place at a'". The earth proceeds, and arrives at the western extremity of its orbit at o. The astronomer renews his observa- tions. . . .The aberration theory tells us where he will find each of the four stars — namely, Alpha will have gone back to a. Beta, which was at the time of the first ob- servation at c' and at the second observation had moved to a', will now be found at 6' . . . And similarly of the others. Gamma will be found at a" and Delta which was first at V" and then at a'" is now at c"'. Lastly, the earth having arrived at the southern extremity of the orbit, the 74 ABBRBATION-OF-LIOHT THIORT. observer finds that each star has again shifted its place . . . Alpha must now be seen at c ; Beta at 'a ; Gamma has gone to b" ; and Delta back again to a'". Here then is the statement of a case as to which the practical astronomer may be called upon for* evidence. How stand the facts of observation ? for this is simply a question as to the places at which the observer sees the stars. Do the facts of observation support the aberra- tion-theory ? Do the constellations in or near to the solar equatorial plane thus continually, independently of any parallax (which is quite distinct from the ques- tion here at issue,) shift their positions backwards and forwards relatively to each other, as the earth progresses in its orbit ; at one time approaching nearer to each other, and again receding from each other ; each of them shift- ing its place throughout an arc • of 40". Let the practi- cal astronomer give evidence in the case. Take four constellations situated, relatively to each other, as we have supposed ; such, for example, as Gemini, Pisces, Sagittarius, and Virgo. Any one star in each of these four constellations may be chosen to try the case. Can- not the question be decided by positive evidence, whether the imperative requisition of the aberration- theory (as stated by Herschel) is in this particular case fulfilled or not T There is a corollary to the aberration-theory, or, at least, what, .s it seems to us, must be a corollary if the theory has any substantiality or definite consistency in itself, which, if stated distinctly and directly, can scarcely fail to startle the practical optician. It is. . .that the angles * The angle of aberration is 20" 5, which has to be doubled because it is at first fully effective in the one direction and afterwards in the reverse. K. N.- ■:i i1^ \ / / / m \ ■^ C .<# ,11 ABBRRATION-OP-LIOHT THIORT. fl of incidence and reflection are not always equal. For the angle of vision, or the angle under which the eye perceives the luminiferous body, cannot be otherwise than equal to the angle of reflection, and this angle of vision is not, according to the aberration-theory, the true angle of incidence if the station of the observer have a progressive motion in such a direction as to form witH the direction of the luminiferous body an angle not much less or greater than a right angle. Therefore the angle of reflection from the earth of the solar-light must always difler from the true angle of incidence f (11) The Nature of Light as assumed by the Tlieory. But the statement of this corollary brings again under notice the anomalous character and, indeed, contradic- tory nature of the qualities which are attributed to * Light ' accordingly as the exigencies of the one oi* the other of the three theories — the velocity, the aberration, and the undulatory, theories — require a decidedly ma- terial nature subject to the laws of matter, or a semi- material nature subject to some of those laws and exempt from others, to be assigned to tho atoms or waves of ' light.* • It is, perhaps, in the exposition of the aber- ration-theory that the want of a definite and real founda- tion becomes most immediately manifest. Referring again to Sir John Herschel's explanation, we have the * The meaning of the ezpreision ' Light ' has now become, in some measure, involved in the vague and indefinite meanings which belong ia common to these theories. It sometimes means luminous particles or atoms of luminous matter travelling with incredible Telocity.. ..sometimes means the particles of a purely suppositious fluid, called Ether, vibrating with iuoonceivable rapidity... sumetimes means an effect produced by impact oC the luminous matter on the eye " , > /;;;;;; 11 1 II M n;S ■"!m 1 II 1 '1 I mm I'm 1 1 76 MATERIAL CHARACTER OF THE THEORY. analogy of light to the shower of rain and to the falling ball, that is.. to matter in the liquid and in the solid condition. Something called ' light ' has motion and velo- city, just as the earth moves iii its orbit v/ith a definite velocity. . . .it enters the advanced end of the telescope tube, which is moving rapidly forwards, it is in the tube, moves through the tube, and, emerging from the posterior end, comes in contact with the eye of an observer, or with tlie ground ; or, again, the observer, who is moving forward with the earth upon which he is stationed, strikes his eye against the descending ray of light, just as the per- son whorunnitig forward strikes his face against the falling rain, .there is impact ; the person whoue eye receives the shock, which is a compounded result of the motion of the ray and ol his own motion, infers the position of the lumi- niferous body from the compounded direction in which that shock is received, and hence is in a measure deceived or misled. The supposed analogj' is here to another form or hind of matter in motion. The fundamental theory of light to which it belongs, appears to be the corpuscular theory of Sir Isaac Newton, in which extremely small particles of luminous matter are ejected from the lumi- niferoiis body and move in right lines with enormous velocity, rather than the undulatory theory. At last we find men the most experienced, eminent and distinguished in the sciences of astronomy and optics, as Sir John Herschel, in order to reconcile these theories of light with the actual and known facts of the phenomena, en- deavouring to suppose the existence of a description of matter from which all the properties and qualities of mat- ter are absent. The note to the ' Outlines of Astronomy,' in which Herschel adopts and endorses tie doctrine of M. Doppler on this subjecct, and which we have already IM3IATERIAL MATTER I 77 lid |0- te ve lor or tm ;es 3r- quoted (page 54), willserve to exemplify this strange hy- pothesis of an immaterial description of matter. " This condition is indispensable. Without it we fall into all those difficulties which M. Doppler has so well pointed out in his paper on Aberration. If light itself, or the luminiferous ether, be corporeal, the condition insisted on amounts to a formal surrender of the dogma, either of the extension or the impenetrability of matter ; at least in the sense in which these terms have been hitherto used by metaphysicians. At the point to which science is probably arrived, few will be found disposed to mention either the one or the other." This supposition of matter without any of the pro- perties of matter seems to be precisely equivalent to supposing an animal without head, body, limbs, bones, flesh, or, in short, without any of those things which especially pertain to an animal. It is true there is, in the foregoiiig, a sort of saving proviso by Herschel, ' if liffht be corporeal,' — but then, if it be not corporeal, what becomes of the undulatory theory, what of the theory of aberration, and what of the velocity-theory of light ? all of which are upheld by Herschel. (12) Aberration a Dynamical Theory. Let us return again to the astronomical theory ; and submit to the astronomer the following case: We will suppose that the areal (absolute) velocities of the three planets, Venus, Earth, and Mars, are exactly equal, and that their angular velocities relatively to the Sun are so proportioned (by their icspt^tive distances from the Sun) that whilst the Earth is moving through an arc of six degrees, Venus moves through ten degrees, and Mars through only four. Now, taking the maximum angle of IF. 78 ABERRATION A DTNAMICAL THEORY. I :i.| aberration at 20" for the terrestrial observer, what will be the angle of aberration for the inhabitant of Venus and of Mars respectively ? From Herschel's illustration of the inclined tube and falling ball, the angular velocity is that which must determine the angle of aberration ; for, if the distance of the plane E. F., upon which the ball falls, from the starting point A. be doubled, and the plane, move with twice the linear velocity relatively to the point A., the same inclination from the perpendicular would still be given to the tube. To appreciate the wlaole case, it must be remembered that this illustration of the tube and ball illustrates the artificial idea upon whtch the aberration-theory is based only, and does not illustrate the case of an eye or of a telescope directed towards a body outside the Earth : if, for instance, a stationarj'' object be supposed a few miles from the Earth which is moving, it is evident that the angular position of a telescope constantly directed towards the object would require to be constantly chang- ed. Now in Herschel's illustration of tube and moving plane, the same inclination of the tube is preserved throughout the movement ; therefore the illustration is defective, and it is also deceptive, because the theory of aberration itself and Herschel's own exposition of it, each expressly supposes {see Fig. 13) such an appre- ciable alt ration in the relative position of the recipient body wl ich moves, and the luminiferous body which remains stationary. The tube or telescope is always sup- posed to advance relatively to a perpendicular drawn vertically or horizontally, as the case may be, from the object to the plane beneath it ; for the effect claimed, as stated by Herschel, is dependent upon and arises out of this motion of the plane relatively to the object at rest. 1 ! ^■j i > i f ■*3 1^ A- -^---"^ I ' ABERRATION A DTNAMIOAL THEORY. ^ Now, if the consideration of the case in this manner be pursued with attention, it will become evident that the theory of aberration breaks down altogether / because if the body move relatively to the perpendicular drawn from the object to the plane, the angular position of the tele- scope must be changed, for if it be not changed the suc- cessive rays of light cannot enter the tube ; and, if the body has no such relative movement, there can be no effect such as claimed, .but, if the angular position of the telescope requires to be changed, whether it be to increase or decrease the inclination* of the telescope, any optical effect necessitating such a change must belong to parallax. The especial point to which the attention should be directed, is that, if there be no appreciable alteration in the relative po&itions of the luminiferous body and the eye, so that the telescope having the same inclination, constantly receives light from the object at the same angle throughout the movement of the plane,, there can be no appreciable aberration even if the possi- bility of the theory be admitted in other respects. And, if there be an appreciable alteration in the relative position, the effect must be parallax and in the reverse direction to that claimed for aberration. When the whole case is cor- rectly apprehended, the utterly unreasonable character of the general result supposed becomes apparent j for, ii a movement of the earth through only nineteen miles of orbit produces aberration, some proportional altera- tion in the relative angular position of the object and the ■M * As the telescope approaches or passes the perpendicular drawn from the object to the moving plane upon which the observer is stationed, paral- lax will require the inclination of the tube to be altered in the opposite direction to that which aberration would require. , 80 THEORT AND FACT. ! i W • ii :ii eye must manifestly take place ; and if the one effect be appreciable so must the other effect be also appreciable ; but what, if instead of the plane moving nineteen miles, it move nineteen hundred or nineteen thousand, nay, nineteen million and even, a distance several times greater than nineteen million miles, and yet without any appre- ciable alteration in the relative angular position of the eye and the object ? A claim of 1" aberration for every 1" angular alteration of position (parallax) might appear to be primarily reasonable until shown to be otherwise, but a claim of 20" aberration and no appreciable altera- tion in the relative angular position is manifestly inad- missible. Even Herschel's own illustration evidences negatively that there cannot be any such effect ; hence. . Note (a.) The theory of aberration is a dynamical the- ory in which the very meaning of the term motion, as a relative expression, seems to be imperfectly appreciated or misapprehended. One body moves relatively to another. A body moves with a certain velocity relatively to '>. stan- dard of velocity. There is angular and linear velocity, and each of these is relative. It may be shown that if tlie earth relatively to the distant stars has no appreciable motion and no velocity such as contemplated by the theory, not even a suppositious case of aberration has been made out in respect to those stars. (13) Distrust in the Gift of Sighc required by the Aberration Theory. Before leaving the theory of aberration — let us, refer- ring to either of the illustrations we have given of the eclipses and occupations of Jupiter's satellites, once more briefly note what the student of astronomy is impera- tively required by that theory to understand in respect THEORY AND FACT. 81 be lies, fay, iter )re- Ithe tevy fear (ise, 3ra- tad- tces to those phenomena.* It is. .that he is not to suppose what he appears to see is actually taking place when and as he sees it, but that it is merely certain reflections of light, and interruptions and interferences with light, which have been occasioned by something which has happened about 35 minutes or 50 minutes previously, according to the place of the earth in its orbit at the moment of observation : for example, if he appears to see the satellite just entering the shadow, he is to believe that the satellite has really entered the shadow some forty or fifty minutes earlier, and, if it be the satellite nearest the planet, is already almost at the middle of the eclipse (or occultation.) But the shadowy messengers of light, belonging to the aberration-theory, have occu- pied all that time in bringing him the intelligence of what formerly happened ; indeed, however, he has not yet sufficiently distrusted his eye-sight — this is pnly a general distortion and displacement of everything, which belongs of right to the velocity-of-light theory, aberra- tion proper has not yet come into play, it has its functions to perform, and, seizing the shadowy record of the past event just as it reaches his eye, distorts it afresh by the angle of aberration proper, making it appear that the event, of which intelligence has at length arrived, hap- pened at some place other than that at whi ^h it actually occurred. We think the student, who has apprehended that this is the demand made upon his faith by these theories, which say to him. .'put your confidence in us, distrust your eye-sight and beware lest it deceive you,' and who, • This refers to our ParC Fifth which has for its subject the undulatory and velocity theories of light. i :82 EXPERIMENTAL INVESTIGATION. i i 1 I : 1 I then taking his telescope, reads apparently, not the record of the past event, but the event itself actually occurring as he watches the clear definition of each successive phase, will act reasonably if he listen atten- tively to the counter-claim made from within ' to put confidence in his eye-sight, to distrust the theories and beware lest they deceive him-' Note (6.) — We suggest that an advantageous means of practically testing the truth of the Aberration-theory may be found in the observation of one of the lesser of Jupiter's Satellites. Let the Earth be supposed (preferably) at a pLce in its orbit near to opposition ; let the (apparent) moment of the satellite passing the centre of the planet during oc- cultation be carefully determined from the ingress and egress : then, let the moment of passing the centre of the planet at the opposite extremity of the Satellite's orbit, namely, the central point of the transit; and, then, the central moment of the succeeding occultation be determined. If there be truth in the theory of aberration there must necessarily be a distinct (apparent) difference be- tween the two semi-revolutions ; for, at the occultation both the Earth and the planet's satellite are moving in the same direction and there will be virtually no aberra- tion ; but at the transit, the Earth moving in one direc- tion, the satellite moves in the reverse; and, consequent- ly, the effect of aberration must be increased and should considerably exceed the 20".5. As the angle of aberration would be an addition to the one side and a deduction from the other, the difference between the two semi-revolutions would be more than 1'. RADIATION INTO SPACE. 83 Ithe \lly iCh m- mt bd ins ny of Note (c). — On the question, .vjhethera luminiferoiis and calcri/erous body, in the absence of a recipient (or recipro- cating) body, radiates light and heat continuously into space. . . .* How has it been ascertained that the sun radiates light into space, and in every direction alike ? Gravitation is also an influence which is communicated from the sun to the planet, or is intercommunicated between them ; and it may also be said to be emitted by the sun. Is, then, the sun supposed to emit or radiate gravitation into space ? Or, is it only emitted in the direction in which there is an aggregated mass of matter, to receive and reciprocate that influence ? Tf the latter, then, suppos- ing we dismiss all foregone conclusion and prejudice, does it appear so certain that the influence which causes light may not be in the same case ?" We wish now, without introducing the case into our main argument, to point out that both the theories, of Aberration and Velocity of Light, are also depen- dent upon the assumption of the continuous radiation of light into space by tki sun or other luminiferous body. We do not mean that the assumption affords any evidence or basis to support the theories but the theories require and are dependent upon the assumption. For, if the assumption be not true in fact, it will follow that, since, by each of the theories, the communication of light requires time (i. e. light has velocity) a star of which the distance from the earth exceeds a certain limited amount must be invisible from the earth. The earth travels in its orbit with a velocity (more than 1000 miles a minute) which will in about 8 minutes remove its entire bulk out of the space which it occupied at the commencement * This question will come uader consideratiou in our Fart Fifth. 84 RADIATION INTO SPACE. of that time. If, therefore, the luminiferous body be at such distance from the earth, that light (being assumed to have velocity) requires more than about 8 jninutes to reach the earth, the body, during a great part of the earth's orbital revolution, would be invisible, because the rays if emitted towards the earth would be too late to arrive and would be projected into space or vacancy. But notwithstanding the enormous and incredible velocity assigned to light by the theory, a quarter of an hour would not nearly sutlice for light to reach the earth from tlie very great majonty of those stars which are in fact visible. In many cases the earth would have ample time, not only to get out of the way of the luminous matter, but to make one or mo"e complete revolutions in its orbit, and might thus occasionally and accidentally (so to speal^) return to its former place just wlien the rays were arriv- ing.* Now, is the assumption of continuous radiation into space established on certainty ? Is it quite reliable, unas- sailable, and not open to any doubt whatever! Or is it itself an unproven theory, plausible, certainly, at a time when the known facts belonging to the subjects of light and radiant heat were comparatively few, but subject now to grave objection and doubt I Such grave objec- tion and doubt respecting the assumption we, for our- selves, entertain. We remember the very reasonable ob- jection taken by Sir D. Brewster to the undulatory theory of light t (against the form of which objection as irrever- • Sir John Herschel estimates the time, required by the light from some of the most distant (visible) stars to reach the earth at about 2000 years. t Part Fifth (of this series). HELIOCENTRIC PARALLAX. 85 at lied of |U8e to flit Hty |ul(} cnt we felt called upon to protest) ; an objection of the same character seems to us to apply with ecjual force to the case now under consideration. It does not seem reasonable, bearing in miiiu the properties and tpialities of light and radiant heat, their great i'liportance, and tlic grand and invaluable services rendered by them in the economy of nature we say, it does not soeni reason- al)le to suppose that a large proportion of tlie ligiit and lieat radiated goes to waste. . .is radiated and lost; yet such is the meaning of radiation into space. If there be a recipient, it is not difficult to understand that there need not be loss, the heat or light is received and (reciprocat- ed) 'returned in the rime or in some other (mode) condi- tion of force. But radiation into space or vacancy means no return.* There is besides, as noticed before, the kindred and analogous force of gravitation. Do masses of aggregat- ed matter gravitate into space? No then why sliould it be positively concluded that they radiate into space ? (14) Direct Heliocentric methods of ohtaininy Parallax of the distant Stars. Referring to the illustration in the preceding chapter, a correct method of computing the distance of the stars, . . . .we are strongly of opinion that the method there t We are mindful of Dr. Wells' theory of dew, but acceptance of this philosophical and felicitous explanation of the phenomena does not neces- sitate the supposition of rf.diation of heat into space from the surface of the earth there are the stars in sufficient number to serve on a clear night as recipients, although we incline to the opinion that the escape of electricity, in some condition of force other than that of free caloric, into the atmosphere, causes that reduction of temperature on the surface of the earth which condenses the wat^^ry vapour. II 86 METHOD OF niLlOrCNTRIC PARALLAX. 1] indicuteil of ascertaining the parallax is not only prac- ticable but is also tiie most simple and direct method. Repeating the illustration of page 69, on the larger scale of Fig. 12 (A.) . . The Earth may be supposed at any definite place m. in its orbit, at which i)lace it i» found by careful observation that a certain star in, or not far from, the solar equatorial plane, is so situated with respect to the sun that the vertical plane, joining the centre of the earth and sun, is at right angles to the vertical plane joining the centre of the earth and star» From the time of that observation, the Earth having made an orbital semi-revolution (exactly), the angle con- tained by the vertical planes is again determined by care- ful observation, and the difference between the two, i.e. the difference between the last angle and a right angle, is the parallax. For ourselves, we are quite sure that aberration of light is a mere phantom of the imagination, but even those, who for the present are persuaded that human sight is deceived in that manner, will allow that aberra- tion could not interfere with parallax ascertained by the method here proposed, for tbe earth would be at the time of the one observation directly receding from, and at the time of the other, directly approaching the star (or vice versa) and, therefore, by the theory there would be no aberration. Or, again, supposing the north polar zenith of the earth, when passing through the sun's equa- torial plane, be accurately determined, and at the com- pletion of 8 semi-orbital revolution of the earth the same place be found, the differenee from a right angle with the sun's equatorial plane will be the parallax of the Pole- star ; from which the approximate distance of the star \ Bk< ./ y Pa.rcLUM,-t:. - Fi^ I'' w i> ty h^. .CQ .^~ t X. \f 1 H) C 5 f^ « 'It "41 ~< «^ -4i. CS "$■- ki f^ y "§ <• 5^ a K.' t*«* c ^ ^ ■i^ ■< c 5 V 5: », -^ •> •^ \^ :? '^ c -.^ "^ > 1^ h u *i ^Si *^, Si- ■^ PARALLAX OF THE STARS. 8r would be readily obtainable by the simple computation shown at page 69 See Fig. 12 (B.) In this case also, 'aberration' could not interfere ; for by that theory its effect would be to shift the star's place back- wards in the vertical plane joining the star and the earth, but it would not affect the angle formed by that plans and the solar equatorial plane. Whereas the parallax would be the deviation of the plane from a right angle in consequence of the removal of the earth to the oppo- site extremity of the orbit.* (Note. — ^We have taken the riglit angle to render the illustration nioreclear, but, if the angle differed from a right angle, the difference between the first and second observation would still give the parallax ; if, however, in the angle first observed the inclination be towards the sun, the star might be a truly solar pole-star, and in that case no parallax would be thus obtained because the angle would be the same from the opposite sides of the earth's orbit.)t Another method,, by which we opine the approximate parallax of the stars may be obtained, is by the com- parison with each other of stars situated 90 degrees apart on or near to the celestial equator. Fig. 11 may serve well to illustrate this method. Suppose the station of the terrestrial observer to be at p. and let him note the actual and relative localities of the stars Delta and. Alpha. At the expiration of six months his station having arrived at n. let him note again the actual and relative localities of the same two stars. Parallax will * Evidently the absolute right angle is not indispensable. Take Polaris, and, determining the exact deviation from a right angle with the equa- torial plane when the earth is at the one node, then determine the increase or decrease in that deviation when the earth has arrived at the other node. t We are in this example assuming that our demonstration of the per- pendicular terrestrial axis of rotation, parallel to the solar axis, will neces- sarily be admitted, but, even otherwise, the method admits of modification accordingly. «8 PARALLAX OF THE STARS. have shifted the apparent place of Delta from h'" to c" but the place of Alpha will have undergone no change, for the observer, on both occasions, sees Alpha at its Actual place, viz., at a. For many astronomical observations an observatory situated at one of the poles vk^oulJ be advantageous, and for the one observer to directly note the position of the two equatorial stars (Delta and Alpha) at the same time a station so situated would be necessary ; indirectly, however, the one astronomer could, we opine, observe the locality of the star in the opposite longitude to his station (which statfon we suppose to oe in the northern hemisphere) with perfect or almost perfect precision. It would be necessary to obtain the exact locality of the pole of the celestial sphere according to the perpen- dicular-axis theory •, having obtained this he would observe the star Gamma when exactly on the meridian of his station, and then continuing the meridianal line through the place of the celestial pole, he would note one or more stars on the produced meridian which would be within the visible hemisphere when his station arrives in the op- posite quarter (i. c, when his station has revolved through' 180"). Evidently he might thus find the place of a star in the exactly opposite longitude to and in the same lati- tude as that of the star Gamma, which would be the place of Alpha. Supposing this method not to admit of sufficient precision in practice, the earth's diurnal rotation can be taken advantage of to observe the four stars suc- cessively, namely four stars, respectively situated in or near to the relative position we have indicated, are to be observed successively at each of the six hours ; these observations being repeated on the second day would I I r I I I :i I I PARALLAX OF THE STARS. 89 furnish the data whereby the precise relative place (longitude) which each of the four stars would apparently occupy, if viewed simultaneously, could be determined.* Our computation (at the conclusion of Chapter II,) . shows for a parallax of 20". 5, a distance of the star pro- portionally about twice as great as the estimate given by Herschel for a parallax of 1" only, f We will conclude thest observations with the decided expression of opinion that, when correctly ascertained, the parallax for the nearer stars will be found to considerably exceed 20". t Note. — Eeferring to page 49 — § (814) of quotation from HerscheVa Outlines of Astronomy. ; ; ; " The paper on parallax by Loi-d Wrottesley, ia Plnl. Trans, for 1851, hero referred to, furnishes, as it seems to us, very strong indirect evidence of the soundness of the per- pendicular-axis theory. In consequence, according to our view, of the non-recognition of the earth's vertical motion. Lord Wrottesley finds unaccountable variations and apparent discrepancies in observations of the same stars made with groat care at different times. Eventually he coiicludos to relinquish the attciiipt to obtain a decided parallax, .ground- ing his resolution to do so, if we apprehend aright, mainly on the apparently irregular and unsatisfactory character of the results actually obtained. * This last is tlie method wc havo already supposed to be made use of in experimentally testing the reality of aberration by tri-monthl^ com- parisons of the four equatorial stars. t See quotation page 31, 5 (801). '" X A helio-centric parallax of 1' would be (of course) equiralent to about one-third of the distance represented by 20".4, and, according to our com- putation, to about COO times the distance of the planet Saturn from tba Sun. o : fV ■ ■'<;. Xi- .'»;,)>•■■ SUPPLEMENTARY NOTE. Heliocentric Parallax of the Earth and Planets. The apparent path of the sun as it travels around the celestial sphere in the undulatory path of the ecliptic, may be considered ac the effect of heliocentric parallax upon the sun itself (the parallax belonging to the horizontal motion of the earth being, in this instance, compounded with that belonging to its vertical motion : thus causing the oblique position of the circle of the sun's apparent path).. For illus- tration of this refer to Plate 12, Page 88 ; or, to Plate, Fig. 20, of Part Second. The eai*th being on the eastern side of its orbit and moving towards the west, the sun is seen on the western side of the celestial sphere and appears to move towards the east ; the earth having moved to the southern side of its orbit, the sun is seen to the north ; the earth having arrived at the western side of its orbit, the sun is seen on the eastern side of the celestial sphere. The sun thus appears to the terrestrial observer to move in the heavens from west to east, or fVom east to west, and so on. Now if we suppose the distance of the sun from the earth to be increased 100 times or 1000 times, tho parallactic angle would be thereby proportionally diminished, or, in other woaIs, the apparent motion of the sun for the same actual movement of the earth would be reduced in proportion to I \ mm 92 HELIOCENTRIC PARALLAX. the increase in the distance. We cannot, however, obtain directly by observation the parallax of the sun resulting from the movement of the earth through the* diameter of its orbit, because, since the earth moves around the sun, the effect is thereby greatly increased and becomes con- tinuous, manifesting itself as an apparent semi-revolution of the sun around the earth. But the geocentric parallax of the sun having been correctly ascertained and the ma^- nitudinal relation of the diameter of the earth's orbit to tho diameter of the earth itself being known, wo possess the means of readily determining by calculatation the helio- centric parallax . <, . 1st. of the Earth itself ; 2nd. of each of the other planets ; 3rd of any star at a definite known distance from the sun. To do this we only require to imagine that the earth occupies at the same time two distinct places in its orbit, fVom one of which the terrestrial observer viers the earth itself at a distance of 90*^. The accompanying figure (Fig. 14) will make perfectly clear this hypothetical supposition, which as famishing a basis for the comparison of the relative angles is not, we opine, open to objection. * As 4000 : 190 millionB : : 8".6 : tang. 0/45" ; therefore 45° is the h. c. parallax of the earth. (This result is obvious because the semi-diameter of the earth's orbit equals the distance of the Sun, and the tangent of 45° equals the radius.) *> The geocentric parallax of the Bua and the distance of the sun from the earth are immediatelj dependent each upon the other. so that if the distance of the sun has been carrectljr ascertained to be a little more than 95 millions, it is certain that the geoceutric parallax of the sun is 8".6, and vice vtna, tBy this method, therefore, we find that a star of which the paral- lax is ascertained to be 20". 4 would have a theoretical distance from the sun of about 1000 times the distance of Saturn, instead of 600 times, at which we have stated the estimate in the foot note to page 69. • HELIOCENTaiO PARALLAX. 98 Ilence, sinco the relative distances of the planets from the sun arc approximately known, we may at once derive the theoretical h. c. parallax of each planet fVom that of the earth, Thus : Taking f The Sun's distance at 95 million miles, the h. c. parallax of the Earth 45* 0' " Venus' distance at one-half that of the Sun, the h. c. parallax of Venus 63** 26' 30" " Mars' distance at twice that of the Sun the h.c. parallax of Mars. 27<' 9' 36" Tapiter's distance at 6 times that of the Sun, the h.c. parallax of Ju- piter. ..;. 110 21' 62" " Saturn's at 10 times that of the Sun, the h. c. parallax of Saturn 6<* 43' 12" 'f The distance of a Star at 10 times that of Saturn, the h. c. parallax of the Star 34' 23" " of a Star at 100 times that of Saturn, theh.c. parallax of the Star ... 3' 26" " of a Star at 1000 times that of Saturn, h. c. parallax of the Star 20". 6 " of a Star at 2000 times that of Saturn, h. c. parallax of the Star 10". 3 " of a Star at 2,500 times that of Saturn, the h. c. parallax of the Star ... about 8". 2 Now in this last quantity we obtain a convenient means of testing and checking these distances by computation based on an independent fact, because 8" .2 almost coincides with the geocentric parallax of the Sun, which is 8" .6 Therefore: — As the semi-diameter of earth : semi-diameter of earth's orbit : : semi-diameter of earth's orbit : the distance of that Star of which the h. c. parallax coincides with the g.c. parallax of the Sun; and accordingly . . , As 4000 : 95 millions : : 95 millions : 2375 times the i M HILIOCINTEIO PAKALLAX. distanc* of Saturn (or 23750 times the distance of the Sun ;) Mrhich result is in close agreement with the pre- ceding.* We would suggest that parallactic observations of the planets with the theoretical quantity iu each case as a guide and a check on the apparent results, might be found a very usefVil and desirable preparation for parallactic observations of the stars. * The diameter of the ptrallaoiic circle or tbg major axis of tliSi parallac- tic ellipM would be (ofooune) twice at great aa the respective quantities here giTea. The Star for example hariag 3'20 ' h. c. parallax, should bare an extreme appareat motion, to and fro, of 6 02." t l\ i !B Si «5 « to ' I ;^; • ■' 5i >0 t • •- * > ft* ■v J \ •.4*iV- i > 1 r ,.fi': ; ,,ii:;!f-«:- j''U;' •>'iC' /■' -• APPENDIX. TOE OBSERVED DEVIATION OF THE PLANET URANCS FROM ITS (supposed) solar orbit. t From HerscheVs Outluics of Astronomt/. Plate 1, Fto. 4. — "The horizontal line, or abscissa, is divided into eqiuil jjarts, each representing 50° of heliocentric longitude in the motion of Uranus round the sun, and in which the distiinces between the horizontal lines represent each 100" of error in longitude. The result of each year's observation of Uranus (or of the mean of all the observations obtained during that year) in longitude is represented by a black dot placed above or beU>w the point of the abscissa, corresponding to the mean of the observed longitudes for the year, above if the observed longitude be in excess of the calculated, below if it fall short of it, and on the line if they agree ; and at a distance from the line corresponding to this difference, on the scale above mentioned. Thus, in Flam- eteed's earliest observations in 1690, the dot so marked is placed above the lino at 65".9 above the line, the observed longitude being so much greater than the calculated." (763.) " If, neglecting the individual points, we draw a curve (indicated in the figure by a fine unbroken line) through their general course, we shall at once perceive a certain regularity in its undulations. It presents two great elevations above, and one nearly as great intermediate de- pression below the medial line or abscissa. And it is evident that these undulations Avould bo very much reduced, and the errors, in consequence, gi-catlj' palliated, if each dot were removed in the vertical direction through a distance. 92 APPENDIX. mid in the diioction iiuliciiLod by tho coiToJpoiidiii^poiii^t ot ihG ctti'vo ABODE FGII, intorsocting tho abscissa at' points li:0° distant, and making eqani oxcursions on oitbor side. :}:**•* " CiGi.) " Let us now consider tho effect of an erroneous assumption of iho place of tho perihelion. Suppose in Fig. 2 X to represent tho longitude of a planet, and x y the excess of its true above its moan longitude, due to ellii)- ticity. * * * * " (7CG.) " Let this increnso of jjcriod be made, and in cor- respondence with that change let tho lonj^itudcs be reckoned at a h, and the residual differences from that line instead of AB, and wo shall have done all that can bo done in the way of reducing and palliating these differences. " The above quotation sufficiently explains the plate in its application to our argument : namely, as indicating the nature of the methods adopted for reconciling the discordance between the theory and the observed facts. For the full and more particular explanation of the plate, the reader is referred to the work to which it belongs. n ^