ASTRONOMY, 
 
 AS IT IS 
 
 KNOWN AT THE PRESENT DAY 
 
 AN ACCOUNT OF THE NATURE AND USE 
 
 OF 
 
 ASTRONOMICAL INSTRUMENTS, 
 
 THE MANNER OF CALCULATING 
 
 THE NOTES OF THE CALENDAR, 
 
 THE DISTANCES AND MAGNITUDES OF 
 
 THE PLANETS, 
 
 AND A NUMBER OF OTHER USEFUL AND INTERESTING 
 CALCULATIONS IN ASTRONOMY. 
 
 BY GEO. G. CAREY, 
 
 LECTURER ON NATURAL PHILOSOPHY, CHEMISTRY, ASTRONOMY, &c. 
 
 Uoutron: 
 
 PRINTED BY AND FOR 
 
 WILLIAM COLE, 10, NEWGATE-STREET. 
 
 1826". 
 
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PREFACE. 
 
 THERE is no science in which progressive improvement is so 
 distinctly marked as in Astronomy. The steps by which it 
 has advanced to the state of excellence in which we now 
 behold it, may be as accurately traced as the principal events 
 of our past lives. But although this be the case, and al- 
 though the improvement of this science has been productive 
 of more important benefits to society than any other that 
 could be named, yet there is no branch of useful knowledge 
 so little studied by the inhabitants of this country, at the 
 present day, as Astronomy. For though great and important 
 discoveries have lately been made in this science, yet a 
 knowledge of these and even of the principles of the 
 science itself, is confined to a few individuals. The chief 
 reason, perhaps, that can be assigned for this well-known 
 fact, is, that the science of Astronomy has been generally 
 cultivated by eminent mathematicians ; and hence an ill- 
 founded opinion has arisen, that it is necessary to study a 
 tedious course of mathematics, previous to entering upon the 
 study of this science. But however necessary mathematical 
 knowledge may be in the pursuit of astronomical studies, 
 much important and useful information may be acquired on 
 this subject, without possessing a knowledge of mathematics. 
 
IV PREFACE. 
 
 It will, however, be necessary to be provided with a work in 
 which the science is explained in a clear and popular man- 
 ner, without having recourse to mathematical diagrams and 
 figures. 
 
 There are many works on Astronomy that profess to be 
 written for the use of those who have not studied mathema- 
 tics; and yet it is impossible to understand any one of the 
 subjects treated of in these works without having an acquaint- 
 ance with mathematics. For wherever geometrical figures 
 arc introduced and attempted to be explained, it is not to be 
 supposed that a person wholly unacquainted with geometry 
 can comprehend the illustration. 
 
 It was, therefore, with a view to render the study of this 
 most sublime and useful branch of knowledge more enter- 
 taining, and more easily understood by the general class of 
 readers than it has hitherto been, that the present little Work 
 is presented to the Public, 
 
 In its compilation, the greatest care has been taken to ren- 
 der the various subjects intelligible to those who harve not 
 studied mathematics, and every character which supposes the 
 reader acquainted with that science has been carefully 
 avoided. But to give the reader an idea of the appearance 
 of the most extraordinary objects described in the Work, a 
 number of neat and accurate engravings have been added, 
 illustrative of those appearances. This must be considered 
 as an advantage by the majority of that class of readers 
 
PREFACE. V 
 
 for whom the Work is intended ; and, should it be intro- 
 duced into any school or academy as a text book, where 
 Astronomy is scientifically taught, the teacher can easily 
 supply the necessary diagrams. 
 
 The subjects treated of in the Volume, comprehend the 
 substance of the Lectures which the author has been in the 
 practice of delivering, for the last ten years, to his Astrono- 
 mical Class, and were not originally intended for publica- 
 tion. But having often felt the want of a book, which he 
 could recommend to the perusal of those who wished to im- 
 prove themselves by reading on these subjects, he has been 
 induced to publish an abridgement of the Lectures themselves. 
 And to render the Work as amusing as possible, he has 
 availed himself of the labours of the most celebrated Astrono- 
 mers of the present day, particularly those of Sir William 
 Herschel and La Place. The numbers, as well as the des- 
 criptions, contained in the following pages, may, therefore, 
 be relied upon as agreeing with the latest and most accurate 
 observations. 
 
 Considerable pains have also been taken to select short 
 apposite extracts from the Poets who have celebrated Astro- 
 nomy in their works. These, it is hoped, will not only con- 
 tribute to the amusement of the reader, without diverting his 
 attention from the subjects, but that they will have a ten- 
 dency to impress them more strongly on his mind. 
 
 Such technical terms as were unavoidable, are either ex- 
 
VI PREFACE. 
 
 plained at the beginning of the Volume, or when they occur 
 in the course of the Work. 
 
 As there is no work yet extant on the same plan as the 
 present, nor one which contains so much astronomical know- 
 ledge in so little compass, it is hoped it may have some effect 
 in rendering the sublime science of Astronomy a more popu- 
 lar study than it has hitherto been. 
 
 Should it fall into the hands of any person who has already 
 made considerable progress in that science, he is requested to 
 keep in mind for what class of readers the Work is intended; 
 and that simplicity, in works of science, is the greatest 
 recommendation they can possess. 
 
CONTENTS. 
 
 Page 
 
 ON the Utility of Astronomy I 
 
 Explanation of Astronomical Terms 5 
 
 General Appearance of the Heavens 13 
 
 Of the Bodies which compose the Solar System 15 
 
 Nature of the Sun - - - - - - 16 
 
 Of the Planets - 20 
 
 Of Mercury - 21 
 
 Of Venus - - - 23 
 
 Of the Earth - - - - 2S 
 
 Of Mars - - - - - 30 
 
 Of Ceres - - - - v - - 32 
 
 Of Pallas - - - - - 33 
 
 Of Juno - - - - - 83 
 
 Of Vesta - - 33 
 
 Of Jupiter ..... 35 
 
 Of Saturn - 37 
 
 Of Uranus or Herschel - 40 
 
 The Planets, as seen through a Telescope - 41 
 
 Of Comets - - 47 
 
 Of the Moon - 53 
 
 Phases of the Moon 54 
 
 Motions of the Moon ... 58 
 
 Of the Harvest Moon 59 
 
 Apparent Size of the Moon . 61 
 
 Spots, Mountains, &c. in the Moon - 62 
 
 Of the Constellations, &c. 66 
 
 Position and Principal Stars in the Constellations : 70 
 
 Lustre and Magnitude of the Stars - 75 
 
 Of the Number of the Stars - 78 
 
 Distance of the Stars - 82 
 Nature of the Stars . .... 84 
 
 Of Eclipses. - - - 87 
 
 On Light - 93 
 
 Of the Aurora Borealis - 96 
 
 Of the Rainbow, -Parhelia, &c. - 100 
 
 Of the Atmosphere^and Astronomical Refraction - 103 
 Unusual Refractiorr-of the Atmosphere ... 107 
 
 Of the Clouds^ - 109 
 
 Motions of the Earth - 120 
 
 On the Change of Seasons - - 125 
 
 On the Regulation of Time - - 130 
 
 Of tfee Tides - 134 
 
 Of the Forces that retain the Planets in their Orbits - 140 
 
 Of the Quantity of Matter in the Sun and Planets - 144 
 
 Of the Principal Systems of Astronomy - 146 
 
 Ptolemaic System - - 148 
 
 Copernican System - - 150 
 
 Tychonic System - - - 150 
 
 Cartesian System - 155 
 
 History of Astronomy - - 156 
 
Till CONTENTS. 
 
 CONTENTS OF THE SUPPLEMENT. 
 
 Pag* 
 
 Introduction 
 
 On Astronomical Tables 1 
 On the^lianges that have happened in the Relative Situation of Double 
 
 Stars - . ;_- 3 
 
 On the great Caronae, &c. 4 
 
 On Meteoric Stones 4 
 
 Upon the Precision to be obtained with Astronomical Instruments 5 
 
 Upon the apparent Size of Objects 6 
 Upon the Meteors which surround the Earth - 8 
 
 On the Ch'ange of Place of the Fixed Stars 8 
 
 Astronomical Telescope - 9 
 
 Galilean Telescope 9 
 
 On Meteors, &c. 11 
 
 On Predicting the Weather by Signs - 13 
 
 'On the Construction of the Heavens 14 
 
 On the Use of the Telescope 15 
 Right Ascension, &c. of the Stars - 16 
 
 Hypothesis respecting the Moon 17 
 
 On the Parallax of the Fixed Stars 20 
 
 On the Method of determining the Figure of the Earth by the Pendulum 21 
 
 Time to be added to the Right Ascension of a Star, &c. 23 
 
 Water Spouts - 24 
 
 Of the Rainbow - 25 
 
 On the Line of Perpetual Congelation 27 
 
 On the manner of Regulating Public Clocks 29 
 
 On Predicting the Weather by the Barometer 32 
 On the Methods proposed for Ascertaining the Longitude, &c. of Places by 
 
 Magnetical Instruments 33 
 
 Latitudes and Longitudes of Observatories 35 
 On the Method of determining the Figure of the Earth 
 
 On the Colours of the Atmosphere 39 
 
 Table for Reducing Sidereal Time, &c. - 41 
 
 Mean Solar Time, &c. - 42 
 
 Reflecting Telescope 43 
 
 Astronomical Quadrant - 45 
 
 On Observing with the Telescope - 46 
 
 To find the Rate of Time-keepers 
 Of the Transit Instrument 
 On the Ether of Newton 
 Achromatic Telescope 
 
 47 
 47 
 49 
 
 50 
 
 Of the Mariner's Compass 53 
 
 Description of Hadley's Quadrant 55 
 
 Of the Calendar 57 
 
 Dominical Letter 57 
 
 Golden Number, &c. 59 
 
 Cycles, Epochs, &c. - 61 
 
 Astronomical Operations and Calculations . 4 
 
AS IT IS KNOWN AT THE PRESENT DAY 
 
 ON THE UTILITY OF ASTRONOMY. 
 
 ASTRONOMY is one of the most ancient and one of the most 
 pleasing branches of knowledge which has ever engaged the human 
 mind. The grandeur and sublimity of the objects it presents ele- 
 vate and improve the mind, banish low and frivolous passions, and 
 become a source of never-ceasing pleasure. 
 
 No species of knowledge that is attained by the light of nature, 
 gives higher or juster notions of the Supreme Being; no science 
 affords stronger arguments by which his existence is demonstrated ; 
 and none gives more convincing proofs of His power and wisdom ; 
 for, as David says, " the heavens declare the glory of God, and the 
 firmament sheweth his handy work." 
 
 Cicero, who was guided only by the light of reason, appears to 
 have had the same sentiments ; for " nothing," says he, " is more 
 evident, nothing is plainer, when we look up to the heavens, and 
 contemplate the celestial bodies, than that there is a Deity of most 
 excellent wisdom who governs them." 
 
 For the certainty and evidence of its demonstrations, Astronomy 
 is not inferior to Geometry : the motions of the heavenly bodies 
 being now as certainly known, and their causes as strictly demon- 
 strated, as any proposition in pure Mathematics. 
 
 The smallest stars we can see, though at an immeasurable dis- 
 tance from us, have their latitude and longitude as exactly deter- 
 mined as any place on the earth ; and the eclipses of the sun and 
 moon, the conjunctions, oppositions, and phases of the planets, are 
 calculated with the greatest precision. 
 
 " There is no science," says Dr. Keil, " in which there remains 
 fewer difficulties to be explained, objections to be answered, or 
 scruples to be removed, than in Astronomy, and no science has 
 attained so high a degree of perfection as it has ; for no philosopher 
 has ever yet discovered the figure of the small particles of matter, 
 or the texture, intervals, form, and composition, of the parts of the 
 most common plant." 
 
 Nor has any Physician yet discovered the reason of the virtues 
 and operations by which his medicines affect the human body. And 
 
 No. 1. B 
 
4 2 - ' USE OF ASTRONOMY. 
 
 in all ANIMAL and VEGETABLE bodies, the fountain and first prin- 
 ciple of LIFE and ACTION are unsearchable, and look like a mys- 
 tery far beyond the reach of our understanding, and perhaps may 
 for ever remain unknown to us. 
 
 But Astronomers (in their proper sphere) meet with no such dif- 
 ficulties, for it is no part -of their business to contemplate the 
 nature of the celestial bodies; but their motions, their magni- 
 tudes, and the various phenomena arising from their motions. 
 
 They not only determine what sort of motions the PLANETS have, 
 how large orbits they describe, and how long they take to complete 
 their revolutions, but they likewise show the crooked tracts in the 
 immense regions of space which the wandering Comets describe, 
 and give us the geometrical dimensions and properties of their orbits, 
 and the laws they observe in describing them. 
 
 Astronomy has at all times been studied by the greatest philo- 
 sophers and men of genius in every part of the world ; and the 
 most celebrated of the ancients speak of it with admiration. When 
 Anaxagorus was asked for what end he was born, he answered, 
 " To contemplate the Stars." If there is much enthusiasm in this 
 reply, we at least see with what admiration a man of genius contem- 
 plated the sublime spectacle of the heavens. 
 
 Plato had also the highest regard for this science ; for in his 
 work, entitled " Epinomis, or the Philosopher," he says, " that no 
 wise man would be ignorant of Astronomy." 
 
 This science not only contributes to the improvement of many 
 other sciences, but it is also of admirable use in strengthening the 
 mind, and arming the reason against the effects of ignorance and 
 superstition. 
 
 Every one must allow that morals would be quite vague, and 
 have but few attractions, if founded on ignorance or error. Ought 
 it then to be accounted of no value, to have the advantage of being 
 preserved from the fatal effects arising from this cause ? 
 
 Can we look without the emotions of compassion and pity on the 
 stupidity of those, who believed that by making a great noise 
 during the time the Moon was eclipsed, that it gave relief to her suf- 
 ferings., and freed her from the disease with which she was supposed 
 to be ; afflicted, and which they believed to be produced by enchant- 
 ment? 
 
 Besides these errors, which degraded the human mind, we find in 
 history many passages which show the FATAL EFFECTS arising from 
 the ignorance of this science. 
 
 Nicias, the Athenian general, had resolved to quit Sicily with his 
 army ; but an Eclipse of the Moon made him lose the favourable 
 opportunity, which was the cause of the death of the general, and 
 the ruin of his army. This disaster was so fatal to the Athenians, 
 that the decay of their country immediately followed it. 
 
 Alexander the Great was so afraid of an Eclipse of the Moon 
 before the battle of Arbella, that he ordered sacrifices to be offered 
 to the moon and to the earth, as to divinities that caused the 
 eclipse. 
 
USE OF ASTRONOMY. 3 
 
 On the contrary, we have many examples of those who possessed 
 a knowledge of Astronomy, turning that knowledge to the greatest 
 advantage, both to themselves and to their country. 
 
 When Pericles commanded the Roman fleet, there happened an 
 Eclipse of the Sun, which caused a general terror throughout the 
 fleet; even the PILOT himself was afraid. 
 
 Pericles, however, knew the true cause of the phenomenon, and 
 reasoned with the Pilot in a very familiar manner ; he took the end 
 of his mantle, and after covering the eyes of the Pilot with it, said 
 to him, " Do you believe that what I now do is a sign of misfor- 
 tune ?" " No" said the Pilot. " This is an Eclipse to YOU," said 
 Pericles, " and it differs nothing from that which has just hap- 
 pened, except in this, that the Moon being larger than my MANTLE, 
 hides the Sun from a greater number of persons.' 7 
 
 Agathocles, king of Syracuse, while engaged in a war in Africa, 
 found terror spreading through his army at the sight of a Solar 
 Eclipse ; he immediately presented himself to his soldiers, and ex- 
 plained the cause of the phenomenon, which had the effect of dis- 
 pelling their fears, and restoring order. 
 
 Many other examples of the application of astronomical know- 
 ledge may be brought from history; but those already mentioned 
 may serve to show the usefulness of Astronomy, even in affairs 
 apparently nowise connected with it. 
 
 The story of Columbus and the natives of Jamaica, is too well 
 known to require to be noticed here. 
 
 The knowledge of Astronomy has also been of great advantage in 
 exposing the absurdities of Astrology, and freeing men's minds from 
 that species of deception to which they were so long the dupes. In 
 the year 1686, all the Astronomers in Europe agreed in announcing 
 to the world a conjunction of all the Planets then known, which 
 they said would be accompanied with such dreadful effects, that 
 there would be great danger of a general overthrow, and every 
 person expected to see the end of the world. That year, however, 
 passed as others had done before it ; but a hundred other false pre- 
 dictions were not sufficient to free the ignorant and credulous from 
 the prepossessions and prejudices of their infancy. It was neces- 
 sary that a spirit of philosophy and research should spread among 
 men; that the extent and limits of NATURE should be unfolded to 
 them; and accustomed no more to fear without examination, and 
 without proof ; yet we still see, from time to time, the credulity of 
 the public, in listening to the reveries of ignorance and supersti- 
 tion. So late as the year 1736, when there happened a very 
 extraordinary HEAT, and furious wind, on the 20th October, it was 
 published in all the Gazettes that the Sun had returned, or gone 
 back to the tropic of Cancer. This was so generally believed, that 
 it became necessary for the learned to take the trouble of unde- 
 ceiving the public. About the end of the year 1768 too, every 
 person believed the Planet Saturn lost; and it was even published 
 in the most sensible periodical publications, and talked of in the 
 most cultivated companies. 
 
 B2 
 
4 USE OF ASTRONOMY. 
 
 Comets were, above all, one of the greatest objects of terror ; 
 but a knowledge of Astronomy has shown these fears to be ground- 
 less, and has even dispelled them from the minds of the most 
 ignorant. 
 
 But it is not only in this way that Astronomy has rendered itself 
 useful : it has been serviceable to mankind in many different ways. 
 It is well known that Geography and Navigation are so intimately 
 connected with Astrpnomy, that they cannot be separated, and that 
 all the improvements and discoveries in these branches of knowledge 
 are entirely owing to the science of Astronomy. 
 
 ^X T ne observation of the altitude of the Pole Star, first taught men 
 that the Earth was round ; and Eclipses of the MOON first served 
 to make known the Longitude of places. " We should not know," 
 said Hypparchus, " whether Alexandria be to the North or South 
 ' of Babylon, without the observation of Climates ; and we cannot 
 know whether a country be East or West of another, without the 
 observation of Eclipses." 
 
 We find also by the Alcoran, that travellers in crossing the desert 
 of Arabia took certain stars for their guides ; for it is there said, 
 that " God has given you the stars to serve you as guides, whether 
 you t(e upon the land or the water." 
 
 s* The discovery of Jupiter's Satellites has given greater perfection 
 $o our geographical and marine charts, than could have been done 
 for a thousand years by voyages and travels; and when their 
 theory shall be rendered still more complete by multiplied observa- 
 tions, the method of finding the longitude will be both more easy 
 and more accurate. 
 
 The improvements which have been made in geography since 
 accurate observations began to be made in Astronomy, will be best 
 understood by mentioning an example or two. 
 
 The length of the Mediterranean Sea was unknown till the be- 
 ginning of the seventeenth century, but is now as well known as 
 the length of Great Britain. 
 
 The difference of Longitude between Cairo, and Toledo in Spain, 
 is stated, in the geography of Gemma Trisius, (published 1530,) to 
 be 53 instead of 34 36' ; and other distances are exaggerated in 
 the same manner. 
 
 Till the year 1769, there were three or four degrees uncertain on 
 the length of the CASPIAN and BLACK Seas ; and before the same 
 year there was an error of half a degree in the Longitude of 
 Gibraltar. 
 
 America was unknown till the year 1502 ; and its discovery 
 js solely to be attributed to the knowledge of Astronomy possessed 
 by Columbus. 
 
 It appears he had an intimate acquaintance with the doctrine of the 
 Sphere, which gave him that confidence which prompted him to 
 direct his course to the westward, certain of either coming on the 
 east continent of Asia, or of discovering a new one. If any thing 
 yet remains for the improvement and security of navigation, it is an 
 Easier and more expiditious method of finding the longitude at sea. 
 
USE OF ASTRONOMY. 5 
 
 There is at present a method of performing this with great ac- 
 curacy, by means of measuring the distance between the sun and 
 moon, or the moon and a star ; and if seamen knew a little of 
 Astronomy, they never could be deceived above ten leagues, whilst 
 they are sometimes more than 200 uncertain, on ordinary voyages, 
 such as going to America and the West Indies. 
 
 The uncertainty that Lord Anson was in, respecting the situation 
 of the island of Juan Fernandez, made him keep the sea much 
 longer than would have been necessary, had not this been the case, 
 winch might have saved the lives of seventy or eighty of his men. 
 But accidents even more fatal than this have been occasioned by 
 errors of a similar kind. 
 
 The advantages of navigation to the success of a nation prove in 
 a very convincing manner the usefulness of Astronomy. 
 
 The trade and prosperity of Great Britain, as well as her success 
 at sea in war, shows that the Navy alone can decide the fate of 
 Empires and give to a nation both wealth and power ; for, as 
 M. le Meire says, " The TRIDENT of Neptune is the Sceptre of the 
 world/' 
 
 Agriculture formerly borrowed from Astronomy most of its 
 rules and indications ; for Job, Hesiod, Verron, Eudoxus, Aratus, 
 Ovid, and Pliny, furnish us with proofs of this ; the HELIACAL 
 rising or setting of the Pleiades, of Arcturus, Orion, and Sirius, 
 gave to the Greeks and Egyptians the signal for different kinds of 
 work. 
 
 For example : the rising of Sirius announced to the Greeks the 
 tim6 of harvest, and to the Egyptians the overflowing of the Nile. 
 
 Ancient Chronology receives, from the knowledge and calculation -*- 
 of Eclipses, the most certain points, or epochs, that it is possible 
 for us to have. The Chronology of the Chinese is all founded on 
 Eclipses of the Sun and Moon ; and if there had always been. 
 Astronomers in the world, there would be no uncertainty in the date 
 of any remarkable event mentioned in history. 
 
 It is by an Eclipse of the Moon that an error has been discovered 
 in the date or commencement of the Christian era, or birth of Jesus * 
 Christ. We know that Herod was king of Judea; and we are 
 informed by Josephus, that there was an Eclipse of the Moon im- 
 mediately before the death of Herod. Now we find that this 
 Eclipse happened in the night of the 12th or 13th of March, four, f X_ 
 years before the commencement of the yulgar era ; therefore that era 
 ought to be put back three years at least. 
 
 It is also by knowing that an Eclipse of the Sun can only happen jf~^. 
 at the time of NEW MOON, and that he can only be totally eclipsed 
 for a few minutes (7^), that Christians are convinced that the dark- 
 ness which took place at the crucifixion of Jesus Christ was super- 
 natural ; for this event took place at the time of the Jews' PASS- 
 OVER, which was kept at the time of FULL MOON. 
 
 It is likewise by means of Eclipses of the Sun, that Castor fixed 
 the termination of the war between the Lydians and Medes to the 
 
6 USE OF ASTRONOMY. 
 
 year 603 before our era ; and the expedition of Xerxes against 
 Greece to the year 478, which is commonly fixed to 480 before our 
 era. Sir I. Newton too has made use of Eclipses in settling the 
 dates of many disputed parts of Grecian history. Abbe Barthelemy 
 has likewise employed the same means to settle some uncertain 
 dates which occur in the history of Greece. 
 
 Another important use of Astronomy is, to furnish us with the 
 means of dividing time, and of regulating our clocks and watches, 
 which is a matter of much greater importance than many are aware 
 of; for the multitude of our affairs, and the necessity for exactness 
 in most of them, have rendered accuracy in the division of time 
 absolutely necessary. Now this cannot be accomplished any other 
 way than by comparing the motion of our timekeepers with the 
 motions of the celestial bodies. 
 
 Meteorology, or the knowledge of the changes of the air, such as 
 winds, rains, droughts, &c. have certainly a very material and im- 
 mediate effect on the state of the human body. It is, therefore, 
 highly probable, that Astronomy would be of very great use in 
 determining these effects, if we could discover the physical influence 
 of the Sun and Moon on the atmosphere, and the changes produced 
 in that fluid by those bodies. It is well known that the Moon not 
 only raises the waters of the ocean twice every day, but that she 
 has considerable effect on the state of the atmosphere. This has 
 led several eminent physicians, such as Mede, Hoffman, &c. to be- 
 lieve that there may be some connection between the Moon and 
 medicine ; but whether this be the case or not, it is well known that 
 the state of the weather has a very material effect on the human 
 body. 
 
 "But," as Fontenelle says, " though astronomy should not be abso- 
 lutely necessary for the purposes of geography, navigation, and even 
 for the cultivation of divinity, yet it is highly worthy of the attention 
 of every rational being, for the noble and sublime spectacle which it 
 presents to the mind." 
 
 " There are," says the same author, " in some deep mines many 
 poor ignorant creatures who have been born there, and have even 
 . lived and died there, without ever once having seen the Sun." 
 Such is nearly the condition of those who are ignorant of the nature, 
 order, and course of those glorious orbs, which roll above their 
 heads, to whom the greatest beauties of the heavens are unknown, 
 and who have not light enough to enjoy the universe. 
 
 To those who love the writings of the ancients, whether histo- 
 rians or poets, a knowledge of astronomy will be found extremely 
 useful. Since it is proved that all the mythology of antiquity took its 
 rise from astronomical symbols and allegories, and that the writings 
 of the ancients abound with allusions to these symbols and allego- 
 ries, it is evident that an acquaintance with astronomy is necessary, 
 in order to understand these writings. 
 
 The poets who have described Greece and Italy, and whose 
 works are sure of immortality, all loved and knew astronomy. Some 
 
USE OF ASTRONOMY. 7 
 
 of them have even made so frequent use of it, that it is impossible 
 to understand their works without possessing some acquaintance 
 with astronomy. Among the Greeks who have introduced this sub- 
 ject into their writings, may be mentioned Homer, Hesiod, and 
 Aratus; among the Latins, Lucretius, Horace, Virgil, Lucian, Me- 
 nelaus, and Claudien. The particular passages it is unnecessary to 
 mention, as every one who looks into these authors will find many 
 passages of this description. 
 
 The knowledge of the heavens has often been the source of many 
 beauties in the works of the ancients, and we rarely find among 
 them that strange ignorance of astronomy, which disgrace some 
 modern works. 
 
 The respect that has always been paid to celebrated astronomers 
 in every country where they have appeared, is a very convincing 
 proof of the high esteem in which this science has always been 
 held. 
 
 The ancient Kings of Persia, and the Praetors of Egypt, rank 
 among the greatest of the ancient astronomers. The Kings of Lace- 
 demon kept astronomers in their councils, and Alexander the Great 
 had them in his suit in all his military expeditions; and we are informed 
 by Aristotle, that he would do nothing of moment without their 
 advice. It is true, that the taste for predictions was carried too 
 far by the astronomers of those days ; but true astronomy profited 
 very much by their labours. 
 
 It is well known how much Ptolemy Philodelphus the Second, 
 King of Egypt, favoured astronomy ; and we find that in his time 
 there flourished many celebrated astronomers, among whom were 
 Hypparchus, Apollonius, Aratus, Bian, and Theocritus. 
 
 Julius Caesar piqued himself very much on his knowledge of 
 astronomy ; and we see by his reformation of the calendar, that he 
 was well acquainted with the subject. 
 
 We find also that the Emperor, Claudius Caesar, was well ac- 
 quainted with astronomy, for he calculated an eclipse which was to 
 happen on the anniversary of his birth; and fearing that it would 
 occasion at Home consternation, and perhaps tumult, he published 
 an advertisement, in which he explained the causes of such a phe- 
 nomenon. 
 
 Many other princes might be mentioned who have cultivated 
 astronomy; such as Adrian, Constantine, Charlemagne, Leon the 
 Fifth, &c. ; but these will be noticed in treating of the improvements 
 and discoveries which have taken place in this science at various 
 periods. 
 
EXPLANATION OF ASTRONOMICAL TERMS 
 
 PREVIOUS to entering upon a description of the motions and ap- 
 pearances of the various bodies that are to be seen on turning our 
 eyes to the heavens, it may be necessary to give a short explanation 
 of some of the terms which most frequently occur in Astronomy,* in 
 order that the reader may be the better enabled to understand what 
 follows. 
 
 1. A Sphere, or Globe, is a solid body, perfectly round, or having every 
 part of its surface equally distant from a point within it, called its centre. 
 
 2. The Diameter of a Sphere is any straight line passing through the 
 centre, and limited on each side by the surface of the sphere. 
 
 3. The Radius of a Sphere, or Circle, is half the diameter. 
 
 4. The Circumference of a Sphere, or Circle, is the line which goes quite 
 round it. 
 
 5. A great Circle divides the surface of the sphere into two equal parts, 
 or hemispheres. 
 
 6. A small Circle divides the sphere into two unequal parts ; the one 
 greater, and the other less than a hemisphere. 
 
 7. The Plane of a Circle is the surface or superfices contained within its 
 circumference, as the level or flat surface which would appear on cutting 
 a sphere through, at any circle drawn upon it. This surface, extended or 
 continued to any distance beyond the circumference of the circle, would 
 still be in the plane of the circle. 
 
 8. Degrees, fyc. All circles, whether great or small, are supposed to be 
 divided into 360 equal parts, called degrees ; each degree into 60 equal 
 parts, called minutes ; and each minute into 60 equal parts, called 
 seconds, &c.f 
 
 9. An Angle is the inclination of two lines which meet in a point, and 
 is always some part of a circle ; that is, contains a certain number of 
 degrees, minutes, &c. 
 
 10. A Right Angle is the fourth part of a circle, or 90, and is formed 
 by making one line perpendicular to another. 
 
 11. An Acute Angle is less than a right angle ; and an Obtuse one is 
 greater. 
 
 * The present work being of a popular nature, it is only necessary to explain 
 here such terms as occur in the following pages. 
 
 t Degrees are always marked thus (), minutes ('), and seconds ("). 
 
EXPLANATION OF ASTRONOMICAL TERMS. 9 
 
 12. A Rectilineal Angle is an Angle which is formed by straight lines ; 
 and a Spherical Angle by curve lines. Most of the angles connected with 
 astronomy are spherical angles. 
 
 13. The Equinoctial is a great circle in the heavens, equidistant from both 
 poles, and right over the equator of the earth. 
 
 14. The Ecliptic is that great circle in the heavens, in which the earth 
 performs its annual revolution round the sun ; half of it being on the north 
 side of the equinoctial, and the other on the south. 
 
 15. The Obliquity of the Ecliptic is the angle formed by the intersection ^ 
 of the equinoctial and the ecliptic ; at present this angle is 23 27' 46" ; but 
 it is subject to a small change. Since it was first observed it has been 
 diminishing at the rate of '52 in a century. 
 
 16. The Equinoctial Points are those two opposite points in the heavens, I 
 where the ecliptic and equinoctial cross each other. 
 
 17. The Zenith is the highest point of a sphere, or that point of the heavens 
 directly over the head of the spectator. 
 
 18. The Nadir is that point of the heavens directly opposite to the 
 Zenith, or under the feet of the spectator. 
 
 19. The Zodiac is a zone, or belt of about 16 broad, which surrounds 
 the heavens ; and in the middle of it is the Ecliptic, or orbit of the earth. 
 It also includes the orbits of all the planets, except those discovered since \ 
 the year 1800. 
 
 20. Tlie. Precession of the Equinoxes is a change of the equinoctial 
 points. These points are found to move backwards 50| seconds every year, 
 or one degree in 72 years ; so that in about 25,920 years, they return 
 again to the same points in the heavens, performing what is called the 
 grand Celestial Period. The retrograde motion of these points is caused 
 by the action of the sun and moon upon the earth, in consequence of its 
 spheroidical figure. * 
 
 21. Meridians are great circles in the heavens, perpendicular to the 
 equinoctial, and passing through its poles. 
 
 22. The Horizon is that great circle which is equally distant from the 
 zenith and nadir, and which divides the visible from the invisible hemis- 
 phere. This is called the Rational Horizon, to distinguish it from the 
 Sensible Horizon, a small circle which terminates the view of the spectator, 
 when placed at any point of the earth's surface. 
 
 23. Vertical Circles are great circles which pass through the zenith and 
 nadir, and cut the horizon at right angles. 
 
 24. The. Altitude of a Celestial Body is its height above the horizon, 
 reckoned on the vertical circle which passes through it ; and its meridian 
 altitude is the altitude when it is on the meridian. 
 
 25. The Parallax of .any celestial object is the diiference of its angular^ 
 position as it would be seen from the centre of the earth, and as it is seen from 
 a point on the surface of the earth. This is called the diurnal parallax, to- ) 
 distinguish it from the annual parallax, which is the diiference between the 
 apparent places of an object in the heavens, when seen from the earth in 
 opposite points of its orbit. 
 
 * The motion of these points backward, makes the fixed stars appear to move 
 forward an equal quantity, their longitude and right, ascension being reckoned 
 from one of those points, which is called the vernal equinox. 
 
10 
 
 EXPLANATION OF ASTRONOMICAL TERMS. 
 
 26. The Orbit of a Planet or Comet is the path or. tract in which it per- 
 forms its revolution. The orbits of all the primary planets are elliptical or 
 oval, with the sun situated in one of the foci, as at S (Fig. 1.)* 
 
 When the planet is at P, it is then nearest the sun, and is said to be in 
 its Perihelion. In moving from P, its distance from the sun gradually in- 
 creases till it reaches the opposite point A, when it is at its greatest distance 
 from the sun, and is then said to be in its Aphelion. When it arrives at the 
 points B and D, it is at its mean distance. 
 
 The straight line A P, which joins the perihelion and apjielian, is called 
 the line of the apsides, and sometimes the greater axis of the orbit; and 
 the line Si), which joins the points of mean distance, the lesser axis ; the 
 line S B or S D the planet's mean distance from the sun ; S C or F C the 
 eccentricity of the orbit, or the distance of the sun from its centre ; S the 
 lower Focus, or that in which the sun is placed ; F the higher Focus ; P the 
 lower Apsis ; and A the higher Apsis. 
 
 27. Although the Primary planets have all nearly the same common 
 focus in which the sun is situated, yet they have not all the same degree of 
 ellipticity. Most of them deviate but little from the circular form, and 
 none of them so much as the above figure. They likewise lie in different 
 or planes, make angles with each other. 
 
 28. If the Ecliptic, or earth's Orbit, be supposed to be a thin solid plane 
 extended in every direction, it would be called the plane of the ecliptic ; 
 and if the orbit of any other planet were extended in a similar manner, it 
 
 ^ would be called the plane of that planet's orbit. Now the orbits of all the 
 ) planets lie in planes different from that of the ecliptic ; and this difference, 
 ) or the angle which any orbit makes with the ecliptic, is called the inclination 
 ( of that orbit.f 
 
 ( One half of each orbit is on the one side of the ecliptic, and the other 
 C half on the other side; consequently it must cross the ecliptic in two 
 
 r * If the two ends of a thread be tied together, and thrown loosely over two 
 pins stuck in a table, as S and F, and if the thread be moderately stretched 
 by the point of a pen, or black-lead pencil, and carried round the pins by an 
 even motion, and slight pressure of the hand, an ellipsis or oval will be described ; 
 and the points S and F, where the pins were fixed, are called the foci, or focuses 
 of the ellipsis. The figure described will be the more elliptical, the tighter the 
 thread is to the pins in the foci. 
 
 t The orbit of Mercury is inclined 7 to the plane of the ecliptic ; Venus 3 23'; 
 Mars 1 51'; Jupiter 1 19'; Saturn 2 30'; Uranus 46$'; Ceres 10 37'; 
 Pallas 34 50' ; Juno 21 ; and Vesta 7 9'. The orbits of the first five of these, 
 as well as that of Uranus, or what are called the old planets, are all included in 
 the Zodiac; but the orbits of the last four, or the new planets, are without the 
 Zodiac. 
 
EXPLANATION OF ASTRONOMICAL TERMS. 11 
 
 opposite points. These points are called the planet's nodes. * These nodes ) 
 are all in different parts of the ecliptic ; and therefore if the planetary 
 tracts remained visible in the heavens, they would in some measure re- 
 semble the different ruts of waggon-wheels on a road, after crossing each 
 other, but never going far asunder. 
 
 29. While the primary planets are performing their revolutions round 
 the sun, and the secondaries round their primaries, they have aH a motion 
 from west to east, round an imaginary line passing through their centre, 
 called their r or5Tlh some of the planets this axis is nearly perpendicular to 
 the plane of its orbit ; and in others it is inclined to the plane of its orbit. 
 On this depends the change of seasons in the planet ; for the smaller the 
 angle which the axis of any planet makes with the plane of its orbit, the 
 greater is the variety of its seasons. 
 
 30. The extremities of the axis is called the poles; and that which 
 points towards the northern part of the heavens is called the north pole ; 
 and the other, pointing towards the southern part, is called the south pole. 
 
 31. As it is necessary to have some method by which the position of 
 any celestial bodyjnay be determined ^at any time, or its distance from 
 some known point* astronomers have fixed on the, ecliptic for this purpose, 
 as well as for reckoning from it, the inclination of the planetary orbits. 
 
 The line of the equinoxes, or that line which joins the equinoctial points, 
 being always in the plane of the ecliptic, must mark out two points of that 
 line traced among the fixed stars; and frjpm,one of these points astronomers 
 reckon distances on the ecliptic. This point is called the vernal equinox, 
 because the sun appears in it in the spring, about the 20th of March; 
 its opposite is called the autumnal equinox, because the sun arrives at it 
 about the middle of autumn, or the 23d of September. 
 
 32. The Ecliptic is supposed to be divided into twelve equal parts, called 
 signs, each of which occupy a space of 30 degrees. 
 
 33. Tbo^Longititde of all the celestial bodies is reckoned eastward, on 
 the ecliptic, from the vernal equinox quite round the heavens, and conse- 
 quently may amount to nearly 360 degrees. 
 
 The Latitudes of the celestial bodies is reckoned from the ecliptic, north 
 and south ; but their declination is reckoned from the equinoctial, in a similar 
 manner. 
 
 34. TJie .Right Ascension of the celestial bodies is reckoned on the equi- 
 noctial^ from the vernal equinox, eastward, quite round the heavens. 
 
 35. Instead of the Vernal Equinox, astronomers sometimes find it con- 
 venient to count the distance of a planet from its aphelian, (as from A, in 
 the foregoing figure.) This distance is called the true anomaly of the 
 planets. 
 
 36. An imaginary line, drawn from the sun to a planet, in any point of 
 its orbit, as S B, is called the radius vector, or great radius. This line has 
 the property of describing equal areas of the orbit, in equal portions of s 
 time.f 
 
 37. The Elongation of a Planet is its angular distance J from the sun, 
 as seen from the earth. 
 
 * The node, where the orbit ascends above the ecliptic, is called the ascending 
 node ; and the other the descending node. 
 t This was discovered by Kepler, and is called his second law. 
 t By angular distance is meant any distance in degrees, minutes, &c. 
 
12 EXPLANATION OF ASTRONOMICAL TEKMS. 
 
 38. The Opposition of two celestial bodies takes place when they are in 
 opposite points of the heavens, as viewed from the earth ; and their Con- 
 junction when they appear in the same point. These points are also some- 
 times termed the syzygies, especially when the bodies are the sun and 
 moon ; And when a planet is between the sun and the earth, at the time 
 of conjunction, it is called its inferior conjunction; but when the sun is 
 
 ! between the earth and the planet, it is called its superior conjunction. 
 39. The Geocentric Place of a Planet, means its place as seen from the 
 earth, and its Heliocentric place as seen from the sun. 
 40. The Direct Motion of a Planet is its motion in the order of the signs, 
 as from Aries to Taurus, &c. ; when it moves in a contrary direction, it is 
 ! said to have a retrograde motion. 
 
 41. The Occultation of a Star or Planet is its obscuration by the moon, 
 or other planet, coming between it and the earth. 
 
 42. By the Siderial Revolution of a Planet is meant the time it requires 
 to move from any fixed star to the same again. 
 
 43. The Disc of the Sun, or a Planet, is its face, which appears flat on 
 account of its immense distance.* 
 
 44. Aberration is an apparent motion or change of place in the heavenly 
 bodies, occasioned by the progressive motion of light, combined with the 
 earth's annual motion in its orbit. 
 
 45. Nutation, or Deviation, is a small inequality which has been ob- 
 served in the precession of the equinoxes, which makes the fixed stars 
 appear to change their positions about 9" of a degree. 
 
 46. Evection is an inequality in the motion of the moon, by which at or 
 near the time of her first and third quarter she is not in the line drawn 
 through the centres of the earth and sun, as she is at the time of new and 
 full moon. This inequality sometimes amounts to 2 51'. 
 
 47. Nebufa are clusters of small stars, which have been chiefly disco- 
 vered by the telescope. They have received this appellation from their 
 cloudy appearance. 
 
 Macula are dark spots which are frequently seen upon the disc of the 
 sun. 
 
 48. Facul<e are certain bright spots frequently seen on the disc of the sun. 
 
 49. Centrefugal Force is that force by which a revolving body endeavours 
 to recede or fly oft' from the orbit or path in which it revolves. 
 
 50. Centripetal Force is that force by which a body is drawn towards the 
 centre of the path or orbit it describes, and prevents it from flying oft'. 
 
 51. Penumbra, a faint shadow which borders the dark shade produced by 
 an eclipse. 
 
 52. Digit, the twelfth part of the sun or moon's diameter. 
 
 * When any planet appears on the face of the sun, it is said to transite his 
 disc. 
 
13 
 
 GENERAL APPEARANCE OF THE HEAVENS TO 
 THE NAKED EYE. 
 
 We, tho' from Heav'n remote, to Heav'n will move 
 With strength of mind, and tread the abyss above : 
 And penetrate, with an interior light, 
 Those upper depths, which nature hid from sight. 
 Pleas'd we will be to walk along the sphere 
 Of shining stars, and travel with the year. 
 To leave this heavy earth, and scale the height 
 Of Atlas who supports the heav'nly weight: 
 To look from upper light, and thence survey 
 Mistaken mortals wand'ring from the way. 
 
 Ovid's Metamorphosis, Book xv. 
 
 THE first and most obvious phenomenon of the heavens is the 
 daily rising of the Sun in the east, and his setting in. the west; after 
 which the moon and stars appear still keeping the same westerly 
 course, till we lose sight of them altogether. By attending to these 
 
 2. C 
 
14 APPEARANCE OF THE HEAVENS. 
 
 appearances, it must soon be perceived that neither the gun nor the 
 moon rises or sets in the same place. If we begin to observe the sun 
 about the middle of March, he will appear to rise every day sensibly 
 more to the northward than he did the day before, to continue longer 
 above the horizon, and to be more elevated at mid-day. This con- 
 tinues to be the case till the 20th of June, when he begins to move 
 backward in the same manner ; and this retrograde motion continues 
 till the 22d of December, when he begins again to move forward, 
 and so on.* 
 
 The motion of the Moon through the heavens, and her appearance 
 at different times, are still more remarkable. When the moon first 
 becomes visible to us, she is called new moon, and appears in the 
 western part of the heavens, at ho great distance from the sun. 
 Every night she increases in size, but removes to a greater distance 
 from the sun, till at last she appears in the eastern part of the hea- 
 vens, just at the time he disappears in the western. 
 
 The western sun withdraws : meanwhile the moon, 
 Full orb'd, and breaking thro* the scatter'd clouds, 
 Shews her broad visage in the crimson'd east. 
 
 THOMSON. 
 
 After this, she gradually moves farther to the eastward, and, there- 
 fore, rises every night later than the preceding night; till at last she 
 seems to approach the sun as nearly in the east as she did in the 
 west, and rises only a little before him in the morning, as in the first 
 part of her course she set in the west not long after him. 
 
 All these appearances take place in the space of a month ; after 
 which they begin again in the same order as before. They are not, 
 however, at all times regular ; for at some seasons of the year the 
 moon appears to differ little in the time of her rising for several nights 
 together, and at others the difference is very considerable. But this 
 will be more fully stated, and the cause explained, when describing 
 what is called the harvest moon. 
 
 In contemplating the stars in a clear night, they all appear at the 
 same distance from us, and therefore seem to be situated in the con- 
 cave surface of a sphere, having the eye for its centre. But when 
 we view them for a considerable time, we find that they change their 
 positions relatively to the objects on the earth, although they still 
 retain their positions relatively to one another, and that they all seem 
 to make progress towards the west, where some of them disappear 
 under the horizon, while others again appear to come above that 
 circle in the east. It will also soon be observed, that many of the 
 stars never go below the horizon at all, but seem to turn round an 
 immoveable point, near which is placed a single star, called the Pole 
 Star.f This point is more or less elevated according to the different 
 parts of the earth from which it is viewed. The inhabitants of Lap- 
 
 * This is only the case in the northern hemisphere, which is the one here 
 alluded to. 
 
 t For an explanation of Astronomical terms, see page 8. 
 
OF THE SUN. 15 
 
 land, for example, see it more elevated above their horizon than the 
 inhabitants of Great Britain ; they see it more elevated than the in- 
 habitants of Spain and Italy ; and they see it still more t4evated tnan 
 the inhabitants of the West India Islands. By continually proceed- 
 ing southward, this star will seem depressed to the horizon, and at last 
 lost sight of altogether ; but another point will appear directly oppo- 
 site to it, round which the stars in the southern hemisphere will ap- 
 pear to turn. There is, however, no star so near this point as in the 
 northern hemisphere ; neither are the stars so numerous in the southern 
 as in the northern half of the heavens. 
 
 The general appearance of the heavens is, therefore, that of a vast 
 concave sphere, turning round two fixed points once in twenty-four 
 hours. 
 
 These are Thy glorious works, Parent of Good ! 
 
 Almighty ! Thine this universal frame, 
 
 Thus wondrous fair ! Thyself how wondrous then ! 
 
 Unspeakable ! who sit'st above the heavens, 
 
 To us invisible, or dimly seen 
 
 In these Thy lowest works ; yet these declare 
 
 Thy goodness beyond thought, and power divine ! 
 
 MILTON. 
 
 OF THE BODIES WHICH COMPOSE THE SOLAK 
 SYSTEM. 
 
 THE SUN. 
 
 Hail, amiable vision ! every eye 
 
 Looks up and loves thee ! every tongue proclaims 
 
 'Tis pleasant to behold thee ! 
 
 FAWCETT. 
 
 O Sun ! 
 
 Soul of surrounding words ! in whom best seen 
 Shines out thy Maker ! 
 'Tis by thy secret, strong, attractive force, 
 As with a chain indissoluble bound, 
 Thy system rolls entire. 
 Informer of the planetary train ! 
 Without whose quick'ning glance their cumbrous orbs 
 Were brute unlovely mass, inert and dead, 
 And not, as now, the green abodes of life ! 
 
 THOMSON. 
 
 Of all the celestial bodies, the Sun is certainly the most wonderful. 
 It is the fountain of light which illuminates the world ; it is the cause 
 of that heat which maintains the productive power of nature, and 
 makes the earth a fit habitation for man ; it is the central body of the 
 planetary system, and is so far superior in lustre to all other celestial 
 bodies, that they disappear in its presence. 
 
 No stars besides their radiance can display 
 In Phoebus' presence, the dread lord of day ; 
 Ev'n Cynthia's self, tho' regent of the night, 
 Is quite obscur'd by his emergent light. 
 
 C2 
 
16 OF THE SUN. 
 
 The sun is the largest body yet known in the universe ; its diameter 
 being 887,693 English miles, its circumference 2,800,000, and its 
 bulk about 1 ,400,000 times that of the earth. The quantity of matter 
 compared with that of the earth has also been stated by La Place to 
 be 337,422 times that of the earth. 
 
 The ancients believed that the sun, and all the other celestial bo- 
 dies, moved round the earth as their common centre ; but since the 
 days of Copernicus, this supposition has been daily losing ground, 
 and has now completely given way to the more rational and well- 
 established theory, taught by all the astronomers of the present day ; 
 namely, that the sun is the centre of the orbits of all those bodies 
 which compose the solar system. 
 
 Hither as to their fountain other stars 
 Repairing, in their golden urns draw light, 
 And hence the morning planet gilds her horns. 
 By his magnetic beam he gently warms 
 The universe, and to each inward part, 
 With gentle penetration, though unseen, 
 Shoots genial virtue even to the deep. 
 
 MILTON. 
 
 It has, however, been discovered that the sun has a motion on its 
 axis, which is completed in about 25 days 10 hours, as appears from 
 the maculae, or spots, which have been discovered on his disc by 
 means of the telescope. 
 
 Besides this motion round his axis, the sun has a small motion 
 round the centre of gravity of the system ; but if he has any motion 
 in the immensity of space, it must be exceedingly small, as it has 
 never yet been discovered. As for the apparent annual motion of 
 this great luminary round the earth, it can easily be shown, that the 
 real annual motion of the earth round the sun is quite sufficient to 
 cause such an appearance. 
 
 NATURE OF THE SUN. 
 
 For many ages the sun was believed to be a globe of fire ; but the 
 majority of modern astronomers have rejected this opinion, and se- 
 veral of them have published very ingenious hypotheses on this cu- 
 rious subject. One of the most plausible and ingenious theories on 
 this subject is given by Dr. Herschel in the Philosophical Transac- 
 tions of the Royal Society. He supposes the sun has an atmosphere 
 resembling that of the earth, and that this atmosphere consists of va- 
 rious elastic fluids, some of which exhibit a shining brilliancy, while 
 others are merely transparent. Whenever the luminous fluid is re- 
 moved, the body of the sun may be seen through those that are 
 transparent. In like manner, an observer placed in the moon will 
 see the solid body of the earth only in those places where the transpa- 
 rent fluids of our atmosphere will permit him. In others, the opaque 
 vapours will reflect the sun's light, without permitting his solid body 
 to be seen on the surface of our globe. 
 
OF THE SUN. 
 
 17 
 
 In lh same manner the Doctor illustrates the various appearances 
 of spots in the sun, some of which have the following forms : 
 
 Such appearances, he thinks, may be easily and satisfactorily ex- 
 plained, if it be allowed that the real solid body of the sun itself is 
 seen on these occasions, though we seldom see more than its shining 
 atmosphere. He apprehends that there are considerable inequalities 
 in the surface of the sun, and that there may be elevations, not less 
 than 500 or 600 miles in height; that a very high country, or chain 
 of mountains, may oftener become visible by the removal of the ob- 
 structing fluid than the lower regions, on account of its not being so 
 deeply covered by it. In the year 1779, the Doctor observed a spot 
 on the sun large enough to be discerned by the naked eye ; for it 
 extended more than 50,000 miles. The following are sections of 
 these, with their various formations of nuclei and umbrae: 
 
 He also says, that he observed a fine large spot in 1783, which he fol- 
 lowed up to the edge of the sun's limb ; that he plainly perceived it to 
 be depressed below the surface of the sun, and that it had very broad 
 shelving sides. This appearance, he says, may be explained by a 
 gentle and gradual removal of the shining fluid which permits us to 
 see the globe of the sun. The Doctor also says, that on the 26th of 
 August, 1792, he examined the sun with several powers, from 90 to 
 500, and that it evidently appeared that the black spots were the 
 opaque ground, or body of 'the sun ; and that the luminous part was 
 an atmosphere, which, being interrupted, or broken, gave a transient 
 glimpse of the sun himself. He farther adds, that with his seven 
 feet reflector, which was in excellent perfection, he could see the 
 spots, as on former occasions, with the same telescope, much de- 
 pressed below the surface of the luminous part. On the 8th of Sep- 
 tember, 1792, he made a small speculum, which he brought to a per- 
 fect figure on hones, without polish ; this had the effect of stifling a 
 great part of the sun's rays ; and on this account the object speculum 
 admitted a greater aperture, which enabled him to see with more 
 comfort and less danger. He then discovered that the surface of 
 the sun was unequal, many parts of it fyeing elevated, and others de- 
 pressed : but this inequality was in the shining surface only ; for he 
 
18 OF THE SUN. 
 
 thinks the real body of the sun can seldom be seen otherwise than in 
 its black spots, which resemble the following : 
 
 As light is a transparent fluid, it may not be impossible that 
 the sun's real surface may be now and then perceived; as the 
 shape of the wick of a candle may sometimes be seen through its 
 flame, or the contents of a furnace in the midst of the brightest glare 
 of it. But this the Doctor thinks can only happen where the luminous 
 matter of the sun is not very accumulated. 
 
 From these appearances Dr. H. draws the following conclusions : 
 that the sun has a very extensive atmosphere, which consists of va- 
 rious elastic fluids, that are more or less lucid and transparent, and 
 that the lucid one is that which furnishes us with light ; that the ge- 
 neration of this lucid fluid on the solar atmosphere is a phenomenon 
 similar to the generation of clouds in our atmosphere, which are pro- 
 duced by the decomposition of its constituent elastic fluids ; but with 
 this difference, that the continual and very extensive decompositions 
 of the elastic fluids of the sun are of a phosphoric nature, and attended 
 with lucid appearances, by giving out light. To the objection that 
 such decompositions, and consequent emissions of light, would ex- 
 haust the sun, Dr. H. replies, that, in the decomposition of phos- 
 phoric fluids, every other ingredient except light may return to the 
 body of the sun ; and, besides, the exceeding subtilty of light is such, 
 that, in ages of time, its emanation from the sun cannot very sensibly 
 lessen the size of so great a body. 
 
 From the atmosphere, the Doctor next proceeds to state that the 
 body of the sun is opaque, of great solidity, and its surface diversified 
 with mountains and valleys ; that the sun is nothing else but a large, 
 eminent, lucid planet, evidently the first, or, strictly speaking, the 
 only primary one of our system, all others being truly secondary to it. 
 Its similarity to the other globes of the solar system, with regard to 
 its solidity, its atmosphere, and its diversified surface, the rotation on 
 its axis, and the fall of heavy bodies, lead to the supposition that it is 
 inhabited, like the rest of the planets, by beings, whose organs are 
 adapted to the peculiar circumstances of that vast globe. Should it 
 be objected that the heat of the sun renders it unfit for a habitable 
 world, Dr. H. answers, that heat is produced by the sun's rays only 
 when they act on a calorific medium, and that they are the cause of 
 the production of heat by uniting with the matter of fire which is con- 
 tained in the substances that are heated. The Doctor also suggests 
 other considerations intended to invalidate the objection ; but these 
 are too abstruse and extended to be given in this work. 
 
 After the Doctor thinks he has shown that the heat of the sun is 
 not so great as to prevent it from being inhabited, he then deduces 
 
OF THE SUN. 19 
 
 from analogy a variety of arguments to confirm the notion of the sun 
 being a habitable body ; and then infers, that, if the sun be capable 
 of accommodating inhabitants, the other stars, which are suns, may 
 be appropriated to the same use ; and thus, says he, we see at once 
 what an extensive field for animation thus opens to our view. 
 
 The late Dr. Wilson, Professor of Astronomy, Glasgow, sup- 
 poses the spots of the sun are depressions, or excavations, rather 
 than elevations, and that the dark nucleus of each spot is the opaque 
 body of the sun seen through an opening in the luminous atmosphere 
 with which he is surrounded. 
 
 To this opinion of Dr. Wilson's, several celebrated astronomers 
 have started objections; among others, M. Lalande, a French astro- 
 nomer, contends that the spots are appearances arising from dark 
 bodies like rocks, which, by an alternate flux and reflux of the liquid 
 igneous matter of the sun, sometimes raise their heads above the ge- 
 neral surface. That part of the opaque rock which at any time thus 
 stands above, gives the appearance of the nucleus, while those parts 
 that lie only a little under the igneous matter appear to us as the 
 umbra which surrounds the dark nucleus. 
 
 Respecting the nature of fire, and the heating power of the sun's 
 rays, philosophers have been much divided in their opinions ; but 
 these opinions are both too numerous and too vague to be noticed 
 in a work like the present. In one particular they all agree, namely, 
 that the sun is either composed of, or surrounded by, some substance 
 that has a very powerful effect in heating or raising the temperature 
 of bodies exposed to the rays which proceed from it. 
 
 Many experiments have been made both in this country and on 
 the continent, to determine the intensity of those rays when concen- 
 trated in the focus of a lens, or by reflecting mirrors. Among the 
 most powerful of these may be mentioned the mirror constructed by 
 M. Villette, a French artist at Lyons, and publicly exhibited in 
 England. This mirror was 47 inches in diameter, and its focal dis- 
 tance 38 inches. From the experiments of Mr. Harris and Dr. Des- 
 aguliers, it appears that it melted a silver sixpence in 7J seconds ; a 
 fossil shell was calcined in 7 seconds ; a copper halfpenny melted 
 in 20 seconds ; iron ore melted in 24 seconds ; a great fish's tooth 
 melted in 32f seconds ; tin melted in 3 seconds ; and bone was cal- 
 cined in 4 seconds. 
 
 Sir I. Newton presented a burning glass to the Royal Society, 
 consisting of 7 concave glasses, so placed that the focus of each 
 united in one point. This glass vitrifies brick or tile in 1 second, 
 and melts gold in 30 seconds. So powerful are the sun's rays when 
 condensed, that it is said Archimedes set fire to the Roman fleet, at 
 the siege of Syracuse, by a combination of burning glasses; and 
 Buffon, in the year 1747, constructed a reflecting mirror of 16$ 
 plane glasses, moveable on hinges, with which he set wood on fire 
 at the distance of 150 feet, and melted lead at 145 feet. 
 
 The time which the light of the sun takes to arrive at the earth is 
 eight minutes and thirteen seconds; but this will be more fully treated 
 of in another part of this work. 
 
20 
 
 OF THE PLANETS. 
 
 The Sun revolving on his axis turns. 
 And with creative fire intensely burns ; 
 First Mercury completes his transient year, 
 Glowing, refulgent, with reflected glare ; 
 Bright Venus occupies a wider way, 
 The early harbinger of night and day ; 
 More distant still our globe terraqueous turns, 
 Nor chills intense, nor fiercely heated burns; 
 Around she rolls the lunar orb of light, 
 Trailing her silver glories through the night. 
 Beyond our- globe the sanguine Mars displays 
 A strong reflection of primeval rays ; 
 Next belted Jupiter far distant gleams, 
 Scarcely enlightened with the solar beams ; 
 With four unfix'd receptacles of light, 
 He towers majestic thro' the spacious height : 
 But farther yet the tardy Saturn lags, 
 And six attendant luminaries drags ; 
 Investing with a double ring his pace, 
 He circles thro' immensity of space. 
 
 CHATTERTON. 
 
 Beside the Earth and Moon, ten of the stars have motions eastward 
 peculiar to themselves. These are called Planets," 1 and are distin- 
 guished by particular names; which, taken in the order of their 
 proximity to the sun, or of the celerity of their motions round that 
 body, are, Mercury, Venus, Mars, Juno, Vesta, Ceres, Pallas, Ju- 
 piter, Saturn, and Uranus,f or Herschel. The first two of these per- 
 form their revolution round the sun in less than a year ; and as their 
 orbits are included in that of the earth, they are called inferior planets. 
 
 The rest require a longer period than a year to complete their 
 revolutions round the sun ; and as their orbits include that of the 
 earth's, they are called superior planets. 
 
 Five of the planets; viz. Mercury, Venus, Mars, Jupiter, and 
 Saturn, are very conspicuous, and have been known from the ear- 
 liest ages. The other five are visible only through the telescope, 
 and have been very lately discovered : Uranus, by Dr. Herschel, 
 in 1781 ; Ceres, by Piazzi, in 1801 ; Pallas, by Gibers, in 1802 ; 
 Juno, by Harding, in 1803; Vesta, by Olbers, in 1807. 
 
 The planets have also particular characters, by which they are 
 distinguished ; these, in the order in which they have been enumer- 
 ated, are $ ? f & ^ $ It T? tf- 
 
 The planets distinguished by these characters are termed primary 
 planets, because they perform revolutions round the sun in their 
 respective periodic times ; but besides these there are a number of 
 other small planets, that circulate round several of the primary ones, 
 and on that account are called secondary planets, or satellites. 
 
 * From a Greek word signifying to wander, because these bodies are conti- 
 nually changing their places. 
 t Those planets that are nearest the sun move quickest in their orbits. 
 
OF MERCURY. 21 
 
 The moon is therefore considered as a secondary, or satellite, be- 
 cause it performs its revolutions round the earth. The number of 
 secondary planets at present known is 18. 
 
 Of these, one circulates round the earth ; four round Jupiter ; 
 seven round Saturn ; and six round Uranus. 
 
 t 
 
 With what an awful worlcUrevolving power, 
 Here first the unwieldy planets launched along 
 The illimitable void ! There to remain 
 Amid the flux of many thousand years, 
 That oft have swept the toiling race of men 
 And all their laboured monuments away. 
 Firm, unremitting, matchless in their course, 
 To the kind-tempered change of night and day, 
 And of the seasons ever stealing round 
 Minutely faithful : such the All-perfect hand 
 That poised, impels, and rules the whole. 
 
 OF MERCURY. $ 
 
 Mercurius nearest to the central sun 
 
 Does in an oval orbit circling run ; 
 
 But rarely is the object of our sight, 
 
 In solar glory sunk, and more prevailing light. 
 
 BLACKMORE. 
 
 Mercury is the nearest planet to the sun, and performs his revo- 
 lution round that luminary in the shortest period of all the planets. 
 The time he takes to perform this revolution is 87<* 23h 14' 32'7",* 
 which is the length of his year. The length of his day, or the time 
 he takes to perform a revolution round his axis, is not known ; for, 
 by reason of his proximity to the sun, few observations can be made 
 upon him. The German astronomer, Shroeter, is however of opinion, 
 from some observations that he made on this planet, that the length 
 of his day is 24 hours 5 minutes ; he also conceives that there is a 
 mountain on the surface of Mercury not less than lOf miles in 
 height, but this has not yet been correctly ascertained. He is so 
 near the sun, that he can seldom be seen; and when he does make 
 his appearance, his motion is so rapid towards the sun that he can 
 only be discerned for a very short time. When he can be seen, it 
 is a little before the sun rises in the morning, and a little after he is 
 set in the evening. His distance from the sun is 36,668,373 English 
 miles, and his diameter is 3,241 miles, which makes him about T f ? th 
 part of the size of the earth. The rate at which he moves in his 
 orbit is not known. His situation with regard to the sun is such, 
 that water would be kept continually boiling on that part of his sur- 
 face which is opposite to the sun. The light and heat he receives 
 
 * The time which any planet takes to perform its revolution round the sun, is 
 called the length of its year ; and the time which it takes to revolve round its 
 axis, the length of its day. 
 
22 OF MERCURY. 
 
 from the sun are seven times greater than the earth, and the sun 
 appears seven times as large to him as to the earth. 
 
 This planet appears to us with all the various phases of the moon, 
 when viewed at different times with a good telescope ; but he never 
 appears quite full, because his enlightened side is never turned 
 directly towards the earth, except when he is so near the sun as to 
 be lost to our sight in his beams. His enlightened side being thus 
 always turned towards the sun, proves that he shines not by any 
 light of his own ; for if he did, he would always appear round, and 
 fully enlightened. It is also plain he moves in an orbit within that 
 of the earth's, because he is never seen opposite to the sun, nor 
 above 56 times the sun's breadth from him, his greatest Elongation 
 being about 28. 
 
 Mercury is the smallest of all the primary planets, and moves the 
 quickest in his orbit. Hence it was that the Greeks gave this planet 
 its name after the nimble messenger of the gods, and represented it 
 by the figure of a youth with wings at his head and feet ; whence is 
 derived 5 , the character by which it is commonly represented. 
 
 The inclination of the orbit of Mercury to the plane of the ecliptic 
 is the greatest of all the planets, being 7; and it is also far more 
 eccentric than that of any of the other planets, being not less than 
 th of his mean distance from the sun. The best observations which 
 can be made on this planet are, when it is seen on the sun's disc, 
 called its transit; for in its inferior conjunction, or when it is between 
 the earth and the sun, it sometimes appears to cross the sun like a 
 little dark spot, eclipsing a small part of the sun's body, which is 
 only visible with a telescope. The first observation of this kind was 
 made by Gassendi, a French astronomer, in November 1631. Seven 
 transits of this planet have been observed since that time. The 
 next one that will take place will be in May 1832, but it will not be 
 visible in Great Britain. 
 
 It has been very justly observed by the celebrated Huygens, that 
 the astronomy of those who live in Mercury may be easily under- 
 stood by the Copernican system ; and that the planets, Venus and 
 the earth, at the time of their opposition, must appear very bright 
 and large to the inhabitants of Mercury. For if Venus shines so 
 splendidly to us when she is new and horned, she must appear six 
 or seven times larger to the inhabitants of Mercury when she is in 
 opposition to the sun, and afford them so strong a light, that they 
 can have no reason to complain of the want of a moon. 
 
 Whether they have any difference of seasons is quite uncertain, 
 because it is not known whether the axis of this planet has any in- 
 clination to its orbit, or what is the time of its diurnal revolution. 
 But as Mars, the Earth, Jupiter, and Saturn, certainly have such 
 successions, there can be no doubt that days and nights, and a 
 vicissitude of seasons, are experienced in Mercury in some degree, 
 as well as in the other planets. 
 
OF VENUS. 23 
 
 OF VENUS. 
 
 Next Venus, to the westward of the Sun, 
 Full orbed her face, a golden plain of light 
 Circles her larger round. Fair morning star, 
 That leads on dawning day to yonder world, 
 The seat of man. 
 
 Fair Venus shines 
 
 Even in the eye of day ; with sweetest beam 
 Propitious shines, and shakes a trembling flood 
 Of softened radiance from her dewy locks. 
 
 BARBAULD. 
 
 Venus is the next planet in order, after Mercury, and the most 
 brilliant of all the planets, Jupiter not excepted. She is represented 
 by the character ? , which is supposed to be a rude representation of a 
 female figure, with a trailing or flowing robe. It is the only planet 
 mentioned in the sacred writings, or by the most ancient poets, such 
 as Hesiod and Homer. Venus never recedes far from the sun, her 
 greatest Elongation being about 47 ; which proves that her orbit 
 includes that of Mercury, but is included by that of the earth. 
 When Venus is to the west of the sun, she is to be seen before the 
 sun rises, and is then called the^V/iormwg star ; but when she is to the 
 east of the sun, she is to be seen after he is set, and is then called 
 the evening star. When in the former of these situations, she was 
 called by the Greeks Phosphorus, and in the latter Hesperus. The 
 evening and morning stars were at first supposed to be different; and 
 it is said that Pythagoras was the first person who discovered that 
 they were the same. 
 
 Now came still evening on ; and twilight grey 
 Had in her sober livery all things clad ; 
 Silence was pleas'd : now glow'd the firmament 
 With livid sapphires : Hesperus, that led 
 The starry host, rode brightest; till the moon 
 Rising in clouded majesty, at length, 
 Apparent queen, unveil'd her peerless light, 
 And o'er the dark her silver mantle threw. 
 
 MILTON. 
 
 Venus is computed to be 68,518,044 miles distant from the sun ; 
 she moves at the rate of 76,000 miles per hour ; and completes her 
 siderial revolution round the sun in 224 days, 16 hours, 49 minutes, 
 10 seconds. 
 
 The time she takes to revolve round her axis, or the length of her 
 day, is by some astronomers stated at 23h 21', and by others at 
 24d 8h. Venus is much about the size of our earth, her diameter 
 being 7687 English miles. When examined by a good telescope, 
 she exhibits the same phases as Mercury and the moon ; and her 
 surface is occasionally variegated by darkish spots. These spots 
 were employed by Cassini and Bianchini in determining the revolu- 
 tion of Venus about her axis. 
 
 When Venus is an evening star, and at her greatest distance from 
 the sun, or at what is termed her greatest eastern elongation, she ap- 
 pears, when viewed with a telescope, to have a semicircular disc, 
 
24 OF VENUS. 
 
 like the moon in the last quarter, with its convexity turned to the 
 west. From that time, during her approach to the sun, her splendour 
 increases for a while, though the quantity of the illuminated disc 
 diminishes like the moon in the wane ; but her diameter, when mea- 
 sured by the distance of the horns, is found to be increased. 
 
 At the time of her greatest elongation, Venus appears to be sta- 
 tionary, with respect to the sun, for some time. After this, her mo- 
 tion eastward becomes slower than the sun's, and then she ap- 
 proaches nearer to the sun, as just remarked. At a certain point she 
 becomes stationary with respect to the fixed stars, and then her mo- 
 tion becomes retrograde, or appears to be directed westward, with 
 respect to the fixed stars. At last she approaches the sun, so as to 
 be lost in his light; but after some time, she is to be seen to the west 
 of the sun, and appears in the morning before he rises. As she pro- 
 ceeds to the westward, her illuminated disc is seen as a crescent 
 continually increasing, at the same time that her diameter is dimi- 
 nishing. When she has got 45 to the west of the sun, her disc is a 
 semicircle ; and as she again approaches the sun, it increases till she 
 is lost in the sun's rays ; her orb being almost a circle, but its dia- 
 meter not more than one-sixth of what it was at the former conjunc- 
 tion. The conjunction, which takes place after the western elonga- 
 tion of Venus, is called the superior conjunction, as she is then far- 
 thest from the earth ; and that which follows the eastern elongation 
 is called the inferior conjunction, as she is then nearest the earth. 
 At the former of these periods, Venus is the breadth of her orbit far- 
 ther from the earth than at the latter ; for at the time of the superior 
 conjunction, she is on the opposite side of the sun to what the earth 
 is; but at the time of the inferior conjunction, Venus and the earth 
 are both on the same side of the sun. This planet appears to keep 
 on the same side of the sun for 290 days together, although this is a 
 longer period than she takes to perform a complete revolution round 
 that luminary. This may appear strange to those who are but little 
 acquainted with astronomy ; but when it is considered that the earth 
 is all the while going round the sun the same way, though not so 
 quick as Venus, the difficulty vanishes ; because she must continue 
 to appear on the same side with the earth, till the excess of her daily 
 motion above that of the earth's amounts to 179; or nearly to half a 
 circle ; which, at the rate of 37 minutes per day, will be in about 290 
 days, as stated above. 
 
 After the superior conjunction, the orb of Venus increases in mag- 
 nitude as she approaches her greater eastern elongation, but the en- 
 lightened part diminishes, just reversing the order of what has already 
 been stated to take place from the inferior conjunction to her greatest 
 western elongation; the period which includes all those changes, 
 or the time which elapses between any conjunction, and the next of 
 the same sort, is 584 days. This is called the Synodical Revolution 
 of Venus, during 42 days of which she is retrograde, with respect to 
 the fixed stars. To us Venus appears brightest when her elongation 
 is about 40, which happens about 70 days both before and after her 
 inferior conjunction. 
 
OF VENUS. 25 
 
 The different phases, or appearances of Venus, described above, 
 were first discovered by the astronomer Galileo in 1611, which ful- 
 filled the predictions of Copernicus ; who foretold, before the disco- 
 very of the telescope, that the phases of the inferior planets would be 
 one day discovered to be similar to those of the moon. The accom- 
 plishment of this prediction affords some of the strongest and most 
 convincing proofs of the truth of the Copernican system of the worl(J 
 that can be obtained. 
 
 It was long doubted whether Venus be surrounded by an atmos 
 phere or not ; but this question has been completely settled by the 
 very nice and accurate observations of the German astronomer 
 Shroeter, who has ascertained the existence of a pale faint light ex- 
 tending along the line of the dark hemisphere of this planet, which 
 he supposes to be a kind of twilight occasioned by the^-sun illumi- 
 nating its atmosphere. From this circumstance, Shroeter has been 
 enabled to determine the density of this atmosphere, and that it ex- 
 tends to a very great height, which must necessarily prevent the sun 
 from overpowering the inhabitants with his heat and splendour, 
 which is more than double what it is on the earth. 
 
 Dr. Herschel, after a long series of observations on this planet, 
 says, that it is highly probable that its surface is diversified by hills 
 and valleys, although he has never been able to see much of them, 
 owing, perhaps, to the great density of its atmosphere; and, he adds, 
 that no eye which is not considerably better than his, or assisted by 
 much better instruments, will ever get a sight of them. 
 
 Some astronomers have imagined that they perceived a satellite 
 near Venus ; but this has since been proved to be an illusion : for, 
 in her transit over the sun's disc, she appeared unaccompanied by 
 any satellite. Mr. Ferguson, however, thinks that Venus may have 
 a satellite revolving round her, though it has not yet been discovered; 
 and adds, " that this will not appear very surprising, if we consider 
 how inconveniently we are placed for seeing it." 
 
 Venus, as well as Mercury, is sometimes seen like a dark spot 
 on passing over the body of the sun. This phenomenon, as already 
 stated, is called a transit ; but such an appearance can only happen 
 at the time of an inferior conjunction, and when that conjunction 
 takes place at the time Venus is in that part of her orbit which 
 crosses the earth's orbit.* Transits of Venus but seldom happen. 
 The first that ever was observed was seen by our countryman, Mr. 
 Horrox, in 1639; two others have taken place since: viz. in 1761, 
 and the other in 1769 ; but there will not be another till 1874. 
 
 When a transit of Venus is observed, it not only proves that she 
 is an opaque body, and that her orbit is included by the earth's, but it 
 is of admirable use in determining what is called the sun's parallax, 
 which is of so much use in practical astronomy. See page 9th of this 
 work, Art. 25. 
 
 * The two points where the orbit of a planet crosses the ecliptic, or earth'& 
 prbit, i called its nodes. 
 
 3. D 
 
26 OF THE EARTH. 
 
 OF THE EARTH. 
 
 More distant still our Earth comes rolling on, 
 And forms a wider circle round the sun ; 
 With her the moon, companion ever dear ; 
 Her course attending through the shining year. 
 
 BAKER. 
 
 The earth performs its revolution round the Sun in an orbit be- 
 tween that of Venus and Mars, at the distance of 95,173,000, in 
 365 days, 5 hours, 48 minutes, 49 seconds, which is called the solar 
 or tropical year. In performing its annual circuit, the Earth travels 
 at the rate of 68,000 miles every hour, which is 140 times faster than 
 that of a cannon ball. The diameter of the Earth is 7,912 English 
 miles, and its circumference 24,855*42 miles.* 
 
 The Earth is usually represented by the character , in works 
 which treat of Astronomy. 
 
 In the early ages of the world, many fanciful and absurd notions 
 respecting the figure of the Earth prevailed ; some of which were 
 adopted because they appeared to agree with the slight and inaccu- 
 rate observations of the vulgar, whilst others represented this matter 
 in the way which best accorded with their preconceived opinions in 
 philosophy or religion. The most general opinion was, that the 
 Earth was a great circular plane, extending on all sides to an infinite 
 distance ; that the firmament above, in which all the heavenly bodies 
 seem to move daily from east to west, was at no great distance from 
 the Earth ; and that all the celestial bodies were created solely for 
 its use and ornamentf Cosmas Indopleustes supposed that it was 
 an immense plane, whose length was much greater than its breadth, 
 and surrounded by an unpassable ocean. Towards the north he 
 placed a huge mountain, round which the sun and stars performed 
 their diurnal revolutions ; and from the conical shape which he as- 
 cribed to it, with the oblique motion of the sun, he accounted for the 
 inequality of the days and the variety of the seasons. The vault of 
 heaven he conceived rested upon the earth, which extended beyond 
 the ocean, and supported by two vast columns. Beneath the arch, 
 angels conducted the stars in their various motions ; above it were 
 the celestial waters, and over all he placed the supreme heavens. 
 
 Concerning the figure and infinitude of the Earth no accurate in- 
 formation can be derived from the ancients. But this is not to be 
 wondered at when we consider that they were not only unacquainted 
 with the laws of motion, and the use of alloptical and mathematical in- 
 struments ; but they were unacquainted with the very existence of 
 extensive islands and countries at no great distance from their own. 
 
 * This is what the French mathematicians have lately deduced from a mea- 
 surement of above 12 of the meridian. 
 
 t Heraclitus imagined the earth to have the shape of a canoe ; Anaximander 
 supposed it to be cylindrical ; and Aristotle, the great oracle of antiquity, gave 
 it the form of a timbrel. 
 
OF THE EARTH. 27 
 
 A very little reflection, however, and a very little travelling either 
 by sea or land, must soon convince any one that the earth is of a 
 spherical form. For let a person occupy any station in a level coun- 
 try, and mark carefully the objects within the range of his horizon, 
 let him then advance in any direction, and as he moves the objects 
 behind him gradually disappear and new objects in front come in 
 view. Before he has travelled twenty miles in the same direction, 
 he will find that every object which was at first visible to him is lost 
 to his view, and that he is now in the centre of a new horizon. As a 
 similar change takes place at every part of the globe where the expe- 
 riment is tried, it follows that the earth is a spherical body. The 
 same inference may be deduced from observing the appearance of a ship 
 at a distance at sea, or from observing the gradual rising of the coast as 
 a ship approaches the shore. In the former case the top'of the mast 
 is first seen, and as the vessel approaches the land the whole of her 
 gradually becomes visible : in the latter, the hills, or the higher 
 parts of the buildings, are first discovered, but by degrees every part 
 of the buildings, and even the beach itself is seen. 
 
 These are appearances which can only be reconciled with the 
 spherical figure of the earth. The same conclusion may be drawn 
 from observing the altitude of the Pole star after travelling north or 
 south a considerable number of miles. In travelling northward its 
 altitude will be increased ; but in travelling south it will be dimi- 
 nished. 
 
 The globular figure of the earth is also inferred from the operation 
 of levelling, in which it is found necessary to make an allowance for 
 the difference between the true and apparent level and the allow- 
 ance which is made, and found to answer, is on the principle that 
 the earth is spherical. 
 
 Another proof of the earth being of a spherical form is obtained 
 from its shadow in an eclipse of the moon. For when the shadow 
 of the earth falls on the moon she is eclipsed, and the shadow 
 always appears circular upon the face of the moon, when she is 
 not totally eclipsed, although the earth is constantly turning on its 
 axis. Hence it follows that the body that projects it must be 
 spherical. 
 
 But the most convincing proof of the spherical figure of the earth, 
 is that many navigators have sailed round it ; not on an exact circle 
 it is true, because the winding of the shores would not admit of it, 
 but by going in and out as the shores happened to lie, and still keep- 
 ing the same course, they have at last arrived at the port from which 
 they departed. Among those who have succeeded in this daring 
 enterprise, may be mentioned Magellan, a Portuguese, in the year 
 1519, who completed the voyage in 1124 days ; Francis Drake per- 
 formed the same in 1056 days; Sir Thomas Cavendish in 777 days ; 
 Van Schouien in 749 days ; and many others have since performed 
 the same navigation, particularly Anson, Baugainville, and Cook. 
 Some of these navigators sailed eastward, some westward, till they 
 again arrived in Europe ; and in the course of their voyage observed 
 
 D 2 
 
28 OF THE EARTH. 
 
 that all the phenomena, both of the heavens and the earth, confirmed 
 the doctrine of the spherical figure of the earth. 
 
 The unevenness or irregularity of the earth's surface, such as 
 mountains and valleys, afford no objection to its being considered as 
 a globular body ; for the loftiest mountains bear no greater propor- 
 tion to the vast magnitude of the earth, than grains of sand to the 
 size of an artificial globe of twelve inches in diameter. This is the 
 reason that no deviation from the spherical figure of its shadow is 
 perceptible in an eclipse of the moon. 
 
 Although every one of the observations which have just been 
 made respecting the figure of the earth, affords sufficient evidence 
 that the surface of the earth is curved, yet none of them, except, 
 perhaps, the form of the shadow on the disc of the moon in a lunar 
 eclipse, entitles us to infer that the figure of the earth is that of a 
 globe, or perfect sphere. It was natural, however, for those who 
 first discovered that the earth had a round shape, to suppose that it 
 was truly spherical. This, however, is now known not to be the 
 case. Its true figure being that of an oblate spheroid, or sphere, flat- 
 tened a little at the poles, and raised about the equator, so that the 
 polar diameter is less than the equatorial. What first led to this 
 discovery was the observations of some French and English philoso- 
 phers in the East Indies and other parts, who found that pendulums 
 required longer time to perform their vibrations the nearer they were 
 to the equator. For Mr. Richer in a voyage to Cayenne, near the 
 equator, found that it was absolutely necessary to shorten the pendu- 
 lum of his clock about one-eleventh part of a Paris inch, in order to 
 make it vibrate in the same time as it did in the latitude of Paris. 
 
 From this it appeared that the force of gravity was less at places 
 near the equator than at Paris ; and consequently that those parts 
 are at a greater distance from the earth's centre. This circumstance 
 put Newton and Huygens upon attempting to discover the cause, 
 which they attributed to the revolution of the earth on its axis. If the 
 earth were in a fluid state, its rotation on its axis would necessarily 
 make it assume such a figure, because the centrifugal force being 
 greatest towards the equator, the fluid would there rise and swell 
 most ; and that its figure really should be so now, seems necessary to 
 keep the sea in the equatorial regions from overflowing the land 
 about those parts. 
 
 Newton in his Principia demonstrates, that by the operation of the 
 power called gravity, the figure of the earth must be that of an oblate 
 spheroid, if all parts of the earth be of a uniform density throughout, 
 and that the proportion of the polar to the equatorial diameter would 
 be 229 to 230 nearly. 
 
 As all conclusions, however, deduced from the length of pendu- 
 lums at different places of the earth's surface, proceed upon the sup- 
 position that the earth is a homogeneous body, which is very impro- 
 bable, the true figure of the earth can scarcely be expected to be 
 discovered by the pendulum; and at any rate it can be of no use in 
 determining the magnitude of the earth. A solution of this important 
 problem has, however, been attempted at various periods, by other 
 
OF THE EARTH. 29 
 
 means, and has at last been accomplished in a most accurate and 
 satisfactory manner, by the actual measurement of a very large arc 
 of a meridian circle on the earth's surface. The earliest attempt of 
 this kind of which we have any account, is that of Eratosthenes of 
 Alexandria, in Egypt. By measuring the sun's distance from the 
 zenith of Alexandria, on the solstitial day, and by knowing, as he 
 thought he did, that the sun was in the zenith of Syene, on the same 
 day, he found the distance in the heavens between the parallels of 
 these places to be 7 12', or a fiftieth part of the circumference of 
 a great circle. Supposing, then, that Alexandria and Syene were 
 on the same meridian, nothing more was required than to find the 
 distance between them, which multiplied by 50, would give the cir- 
 cumference of the globe. But it does not appear that Eratosthenes 
 took any trouble either to ascertain the bearing or the distance of the 
 two places ; for Syene is considerably east of Alexandria, and it ap- 
 pears that the distance was not measured till long afterwards, when 
 it was done by the command of the Emperor Nero, A similar at- 
 tempt was made by Passedonius, who lived in the time of Pompey ; 
 but it is impossible for us to judge how far these results correspond 
 with the more accurate measurements of the moderns, as we are un- 
 acquainted with the stadium, the measure in which the results were 
 expressed. 
 
 The first arc of the meridian measured in modern times with any 
 degree of accuracy, was by Snellius, a Dutch mathematician. The 
 arc was between Bergen-op-zoom and Alkmaar, and the length of 
 the degree that resulted was 55,021 toises ; but upon repeating the 
 operations afterwards with greater accuracy, the degree came out 
 57,033 toises, which is not far from the truth. 
 
 Our countryman, Mr. Norwood, measured the distance between 
 London and York, from whence he deduced the length of a degree 
 to be 57,800 toises, which has been found to be a near approximation, 
 considering the method he took to determine it. For he says, " Some- 
 times I measured, sometimes I paced, and i believe I am within a 
 scantling of the truth." 
 
 Picard was the first person who employed the trigonometrical 
 method with any degree of accuracy ; but since his time very large 
 arcs of the meridian have been measured in various parts of the world, 
 particularly in Lapland, Peru, India, France, and England. The 
 arc which has been measured in France- extends from Dunkirk in 
 lat. 51 2' 9" N. to Formentera, the southernmost of the Balearic isles 
 in lat. 38 38 56" N. comprising an arc of 12 23 13". But this has 
 lately been extended to the Shetland islands. The whole ampli- 
 tude of the arc is therefore above 22. 
 
 From comparing the lengths of the degrees of the meridian which 
 have thus been measured at different parts of the earth with each 
 other, it is found that they gradually increase in length from the equa- 
 tor to the poles ; which proves beyond the possibility of doubt, that 
 the true figure of the earth is that of an oblate spheroid, its polar dia- 
 meter being to the equatorial as 311 to 312. And by taking the 
 mean length of a degree, or that measured in France at latitude 45, 
 
30 OF MARS. 
 
 and multiplying it by 300, the degrees in the circle, the circumference 
 of the earth in the direction of the meridian is found to be 24,855*84 
 English miles. The circumference of the equator is 24,896-16 miles, 
 which is about 40 miles greater than the preceding. The mean dia- 
 meter of the earth is therefore 7910 nearly, and the length of one de- 
 gree 69& English miles. 
 
 OF MARS. 
 
 In larger circuit rolls the orb of Mars, ' 
 Guiltless of stern debate, and wasteful wars, 
 As some have erring taught : he journies on, 
 Impell'd and nourish'd by the attractive sun ; 
 Like us, his seasons and his days he owes 
 To the vast bounty which from Phoebus flows. 
 
 BROWN. 
 
 Mars is the next planet, after the earth, in the order of distance 
 from the sun ; and as his orbit includes that of the earth, he is called 
 the first of the superior planets. He is usually represented by the 
 character $ , which is said to be rudely formed from a man holding 
 a spear protruded, representing the god of war, which is the title of 
 Mars in the heathen mythology. 
 
 He may easily be distinguished from any other planet, or star, by 
 the red colour of his light. 
 
 Mars is the smallest of all the ancient planets, except Mercury, 
 his diameter being about 4200 miles. The time he takes to perform 
 his sedereal revolution round the sun is 686 days, 23 hours, 30 mi- 
 nutes, 36 seconds, which is performed at the distance of about 145 
 millions of miles, at the rate of 55,000 miles per hour. The time he 
 takes to revolve on his axis is 24 u 39' of our time. The quantity of 
 light and heat which Mars receives from the sun is only about half 
 what the earth receives from him ; and the sun only appears half 
 as large to Mars as to the earth. If any satellite revolves round 
 Mars it must be very small, as it has not yet been discovered, not- 
 withstanding the great number of observations which have been made 
 on this planet with the most powerful telescopes. 
 
 To Mars, the earth and moon appear like two moons, a larger and 
 a smaller, changing places with each other, and appearing sometimes 
 horned, sometimes half and three quarters enlightened, but never 
 full ; and never above a quarter of a degree distant from one another, 
 although they are 240,000 miles asunder. 
 
 The red colour of this planet is ascribed to the density of its at- 
 mosphere. For the atmosphere which surrounds Mars is not only of 
 great density, but of great height, that is, extends a great way from 
 his surface, as appears from the occultations to which the fixed stars 
 are subject on approaching his disc. 
 
 Dr. Smith, in his Optics, mentions an observation made by Cassini, 
 on a star in the constellation Aquarius, at Hie distance of six 
 
, OF MARS. 31 
 
 minutes from the disc of Mars, that became so faint before its oc- 
 cultation that it could not be seen by the naked eye, nor even with a 
 three-feet telescope. 
 
 From a series of observations, Dr. Herschel found that the poles 
 of Mars were distinguished by very remarkable luminous spots. 
 These he employed to determine the situation of the axis of the 
 planet, and its inclination to the ecliptic, &c. Their magnitude and 
 splendour were sometimes very considerable, but subject to very 
 great variations. The Dr. supposes that they are produced by the 
 reflection of the sun's light from the snow near the poles ; and that 
 the variations in their size and brightness is owing to the melting of 
 the polar ice. 
 
 Dr. H. has also determined that Mars is of a spheroidical form, 
 somewhat similar to that of the earth, having its equatorial diameter 
 to the polar as 103 to 98. When we reflect on the general appear- 
 ance of this planet, we soon find that opportunities for making ob- 
 servations on its real form cannot be very frequent : for when it is 
 near enough to be viewed to advantage, we generally see it gibbous, 
 or more than half illuminated, and its oppositions are so seldom, and 
 of so short duration, that in the space of two years there is not above 
 three or four weeks for making such observations. Tt is therefore 
 not at all surprising that the spheroidical form of this planet should 
 not have been discovered before the time of Dr. Herschel. 
 
 As the orbit of Mars includes that of the earth, at the time of his 
 opposition to the sun he is nearly five times nearer the earth than at 
 the time of his conjunction ; he therefore appears nearly five times 
 greater at the former of those periods than at the latter. And by 
 observing his oppositions in different parts of the heavens, or when 
 he is in different parts of his orbit, his apparent diameter is nearly the 
 same ; hence it is inferred that the sun is nearly in the centre of the 
 orbit of Mars, or that it does not deviate much from a circle ;* the 
 same appearance is observed when Jupiter and Saturn are in a similar 
 situation ; it is therefore concluded that the orbits of these planets are 
 also nearly circular. 
 
 Mars appears with his disc perfectly round both at the time of 
 opposition and conjunction. In the intermediate positions, he is 
 found to want something of perfect rotundity, on the side turned 
 farthest from the sun. This not only proves that Mars receives his 
 light from the sun, but that his orbit includes that of the earth. 
 
 When Mars first emerges from the sun's rays, a few days after the 
 conjunction, he rises some minutes before the sun, and his motion is 
 found to be progressive, that is, he changes his place daily a little 
 towards the east. But the earth's motion in the same direction is 
 nearly double that of Mars, which has the effect of making that 
 planet appear to recede from the sun towards the west, though its 
 real motion, with respect to the fixed stars, is toward the east. This 
 
 * Although the orbit of Mars does not deviate greatly from a circle, yet it is 
 the most eccentric of all the ancient planets, except that of Mercury. 
 
32 OF CERES. 
 
 continues for nearly a year, when his angular distance from the suri 
 is about 137, he then appears to be stationary for a few days. After 
 this, his motion becomes retrograde, or toward the west, and conti- 
 nues so till he is 180 distant from the sun, or in opposition, so as to 
 be on the meridian at midnight. His retrograde motion is then swift- 
 est; it afterwards becomes gradually slower, and ceases altogether 
 when the planet has again come to be about 137 distant from the 
 sun on the other side. The motion then becomes progressive again, 
 and continues so till the conjunction, and beyond it, in the manner 
 just described* The period in which all those changes take place, or 
 the interval between one conjunction, or opposition to the next, 
 is 780 days, which is the length of a synodicai revolution of this 
 planet. 
 
 The irregularities of Mars, in his orbit, being the most considera- 
 ble of all the primary planets, Kepler fixed upon it as the first ob- 
 ject of his investigations respecting the nature of the planetary orbits ; 
 and after extraordinary labour, he at last discovered that the orbit 
 of this planet was elliptical ; that the sun is placed in one of the foci ; 
 and that there is no point round which the angular motion is uni- 
 form. 
 
 In the pursuit of this inquiry he found the same thing of the earth's 
 orbit; hence, by analogy, it was reasonable to think, that all the 
 planetary orbits are elliptical, having the sun in their common focus.* 
 
 OF CERES. 
 
 This and the three following planets have all been discovered since 
 the beginning of the present century, and within the space of six 
 years. 
 
 Ceres was discovered on the 1st of January, 1801, by Mr. Piazzi 
 at Palermo in Sicily. 
 
 Its diameter, according to Dr. Herschel, is only 163 miles. But 
 Shroeter makes it 1624 miles. This great difference, says Shroeter, 
 arises from Dr. H. observing with his projection- micrometer at too 
 great a distance from his eye, and measuring only the middle clear 
 part of the nucleus. 
 
 Ceres moves in an orbit between Mars and Jupiter ; and its mean 
 distance from the sun is about 263,000,000 miles. The time it takes 
 to perform its sidereal revolution round the sun in 1681 days, 12 
 hours, 56 minutes. The excentricity of its orbit is a little greater than 
 that of Mercury ; and its inclination to the ecliptic exceeds that of 
 
 * Logarithms not having been discovered at that time, arithmetical calcula- 
 tions, when pushed to great accuracy, required both great patience and great 
 labour. In the calculation of every opposition of Mars, the work filled ten folio 
 pages, and Kepter composed together seven oppositions of this planet, repeating 
 each calculation ten times ; so that the work for each opposition filled 100 such 
 pages, and the whole calculation for the seven oppositions produced a large folio 
 volume. 
 
OF PALLAS, JUNO, VESTA; 33 
 
 all the old planets very considerably. Ceres is not visible to the 
 naked eye ; but when observed by a telescope, appears of a ruddy 
 colour, and about the size of a star of the eighth magnitude. It also 
 seems to be surrounded by an extensive and dense atmosphere; but 
 when examined by a telescope, which magnifies it above two hundred 
 times, its disc may be very distinctly perceived. 
 
 OF PALLAS. $ 
 
 The planet Pallas was discovered at Bremen, in Lower Saxony, 
 on the 28th March, 1802, by Dr. Olbers. It moves in an orbit 
 between that of Mars and Jupiter, and its mean distance from the sun 
 is nearly the same as Ceres ; but the inclination of its orbit to the 
 ecliptic is much greater, being not less than 34f. The time it 
 takes to perform its sidereal revolution round the sun, is about five 
 hours more than Ceres ; and it appears also to be about the same 
 magnitude. It is less ruddy than Ceres ; but is surrounded by an 
 atmosphere similar to what surrounds that planet. It likewise un- 
 dergoes similar changes, but its light exhibits greater variations. 
 
 OF JUNO. $ 
 
 The planet Juno was discovered by Mr. Harding at the observa- 
 tory of Lilianthal, near Bremen, on the evening of the 1st of Septem- 
 ber, 1804, while he was making a catalogue of all the stars which 
 were near the orbits of Ceres and Pallas. Its diameter, according to 
 Shroeter, is 1425 miles ; and its mean distance from the sun is about 
 253,000,000 miles. The time it takes to perform its sidereal revolu- 
 tion round the sun is nearly 1590 days. The orbit in which it per- 
 forms its revolution round the sun is situated between that of Mars 
 and Jupiter, and is so eliptical that its greatest distance from the sun 
 is nearly double its least distance. This great excentricity has a re- 
 markable effect on the motion of the planet in its orbit : for it moves 
 through that half of its orbit which is nearest the sun nearly in half 
 the time that it moves through the other. The inclination of the 
 orbit to the ecliptic is about 13. 
 
 Juno is of a reddish colour, and free from that whitish light which 
 surrounds Pallas. 
 
 OF VESTA. j 
 
 This planet was discovered by Dr. Olbers, of Bremen, on the 29th 
 March, 1807. Its' diameter is stated at 238 miles ; but Shroeter 
 makes it much greater. The orbit of Pallas is situated between the 
 orbits of Mars and Jupiter ; but nearer the former than any of the 
 other new planets. The time it takes to perform its sidereal revolu- 
 
34 VESTA. 
 
 lion round the sun is 1335 days, 4 hours, 54 minutes. Its mean 
 distance from the sun is about 225,000,000 miles. 
 
 In a clear evening this planet may be seen by the naked eye, 
 like a star of the sixth magnitude, of a dusky colour, similar in ap- 
 pearance to Uranus, its light being more intense, pure, and white, 
 than any of the other three new planets. 
 
 It appears rather extraordinary that the orbits of the four new 
 planets, just described, should all be nearly at the same distance 
 from the sun, and in a part of the heavens, where it was conjectured 
 some planet might perform its revolution round the sun, although no 
 astronomer had ever been so fortunate as to discover it. What led 
 to this supposition was the great distance between the orbits of Mars 
 and Jupiter, a thing so unlike the regular order in which the orbits 
 of the planets between the sun and Mars were disposed. Accord- 
 ingly, upon the discovery of Ceres, the harmony and regularity of the 
 system seemed to be established ; but the subsequent discovery of 
 Pallas and Juno, seemed again to overturn these speculations. This 
 new difficulty suggested to Dr. Olbers, what may perhaps be consi- 
 dered a very romantic idea, namely, that the three recently disco- 
 vered planets might be fragments of a planet, which had been burst 
 asunder by some internal convulsion. This opinion seemed to receive 
 considerable support from a comparison of their magnitudes with 
 that of all the other planets : from the circumstance of their orbits 
 being nearly at equal distances from the sun ; and from the very 
 singular fact, that all their orbits cross one another in two opposite 
 points in the heavens. 
 
 The support which this hypothesis derived from the last of these 
 circumstances is peculiarly strong and conclusive; for it can be de- 
 monstrated, that if a planet, in motion, be rent asunder by any inter- 
 nal force, however different the inclinations of the orbits of the 
 fragments may be, they must all meet again in two opposite points. 
 Prosecuting this idea, Dr. Olbers every year examined the small 
 stars that were near these points in the heavens, and was so fortu- 
 nate as to discover a fourth fragment, or the last discovered planet 
 Vesta. Dr. Brewster, of Edinburgh, has suggested another view of 
 the subject, which seems to give additional support to the theory of 
 Olbers. If a planet, says Dr. B., be rent asunder by any explosive 
 force, the form of the orbits assumed by the fragments, and their in- 
 clination to the ecliptic, or to the orbit of the original planet, will 
 depend upon the size of the fragments, or the weight of their respect- 
 ive masses : the larger masses will deviate least from the original 
 path, while the smaller fragments being thrown off with greater ve- 
 locity, will revolve in orbits more eccentric, and more inclined to the 
 ecliptic. Now this is precisely what happens. Ceres and Vesta 
 are found to be the largest, and their orbits have nearly the same in- 
 clination to the ecliptic as some of the old planets ; while the orbits 
 of the smaller ones, Juno and Pallas, are inclined to the ecliptic, 21 
 and 34 respectively. 
 
 As to these four bodies, so very unlike the other primary planets, 
 Dr. Herschel has given the name of Asteroids. La Lande and some 
 
OF JUPITER. 35 
 
 others have named each of them after the person who discovered it ; 
 but this produces some degree of confusion, because Dr. Olbers dis- 
 covered both Pallas and Vesta. 
 
 OF JUPITER. 2 
 
 Beyond the sphere of Mars, in distant skies, 
 Revolves the mighty magnitude of Jove, 
 With kingly state, the rival of the Sun. 
 About him round, four planetary moons, 
 On earth, with wonder, all night long beheld, 
 Moon above moon, his fair attendants dance. 
 
 Jupiter performs his revolution round the sun in an orbit, which 
 includes all the planets yet described. His mean distance from the 
 sun is about 490 millions of miles; and the time he takes to complete 
 a sidereal revolution round that luminary is 4332 days, 14 hours, 
 27 minutes. The motion on his axis is extremely rapid, being per- 
 formed in the short space of 9 hours, 56 minutes ; but his hourly 
 motion in his orbit is only 25,000 miles. 
 
 Jupiter is the largest of all the planets, his diameter being 89,170 
 English miles. 
 
 Next Jove, prodigious planet of the skies ! 
 His orb presents of huge amazing size. 
 
 BROWN. 
 
 Jupiter is also the brightest of all the planets, except Venus, which, 
 on some occasions, exceeds him in splendour. The character by 
 which he is represented is If. 
 
 Jupiter is surrounded by faint substances, called zones, or belts, 
 which lie parallel to each other on his surface. They are, however, 
 subject to considerable variation both in breadth and number and 
 are on some occasions more conspicuous than at others. They are 
 not only parallel to each other, but, in general, parallel to the equator 
 of Jupiter. Bright and dark spots are also frequently to be seen in 
 the belts; and when a belt vanishes, these spots vanish with it. 
 The broken ends of some belts have often been observed to revolve 
 in the same time with the spots ; only those near the equator of the 
 planet more quickly than those nearer the poles. This is, perhaps, 
 on account of the greater heat of the sun near the equator than the 
 poles ; the equator being parallel to the belts and course of the spots. 
 On some occasions the spots have been observed to change their 
 forms gradually, and sometimes with very unequal velocities. 
 
 Astronomers are very different in their opinions respecting the 
 cause of these appearances. Some consider them as the effect of 
 changes in the atmosphere that surround Jupiter ; while others re- 
 gard them as indications of great physical revolutions on the surface 
 of that planet. The first of these hypotheses appears to explain the 
 variations in the form and magnitude of the belts ; but it by no means 
 accounts for their parallelism, nor for the permanence of some of the 
 
36 OF JUPITER. 
 
 spots. The spot first observed by the astronomer Cassini, in 1665, 
 which has both disappeared and reappeared in the same form within 
 the space of 50 years, seems evidently to be connected with the 
 surface of the planet. The form of the belts, says Dr. Brewster, 
 may be accounted for, by supposing that the atmosphere of Jupiter 
 reflects more light than the body of the planet, and that the clouds 
 which float in it, being thrown into parallel strata by the rapidity of 
 his diurnal motion, form regular interstices, through which are seen 
 the opaque body of Jupiter, or any of the permanent spots which may 
 happen to come within the range of the opening. 
 
 The form of Jupiter, like that of the Earth, is an oblate spheroid, 
 the equatorial diameter being to the polar as 14 to 13. This is occa- 
 sioned by his extraordinary rapid motion on his axis ; for the fluids, 
 together with the light particles which they can carry or wash away 
 with them, recede from the poles which are at rest towards the 
 equator, where the motion is quickest. 
 
 The axis of Jupiter is so nearly perpendicular to his orbit, that he 
 has no sensible change of seasons, which is very wisely ordered by 
 the Author of Nature ; for if this were not the case, just as many 
 degrees round each pole, as the axis was inclined, would be in dark- 
 ness for nearly six months. 
 
 To Jupiter the sun only appears l-28th part of the size he does to 
 the Earth, and the light and heat he receives from that luminary are 
 in the same proportion. But he is in some measure compensated for 
 this want by the quick return of the sun, occasioned by the prodi- 
 giously rapid motion round his axis ; and, in order to supply him 
 with additional light, he is accommodated with four satellites, or 
 moons, which revolve round him. 
 
 Four second planets his dominion own, 
 
 And round him turn, as round the earth the moon. 
 
 BLACKMORE. 
 
 The discovery of these satellites were made by Galileo in 1610 ; 
 and they may be considered as one of the first fruits of the invention 
 of the telescope. They cannot be seen by the naked eye, but are 
 distinctly visible with a telescope of a moderate power. Their rela- 
 tive situation with regard to Jupiter, as well as to each other, is 
 constantly changing. Sometimes they all may be seen on one side 
 of Jupiter, and sometimes all on the other ; but most frequently some 
 of them on one side, and some on the other. They are designated 
 by their distances from Jupiter, that being called the first whose 
 distance from Jupiter is least, when at the greatest elongation, and 
 so on with the others. They are of very different magnitudes, some 
 of them being greater than our earth, while others are not so large 
 as the moon. Their apparent diameters being insensible, their real 
 magnitudes cannot be exactly measured. The attempt has been made 
 by observing the time they take to enter into the shadow of Jupiter ; 
 but there is a great discordance in the observations which have been 
 made to ascertain this circumstance; and, of course, the results of 
 these observations must also be very discordant. The third, how- 
 
OF SATURN. 37 
 
 ; 
 
 ever, is the greatest ; the fourth is the second in magnitude ; the 
 first, the third in magnitude ; and the second is the least. The first 
 goes round Jupiter in 1 day, 18 hours, 27 minutes, 33 seconds, at 
 the distance of 5J times the semidiameter of Jupiter; the second in 
 3 days, 13 hours, 13 minutes, 42 seconds, at the distance of 9 semi- 
 diameters ; the third in 7 days, 3 hours, 42 minutes, 33 seconds, at 
 the distance of 14^ semidiameters ; and the fourth in 16 days, 16 
 hours, 32 minutes, 8 seconds, at the distance of 25g semidiameters 
 of Jupiter. The three nearest of these satellites fall into the shadow 
 of Jupiter, and are eclipsed in every revolution ; but the orbit of the 
 fourth is so much inclined, that it is not eclipsed every time it is in 
 opposition to Jupiter. Sometimes the satellites pass between us and 
 Jupiter, and then their shadows are seen crossing his disc. From 
 this it is evident that both Jupiter and his satellites are opaque 
 bodies, which derive their light from the sun ; and as they are 
 always observed to move eastward when they are entering into the 
 shadow of Jupiter, and westward when they pass over his disc, it is 
 evident that their motion is progressive, or in the same direction 
 with the motion of the primary planets round the sun. The eclipses 
 of these satellites were not only the cause of that most curious dis- 
 covery made by Roemer in the year 1675, that light required 
 8 minutes 13 seconds to pass from the sun to the earth; but they 
 are of the greatest use in determining the longitude of places on the 
 earth, because this difficult and important problem can be more 
 easily and accurately solved by means of these eclipses than by any 
 other method yet known. As a proof of these satellites passing into 
 the shadow of Jupiter when they disappear, we may remark, that the 
 satellite which is eclipsed always disappears on that side of Jupiter 
 which is opposite to the sun, or where his shadow falls. We may 
 also remark, that the side of the satellite which is nearest to the disc 
 of the planet is first eclipsed ; and that the duration of the eclipse 
 corresponds exactly to the time necessary for the satellite to pass 
 through the shadow. The form of the orbits of the satellites is found 
 to be nearly circular, especially that of the 1st, 2d, and 3d ; and 
 the velocity of their motions nearly uniform. 
 
 In consequence of observing periodical changes in the intensity of 
 thf light of the satellites, Dr. Herschel inferred that they revolve on 
 their axis, and that the period of their rotation is equal to the time of 
 their revolution round Jupiter, 
 
 OF SATURN. % 
 
 But farther yet the tardy Saturn lags, 
 And seven attendant luminaries drags ; 
 
 Investing with a double ring his pace, 
 He circles through immensity of space. 
 
 The planet Saturn moves in a still more extensive orbit than that of 
 Jupiter, his distance from the sun being about 903 millions of miles. 
 The period in which he performs his sidereal revolution round the sun, 
 
 4 E 
 
38 OF SATURN. 
 
 is 10758 days, 23 hours, 16 minutes ; the velocity of his motion is 
 therefore about 18,000 miles per hour. 
 
 The time he takes to revolve on his axis is ten hours sixteen 
 minutes. 
 
 The diameter of Saturn is 79,491 miles, which is about ten 
 thousand less than that of Jupiter. His shape is that of an oblate 
 spheroid, like that of Jupiter, but still more elliptical, the equatorial 
 diameter being to the polar as 12 to 11. 
 
 Saturn shines with a very feeble light compared with that of 
 Jupiter, on account of his great distance from the sun. But not- 
 withstanding this he is one of the most extraordinary and engaging 
 objects which astronomy presents to our view. He is distinguished 
 from all the other planets by a broad luminous ring which surrounds 
 his body. This extraordinary phenomenon was discovered about the 
 end of the 17th century, by the astronomer Huygens. When seen 
 through a good telescope, the- ring appears double, and is seen to 
 cast a deep shadow on the planet. Dr. Herschel was of opinion that 
 the ring has a motion, an axis which is at right angles to its own 
 plane ; and that it is completed in the same time with that of the planet 
 itself, that is, in a little more than 10 hours. The plane of the ring 
 coincides with the equator of Saturn, but it makes an angle with the 
 ecliptic of about 30, and remains always parallel to itself. The 
 upper surface of it will, therefore, be illuminated during half the 
 period of Saturn's revolution round the sun, or about 15 years, and 
 the under surface during the other half of the period. For the same 
 reason the plane of the ring must, in the course of one revolution, 
 twice intersect the plane of the ecliptic, and then the thin edge only 
 of the ring being illuminated, it will be invisible while it remains in 
 that position. When the ring is seen under the most favourable cir- 
 cumstances, it has the appearance of an eclipse, the breadth of 
 which is nearly half its length ; but after this it gradually becomes 
 narrower, till at length its farthest arc is hid behind the planet, and 
 the nearer is confounded with it. It is in this situation that it has 
 been seen to cast a shadow upon the disc of the planet ; from which 
 it is inferred that it is an opaque body, illuminated by the sun. 
 Although we have stated that the ring is invisible when its edge is 
 turned to the earth, on account of the quantity of light which it then 
 reflects being so small that it cannot be observed through ordinary 
 telescopes ; yet with instruments of very great magnifying power it 
 never ceases to be visible. Dr. Herschel says, that when he 
 observed with his 40-feet reflector he could always observe the ring. 
 Although the ring encompasses Saturn, yet it is every where sepa- 
 rated from him ; for stars have been seen between it and the planet. 
 The apparent breadth of the ring is about one-third that of the pla- 
 net, and about equal to the distance of Saturn from its inner edge. 
 The ring does not appear uniform, for it seems divided by a dark 
 line going all round, concentric with the outer and inner edge, and 
 forming two rings, of which the outermost is only about one-third the 
 breadth of the other. 
 
OF SATURN. 39 
 
 Muse ! raise thy voice, mysterious truth to sing, 
 
 How o'er the copious orb a lucid ring, 
 
 Opake and broad, is seen its arch to spread 
 
 Round the big globe at stated periods led ; 
 
 Perhaps (it's use unknown) with gather'd heat 
 
 To aid the regions of that gelid seat, 
 
 The want of nearer Phoebus to supply, 
 
 And warm with reflex beams his summer sky; 
 
 Else might the high plac'd world expos'd to frost, 
 
 Lie waste, in one eternal winter lost. BROWN, 
 
 The distance of Saturn from the sun being nearly ten times greater 
 than that of the earth, he can only enjoy about one-ninetieth part of 
 the heat and light which the earth enjoys. Besides the ring just 
 described, Saturn is attended by seven satellites, which in a great 
 measure compensate for the scantiness of light that he derives from 
 the sun. 
 
 The fourth satellite is sometimes called the Huygenian satellite ; 
 it was discovered by Huygens, in 1655 ; the first, second, third, 
 and fifth were discovered, some years afterwards, by Cassini; and 
 the sixth and seventh were discovered by Dr. Herschel in 1789. 
 The numbers denote the order in which they were discovered, 
 except in the case of the fourth, and not their distances from the pri- 
 mary, as in the case of Jupiter. When ranked in the order of their 
 distance from Saturn, they must be arranged thus : the sixth, seventh, 
 first, second, third, fourth, fifth ; and if this order be inverted, they 
 will then be ranked according to their comparative brightness, with 
 the exception of the fifth, which never equals the fourth in splendour. 
 The orbits of all of them are nearly circular ; and with the exception 
 of that of the fifth, nearly in the plane of the ring. But the orbit of 
 the fifth is considerably more inclined to the ecliptic ; and when this 
 satellite reaches its greatest western elongation, it exceeds all the 
 others in splendour ; but when it arrives at its greatest eastern elon- 
 gation, it disappears altogether, and continues invisible for half the 
 time it requires to perform its revolution round its orbit. This 
 appearance is not occasional, for it always recurs when the satellite 
 is in the same position. Hence it is inferred, that this satellite, like 
 our moon, revolves on its axis in a period exactly equal to the time 
 of its revolution round Saturn. 
 
 The periodical revolutions and distance of these satellites from the 
 body of Saturn, expressed in semi-diameters of that planet, as well 
 as in miles, are exhibited in the following table : 
 
 
 
 Distances in 
 
 Satel- 
 lites. 
 
 Periods. 
 
 
 
 
 
 
 Semi- 
 
 Miles. 
 
 
 
 diameters. 
 
 
 
 d. h. ' " 
 
 
 
 1 
 
 2 
 
 1 21 18 26 
 2 17 44 51 
 
 it 
 
 170,000 
 217,000 
 
 3 
 
 4 12 25 11 
 
 8 
 
 303,000 
 
 4 
 
 15 22 41 14 
 
 18 
 
 704,000 
 
 5 
 
 79 7 54 37 
 
 54 
 
 2,050,000 
 
 6 
 
 1 8 53 9 
 
 ftt 
 
 135,000 
 
 7 
 
 22 37 30 
 
 H 
 
 107,000 
 
40 OF URANUS, OR HERSCHEL. 
 
 These satellites are all so small, and at such a distance from the 
 earth, that they cannot be seen unless with very powerful telescopes. 
 
 The surface of Saturn, like that of Jupiter, is diversified by a num- 
 ber of belts, or regular stripes. Huygens observed five belts, which 
 were nearly all parallel to the equator of Saturn. Dr. Herschel 
 likewise observed several belts, which are in general parallel to the 
 ring. On the llth of November, 1793, he observed a bright, uni- 
 form, and broad belt, close to which was a broad and dark one, 
 divided by two narrow white streaks ; so that he saw the same num- 
 ber of belts as Huygens, three of which were dark and two light. 
 These belts cover a larger zone of the disc of Saturn, than those of 
 Jupiter occupy upon his surface. 
 
 The orbit of Saturn was long considered as the boundary of the 
 solar system, except the cometary orbits, which were believed to 
 stretch far beyond it. The discovery of the planet Uranus has, 
 however, extended the system far beyond the limits formerly 
 assigned to it. 
 
 OF URANUS, OR HERSCHEL. U 
 
 Last, outmost Herschel walks his frontier round 
 
 The boundary of worlds ; with his pale moons 
 
 Faint glimmering through the darkness night has thrown, 
 
 Deep dyed and dead, o'er this chill globe forlorn : 
 
 An endless desart, where extreme of cold 
 
 Eternal sits, as in his native seat, 
 
 On wintry hills of never thawing ice ; 
 
 Such HerscheFs earth. 
 
 A new planet was discovered by Dr. Herschel on the 13th March, 
 1781, and called by him Georgium Sidus, out of respect to his 
 Majesty George III. ; but some astronomers have given it the name 
 of Herschel, after its discoverer, while others have given it the 
 name of Uranus, which is the name now given to it in almost every 
 work on astronomy, and seems to be conformable to the manner of 
 naming the other planets, that is, from the heathen mythology. 
 Besides, if the situation of this planet in the system be considered, 
 the name Uranus is quite apposite. For as Saturn's orbit includes 
 that of Jupiter, and he bears the name of Jupiter's father, there 
 seems an equal propriety in calling the next planet, whose orbit 
 includes that of Saturn, by the name of Uranus, Saturn's father. 
 
 The mark or character by which Uranus is distinguished in 
 astronomical works is y. The orbit of this planet is situated far 
 beyond that of Saturn, being at the immense distance of 1,822,000,000 
 miles from the sun. The time of its sidereal revolution round that 
 luminary is said to be 30,688 days, 17 hours. His diameter is 
 about 4| times greater than that of the earth, or nearly 35,000 
 English miles. 
 
 The distance of this planet is so great, that it cannot be seen by 
 the naked eye, except when the atmosphere is very clear, and then 
 
THE PLANETS. 
 
 41 
 
 it appears like a star of the 6th magnitude. It had been observed 
 by Flamsead and Mayer ; but was considered by them as a fixed 
 star, and put down in catalogues as such. Long before the disco- 
 very of this planet, some disturbances and deviations in the motions 
 of Jupiter and Saturn were observed by astronomers, which they 
 could only account for on the supposition that there existed some 
 planet still more distant from the sun than Saturn. But this can 
 only be considered in the light of mere conjecture. For it is to the 
 indefatigable industry and exertions of Dr. Herschel, that we are 
 indebted for the discovery of this planet, and all the important par- 
 ticulars connected with its motion. 
 
 Uranus is at such an immense distance from the sun, that the 
 light he receives from that luminary must be very small indeed ; but 
 this want is in a great measure supplied by six satellites which 
 revolve round him, all of which were discovered by Dr. Herschel. 
 The first and fourth he discovered in January 1787 ; and the other 
 four in 1790 and 1794. 
 
 The orbits of all the satellites are nearly in the same plane, and 
 almost at right angles to the orbit of Uranus ; but what is rather 
 extraordinary, the motion of these satellites is retrograde, or directly 
 the reverse of the other planets and satellites. 
 
 The distances and periodic times of the satellites are as in the 
 following table : 
 
 Sat. 
 
 Distances \n Seini- 
 diameters of Uranus, 
 
 Periodic times. 
 
 
 
 d. h. m. 
 
 1 
 
 13-120 
 
 5 21 25 
 
 2 
 
 17-022 
 
 8 17 1 
 
 3 
 
 19-845 
 
 10 23 4 
 
 4 
 
 22-752 
 
 13 11 5 
 
 5 
 
 45-507 
 
 38 1 49 
 
 6 
 
 91-008 
 
 107 16 40 
 
 Eclipses of the satellites sometimes take place; but these can only 
 be seen when Uranus is near his opposition. This happened in the 
 year 1799, and also in 1818 ; but they can only be discerned by the 
 most powerful telescope, and when the sky is perfectly clear. 
 
 THE PLANETS, AS SEEN THROUGH A TELESCOPE. 
 
 If eager still in Nature's book to pry, 
 
 Thou should'st the Astronomic tube apply ; 
 
 And trace with careful eye the wide inane, 
 
 The Comet's blaze, and Planetary train : 
 
 Then shalt thou mark the various systems roll, 
 
 And learn the laws that regulate the whole. CAREY. 
 
 Although many of the phenomena mentioned in the foregoing pages 
 have been discovered by means of the telescope, yet this most valuable 
 instrument has been the means of accomplishing many other splendid 
 
42 THE PLANETS. 
 
 discoveries, which could not be noticed, consistently with the plan of 
 this work, at an earlier period. 
 
 The telescope was first turned to the heavens by the celebrated 
 astronomer and philosopher, Galileo ; hence it has been aptly enough 
 styled the Galilean tube.* 
 
 By whose aid are seen 
 
 The planetary phases, the bright cohort 
 
 Of secondary worlds ; and countless suns, 
 
 'Which, hid in the immensity of space, 
 
 Ne'er visited the sight : from whom we learn 
 
 The eclipse in time and quantity exact ; 
 
 And trace the parallax, that wondrous clue, 
 
 By which the distance and the magnitude 
 
 Of the celestial spheres are known on earth. ECDOSIA. 
 
 No astronomer has ever done more to improve the telescope, or 
 made more observations and discoveries in the heavens by means of 
 this most amusing and useful instrument, than the late Dr.Herschel.f 
 It may therefore be gratifying to hear the Doctor's observations 
 respecting the requisites which this instrument ought to possess, 
 in order to enable the observer to make accurate and minute observa- 
 tions on any of the celestial bodies. 
 
 In stating the result of a series of observations on the satellites of 
 Uranus, or the Georgian planet, as the Dr. terms it, he says, 
 " The great distance of this planet renders an attempt to investigate 
 the movements of its satellites a very arduous undertaking ; for their 
 light, having to traverse a space of such vast extent before it can 
 reach us, is so enfeebled, and their apparent diameter so dimi- 
 nished, that an instrument, to be prepared for viewing them, must 
 be armed with the double power of magnifying and of penetrating 
 into space." " The first of these properties," continues the Dr. 
 " seems not to be generally understood : the question how much a 
 telescope magnifies admits of various answers. To resolve it pro- 
 perly, we ought, in all circumstances, to consider how far the mag- 
 nifying power of a telescope is supported by an adequate quantity of 
 light ; for without it, even the highest power and distinctness cannot 
 be efficient. This is abundantly confirmed when a ten-feet reflector 
 is directed to the Georgian planet; for with none of its highest 
 powers can we possibly ascertain even the existence of the 
 satellites. 
 
 " Since, then, it is absolutely necessary that the power of magni- 
 fying should be accompanied with a sufficient quantity of light to 
 reach the satellites of this remote planet, it may be useful to cast an 
 eye upon the action of a power which is become so essential. Its 
 advantages and its inconveniences must equally be objects of 
 consideration. 
 
 " A very material inconvenience is, that mirrors which must be 
 large in order to grasp much light, must also be of a great focal 
 length ; and that in consequence of this we must submit to be encum- 
 bered with a large apparatus. 
 
 * See page 9 of the Supplement to this Work, 
 
 t As he is better known by the little Dr. than Sir William Herschel, we retain? 
 the former* 
 
THE PLANETS. 4# 
 
 " The forty-feet telescope having more light than the twenty-feet 
 one, which I frequently use, it ought to be explained why I have 
 not always used it in making my observations on the satellites of the 
 Georgian planet. Of two reasons that may be assigned, the first 
 relates to the apparatus and the nature of the instrument. The pre- 
 parations for observing with it take up much time, which in fine is 
 too precious to be wasted in mechanical arrangements. The tempe- 
 rature of the air for observations that must not be interrupted, is 
 often too changeable to use an instrument that will not easily accom- 
 modate itself to the change ; and since this telescope, besides the 
 assistant at the clock and writing-desk, requires moreover the 
 attendance of two workmen to execute the necessary movements, it 
 cannot be convenient to have every thing prepared for occasional 
 lucid intervals between flying clouds that may chance to occur ; 
 whereas in less than ten minutes the twenty-feet telescope may be 
 properly adjusted and directed, so as to have the planet in the field 
 of view. 
 
 " In the next place I have to mention, that it has constantly been 
 rule with me, not to observe with a larger instrument when a smaller 
 would answer the intended purpose. To use a manageable apparatus 
 saves not only time and trouble, but what is of still greater conse- 
 quence, a smaller instrument may comparatively be carried to a 
 more perfect degree of action than a larger one ; because a mirror 
 of less weight and diameter may be composed of a metal which will 
 reflect more light than that of a larger one ; it will also accommodate 
 itself sooner to a change of temperature ; and when it contracts tar- 
 nish, it may with less trouble be repolished." 
 
 After describing the effects of different kinds of eye-glasses, the 
 Dr. states that the magnifying power by which the satellites of 
 Uranus were discovered was only 157 ; and that he constantly used 
 the same power in his sweeps of the heavens, and found it to be very 
 effective for the discovery of faint nebulae, and minute clusters of 
 stars, but hardly sufficient to show the satellites steadily. 
 
 The higher powers of 2400, 3600, and 7200, were only employed 
 to scrutinize the closest neighbourhood of the planet, in order to dis- 
 cover additional satellites ; but from the appearance of the known 
 satellites with these powers, they were found too indistinct to be 
 used.* 
 
 It has already been remarked, that both Mercury and Venus 
 exhibit all the various phases of the moon. This, however, can- 
 not be perceived without the aid of a very good telescope. But 
 with this assistance the eye can very distinctly discern all the 
 variety of forms in these two planets, which can be so easily per- 
 ceived in the moon by the naked eye. After their inferior conjunc- 
 tion, that is, when first seen in the morning, rising a little before the 
 sun, they exhibit the form of a crescent. When they have attained 
 their greatest western elongation, they appear nearly half illuminated. 
 As they return towards the sun, their disc becomes more and more 
 illuminated, till they reach their superior conjunction, when it is 
 
 * The telescopes here mentioned are of the reflecting kind, the mirrors of 
 which are metal, or rather an alloy of various metals. The great mirror of the 
 40-feet telescope is four feet in diameter, and weighs above 2000 pounds. 
 
44 THE PLANETS. 
 
 completely illuminated ; but being on the opposite side of the suit 
 with respect to the earth, they are lost in his rays. \Vhen they 
 begin to be seen in the evening, their disc appears gibbous, or more 
 than half; and when they have reached their greatest elongation, it 
 again appears about half enlightened. In their return to the sun, the 
 luminous disc continues to diminish till they arrive at their inferior 
 conjunction, and then their dark side is completely turned towards 
 the earth. 
 
 In the interval between the disappearing of these planets in the 
 evening, and their re-appearing in the morning, they sometimes pass 
 over the sun in the form of a dark spot. See page 25. This ap- 
 pearance would happen at every inferior conjunction of Mercury and 
 Venus, and their passage would be right across his centre, if their 
 orbits were co-incident with the ecliptic. But on account of both 
 their orbits being inclined several degrees to the ecliptic, they are 
 never seen to cross the sun's disc but when they are very near any 
 of their nodes at the time of their inferior conjunction, which is very 
 seldom the case. At all other times they pass either above or below 
 the disc of the sun. The transits of Venus succeed each other at the 
 intervals of eight and one hundred years alternately. 
 
 The planet Mercury is so much immersed in the sun's rays, that 
 few observations can be made upon him. It is, therefore, almost 
 impossible to observe points of unequal splendor on his disc ; and yet 
 certain periodical inequalities have been observed in the horns of the 
 disc. This circumstance has led some astronomers to conclude that 
 Mercury has a revolution on his axis as well as the planets Venus, 
 Mars, Jupiter, and Saturn, each of which has had its revolution on 
 its axis determined by the same means ; namely, the motion of cer- 
 tain spots, distinguished by the colour or intensity of their light from 
 the other parts of the planetary disc. 
 
 The astronomer Shroeter, by continued observations on the horns 
 of Venus, and attending to the variations in the appearance of some 
 luminous points near the edges of the unenlighted parts, has not only 
 ascertained that Venus has a revolution on its axis, but that its surface 
 is diversified with mountains of very great height. The following 
 figure, A, represents Venus according to Herschel, and B and C 
 according to Shroeter; they are, however, inverted. 
 
 The extreme difficulty, however, of seeing the spots on this planet 
 even with the best telescopes, in our climate, prevents such observa- 
 tions from being so often repeated as could be wished. In point of 
 brilliancy, Venus surpasses all the other planets. On some occa- 
 sions it is so bright as to be seen in full day by the naked eye. 
 
THE PLANETS. 
 
 The gibbous appearance, and spheroidical figure of Mars, could 
 never have been discovered without the assistance of very powerful 
 telescopes ; for, as we have already remarked, the true figure of 
 this planet was unknown till the time of Dr. Herschel. But the in- 
 dustry and ingenuity of this celebrated astronomer, in constructing* 
 telescopes of the most powerful kind, and making observations with 
 them, has not only ascertained the real figure of this planet, but also 
 of almost all the other planets ; and by the spots which he discovered 
 near the poles of Mars, he has been enabled to settle the inclination 
 of its axis to the plane of its equator, and consequently to ascertain 
 its change of seasons. The following figures, A, B, C, and D, re- 
 present this planet as seen by Dr. Herschel, with his best tele- 
 scopes : 
 
 From these discoveries it appears, that the analogy between Mars 
 and the Earth is greater than between the Earth and any other 
 planet of the solar system. Their diurnal motion is nearly the same ; 
 the obliquity of their respective ecliptics, on which the seasons de- 
 pend, are not very different; and of all the superior planets, the dis- 
 tance of Mars from the Sun is by far the nearest alike to that of the 
 Earth ; nor is the length of its year very different from ours, when 
 compared with the years of Jupiter, Saturn, and Uranus. 
 
 The telescopic appearance of the planet Jupiter having been 
 pretty fully treated of at page 36, little more remains to be said re- 
 specting it. With a telescope of a very moderate power, the disc of 
 Jupiter appears nearly as large as the Moon ; and though the surface 
 be diversified by regular and parallel belts, yet it appears much 
 smoother than that of the Moon. The following figures, A and B, 
 exhibit the appearance of this planet as seen by Herschel with his 
 best telescope. 
 
46 THE PLANETS. 
 
 The satellites which attend Jupiter cannot bo perceived without 
 the aid of a telescope which magnifies at least thirty times ; but with 
 one which magnifies fifty times, they may be seen most distinctly. 
 The telescope by which they were first discovered magnified thirty 
 two times ; but it required many observations, and great attention to 
 their relative situations, to distinguish them from small stars with 
 such a small power. When the satellites are about to be hid behind 
 the body of Jupiter, they are often observed to disappear, though at 
 some distance from the planet ; and the third and fourth sometimes 
 re-appear on the same side of the disc. 
 
 The only cause which can be assigned for these disappearances is 
 the conical shadow which Jupiter casts behind him ; for the satel- 
 lites are always observed to disappear on that side of the disc oppo- 
 site to the sun, and consequently on the same side to which the co- 
 nical shadow is projected. 
 
 Another proof of this being the cause is, that they are eclipsed 
 nearest to the disc when Jupiter is nearest to his opposition ; and the 
 duration of these eclipses answers precisely to the time which they 
 should employ to pass through the conical shadow of Jupiter.* 
 
 Another singular appearance in the satellites has been remarked 
 by Dr. Herschel ; which is, that the same satellite is more luminous 
 at one time than another, and that the period of these changes is for 
 each satellite the same with the time of its revolution about Jupiter ; 
 hence he has inferred, that each of the satellites revolves on its axis 
 in the same time that it revolves round Jupiter, which is well known 
 to be the law that the moon observes in its revolution. 
 
 Of all the wonderful and extraordinary appearances exhibited by 
 the heavenly bodies, which belong to the solar system, when viewed 
 by a powerful telescope, those which the planet Saturn exhibits are 
 the most to be admired. 
 
 The appearance of this planet, when examined with a powerful 
 telescope, is not only singular and wonderfull, but it is one of the 
 most beautiful and interesting sights which are to be seen in the 
 heavens. The planet itself, with its belts and spots, is an interest- 
 ing object ; but when viewed at a time that the ring is most conspi- 
 cuous, the effect is singularly grand and beautiful. But, having 
 already given an account of the appearance and changes which the 
 ring undergoes, as well as a description of the other phenomena be- 
 longing to this extraordinary planet, little remains to be said respect- 
 ing it here. We shall, however, give a representation of this 
 planet, as observed by Dr. Herschel, on various occasions, with his 
 most powerful telescope. 
 
 * When Jupiter, or any of the superior planets, are in opposition to the sun, 
 they are then at least distance from the earth, and at their greatest when in con- 
 junction with him ; but the contrary is the case with the inferior planets. 
 
OF COMETS. 47 
 
 On accouut of the great distance of this planet from the sun, it 
 appears much fainter than Jupiter. With the naked eye it can 
 scarcely be discovered, except when the sky is very clear. 
 
 The real form of the ring has not yet been accurately determined. 
 When seen in the most favourable position, it appears of an oval or 
 ecliptic form ; but supposing it circular, its breadth has been deter- 
 mined to be about one-third of the diameter of the planet. 
 
 The planet Uranus, being so immensely distant from the earth, 
 and from the sun, which illuminates him, he cannot be discovered at 
 all without the assistance of the telescope; of course, all that we 
 know of this planet we owe to the powerful telescopes and perse- 
 vering industry of its discoverer, Dr. Herschel. But, having already 
 stated the result of the Doctor's observations on this planet, at 
 page 29, as well as his more recent observations on its satellites, at 
 the beginning of this article, nothing remains to be said of them here. 
 
 OF COMETS. 
 
 Hast thou ne'er seen the Comet's flaming flight ? 
 TV illustrious stranger, passing, terror sheds 
 On gazing nations, from his fiery train, 
 Of length enormous ; takes his ample round 
 Through depths of ether ; coasts unnumber'd ; worlds 
 Of more than solar glory ; doubles wide 
 Heaven's mighty cape, and then revisits earth, 
 From the long travel of a thousand years. 
 
 YOUNG. 
 
 Besides the planets just described, which are always nearly at the 
 same distance from the sun, and within our view, there are other 
 bodies belonging to the solar system called Comets, which seldom 
 come within our view. In their appearance, the comets are very 
 remarkable, being generally surrounded by a faintly luminous va- 
 pour, to which the name of coma has been given. As the comet 
 approaches the sun, the coma becomes brighter, and at length shoots 
 out into a long train of luminous transparent vapours, which always 
 keep in a direction opposite to the sun, and is called the tail of the 
 comet. When a comet makes its appearance, it is only for a very 
 
48 OF COMETS. 
 
 short period, seldom exceeding a few months, and sometimes only a 
 few weeks. Instead of moving from west to east, like the planets, in 
 orbits making small angles with the ecliptic, they are observed to 
 cross it at all angles. Their progress among the fixed stars is in ge- 
 neral more rapid than that of the planets, and their change of appa- 
 rent magnitude is much more remarkable. When a comet retires 
 from the sun, its tail decreases, and nearly resumes its first appear- 
 ance. Those comets which never approach very near the sun have 
 nothing but a coma, or nebulosity round them, during the whole 
 time of their continuance in view. 
 
 The tail of a comet is always transparent ; for the stars are often 
 distinctly visible through it ; and it has even been said, that, on some 
 occasions, they have been seen through the nucleus, or head. The 
 length and form of the tail are very different : sometimes it extends 
 only a few degrees, at others it extends more than 90 degrees. In 
 the great comet that appeared in the year 1680, the tail subtended an 
 angle of 70; and the tail of the one which appeared in 1618, an 
 angle of 104. The tail sometimes consists of diverging streams of 
 light; that of the comet which appeared in the year 1744 consisted 
 of six, all proceeding from the head, and all a little bent in the same 
 direction. 
 
 The tail of the beautiful comet which appeared in 1811 was com- 
 posed of two diverging beams of faint light, slightly coloured, which 
 made an angle of 15 to 20, and sometimes much more. Both of 
 these were a little bent outward, and the space between them was 
 comparatively obscure. 
 
 The apparent difference in the length and lustre of the tail of 
 comets has given rise to a popular division of these singular bodies 
 into three kinds ; viz. bearded, tailed, and hairy comets ; but this 
 division rather relates to the several circumstances of the same 
 comet, than to the phenomena of different ones. Thus, when the 
 comet is east of the sun, and moves from him, it is said to be 
 bearded, because the light precedes it in the manner of a beard ; 
 when the comet is west of the sun, and sets after him, it is said to be 
 tailed, because the train of light follows it in the manner of a tail ; 
 and when the sun and comet are diametrically opposite, the earth 
 being between them, the train or tail is all hid behind the body of 
 the comet, except the extremities, which, being broader than the body 
 of the comet, appear to surround it like a border of hair, and on this 
 account it is called hairy. 
 
 But there have been several comets observed, whose disc was as 
 clear, round, and well defined, as that of Jupiter, without either tail, 
 beard, or coma. The magnitude of comets has been observed to be 
 very different ; many of them without their coma have appeared no 
 larger than stars of the first magnitude ; but some authors have given 
 us accounts of others, which appeared much greater. Such was the 
 one that appeared in the time of the Emperor Nero, which, as Seneca 
 relates, was not inferior in apparent magnitude to the sun himself. 
 The comet which Hevelius observed, in the year 1652, did not seem 
 to be less than the moon, though it was deficient in splendor; for it 
 
 
OF COMETS. 49 
 
 had a pale, dim light, and appeared with a dismal aspect. Most 
 Comets have dense and dark atmospheres surrounding their bodies, 
 which weaken the sun's rays that fall upon them ; but within these 
 appears the nucleus, or solid body of the Comet, which, when the 
 sky is clear, will often give a more splendid light. 
 
 Respecting the nature of these singular and extraordinary bodies, 
 philosophers and astronomers in all ages and countries have been 
 very much divided in their opinions. The vulgar have, however, 
 invariably considered them as evil omens, and forerunners of war, 
 pestilence, famine, &c. ; and to adopt the language of an old poet : 
 
 " The blazing star was viewed 
 
 Threatening the world with famine, plague, and war; 
 To princes death ; to kingdoms many crosses ; 
 To all estates inevitable losses ; 
 To herdsmen rot ; to ploughmen hapless seasons ; 
 To sailors storms ; to cities civil treasons." 
 
 The Chaldeans, who were eminent for their astronomical researches, 
 were of opinion, that Comets were lasting bodies, which had stated 
 revolutions as well as the Planets, but in orbits considerably more 
 extensive, on which account they are only visible while near the 
 earth, but disappear again, when they ascend into the higher 
 regions. Pythagoras taught, that Comets were wandering stars, 
 disappearing in the superior parts of their orbits, and becoming 
 visible only in the lower parts of them. Some of the ancient philo- 
 sophers supposed, they were nothing else but a reflection of the 
 beams from the sun or moon, and generated as a rainbow; others 
 supposed they arose from vapours and exhalations. The illustrious 
 Aristotle was of opinion they were meteors. Modern philosophers 
 have been equally perplexed as their predecessors in accounting for 
 the nature of these magnificent celestial appearances. The eccentric 
 but learned Paracelsus gravely affirmed that they were formed and 
 composed by angels or spirits, to foretel some good or bad events. 
 Kepler, the celebrated astronomer, asserted that Comets were mon- 
 sters, and generated in the celestial spaces, by an animal faculty ! 
 The sentiments of Bodin, a learned French writer of the 16th century, 
 were yet more absurd ; for he maintained, that Comets are spirits 
 which have lived upon the earth innumerable ages, and being at last 
 arrived on the confines of death, celebrate their last triumph, or are 
 called to the firmament like shining stars ! 
 
 James Bernoulli, a celebrated Italian philosopher, formed a rational 
 conjecture relative to Comets in viewing them as the satellites of some 
 very distant planets, invisible on the earth on account of its distance, 
 as were also the satellites, unless when in a certain part of their 
 course. Tycho Brahe, the illustrious but unfortunate philosopher of 
 Denmark, supported a true hypothesis on this subject; he averred, 
 that a Comet had no sensible diurnal parallax, and therefore was not 
 only far above the regions of our atmosphere, but much higher than 
 the moon ; that few have come so near the earth as to have any 
 diurnal parallax, yet all Comets have an annual parallax, the revolu- 
 tion of the earth in their orbit, causes their apparent motion to be 
 
 5 F 
 
50 OF COMETS. 
 
 very different from what it would be, if viewed from the sun, which 
 demonstrates that they are much nearer than the fixed stars which 
 have no such parallax. 
 
 Descartes advanced aother opinion, which is, that Comets are 
 only stars, that were formerly fixed like the rest, but becoming gra- 
 dually covered with maculae or spots, and at length wholly deprived 
 of their light, cannot keep their places, but are carried off by the 
 vortices * of the circumjacent stars ; and in proportion to their mag- 
 nitude and solidity, moved in such a manner, as to be brought nearer 
 to the orb of Saturn ; and thus coming within the reach of the sun's 
 light, are visible. 
 
 The absurdity of most of these hypotheses is now proved by the 
 observations which have been made on these bodies, by the celebrated 
 astronomers who have lived since the time of Descartes ; and parti- 
 cularly by our countrymen, Dr. Halley and Sir I. Newton. According 
 to the theory of Newton, the Comets are compact, solid, and durable 
 bodies ; in fact a species of planets, which move in very oblique and 
 eccentric orbits, in every direction, with the greatest freedom ; per- 
 severing in their motions even against the course and direction of the 
 planet. 
 
 The number of Comets which have been observed and recorded 
 with more or less accuracy, exceed 350 ; but not one-third of these 
 have been observed with such accuracy as to allow the elements of 
 their orbits to be ascertained .f Dr. Halley, following the theory of 
 Newton, set himself to collect all the observations which had been 
 made on Comets, and calculated the elements of 24 of them. And 
 by computations founded on these elements, he concluded that the 
 Comet of 1682, was the same that had appeared in 1607, 1531, and 
 1456 ; that it had a period of 75 or 76 years ; and that it might, of 
 course, be expected to appear again about the year 1759, which it 
 actually did. It therefore could be no longer doubted, that the 
 Comet observed in each of these years was the same, although its 
 appearance was very different. When it appeared in 1531, it was of 
 a bright gold colour ; in 1607, it was dark and livid ; in 1682 it was 
 bright ; and in 1759, it was faint and obscure. The return of some 
 of the other Comets is probable, though not certain. 
 
 * Descartes supposed that every thing in the universe was formed from very 
 minute bodies called atoms, which had been floating in open space. To each 
 atom he attributed a motion on its axis ; and he also maintained that there was a 
 general motion of the whole universe round like a vortex or whirlpool. In the 
 centre of this vortex was the sun, with all the planets circulating round him, at 
 different distances ; and that each star was also the centre of a general vortex, 
 round which its planets turned. Besides these general vortices, each planet had 
 a vortex of its own, by which its satellites (if it had any) were whirled round, 
 and any other body that came within its reach ! 
 
 t The elements of a planet or comet are, 1st. The inclination of the orbit ; 
 2d. The position of the line of the nodes ; 3d. The longitude of the perihelion; 
 4th. The perihelion distance from the sun ; 5th. The time when a planet or comet 
 is in its perihelion. 
 
OF COMETS. 51 
 
 The great Comet of 1680, was supposed by Dr. Halley to have a 
 period of 575 years, and to be the same that appeared a little before 
 the death of Julius Caesar, in the year 44 A.C. ; again in the reign 
 of Justinian, in the year 531 P.C. ; and in 1106, in the reign of 
 Henry I. At all of these periods, appearances of a great and ter- 
 rible Comet are recorded, but no such observations have been made 
 on them as to ascertain their elements. 
 
 The Comet of 1680, just mentioned, approached nearer to the sun 
 than any other that is known. At its perihelion, its distance from 
 the sun was only ,Jgth part of the earth's, or about 572,000 miles, 
 whilst its aphelion distance is stated by Sir I. Newton to be not less 
 than 11,200,000,000 miles. It descended to the sun with a velocity 
 of 880,000 miles per hour, almost perpendicularly, and ascended in 
 the same manner, remaining in sight for four months ! 
 
 Some Comets have come very near the earth, particularly one 
 which appeared in 1472, and another in 1760. The former of these, 
 it is said, moved over an arc of 120 in one day, and the latter 41 in 
 the same space of time. These extraordinary changes can scarcely 
 be accounted for on any other principle but their proximity to the 
 earth. 
 
 It appears that Comets contain very little matter ; for in the year 
 1454, one approached so near the earth, that it is said to have 
 eclipsed the moon ; and yet it produced no sensible effects. Neither 
 did those just mentioned. And in 1770 a Comet approached very 
 near to the satellites of Jupiter, without producing any derangement 
 of these bodies. 
 
 It has, however, been supposed by some astronomers, that too 
 near an approach of a Comet to any other planet, might be produc- 
 tive of very great changes in the system to which they belong. The 
 celebrated Mr. Whiston and other eminent writers have indulged an 
 idea that the dissolution of this globe by fire will be occasioned by the 
 near approach of a Comet which will cause the general conflagration. 
 This supposition is assuredly worthy of due consideration, and 
 appears founded on the basis of sound reason. 
 
 Whatever difference of opinion prevails among the various sects 
 professing the Christian Faith, they all unite in believing that, at the 
 final consummation of all things, a general conflagration will take 
 place, and that this earth will be destroyed by fire. Our Lord, in 
 describing the awful scenes of the last judgment, observes, that 
 " the powers of Heaven shall be shaken/' Luke, xxi. 16. Now if a 
 Comet, in its revolution, should approach too near the orbit of 
 another planet, and a derangement of the order of the heavenly bo- 
 dies ensue, those powers must be shaken. Therefore in this point 
 of view Comets are particularly calculated to impress a serious and 
 religious awe, but not a superstitious fear, on every spectator. 
 They blaze forth in the Heavens, not as signs of approaching events, 
 either of good or evil, but to warn us of the final dissolution of this 
 globe on which we dwell by such a phenomenon. He who hath 
 placed his bow in the cloud to testify that the world shall no more 
 be destroyed by water, has also appointed those extraordinary 
 
52 OF COMETS. 
 
 bodies to illuminate the firmament, to demonstrate that by the 
 agency of a Comet the earth and all that is therein shall be 
 burnt up. 
 
 This hypothesis, supported by so able a mathematician, and 
 learned a man, as Mr. Whiston, while it is in perfect congruity with 
 true philosophical principles, is neither founded on the basis of 
 ignorant superstition or wild enthusiasm, but culculated to promote 
 moral and religious improvement. 
 
 At his command affrighting human kind, 
 
 Comets drag on their blazing lengths behind : 
 
 Nor as we think, do they at random rove, 
 
 But in determined times, through long ellipses move : 
 
 And though sometimes they near approach the sun, 
 
 Sometimes behind our system's orbit run ; 
 
 Throughout their race they act their Maker's will, 
 
 His power declare, his purposes fulfil. BAKER. 
 
 The conjectures which have bee.n advanced by several celebrated 
 astronomers respecting the nature and cause of the tail which usually 
 accompanies a Comet, are not only curious, but plausible and 
 ingenious. Tycho Brahe, who was the first that gave the Comets 
 their true rank in the creation, supposed that the tail was occasioned 
 by the rays of the sun passing through the head, or nucleus of the 
 Comet, which he believed to be transparent. Kepler thought that it 
 was the atmosphere of the Comet which was driven behind it by the 
 force of the solar rays. Sir Isaac Newton maintained that the tail 
 was a thin vapour, ascending by means of the sun's heat, as smoke 
 does from the earth.* Euler supposes that the tail is produced by 
 the impulse of the solar rays driving off the atmosphere from the 
 Comet. The late Dr. Hamilton, of Dublin, supposes them to be of 
 electric matter. 
 
 Notwithstanding the ingenuity and even probability of some of 
 these hypotheses, yet there is little in any one of them to entitle it to 
 preference above the others ; and till multiplied observations shall 
 have added to the imperfect knowledge which we at present possess 
 of these bodies, it is perhaps better not to give a decided preference 
 to any of them. For as Dr.Herschel very justly observes, " Many 
 of the operations of Nature are carried on in her great laboratory 
 which we cannot comprehend ; but now and then we see some of the 
 tools with which she is at work. We need not wonder that their 
 construction should be so singular as to induce us to confess our 
 ignorance of the method of employing them, but we may rest assured 
 that they are not mere lusus naturae. I allude to the great number of 
 small telescope Comets that have been observed ; and to the far 
 greater number still, that are probably much too small for being 
 noticed by our most diligent searchers after them. Those six, for 
 
 * It is evident that this hypothesis is founded on the supposition which then 
 prevailed, that the sun was a body of fire; but as the truth of this supposition is 
 now doubted by most philosophers, and abandoned by many, the hypothesis of 
 Newton on this subject does not now meet with many advocates. 
 
OF THE MOON. 53 
 
 instance, which my sister has discovered, I can, from examination, 
 affirm, had not the least appearance of any solid nucleus, and seemed 
 to be mere collections of vapours condensed about a centre. Five 
 more that 1 have also observed, were nearly of the same nature. 
 This throws a mystery over their destination, which seems to place 
 them in the allegorical view of tools, probably designed for some 
 salutary purposes to be wrought by them ; and, whether the restora- 
 tion of what is lost to the sun by the emission of light, may not be 
 one of these purposes, I shall not presume to determine. The motion 
 of the Comet discovered by M. Messier, in June 1770, plainly indi- 
 cated how much its orbit was liable to be changed, by the perturba- 
 tion of the planets ; from which, and the little agreement that can be 
 found between the elements of the orbits of all the Comets that have 
 been observed, it appears clearly that they may be directed to carry 
 their salutary influence to any part of the heavens." 
 
 -" To shake 
 
 Reviving moisture on the numerous Orbs 
 Through which his long ellipsis winds ; perhaps 
 To lend new fuel to declining Suns, 
 To light up Worlds and feed th' eternal fire." 
 
 THOMSON. 
 
 OF THE MOON. > 
 
 Next to the Sun, the Moon is the most remarkable of all the 
 heavenly bodies, and is particularly distinguished by the periodical 
 changes to which her figure and Hght are subject. 
 
 Among the ancients, Luna > , or the Moon, was an object of very 
 great respect. By the Hebrews she was more regarded than the 
 Sun : and it appears they regulated their time by her motions and 
 appearances. The new moon, or first day of every month, was 
 observed as a festival among them, which was celebrated with sound 
 of trumpets, entertainments, and sacrifices. In the Bible, the 
 Moon is mentioned under several names, as the Queen of Heaven, 
 the Goddess of the Zidonians, and the abomination of the Zido- 
 nians, because she was worshipped by the inhabitants of Zidon or 
 Sidon. The ancient bards and poets have also celebrated the praises 
 of the Moon under various appellations; as Cynthia, Cyllene, 
 Phoebe, Silver Queen of Night, Queen of the Silver Bow, &c. 
 
 Sister of Phoebus, gentle queea, 
 Of aspect mild and ray serene ; 
 Whose friendly beams by night appear, 
 The lonely traveller to cheer ! 
 
 The Moon is not a primary planet, but a secondary or satellite, 
 which revolves round the earth, and accompanies it in its annual 
 revolution round the sun. The mean time of a revolution of the 
 Moon round the earth, or the time between two successive conjunc- 
 tions, is 29 days, 12 hours, 44 minutes ; but the time she takes to 
 
54 PHASES OF THE MOON. 
 
 perform a revolution round her orbit, is only 27 days, 7 hours, 43 
 minutes. The former of these periods is called the Synodical, and 
 the latter the Periodical revolution. The difference between these 
 periods is occasioned by the motion of the earth in the ecliptic ; for 
 while the Moon is going round the earth, the earth advances about 
 29 in the ecliptic, which is nearly 1 per day ; and, therefore, the 
 Moon must advance 29 more than a complete revolution round her 
 orbit, before she can overtake the earth, or be again in conjunction 
 with the sun, which will require 2d. 5h., her daily motion being 
 about 13 degrees. 
 
 Of all the celestial bodies, the Moon is the nearest to the earth, 
 her mean distance being only 240,000 miles, which is scarcely a 
 four hundred part of the sun's distance from the earth ; but her 
 apparent size is nearly equal to that of the sun, she must therefore 
 be a very small body compared with the sun. Her diameter is only 
 about 2161 miles ; and, therefore the earth is about 48^ times 
 greater ; but the density of the Moon is said to be to that of the 
 earth as 5 to 4, consequently the quantity of matter contained in the 
 earth is only about 39 times that contained in the Moon. 
 
 Although the Moon moves over a very considerable portion of her 
 orbit in the course of a day, yet on account of its smallness her 
 hourly motion is only about 2290 miles, which is only about 3 oth part 
 of the space passed over by the earth in the same time. 
 
 But in ail her motions, the Moon is subject to great irregularities, 
 which arise from the eccentricity of her orbit, and her proximity 
 to the earth. The eccentricity of her orbit, as determined from 
 the latest and most accurate observations, is 12,960 miles, or 
 nearly ,gth part of her mean distance ; of course she is about jth part 
 nearer the earth on some occasions than at others. 
 
 PHASES OF THE MOON. 
 
 By Thy command the Moon, as daylight fades, 
 
 Lifts her broad circle in the deep'ning shades ; 
 
 Arrayed in glory, and enthroned in light, 
 
 She breaks the solemn terrors of the night ; 
 
 Sweetly inconstant in her varying flame 
 
 She changes still, another yet the same ! 
 
 Now in decrease by slow degrees she shrouds, 
 
 Her fading lustre in a vale of clouds ; 
 
 Now of increase, her gathering beams display 
 
 A blaze of light, and give a paler day. 
 
 Ten thousand stars adorn her glittering train, 
 
 Fall when she falls, and rise with her again. BROOME. ' 
 
 Although the phases of the Moon are among the most frequently 
 observed phenomena of the heavens, yet they are also among the 
 most wonderful. But on account of the frequency and regularity of 
 the changes in the appearances and situation of this beautiful object, 
 the cause of these phenomena are perhaps less thought of by ordinary 
 observers, than if they were less frequent. The Moon being an 
 
PHASES OF THE MOON. 
 
 55 
 
 opaque spherical body, which appears luminous only in consequence 
 of reflecting the light of the sun, can only have that side illuminated 
 which is at any time turned towards the sun, the other side remaining 
 in darkness; and as that part of her can only be seen which is 
 turned towards the earth, it is evident that we must perceive different 
 portions of her illuminated, according to her various positions with 
 respect to the earth and sun. 
 
 At the time of conjunction, or when the Moon is between the 
 earth and the sun, she is then invisible on the earth, because her 
 enlightened side is then turned towards the sun, and her dark side 
 towards the earth. In a short time after the conjunction, she appears 
 like a fine crescent to the eastward of the sun a little after he sets, as 
 represented by the following figure. 
 
 This crescent begins to fill up, and the illuminated part to increase, 
 as she advances in her orbit ; and when she has performed a fourth 
 part of a revolution, she appears to be half illuminated, and is then 
 said to be in her first quarter. After describing the second quadrant 
 of her orbit, she is then opposite to the sun, and shines with a round 
 illuminated disc, which is called full moon.* Her appearance at this 
 time is very accurately represented by the following figure. 
 
 * At the time of full Moon, the Moon appears to be as large as the sun ; for 
 the angle under which the Moon appears when viewed from the earth, is the 
 same as the angle under which the sun appears, and therefore the Moon may 
 hide the sun's whole disc from us, as she sometimes does in solar eclipses, 
 which see. 
 
CHASES OF THE MOON. 
 
 It is necessary, however, to remark, that the Moon does not 
 appear perfectly round when she is full in the highest or lowest part 
 of her orbit ; because we have not a full view of her enlightened 
 side at that time. "When full in the highest part of her orbit, a small 
 deficiency appears on her lower edge ; and the contrary, when full 
 in the lowest part of her orbit. 
 
 After the full she begins to decrease gradually as she moves 
 through the other half of her orbit ; and when the eastern half of her 
 only is enlightened, she is said to be in her third quarter, and has 
 the following appearance : thence she continues to decrease until she 
 again disappears at the conjunction, as before.* 
 
 * These various phases may be satisfactorily and pleasantly illustrated, by 
 placing a lighted candle on a table to represent the sun, and a small ball at 
 some distance from it to represent the earth, and then carrying a smaller ball 
 round it, to represent the moon revolving round the earth. 
 
PHASES OF THE MOON. 
 
 Between the third quarter and change, the Moon is frequently 
 visible in the forenoon, even when the sun shines ; and then she 
 affords us an opportunity of seeing a very agreeable appearance, 
 wherever we find a globular stone above the level of the eye, as sup- 
 pose on the top of a gate. For, if the sun shines on the stone, and 
 we place ourselves so as the upper part of the stone may just seem 
 to touch the point of the Moon's lowermost horn, we shall then see 
 the enlightened part of the stone exactly of the same shape with the 
 Moon ; horned as she is, and inclined the same way to the horizon. 
 The reason is plain ; for the sun enlightens the stone the same way 
 as he does the Moon : and both being globes, when we put ourselves 
 into the above situation, the Moon and stone have the same position 
 to our eyes ; and therefore we must see as much of the illuminated 
 part of the one as of the other. 
 
 The position of the Moon's cusps, or a right line touching the 
 points of her horns, is very differently inclined to the horizon at 
 different hours of the same days of her age. Sometimes she stands, 
 as it were, upright on her lower horn, and then such a line is perpen- 
 dicular to the horizon ; when this happens, she is in what the 
 astronomers call the Nonagesimal Degree ; which is the highest point 
 of the ecliptic above the horizon at that time, and is 90 degrees from 
 both sides of the horizon where it is then cut by the ecliptic. But 
 this never happens when the Moon is on the meridian, except when 
 she is at the very beginning of Cancer or Capricorn. 
 
 The inclination of that part of the ecliptic to the horizon in which 
 the Moon is at any time when horned, may be known by the position 
 of her horns ; for a right line touching their points is perpendicular to 
 the ecliptic. And as the angle which the Moon's orbit makes with 
 
58 MOTIONS OF THE MOON. 
 
 the ecliptic can never raise her above, nor depress her below, the 
 ecliptic, more than two minutes of a degree, as seen from the sun, it 
 can have no sensible effect upon the position of her horns. There- 
 fore, if a quadrant be held up, so as one of its edges may seem to 
 touch the Moon's horns, the graduated side being kept toward the 
 eye, and as far from the eye as it can be conveniently held, the arc 
 between the plumb-line and that edge of the quadrant which seems to 
 touch the Moon's horns, will shew the inclination of that part of the 
 ecliptic to the horizon. And the arc between the other edge of the 
 quadrant and plumb-line, will shew the inclination of a line, touching 
 the Moon's horns, to the horizon. 
 
 These various phases plainly demonstrate that the Moon does not 
 shine by any light of her own ; for if she did, being globular, she 
 would always present a fully illuminated disc like the sun. That the 
 Moon is an opaque body, is not only proved from her phases, but 
 also by the occultation of stars, for her body often comes between 
 the earth and a star, and while she is passing it, the star is hid from 
 our view. 
 
 MOTIONS OP THE MOON. 
 
 The neighbouring moon her monthly round 
 
 Still ending, still renewing, through mid heaven, 
 
 With borrowed light her countenance triform ;* 
 
 Hence fills and empties to enlighten th* earth, 
 
 And in her pale dominion checks the night. MILTON. 
 
 It has already been remarked, that the motions of the Moon are 
 very irregular. The only equable motion she has, is her revolution on 
 her axis, which is completed in the space of a month, or the time in 
 which she moves round the earth. This has been determined by the 
 important and curious circumstance, that she always presents the 
 same face to the earth, at least with very little variation. But as her 
 motion in her orbit is alternately accellerated and retarded, while 
 that on her axis is uniform, small segments on the east and west 
 sides alternately appear and disappear. This occasions an apparent 
 vibration of the Moon backwards and forwards, which is called her 
 libration in longitude. 
 
 A little more of her disc is also seen towards one pole, and some- 
 times towards the other, which occasions another wavering or vacil- 
 lating kind of motion, called the libration in latitude. This shows 
 that the axis of the Moon is not exactly, though nearly, perpendicular 
 to the plane of her orbit ; for if the axis of the Moon were exactly 
 perpendicular to the plane of her orbit, or if her equator coincided 
 with that plane, we should perceive no other libration than that in 
 longitude. 
 
 When the place of the Moon is observed every night, it is found 
 
 * Increasing with horns towards the east ; decreasing with horns towards the 
 west ; and at the full. 
 
OF THE HARVEST MOON. 59 
 
 that the orbit in which she performs her revolutions round the earth, 
 is inclined to the ecliptic at an angle of 5 9' at a mean rate ; this 
 angle is not only subject to some variation, but the very orbit itself 
 is changeable, and does not always preserve the same form: for 
 though it is elliptical, or nearly so, with the earth in one of the foci, 
 yet its eccentricity is subject to some variation, being greater when 
 the line of the apsides coincides with that of the syzygies, and least 
 when &ese lines are at right angles to each other. But the eccen- 
 tricity always very considerable, and, therefore, the motion of the 
 Moon is very unequal, for like all other planets, it is quickest in 
 perigee and slowest in apogee. At a mean rate she advances, in 
 her orbit, 13 10' per day, and comes to the meridian about 48 
 minutes later every day. As the Moon's axis is nearly perpendicu- 
 lar to the plane of the ecliptic, she can scarcely have any change of 
 seasons. But what is still more remarkable, one half of the Moon 
 has no darkness at all, while the other half has two weeks of light 
 and darkness alternately. For the earth reflects the light of the Sun 
 to the Moon, in the same manner as the Moon does to the earth ; 
 therefore, at the time of conjunction, or new Moon, one half of the 
 Moon will be enlightened by the Sun, and the other half by the 
 earth : and at the time of opposition, or full Moon, one half of the 
 Moon will be enlightened by the Sun, but the other half will be in 
 darkness. The earth also exhibits similar phases to the Moon to 
 what she does to the earth, but in a reverse order, for when the 
 Moon is full, the earth is invisible to the Moon; and when the Moon 
 is new, the earth will appear to be full to the Moon, and so on. It 
 has been already mentioned, that the Moon always presents the same 
 face to the earth, from hence it is inferred, that one half of the Moon 
 can never see the earth at all ; whilst from the middle of the other 
 half it is always seen overhead, turning round almost thirty times as 
 fast as the Moon does. 
 
 From the circle which limits our view of the Moon, only one half 
 of the earth's side next her is seen, the other half being hid below the 
 horizon of all places on that circle. 
 
 To the Moon, the earth seems to be the largest body in the uni- 
 verse, for it appears about thirteen times greater than the Moon does 
 to the earth. 
 
 OF THE HARVEST MOON. 
 
 IT has long been known that the Moon when full, about the time 
 of harvest, rises for several nights nearly at the time of Sun setting ; 
 but the cause of this remarkable phenomenon has not been so long 
 known. This appearance was observed by the husbandman long 
 before it was noticed by the Astronomer ; and on account of its bene- 
 ficial effects in affording a supply of light immediately after Sun-set, 
 at this important season of the year, it is called the Hawest Moon. 
 
 In order to conceive the reason of this phenomenon it must be 
 recollected, that the Moon is always opposite the Sun when she is 
 
60 OF THE HARVEST MOON. 
 
 full, and of course in the opposite sign and degree of the zodiac. 
 Now the Sun is in the signs Virgo and Libra in August and Sep- 
 tember, or the time of harvest ; and therefore the Moon when full, 
 in these months, is in the signs Pisces and Aries. But that part of 
 the ecliptic in which Pisces and Aries is situated makes a much less 
 angle with the horizon of places that have considerable northern 
 latitude, than any other part of the ecliptic, and therefore a greater 
 portion of it rises in any given time than an equal portion at any other 
 part of it. Or, which is the same thing, any given portion of the 
 ecliptic about Pisces and Aries rises in less space of time than an 
 equal portion of it does at any other part. And as the Moon's daily 
 motion in her orbit is about 13, this portion of it will require less 
 time to rise about those signs, than an equal portion at any other 
 part of the ecliptic ; consequently, there will be less difference 
 between the times of the Moon's rising when in this part of her orbit 
 than in any other.* 
 
 At a mean rate the Moon rises 50 minutes later on any evening 
 than she did the preceding evening ; but when she is full about the 
 beginning of September, or when she is in that part of her orbit 
 which rises with the signs Pisces and Aries, she rises only about 
 16 or 17 minutes later than on the preceding evening ; consequently, 
 she will seem to rise for a few evenings at the same hour. 
 
 Although this is the case every time that the Moon is in this part 
 of her orbit ; yet it is little attended to, except when she happens to 
 be full at the time, which can only be in August or September. 
 
 In some years this phenomenon is much more perceptible than in 
 others, even although the Moon should be full on the same day, or 
 in the same point of her orbit. This is owing to a variation in the 
 angle which the Moon's orbit makes with the horizon of the place 
 where the phenomenon is observed. If the Moon moved exactly in 
 the ecliptic, this angle would always be the same at the same time 
 of the year. But as the Moon's orbit crosses the ecliptic and makes 
 an angle with it of 5 9', the angle formed by the Moon's orbit and 
 the horizon of any place is not exactly the same as that made by the 
 ecliptic and the horizon. Some years it is greater, and others less, 
 even at the same time of the year; for it is subject to considerable 
 variations, owing to the retrograde motion of the moon's nodes.-]- 
 
 If the ascending node should happen to be in the first degree of 
 Aries, it is evident, that this part of the Moon's orbit will rise with 
 the least possible angle, and, of course, any given portion of it will 
 require less time to rise than an equal portion in any other part of the 
 orbit. The most favourable position of the nodes for producing the 
 most beneficial harvest Moons is, therefore, when the ascending node 
 
 * It would tend very much to make this phenomenon understood, if a terres- 
 trial globe were at hand, and rectified for the latitude of London, when reading 
 this description. 
 
 t The nodes, or points where the moon's orbit crosses the ecliptic, move back- 
 ward about 19 in a year, by which means they move round the ecliptic in 18 
 years 225 days. 
 
OF THE HARVEST MOON. 61 
 
 is in the first of Aries, and of course the descending in the first of 
 Libra. When the nodes are in these points 13 of the Moon's orbit, 
 about the first of Aries, rises in the space of 16 minutes, in the lati- 
 tude of London, and consequently, when the Moon is in this part of 
 her orbit, the time of her rising will differ only 16 minutes from the 
 time she rose on the preceding evening. When the Moon is in the 
 opposite part of her orbit, or about the signs Virgo and Libra, which 
 make the greatest angle with the horizon at rising, 13 of her orbit 
 will require 1 h. 15' to rise, although it were coincident with the eclip- 
 tic ; and if the nodes be in the points just mentioned, the same por- 
 tion of the orbit will require 1 h. 20' to ascend above the horizon of 
 the same place ; and so much later will the Moon rise every night for 
 several nights when in this part of her orbit. As the Moon is full' in 
 these signs in the months of March and April they may be called 
 vernal full Moons. 
 
 Those signs of the ecliptic which rise with the greatest angle, set 
 with the least; and those that rise with the least, set with the greatest. 
 Therefore, the vernal full Moons differ as much in their times of 
 rising, every night, as the autumnal, or harvest, Moons differ in the 
 times of their setting ; and they set with as little difference of time as 
 the autumnal ones me, supposing the full Moons to happen in oppo- 
 site points of the Moon's orbit, and the nodes to remain in the same 
 point of the ecliptic. 
 
 In southern latitudes, the harvest Moons are just as regular as in 
 the northern, because the seasons are contrary ; and those parts of 
 the Moon's orbit about Virgo and Libra, where the vernal full 
 Moons happen in northern latitudes, (and the harvest ones in southern 
 latitudes) rise at as small an angle at the same degree of south lati- 
 tude, as those about Pisces and Aries in north latitude, where the 
 autumnal full Moons take place. 
 
 At places near the Equator, this phenomenon does not happen ; 
 for every point of the ecliptic, and nearly every point of the Moon's 
 orbit, makes the same angle with the horizon, both at rising and 
 setting, and therefore equal portions of it will rise and set in equal times. 
 
 As the Moon's nodes make a complete circuit of the ecliptic in 18 
 years 225 days, it is evident, that when the ascending node is in the 
 first of Aries at any given time, the descending one must be in the 
 same point about 9 years 112 days afterwards ; consequently, there 
 will be a regular interval of about 9j-years between the most bene- 
 ficial and least beneficial harvest Moons. 
 
 APPARENT SIZE OF THE MOON. 
 
 It has been already remarked at page 55, that the apparent size 
 of the Moon is nearly equal to that of the sun ; but the apparent size 
 of the Moon is not always the same, for she is often much nearer the 
 earth at one time than another ; hence, it is evident, her apparent 
 magnitude must vary, and that it will be greatest when she is nearegt 
 the earth. (See page 54.) 
 
 6 G 
 
G2 SPOTS, &C. IN THE MOON. 
 
 But she appears larger when in the horizon than in the zenith even 
 on the same evening ; and yet it may easily be proved, that she is a 
 s.emi-diameter of the earth, or about 4000 miles, farther from the spec- 
 tator when she is in the horizon than when she is in the zenith, and 
 consequently ought to appear smaller, which will be found to be 
 really the case if accurately measured. 
 
 This apparent increase of magnitude in the horizontal Moon, must 
 therefore be considered as an optical illusion ; and may be explained 
 upon the well known principle, that the eye in judging of distant 
 objects is guided entirely by the previous knowledge which the mind 
 has acquired of the intervening objects. .Hence arise the erroneous 
 estimates we make of the size of distant objects at sea, of objects 
 below us when viewed from great heights, and of objects highly 
 elevated when viewed from below. Now when the Moon is near the 
 zenith, she is seen precisely in this last situation, of course there is 
 nothing near her, or that can be seen at the same time with which her 
 size can be compared ; but the horizontal Moon may be compared 
 with a number of objects whose magnitude is previously known. 
 
 That the Moon appears under no greater an angle (or is not larger) 
 in the horizon, than when she is on the meridian, may be proved by 
 the following simple experiment. 
 
 Take a large sheet of paper and roll it up in the form of a tube, 
 of such width as just to include the whole of the Moon when she 
 rises ; then tie a thread round it to keep it exactly of the same size, 
 and when the Moon comes to the meridian, where she will appear to 
 the naked eye to be much less, look at her again through the same 
 tube, and she will fill it as completely as she did before. 
 
 When the Moon is full and in the horizon, she appears of an oval 
 form, with her longest diameter parallel to the horizon. This appear- 
 ance is occasioned by the refraction of the atmosphere, which is 
 always greatest at the horizon, consequently the lower limb or edge 
 must be more refracted than the upper edge, and therefore these two 
 edges will appear to be brought nearer each other, or the vertical 
 diameter will appear to be shortened ; and as the horizontal diameter 
 is very little affected by the refraction, she must appear to have some- 
 what of an oval shape. The sun is affected in the same manner when 
 in the horizon. 
 
 SPOTS, MOUNTAINS, &C. IN THE MOON. 
 
 Turn'd to the sun direct, her spotted disk 
 
 Shows mountains rise, umbrageous dales descend, 
 
 And caverns deep, as optic tube descries. THOMSON. 
 
 When the Moon is viewed through a good telescope, her surface 
 appears to be diversified with hills and valleys ; but this is most dis- 
 cernable when she is observed a few nights after the change or oppo- 
 sition ; for when she is either horned or gibbous, the edge about the 
 confines of the illuminated part is jagged and uneven. 
 

 SPOTS, &C. IN THE MOON. 63 
 
 Many celebrated astronomers have delineated maps of the face of 
 the Moon ; but the most celebrated are those of Hevelius, Grimaldi, 
 Riccioli, and Cassini ; in which the appearance of the Moon is repre- 
 sented in its different states, from new to full } and from full 
 to new. 
 
 The plate which we have given at page 56, represents the face of 
 the Moon as viewed by the most powerful telescopes, the light or 
 illuminated parts being elevated tracts, some of which rise into very 
 high mountains, while the dark parts appear to be perfectly smooth 
 and level. This apparent smoothness in the faint parts, naturally led 
 astronomers to conclude that they were immense collections of water; 
 and the names given to them, by some celebrated astronomers, are 
 founded on this supposition. For Hevelius distinguished them by 
 giving them the names of the seas on the earth ; while he distinguished 
 the bright parts by the names of the countries and islands on the 
 earth. But Riccioli and Langreni distinguished both the dark and 
 light spots, by giving them the names of celebrated astronomers and 
 mathematicians, which is now the general manner of distinguishing 
 them. 
 
 That the spots which are taken for mountains and valleys are 
 really such, is evident from their shadows. For in all situations in 
 which the Moon is seen from the earth, the elevated parts are con- 
 stantly found to cast a triangular shadow in a direction from the sun; 
 and on the contrary, the cavities are always dark on the side next 
 the sun, and illuminated on the opposite side, which is quite con- 
 formable to what we observe of hills and valleys on the earth. And 
 as the tops of these mountains are considerably elevated above the 
 other parts of the surface ; they are often illuminated when they are 
 at a considerable distance from the line which separates the enlightened 
 from the unenlighted part of the disc, and by this means afford us a 
 method of even determining their height. 
 
 Previous to the time of Dr. Herschel, some of the lunar moun- 
 tains were considered to be double the height of any on the earth ; 
 but by the observations of that celebrated astronomer, their height is 
 considerably reduced. 
 
 For after measuring many of the most conspicuous prominences, he 
 says, " From these observations I believe it is evident, that the 
 height of the lunar mountains is, in general, overrated; and that 
 when we have excepted a few, the generality do not exceed half a 
 mile in their perpendicular elevation." 
 
 As the Moon's surface is diversified by mountains and valleys as 
 well as the earth, some modern astronomers say they have disco- 
 vered a still greater similarity ; namely, that some of these are really 
 volcanoes, emitting fire, as those on the earth do. An appearance 
 of this kind was discovered by Don Ulloa in an eclipse of the sun, 
 which happened on the 24th June, 1778. It was a small bright spot 
 like a star, near the margin of the Moon, which he supposed at the 
 time to be a hole or valley, which permitted the sun's light to shine 
 through it. Succeeding observations have, however, led astrono- 
 mers to believe, that appearances of this kind are occasioned by the 
 
 G 2 
 
64 SPOTS, &C. IN THE MOON. 
 
 eruption of volcanic fire. Dr. Herschel, in particular, has observed 
 several eruptions of this kind, the last of which he has described in 
 the Philosophical Transactions for 1787, as follows : " On April the 
 19th, at lOh. 6m. I perceived three volcanoes in different places of 
 the dark part of the new Moon. Two of them are either already 
 nearly extinct, or otherwise in a state of going to break out, which 
 perhaps may be decided next lunation. The third shows an actual 
 eruption of fire or luminous matter : its light is much brighter than 
 the nucleus of the Comet which M. Mechain discovered at Paris on 
 the 10th of this month." The following night the Doctor found it 
 burned with greater violence ; and by measurement he found that the 
 shining or burning matter must be more than three miles in diameter, 
 of an irregular round figure, and very sharply defined about the 
 edges. The other two volcanoes resembled large faint nebulae, 
 which appeared to be gradually brighter towards the middle, but no 
 well defined luminous spot could be discovered in them. Dr. 
 Herschel adds, " the appearance of what I have called the actual 
 fire, or eruption of a volcano, exactly resembled a small piece of 
 burning charcoal, when it is covered by a very thin coat of white 
 ashes, which frequently adhere to it when it has been some time 
 ignited ; and it had a degree of brightness about as strong as that 
 with which a coal would be seen to glow in fair daylight." 
 
 The appearance which Dr. Herschel here describes so minutely, 
 was also observed at the Royal Observatory of Paris, about six days 
 before, by Dominic Nouet, like a star of the sixth magnitude, the 
 brightness of which occasionally increased by flashes. Other astrono- 
 mers also saw the same thing, for M. de Villeneiive observed it on 
 the 22d of May, 1787. This volcano is situated in the north-east 
 part of the Moon, about 3' from her edge, towards the spot called 
 Helicon. After considering all the circumstances respecting these 
 appearances which have just been mentioned, we must subscribe to 
 Dr. Herschers opinion, that volcanoes exist in the Moon as well as 
 the earth. 
 
 It has long been a disputed point among astronomers, whether or 
 not the Moon is surrounded by an atmosphere. Those who deny 
 that she is, say that the Moon always appears with the same bright- 
 ness when our atmosphere is clear ; which could not be the case if 
 she were surrounded by an atmosphere like ours, so variable in den- 
 sity, and so often obscured by clouds and vapours. 
 
 A second argument is, that when the Moon approaches a star, 
 Before she passes between it and the earth, the star neither alters its 
 colour nor its situation, which would be the case if the Moon had an 
 atmosphere, on account of the refraction, which would both alter 
 the colour of the star, and also make it appear to change its place. 
 
 A third argument is, that as there are no seas or lakes in the Moon, 
 there is, therefore, no atmosphere, as there is no water to be raised 
 up into vapour. But those who contend that the Moon is surrounded 
 by an atmosphere, deny that she always appears of the same bright- 
 ness, even when our atmosphere appears equally clear. Instances of 
 the contrary are mentioned by Hevelius and some other astronomers, 
 
SPOTS, &C. IN THE MOON. 65 
 
 but it is unnecessary to take any farther notice of them here. In the 
 case of total eclipses of the Moon, it is well known that she exhibits 
 very different appearances, which it is supposed are owing to changes 
 in the state of her atmosphere. It is remarked by Dr. Long, that 
 Newton had shown that the weight of any body on the Moon, is 
 but a third part of the weight of what the same body would be on 
 the earth; from which he concludes that the atmosphere of the 
 Moon is only one-third part as dense as that of the earth, and there- 
 fore it is impossible to produce any sensible refraction on the light of 
 a fixed star which may pass through it. Other astronomers assert 
 that they have observed such a refraction ; and that Jupiter, Saturn, 
 and the fixed stars had their circular figures changed into an elliptical 
 one, on these occasions. 
 
 But although the moon be surrounded by an atmosphere of the same 
 nature as that which surrounds the earth, and to extend as far from 
 her surface ; yet no such effect as a gradual diminution of the light 
 of a fixed star could be occasioned by it, at least none, that could be 
 observed by a spectator on the earth. For at the height of 44 miles 
 our atmosphere is so rare, that it is incapable of refracting the rays 
 of light, now this height is only the 180th part of the earth's diameter; 
 but as clouds are never observed higher than 4 miles, it therefore 
 follows that the obscure part of our atmosphere is about the 2000th 
 part of the earth's diameter, and if the Moon's apparent diameter be 
 divided by this number, it will give the angle under which the obscure 
 part of her atmosphere will be seen from the earth, which is not quite 
 one second, a space passed over by the Moon in less than two 
 seconds of time. It can, therefore, scarcely be expected that any 
 obscuration of a star could be observed in so short a time, although 
 it do take place. 
 
 As to the argument against a lunar atmosphere drawn from the 
 conclusion, that there are no seas or lakes in the Moon, it proves 
 nothing, because it is not positively known whether there is any 
 water in the Moon or not. 
 
 The question of a lunar atmosphere seems to be at last settled by 
 the numerous and accurate observations of the celebrated Astrono- 
 mers Shroeter and Piazzi, who have proved as convincingly as the 
 nature of the subject seems to allow, that the Moon has really an 
 atmosphere, though much less dense than ours, and scarcely exceed- 
 ing in height some of the lunar mountains. 
 
 It is remarked by Dr. Brewster, " The mountain scenery of the 
 Moon bears a stronger resemblance to the lowering sublimity and 5 
 terrific ruggedness of the Alpin regions, than to the tamer inequalities 
 of less elevated countries. Huge masses of rock rise at once from 
 the plains, and raise their peaked summits to an immense height in 
 the air, while projecting craggs spring from their rugged flanks, and 
 threatening the vallies below seem to bid defiance to the laws of 
 gravitation. Around the base of these frightful eminences, are 
 strewed numerous loose and unconnected fragments, which time 
 seems to have detached from their parent mass, and when we exa- 
 mine the rents and ravines which accompany the overhanging cliffs, 
 
06 CONSTELLATIONS* OR ASTERISMS. 
 
 we expect every moment that they are to be torn from their base, 
 and that the process of destructive separation which we ha$ only 
 contemplated in its effects, is about to be exhibited before us in tre- 
 mendous reality. The mountains called the Appennines, which 
 traverse a portion of the Moon's disc from north-east to south-west, 
 rise with a precipitous and craggy front from the level of the Mare 
 Imbnim. In some places their perpendicular elevation is above, four 
 miles ; and though they often descend to a much lower level, they 
 present an inaccessible barrier to the north-east, while on the south- 
 west they sink in gentle declivity to the plains." 
 
 The caverns which are observed on the Moon's surface, are no 
 less remarkable than the rocks and mountains, some of them being 
 three or four miles deep, and forty in diameter. A high angular ridge 
 of rocks marked with lofty peaks and little cavities, generally en- 
 circles them, an insulated mountain frequently rises in their centre, 
 and sometimes they contain smaller cavities of the same nature with 
 themselves. These hollows are most numerous in the south-west 
 part of the Moon, and it is from this cause that this part of the 
 Moon is more brilliant than any other part of her disc. The moun- 
 tainous ridges which encircle the cavities, reflect the greatest quan- 
 tity of light; and from their lying in every possible direction, they 
 appear, near the time of full Moon, like a number of brilliant radia- 
 tions issuing from the small spot called Tycho. 
 
 It is difficult to explain, with any degree of probability, the forma- 
 tion of these immense cavities ; it is highly probable, that the earth 
 would assume the same figure, if all the seas and lakes were removed ; 
 and that the lunar cavities are either intended for the reception of 
 water, or that they are the beds of lakes and seas which have for- 
 merly existed in the Moon. 
 
 The circumstance of there being no water in the Moon, affords a 
 strong proof of the truth of this theory." 
 
 OF THE CONSTELLATIONS, OR ASTERISMS. 
 
 A spectator who observes the heavens with a tolerable degree of 
 attention, will soon perceive that by far the greater number of the 
 stars never change their situation with respect to each other. Such 
 stars as always appear to occupy the same situation in the heavens, 
 or the same relative distance from one another, have been called 
 fixed stars ; to distinguish them from the planets, whose situations 
 are constantly changing.* The fixed stars constitute by far the most 
 numerous class of celestial bodies ; for on casting the eye quickly to 
 the heavens in a clear winter evening, they appear to be innumerable. 
 
 * A planet may be known from a fixed star, by the steadiness of its light ; for 
 a fixed star appears to emit a twinkling light, but a planet gives a mild steady 
 light. 
 
CONSTELLATIONS, OR ASTERISMS. 67 
 
 The grandeur of such a scene with the perpetual and regular change, 
 which the whole appears to undergo by the daily revolution of the 
 earth on its axis, must have attracted the attention of mankind at a 
 very early period. But previous to attempting to make either regular 
 or accurate observations, on the motions aud relative situations of the 
 various booses which compose this splendid scene, it was necessary 
 to invent some method by which the one might be distinguished from 
 the other. To give a particular name to every star which was visible 
 to the naked eye, was impossible. 
 
 It therefore became necessary to adopt a more general method of 
 distinguishing them. This was accomplished by portioning out the 
 heavens into imaginary figures, of men, birds, fishes, &c. called Con- 
 stellations or Asterisms. After this, the situation of a star could be 
 known by mentioning its place in the Constellation in which it was 
 situated ; as the bull's eye, the lion's heart, the dog's nose, &c. In 
 what age of the world this arrangement of the stars into constellations 
 took place is not known, but it was certainly antecedent to any 
 authentic record ; so that whether the shepherd or the sage, was em- 
 ployed in their formation, cannot now be ascertained. Homer and 
 Hesiod who lived at least 800 years before the Christian era, men- 
 tion several of the constellations. 
 
 The Pleids, Hyads, with the northern team, 
 
 And great Orion's more refulgent beam ; 
 
 To which, around the axle of the sky, 
 
 The bear revolving points his golden eye, 
 
 Still shines exalted in th* ethereal plain, 
 
 Nor bathes his blazing forehead in the main. POPE'S HOMER. 
 
 In the book of Job, Arcturus, Orion, and the Pleiades, are twice 
 mentioned. 
 
 Canst thou the sky's benevolence restrain, 
 And cause the Pleiads to shine in vain ? 
 Or, when Orion sparkles from his sphere, 
 
 PThaw the cold season, and unbind the year ? 
 Bid Mazzaroth his destined station know, 
 And teach the bright Arcturus where to glow ? 
 
 The writer of the book of Amos has also mentioned Orion and the 
 seven stars; which plainly shews that the constellations must not 
 only have been invented before his time, but that they must have 
 been of some standing at that period. 
 
 These signs, which now seem so whimsical and uncouth, were not 
 however the offspring of unsystematic fancy ; they appear to have 
 been intended to signify the state of the earth at the different seasons 
 of the year, particularly the figures of the constellations in the 
 Zodiac, which are supposed by some astronomers to be Egyptian 
 hieroglyphics. Among these there are some that have as it were a 
 common relation to every portion of the globe, while others seem to 
 relate to circumstances or events merely local. Aries, is said to 
 signify that the lambs begin to follow the sheep about the time of the 
 
68 CONSTELLATIONS, OR ASTERISMS. 
 
 vernal equinox, when the sun enters this sign ; and that the cows 
 bring forth their young about the time he approaches the second con- 
 stellation, Taurus, or the Bull. The third sign now called Gemini, 
 was originally two kids, and signified the time of the goats bringing 
 forth their young, which are usually two at a time, while the former 
 (the sheep and the cow) commonly produce only one. A 
 
 The fourth sign, Cancer the Crab, an animal that goes sideways 
 and backwards, was placed at the northern tropic, or that point of 
 the ecliptic, where the sun begins to return back again from the 
 north to the southward. The fifth sign, Leo, the Lion, as being a 
 furious animal, was thought to denote the heat and fury of the burn- 
 ing sun after he had left Cancer, and entered the next sign Leo. 
 
 The sixth sign received the sun at the time of the ripening of corn, 
 and the approach of harvest ; which was aptly expressed by one of 
 the female reapers, with an ear of corn in her hand, namely Virgo, or 
 the Virgin. 
 
 The next sign, Libra, or the Balance, evidently denotes the 
 equality of days and nights, which take place at that season ; and 
 Scorpio, the next sign in order, denotes the time of gathering in the 
 fruits of the earth, which being generally an unhealthily season, is 
 represented by this venomous animal, extending his long claws, 
 threatening the mischief which is to follow. The fall of the leaf was 
 the season of the ancient hunting ; and for this reason the constella- 
 tion Sagittarius represents a huntsman with his arrows and his club ; 
 the weapons of destruction employed by huntsmen at that time. The 
 reason of the Goat being chosen to mark the farthest south point of 
 the ecliptic, is obvious enough, for when the sun has attained his 
 extreme limit in that direction, he begins to return, and mounts again 
 to the northward, which is very well represented by the goat, an 
 animal that is always found climbing and ascending some mountain 
 as it browses. As the winter has always been considered a wet and 
 uncomfortable season, this was expressed by Aquarius, the figure of 
 a man pouring out water from an urn. The last of the zodiacal con- 
 stellations was Pisces, a couple of fishes tied together, which had been 
 caught, which signified that the severe season was over, and though 
 the flocks did not yet yield their store, yet the seas and rivers were 
 open, and fish might be caught in abundance. These ideas have 
 been beautifully expressed by Chatterton, in the following lines : 
 
 Ou the earth's orbit see the various signs, 
 Mark where the sun our year completing, shines : 
 First the bright Ram his languid ray improves j 
 Next glaring wat'ry thro' the Bull he moves : 
 The am'rous Twins admit his genial ray ; 
 Now burning, thro' the Crab he takes his way ; 
 The Lion, flaming, bears the solar power ; 
 The Virgin faints beneath the sultry shower. 
 Now \hejust Balance weighs his equal force, 
 The slimy Serpent swelters in his course ; 
 The sable Archer clouds his languid face ; 
 The Goat with tempests urges on his race ; 
 Now in the Water his faint beams appear, 
 And the cold Fishes end the circling year. 
 
CONSTELLATIONS, OR ASTERISMS. 69 
 
 Although these signs might have served to distinguish the seasons 
 of the year when they were first formed, or employed for that pur- 
 pose, yet this is not altogether the case at the present day. For 
 owing to the retrograde motion of the equinoctial points, the constel- 
 lations of the Zodiac have now so far changed their positions, as to 
 be found more than a sign advanced.* The constellation Aries, for 
 example, is now three or four degrees within the sign Taurus, or the 
 first point of Aries, which used to coincide with the equinoctial point, 
 is now about thirty-four degrees farther advanced ; however, the first 
 point of the sign Aries still continues to be reckoned from the 
 equinoctial point. The signs of the Zodiac must therefore now be 
 distinguished from the constellations, the signs merely being ideal, 
 and serving only to designate the course of the sun in thtf ecliptic, 
 while the constellations continue to signify a group or cluster of stars, 
 designated by some particular name. 
 
 Besides the constellations in the Zodiac, the catalogue of Ptolomy, 
 (which is the first or earliest on record) enumerate 21 to the north, and 
 15 to the south of it, making in all 48, but these included only the 
 visible part of the heavens, or such as came under their notice. The 
 number of constellations, however, increased, as the knowledge of the 
 stars became more extensive ; and at the same time more stars 
 were introduced into each constellation, as their positions became 
 known. 
 
 Such stars as were not included in any of these constellations, were 
 called by the ancients informs or sporades stars ; but modern astrono- 
 mers have now reduced these informs, or unformed stars into new 
 constellations, which have now swelled the number to 95. Of these 
 12 are in the zodiac, the names of which have already been men- 
 tioned; 37 to the north of it, and 46 to the south of it. The northern 
 constellations are 
 
 Ursa Major 
 
 Corona Borealis 
 
 Aquila 
 
 Ursa Minor 
 
 Hercules 
 
 Antinous 
 
 Draco 
 
 Cerberus 
 
 Delphinus 
 
 *Cepheus 
 
 Lyra 
 
 *Taurus Poniatowski 
 
 Andromeda 
 
 Cygnus 
 
 Equulus 
 
 Cassiopeia 
 
 *Vulpecula 
 
 Sagitta 
 
 Perseus 
 
 *Anser 
 
 Auriga 
 
 Pegasus 
 
 Lacerta Stellio 
 
 *Lynx 
 
 *Canes Venatici 
 
 *Camelopardalus 
 
 *Leo Minor 
 
 Bootes 
 
 Serpens 
 
 *Triangulum 
 
 *Mons Maenalus 
 
 Serpentarius 
 
 Triangulum Minus 
 
 *Coma Berenices 
 
 Scutum Sobieski 
 
 *Musca.f 
 
 *Cor Caroli 
 
 
 
 * See Precession of the Equinoxes, page 9. 
 
 t The new constellations are those marked thus (*). 
 
70 POSITION OF THE CONSTELLATIONS, &C. 
 
 The southern constellations are the following : 
 
 Cetus *Pavo *Octans Hadleianus 
 
 Eridanus Corona Australia *Cameleon 
 
 Phoenix *Grus *Piscis Volans 
 
 Toucan Piscis Australia *Xiphias 
 
 Orion *Lepus *Officina Sculptoris 
 
 Monoceras *Columba Noachi *Hydrus 
 
 Canis Major *Robur Carol! *Fornax Chemica 
 
 Apus *Crux *Horologium 
 
 Hydra Argo Navis *Reticulus RhomboidalU 
 
 Sextans Uraniae Canis Minor *Praxiteles 
 
 Crater *Apis Musca *EquuIeus Pictorius 
 
 Corvus Hirundo *Pyxis Nautica 
 
 Centaurus *Indus *Machina Pneumatica 
 
 Lupus *Telescopium *Circinus 
 
 Ara *Microscopium *Quadra Euclidis.t 
 *Triangulum Australe 
 
 Though the division of the heavens into the constellations above 
 enumerated, be entirely fanciful, yet it is of great advantage in 
 describing the position of particular stars. The judicious and practi- 
 cal astronomer has therefore always resisted every attempt, either to 
 change their names, or to lay them aside, because better could not 
 be substituted in their place ; and because they keep up the greater 
 correspondence and uniformity between the old astronomy and the 
 new. 
 
 ON THE POSITION OF THE CONSTELLATIONS, AND PRINCIPAL 
 STARS IN THE NORTHERN HEMISPHERE. 
 
 As there is no particular constellation, or star, in the heavens, so 
 singular in its appearance, or so singularly situated with respect to 
 the rest, as to entitle it to the distinction of being first described, but 
 as the constellation Ursa Major, or the Great Bear, never goes below 
 the horizon of places of considerable northern latitude ; and as it is 
 one of the most conspicuous constellations in the northern hemis- 
 phere, we shall not only begin to describe it first, but endeavour to 
 trace out the others by means of it. 
 
 In the Great Bear there are seven very conspicuous stars, four of 
 which form a trapezium in the body, and the other three are in the 
 tail of that animal. The two former stars in the trapezium are called 
 the guards, or pointers, because a straight line passing through them 
 points out the pole, The pointer which is nearest the pole star is 
 called Dubhe; the first in the tail next the body, Alioth; and the 
 last in the tail, Benetnach.t 
 
 Nearly in the direction of the pointers, and about five times the 
 interval between them, reckoning from Dubhe, is Alruccabah, or 
 the Pole Star, situated in the tip of the tail of the constellation 
 Uursa Minor, in which there are also seven stars, forming a figure 
 
 , f The new constellations are those marked thus (*). 
 
 $ These seven stars form a figure somewhat resembling a plough : hence it is 
 often called Charles' Wain, or the Plough. 
 
POSITION OF THE CONSTELLATIONS, &C. 71 
 
 like those in the Great Bear, but both the figure and the stars are 
 considerably less. 
 
 The Lesser Bear 
 
 Leads from the pole the lucid band : the stars 
 Which from this constellation, faintly shine 
 Twice twelve in number ; only one beams forth 
 Conspicuous in high splendor, nam'd by Greece 
 The CYNOSURE ; by us the POLAR STAR. EUDOSIA. 
 
 An imaginary line passing from Dubhe through the star in the oppo- 
 site corner of the trapezium, will nearly intersect Cor Caroli, a single 
 star of the second magnitude, whose distance from the latter star is 
 nearly double that between the two former. A straight line from 
 Alioth passing through Cor Caroli, produced a little farther than the 
 distance between them, will reach Vindemiatrix, the farthest northern 
 star in the constellation Virgo. Between Cor Caroli and Virgo is 
 the constellation Coma Berenices, or Berenice's Hair, so named from 
 its resemblance to hair. 
 
 Then Berenice's locks first rose so bright, 
 
 The heavens bespangling with dishevelled light. POPE. 
 
 A straight line from Benetnach passing through Cor Caroli, an$ 
 extending downwards or towards the horizon about double the dis- 
 tance between these two stars, will reach Deneb, a star of the 
 second magnitude in the constellation Leo, or the Lion, and about 
 25 degrees to the west of Deneb ; and about 3 degrees lower is 
 Regulus, a star of the first magnitude, in the heart of Leo, and 
 almost in the plane of the ecliptic. 
 
 To the eastward of Deneb, at the distance of about 35 degrees, ib 
 Arcturus, in the constellation Bootes, called the Waggoner. 
 
 Wide o'er the spacious regions of the North, 
 Bootes urges on his tardy wain. THOMSON. 
 
 Bootes with his wain the North unfolds ; 
 
 The southern gate Orion holds. CLAUDIAN. 
 
 Under Bootes is the constellation Virgo, in which there is a very 
 bright star, called Spica Virginis, which forms with Deneb and 
 Arcturus a very large equilateral triangle. 
 
 A little to the south-west of Spica Virginis, is the constellation 
 Corvus, the stars of which form a long trapezium, but none of them 
 exceed the third magnitude. The first star is named Algorab, and 
 is in the lower corner of the trapezium, about 18 degrees from Spica 
 Virginis. 
 
 A line from Vindemiatrix, the third star in Virgo; through 
 Arcturus, will intersect Alphacca, a star of the second magnitude in 
 the constellation Corona Borealis, or the Northern Crown ; the dis- 
 tance between Alphacca and Arcturus being nearly equal to that 
 between the latter and Vindemiatrix. This constellation is very con- 
 spicuous, the stars in it being arranged in a circular form, somewhat 
 resembling a crown. A line passing from Regulus through Spica 
 Virginis, and extending an equal distance beyond the latter, will 
 
72 POSITION OF THE CONSTELLATIONS, &C. 
 
 reach Antares, a star of the first magnitude in the constellation 
 Scorpio. Between Scorpio and Virgo is the constellation Libra, 
 containing a number of small stars ; and to the south of Scorpio is 
 the constellation Lupus, or the Wolf, which also contains a number 
 of stars ; but none of them exceed the third or fourth magnitude. 
 
 Nearly in the line produced from Arcturus, through the Northern 
 Crown, and about twice the distance between them, and beyond 
 Alphacca, is one of the brightest stars in the heavens, called Vega, 
 in the constellation Lyra. In the line joining this star and the guards 
 of Ursa Minor, and about 15 degrees distant from the former, is 
 Rastaban, a star of the third magnitude in the constellation Draco, 
 or the Dragon ; and in the opposite direction from Vega, a little to 
 the east of the line, and about 34 degrees distant, is Altair, a star 
 between the first and second magnitude in the constellation Aquila. 
 The stars Altair, Vega, and Deneb, a star of the second magnitude 
 in the constellation Cygnus, form nearly a right-angled triangle, the 
 right angle being at Vega. About 14 degrees north-east of Altair, is 
 a romboidal figure, formed by four stars in the constellation 
 Delphinus ; and about 35 or 36 degrees east of this figure, is the 
 constellation Pegasus, in which there is a bright star in the neck 
 called Scheat. About 13 degrees south of that is Markab, a star of 
 the second magnitude j 16 degrees to the east of Markab is another 
 star of the second magnitude, in the same constellation ; and nearly 
 14 degrees east of Scheat is a star of the third magnitude, in the head 
 Andromeda. These four stars form a square, usually called the 
 Square of Pegasus. 
 
 A line from Scheat through Markab, at the distance of 45 degrees 
 from the latter, will nearly intersect Fomalhaut, a star of the first 
 magnitude in the constellation Pisces Austraulis, or the Southern 
 Fish. Between Markab and Fomalhaut, and about 10 degrees south 
 of the former, is the constellation Pisces. To the west of the line 
 joining the two last mentioned constellations is Aquarius, one of the 
 zodiacal constellations. 
 
 A line from Deneb in Cygnus, passing through Markab, and dis- 
 tant from it about 41 degrees, will point out the second brightest star 
 in the constellation Cetus : and a line from the rhomboid already 
 mentioned, in Delphenus, through Markab, at the distance of nearly 
 60 degrees from this last star, will intersect Menkar, a star of the 
 second magnitude in the jaw of Cetus. About 37 degrees north of 
 Menkar is Algol, the second star in the constellation Perseus, which 
 is one of those stars that vary in brightness. 
 
 At the distance of about 27 degrees from the star in the head of 
 Andromeda, and a little to the south of the line, joining it and Markab, 
 is Almaach, a star of the second magnitude in the southern foot of 
 Andromeda : and about half way between it and Markab, is Mirach, 
 a star of the third magnitude in the girdle of that constellation. A 
 little to the north of the same line, at the distance of about 42 
 degrees, is Algenib, a star of the second magnitude in the constella- 
 tion Perseus. The three stars, Almaach, Algol, and Algenib, form 
 nearly a right-angled triangle, Algol being at the right angle. 
 
POSITION OF THE CONSTELLATIONS, &C. 73 
 
 Between Mirach and Menkar, about 17 degrees from the former, 
 is a tolerably bright star of the second magnitude in the constellation 
 Aries, between which and Almaach are the two triangles, and 
 about 10 degrees south-east of the triangles is the small constellation 
 Musca, or the Fly. To the north-east of Menkar, about 26 degrees, 
 and as many south-east of Musca, is Aldebaran, a star of the first 
 magnitude, of a red colour, in the constellation Taurus. This star, 
 with several other small ones called the Hyades, forms a triangle. 
 Between this triangle and Musca, is that well-known cluster of stars 
 called the Pleiades, or Seven Stars, which are situated in the neck 
 of Taurus. A line from Aldebaran through Algol, at the distance 
 of 28 degrees from Algol, will intersect Schedar, a star of the third 
 magnitude in the constellation Cassiopeia. This constellation will 
 easily be known, being composed of five or six stars of nearly the 
 same magnitude, and being always on the opposite side of the pole, 
 with respect to the star Alioth, in Ursa Major. 
 
 About 22 degrees south-east from Aldebaran, are three stars of 
 the second magnitude, in a straight line, and at equal distances from 
 each other, which form the belt of Orion. Below the belt are a 
 few stars that compose the Sword of Orion, in a beautiful nebulae. 
 Above these are two bright stars, distant from each other about 7| 
 degrees; the farthest west one is called Bellatrix, and the other 
 Betelguese ; and, about as far distant on the other side of the belt is 
 Rigel, a star of the first magnitude; all of these are in the constella- 
 tion Orion, which is one of the most beautiful constellations in the 
 heavens. About half way between Rigel and the north pole is 
 Capella, a star of the first magnitude in the constellation Auriga. 
 A line from Menkar through Rigel, at the distance of 23 degrees 
 from the latter, or from Aldebaran, through the middle star of Orion's 
 belt, and about as far below it as Aldebaran is above it, is Sirius, 
 a star of the first magnitude in the constellation Canis Major.* About 
 5f degrees west from Sirius is a star between the second and third 
 magnitude, and about 11 degrees farther south than Sirius there are 
 three others in a straight line, all of the third magnitude, and in the 
 same constellation. About 26 degrees to the east of Betelguese, 
 and the same distance north-east from Sirius, is Procyon, a star 
 between the first and second magnitude in Canis Minor. In a line 
 with Rigel and the middle star in the belt of Orion, about 44 degrees 
 from the latter, is Castor, a star between the first and second magni- 
 tude, in the constellation Gemini ; and about 4| degrees south-east 
 of Castor is Pollux, a star between the second and third magnitude, 
 in the same constellation. Pollux may also be known by observing, 
 that it is about 45 degrees distant from Aldebaran, in the line pro- 
 duced, passing through it from Menkar. About half way between 
 Procyon and Regulus is Acubens, a star of the third magnitude, in 
 the sign Cancer. Aline from Alioth through Regulus being pro- 
 duced about 23 degrees, will intersect Alphared, a star of the second 
 
 * Sirius is the brightest star in the heavens, and is by some astronomers 
 supposed to be nearest the earth. 
 
 No. 7. H 
 
74 POSITION OF THE CONSTELLATIONS, &C. 
 
 magnitude in the constellation Hydra; and a line from Procyon 
 through Alphared, produced about 24 degrees beyond Alphared, 
 will intersect Alkes in the constellation Crater. This star may also 
 be known by being on the meridian nearly at the same time with the 
 pointers in the Great Bear. 
 
 As the constellations and stars now described comprise the 
 greater number of those that can be seen in any part of Great 
 Britain, it is unnecessary to take any notice of the others.* 
 
 The situation of the principal constellations which appear above 
 the horizon of London, during a night about the middle of Decem- 
 ber, are so beautifully and accurately described in the following 
 extract from the philosophic poem entitled Eudosia, that it cannot 
 but be admired by all lovers of Astronomy : 
 
 Now let us watch the rising of the stars ; 
 And look where mid December points the hour 
 Most apt for contemplation of the scene. 
 The fourth from noon is pass'd, and half the space 
 Fled to the fifth ; in the meridian view 
 Cepheus, sublime ; the Dragon's tortile spire, 
 Where shines to Britain's great metropolis, 
 The correspondent star ; alike remote 
 This from the heavenly, that the earthly pole, 
 And perfectly coincident in place, 
 The greater Bear is seen ; and Pegasus 
 Tends to the south ; the beauteous Twins emerge 
 from the horizon ; Taurus climbs oblique ; 
 Still higher Aries ; the declining Fish 
 Verge to the southern wave ; and Capricorn 
 Glistens, diminish'd, in the western sky : 
 And, near the goal, with languid ray appears 
 Chiron ; but, nigh to the direct of east, 
 Orion half is risen ; nor prevails 
 The horizon even now to eclipse the pomp 
 Of the proud constellation ; his right side 
 Blazes ; the star, which lightens on the left, 
 Is winning now upon our hemisphere : 
 And near him the vast Whale conspicuous shines. 
 The sixth hour is elaps'd, Orion shows 
 His flaming belt ; the Twins are wholly risen ! 
 Soon Procyon appears ! and now the Crown 
 Of Ariadne rises : Charles, thy star, 
 Though never setting to the horizon, stoops. 
 And of the Crab the far distinguish'd light 
 Emerges. Little later than the seventh, 
 Sirius appears : the ninth the Lion shines ; 
 And in the vertex is Medusa seen. 
 Near the tenth hour from noon Hydra appears 
 Southward ; at mid of night Orion's form 
 Fires the meridian ; but the Whale retired ; 
 The radiant Lyra meets the horizons' bound ; 
 The Virgin form shows her ascendant wing ; 
 
 * Those who are possessed of a celestial globe, and know how to use it, will, in 
 a few evenings, acquire a knowledge of the principal stars that may be above 
 their horizon at that season ; but the foregoing directions will be found to answer 
 the same purpose, with the assistance either of a globe or map of the heavens. 
 
THE LUSTRE AND MAGNITUDE OF THE STARS. 75 
 
 Capella in the zenith glows ; an hour 
 Is pass'd; Areturus rises : ere the night 
 ' Has mark'd the second hour from its mid space, 
 Shoots in full beam the great NEWTONIAN Star.* 
 The fourth approaches, when the golden star 
 Of Libra gains the eye : the sails retire 
 Of the resplendent Ship ; her lucid mast 
 Shines eminent. The sixth her fetter'd arm 
 Andromeda discovers ; and the heart 
 Of Scorpio rises ; Hydra fills the west ; 
 Medusa's Head sinks, and Orion bears 
 With difficulty his shoulders unsubmerg'd : 
 Monocerous succeeds. Why should I name 
 The Snake or Serpentarius fully risen ? 
 Or why repeat the wonders which before 
 Engag'd our eye ? The great and smaller Bear, 
 With the Camelopard and varied Lynx ! 
 Or gaze on thee, O Perseus ! thee admire, 
 Aquila ; or the Lyre, which re-ascends ? 
 But, rising eastward, beams the glorious arch 
 Of the pure Galaxy ? And now appears 
 Urania's Sextant, and persuades to leave 
 The starry theatre, and yield to dawn ; 
 For now Aurora's fiery coursers gild 
 The frosty summit of the eastern hills. 
 All this delightful scene revolving earth 
 Produces, visiting the several stars ; 
 While undisturb'd remain the heavenly spheres. EUDOSIA. 
 
 OF THE LUSTRE AND MAGNITUDE OF THE STARS. 
 
 One sun by day, by night ten thousand shine ; 
 And light us deep into the DEITY. 
 
 O how loud 
 
 They call devotion, genuine growth of night ! 
 Devotion, daughter of Astronomy ! 
 An undevout astronomer is mad. YOUNG. 
 
 The stars are divided into orders or classes according to their 
 apparent magnitudes. Those that appear largest to the naked eye, 
 have been called stars of the first magnitude ; those that appear next 
 largest, the second magnitude ; and so on to the sixth, which compre- 
 hends the smallest stars that are visible to the naked eye. All those 
 that can only be perceived by the help of a telescope, are called 
 telescopic stars. 
 
 The stars of each class are not all of the same apparent magnitude. 
 In the first class, or those of the first magnitude, there are scarcely 
 two that appear of the same size. 
 
 There are also other stars, of intermediate magnitudes, which 
 astronomers cannot refer to any particular class, and therefore they 
 place them between two; but on this subject astronomers differ con- 
 
 * Spica Virginus, the ear of wheat in the constellation Virgo : 
 
 The star which crowns the golden sheaf, 
 
 And wants a name, O glory of the skies ! 
 And shall not justice dignify thy sphere 
 With the great name of NEWTON ? Be at least 
 To me. for ever the Newtonian Star. EUDOSIA. 
 
 H 2 
 
76 OF THE LUSTRE AND MAGNITUDE OF THE STARS. 
 
 siderably ; some of them classing a star among those of the first 
 magnitude, while others class it among those of the second, and so 
 on with others. 
 
 In fact it may be said, that there are almost as many orders of 
 stars as there are stars, on account of the great variations observa- 
 ble in their magnitude, colour, brightness, &c. Whether these varie- 
 ties of appearance are owing to a diversity in their real magnitude, 
 or from their different distances, is impossible to determine ; but it is 
 highly probable that both of these causes contribute to produce these 
 effects. 
 
 To the naked eye, the stars appear of a sensible magnitude, owing 
 to the glare of light arising from the numberless reflections from the 
 aerial particles, &c. about the eye ; this makes us imagine the stars 
 to be much larger than they would appear, if we saw them only by 
 the few rays which come directly from them, so as to enter our eyes 
 without being intermixed with others. Any person may be sensible 
 of this by looking at a star of the first magnitude through a long nar- 
 row tube, which, though it takes in as much of the heavens as would 
 hold a thousand such stars, scarcely renders that one visible. The 
 stars being so immensely distant from the earth, there seems to be 
 but little probability of ascertaining with certainty the real magnitude 
 of any of them. And as Dr. Herschel has very justly remarked, 
 " that, in the classification of stars into magnitudes, there is either no 
 natural standard, or at least none that can be satisfactory ; and that 
 the astronomers who have thus classed them, have referred their 
 size or lustre to some imaginary standard." 
 
 The same illustrious astronomer observes, " that the inconveni- 
 ence arising from this unknown, or at least ill-ascertained, standard, 
 to which we are to refer, is such, that now our most careful obser- 
 vations labour under the greatest disadvantage. If any dependence 
 could be placed on the method of magnitudes, it would follow, that 
 many of the stars had undergone a change in their lustre or apparent 
 magnitude, even since the time of Dr. Flamstead. Not less than 
 eleven stars, in the constellation Leo, have undergone a change of 
 lustre since his time." This change, Dr. Herschel believes, has 
 arisen from the uncertainty of the standard of magnitudes, and not 
 from any real change in the lustre of the stars : and in order to pre- 
 vent mistakes of this nature to future observers, the Doctor proposes 
 to compare the lustre of any particular star with that of one which is 
 greater, and also one that is less, both of which to be as near the 
 proposed star as possible. This he thinks would answer much better 
 for detecting a change in the lustre of any suspected star than the 
 vague method of magnitudes, which has been hitherto in use among 
 astronomers. 
 
 As a full display of the Doctor's method would occupy more 
 space than can be allotted to it in this work, those who wish to 
 have more information on the subject, may consult the Phil. Trans, 
 vol. 86. 
 
 That many real changes in the lustre of stars have taken place, 
 Dr. Herschel acknowledges ; for he says, " If we consider how 
 
OF THE LUSTRE AND MAGNITUDE OF THE STARS. 77 
 
 little attention has been paid to this subject, and that most of the 
 observations which we have are of a very late date, it will perhaps 
 not appear extraordinary were we to admit the number of alterations 
 that have probably happened to different stars to be 100 ; this, com- 
 pared with the number of stars that have been examined, with a view 
 to ascertain their changes, which we can hardly rate at 3000, will 
 give us a proportion of 1 to 30. But we are certain, that had a num- 
 ber of observers applied themselves to the same subject, many more 
 discoveries might probably have been made of changeable and 
 periodical stars, whose variations are too small to strike a general 
 observer. By observations of this nature," continues this celebrated 
 astronomer. " we are enabled to resolve a problem, not only of great im- 
 portance in itself, but one in which we are all immediately concerned. 
 Who, for instance, would not wish to know what degree of perma- 
 nency we ought to ascribe to the lustre of our sun? Not only the 
 stability of our climates, but the very existence of the whole animal 
 and vegetable creation, are involved in the question. Where can 
 we hope to receive information on this subject, but from astronomical 
 observations ? If the similarity of the stars to our sun be admitted, 
 how necessary does it become to observe the fate of neighbouring 
 suns, in order to guess at that of our own ! That star among the 
 multitude which we have dignified with the name of sun, to-morrow 
 may slowly begin to undergo a gradual decay of brightness, like & in 
 Leo, in Cetus, a in Draco, * in Ursa Major, and many others. 
 It may suddenly increase, like the wonderful star in the back of 
 Cassiopeia's Chair, and the no less remarkable one in the foot of the 
 Serpent; a gradual increase, like & in Gemini, # in Cetus, and many 
 other stars which have been known to increase in lustre. And 
 lastly, it may turn into a periodical one of 25 days, as Algol is of 
 3 days, * in Cepheus of 5, in Lyre of 6, or as many others are 
 of various periods."* 
 
 " If by proper attention to this subject," continues the Doctor, 
 " it should be found that all, or many of the stars which we now 
 have reason to suspect to be changeable, are really subject to an 
 alteration in their lustre, it will much lessen the confidence we have 
 hitherto placed on the permanency of the equal emission of light by 
 our sun. Many phenomena in natural history seem to point out some 
 past changes in our climates. Perhaps the easiest way of accounting 
 for them may be to surmise that our sun has been formerly sometimes 
 more and sometimes less bright than it is at present : and that many 
 of the unaccountable varieties which happen in our seasons, such as 
 a general severity or mildness of uncommon winters, or burning 
 
 * The stars in each constellation are marked or distinguished by the letters of 
 the Greek alphabet; and some remarkable ones have particular names, as 
 Aldebaran, Sirius, Algol, &c. The brightest star in each constellation is 
 marked with the first letter, the next brightest with the second letter, and so on ; 
 but if there should be a greater number of stars in any constellation, than there 
 are letters in the Greek alphabet, the Roman alphabet is then employed, and 
 afterwards the italic. 
 
78 OF THE NUMBER OF THE STARS. 
 
 sumrters, may possibly meet with an easy solution in the real inequa- 
 lity of the sun's rays." 
 
 Various hypotheses have been devised to account for the changes 
 and appearances of the stars. Some astronomers have supposed that 
 the periodical stars have vast dark spots, or dark sides, and very 
 slow rotations on their axes, by which means they must disappear 
 when the dark side is turned to the earth. Others are of opinion 
 that the luminous surfaces of these bodies is subject to perpetual 
 change, which sometimes increases their light, and at others extin- 
 guishes it. 
 
 Some have also ascribed the variation in the light of the stars, to 
 the intesposition of the planets that revolve round them ; but it is not 
 very probable that these planets are sufficiently large to produce such 
 an effect. Several other hypotheses might be mentioned, which have 
 been advanced at different periods to account for these extraordinary 
 changes ; but as they rest upon mere conjecture, and are still more 
 improbable than any of those just mentioned, it is unnecessary to 
 give any account of them. 
 
 OF THE NUMBER OF THE STARS. 
 
 Why from yon arch, that infinite of space, ] 
 t With infinite of lucid orbs replete, 
 Which set the living firmament on fire, 
 At the first glance, in such an overwhelm 
 Of wonderful, on man's astonished sight 
 Rushes Omnipotence ? 
 
 The number of the stars appears to be uncommonly great on first 
 casting the eye to the heavens in a very clear winter evening ; but 
 astronomers have long ago ascertained, that the number of such as 
 are visible to the naked eye in both hemispheres, does not amount 
 to 2000. This may at first appear incredible to some, because at 
 first sight they seem to be innumerable ; but the deception arises 
 from looking upon them hastily, without reducing them into any kind 
 of order. For let any person look steadily for some time upon a 
 large portion of the heavens, and count the number of stars in it, aod 
 he will be surprised to find the number so small. And if the moon 
 be observed for a short space of time, she will be found to pass very 
 few in her way, although there are as many about her path as in any 
 other part of the heavens. Flamstead's Catalogue contains only 
 3000 stars, and many of these are not visible without a telescope. 
 
 But although the number may be small when examined with the 
 naked eye, yet when examined with a powerful telescope the number 
 exceeds all computation. For a good telescope directed to almost 
 any part of the heavens, discovers multitudes that are lost to the 
 naked eye. In some places, however, they are crowded together ; 
 and in others there are considerable spaces where no stars can he 
 seen. Tn the small group called the Pleiades, in which 6 or 7 stars 
 
OF THE NUMBER OF THE STARS. 79 
 
 can only be seen by the naked eye, Dr. Hook discovered 78 stars 
 with a telescope, and F. de Rheita 188. The same astronomer 
 affirms, that he has observed above 2000 stars in the single constel- 
 lation Orion. And Huygens, when looking at the star in the middle 
 of Orion's sword, instead of one, found that there were 12. Galileo 
 found 80 in the space of the belt of Orion's sword, 21 in the nebulous 
 star in his head, and above 500 in another part of him, within the 
 compass of one or two degrees space, and more than 40 in the 
 nebulous star Praesepe. 
 
 There are also many stars which have the appearance of being 
 single to the naked eye, but when examined with a good telescope, 
 are found to be double, treble, &c. Of these, several have been ob- 
 served by Cassini, Hook, Long, Maskelyne, and some other 
 astronomers ; but Dr. Herschel has been the most successful ob- 
 server of these remarkable objects. Be has already given a cata- 
 logue of above 700 double stars, most of which have never been 
 noticed before by any other person. Among these there are also 
 some stars that are treble, double- double or quadruple, double-treble, 
 and multiple.* 
 
 So late descried by Herschel's piercing sight, 
 Hang the bright squadrons of the twinkling night : 
 Ten thousand marshall'd stars, or silver zone, 
 Effuse their blended lustres round her throne ; 
 Suns 'call to suns, in lucid clouds conspire, 
 And light exterior skies with golden fire. 
 Resistless rolls th' illimitable sphere, 
 And one great circle forms the unmeasured year. 
 
 Besides those starry groups, where the individual stars are 
 distinctly visible, there are numbers of small luminous spots, of a 
 cloudy appearance, called Nebulae. Of these a few have been 
 noticed by the ancients ; but since the invention of the telescope, 
 many more have been discovered, particularly by Dr. Herschel, who 
 has given a catalogue of 2500 nebulae. The largest of these nebulse 
 is the Galaxy, or Milky Way, a broad, irregular, luminous zone, 
 which nearly encircles the heavens, and appears to be the nearest of 
 all the nebulae. 
 
 Nor need we with a prying eye survey 
 
 The distant skies to find the Milky-Way : 
 
 It forcibly obtrudes upon our sight. CREECH. 
 
 From the observations of Dr. Herschel, it appears that this exten- 
 sive portion of the heavens is completely crowded with stars ; for he 
 says, " On applying the telescope to a part of the Via Lactea, (that 
 
 * This catalogue is contained in the 72d and 75th Vol. of the Transactions of 
 the Royal Society. 
 
80 OF THE NUMBER OF THE STARS. 
 
 is, the Milky Way) I found that it completely resolved the whole 
 whitish appearance into small stars, which my former telescope had 
 not light enough to effect.* 
 
 A way there is in heaven's extended plain, 
 
 Which when the skies are clear is seen below, 
 
 And mortals, by the name of Milky, know : 
 
 The ground-work is of stars ; through which the road 
 
 Lies open to great Jupiter's abode. DRYDEN from OVID. 
 
 The portion of this extensive tract which it has hitherto been conve- 
 nient for me to observe, is that immediately about the hand and club 
 of Orion. The glorious multitude of stars of all possible sizes that 
 presented themselves here to my view, was truly astonishing ; but as 
 the dazzling brightness of glittering stars may easily mislead us so 
 far as to estimate their number greater than it really is, I endeavoured 
 to ascertain this point, by counting many fields, and computing from 
 a mean of them, what a certain given proportion of the Milky Way 
 might contain. Among many trials of this sort, I found that six 
 fields, promiscuously taken, contained 110, 60, 70, 90, and 74 
 stars each. I then tried to pick out the most vacant place that was 
 to be found in that neighbourhood, and counted 63 stars. A mean 
 of the first 6 gives 79 stars for each field. Hence, by allowing 15 
 minutes of a great circle for the diameter of any field of view, we 
 gather, that a field of 15 degrees long, and 2 broad, or the quantity 
 which I have often seen pass through the field of my telescope in one 
 hour's time, could not well contain less than 50,000 stars that were 
 large enough to be distinctly numbered. But, besides these, I sus- 
 pected at least twice as many more, which, for want of light, I 
 could only see now and then, by faint glittering and interrupted 
 glimpses." 
 
 The Doctor goes on to make some remarks on nebulae and clusters 
 of stars in general, and then observes, " That they are generally 
 arranged in strata, which seems to run on to a great length, some of 
 which I was able to pursue, so as to guess pretty well their form 
 and direction. It is probable enough that they may surround the 
 whole apparent sphere of the heavens not unlike the Milky Way, 
 which undoubtedly is nothing but a stratum of fixed stars. And as 
 this latter immense starry bed is not of equal breadth or lustre in 
 every part, nor runs on in one straight direction, but is curved and 
 even divided into two streams along a very considerable portion of 
 it, we may likewise expect the greatest variety in the strata of 
 other clusters of stars and nebulae. One of these nebulous beds is 
 so rich, that in passing through a section of it, in the time of 36 
 minutes, I detected no less than 31 nebulae, all distinctly visible on 
 a fine blue sky. Their situation and shape, as well as condition, 
 
 * The telescope here alluded to was a reflector of 20 feet focal distance, and 
 its aperture 18f g inches. 
 
OF THE NUMBER OF THE STARS. 81 
 
 seems to denote the greatest variety imaginable. In another stra- 
 tum, or perhaps a different branch of the former, I have seen double 
 and treble nebuloe variously arranged ; large ones with small, seem- 
 ing attendants ; narrow but much extended, lucid nebulae or bright 
 dashes ; some of the shape of a fan, resembling an electric brush, 
 issuing from a lucid point ; others of a cometic shape, with a seem- 
 ing nucleus in the centre ; or like cloudy stars, surrounded with a 
 nebulous atmosphere ; a different sort again contain a nebulosity of 
 the milky kind ; while others shine with a fainter, mottled kind of 
 light, which denotes their being resolvable into stars/' 
 
 These observations serve to prove the intimate connection between 
 the nebulous and sidereal condition ; and, although in passing from 
 the one to the other, a number of ambiguous objects are to be met 
 with, yet this apparent uncertainty in the construction is only the 
 consequence of the want of an adequate power in our telescopes to 
 shew them of their real form. There is, however, no reason to 
 expect that an increase of light and distinctness in our telescopes 
 would free us altogether from ambiguous objects ; for by improving 
 our power of penetrating into space, and of defining those which at 
 present appear indistinct, we should probably reach so many new 
 objects, that others, of an equally obscure construction, would 
 obtrude themselves, even in greater number, on account of the 
 increased space of the more distant regions in which they were 
 situated. 
 
 Dr. Herschel is of opinion that there is some operation going on in' 
 the heavens, by which new sidereal bodies are gradually and pro- 
 gressively formed or drawn into clusters or nebulae ; and that these 
 clusters in time become more compressed or condensed, and ulti- 
 mately assume a globular form. The power by which these extra- 
 ordinary operations are performed, Dr. H. calls the clustering power. 
 And he thinks that in time this power will have the effect of com- 
 pletely breaking up the Milky Way, and of converting it into glo- 
 bular insulated clusters. For he says, " Since the stars of the 
 Milky Way are permanently exposed to the action of a power 
 whereby they are irresistibly drawn into groups, we may be certain 
 that from mere clustering stars they will be gradually compressed 
 through successive stages of accumulation, till they come up to what 
 may be called the ripening period of the globular form, and total 
 insulation ; from which it is evident that the Milky Way must 
 be finally broken up, and cease to be a stratum of scattered 
 stars." 
 
 " From this gradual dissolution of the Milky Way," continues 
 the Doctor, " we may draw a very important conclusion ; for the 
 state into which the incessant action of the clustering power has 
 brought it at present, is a kind of chronometer, that may be used to 
 measure the time of its past and future existence ; and although we 
 do not know the rate of going of this mysterious chronometer, it is 
 nevertheless certain, that, since the breaking up of various parts of 
 the Milky Way affords a proof that it cannot last for ever, it equally 
 
d2 O? THE DISTANCE OF THE STARS. 
 
 bears witness that its past duration cannot be admitted to be 
 infinite.* 
 
 If we reflect for a moment on the amazing number of stars which 
 the Milky Way contains, and grant that all the other nebulae which 
 the powerful telescopes of Dr. Herschel have enabled him to disco- 
 ver, are composed of distinct individual stars, then may we exclaim 
 with the Psalmist, 
 
 " The heavens declare the glory of God, and the firmament sheweth his handy 
 work. 
 
 OF THE DISTANCE OF THE STARS. 
 
 How distant some of the nocturnal suns ! 
 
 So distant says the sage, 'twere not absurd 
 
 To doubt, if beams set out at Nature's birth, 
 
 Are yet arrived at this so foreign world ; 
 
 Though nothing half so rapid as their flight. 
 
 An eye of awe and wonder let me roll, 
 
 And roll for ever. Who can satiate sight 
 
 In such a scene, in such an ocean wide 
 
 Of deep astonishment? Where depth, heighth, breadth, 
 
 Are lost in their extremes ; and where to count 
 
 The thick-sown glories in this field of fire, 
 
 Perhaps a seraph's computation fails. YOUNG. 
 
 To find the distance of the fixed stars is a problem which many 
 eminent astronomers have attempted to solve ; but notwithstanding 
 all their skill and exertions, this desirable object has never been 
 satisfactorily accomplished. Various methods have been pursued 
 without success ; and the result of the finest observations has 
 scarcely given us more than a distant approximation. For trigono- 
 metry, by whose powerful assistance the mathematician has boldly 
 ascended to the planetary regions, and measured the diameters and 
 orbits of the various bodies which compose the solar system, for 
 want of a proper base, is here but of little service ; for the whole 
 diameter of the earth's orbit, which is nearly 190 millions of miles, 
 is a mere point when compared with the immense distance of the 
 fixed stars. Now as this base cannot be enlarged, the only chance 
 that remains of solving the problem mathematically, is to endeavour 
 to improve the instruments which are employed in measuring their 
 parallax j for unless this is accurately ascertained, it is impossible 
 to find their real distance. f But the accuracy and nicety of the 
 instruments which have already been employed by the most skilful 
 and assiduous astronomers, in attempts to find the parallax of some 
 of the stars, leave us little hope of this important discovery ever 
 
 , ' "-" 
 
 * In Bode's Atlas Coelestis, 157 clusters are given as existing in the Milky 
 Way, to which Dr. Herschel says 68 more must be added, which are to be found 
 in the less rich parts of that surprising region of the heav ens. 
 
 t See an explanation of this term at page 9. 
 
OF THE DISTANCE OF THE STARS. 83 
 
 being made. Dr. Bradley assures us, that had the parallax of 
 Y Draconis amounted to a single second, he must have perceived it 
 in the great number of observations he made upon it ; and that it 
 seemed to him, that the annual parallax of this star does not amount 
 to a single second, and consequently that it is above 400,000 times 
 farther from us than the. sun, or 38,000,000,000,000 miles.* But as 
 this is only a bright star of the third magnitude, " it is probable," 
 says Dr. Herschel, " that its parallax is much less than that of a 
 star of theirs* magnitude." 
 
 Allowing this to be the case, and supposing the parallax of a star 
 to amount to one second, its distance cannot be less than 103,130 
 times the breadth of the earth's orbit, or 19,594,700,000,000 miles. 
 As these distances are so immensely great, it may amuse as well as 
 assist the mind, in forming a more correct idea of their vastness, to 
 compare them with the velocity of some moving body which may be 
 measured. 
 
 The swiftest motion of which we have any knowledge, is that of 
 light, which passes from the sun to the earth, or 95 million of miles 
 in 8 minutes 13 seconds, would require more than 6 years to pass 
 over the former of the above distances, or to arrive at the earth from 
 y Draconis : and above 3 years to pass over the latter, or from one 
 of the nearest of the fixed stars. But a cannon-ball, though continu- 
 ing to move at the rate of 20 miles per minute, would be 3 millions 8 
 hundred thousand years in passing from ? Draconis to the earth, and 
 1 million 960 thousand years in passing from the nearest fixed star. 
 Sound, which moves at the rate of about 13 miles in a minute, would 
 be 5 million 600 thousand years in traversing the former distance, 
 and 2 million 800 thousand, in passing through the latter. 
 
 The celebrated astronomer, Huygens, pursued speculations of this 
 kind so far, as to believe it not impossible that there may be stars at 
 such inconceivable distances, that their light has not yet reached the 
 earth since their creation. 
 
 The late Professor Playfair, in speaking of the fixed stars, says, 
 " As it cannot be doubted that the fixed stars are luminous bodies 
 like the sun, it is probable that they are not nearer to one another 
 than the sun is to the nearest of them. When, therefore, two stars 
 appear like a double star, or very near to one another, the one must 
 be placed far behind the other, but nearly in the same straight line, 
 when seen from the earth. The same must hold, at least in a certain 
 degree, wherever a great number of stars are seen concentrated in a 
 small spot. In the starry Nebulae, such as the Milky Way, which 
 derive their light from the number of small stars, appearing as if in 
 contact with each other, it is plain that the most distant of these 
 must be many thousand times farther off than the nearest, and light 
 must of course require many thousand years to come from them to 
 
 * Various methods have been proposed and repeatedly attempted, in order to 
 discover the parallax of the stars, by many celebrated astronomers, without suc- 
 cess j but this is a subject which does not belong to a work like the present. 
 
84 OF THE NATURE OF THE FIXED STARS. 
 
 *4 ' V SI- ' : J. fK, > 
 
 the earth. The poet has been taxed with exaggeration who 
 spoke of 
 
 Fields of radiance, whose unfading light 
 Has travelled the profound six thousand years, 
 Nor yet arrived in sight of mortal things. 
 
 Yet the fields which he describes are far within the circle to which 
 the observations of the astronomer extend." 
 
 Dr. Halley has also advanced what, he says, seems to be a meta- 
 physical paradox ; namely, that the number of the fixed stars must 
 be more than finale, and some of them at more than finate distances 
 from us ; and Addison has justly observed, " That this thought is 
 far from being extravagant, when we consider that the universe is the 
 work of infinite power, prompted by infinite goodness, and having 
 an infinite space to exert itself in, so that our imagination can set no 
 bounds to it." 
 
 OF THE NATURE OF THE FIXED STARS. 
 
 Ten thousand suns appear, 
 Of elder beam ; which ask no leave to shine 
 Of our terrestrial star, nor borrow light 
 From the proud regent of our scanty day. 
 
 BARBAWLD. 
 
 The immense distance of the fixed stars leaves us but little hope of 
 ever being able to determine their nature with complete certainty. 
 By analogical reasoning, and a careful attention to the various phe- 
 nomena which they present, we may make approaches to this inte- 
 resting and important discovery. 
 
 From the fruitless attempts which have often been made to deter- 
 mine their annual parallax, it is fully ascertained that they are many 
 thousand times farther distant from us, than the most remote planet 
 which belongs to the solar system ; and yet some of them shine with 
 a degree of brilliancy, which even rivals that of Venus or Jupiter. 
 Hence it is evident they cannot derive their light from the same 
 source as these planets do, viz. from the sun ; and if they derived 
 their light from any other luminous body which was nearer them, that 
 body would certainly be visible to us, as well as those to which it 
 communicated the light which rendered them visible. But as we 
 know of no other luminous body beside the sun from which they 
 could derive their light, it follows that they shine with their own 
 native light. One powerful argument in support of this opinion is, 
 that the stars appear to be much less when examined with a powerful 
 telescope, than they do to the naked eye ; for they appear to be mere 
 luminous points when viewed through a telescope, which magnifies 
 three or four hundred times. Now, if they shone by a borrowed 
 light, they would be as invisible to the naked eye as the satellites of 
 Jupiter or Saturn. But though these satellites be invisible to the 
 naked eye, yet, when viewed through a telescope of a tolerable 
 
OP THE NATURE OF THE FIXED STARS. 8S 
 
 magnifying power, they are not only seen distinctly, but they appear 
 to be much larger than any of the fixed stars. Hence it is inferred 
 that the fixed stars shine by their own proper light ; and when their 
 immense distances are taken into account, we cannot hesitate to ad- 
 mit that their real magnitude considerably exceeds that of any of the 
 planets. The fixed stars, then, seem to be of a nature very similar to 
 the sun ; and that they are suns in reality scarcely admits of a doubt; 
 for the analogy between them may be traced in many particulars. 
 The sun turns on his axis; so do many of the fixed stars, and most 
 probably all.* The suit has spots on his surface ; so has the star 
 Algol and some others, and probably all the stars of the heavens. On 
 the sun these spots are changeable ; so they are on several of the 
 stars, as Dr. Herschel and some other astronomers have repeatedly 
 observed. If, then, the fixed stars resemble the sun in so many par- 
 ticulars, is it not highly probable that each of them is designed to 
 answer similar purposes ? Is it not reasonable to conceive that each 
 star is the centre of a system, and has planets revolving round it, 
 which are illuminated, warmed, and cherished by its light and heat? 
 
 We certainly cannot imagine that the fixed stars were formed for 
 no other purpose than to cast a faint light upon the earth, especially 
 when we consider that we have incomparably more light from the 
 moon than from all the stars put together, and that innumerable stars, so 
 far from giving us light, are not even discernable, without the aid of 
 the most powerful telescopes. 
 
 If our sun, with the whole system of planets, moons, arid comets, 
 were to be removed to the distance of the nearest fixed star, not one 
 of them would be visible except the sun, which would then appear, 
 not with the brilliancy and lustre which he does at present, but like 
 a star of the first or second magnitude. Instead, therefore, of looking 
 upon the fixed stars as a curious species of twinkling flames hung-up 
 in the spacious canopy of heaven, merely to ornament it, or to add to 
 the delight of man, let us suffer our conceptions to expand till they 
 embrace a wider field of contemplation : but in doing this let us also 
 keep within the bounds of probability, which the true astronomef 
 on no occasion goes beyond. 
 
 When the immense distance of the fixed stars is taken into consi- 
 deration, we shall not be accused of soaring into the regions of fancy, 
 although we affirm each of these stars not only to be a sun with a 
 system of planets and comets moving round it, but that it is highly 
 probable each star is at least equal, both in brilliancy and magnitude, 
 to the sun himself. And if it once be admitted that each star is the 
 centre of a system, and has planets or earths revolving round it in the 
 same manner as our sun has, is it not agreeable both to reason and 
 analogy to suppose these planets inhabited by rational creatures ? 
 When every part of matter upon which we have any opportunity of 
 making observations, is found fitted for the habitation and support of 
 
 * The period in which the star Algol goes through its variations is two days 
 twenty-one hours. 
 
 8. I 
 
86 OF THE NATURE OF THE FIXED STARS. 
 
 living creatures peculiar to itself; when we meet with no part of na- 
 ture lying waste and useless; and when we find that not only seas, 
 lakes and rivers, mountains and valleys, trees and herbs, grasses and 
 the animals that feed upon them, teem with life ; but even the blood 
 and humours of animals, when alive as well as dead, support their 
 respective inhabitants ; shall we, with such scenes before our eyes, 
 and in direct opposition, as it were, to the voice of nature, indulge the 
 contracted and unreasonable notion, that the millions of globes which 
 compose the universe are barren and void ? Is it not more rational 
 to suppose them the abodes of intelligent beings; of beings capable 
 of loving and adoring their Creator, provided with every thing neces- 
 sary for their comfort and support, and possessed of capacities neces- 
 sary for social intercourse and active life ? 
 
 Where things do not admit of mathematical certainty, moral cer- 
 tainty ought to be indulged, especially when aided by the analogy of 
 things which are both known and natural. It would almost be as 
 irrational to suppose animals with eyes destined to live in eternal dark- 
 ness, or without eyes to live in perpetual light, as to imagine space illu- 
 minated where there is nothing to be acted upon. The fixed stars were 
 surely not created merely for the purpose of enlightening a void ! All 
 great astronomers, with Newton at their head, have maintained that the 
 stars are all suns, and surrounded with planetary bodies which they 
 enlighten, warm, and cherish in the same manner as the sun does the 
 bodies which circulate round him. And the celebrated Huygens 
 says, " Why should we conclude that our star (that is the sun) has 
 better attendance than others ? They must all have their planets and 
 animals ; nay their rational creatures too." But we forbear to proceed 
 further in the path of speculation on this sublime subject, although it 
 is almost impossible to avoid it ; for when we reflect on the millions 
 of millions of worlds placed at the distance of millions of miles from 
 each other, and each of these worlds inhabited by millions of rational 
 creatures, formed for never-ending felicity, the idea though delightful 
 must necessarily be vague and indefinite. Really when indulging 
 such contemplations, we can scarcely help acknowledging, that all 
 our science is as nothing, and that we have yet to be initiated in the 
 principles of a new notation, which may enable us to comprehend 
 these astonishing numbers. 
 
 My soul unused to stretch her powers, 
 
 In flights so daring, drops her weary wing, 
 
 And seeks again the known accustomed spot, 
 
 Drest up with sun and shade, and lawns, and streams, 
 
 A mansion fair and spacious for its guest, 
 
 And full replete with wonders. 
 
 BARBAUI.D. 
 
OF ECLIPSES. 87 
 
 OF ECLIPSES. 
 
 Of all the various phenomena of the heavens there are none which 
 have created so much curiosity, excited so much interest, or caused 
 so great terror throughout the world, as eclipses of the sun and moon ; 
 and to those who are unacquainted with the principles of astronomy 
 there is nothing perhaps which appears more extraordinary than the 
 accuracy with which they can be predicted. 
 
 In the earlier ages of the world, before science had enlightened the 
 minds of men, appearances of this kind were generally regarded as 
 alarming deviations from the established laws of nature ; and but few, 
 even among philosophers themselves, were able to account for these 
 extraordinary appearances. At length, when men began to apply 
 themselves to observations, and when the motions of the celestial bo- 
 dies were better understood, their phenomena were not only found to 
 depend upon a regular cause, but to admit of a natural and easy so- 
 lution. There are, however, nations that still entertain the most 
 superstitious notions respecting eclipses, particularly the Mexicans 
 and Chinese, whose conduct on the appearance of a phenomenon of 
 this kind is well described in the fpllowing lines : 
 
 Thus when the infant moon her circling sphere 
 Wheels o'er the sun's broad disk, her shadow falls 
 On earth's fair bosom ; darkness chills the fields, 
 And dreary night invests the face of heaven. 
 Reflected from the lake full many a star 
 Glimmers with feeble languor. India's sons 
 Affrighted in wild tumult rend the air. 
 Before his idol god with barb'rous shriek 
 The Brachman* falls : when soon the eye of day 
 Darts his all-cheering radiance, from the gloom 
 Emerging. Joy invades the wondring crowd. 
 And acclamation rushes from the tongues 
 Of thousands, that around their blazing pile 
 Riot in antic dance and dissonant song. 
 
 ZOUCH. 
 
 Many instances are to be found, not only in ancient, but even in 
 comparatively modern history, where the superstition of the times has 
 continued to connect the records of eclipses with the details of some 
 remarkable event, which either happens soon after or during their con- 
 tinuance. But these details being foreign to the nature of the present 
 work, we shall proceed to give an account of the causes, and various 
 kinds of eclipses of the sun and moon. 
 
 Teach me the various labours oi the moon, 
 And whence proceed th' eclipses of the sun. 
 
 * Although the Chinese perform the most ridiculous and superstitious ceremo- 
 nies during the time of an eclipse, yet they can calculate them with the greatest 
 precision. 
 
 I 2 
 
88 OF ECLIPSES, 
 
 As every planet belonging to the solar system, both primary and 
 secondary, derives its light from the sun, it must cast a shadow to- 
 wards that part of the heavens which is opposite to the sun. This 
 shadow is of course nothing but a privation of light in the space hid 
 from the sun by the opaque body, and will always be proportionate 
 to the relative magnitudes of the sun and planet. If the sun and 
 planet were both of the same size, the form of the shadow cast by the 
 planet would be that of a cylinder, the diameter of which would be the 
 same as that of the sun or planet, and it would never converge to a 
 point. If the planet were larger than the sun, the shadow would 
 continue to spread or diverge ; but as the sun is much larger than the 
 greatest of the planets, the shadows cast by any one of these bodies 
 must converge to a point, the distance of which from the planet will 
 be proportionate to the size and distance of the planet from the sun. 
 The magnitude of the sun is such that the shadow cast by each of the 
 primary planets always converges to a point before it reaches any 
 other planet; so that not one of the primary planets can eclipse ano- 
 ther. The shadow of any planet which is accompanied by satellites 
 may, on certain occasions, eclipse these satellites; but it is not long 
 enough to eclipse any other body. The shadow of a satellite or 
 moon may also, on certain occasions, fall on the primary and 
 " eclipse it. 
 
 Eclipses of the sun and moon happen when the moon is near her 
 nodes, that is, when she is either in the plane of the ecliptic or very 
 near it. Those of the sun happen only at new moon, or when the 
 moon is in conjunction with the sun; whilst those of the moon happen 
 at the time of full moon, or when the moon is in opposition to the sun. 
 The sun, earth, and moon, must therefore always Jbe nearly in the 
 same straight line at the time of an eclipse ; and ^cbriv&sely^ when 
 these three bodies are nearly in a straight line, an eclipse must take 
 place. Hence, it is evident, that an eclipse happens in consequence 
 of one of the two opaque bodies, the earth and the moon, being so 
 placed as to prevent the sun's light from falling on the other. See 
 the following figure, which represents the moon passing through the 
 dark shadow of the earth, as she moves in her orbit n z, while tlje 
 earth moves in the ecliptic r g. 
 
 The interposition of the moon between the sun and the earth pro- 
 duces an eclipse of the sjm ; and the interposition of the earth between 
 the moon and the sun, so that its shadow falls on the moon, produces 
 
OF ECLIPSES. 89 
 
 an eclipse of the moon. On these principles the whole phenomena 
 of eclipses depend, and admit of complete explanation. 
 
 If the moon's orbit were coincident with the plane of the ecliptic, '\ 
 the moon's shadow would fall upon the earth, and occasion a central { 
 eclipse of the sun at every conjunction, or new moon; whilst the j 
 earth's shadow would fall on the moon, and occasion a total eclipse \ 
 of that body at every opposition or full moon. For as the moon 
 would then always move in the ecliptic, the centres of the sun, earth, 
 and moon, would all be in the same straight line at both of these 
 times. But the moon's orbit is inclined to the ecliptic, and forms A 
 with it an angle of about 5 10' ; and, therefore, the moon is never in ^ 
 the ecliptic except when she is in one of her nodes: hence, there may 
 be a considerable number of conjunctions and oppositions of the sun ) 
 and moon without any eclipse taking place. 
 
 The moon is always at some distance from the ecliptic, except -. 
 when she is in one of her nodes ; and this distance is called her lati- \ 
 tude y which is north or south, according as the moon is on the north \ 
 or south side of the ecliptic. Now if the moon has any latitude, / 
 there cannot be a central eclipse, for this can only happen when the 
 moon is in one of her nodes at the moment of conjunction, which is ) 
 very seldom the case ; and, of course, very few central eclipses of \ 
 the sun have taken place since the creation of the world/ But the , 
 section of the earth's shadow (through which the moon passes when 
 she is eclipsed) being much larger than the disc of the moon, the 
 moon may be totally eclipsed, although she be at some distance from / 
 her node at the time of opposition ; but its duration will be the greater ^ 
 the nearer she is to the node. An eclipse of the sun may also happen / 
 although the moon be at some distance from her node at the time of 
 conjunction ; but its form, as well as its duration, depend very much / 
 upon that distance. This circumstance has occasioned the division 
 of eclipses into central, total, annular, and partial. 
 
 As the meaning of these terms must be obvious to the reader, it is 
 almost unnecessary to give an explanation of them. 
 
 A central eclipse, is that in which the centre of the shadow falls 
 on the centre of the body which is eclipsed. 
 
 A total eclipse is the obscuration of the whole body eclipsed. 
 
 An annular eclipse is that in which the whole of the body eclipsed 
 is hid, except a ring round its edge, which remains luminous. 
 
 A partial eclipse is that in which part of the eclipsed body is hid 
 from view. 
 
 The following figure represents a partial eclipse of the sun, which 
 will be visible to that tract of the earth marked npo, the line m n 
 marks when the greatest obscuration. 
 
 * One of the most remarkable eclipses of this kind which has ever happened, 
 was visible in Britain and several other countries, on the Tth of September, 
 1820. 
 
90 OF ECLIPSES. 
 
 If the distance be very small, the eclipse will be the greater and 
 continue the longer ; but no eclipse of the sun can be either central 
 or total, except the moon be in the very node at the time of conjunc- 
 tion. But should she be in this situation, when she is at her least 
 distance from the earth, and the earth, at the same time, at its least 
 distance from the sun, then the eclipse will not only be central but 
 total, and continue so for a few minutes. But if the moon happens 
 to ]be at her greatest distance from the earth, and the earth at its 
 greatest distance from the sun, the eclipse will be annular, or a small 
 space round the sun's centre only will be hid from view, and a bright 
 lucid ring round his edge will remain visible. 
 
 If the moon be less than 17|- degrees from either node at the time 
 of conjunction, her shadow will fall more or less upon the earth, ac- 
 cording as she is more or less within this limit; and, of course, the 
 sun will suffer a partial eclipse. And if she be less than 12| degrees 
 from either node at the time of orrrjosition, she will pass through 
 more or less of the earth's shadow, according as she is more or less 
 within these lines, and of course she will suffer an eclipse. 
 
 As these limits form but a small part of the moon's orbit, which is 
 360 degrees, eclipses happen but seldom ; however in no year can 
 there be fewer than two, and there may be seven of the sun and moon 
 together but taking one year with another, there are about four each 
 year. But as the sun and moon spend as much time below the hori- 
 zon of any place as above it, half the number of the eclipses will be 
 invisible at any particular place, and consequently there will be only 
 two eclipses visible in a year at that place, the one of the sun and the 
 other of the moon.* 
 
 Every eclipse, whether of the sun or moon, is visible at some place 
 
 of the earth's surface, and invisible at others; for the rational horizon 
 
 of every place divides both the earth and heavens into two equal 
 
 portions or hemispheres ; and as no celestial body can be seen except 
 
 ) it be above the spectator's horizon, it follows that any eclipse which 
 
 / is visible in the one hemisphere cannot be visible in the other, because 
 
 ^ the body which is eclipsed is below the horizon of that other. If a 
 
 ) lunar eclipse, for example, happens at any hour of the night, between 
 
 * If there be seven eclipses in any year, five of them must be of the sun and 
 two of the moon. 
 
OF ECLIPSES. 91 
 
 the time of sun-setting and sun-rising, at any particular place, it will 
 be visible there and invisible to the inhabitants of the opposite hemis- < 
 phere, who have the sun above their horizon at that time ; for the sun 
 and moon are in opposite^ parts of the heavens at the time of a lunar 
 eclipse. And with respect to solar eclipses, it is evident that they 
 can only be seen at any place when the sun is above the horizon of 
 that place. There is, however, a difference with regard to the visi- 
 bility of a solar and lunar eclipse ; for an eclipse of the moon has the 
 same appearance to all the inhabitants of that hemisphere to which 
 the moon is visible at the time, owing, in, part, to the small dis- 
 tance of the moon from the earth. But an eclipse of the sun may be 
 visible to some places and invisible to others in the same hemisphere 
 of the earth, because the moon's shadow is small in comparison of 
 the earth ; for its breadth, excluding the penumbra, is only about 180 
 miles even in central eclipses.* Hence those places which are con- 
 siderably distant from the path of the shadow will either have no 
 eclipse at all, or a very small one ; while places near the middle of 
 the shadow will have the greatest possible. There is also a difference 
 in the absolute time at which a solar eclipse happens at the various 
 places where it is visible; for it appears more early to the western 
 parts, and later to the eastern, on account of the motion of the moon 
 (and of course her shadow) from west to east. 
 
 In most solar eclipses the moon's disc may be observed by a teles- 
 cope to be covered by a faint light, whieh is attributed to the re- 
 flexion of light from the illuminated part of the earth. When the 
 eclipses are total, the moon's limb is surrounded by a pale circle of 
 light, which some astronomers consider as an indication of a lunar 
 atmosphere, but others, as occasioned by the atmosphere of the sun ; 
 because it has been observed to move equally with the sun and not 
 with the moon. 
 
 Dr. Halley, in describing a central eclipse of the sun, which hap- 
 pened at London in April, 1715, says, that although the disc of the 
 sun was wholly covered by the moon, a luminous ring of a faint 
 pearly light surrounded the body of the moon the whole time ; and its 
 breadth was nearly a tenth of the moon's diameter. 
 
 In lunar eclipses, the moon seldom disappears entirely; and on 
 some occasions, even the spots may be distinguished through the 
 shade ; but this can only be the case when the moon is at her greatest 
 distance from the earth at the time of the eclipse, for the nearer the 
 moon is to the earth the darkness is the greater. In some instances, 
 the moon has disappeared entirely ; and the celebrated astronomer 
 JHeraclius, has taken notice of one where the moon could not be seen 
 even with a telescope, though the night was remarkably clear. 
 
 Although eclipses of the sun and moon were long considered by 
 the ignorant and superstitious as presages of evil, yet they are of the 
 greatest use in astronomy, and maybe employed to improve some of 
 
 * A penumbra is the faint shadow produced by an opaque body when opposed 
 to a luminous one. 
 
0$ OF ECLIPSES, 
 
 / the most important and useful of the sciences. By eclipses of the 
 \ moon the earth is proved to be of a. globular form, the sun to be greater 
 ( than the earth, and the earth greater than the moan. When they are 
 similar in all their circumstances, and happen at considnrable intervals 
 of time, they also serve to ascertain the real period of the moon's mo- 
 tion. In geography, eclipses are of considerable use in determining 
 the longitude of places, and particularly eclipses of the moon, because 
 they are oftener visible than those of the sun, and the same eclipse is 
 of equal magnitude and duration at all places where it is seen. In 
 chronology, both solar and lunar eclipses serve to determine exactly 
 the time of any past event. 
 
 We, in the dark eclipse, with filial awe 
 
 i *^ Trace the all-gracious Parent of the spheres ; 
 
 Their distances and their proportion learn ; 
 Extending navigation ; securing 
 The mariner thro' the tremendous waves. 
 
 EODOSIA. 
 
 For the purpose of finding the longitude at places on the earth, 
 eclipses of Jupiter's satellites are found much more useful than eclipses 
 of the moon ; not only on account of their happening more frequently, 
 but on account of their instantaneous commencement and termi- 
 nation. 
 
 When Jupiter and any of his satellites are in a line with the sun, 
 and Jupiter between the satellite and the sun, it disappears, being 
 then eclipsed, or involved in his shadow. When the satellite goes 
 behind the body of Jupiter, with respect to a spectator on the earth, 
 it is said to be occulted, being hid from our sight by his body, whether 
 in his shadow or not. And when the satellite comes into a position 
 between Jupiter and the sun, it casts a shadow on the face of that 
 planet, which is seen by a spectator on the earth as an obscure round 
 spot. Lastly, when the satellite is in a line with Jupiter and the 
 earth, it appears on his disc as a round black spot, which is termed a 
 transit of the satellite. 
 
 As these phenomena appear at the same moment of absolute time 
 at all places on the earth to which Jupiter is then visible, but at dif- 
 ferent hours of relative time, according to the distance between the 
 meridian of the places at which observations are made, it follows that 
 this difference of time converted into degrees will be the difference of 
 longitude between those places.* Suppose, for example, that a per- 
 son at London observed an eclipse to begin at 11 o'clock in the 
 evening, and that a person at Barbadoes observed the same at 7 
 o'clock in the evening, it is certain the eclipse was seen by both per- 
 sons at the same moment of absolute time, although there is four 
 hours' difference in their manner of reckoning that time : and this 
 converted into degrees (at the rate of 15 degrees to an hour) is the 
 
 * Absolute time is that which is computed from the same moment ; relative is 
 that which is computed from different moments. 
 
ON LIGHT. 9# 
 
 difference of longitude between these two places therefore Barba- 
 does is 60 degrees west from London, the time not being so far ad- 
 vanced there as at London. 
 
 Another phenomenon, somewhat similar to an eclipse, sometime? 
 takes place, by which the longitude of places may be determined, 
 although not quite so easily, nor perhaps so accurately, as by the 
 eclipses of Jupiter's satellites. This is the hiding or obscuring of a 
 fixed star or planet by the moon or other planet, which takes place 
 when the moon or planet is in conjunction with the star. Appear- 
 ances of this kind are termed occultations. They are very little at- 
 tended to except by practical astronomers, who employ them for the 
 correction of the lunar tables, and settling the longitude of places, as 
 already stated. 
 
 ON LIGHT. 
 
 Fairest of beings ! first created light ! 
 
 Prime cause of beauty ! for from thee alone 
 
 The sparkling gem, the vegetable race, 
 
 The nobler worlds that live and breathe their charms, 
 
 The lovely hues peculiar to each tribe, 
 
 From thy unfading source of splendour draw 
 
 In thy pure shine, with transport I survey 
 
 This firmament, and these her rolling worlds 
 
 Their magnitudes and motions. 
 
 MALLET. 
 
 The nature of Light has been the subject of speculation and con- 
 jecture among philosophers, from the iirst dawnings of philosophy to 
 the present day. But of all the conjectures which have been ad- 
 vanced on this curious and interesting subject, there is scarcely one 
 supported by evidence sufficient to entitle it to preference over the 
 other. There are, however, two opinions on this subject which have 
 prevailed more generally than any of the others, and therefore, it may 
 be proper to notice them here, although the design of the present 
 work is rather to state what is known respecting any phenomenon, 
 than to indulge in conjectures concerning it. 
 
 The celebrated Huygens considered light as a subtle fluid filling 
 space, and rendering bodies visible by the undulations into which it 
 was thrown. According to this theory, when the sun rises it agitates 
 this fluid, the undulations gradually extend themselves, and at last 
 striking against our eyes, we see the sun. This opinion of Hyugens 
 was adopted by Euler, one of the best mathematicians that ever 
 lived, who exerted the whole of his consummate mathematical skill 
 in its defence. 
 
 Sir I. Newton and many other distinguished philosophers consider 
 light as a substance consisting of small particles, constantly separating 
 from luminous bodies, moving in straight lines, and rendering other 
 bodies luminous by passing from them and entering the eye. New- 
 ton has been at great pains to establish this theory, and has certainly 
 
94 ON LIGHT* 
 
 shown that all the phenomena of light may be mathematically deduced 
 from it. 
 
 While Huygens and Euler have attempted to support their hypo- 
 thesis, rather by starting objections to Newton's, than by bringing 
 forward direct proofs, Newton and his disciples, on the contrary, 
 have shown that the known phenomena of light are mcfmsistent with 
 the undulations of a fluid, and that on such a supposition there can 
 be no such thing as darkness at all. They have also brought forward 
 a great number of direct arguments in support of their theory, which 
 it has been impossible to answer.* But without giving' a decided pre- 
 ference to any theory, we shall proceed to state some of its properties. 
 
 Roemer, a Danish astronomer, while engaged in making observa- 
 tions on the satellites of Jupiter, found that in eclipses they emerged 
 from the shadow at certain times a few minutes later, and at others 
 a few minutes sooner than they ought to have done according to the 
 tables, which had been previously constructed to shew the times of 
 their revolutions, eclipses, &c. On comparing these apparent irre- 
 gularities together, he found that the eclipses happened before or after 
 the computed time, according as the earth was nearer to or farther 
 from Jupiter. Hence he formed the ingenious conjecture, which was 
 soon demonstrated to be the case, that the motion of light is not in- 
 stantaneous, as was then generally believed, but that it required a 
 certain portion of time, to pass from the luminous body to the eye of 
 the observer. According to Roemer's calculation, it was about seven 
 minutes in traversing the radius of the earth's orbit ; but it has since 
 been found, that when the earth is exactly between Jupiter and the 
 sun, his satellites are eclipsed about 8 \ minutes sooner than the time 
 found by the tables ; but when the earth is nearly in the opposite 
 point these eclipses happen about 8^ minutes later than that deter- 
 mined by the tables. It is therefore concluded that light takes up about 
 16f minutes of time to pass over a space equal to the diameter of the 
 earth's orbit, which is at least one hundred and ninety millions of 
 miles; it therefore moves at the rate of nearly 200,000 miles per 
 second, which is about 10,300 times faster than the earth in its orbit, 
 and 1,550,000 times quicker than a cannon ball.f 
 
 Behold the light emitted from the sun ! 
 What more familiar, and what more unknown ? 
 While by its spreading radiance it reveals 
 All Nature's face, it still itself conceals. 
 See how each morn it does its beams display, 
 And on its golden wings bring back the day ! 
 
 * M. Delaval maintains, that all light is reflected by white particles, and 
 coloured in its transmission. No transparent medium reflects any light when 
 examined within a blackened bottle ; this is shewn by experiments on 68 kinds 
 of fluids, and on many kinds of glasses, and other substances. For this, and for 
 the colours of the sea, M. Delaval proposes a very singular theory; but those 
 who wish to become particularly acquainted with it, must consult his work on 
 the permanent colours of opaque bodies. 
 
 t The real time which light takes to pass from the sun to the earth is 8 minute 
 13 seconds. 
 
ON LIGHT* 
 
 Haw soon the effulgent emanations fly 
 Thro' the blue gulf of interposing sky ! 
 How soon their lustre all the region fills, 
 Smiles on the valleys, and adorns the hills : 
 Millions of miles, so rapid is their race, 
 To cheer the earth, they in few minutes pass. 
 Amazing progress ! At its greatest stretch, 
 What human mind can this swift motion reach ? 
 
 BLACKMOR&. 
 
 The velocity of light being known, it is easy to know the time it 
 requires to arrive at the earth from any of the planets, or even the fixed 
 stars if their distance be known. For it has been ascertained, that 
 the reflected light of the planets and satellites, travels with the same 
 velocity as the direct light of the sun or fixed stars ; and that the 
 velocity is the same from whatever distance it comes. 
 
 The discovery of Roemer has been completely confirmed by ano- 
 ther most important discovery made by our countryman Dr. Brad- 
 ley, while engaged in making a series of observations, with a view to 
 determine the annual parallax of the fixed stars. This celebrated as- 
 tronomer found that the aberration or difference between the true 
 and apparent place of a fixed star, is occasioned by the progressive 
 motion of light, combined with the motion of the earth in its orbit ; 
 and that this aberration when greatest amounted to 20>232. Now the 
 earth describes an arc of 20"-232, in 8' 13", the time that light takes 
 to pass over the semidiameter of the earth's orbit. This circumstance, 
 therefore, not only affords one of the most convincing proofs of the 
 motion of the earth in its orbit, but entirely overthrows both the Pto- 
 lemaic and Tychonic systems, and completely establishes the motion 
 of the earth. 
 
 As the rays of light are known to proceed only in straight lines from 
 luminous bodies, and as the earth is constantly moving forward in its 
 orbit, it is evident that a ray of light proceeding from any celestial 
 body will impinge on the earth at a different point from what it 
 would have done had the earth been stationary. It is therefore ne- 
 cessary, in making astronomical observations with nicety, to make 
 allowance for the aberration. When a fixed star or planet, for ex- 
 ample, is seen through a tube or telescope, the tube does not point 
 exactly to the true place of the star or planet, but to its apparent 
 place, which is always more advanced in the direction we are moving 
 than its true place, by a quantity equal to the aberration of the ob- 
 ject.* But this will, perhaps, be better understood by the following 
 illustration, which is given by M. Maupertius in his Elements of Geo- 
 
 "The direction," says he, "in which a gun must be pointed to 
 strike a bird in its flight, is not exactly that of the bird, but of a 
 point a little before it, in the path of its flight; and that so much the 
 more as the flight of the bird is more rapid, with respect to the flight 
 
 * The aberration not only affects the longitude of a star or planet, but also its 
 atitude, declensions, and right ascension. 
 
(i OF THET AURORA BOREALIS. 
 
 of the shot. In this way of considering the matter, the flight of the 
 bird represents the motion of the earth, and the flight of the shot the 
 motion of the light proceeding from the object." 
 
 Many philosophers have attempted, not only to compare the light 
 of the stars with that of the sun, but also to ascertain their distances 
 by comparisons of this kind. 
 
 The Rev. Mr. Mitchell, in an elaborate and ingenious paper in the 
 Transactions of the Royal Society, states, that our sun would still 
 appear as luminous as the star Sirius, although removed to 400,000 
 times his present distance ; and that the fixed stars cannot be nearer 
 than this, if they be equal to the sun in lustre and magnitude, and that 
 they are so is the opinion of the most celebrated astronomers of the 
 present day. Euler, who has already been mentioned, makes the 
 light of the sun equal to 6,500 candles at one foot distance ; the 
 moon equal to one candle at 7-| feet distance ; Venus to one at 421 
 feet ; and Jupiter to one at 1320 feet. From this comparison it fol- 
 lows, the light of the sun exceeds that of the moon 364,000 times. 
 It is therefore no wonder that the attempts which have been made 
 by some philosophers to condense the light of the moon by lenses, 
 have been attended with so little success. Fjor, should one of the 
 largest of these lenses even increase the light of the moon one thou- 
 sand times, still, in this increased state, it will be three hundred and 
 sixty-four times less than the intensity of the common light of the sun. 
 
 The intensity of light has been found to vary as the square of the 
 distance ; for, if an object be placed one foot distant from a candle, 
 it will receive four times more light than when it is removed to double 
 the distance; nine times more than when it is removed to three times the 
 distance, and so on. The refraction, &c. of light will be noticed whert 
 treating of the atmosphere. 
 
 OF THE AURORA BOREALIS. 
 
 Silent from the north 
 
 A blaze of meteors shoots : ensweeping first 
 The lower skies, they all at once converge 
 High to the crown of heaven, and all at once, ' 
 Relapsing quick, as quickly reascend, 
 And mix, and thwart, extinguish, and renew, 
 All ether coursing in a blaze of light. 
 
 THOMSON. 
 
 The Aurora Borealis, or Northern Lights, are luminous meteors, 
 which sometimes appear in the northern part of the heavens in the 
 winter season, and particularly in frosty weather. They are usually 
 of a reddish colour, inclining to yellow, but they frequently send out 
 coruscations of pale whitish light. These seem to rise from the ho- 
 rizon in a pyramidical form, and move backwards and forwards with 
 a tremulous undulating motion; but on some occasions they shoot 
 to the zenith with the greatest velocity, and then form themselves 
 
OF THE AURORA ROREALIS. 97 
 
 into the most whimsical figures. This has led M. Godin to suppose, 
 that most of the extraordinary meteors and prodigies which are stated 
 in history to have been seen in the skies, such as battles, and the 
 like, may probably enough have been produced by particular forms 
 assumed by Aurora Borealis. 
 
 From look to look, contagious thro' the crowd 
 The panic runs, and into wondrous shapes 
 Th' appearance throws : armies in meet array 
 Throng'd with aerial spears and steeds of fire, 
 Till the long lines of full-extended war, 
 In bleeding fight commixt, the sanguine flood 
 Rolls a broad slaughter o'er the plains of heaven. 
 As thus they scan the visionary scene, 
 On all sides swells the superstitious din, 
 Incontinent, and busy Frenzy talks 
 Of blood and battle, cities overturn'd, 
 And late at night in swallowing earthquake sunk, 
 Or hideous wrapt in fierce ascending flame ; I 
 
 Of sallow famine, inundation, storm ; 
 Of pestilence, and every great distress ; 
 Empires subvers'd, when ruling Fate has struck 
 Th' unalterable hour : even Nature's self 
 Is deem'd to totter on the brink of time. 
 Not so the man of philosophic eye, 
 And inspect sage ; the waving brightness he 
 Curious surveys, inquisitive to know 
 The causes and materials, yet unfix'd, 
 Of this appearance, beautiful and new. 
 
 THOMSON. 
 
 This kind of meteor never appears near the equator ; but has fre- 
 quently been seen towards the south pole, as well as the north. 
 
 Forster, in the account of his voyage round the world with Captain 
 Cook, says he observed them for several nights together, in sharp 
 frosty weather, and that they had much the same appearance as those 
 observed in the north, except that they were of a lighter colour. 
 
 In the Shetland Islands these phenomena are the constant attend- 
 ants of clear evenings, and afford great relief to the inhabitants in the 
 long and gloomy nights of winter experienced in this part of the 
 world. 
 
 The same kind of appearances are also seen in the northern parts 
 of Sweden and Lapland, where they are particularly beautiful, and 
 afford light to travellers during the whole night. 
 
 By dancing meteors then, that ceaseless shake 
 A waving blaze refracted o'er the heavens, 
 And vivid moons, and stars that keener play 
 With keener lustre from the glossy waste. 
 Even in the depth of Polar Night they find 
 A wondrous day : enough to light the chase, 
 Or guide their daring steps to Finland fairs. 
 
 THOMSON. 
 
 In Hudson's Bay the Aurora Borealis spread a variegated splendour 
 9 K 
 
OF THE AURORA BOREALIS. 
 
 over the whole sky, not to be defaced even by the splendour of the 
 full moon. In the north-east parts of Siberia these northern lights 
 are observed to begin -with single bright pillars, rising in the north, 
 and almost at the same time in the north-east, which gradually in- 
 creasing, comprehend a large space of the heavens, rush about from 
 place to place, with incredible velocity, and finally almost cover the 
 whole sky up to the zenith, producing an appearance, as if a vast 
 tent were expanded in the heavens, glittering with gold, rubies, and 
 saphires. A more beautiful spectacle cannot be painted; but no 
 person could behold it for the first time without terror. For, however 
 grand the illumination may appear, it is attended with as much hiss- 
 ing, crackling, and tumult, as if the largest fire-works were playing 
 off. The hunters who pursue the white and blue foxes on the con- 
 fines of the icy sea, are often overtaken in their courses by these 
 northern lights ; their dogs are then so much frightened, that they 
 will not move, but lie obstinately on the ground till the noise has 
 passed. 
 
 It is chiefly in the arctic regions that the Aurora Borealis are most 
 striking in their appearance. In England it is only their extremities 
 that are seen, and even these have been noticed very seldom : for 
 there are none recorded in our annals between the appearance of the 
 remarkable one of Nov. 14th, 1574, and the surprising one of March 
 6th, 1716, which appeared for three nights successively. This one 
 was visible from the west of Ireland to the confines of Russia and 
 east of Poland, and from the 30th degree of latitude, over almost all 
 the north of Europe ; and in all places, at the same time, it exhibited 
 the same wonderful appearances. Father Boscovich calculated the 
 height of an Aurora Borealis which appeared on the 16th December, 
 1737, and found that it was 825 miles; and the celebrated Bergman, 
 from a mean of thirty computations, makes the average height of the 
 Aurora Borealis 70 Swedish or 469 English miles. But Euler and 
 some other philosophers suppose their height to be several thousand 
 miles. 
 
 Aurora Borealis were long considered by the ignorant and super- 
 stitious as portending war, pestilence, and famine. And this was 
 not only the opinion of the inhabitants of the northern islands, but 
 even the inhabitants of this country were alarmed at their appearance. 
 
 When the splendid Aurora Borealis of 1716 first made its appear- 
 ance, it was viewed with the greatest consternation by the vulgar ; 
 and considered by them as marking the introduction of a foreign race 
 of princes into this country.* Since that time, these meteors have 
 been so common that they have not excited any particular interest, 
 and are now viewed with the greatest indifference by all classes of 
 society. 
 
 Many conjectures have been made, at various periods, respecting 
 the cause of this phenomenon; but since the identity of lightning 
 
 * George the First came to the throne of Great Britain on the 1st of August, 
 1714. 
 
OF THE AURORA BOREALIS. 90 
 
 With the electric fluid has been ascertained, philosophers have been 
 naturally led to seek for the explication of aerial meteors in the prin- 
 ciples of electricity ; and there is now little doubt but most of them, 
 and especially Aurora Borealis, are electrical phenomena. Besides 
 the more obvious and known appearances which constitute a resem- 
 blance between this meteor and the electric matter by which lightning 
 is produced, it has been observed, that the Aurora Borealis produces 
 a very sensible fluctuation in the magnetic needle ; and that when it 
 has extended lower than usual into the atmosphere, the flashes have 
 been attended with various sounds of rumbling and hissing, especially 
 in Russia and the other northern parts of Europe. 
 
 Mr. Canton, soon after he had obtained electricity from the clouds, 
 offered a conjecture that the Aurora is occasioned by the flash- 
 ing of electric fire from positive towards negative clouds at a great 
 distance, through the upper part of the atmosphere, where the 
 resistance is least ; and this appears chiefly in the northern re- 
 gions, as the alteration in the heat of the air in those parts is the 
 greatest. 
 
 Signior Beccaria supposes that there is a constant and regular cir- 
 culation of the electric fluid from north to south ; and he thinks, that 
 the Aurora Borealis may be this electric matter, performing its 
 circulation in such a state of the atmosphere as renders it visible. 
 Dr. Franklin thinks, that the electric fire discharged into the polar 
 regions, from many miles of vapour raised from the ocean between 
 the tropics, accounts for the Aurora Borealis ; and that this pheno- 
 menon appears first, where it is first put in motion, namely, in the 
 northern regions, and the appearance proceeds southward, though the 
 fire really moves in the opposite direction. Several other eminent 
 philosophers have advanced conjectures respecting the cause of 
 this phenomenon, but our limits will not permit us to insert 
 them.* 
 
 There is another luminous appearance occasionally seen in the hea- 
 vens after sun-set, and before sun-rise, which somewhat resembles the 
 milky way, but of a fainter light. This phenomenon is called the 
 zodiacal light, because it is only to be seen in the zodiac. Its figure 
 resembles an inverted cone or pyramid, with its base toward the sun, 
 and its axis lying along the zodiac, somewhat inclined to the horizon. 
 It was first discovered by Cassini, in the year 1683; but there is 
 some reason to think it had been observed before that period. The length 
 of this phenomenon, taken from the sun upwards to its vertex, varies 
 from 45 degrees to 100, and even 120 degrees. The season most 
 favourable for observing it, is the beginning of March after sun-set* 
 But its aspect is very different in different years. One of the most 
 brilKant appearances of it was observed at Paris on the 16th of 
 February, 1769. 
 
 * Seamen who have often visited the north seas consider the appearance of 
 Aurora Borealis as indicative of a gale of wind. 
 
 K 2 
 
100 OF RAINBOWS, PARHELIA, &C. 
 
 Various opinions have been advanced respecting the cause of the 
 zodiacal light, as well as the Aurora Borealis ; but the greater num- 
 ber of philosophers agree in ascribing both phenomena to the same 
 cause, namely, the electric fluid. 
 
 But the celebrated M. de Mairan, who has written a treatise ex- 
 pressly on the Aurora Borealis, supposes that the zodiacal light 
 causes the Aurora Borealis ; and that this light is nothing more 
 than the sun's atmosphere, which is thrown off by means of the rota- 
 tion of that luminary on his axis to such a distance, as to strike on the 
 upper part of the earth's atmosphere, and produce the luminous ap- 
 pearance which we call the zodiacal light. And as this is chiefly 
 collected towards the polar regions, by means of the diurnal revolu- 
 tion of the earth, it will produce the Aurora Borealis. 
 
 OF RAINBOWS, PARHELIA,* &c. 
 
 Refracted from yon eastern cloud, 
 
 Bestriding earth, the grand etherial bow ; 
 
 Shoots up immense ; and every hue unfolds, 
 
 In fair proportions running from the red, 
 
 To where the violet fades into the sky. 
 
 Here, awful Newton, the dissolving clouds 
 
 Form, fronting on the sun thy showery prism ; 
 
 And lo the sage-instructed eye unfold 
 
 The various twine of light, by thee disclosed 
 
 From the white mingling maze. THOMSON. 
 
 Besides the Aurora Borealis, there are several other beautiful phe- 
 nomena occasionally seen in the heavens. Among these may be 
 ranked the Rainbow ; which is, unquestionably, the most beautiful 
 meteor with which we are acquainted. 
 
 It is never seen but in rainy weather, and in that point of the hea- 
 vens which is opposite to the sun, being occasioned by the refraction 
 and reflection of his rays falling on the drops of rain as they descend 
 to the earth. There are frequently two bows to be seen at the same 
 time an interior and an exterior one. The interior is the brightest, 
 being formed by the rays of the sun falling on the upper parts of the 
 drops of rain ; for a ray of light entering the upper part of a drop 
 of rain, will, by refraction, be thrown upon the inner part of the 
 spherical surface of that drop, whence it will be reflected to the lower 
 part of the drop, where, undergoing a second refraction, it will be 
 bent toward the eye of the spectator. Hence, the rays which fall 
 upon the interior bow come to the eye after two refractions and one 
 reflection; and the colours of this bow from the upper part, are red, 
 orange, yellow, green, blue, indigo, and violet. The exterior bow is 
 
 * Although we have given a short account and representation of the Rainbow 
 in the supplementary part of this work, we have deemed it necessary to give a 
 still more popular account of it here. 
 
OF RAINBOWS, PARHELIA, &e. ' 101 
 
 formed by the rays of the sun falling on the lower parts of the drops 
 of rain ; these rays also undergo two refractions ; one when they enter 
 the drops, and another when they emerge from them to proceed to 
 the eye : but they suffer two, or more, reflections in the interior sur- 
 face of the drops; hence, the colours of these rays are not so strong 
 and well defined as those in the interior bow, and appear in an inverted 
 order; viz. from the under part they are red, orange, yellow, green, 
 blue, indigo, and violet. 
 
 The rays which fall on the drops that produce the interior bow pro- 
 ceed to the eye of the spectator in a direction, that makes an angle of 
 about 42 degrees with the direction in which they entered the drops ; 
 and those that form the exterior bow at an angle of about 54 de- 
 grees.* 
 
 This may be proved by a simple experiment, as follows : let a glass 
 globe, filled with water, be suspended in the sun-shine, and let a per- 
 son turn his back to the sun, and view the globe at such a distance, 
 that the part of it which is farthest from the sun may appear of a full red 
 colour ; then will the rays which come from the globe to the eye 
 make an angle of 42 degrees with the sun's direct rays; and, if the eye 
 remain in the same position, while another person gradually lowers the 
 globe, the orange, yellow, and other colours, will appear in succession, 
 as in the interior rainbow. Again : if the glass globe be elevated, 
 till the side nearest the sun appear red, the rays which come from the 
 globe to the eye will make an angle of about 50 degrees; and if the 
 globe be again gradually raised as before, the rays will successively 
 change from red to orange, yellow; &c. as in the exterior bow. 
 
 Alt rainbows are arcs of equal circles , and, consequently, are all 
 equally large, though we do not always see an equal quantity of them: 
 for the eye of the spectator is the vertex of a cone, and its circular 
 base is the rainbow, of which one half is the greatest portion that can 
 be seen at once. 
 
 Although lunar rainbows have been observed, yet they occur but 
 very seldom. A very brilliant and remarkable one was seen in the 
 year 1710, at Glopwell Hall, in Derbyshire, about eight o'clock in the 
 evening. The moon had passed the full about twenty-four hours, and 
 the evening had been rainy; but the clouds were dispersed, and the 
 moon then shone very clear. 
 
 This iris /wwamhad all the colours of the solar iris exceedingly beauti" 
 ful and distinct, but faint in comparison with those that are seen when the 
 sun is shining very bright ; as must necessarily have been the case, 
 both from the different beams by which it was occasioned, and the 
 disposition of the medium. What most surprised the observer was, 
 the largeness of the arc, k which was not much less than that pro- 
 duced by the sun. 
 
 Several complete and concentric solar rainbows have sometimes 
 
 * The angle which the emerging ray makes with the incident ray in the Interior 
 bow is 42 2' for the red, and 40 17' for the violet ; and for the Exterior bow, 
 these angles are 50 57' and 54 7'. Therefore, the space between the bows is 
 about 9 degrees broad. 
 
102 OF RAINBOWS, PARHELIA, &C. 
 
 been observed in mountainous countries. This extraordinary pheno- 
 menon, first seen by Don TJlloa and his companions in fhe wild 
 heaths of Pambamarca, which he describes as follows.'" At the 
 side opposite to that where the sun rose on the mountain, at the dis- 
 tance of about sixty yards from the spot where we were standing, the 
 image of each of us was represented as if in a mirror ; three concen- 
 tric rainbows, the last or more exterior colour of one of them touched 
 the first or interior colours of the following one, being centred on the 
 head. On the outside of these, at an inconsiderable distance from 
 them, was seen a fourth arc, purely white. They were all perpendi- 
 cular to the horizon ; and as any one of us moved from one side to the 
 other, he was accompanied by the phenomenon, which preserved the 
 same order and disposition. But what seemed most remarkable was, 
 that, although six or seven persons were standing close together, each 
 of us saw the phenomenon as it regarded himself, but did not per- 
 ceive it in the others," 
 
 A similar phenomenon is described by Mr. Hagarth, F. R.S. as 
 having been seen by him on the evening of the 13th of February, 
 1780, when ascending a mountain at Rhealt, in Denbighshire. 
 
 Another singular phenomenon is sometimes to be seen in the hea- 
 vens, which very much resembles the sun ; and, on that account, it 
 has received the name of Parhelion, or mock sun. An extraordinary 
 appearance of this kind was seen near Marienberg, in Prussia, on the 
 5th of February, 1674. It was of the same apparent size with the 
 sun, which was several degrees above the horizon at the time, and 
 shone with great lustre. The mock sun appeared under the real one, 
 and seemed to increase in lustre as the true sun descended to the ho- 
 rizon, insomuch, that the reddish colour it first exhibited completely 
 vanished ; and it put on the genuine solar light, in proportion as the 
 disc of the real sun approached it. At last the real sun immerged 
 into the counterfeit sun, and remained alone. This phenomenon was 
 considered the more extraordinary, as it appeared perpendicularly 
 under the sun, instead of being to the right or left of it, as parhelia 
 usually are, and of a colour so different from that which mock suns 
 usually exhibit. 
 
 One or two appearances of the same kind have been seen in Eng- 
 land since that time. On the 28th of August, 1698, about eight 
 o'clock in the morning, there was seen at Sutfbury, in Suffolk, the 
 appearance of three suns at the same time, all extremely brilliant, 
 Beneath a dark watery cloud, in the east, the true sun shone with 
 such splendour that the spectators could not look at it ; and on each 
 side were the reflections. The circles were pot coloured like the 
 rainbow, but white. At the same time, the form of a half moon was 
 visible toward the south, at a considerable distance from the other 
 phenomena, but apparently double the size of the half moon, and of a 
 red colour like that of the rainbow. These phenomena faded away 
 gradually, but continued visible for more than two hours. Two mock 
 suns, an arc of a rainbow, and a halo, were seen at Lyndon, in the 
 county of Rutland, on the !>2d of October, 1721, at eleven in the 
 
OF THE ATMOSPHERE, AND ASTRONOMICAL REFRACTION. 163 
 
 morning. The parhelia or mock suns were bright and distinct.* 
 They were of a reddish colour towards the sun, but pale or whitish 
 toward the opposite sides, which was also the case with the halo. 
 Still higher in the heavens was an arc of a rainbow, of a curiously 
 inverted form, situated about half way between the halo and the 
 zenith. This arc was as distinct in its colours as the common rain- 
 bow, and of the same breadth. 
 
 The red colour was on the convex, and the blue on the concave of 
 the arc, which seemed to be about 90 degrees in length ; its centre 
 being very near the zenith. On the top of the halo was a kind of 
 inverted bright arc, of considerable extent. This phenemenon was 
 seen on the following day, and again on the 26th of the same month. 
 
 Several other phenomena are sometimes to be seen in the heavens, 
 but these are too ephemeral to merit any notice here. 
 
 OF THE ATMOSPHERE, AND ASTRONOMICAL 
 REFRACTION. 
 
 The earth is surrounded by a thin fluid mass of matter, called the 
 Air or Atmosphere, which revolves with it in its diurnal motion, and 
 goes round the sun with it every year. This fluid is both ponderous 
 and elastic. Its weight is known from the Torricilian experiment, or 
 that of the barometer ; and its elasticity is proved by simply inverting 
 a vessel full of^air in water. 
 
 The atmosphere of the earth's surface being pressed by the weight of 
 all above it, is there pressed the closest together ; and therefore the at- 
 mosphere is densist of all at the earth's surface ; and its density necessa- 
 rily diminishes the higher up. For each stratum of air is compressed only 
 by the weight of those above it; the upper strata are therefore less 
 compressed, and consequently less dense, than those below them. 
 
 The pressure or weight of the atmosphere has been repeatedly de- 
 termined, by various experiments, to be about fourteen pounds on 
 every square inch of the earth's surface. Hence, the total pressure 
 on the whole surface of the earth is 10,686,000,000 hundreds of mil- 
 lions of pounds avoirdupois. 
 
 From a number of experiments made on the density of the atmos- 
 phere, at various altitudes, by means of the barometer, it has been 
 ascertained, that if heights, from the earth's surface, be taken in 
 arithmetical progression, the density of the corresponding strata of 
 air decrease in geometrical progression. Thus the density of the 
 atmosphere is reduced one-half for every 3f miles of perpendicular 
 ascent. At seven miles in height, the corresponding density is only 
 one-fourth- at 10i miles, one-eighth; at 14 miles, one-sixteenth; 
 
 * A Halo is an extensive luminous ring, which is sometimes seen to surround 
 the sun and moon, and is supposed to be occasioned by the light of these bodies 
 through the intervening clouds. This appearance is most frequent about the 
 moon. 
 
104 OF THE ATMOSPHERE, AND ASTRONOMICAL REFRACTION. 
 
 and so on. Since the density of the air decreases at this rapid rate, 
 it is evident that at a very moderate distance from the surface of the 
 earth, its density would be so much diminished, as to render it inca- 
 pable of sustaining animal life. From observation and experiment, it 
 is pretty well known that 45 or 50 miles is the utmost height at which 
 the density is capable of refracting a ray of light ; and, therefore, this 
 may be considered the altitude corresponding to the least sensible de- 
 gree of density ; for, according to the law of its decrease, just stated, 
 the density at this altitude is above 10,000 times less than at the 
 earth's surface. , 
 
 One of the most extraordinary and useful properties of the atmos- 
 phere, is its reflective power, which causes the heavens to appear 
 luminous when the sun shines ; for were it not for this power, the 
 whole of the heavens, and every thing on the earth, would appear 
 black, or completely dark, except what the sun's rays directly im- 
 pinged upon. The stars would be visible by day as well as by night; 
 and we could see nothing except what was fully exposed to the sun. 
 There could be no twilight, and, consequently, the blackest darkness 
 would immediately succeed the brightest sun- shine when the sun sets ; 
 and the transition would be equally sudden frcm the blackest dark- 
 ness to the brightest sun-shine when the sun rose. But by means of 
 the atmosphere we enjoy the sun's light, reflected from the aerial par- 
 ticles for some time before he rises, and also for some time after he 
 sets. For when the earth, by its revolution on its axis, has turned 
 any particular place away from the sun, the atmosphere above that 
 place will continue to be illuminated for some time. However, as the 
 sun gets farther below the horizon, the less will the atmosphere be 
 illuminated; and when he has got eighteen degrees under the horizon, 
 cease to be illuminated, and then all that part of the heavens which is 
 over the place will become dark : for the place will then be turned 
 too far from the sun, and his rays will strike too high on the atmos- 
 phere to be refracted or bent downwards at that place. In conse- 
 quence of the refractive power of the atmosphere, all the heavenly 
 bodies appear higher than they really are ; for, on account of the va- 
 riation in the density of the air, a ray of light in passing through it will 
 be refracted at every instant, and consequently the path of the ray 
 will be a curve. And as an object is always seen in the direction in 
 which the rays of light proceeding from it enter the eye, it is evident 
 every celestial body will appear more elevated above the horizon 
 than it actually is, by a quantity equal to the refraction which a ray 
 of light suffers in passing from it through the atmosphere to the eye 
 of the observer. 
 
 When the object is in the zenith, the refraction is quite insensible ; 
 but it increases as the altitude of the object diminishes, till it reaches 
 the horizon, and then the refraction is greatest ; for the rays which 
 proceed from the object, in that situation, enter the atmosphere more 
 obliquely than in any other, and consequently are more turned out of 
 their course. This will be evident from an inspection of the following 
 figure. 
 
OF THE ATMOSPHERE, AND ASTRONOMICAL REFRACTION. 105 
 
 Where BOD represents the surface of the earth, O the place of 
 an observer, and FGH the surrounding atmosphere. A ray of 
 light proceeding from a body, Z, in the zenith, is not refracted ; but if 
 it proceed from a body at A, it will enter the eye at O, and appear 
 in the direction Oa; if the body be in the horizon, as at E, the rays 
 proceeding from it will enter the eye at O, and appear to come in the 
 direction eO. 
 
 On some occasions, the horizontal refraction amounts to 36 or 37 
 minutes, and, generally, to about 33 minutes, which is equal to the 
 diameter of the sun or moon ; and therefore the whole disc of the 
 sun or moon will appear above the horizon, both at rising and setting, 
 although actually below. This is the reason 'that the full moon has 
 sometimes been seen above the horizon before the sun was set. A 
 remarkable instance of this kind was observed at Paris, on the 19th 
 of July, 1750, when the moon appeared visibly eclipsed, while the 
 sun was distinctly to be seen above the horizon. 
 
 At some seasons of the year the sun appears ten minutes sooner 
 above the horizon in the morning, and continues as much longer above 
 
106 OF THE ATMOSPHERE, AND ASTRONOMICAL REFRACTION. 
 
 it in the evening, than he would do were there no refraction; and at a 
 mean rate, about seven minutes on any day of the year. The refraction 
 varies, however, very much with the state of the atmosphere. In 
 cold dry weather the air is more dense than in warm weather ; conse- 
 quently the refraction is greater in cold weather than in warm ; and 
 for the same reason, it is greater in cold countries than in hot ones. 
 
 A remarkable instance of this is mentioned by Dr. Smith in his 
 Optics, where he states, that some Hollanders who wintered in Nova 
 Zembla, in the year 1596, were surprised to find that, after three 
 months' constant darkness, the sun began to appear seventeen days 
 sooner than the time by computation deduced from the latitude, which 
 was 76 degrees. Now this phenomenon can only be accounted for 
 by the extraordinary refraction of the sun's rays in passing through 
 the cold dense air in that climate. 
 
 At the same altitudes, the sun, moon, and stars, all undergo the 
 same refraction ; for at equal altitudes, the rays which proceed from 
 any of these bodies suffer the same inclination. 
 
 The horizontal refraction being the gteatest, causes the sun and 
 moon, at rising and setting, to appear of an oval form ; for the lower 
 edge of each being seen through denser atmosphere than the upper 
 edge, is more refracted; consequently, the perpendicular diameter 
 must appear shortened, while the horizontal diameter (which is not 
 affected by refraction) remains the same, and in this way the oval ap- 
 pearance is produced. For the same reason, two fixed stars that are 
 nearer the horizon, and right above each other, appear nearer than 
 when they are high above the horizon ; and if they are both in the 
 horizon, but at some distance from each other, then they will appear 
 at a less distance than they really are ; for the refraction makes each 
 of them higher, and consequently must bring them into parts of their 
 respective vertical circles which are nearer to each other, because all 
 vertical circles converge and meet in the zenith. Hence, in all astro- 
 nomical calculations allowance must be made for refraction, before 
 the true altitude of any celestial body can be obtained. Tables, con- 
 taining this allowance for all altitudes, is to be found in every work 
 on practical astronomy. 
 
 The atmosphere not ortly occasions celestial bodies to appear higher 
 than they really are, by bending the rays of light as they pass through 
 it, but it also affects terrestrial bodies in the same way. The quan- 
 tity of this refraction is, however, found to vary considerably with the 
 different states of the atmosphere, and is therefore very uncertain. 
 But at a mean rate it may be taken at one-fourteenth part of the 
 distance expressed in degrees in a great circle : or, according to 
 Professor Playfair, it is about one-seventh part of the correction for 
 the earth's curvature, answering to the distance between the ob- 
 server and the object.* 
 
 * For example, suppose the distance between a person and any conspicuous 
 object to be 5 English miles, and he wishes to know how much it is elevated by 
 refraction. The coitectioa for the earth's curvature on this distance is 16* feet, 
 on-seventti part of which is 2 feet 4 inches, which it rawed by refraction. 
 
UNUSUAL REFRACTION OF THE ATMOSPHERE. 107 
 
 Many carious and even whimsical effects of terrestrial refraction 
 are mentioned by various authors ; but as our business is chiefly with 
 astronomical refraction, we shall only mention a few of these ef- 
 fects, which have been lately noticed by some of the most intelligent 
 philosophers of the present day. 
 
 UNUSUAL REFRACTION OF THE ATMOSPHERE. 
 
 Although the phenomena of unusual refraction have been often ob- 
 served by atrononlers and navigators, yet they do not seem to have 
 attracted particular notice till the year 1797. The unusual elevation 
 of coasts, mountains, and ships, have been long known under the 
 name of looming ; and the same phenomena, when accompanied with 
 inverted images, have been distinguished in France by the name of 
 mirage. 
 
 Mr. Huddart seems to have been the first person who described 
 an inverted image beneath the real objects; he accounts for this, and 
 other phenomena of elevation, by supposing that, in consequence of 
 the evaporation of the water, the refractive power of the air is not 
 greatest at the surface of the sea, but at some distance above it, in- 
 creasing gradually from the surface of the sea to a line, which he calls 
 the tine of maximum density, and thence diminishing gradually till it 
 becomes insensible. 
 
 He then shows, that, in passing through such a medium, the rays 
 of light would move in curve lines convex upwards, when they passed 
 above the line of maximum density, and convex downwards when 
 they passed below that line. 
 
 Hence, two pencils from the object will arrive at the eye, which 
 will produce an inverted image of the object. 
 
 In the year 1798, the Rev. Dr. Vince, of Cambridge, made a 
 series of interesting observations at Ramsgate, on the unusual refrac- 
 tion of the atmosphere. He made his observations with a terrestrial 
 telescope, magnifying between thirty and forty times, when the height 
 of the eye was about twenty-five feet above the surface of the sea. 
 Sometimes the height of the eye was eighty feet ; but this produced 
 no variation in the phenomena. 
 
 On the 1st of August, between four and eight o'clock, p. M. he 
 saw the topmast of a ship as at A, 
 
106 UNUSUAL REFRACTION OF THE ATMOSPHERE. 
 
 above the horizon xy of the sea : at the same time, he also discovered 
 in the field of view two complete images, B, C, of the ship in the air, 
 vertical to the ship itself, B being inverted, and C erect, having their 
 hulls joined. As the ship receded from the shore, less and less of 
 its mast became visible; and as it descended, the images B and 
 C ascended; but as the ship did not recede below the horizon, Dr. 
 Vince did not observe at what time, and in what order, the images 
 vanished. 
 
 He then directed his telescope to another ship A, 
 
 whose hull was just in the horizon x y, and he observed a complete 
 inverted image B, the mainmast of which just touched that of the 
 ship itself. In this case there was no second image as before. While 
 the ship A moved along, B followed its motion, without any change 
 of appearance. 
 
 Dr. Vince observed a number of other ships, which produced va- 
 riously formed images ; but our limits will not permit us to give a 
 particular description of them, nor of similar appearances which have 
 been observed on various occasions at land* 
 
 We shall, however, notice a few of the experiments made by Dr. 
 Wollaston, to illustrate his theory of the cause of unusual refraction. 
 
 According to this ingenious philoshpher, the varying density of the 
 atmosphere is the principal cause of the singular appearances which 
 we have just mentioned ; and from a number of interesting experi- 
 ments, he found, that the results were perfectly conformable to this 
 hypothesis. 
 
 He took a square phial, and poured a small quantity of clear syrup 
 into it, and above this an equal quantity of water, which gradually 
 incorporated with the syrup, between the pure water and the pure 
 syrup. The word syrup written on a card, and held behind the 
 bottle, appeared erect through the piire syrup ; but when seen through 
 the visible medium of the syrup and water, it appeared inverted with 
 an erect image above. 
 
 * This subject has been fully treated by Dr. Wollaston, in the Philosophical 
 Transactions for 1810. 
 
/ ":. OF THE CLOUDS. 109 
 
 Dr. Wollaston then put nearly the same quantity of rectified spirit 
 of wine above the water, and he observed a similar appearance ; only 
 in this case, the true place of the object was seen uppermost, and the 
 inverted and erect images below. 
 
 When the variations of density are great, the object may be held 
 close to the phial; but when they become more gradual, the object 
 is only elongated, and in order to be seen inverted, must be held one 
 or two inches behind the phial. 
 
 By examining an oblique line seen in this way, he found, that the 
 appearances continue many hours even with spirit of wine; with syrup, 
 two or three days ; with sulphuric acid, four or five ; and still longer 
 with a solution of gum-arabic. 
 
 Dr. Wollaston next heated a poker red hot, and looked along the 
 side of it at a paper ten or twelve feet distant. A perceptible refrac- 
 tion took place at the distance of three-eighths of an inch from it. A 
 letter, more than three-eighths of an inch distant, appeared erect as 
 usual ; at a less distance there was a faint reversed image of it ; and 
 still nearer the poker was a second image erect. 
 
 Although the experimental method of illustrating the phenomena of 
 unusual refraction, as given by Dr. Wollaston, is in every respect an 
 excellent one, yet the employment of different fluids does not repre- 
 sent the case which actually exists in nature. 
 
 The method employed by Dr. Brewster seems more agreeable to 
 nature. 
 
 His method consists in holding a keat ed iron above a mass of water, 
 bounded by parallel plates of glass. 
 
 As the heat descends through the fluid, a regular variation of den- 
 sity is produced, which gradually increases from the surface to the 
 bottom. 
 
 If the heated iron be withdrawn, and a cold body substituted in 
 its place, or even the air allowed to act alone, the superficial strata 
 of water will give out their heat so as to have an increase of density 
 from the surface to a certain depth below it. Through the medium 
 thus constituted, all the phenomena of unusual refraction may be seen 
 in the most beautiful manner ; the variation of density being produced 
 by heat alone. 
 
 OF THE CLOUDS. 
 
 Ye mists and exhalations that now rise 
 
 From hill or steaming lake, dusky or gray, 
 
 Till the sun paint your fleecy skirts with gold, 
 
 In honour to the world's Great Author rise, 
 
 Whether to deck with clouds th' uncoloured sky, 
 
 Or wash the thirsty earth with falling showers, 
 
 Rising or falling, still advance his praise. MILTON. 
 
 Clouds are generally supposed to consist of vapour which has been 
 raised from the sea and land by means of heat. These vapours 
 ascend till they reach air of the same specific gravity with themselves, 
 10 L 
 
HO OP THE CLOUDS. 
 
 when they combine with each other, become more dense and opaque, 
 and then become visible. 
 
 The thinner or rarer the clouds are, the higher do they ascend in 
 the air; however, it seldom happens thatjtheir height exceeds two 
 miles. The greater number of clouds are suspended at the height of 
 one mile ; and when they are highly electrified, their height is not 
 above eight or nine hundred yards. 
 
 While Don Ulloa was in South America, measuring a degree of 
 the meridian, he was for some time stationed on the summit of Cota- 
 paxi, a mountain about three miles above the level of the sea, where 
 he says the clouds could be seen at a great distance below, and that 
 he could hear the horrid noise of the thunder and tempests, and even 
 see the lightnings issue from the clouds far below him. 
 
 The wonderful variety observable in the colours of clouds is owing 
 to their particular position with respect to the sun, and the different 
 reflections of his light. The various figures which they so readily 
 assume, is supposed to proceed from their loose and voluble texture, 
 revolving in any form, according to the direction and force of the 
 wind, or to the quantity of electric matter which they contain. 
 
 Sometime we see a cloud that's dragonish ; 
 
 A vapour, sometime, like a bear or lion, 
 
 A towered citadel, a pendent rock, 
 
 A forked mountain, a blue promontory, 
 
 With trees upon't that nod unto the world, 
 
 And mock our eyes with air. 
 
 That which is now a horse, even with a thought, 
 
 The rock dislimns, and makes it indistinct 
 
 As water is in water. SHAKSPEARE. 
 
 About the tropics the clouds roll themselves into enormous masses, 
 as white as snow, turning their borders into the forms of hills, piling 
 themselves upon each other, and exhibiting the shapes of mountains, 
 caverns, and rocks. "There," says St. Pierre, "may be perceived 
 amid endless ridges, a multitude of valleys, whose openings are dis- 
 tinguished by purple and vermillion." These celestial valleys exhibit, 
 in their various colours, matchless tints of white, melting into shades 
 of different colours. Here and there may be observed torrents of 
 light issuing from the dark sides of the mountains, and pouring their 
 streams, like ingots of gold and silver, over rocks of coral. These 
 appearances are not more to be admired for their beauty than for their 
 endless combinations, for they vary every instant. What, a moment 
 before, was luminous, becomes coloured ; what was coloured, min- 
 gles into shade ; forming singular and most beautiful representations 
 of islands and hamlets, arched bridges stretched over wide rivers, 
 immense ruins, huge rocks, and gigantic mountains. 
 
 Among the Highlands of Scotland the clouds also display the finest 
 outlines, and assume the most beautiful figures ; more especially when 
 viewed from their rugged and lofty summits. These bold and mag- 
 nificent scenes are finely described by Dr. Beattie in the following 
 lines : 
 
OF THE CLOUDS. Ill 
 
 Oft when the wintry storm had ceased to rave. 
 He roamed the snowy waste at even, to view 
 
 The clouds stupendous, from the Atlantic wave 
 High lowering, sail along the horizon blue ; 
 
 Where, 'midst the changeful scenery, ever new, 
 Fancy a thousand wondrous forms descries, 
 
 More wildly great, than ever pencil drew; 
 
 Rocks, torrents, gulfs, and shapes of giant size, 
 And glitt'ring cliff's on cliffs and fiery ramparts rise. 
 
 Minstrel. 
 
 "Clouds," says Dr. Thompson, " are not formed in all parts of the 
 horizon at once ; the formation begins in one particular spot, while the 
 rest of the air remains clear as before ; and though the greatest quan- 
 tity of vapour exists in the lower strata of the atmosphere, clouds 
 never begin to form there, but always at some considerable height." 
 It is remarkable, says the same author, that the part of the atmos- 
 phere at which they form has not arrived at the point of extreme 
 moisture, nor near that point, even a moment before their formation. 
 
 They are not formed, then, because a greater quantity of vapour 
 has got into the air than could remain there without passing its maxi- 
 mum. It is still more remarkable, that when clouds are formed, the 
 temperature of the spot does not always suffer a diminution, although 
 this may sometimes be the case. On the contrary, the heat of the 
 clouds themselves is sometimes greater than that of the surrounding 
 air. Neither, then, is the formation of the clouds owing to the capa- 
 city of air for combining with moisture being lessened by cold. So 
 far from this being the case, we often see clouds, which had remained 
 in the atmosphere during the heat of the day, disappear in the night, 
 after the heat of the air was diminished. 
 
 The formation of clouds and rain, then, cannot be accounted for by 
 the principles with which we are acquainted. It is neither to the 
 saturation of the atmosphere, nor the diminution of heat, nor the mix- 
 ture of airs of different temperatures, as Dr. Hutton supposed; for 
 clouds are often formed without any wind at all either above or below 
 them : and even if this mixture constantly took place, the precipitation, 
 instead of accounting for rain, would be almost imperceptible. 
 
 It is a well-known fact, that evaporation goes on for a month or 
 two together in hot weather without any rain. This sometimes happens 
 in the temperate zone ; and every year in the torrid zone. At Cal- 
 cutta, during the month of January, in the year 1785, it never rained 
 at all : the mean of the thermometer for the whole month was 66f de- 
 grees : there were no high winds, and, during the greater part of the 
 month, scarcely any wind at all. 
 
 As the moisture which is thus raised by evaporation is not accu- 
 mulated in the atmosphere, above the place from which it was evapo- 
 rated, it must be disposed of in some othe* way ; but the manner in 
 which this is accomplished is not so well known. If it be carried on 
 daily through the different strata of the atmosphere, and wafted 
 to other regions by superior currents of air, it is impossible to account 
 for the different electrical states of the clouds, situated between dif- 
 ferent strata, which often produce the most violent thunder storms. 
 
 L 2 
 
112 OF THE CLOUDS THE CIRRUS. 
 
 For vapours are conductors of the electric fluid, and, of course, 
 would daily restore the equilibrium of the whole atmosphere through 
 which they passed. There would, therefore, be no positive and nega- 
 tive clouds, and consequently no thunder storms. Clouds could not 
 have remained in the lower strata of the atmosphere and been daily 
 carried off by winds to other countries ; for there are often no winds 
 at all, during several days, to perform this office ; nor would the dews 
 diminish as they are found to do when the dry weather continues for 
 a long time. 
 
 It is impossible for us to account for this remarkable fact upon any 
 principle with which we are acquainted. The water can neither 
 remain in the atmosphere, nor pass through it in the state of vapour. 
 It must, therefore, assume some other form ; but what that form is, or 
 how it assumes it, we do not know. 
 
 In order to render the study of meteorology more systematic, Mr. 
 Luke Haward has lately introduced a scientific nomenclator for dis- 
 tinguishing the various forms or modifications of clouds, which pro- 
 mises to be of great use in this important, but hitherto neglected, 
 branch of physical science. 
 
 The simple forms, or modifications, are three in number, and 
 named, Cirrus, Cumulus, and Stratus. These are defined by Mr. 
 Haward as follows : The Cirrus is composed of parallel, flexuous, 
 or diverging fibres, extensible in any or in all directions. 
 
 The Cumulus, convex or conical, heaps, increasing upwards from a 
 horizontal base. 
 
 The Stratus, is a widely extended, continuous, horizontal sheet, 
 increasing from below. 
 
 The intermediate modifications are four in number, each of which 
 is formed from various combinations of the simple modifications just 
 mentioned. They are the Cirro-cumulus, the Cirro-stratus, the Cu- 
 mulo-stratus, and the Cumulo-cirro-stratus, or Nimbus ; and are de- 
 fined as follows. 
 
 Cirro-cumulus. Small well-defined roundish masses, in close hori- 
 zontal arrangement. 
 
 Cirro-stratus. Horizontal or slightly-inclined masses, bent down- 
 ward, or undulated, separate, or in groups consisting of a number of 
 small clouds. 
 
 Cumulo-rstratus. The cirro-stratus blended with the cumulus, and 
 either appearing intermixed with the heaps of the latter, or super- 
 adding a wide-spread structure to its base. 
 
 Cumulo-cirro-stratus. The rain cloud. A cloud, or system of 
 clouds, from which rain is falling. It is a horizontal sheet, above 
 which the cirrus spreads, while the cumulus enters it laterally, and 
 from beneath. 
 
 OF THE CIRRUS. 
 
 Clouds in this modification appear to have the least density, the 
 greatest elevation, and the greatest variety of extent and direction. 
 They are the earliest appearance after serene weather. They are 
 first indicated by a few threads pencilled, as it were, on the sky. 
 
OF THE CLOUDS THE CIRRUS. 
 
 113 
 
 These increase in length, and new ones are in the mean time added 
 laterally. Often the first-formed threads serve as stems to support 
 numerous branches, which in their turn give rise to others. This 
 modification is represented by the following figure. 
 
 The increase is sometimes perfectly indeterminate, at others it has 
 a very decided direction. Thus the first few threads being once 
 formed, the remainder shall be propagated either in one, wo, or more 
 directions laterally, or obliquely upward or downward, the direction 
 being often the same in a great number of clouds visible at the same 
 time. 
 
 Their duration is uncertain, varying from a few minutes after the 
 first appearance to an extent of many hours. It is long when they 
 appear alone and at great heights, and shorter when they are formed 
 lower and in the vicinity of other clouds. 
 
 This modification, although in appearance almost motionless, is 
 intimately connected with the variable motions of the atmosphere. 
 Considering that clouds of this kind have long been deemed a prog- 
 nostic of wind, it is extraordinary that the nature of this connection 
 should not have been more studied, as the knowledge of it might 
 have been productive of useful results. 
 
 In fair weather, with light variable breezes, the sky is seldom 
 quite clear of small groups of the oblique cirrus, which frequently 
 come on from the leeward, and the direction of their increase is to 
 windward. Continued wet weather is attended with horizontal 
 sheets of this cloud, which subside quickly and pass to the cirro- 
 stratus. 
 
 Before storms they appear lower and denser, and usually in the 
 
114 
 
 OF THE CLOUDS THE CUMULUS. 
 
 quarter opposite to that from which the storm arises. Steady high 
 winds are also preceded and attended by streaks running quite across 
 the sky in the direction they blow in. 
 
 The relations of this modification with the state of the barometer, 
 thermometer, hygrometer, and electrometer, have not yet been at- 
 tended to. 
 
 OF THE CUMULUS. 
 
 Clouds iii this modification are commonly of the most dense 
 structure : they are formed in the lower atmosphere, and move along 
 with the current which is next the earth. 
 
 A small irregular spot first appears, and is, as it were, the nucleus 
 on which they increase. The lower surface continues irregularly 
 plane, while the upper rises into conical or hemispherical heaps; 
 which may afterwards continue long nearly of the same bulk, or ra- 
 pidly rise to mountains, as represented by the following figure. 
 
 In the former case they are usually numerous and near together, 
 in the latter few and distant; but whether there are few or many, 
 their bases always lie nearly in one horizontal plane, and their in- 
 crease upward is somewhat proportionate to the extent of base, and 
 nearly alike in many that appear at once. 
 
 Their appearance, increase, and disappearance, in fair weather, are 
 often periodical, and keep pace with the temperature of the day. 
 Thus they will begin to form some hours after sun-rise, arrive at 
 their maximum in the hottest part of the afternoon, then go on dimi' 
 nishing, and totally disperse about sun-set. 
 
 But in changable weather they paitake of the vicissitudes of the 
 atmosphere; sometimes evaporating almost as soon as formed, at 
 others suddenly forming and as quickly passing to the compound 
 modifications. 
 
 The cumulus of fair weather has a moderate elevation and extent, 
 and a well defined rounded surface. Previous to rain it increases 
 more rapidly, appears lower in the atmosphere, and with its surface 
 full of loose fleeces or protuberances. 
 
OF THE CLOUBS THT STRATUS. 
 
 Independently of the beauty and magnificence it adds to the face of 
 nature, the cumulus serves to screen the earth from the direct rays of 
 the sun, by its multiplied reflections to diffuse, and, as it were, eco- 
 nomise the light, and also to convey the product of evaporation to a 
 distance from the place of its origin. The relations of the cumulus 
 with the state of the barometer, &c. have not yet been sufficiently 
 attended to. 
 
 The formation of large cumuli to leeward in a strong wind, indicates 
 the approach of a calm with rain. When they do not disappear or 
 subside about sun-set, but continue to rise, thunder is to be expected 
 in the night. 
 
 - 
 
 OF THE STRATUS. 
 . 
 
 This modification has a mean degree of density. 
 It is the lowest of clouds, since its inferior surface commonly rests 
 on the earth or water, as represented by the following figure. 
 
 Contrary to the last, which may be considered as belonging to the 
 day, this is properly the cloud of night; the time of its first appear- 
 ance being about sun-set. It comprehends ail those creeping mists 
 which in calm evenings ascend in spreading sheets (like an inundation 
 of water) from the bottom of valleys and the surface of lakes, 
 rivers, &c. 
 
 Its duration is frequently through the night. 
 
 On the return of the sun the level surface of this cloud begins to 
 put on the appearance of cumulus, the whole at the same time sepa- 
 rating from the ground. The continuity is next destroyed, and the 
 cloud ascends and evaporates, or passes off with the appearance of 
 the nascent cumulus. 
 
 This has been long experienced as a prognostic of fair weather, 
 and indeed there is none more serene than that which is ushered in by 
 it. The relation of the stratus to the state of the atmosphere as indi- 
 cated by the barometer, &c. appears notwithstanding to have passed 
 hitherto without much attention. 
 
1,6 
 
 OF THE CLOUDS THE CIRRO-CUMULUS. 
 
 OF THE CIRRO-CUMULUS. 
 
 The cirrus having continued for some time increasing or stationary, 
 usually passes either to the cirro-cumulus or the cirro-stratus, at the 
 same time descending to a lower station in the atmosphere. 
 
 The cirro-cumulus is formed from a cirrus, or from a number of 
 small separate cirri, by the fibres collapsing as it were, and passing 
 into small roundish masses, in which the texture of the cirrus is no 
 longer discernible, although they still retain somewhat of the same 
 relative arrangement, as exhibited by the following figure. 
 
 This change takes place either throughout the whole mass at once, 
 or progressively from one extremity to the other. In either case, the 
 same effect is produced on a number or adjacent cirri at the same 
 time and in the same order. It appears in some instances to be ac- 
 celerated by the approach of other clouds. 
 
 This modification forms a very beautiful sky, sometimes exhibiting 
 numerous distinct beds of these small connected clouds, floating at 
 different altitudes. 
 
 The cirro-cumulus is frequent in summer, and is attendant on warm 
 and dry weather. It is also occasionally and more sparingly seen in 
 the intervals of showers, and in winter. The following passage is 
 beautifully descriptive of the appearance of this modification by 
 moonlight : 
 
 For yet above these wafted clouds are seen 
 
 (In a remoter sky, still more serene) 
 
 Others, detached in ranges through the air, 
 
 Spotless as snow, and countless as they're fair ; 
 
 Scattered immensely wide from east to west, 
 
 The beauteous semblance of a flock at rest. 
 
 These to the raptur'd mind aloud proclaim 
 
 Their mighty shepherd's everlasting name. RLOOMFIELIK 
 
 It may either evaporate or pass to the cirrus or cirro-stratus. 
 
THE CLOUDS THE CUMULO-STRATtfS. 
 
 117 
 
 OF THE CIRRO-STRATUS. 
 
 This cloud appears to result from the subsidence of the fibres of 
 the cirrus to a horizontal position, at the same time that they approach 
 towards each other laterally. The form and relative position, when 
 seen in the distance, frequently give the idea of shoals of fish. Yet 
 in this, as in other instances, the structure must be attended to rather 
 than the form, which varies much, presenting at other times the ap- 
 pearance of parallel bars, interwoven streaks like the grain'of polished 
 wood, &c. It is always thickest in the middle, or at one extremity, 
 and extenuated towards the edge, as represented by the following 
 figure. 
 
 The distinct appearance of a cirrus does not always precede the 
 production of this and the last modification. 
 
 The cirro-stratus precedes wind and rain, the near or distant approach 
 of which may sometimes be estimated from its greater or less abun- 
 dance and permanence. It is almost always to be seen in the inter- 
 vals of storms. Sometimes this and the cirro-cumulus appear together 
 in the sky, and even alternate with each other in the same cloud, 
 when the different evolutions which ensue are a curious spectacle, 
 and a judgment may be formed of the weather likely to ensue by ob- 
 serving which modification prevails at last. The cirro-stratus is the 
 modification which most frequently and completely exhibits the phe- 
 nomena of the solar and lunar halo, and (as supposed from a few 
 observations) the parhelion and paraselene also. Hence the reason 
 of the prognostic for foul weather, commonly drawn from the appear- 
 ance of the halo. 
 
 OF THE CUMULO-STRATUS. 
 
 The different modifications which have been just treated of some- 
 times gives place to each other, at other times two or more appear in 
 
118 
 
 OF THE CLOUDS THE CUMULO STRATUS. 
 
 the same sky; but in this case the clouds in the same modification lie 
 mostly m the same plane of elevation, those which are more elevated 
 appearing through the intervals of the lower, or the latter showing 
 dark against the lighter ones above them. When the cumulus in- 
 creases rapidly, a cirro-stratus is frequently seen to form around its 
 summit, reposing thereon as on a mountain, while the former cloud 
 continues discernible in some degree through it. This state conti- 
 nues but a short time. The cirro-stratus speedily becomes denser 
 and spreads, while the superior part of the cumulus extends itself and 
 passes into it, the base continuing as before, and the convex protube- 
 rances changing their position till they present themselves laterally 
 and downward. These are well represented by the following figure 
 
 More rarely the cumulus alone performs this evolution, and its 
 superior part constitutes the incumbent cirro-stratus 
 
 Cither case a large lofty dense cloud is formed, which may be 
 
 -ompared to a mushroom with a very thick short stem. But when a 
 
 whole sky is crowded with this modification, the appearances are 
 
 more mdistmct. The cumulus rises through the interstices of the 
 
 superior clouds, and the whole, seen as it passes off in the distant ho- 
 
 ori presents to the fancy mountains covered with snow, intersected 
 
 with darker ridges and lakes of water, rocks and towers, &c The 
 
 earanceof ^" S fl tratUS " ^ ^ ? inteFVaI bet ^^n the first ap- 
 
 .e of the fleecy cumulus and the commencement of rain, while 
 
 B lower atmosphere is yet too dry; also during the approach of 
 
 Sffi St0rmS : i he l ndistinCt a PP earance of it is chiefly in the longer 
 or shorter intervals of showers of rain, snow, or hail 
 
 The cumulo-stratus chiefly affects a mean state of the atmosphere 
 i to pressure and temperature ; but in this respect, like the other 
 modifications, it affords much room for future observation 
 
OF THE NIMBUS, OR CUMULO-CIRRO-STRATUS. 
 
 119 
 
 OF THE NIMBUS, OR CUMULO-CIRRO-STRATUS. 
 
 Clouds in any one of the preceding modifications, at the same 
 degree of elevation, or in two or more of them, at different elevations, 
 may increase so as completely to obscure the sky, and at times put on 
 an appearance of density which to the inexperienced observer indicates 
 the speedy commencement of rain. It is nevertheless extremely pro- 
 bable, as well from attentive observation as from a consideration of 
 the several modes of their production, that the clouds, while in any 
 one of these states, do not at any time let fall rain. 
 
 Before this effect takes place they have been uniformly found to un- 
 dergo a change, attended with appearances sufficiently remarkable to 
 constitute a distinct modification, which is represented by the follow- 
 ing figure, called the Nimbus, or Cumulo-cirro-stratus cloud. 
 
 In this figure a shower is represented as coming from behind an 
 elevated point of land. 
 
 The nimbus, although in itself one of the least beautiful clouds, is 
 yet now and then superbly decorated with its attendant the rainbow ; 
 which can only be seen in perfection when backed by the widely ex- 
 tended uniform gloom of this modification. 
 
 The relations of rain, and of periodical showers more especially, 
 with the varying temperature, density, and electricity of the atmos- 
 phere, will probably now obtain a fuller investigation, and with a 
 better prospect of success, than heretofore. 
 
120 MOTIONS OF THE EARTH 
 
 MOTIONS OF THE EARTH. 
 
 She from the West her silent course advances 
 With inoffensive pace, that spinning sleeps 
 On her soft axle ; while she paces even, 
 And bears us soft with the smooth air along. 
 
 MILTON. 
 
 "When we consider the apparent diurnal motion of all the celestial 
 bodies, we cannot but recognise the existence of one general cause, 
 which produces this appearance. But when we consider that these 
 bodies are not only at different distances from the earth, but at dif- 
 ferent distances from each other, and that these distances are not 
 always the same, we shall find it difficult to conceive that it is the 
 same cause that produces this appearance on all of them. 
 
 The difficulty, however, becomes considerably less when it is 
 recollected, that a person in motion, looking at an object at rest, per- 
 ceives the same change of position in the object as if he were himself 
 at rest, and the object in motion in the opposite direction. Every one 
 who has looked, for the first time, from the window of a carriage 
 moving quickly along the road ; or from the deck of a ship sailing 
 smoothly along the shore ; fancies that every thing which the carriage 
 or vessel passes is in motion, and that he is himself at rest. 
 
 An appearance still more deceiving takes place, when a person 
 looks out of the cabin window of a ship, in a dark night, at a distant 
 light apparently in motion. For the change of place in the light may 
 arise either from its being really in motion, or on board of another 
 vessel, while the vessel in which the spectator is placed is at anchor; 
 or the light may be stationary, and its apparent motion occasioned by 
 the motion of the ship which carries the spectator; or it may even be 
 occasioned by the motion of the vessel which carries the light being 
 quicker or slower than the one which carries the spectator. The 
 difficulty in determining to which of these causes the motion of the 
 light is to be attributed, arises from the want of some intervening 
 object whose state is known, and by which the apparent motion may 
 be compared. Now this is precisely the situation in which we stand 
 with regard to the heavenly bodies. For the motion of the earth on 
 its axis, if it really has such a motion, must be incomparably smoother 
 than any vessel or machine made by human art ; and as there is no 
 fixed intermediate object between it and the heavenly bodies, no 
 direct proof of this motion can be obtained. 
 
 As far, then, as appearances enable us to judge, either the earth 
 may be at rest, and the heavens carried round it every twenty-four 
 hours, or the heavens may be at rest, and the earth revolve round its 
 axis, in the same time. For the rising and setting of the sun and 
 stars, with all the other celestial phenomena, will be presented in the 
 same order whether the heavens revolve round the earth, or the earth 
 round its axis. 
 
 However, on comparing these appearances with others which are 
 more within our reach, and with the established laws of motion, we 
 
MOTIONS OF THE EARTH. 121 
 
 shall find it is much more probable they are occasioned by the revo-" 
 iution of the earth on its axis, than the revolution of the whole 
 heavens. For as the heavenly bodies present the same appearances 
 to us, whether the firmament carries them round the earth, or the 
 earth itself revolves in a contrary direction, it seems much more 
 natural to admit the latter hypothesis than the former, and to regard 
 the motion of the heavens as only apparent. 
 
 The semidiameter of the earth is only about 4000 miles, and conse- 
 quently its circumference is about 25,000 miles. 
 
 This is, therefore, the space every point of its equator must pass 
 through, if the earth revolves on its axis, which is little more than 
 1000 miles per hour, or about 17 miles per minute. This velocity is 
 certainly very considerable, being nearly equal to that of a cannon- 
 ball when it leaves the mouth of a cannon ; but it becomes totally 
 insignificant when compared with the motion of some of the heavenly 
 bodies, required on the other supposition. The distance of the sun 
 from the earth is about ninety-five millions of miles ; * and therefore 
 if he revolves round the earth in twenty -four hours, he must pass over 
 more than six times this space in the same time, and consequently 
 must move at the rate of about.25,000,000 miles per hour, which is 
 more than 20,000 times quicker than a cannon-ball. The planet 
 Uranus is about twenty times farther distant from the earth than the 
 sun, and consequently the velocity of its daily motion must be twenty 
 times greater, f But although these velocities are sufficient to startle 
 the imagination, they are really nothing when compared to the ra- 
 pidity with which the fixed stars must move to accomplish a revolution 
 round the earth in twenty-four hours. If the distance of the fixed 
 stars be assumed at 200,000 times the distance of the sun from the 
 earth,; they must move over the space of 1,400,000,000 miles per 
 second, in order to complete a rovolution round the earth in twenty- 
 four hours ! This is a degree of velocity of which we can have no 
 kind of conception ; and yet, if we consider the velocity which those 
 stars must have that are many thousands of times more distant from 
 the earth, it must be almost infinitely greater. If we, therefore, take 
 into consideration the number of bodies that must move, arid the pro- 
 digious rapidity of their motions, to produce the same appearances 
 which the revolution of one body, with a comparatively moderate 
 velocity, can produce, we shall scarcely hesitate a moment in con- 
 cluding that the motion of this one body is the true cause of these 
 appearances. 
 
 This conclusion must appear still more obvious when we attend to 
 the comparative bulk of these different bodies. Of the planets which 
 belong to the solar system, three of them are known to be much 
 greater than the earth ; Jupiter being nearly fifteen hundred times ; 
 Saturn nine hundred times; and Uranus eighty times. But the sun 
 exceeds them all in magnitude, being considerably more than a mil- 
 lion of times greater than the earth. Our ignorance of the real dis- 
 tances of the fixed stars prevents us fiorn ascertaining correctly their 
 
 * See page 26. f Page 40. J Page 83. 
 
 11 M 
 
MOTIONS OF THE EARTH. 
 
 real magnitudes; bat, from what we know of their distances, we are 
 entitled to conclude that they are at least equal in size to the largest 
 of the planets. If such, therefore, be the magnitude of these bodies, 
 how inconsistent would it be with every idea of order and arrange- 
 ment to suppose, that such a vast number of immense bodies daily 
 revolve round such a little and comparatively insignificant body as 
 the earth ! What extraordinary power would be necessary to retain 
 them in their orbits, and counterbalance the amazing centrifugal force 
 which they must possess ! The idea, too, of so many immense and 
 independent bodies, so vastly distant from the earth and from each 
 other, performing their revolutions round this little ball, exactly in the 
 same number of seconds, is scarcely to be entertained for a single 
 moment : all the phenomena, especially when supposed to arise from 
 these revolutions, can be satisfactorily and easily accounted for, by 
 supposing the earth to revolve oft its axis. 
 
 If we suppose the planets to be carried round the earth, from east 
 to west, every twenty-four hours, and also allow them a motion pecu- 
 liar to themselves from west to east (which they are observed to 
 have), we produce such a combination of opposite motions, as has 
 never yet been observed in any of the heavenly bodies, and which it 
 would be impossible to reconcile with any of the known principles of 
 mechanics. But the rotation of a body on its axis, combined with a 
 motion in its curvilineal orbit, is what we are quite familiar with, and 
 what is exhibited by a school-boy by spinning his top. 
 
 But one of the strongest proofs of the rotation of the earth is its 
 figure. For it is now well known tlmt the earth is not a perfect 
 sphere ; its polar diameter being considerably less than its equatorial.* 
 It is also known that this is the shape which a spherical body would 
 in time assume, if it revolved on a fixed axis ; and therefore it is rea- 
 sonable to conclude that the spheroidical figure of the earth is occa- 
 sioned by its rotatory motion. This conclusion is supported by the 
 extraordinary fact, that the difference between the polar and equato- 
 rial axis of the earth, as deduced from theory alone, is nearly the 
 same as from actual measurement of various arcs of meridian circles. 
 The same conclusion is farther supported by analogy. 
 
 A rotatory motion has been observed in several of the other pla- 
 nets, and from west to east, the direction in which the earth must revolve 
 in order to occasion the apparent diurnal motion of the heavens from 
 east to west. Jupiter, a much larger body than the earth, turns round 
 his axis in less than twelve hours. Now both the earth and Jupiter 
 are known to be flattened at the poles. All these facts, therefore, 
 lead us to conclude that the eartli has really a motion of rotation, and 
 that the diurnal motion of the heavens is only an illusion produced by 
 this rotation. 
 
 The diurnal rotation of the earth being assented to, its annual 
 motion will scarcely be denied ; for its similarity to the other planets 
 
 * Some of the objections which have been stated against the rotation of the 
 earith will be noticed in treating of the Ptolemaic and Tychonic systems. 
 
MOTIONS OF THE EARTH. 123 
 
 is considerably strengthened by this circumstance. For the planets 
 being found to revolve on their axis, and to be flattened at the poles 
 like the earth ; and being found to have periodical revolutions from 
 west to east, we are led to suppose, that the earth has a similar revo- 
 lution, in order to render the analogy between it and the rest of the 
 planets complete. But the appearances afford us as little assistance 
 in ascertaining the truth of this supposition, as in the case of the 
 diurnal motion ; for whether we suppose the earth to be at rest and 
 the sun to move round it in the ecliptic in the course of a year, or the 
 sun to be at rest and the earth to describe this path in the same time ; 
 the phenomena of the seasons, eclipses, and all other appearances 
 connected with the sun's annual motion, may be explained on either 
 hypothesis. But, although this be the case, it is much more pro- 
 bable that these appearances are produced by the annual motion of 
 the earth round the sun, than by the motion of the sun round the 
 earth. For by supposing the earth to move round the sun, we not 
 only give order and simplicity to the solar system, and preserve the 
 analogy, which is so conspicuous among the other bodies which com- 
 pose that system, but we remove several difficulties which unavoidably 
 attend the opposite hypothesis. It has already been remarked, that 
 the earth is considerably smaller than several of the other planets, 
 and that it is about fourteen hundred thousand times less than the 
 sun; it is therefore quite inconsistent with every idea of order 
 aud arrangement to suppose, that bodies of such extraordinary 
 size should revolve round one of comparatively small magni- 
 tude. For, independent of the complication of the planetary 
 motions which such a supposition would introduce, it would overthrow 
 one of the best established principles of mechanics and is quite inconsist- 
 ent with the law which is known to subsist between the times of the 
 revolutions of the planets, and their distance from the sun. For tjhe 
 farther they are from the sun, their motion is the slower. Their 
 periodic times of revolution being to each other as the cubes 
 of their mean distances from the sun. Now according to this remark- 
 able law, the length of a revolution of the earth round the sun, should 
 be exactly a sidereal year. This is therefore an incontestible proof 
 that the earth moves round the sun, like the other planets, and is sub- 
 ject to the same laws. To this we may add, that the aspects of 
 increase and decrease of the planets, the times of their seeming to 
 stand still, and move direct and retrograde, answer precisely with the 
 motion of the earth : but cannot be reconciled with that of the sun, 
 without introducing the most absurd and monstrous suppositions, 
 which would destroy all order, harmony, and simplicity, in the 
 system. 
 
 But the most direct proof of the earth's annual motion is derived 
 from the aberration of light. For during the time which light takes to 
 pass over the semidiameter of the earth's orbit, which is 8' 13", the 
 earth ought to move 20"-232 in its orbit, and this is found by 
 observations to be actually the case. 
 
 M 
 
124 MOTIONS OF THE EARTH. 
 
 The annual as well as the diurnal motion of the earth may there- 
 fore be considered as completely established. The objections which 
 have been urged against these motions, by the supporters of the Pto- 
 lemaic and Tychonic systems of the heavens, will be noticed when 
 treating of these systems. 
 
 To the texts of Scripture which seem to contradict the motion ot 
 the earth, the following reply may be made to them all. That it is 
 plain from many instances, that the Scriptures were never designed 
 to instruct men in philosophy, but in matters of religion, and are not 
 always to be taken in the literal sense. For Job describes the earth 
 as being supported upon pillars, and in another place as being hung upon 
 nothing ; and Moses calls the moon a great luminary, although it is 
 well known to be an opaque body, which shines only by reflecting 
 the light of the sun. 
 
 It is perfectly certain these expressions were not meant to convey 
 any astronomical opinion; but employed because they would be 
 easily understood by those to whom they were immediately addressed. 
 In familiar discourse, astronomers themselves speak of the sun's 
 place in the ecliptic, of his rising and setting, &c. ; for if they did 
 not, they would be under the necessity of explaining their meaning 
 every time they had occasion to mention those appearances to those 
 who knew nothing of astronomy. 
 
 The poet Thomson, though perfectly well convinced of the annual 
 motion of the earth, says 
 
 At last from Aries rolls the bounteous sun, 
 And the bright Bull receives him. 
 
 And Baker, in his elegant and truly philosophical poem, entitled the 
 " Universe," says 
 
 Along the skies the sun obliquely rolls, 
 
 Forsakes, by turns, and visits both the poles. 
 
 Diff 'rent his tract, but constant his career, 
 
 Divides the times, and measures out the year. 
 
 To climes returns where freezing winter reigns, 
 
 Unbinds the glebe, and fructifies the plains; 
 
 The crackling ice dissolves ; the rivers flow ; 
 
 Vines crown the mountain-tops, and corn the vales below. 
 
 BAKER. 
 
ON THE CHANGE OF SEASONS. 125 
 
 ON THE CHANGE OF SEASONS.* 
 
 At one wide view God's eye surveys 
 His works in every distant clime ; 
 He shifts the seasons, months, and days, 
 The short-lived offspring of revolving time ; 
 By turns they die, by turns are born. 
 Now cheerful Spring the circle leads, 
 And strews with flowers the smiling meads ; 
 Gay Summer next, whom russet robes adorn, 
 And waving fields of yellow corn ; 
 
 Then Autumn, who with lavish stores the lap of Nature spreads. 
 Decrepid Winter, laggard in the dance, 
 (Like feeble age opprest with pain) 
 A heavy season does maintain, 
 With driving snows, and winds, and rain, 
 Till Spring, recruited to advance, 
 
 The various years rolls round again. 
 
 HUGHES. 
 
 The earth's rotation makes the night and day ; 
 
 The sun revolving through th' ecliptic way, 
 
 Effects the various seasons of the year. BLACKMORI;. 
 
 The alternate succession of day and night, as well as the variety 
 of seasons, depend entirely on the motions of the earth. For if the 
 sun and the earth were perfectly at rest with respect to each other, it 
 is evident that one half of the earth would always be in the light, and 
 the other half in darkness, as the sun can only enlighten one half of 
 its surface at a time. But as the earth turns round its axis once in 
 twenty-four hours, any particular place on its surface will pass through 
 light and darkness alternately. As long as it continues in the en r 
 lightened hemisphere, it will be day at that place ; but while it passes 
 through the opposite hemisphere, it will be night. But although the 
 regular succession of day and night be occasioned by the diurnal 
 revolution of the earth on its axis, yet this motion is not of itself 
 sufficient to produce that variety in the lengths of days and nights, 
 which the various places of the earth experience in the course of a 
 year. 
 
 For should it revolve on its axis, with one of its poles always 
 pointed exactly to the sun, one half of the earth would be constantly 
 in the light and the other half in darkness, notwithstanding its rota- 
 tion. Again, if we suppose the earth to turn on its axis, with its 
 equator directly pointed to the sun, then the light would just reach 
 both poles, consequently all places would be in light and darkness 
 alternately, and the days and nights would be exactly twelve hours 
 each at every part of the globe. 
 
 If either extremities of the earth's axis, suppose the northern, were 
 to make an acute angle with an imaginary line joining the centre of 
 
 * If a terrestrial globe be placed in the various positions mentioned in this 
 article, it will contribute very much to impress the mind with the true sause of 
 the change of the seasons. 
 
126 
 
 ON THE CHANGE OF SEASONS. 
 
 the sun with any point of the earth's equator, it would follow that the 
 north pole, and a certain tract round it, would remain always in the 
 light, notwithstanding the revolution of the earth on its axis. Even 
 those places in the northern hemisphere to which the sun appeared to 
 rise and set, would have their days always longer than their nights; 
 at the equator the days and nights would be equal ; but in the 
 southern hemisphere the reverse would happen to what took place in 
 the northern. For those places to which the sun appeared to rise 
 and set would have their nights longer than their days ; and the south 
 pole would be constantly in darkness, with a tract around it equal to 
 what was constantly in the light round the north pole. It is evident, 
 also, that in this case the sun would be always on the north side of 
 the equator, and vertical to a certain circle parallel to it, which would 
 be as many degrees from the equator as the angle contained between 
 the earth's axis and the imaginary line wanted of a right angle. 
 
 This last supposition is in some degree similar to what actually 
 takes place in nature; for the axis of the earth makes an angle of 23^ 
 degrees, with a perpendicular to its orbit ; and as the axis always 
 remains parallel to itself, or points in the same direction, this angle 
 must be constantly changing as the earth moves forward in its 
 orbit.* 
 
 Some say he bid his angels turn askance 
 The poles of earth twice ten degrees and more 
 From the sun's axle ; they with labour push'd 
 Oblique the central globe. 
 
 MILTON. 
 
 This is well represented by the following figure, which shews the 
 earth in twelve different positions, or at twelve different times of the 
 year. 
 
 The line # b is the equator, n the north pole, and * the south. 
 The signs of ^, ~, &c. denote the points of the ecliptic in which the 
 earth is when it has the positions in the figure. 
 
 * Or, what amounts to the same thing, the axis of the earth makes au angle 
 with the plane of the ecliptic of 664 degrees. 
 
ON THE CHANGE OF SEASONS. 127 
 
 As the position of the poles of the earth, with respect to the sun, 
 depends entirely on this angle, their position must always be chang- 
 ing; and, of course, every point on the earth's surface must also 
 alter its position with respect to the sun. About the 20th of March, 
 when the sun, as seen from the earth, enters the sign Aries, the line 
 supposed to join the centres of the earth and sun is perpendicular to 
 the earth's axis ; consequently both poles are similarly situated with 
 respect to the sun, as he is then directly over the equator, and the 
 days and nights are equal at every place on the globe. This time of 
 the year is called the vernal equinox, because spring commences to 
 the inhabitants of the northern hemisphere, while autumn begins to 
 those of the southern. 
 
 After the 20th of March the sun appears to rise every day sensibly 
 more to the northward than he did the day before, to be more elevated 
 at mid-day, and to continue longer above the horizon, till the 21st of 
 June, which is the longest day at all places in the northern hemis- 
 phere. At this time the angle formed by the northern half of the 
 earth's axis and the line joining the centre of the earth and sun is 
 then at the least, which is 66f degrees. The sun will then appear 
 to touch the tropic of Cancer, and be vertical to all places 23 
 degrees north of the equator. This time of the year is called the 
 summer solstice, because it is the middle of summer, and the sun 
 seems to remain stationary for a few days. 
 
 After the 21st of June, the angle joining the centres of the earth 
 and sun gradually increases, and the sun appears to recede from the 
 tropic of Cancer, in the same manner as he advanced to it, rising 
 every day a little farther to the south than he did the day before, till 
 the 23 of September, when the axis has a similar position to what it 
 had on the 20th of March, being again at right angles to the line just 
 mentioned, consequently the days and nights are again equal all over 
 the globe, which constitutes the autumnal equinox. 
 
 The sun now appears to cross the equinoctial, and the south pole^ 
 which, during the last six months, was in the dark, begins to turn 
 towards the sun ; and precisely the same phenomena are exhibited to 
 the southern hemisphere as those already described in the case of the 
 northern half of the eartfi. On the 22d of December the sun appears 
 to touch the tropic of Capricorn, and is vertical to all those places on 
 the earth that are 23^ degrees south of the equator. The days are 
 then longest at all places in the southern hemisphere, but at the 
 shortest in the northern. This time of the year is termed the winter 
 solstice. 
 
 From the tropic of Capricorn the sun again appears to move for- 
 ward, and to arrive at the equinoctial again on the 20th of March. 
 
 Thus by a combination of the annual and diurnal motions of the 
 earth, with the parallelism of its axis, and the obliquity of its orbit to 
 the plane of its equator, the various seasons are produced, and the 
 same quantity of light and darkness, in the space of a year, are dis- 
 tributed to every region of the globe. 
 
 The manner in which the sun enlightens the earth, the parallelism 
 of its axis, and the increase and decrease of the days and nights, 
 
128 
 
 ON THE CHANGE OF SEASONS. 
 
 may be well illustrated by a small terrestrial globe, suspended by a 
 string fastened to its north pole, as represented by the following 
 figure. 
 
 A circle of wire a b, representing the plane of the earth's equator, 
 may be held parallel to a table, and equal in height with the flame 
 of a candle standing upon it. If the string be twisted a little towards 
 the left hand, and the globe suspended within the circle, with its 
 equator at the same height, the globe will begin to turn on its axis 
 from west to east, and day and night will be represented by the light 
 .and shade produced by the candle on its surface. But if the globe 
 be carried round the wire, to represent a year, the candle will illu- 
 minate both poles, and every spot on its surface will describe half 
 a circle in the enlightened part, and half in the dark part, and make 
 equality of day and night through the year. This is, however, not 
 the case in nature, as has already been fully explained. If then the 
 wire be inclined to the table at an angle of 23* degrees, as represented 
 by the circle abed, and the globe be carried gently round it, the 
 seasons, and increase of day and night, will appear as they are in 
 nature; i. e. when the globe is at , the candle enlightens it no far- 
 ther northward than the arctic circle no; all within which, in the 
 middle of our winter, is deprived of a sight of the sun ; while all 
 places within the antarctic, or opposite circle, have perpetual day : 
 at this time the candle shines vertically on the tropic of Capricorn. 
 As the earth moves towards 6 (the vernal equinox), if a small patch 
 be laid on latitade 51| north, it will shew how the days increase at 
 London, and how the nights decrease. When it has arrived at b, the 
 candle will then be perpendicularly over the equator, and, shining to 
 both poles, equality of day and night will take place: as it proceeds 
 towards c (the summer solstice), the days increase, and the candle 
 shines more and more over the north pole: when it has arrived at c, 
 
ON THE CHANGE OF SEASONS. 129 
 
 the whole arctic circle, and the countries it includes, will revolve in 
 continual sight of the sun ; and all within the antarctic circle will be 
 deprived of that sight. At this time the candle shines vertically on 
 the tropic of Cancer. Moving from midsummer towards d (the au- 
 tumnal equinox), the days will be found to decrease, and the nights 
 to increase in length, till they come again to equality at d, and thence 
 to the winter solstice, and so on. 
 
 The particular temperature which distinguishes each of the seasons, 
 at any paiticular place, is owing to a difference in the sun's altitude, 
 and the time of his continuance above the horizon of that place. In 
 winter, th^ rays of the sun fall so obliquely, and the sun is such a 
 short time above the horizon, that his influence in heating the earth is 
 but very little, compared with what it is in summer. For at this 
 season, the sun is so much higher than in winter, that his rays not 
 only fall more perpendicularly, but more of them fall on any given 
 space ; and as the day is also much longer than the night, the tem- 
 perature of the earth and the surrounding atmosphere must be much 
 greater than in winter. 
 
 Since the power of the sun is greater in heating the earth at any 
 particular place, when his rays fall most directly, and when the days 
 are longest at that place, it may be asked, how does it happen 
 that the heat is greatest about the end of July, when the sun is 
 highest and the day longest about the 21st of June? The reason of 
 this may easily be discovered by attending a little to the manner in 
 which bodies are heated. The heat which the earth receives is not 
 transient, but is retained by it for some time. For, like other solid 
 bodies, it receives heat and parts with it gradually. Now as the 
 earth continues to receive more heat in the day than it gives out in 
 the night, for a considerable time after the 21st of June, its tempe- 
 rature will continue to increase, till the days and nights begin to 
 approach to an equality. But this is not the case till the end of July, 
 at least; the earth goes on increasing in temperature, till about this 
 time, when it is found to be much greater than about the 21st of June, 
 although the sun be then higher at raid-day, and the day longer than 
 at any other time of the year in the northern hemisphere.* The heat 
 in July would be still greater were the sun at his mean distance from 
 the earth ; but this is not the case, for he is then at his greatest dis- 
 tance. However, the difference between his distance at this time 
 and the mean distance being only 6 ^th part of the whole, it could not 
 make a great alteration in the heating power of the rays. But if it 
 does operate in any degree in diminishing the heat in the northern 
 hemisphere in July, the same cause must operate in increasing the 
 heat, but in a double degree, in the southern hemisphere in January. 
 For the sun is ^th part nearer the earth than his mean distance ori 
 the 1st of January. Consequently the heat must be greater in the 
 southern hemisphere in January than in the northern in July, all 
 other circumstances being the same. The effects of the direct in- 
 
 * The same phenomena take place in the southern hemisphere in a reverse 
 order, or at six months' difference of time. 
 
130 ON THE PECULATION OF TIME, &c. 
 
 fluence of the sun are, however, greatly modified by the transportation 
 of the temperature of one region into another, in consequence of that 
 disturbance in the equilibrium of the atmosphere which the action of 
 the sun's rays necessarily produce. 
 
 Thus we see by what simple means the whole variety of the sea- 
 sons are produced; and also how admirably iitted the means are t 
 accomplish the end. 
 
 These, as they change, Almighty Father, these 
 Are but the varied God. The rolling year 
 Is full of Thee. Forth in the pleasing Spring 
 Thy beauty walks, Thy tenderness and love. 
 Wide flush the fields ; the softening air is balm ; 
 Echo the mountains round ; the forest smiles ; 
 And every sense, and every heart is joy. 
 Then comes Thy glory in the Summer months, 
 With light and heat refulgent. Then Thy sun 
 Shoots full perfection through the swelling year : 
 And oft Thy voice in dreadful thunder speaks j 
 And oft at dawn, deep noon, or falling eve, 
 By brooks, and groves, in hollow-whispering gales. 
 Thy bounty shines in Autumn unconfin'd, 
 And spreads a common feast for all that lives. 
 In Winter awful Thou ! with clouds and storms 
 Around Thee thrown, tempest o'er tempest roll'd, 
 Majestic darkness ! on the whirlwind's wing, 
 Riding sublime ! Thou bidst the world adore. 
 
 ON THE REGULATION OF TIME BY THE HEAVENLY 
 
 BODIES. 
 
 Time of itself is nothing, but from thought 
 Receives its rise ; by labouring fancy wrought 
 From things considered, while we think on some 
 As present, some as past, or yet to come. 
 No thought can think on time that's still confest, 
 But thinks on things in motion or at rest. 
 
 Though time, considered in an abstract and philosophical point of 
 view, was certainly coeval with the Deity, since nothing can possibly 
 exist but in some portion of it, yet the measuring; of time is a matter 
 of a very different nature; and though various nations have differed 
 on this subject, it is, nevertheless, a subject of the utmost importance 
 to every human being. For the opposite and contradictory me- 
 thods of calculating time have often been productive of very great 
 mischief in the world ; while chronologers, sometimes from igno- 
 rance, and as often from prejudice, have misrepresented events, 
 which, however trifling they might appear to them, may nevertheless 
 affect the happiness of future ages. During the general chaos, or 
 that period when the materials of which the beautiful fabric of the 
 universe was what Ovid calls rudis indigcstaqiie moles, a rude and 
 indigested heap, there were no human beings, and consequently no 
 occasion for any method of measuring or regulating time. But as 
 
ON THE REGULATION OF TIME, &C. 131 
 
 soon as the world was made a fit habitation for man, the measure- 
 ment of time became necessary on many accounts ; our pleasures as 
 well as our interests, require that this object should be accomplished; 
 but it is only an acquaintance with astronomy that can furnish the 
 means of doing it correctly. For time has always been measured 
 and defined by the motions of the heavenly bodies, and particularly 
 by the sun, as being the most regular and constant in his apparent 
 revolutions.* 
 
 The principal divisions of time are the year and the day, which are 
 measured by the annual and diurnal revolution of the sun. The day, 
 or the time in which the sun appears to go round the earth, has been 
 divided into twenty-four equal parts, which are called hours, and 
 these again subdivided into minutes, &c. This division is, however, 
 merely arbitrary ; there being no astronomical appearance to warrant 
 or regulate such a division of the day, more than a division into 
 twenty-two, forty-eight, or any other number of equal parts. 
 
 The length of the tropical year, or the time the sun is in going 
 from any point of the ecliptic to the same again, is 365 days, 5 hours, 
 48 minutes, 49 seconds. But the sidereal year, or the time which 
 intervenes between the conjunction of the sun and any fixed star and 
 his next conjunction with the same star, is 365 days, 6 hours, 9 
 minutes, 11^ seconds. The difference between these two periods, 
 which amounts to 20' 22^", is occasioned by the recession of the 
 equinoxes, or the falling back of the equinoctial points 50i seconds 
 of a degree every year. This retrograde motion of the equinoctial 
 points is caused by the joint attraction of the sun and moon upon the 
 earth, in consequence of its spheroidical figure. f 
 
 Time is distinguished according to the manner of measuring the 
 day, into apparent, mean, and sidereal. Apparent time, which is 
 also called true, solar, and astronomical time, is derived from 
 observations made on the sun. Mean, or mean solar time, some- 
 times called equated time, is a mean or average of apparent time, 
 which is not always equal ; for the intervals between two successive 
 transits of the sun over the meridian are not always the same. This 
 is owing to the eccentricity of the earth's orbit, and its obliquity to 
 the plane of the equinoctial. If the earth's orbit were an exact 
 circle, and coincident with the equinoctial, the sun would always 
 return to the meridian of any place at equal intervals of time, and 
 apparent and mean solar time would be the same. But as this is not 
 the case, mean time is deduced from apparent by adding or subtract- 
 ing the difference between them, which is usually called the equation 
 of time. 
 
 Mean solar days are all equal, being twenty-four hours each ; but 
 apparent solar days are sometimes more than twenty-four hours, and 
 
 * As it may contribute to perspicuity in treating of this important subject, we 
 shall consider the apparent motions of the sun as real. 
 
 t These variations are computed and inserted in a table, which is called a 
 Table of the Equation of Time. 
 
132 ON THE REGULATION OF TIME, &C. 
 
 sometimes less. A sidereal day is the interval between two succes- 
 sive transits of a star over the same meridian, and is always of the 
 same length ; for all the fixed stars make their revolutions in equal 
 times, owing to the uniformity of the earth's diurnal rotation about its 
 axis. The sidereal day is however shorter than the mean solar day 
 by 3' 5G*". This difference arises from the sun's apparent annual 
 motion from west to east, by which he leaves the star as it were be- 
 hind him. Thus if the sun and a star be observed on any day to pass 
 the meridian at the same instant, the next day, when the star passes 
 the meridian, the sun will have advanced nearly a degree to the east- 
 ward; and, as the earth's diurnal rotation on its axis is from west to 
 east, the star will come to the meridian before the sun, and in the 
 course of a year the star will have gained a whole day on the sun, 
 that is, it will have passed the meridian 366 times while the sun will 
 only have passed it 365 times. Now as the sun appears to perform 
 the whole of the ecliptic in 365 days, 5 hours, 48 minutes, 49 seconds, 
 he describes 59' 83", or nearly one degree of it per day, at a mean 
 rate ; and this space reduced to time is exactly 3' 56^', the excess 
 of a mean solar day above a sidereal day.* 
 
 The equation of time, or the difference between mean and apparent 
 time, as already mentioned, arises from two causes; namely, the ob- 
 liquity of the ecliptic to the plane of the equinoctial, and the eccentri- 
 city of the earth's orbit. There are, however, four days in the year 
 when the equation of time is nothing, or when the mean and apparent 
 time coincide; these days are, at present, the 15th of April, the 15th 
 of June, the 1st of September, and the 24th of December. From the 
 first of these days to the second, the apparent time is before the 
 mean ; from the second to the third, the mean time is before the appa- 
 rent; from the third to the fourth, the apparent is before the mean ; 
 and from the last of those days to the first, the mean is again before 
 the apparent, and so on alternately.! 
 
 If the revolution of the sun consisted of an entire number of days, 
 for instance 365, the year would naturally be made to do the same, 
 and there would be no difficulty in the formation of the calendar, or 
 in adjusting the reckoning in years and in days to one another. 
 
 All the years would thus contain precisely the same number of 
 days, and would also begin and end with the sun in the same point 
 of the ecliptic. But the sun's revolution includes a fraction of a day, 
 and therefore a year and a revolution of the sun cannot be precisely 
 completed at the same moment. However, as this fraction makes a 
 whole day in four revolutions, one day is added every four years, in 
 order to make this number of years equal to the same number of re- 
 volutions. The year to which this clay is added therefore contains 
 366 days. 
 
 This is the arrangement of what is called the Julian Calendar, and 
 
 * This excess is sometimes called the acceleration of the fixed stars, 
 t Clocks and watches ought to be regulated by mean time, as none of them can 
 shew apparent time, because they are all constructed on the principle of uniform 
 and equable motion. 
 
ON THE REGULATION OF TIME, &C. 133 
 
 the year thus computed, is termed the Julian year, from Julius Caesar, 
 by whom it was introduced at Rome.* But as the real length of the 
 year is 365 days, 5 hours, 49 minutes, nearly, the manner of rec- 
 koning adopted by Julius Caesar was not sufficiently exact to preserve 
 the seasons in the same time of the year ; for in four years the dif- 
 ference between the year thus regulated and the true solar year 
 amounted to about 44 minutes, and in 132 years to one entire day. 
 The Julian year must, therefore, have begun one day earlier than the 
 solar year at the end of this period. Consequently, the continuance 
 of this erroneous mode of reckoning would have made the seasons 
 change their places altogether in the course of twenty-four thousand 
 years. 
 
 At the time of the Council of Nice, in the year 325 of the Christian 
 era, the Julian calendar was introduced into the church ; and at that 
 time the vernal equinox fell on the 21st of March ; but on account 
 of the imperfection of the mode of reckoning just noticed, the reck- 
 oning fell constantly behind the true time : so that in the year 1582, 
 the Julian year had fallen nearly ten days behind the sun ; and the 
 equinox, instead of falling on the 21st of March, fell on the llth of 
 March. 
 
 The defects of the calendar were discovered long before the 
 year 1582 ; but all attempts made to reform it proved in vain. At 
 last, Pope Gregory, who was desirous of rendering his pontificate 
 illustrious by bringing about a reformation, which his predecessors 
 had failed to accomplish, invited all the astronomers in Christendom 
 to give their opinions on this important affair. This invitation had 
 the effect of bringing forth many ingenious plans, but the one which 
 he ordered to be adopted was afforded by an astronomer of Verona, 
 named Lilius. 
 
 The first step was to allow for the loss of the ten days; which was 
 done by counting the 5th of October, 1582, the 15th of that month. 
 By this means, the vernal equinox was again brought to the 2lst of 
 March, as it was at the time of the Council of Nice. And to pre- 
 vent the like inconvenience in future, it was decreed that the last year 
 of every century, not divisible by four, should be accounted a com- 
 mon year, which, according to the Julian reckoning, should be leap 
 year ; but that those hundreds which were divisible by four, such as 
 1600, 2000, 2400, &c. should still be accounted leap year. Although 
 this correction be sufficiently exact to keep the seasons to the same 
 time of the year, yet it does hot altogether correspond with the real 
 length of the year, for the time that the Julian year exceeds the 
 true, will amount to 3 days in 390 years. If, therefore, at the end 
 of 390 years, three days were expunged, the equinox would very 
 nearly keep to the same day of the month ; but by suppressing 3 days 
 
 * The intercalary day, or the day which was added every fourth year, was 
 accounted the 24th of February, and. called by the Romans the 6th of the Ka- 
 lends of March; on this account there were every fourth year two 6ths of the 
 Kalends of March, and therefore they called this year Bissextile. With us it ii 
 "called Leap Year. 
 
 12 N 
 
134 OF THE TIDES. 
 
 only in 400 years, as in the Gregorian account, a small deviation will 
 take place in the course of twelve or sixteen centuries, but so trifling 
 as scarcely to deserve notice. 
 
 As this reformation of the calendar was brought about under the 
 auspices of Pope Gregory, it is called the Gregorian Calendar, and 
 sometimes the New Style, to distinguish it from the Julian account. 
 This new calendar was immediately adopted in all Catholic coun- 
 tries; but it was not adopted in this country till the year 1752. In 
 Russia, Prussia, and some other countries, the Julian account is 
 still used. 
 
 OF THE TIDES. 
 
 The ebbs of tides, and their mysterious flow, 
 He, as art's elements, shall understand. 
 
 DRYDEN. 
 
 The Tides have been always found to follow, periodically, the 
 course of the sun and moon ; and hence it has been suspected, in 
 all ages, that the tides were, some way or other, produced by these 
 bodies. 
 
 The celebrated Kepler was the first person who formed any con- 
 jectures respecting their true cause. But what Kepler only hinted, 
 has been completely developed and demonstrated by Sir Isaac 
 Newton. 
 
 After his great discovery of the law of gravitation, he found it an 
 easy matter to account for the whole phenomena of the tides : for, 
 according to this law of nature, all the particles of matter which com- 
 pose the universe, however remote from one another, have a continual 
 tendency to approach each other, with a force directly proportional 
 to the quantity of matter they contain, and inversely proportional to 
 the square of their distance asunder. It is therefore evident, from 
 this, that the earth will be attracted both by the sun and moon. But 
 although the attraction of the sun greatly exceeds that of the moon, 
 yet the sun being nearly four hundred times more distant from the 
 earth than the moon, the difference of his attraction upon different 
 .parts of the earth is not nearly so great as that of the moon ; and 
 therefore the moon is the principal cause of the tides. 
 
 Attractive pow'r ! whose mighty sway 
 The Ocean's swelling waves obey, 
 And, mounting upward, seem to raise 
 A liquid altar to thy praise. 
 
 If all parts of the earth were equally attracted by the moon, it 
 would always retain its spherical form, and there would be no tides 
 at all. But the action of the moon being unequal on different parts 
 of the earth, those parts being most attracted that are nearest the 
 moon, and those at the greatest distance least, the spherical figure 
 must suffer some change from the moon's action. Now as the 
 waters of the ocean directly under the moon are nearer to her than 
 the central parts of the earth, they will be more attracted by her 
 
OF THE TIDES. 
 
 135 
 
 than the central parts. For the same reason, the central parts will 
 be more attracted than the waters on the opposite side of the earth, 
 and therefore the distance between the earth's centre and the waters 
 on its surface, both under the moon and on the opposite side, will be 
 increased ; or the waters will rise higher, and it will then be flood, or 
 high water, at those places. But this is not the only cause that pro- 
 duces the rise of the waters at these two points ; for those parts of 
 the ocean which are 90 from them will be attracted with nearly 
 the same force as the centres of the earth, the effect of which will be 
 a small increase of their gravity towards the centre of the earth. 
 Hence, the waters at those places will press towards the zenith and 
 nadir, or the points where the gravity of the waters is diminished, to 
 restore the equilibrium, and thus occasion a greater rise at those 
 points. But in order to know the real effect of the moon on the 
 ocean, the motion of the earth on its axis must be taken into account. 
 For if it were not for this motion, the longest diameter of the watery 
 spheroid would point directly to the moon's centre ; but by reason of 
 the motion of the whole mass of the earth on its axis, from west to 
 east, the most elevated parts of the water no longer answer precisely 
 to the moon, but are carried considerably to the eastward in the di- 
 rection of the rotation. The waters also continue to rise after they have 
 passed directly under the moon, though the immediate action of the moon 
 begins there to decrease ; and they do not reach their greatest height 
 till they have got about 45 farther. After they have passed the 
 point which is 90 distant from the point below the moon, they con- 
 tinue to descend, although the force which the moon adds to their 
 gravity begins there to decrease. For still the action of the moon 
 adds to their gravity, and makes them descend till they have got 
 about 45 farther; the greatest elevations, therefore, do not take 
 take place at the points which are in a line with the centres of the 
 earth and moon, but about half a quadrant to the east of these points, 
 in the direction of the motion of rotation. 
 
 Thus it appears, if the earth were entirely covered by the ocean, 
 as represented by the the circle b dec in the following figure, 
 
 N 2 
 
138 
 
 OP THE TIDES. 
 
 that the spheroidical form which it would assume, would be s& 
 situated, that its longest diameter would point to the east of the moon, 
 or the moon would always be to the west of the meridian of the parts 
 of greatest elevation. And as the moon apparently shifts her posi- 
 tion from east to west in going round the earth every day, the longer 
 diameter of the spheroid following her motions will occasion two 
 floods and two ebbs in the space of a lunar day, or 24 hours 48 min^ 
 
 The moon turns Ocean in his bed 
 
 From side to side, in constant ebb and flow,j 
 
 And purifies from stench his wat'ry realms. YOUNG. 
 
 These are the effects produced by the action of the moon only ; 
 but the sun has also a considerable effect on the waters of the ocean, 
 although it must be much less on account of his immense distance. 
 For, as already observed, it is not the action of these bodies on the 
 arth, but the inequalities of their actions which produce these 
 effects. The sun's action on the whole mass of the earth is much 
 greater than of the moon's ; but his distance is so great, that the dia- 
 meter of the earth is a mere point compared with it ; and, therefore, 
 the difference between his effects on the nearest and farthest side of 
 the earth, becomes on this account vastly less than it would be if the 
 sun were as near as the moon.* However, the immense bulk of the 
 sun makes the effect still sensible^ even at so vast a distance ; and 
 although the action of the moon has the greatest share in producing 
 the tides, yet the action of the SUB adds sensibly to this effect, when 
 his action is exerted in the same direction, as at the time of new and 
 full moon, when these two bodies are nearly in the same straight line 
 with the centre of the earth. When this is the case, the effects of 
 these two bodies are united, so that the tides rise higher than at any 
 other time, and are called spring tides; as represented by the follow- 
 ing figure, where S denotes the sun, dnez the moon, and c the 
 earth. 
 
 * The mean distance of the moon from the earth is 240,000 miles 
 
OF THE TIDES. 
 
 The action of the sun diminishes that of the moon in the quarters, 
 because his action is opposed to that of the moon ; consequently, the 
 effect must be to depress the waters where the moon's action has a 
 tendency to raise them. These tides are considerably lower than at 
 any other time, and are called neap tides. 
 
 The spring tides do not take place on the very day of the new and 
 full moon, nor the neap tides on the very day of the quadratures, but 
 a day or two after; because in this case, as in some others, the 
 effect is neither the greatest nor least when the immediate influence of 
 the cause is greatest or least : as the greatest heat, for example, ia 
 not on the solstitial day, when the immediate action of the sun is 
 greatest, but some time after it. And although the action of the sun 
 and moon were to cease, yet the ocean would continue to ebb and 
 flow for some time, as its waves continue in violent motion for some 
 time after a storm. 
 
 The high water at a given place does not always answer to the 
 same situation of the moon, but happens sometimes sooner and some- 
 times later than if the moon alone acted on the ocean. This proceeds 
 from the action of the sun not conspiring with that of the moon. The 
 different distances of the moon from the earth also occasions a sensi- 
 ble variation in the tides. 
 
 When the moon approaches the earth, her action in every part 
 increases, and the differences in that action, upon which the tides 
 depend, likewise increase. For the attraction of any body is in the 
 inverse ratio of the square of its distance; the nearer, therefore, the 
 moon is to the earth the greater is her attraction, and the more re- 
 mote, the less. Hence, her action on the nearest parts increases 
 more quickly than it does on the more remote parts, and therefore the 
 tides increase in a higher proportion as the distance of the moon 
 diminishes. 
 
 Sir Isaac Newton has shown that the tides increase as the cube of 
 the distances decrease, so that the moon, at/ta/f her present distance, 
 would produce a tide eight times greater. Now the moon describes 
 an ellipse about the earth, and, of course, must be once in every 
 revolution nearer the earth than in any other part of her orbit ; con- 
 sequently, she must produce a much higher tide when in this point of 
 her orbit than in the opposite point. 
 
 This is the reason that two great spring tides never take place 
 immediately after each other; for if the moon be at her least distance 
 at the time of new moon, she must be at her greatest distance at the 
 time of full moon, having performed half a revolution in the intervening 
 time, and therefore the spring tide at the full will be much less than 
 that at the preceding change. For the same reason, if a great spring 
 tide happens at the time of full moon, the tide at the following change 
 will be less. 
 
 The spring tides are highest and the neap tides lowest about the 
 beginning of the year; for the earth being nearest the sun about the 
 1st of January, must be more strongly attracted by that body than 
 at any other time of the year : hence, the spring tides which happen 
 about that time will be greater than at any other time. And should 
 
138 OF THE TIDES. 
 
 the moon be new or full in that part of her orbit which is nearest to 
 the earth, at the same time the tides will b.e considerably higher than 
 at any other time of the year. 
 
 The tide which happens at any time, while the moon is above the 
 horizon, is called the superior tide, and the other the inferior tide. 
 "When the moon is in the equinoctial, other things remaining the 
 same, the superior and inferior tides are of the same height ; but when 
 the moon declines towards the elevated pole, the superior tide is 
 higher than the inferior. If the latitude of the place and the decli- 
 nation of the moon are of contrary names, the inferior tide will be the 
 highest. But the highest tide at any particular place, is when the 
 moon's declination is equal to the latitude of the place, and of the 
 same name ; and the height of the tide diminishes, as the difference 
 between the latitude and declination increases ; therefore, the nearer 
 any place is to that parallel whose latitude is equal to the moon's decli- 
 nation and of the same name, the higher will the tide be at that place.* 
 
 Such would the tides regularly be if the earth were all covered 
 over with the ocean to a great depth ; but as this is not the case, it 
 is only at places situated on the shores of large oceans where such 
 tides, as above described, take place. 
 
 The tides are also subject to very great irregularities from local cir- 
 cumstances; such as meeting with islands, shoals, headlands, passing 
 through straits, &c. In order that they may have their full motion, 
 the ocean in which they are produced ought to extend 90 from east 
 to west, because that is the distance between the greatest elevation 
 and the greatest depression produced in the waters by the moon. 
 Hence it is, that the tides in the Pacific Ocean exceed those of the 
 Atlantic, and that they are less in that part of the Atlantic which is 
 within the torrid zone, between Africa and America, than in the tem- 
 perate zones, on either side of it where the ocean is much broader. 
 
 In the Baltic, the Mediterranean, and the Black seas, there are no 
 sensible tides ; for they communicate with the ocean by so narrow 
 inlets, and are of so great extent, that they cannot speedily receive 
 and let out water enough to raise or depress their surfaces in any 
 sensible degree. 
 
 The power of the moon to raise the waters, Sir I. Newton has 
 shown to be about 4| times that of the sun, and that the moon raises 
 the waters 8 feet 7 inches, while the sun and moon together raise them 
 10^ feet, when at their mean distances from the earth, and about 12 
 feet when the moon is at her least distance. These heights are found 
 to agree very well with observations onthe coasts of open and deep 
 oceans, but not well on the coasts of small seas, and where the water 
 is shallow. 
 
 The mean retardation of the tides, or of the moon's coming to the 
 meridian in 24 hours is 48' 45"*7, and the mean interval between two 
 successive tides is 12 h , 25', 14"'2 ; hence, the mean daily retardation 
 of high water is 50' 28"-4 
 
 * In comparing the height of the tides at different places, it is supposed that 
 the sun and moon are at the same distances from the earth, and in the same posi- 
 tion with respect to the meridian of these places. 
 
OF THE FORCES WHICH RETAIN THE PLANETS, &C. 139 
 
 About the time of new and full moon the interval is least, being 
 only 12 h , 19', 28" ; and at the quadratures the interval is the greatest, 
 being 12 h , 30', 7". 
 
 The common method of calculating the time of high water at any 
 place, is to multiply 50' 28", or the mean daily retardation of the tides 
 by the moon's age, and then to divide the product by 60, which gives 
 the mean time of the moon coming to the meridian on that day, in 
 hours ; to this is added the time of high water on the days of full and 
 change at the given place, and the sum is the time of high water at 
 that place on the afternoon of the given day, if the sum be less than 
 12 hours; but if greater, 12 hours 25 minutes must be subtracted, in 
 order to have the time on the afternoon of the given day ; and 25 
 minutes subtracted from this time will give the time of high water on 
 the morning 6f the given day.* 
 
 The following figure exhibits the progress of the tides from the 
 Atlantic through the channels surrounding the British islands ; the 
 lunar tides happening in any part of the shaded lines nearly at the 
 hour after the moon's southing, which is indicated by the figure an- 
 nexed to it. 
 
 * This method is far from being exact ; but affords an approximation, which 
 may be useful on some occasions. When accuracy is wanted recourse must be had 
 to other methods; some of which will be given in the Supplement to this work. 
 
140 OF THE FORCES WHICH RETAIN THE PLANETS, &C. 
 
 OF THE FORCES WHICH RETAIN THE PLANETS IN 
 THEIR ORBITS. 
 
 Thine these noble works 
 Great universal Ruler! 
 Thy virtual energy the frame of things 
 Pervading actuates ; as at first thy hand 
 Diffused, through endless space this limpid sky, 
 Vast ocean without storm, where these huge globes 
 Sail undisturbed, a rounding voyage each ; 
 Observant all of one unchanging law. 
 Simplicity divine ! by this sole rule, 
 The Maker's great establishment, these worlds 
 Revolve harmonious, world attracting world 
 With mutual love, and to their central sun 
 All gravitating. MALLET. 
 
 Before the time of Kepler, who flourished about the end of the l(5th 
 century, the planets were supposed to move in circular orbits ; but 
 since his great discovery of the laws which regulate the motions of 
 these bodies, astronomers have been enabled to determine their 
 periods, and the figure of their orbits, with the greatest exactness. 
 
 The laws of Kepler are, 
 
 1. That all the planets move round the sun, in such a manner, 
 that the Radius Vector, or a line joining the sun and planet, passes 
 over equal areas or spaces of the orbit in equal portions of time. 
 
 2. That each of the primary planets describes an ellipse, having 
 the sun in one of its foci.* 
 
 3. That the squares of the periodic times of the planets are to each 
 other as the cubes of their mean distances from the sun. 
 
 These three laws are the basis of all physical astronomy. But in 
 a popular work like the present, it would be improper to enter upon 
 any demonstrations of them. However, as it may, perhaps, gratify 
 the reader to see an illustration of the third law, we shall give an 
 example, by comparing the distance and periodic time of Mercury 
 with those of the earth. 
 
 Suppose the distance of Mercury were given, and it was required 
 to find the time it required to perform a revolution round the sun, 
 having the distance of the earth from the sun and the length of the 
 year given. By the third law of Kepler it would be determined 
 thus : As the cube of the earth's distance (95 3 millions of miles) is to 
 -the cube of Mercury's distance (36| 3 millions), so is the square of 
 ihe earth's periodic time (365^ 2 days) to the square of Mercury's 
 year (88 2 days nearly). 
 
 The distance may also be found by the same law, if the periodic 
 time be known. Let it be required to find the distance of Mercury, 
 having its periodic time given, then it would be determined thus : as 
 4he square of 365* days is to the square of 88 days, so is the 
 -cube of 95 millions of miles to the cube of 36| millions of miles, 
 
 * See fig. page 10. 
 
OF THE FORCES WHICH RETAIN THE PLANETS, &C. 141 
 
 the distance of Mercury from the sun. In the same way, the 
 distance of any other planet may be determined, if its period be known, 
 or its period if its distance be known.* 
 
 After the laws of gravitation were known, it was demonstrated by 
 Sir Isaac Newton, a priori, that the laws of Kepler must be those 
 that regulate the system of the world. 
 
 This extraordinary man found that the laws of motion, and even 
 the general properties of matter, are the same in the heavens as on 
 the earth. That the elliptical figure of the orbits described both by 
 the primary and secondary planets ; the small deviations in the form 
 and position of their orbits, as well as in the place of the planets; 
 the facts which concern the shape, rotation, and position of their 
 axis ; and the oscillation of the waters which surround the earth, 
 are all explained by one principle ; namely, that of the mutual gravi- 
 tation of all bodies with forces directly as their quantities of matter, 
 and inversely as the squares of their distances. 
 
 But as we cannot follow this celebrated philosopher in all his de- 
 monstrations on this important subject, in a work of this kind, we 
 shall endeavour to give as clear and comprehensive a view of the 
 doctrine of gravitation, as our limits will permit, at the same time 
 avoiding every thing abstruse. 
 
 Thus, if one body contain double the quantity of matter that another 
 contains, its attractive power will also be double ; if it contain ten, 
 times the quantity of matter, its attractive power will be ten times 
 greater, and so on. 
 
 But if a body be placed at any distance from another body, and 
 then removed to double the distance, it will attract it only with a 
 fourth part of the force it did before; at three times the distance, 
 with a ninth part of the force ; and at four times the distance only 
 with a sixteenth part, and so on. 
 
 These are termed the laws of gravitation ; and are known to affect 
 every species of matter, and to connect the most distant bodies in the 
 universe. But what the power or principle is which causes bodies to 
 affect each other according to these laws, we shall not attempt to 
 enquire. Because any enquiry of this kind is not likely to be at^ 
 tended with much success; nor is it necessary to know the cause 
 which produces these effects : for all that the astronomer is concerned 
 to know is, whether such a power or force is exerted by one body ore 
 another, and if it is, what are the laws of its action. Now both of 
 these important facts have been determined with the greatest preci- 
 sion, not only by calculation, but by observation and experiment. 
 
 Every person knows that a heavy body dropped from any height 
 above the earth's surface descends in a straight line towards the 
 centre of the earth, where the whole force of gravity seems to be 
 accumulated. And although it be difficult to discover any sensible 
 change in the intensity of this force by a direct experiment on the 
 weight of a body, on account of the distances to which we can either 
 
 * In order to perform the calculation in this example, it is necessary to be ac- 
 quainted with proportion, and the method of extracting the square arid cube 
 roots. 
 
142 OF THE FORCES WHICH RETAIN THE PLANETS, &C. 
 
 ascend or descend from the earth's surface being so small ; yet the 
 experiments which have been made with the pendulum, lead us to 
 infer, that the force of gravity diminishes as we recede from the 
 centre of the earth, at the rate we have stated above, namely, as the 
 square of the distance increases. The effect of terrestrial gravity, as 
 exhibited in the descent of falling bodies, has been accurately mea- 
 sured, and the law which it observes fully ascertained and confirmed. 
 It had been long known that falling bodies acquire an increase of 
 velocity as they approach the earth ; and consequently that they pass 
 over a greater space in any given time. But Galileo was the first 
 person who made known the law which regulates their descent, which 
 is as follows. When a body falls freely from a state of rest, it 
 passes through the space of sixteen feet one inch in the first second 
 of time ; and at the end of the first second it will have acquired such 
 a degree of velocity as would carry it thirty-two feet two inches in 
 the next second, though it should acquire no new impulse from 
 gravity. But as the same accelerating cause continues constantly to 
 act, it will move sixteen feet and one inch more the next second ; 
 consequently at the end of two seconds it will have fallen sixty-four 
 feet four inches, and acquired such a velocity as would, in the next 
 second, carry it over forty-eight feet, although it received no new 
 impulse, and so on. If a body b'e projected perpendicularly upwards, 
 its motion is continually retarded by the same cause which accele- 
 rates it in descending. But if it be projected in a direction different 
 from the vertical line, that direction will be continually varying, and 
 a curved line will be described in consquence of the incessant power 
 of gravity, which, in such cases, is measured by the degree of curva- 
 ture of the line described by the body. 
 
 This phenomenon affords a very good illustration of the theory of the 
 planetary motions; for the effect produced is perfectly analogous to 
 the motion of a planet in its orbit. Every person knows that the 
 greater the velocity with which any body is thrown, in a horizontal 
 direction, from an engine, the further will it range before it falls. 
 And though a body cannot be thrown to a very great distance on the 
 earth, yet we can conceive a body projected with such a velocity as 
 to carry it quite round the earth without touching it, and to continue 
 to circulate round it in the same path with undiminished velocity, in 
 every respect as the moon does. By reasoning in this manner, Sir 
 Isaac Newton conceived, that the force that produces pressure in a 
 body that is supported, or that causes a heavy body to fall to the 
 ground, or a body thrown obliquely in the air, to describe a curvi- 
 lineal path, might perhaps be the same that retains the moon in her 
 orbit ; and makes the planets and comets revolve round the sun. Though 
 this was at first only a plausible conjecture, yet, upon an appeal to the 
 phenomena exhibited by these bodies, he was enabled to verify this 
 conjecture. 
 
 It was, however, a fortunate circumstance for science, as well as 
 for Newton, that the real motions of the heavenly bodies, as well as 
 the laws of Kepler, were known before he undertook the investigation 
 of this subject. For these laws were not only the basis upon which 
 
OF THE QUANTITY OF MATTER IN THE SUN, &C. 143 
 
 he founded his investigations, but they suggested to him the manner 
 of conducting them. 
 
 The first law, for example, led him to the important discovery, that 
 the action of a force always directed towards the sun bends the path 
 of each planet into a curve; and the second law not only led him to 
 the knowledge of the changes produced in the intensity of this force, 
 by distance, but to the law which regulates the intensity. 
 
 And as it was previously known that the planets move round the 
 sun in elliptical orbits, he was enabled to establish this important law, 
 that the force by which a planet describes areas proportional to the 
 times round the focus of its elliptical orbit, is inversely as the square 
 of the distance from that focus. Hence it follows, that each planet 
 is under the influence of a force directed towards the sun, and urging 
 it in that direction, and that the intensity of this force is inversely 
 proportional to the square of the planet's distance from the sun. 
 
 This power or force is sometimes called the centripetal force ; be- 
 cause it urges the planet in the direction of the centre of its orbit, and 
 prevents it from flying off in a straight line, which every body moving 
 in a curve has a tendency to do ; and that force by which it is urged 
 in a straight line, or endeavours to fly off from the centre, is called 
 the centrifugal force. It is by the nice combination of these two 
 forces, that the whole solar system is preserved in the order in which 
 we behold it, and that every body which forms any part of the whole, 
 performs its revolution round the common centre of the system. 
 
 If the projectile or centrifugal force that urges the planets forward 
 in their orbits were destroyed, each of them would fall to the sun, by 
 the force of gravity, just as a stone descends to the earth. 
 
 The time in which the different planets would fall to the sun, from 
 a state of rest, by the action of the centripetal force, or the power of 
 gravity, is as follows: Mercury, in 15 days 13 hours; Venus, 39 
 days 17 hours; the Earth, 64 days 13 hours; Mars, 121 days 10 
 hours ; Jupiter, 765 days 19 hours ; Saturn, 1901 days ; Uranus, 
 5425 days ; and the Moon to the earth, in 4 days 20 hours. 
 
 As the centripetal force or attractive power of the sun increases, as 
 the square of the distance decreases, it is obvious that the nearer any 
 body is to the sun, the more powerfully will it be attracted by him. 
 This not only accounts for the planets which are nearest the sun 
 moving faster in their orbits than those that are most remote from 
 him ; but also for the motion of a planet being quickest in that part 
 of its orbit which is nearest the sun, and slowest in that part which 
 is farthest distant from him.* For the centrifugal force must always 
 be equal to the centripetal, in order that the planet may continue to 
 revolve in the same orbit. In this manner, all the bodies which com- 
 pose the solar system are attracted by the sun, and made to perform 
 their revolutions round him ; and as action, and re-action are equal, 
 and in opposite directions, the sun is equally attracted by all the 
 bodies that revolve round him. Hence the order and regularity of 
 the whole system is preserved. 
 
 J* See page 10. 
 
144 OF THE QUANTITY OF MATTER IN THE SUN, &C. 
 
 As neither our limits nor the nature of the present work will permit 
 us to give a particular account of the planetary disturbances, or the 
 effect which they have on each other, we shall conclude the present 
 article by mentioning the discoveries which have been the result of 
 the investigations of astronomers on this intricate subject. These 
 may be reduced to the two following ; viz. 1st. That all the inequa- 
 lities produced by the mutual action of the planets are periodical; 
 that is, after a certain time they all run through the whole series of 
 changes to which they are subject. 2d. That amid all these changes, 
 two of their elements remain the same the greater axis of the orbit, 
 and the periodic time. Hence, the mean motion of a planet, and its 
 mean distance are constant quantities. For these important disco- 
 veries we are indebted to the celebrated French mathematicians, 
 La Grange and La Place. And, as the late Professor Playfair 
 has observed, they have made known to us one of the most important 
 truths in Physical Astronomy ; namely, that the system is stable ; 
 that it does not involve any principle of destruction in itself; but is 
 calculated to endure for ever, unless the action of an external power 
 be introduced; 
 
 OF THE QUANTITY OF MATTER IN THE SUN AND 
 
 PLANETS, 
 
 AND THE FORCE OF GRAVITY AT THEIR SURFACES. 
 
 On first view, it almont appears impossible to determine the res- 
 pective masses of the sun and planets, and to measure the height 
 ironi which bodies fall in a given time, by the action of gravity at 
 their surfaces. But the connection of facts with each other, often leads 
 to results which appear inaccessible, when the principle on which they 
 depend is unknown. 
 
 It was, therefore, perfectly natural even for astronomers to consi- 
 der it impossible to determine the intensity of gravity at the surface 
 of the planets, while the principle of universal gravitation remained 
 unknown;* and it is just as natural for those who are unacquainted 
 with mathematics and astronomy to consider the same thing impos- 
 sible, even although they have heard of such a principle as universal 
 gravitation. We shall, therefore, state what has been the result of 
 the calculations of some of the first-rate astronomers of the present 
 day on this curious and interesting subject. 
 
 From the fact that action is always accompanied by re-action, 
 astronomers conclude, that gravitation among terrestrial bodies, is the 
 mutual tendency of the particles of matter to one another. And, 
 from analogy, they think it perfectly reasonable to suppose, that this 
 is true in all cases ; and that the force of gravitation towards different 
 
 * It was this discovery which rendered it practicable to measure the intensity 
 of gravity at the surfaces of the planets. 
 
OF THE QUANTITY OF MATTER IN THE SUN, &C. 145 
 
 bodies, the distance being the same, is proportional to the quantities of 
 matter, or the masses of the bodies. 
 
 This supposition is the foundation of ail the calculations respecting 
 the masses of the planets ; and from it formulas have been deduced 
 for calculating the relative quantity of matter in such of the primary 
 planets as have satellites revolving round them ; but the quantity of 
 matter in those that have no satellites can only be guessed at by the 
 effect they produce in disturbing the motions of the other planets.* 
 
 The quantity of matter in the moon, however, may be determined 
 by comparing its influence with that of the sun in producing the 
 tides, and the precession of the equinoxes. By these means it has 
 been ascertained, that the mass of the moon is about -^th part of 
 that of the earth. And La Place, in his Mecanique Celeste, has de- 
 termined the quantity of matter in each of the primary planets, front 
 the most exact data, to be as follows : 
 
 Quantity of matter in the Sun ..... 1 
 
 Mercur Y ......... 
 
 The Earth 
 
 Marc 
 
 
 
 ......... TTTBT'TTS 
 
 Saturn .......... 
 
 TJranusf .......... 
 
 The masses of the planets being known, and their bulks being also 
 known, their densities are easily determined, for these are propor- 
 tional to the masses divided by the bulks. 
 
 La Place, taking the mean density of the sun as unity, finds the 
 density of such planets as have satellites to be as follows : 
 The Earth, 3-9395; Jupiter, 0-8601; Saturn, 0-4951; Uranus, 
 1-1370. 
 
 Knowing the masses of the planets, and their diameters, the force 
 of gravity at their surface maybe determined; for, supposing them 
 to be spherical, and to have no rotation on their axis, the force with 
 which a body placed on their surface gravitates to them, will be pro- 
 portional to their masses divided by the squares of their diameters. 
 From the masses of Jupiter and the Earth, La Place calculates that 
 a body which weighs one pound at the earth's equator, if carried to 
 Jupiter's equator would weigh 2J pounds, supposing these bodies to 
 have no rotation, and supposing the weights to be measured by the 
 pressure exerted in the two situations. If the same body were carried 
 to the surface of the sun, it would weigh about 27 J pounds; from 
 which it follows, that a heavy body would there descend about 444 
 feet in the first second of time. 
 
 * The quantities of matter in any two primary planets are directly as the cubes 
 of the mean distances at which their satellites revolve, and inversely as the squares 
 of their periodic times. 
 
 t By adding these fractions together it will be found that the quantity of 
 matter in all the planets together is not j l 5 th part of the matter in the sun ! 
 
 13 O 
 
146 OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, &C, 
 
 Although all the planets gravitate to the sun, yet the centre of the 
 surt is not the centre of gravity of the whole solar system. The> 
 centre of the sun is, however, never distant from that point so much 
 as his own diameter, consequently the centre of gravity of the whole 
 system is always within the body of the sun. But as this point and 
 the centre of the sun do not coincide exactly, and as the gravitation 
 of the planets to the sun must be accompanied by the gravitation of 
 the sun to the planets, from the quality of action and re-action, it 
 follows that the sun must have a motion in a small orbit round the 
 centre of gravity of the whole system. The form of this orbit is, 
 however, very complicated, on account of the disturbing forces of so 
 many planets, which are sometimes exerted toward one side and 
 sometimes toward another; and even unequally exerted on different 
 sides at the same time, according to the situation of the planets in 
 their orbits. 
 
 Thus we see the extraordinary and universal principle called gravi- 
 tation has not only been the means of making us acquainted with a 
 great number of inequalities in the motion of the heavenly bodies, 
 which it would have been impossible to have discovered by observa- 
 tion, but it has furnished us with the means of subjecting these 
 motions to precise and certain rules. 
 
 The motion of the earth, which had obtained the assent of astro- 
 nomers, on account of the simplicity with which it explained the 
 celestial phenomena, has received a new confirmation, which has 
 carried it to the highest degree of evidence of which physical science 
 is susceptible. Without the knowledge of this universal principle, 
 the ellipticity of the planetary orbits ; the laws which the planets and 
 comets obey in their revolution round the sun ; their secular and 
 periodical inequalities; the numberless inequalities of the moon, and 
 the satellites of Jupiter; the precession of the equinoxes ; the nutation 
 of the earth's axis ; the motions of the lunar axis ; and the ebbing and 
 flowing of the sea, would only be insulated facts, and unconnected 
 phenomena. It is, therefore, a circumstance which can scarcely be 
 sufficiently admired, that all these phenomena, which at first sight 
 appear so unconnected, should be explained by one principle that 
 of the mutual gravitation of all bodies with forces directly as their 
 quantities of matter, and inversely as the squares of their distances. 
 
 OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, 
 
 WHICH HAVE BEEN PROPOSED TO ACCOUNT FOR THE CELESTIAL 
 
 PHENOMENA* 
 
 After the description which has been given of the various pheno- 
 mena of the heavens, both as viewed with the naked eye and the 
 telescope, it may not be unnecessary, nor unacceptable to the reader, 
 to give a short account of the principal theories, or systems, which 
 have been formed at various periods to account for some of these 
 appearances, and particularly for the apparent motions of the celestial 
 bodies, 
 
OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, &C. 147 
 
 The explanation of the celestial motions which naturally occurred 
 to those who began the study of the heavens, was, that the stars are 
 so many luminous points fixed in the surface of a sphere, having the 
 earth in its centre, and revolving on an axis passing through that 
 centre, in the space of twenty-four hours. When it was observed, 
 that all the stars did not partake of this diurnal motion in the same 
 degree, bat that some were carried slowly towards the east, and 
 that their paths estimated in that direction, after certain intervals of 
 time, returned into themselves, it was believed that they were fixed in 
 the surfaces of spheres, which revolved westward more slowly than 
 the sphere of the fixed stars. The spheres were supposed transpa- 
 rent, or made of some crystalline substance, and from this arose the 
 name of the crystalline spheres, by which they were distinguished* 
 Though this system grew more complicated, as the number and 
 variety of the apparent phenomena increased, yet it was the system 
 of Aristotle and Eudoxus; and, with few exceptions, of all the 
 philosophers of antiquity.* 
 
 But when the business of observation came to be regularly pur- 
 sued, little was said either of the fixed stars, or of the crystalline 
 spheres ; astronomers being chiefly bent on ascertaining the laws or 
 general facts connected with the motions of the planets. 
 
 To do this, however, without the introduction of hypothesis, at 
 this period, was scarcely possible. The simplest and most natural 
 hypothesis was, that the planets moved eastward in circles, at a uni- 
 form rate. But when it was found that, instead of moving uniformly 
 to the eastward, every one of them was subject to great irregularity, 
 the motion eastward becoming slower, at certain periods, and at 
 length vanishing altogether, so that the planet became stationary, 
 and afterwards acquiring a motion in the contrary direction, and pro- 
 ceeded for a time to the westward, it was far from obvious that all 
 these appearances could be reconciled with the idea of a uniform 
 circular motion. 
 
 The solution of this difficulty is attributed to Apollonius Pergaeus, 
 one of the most celebrated mathematicians of antiquity. He con- 
 ceived that each planet moved in a small circle, and that the centre 
 of this small circle moved in the circumference of a large circle, 
 which had the earth for its centre. The first of these circles was 
 called the epicycle, and the second the deferent; and the motion in 
 the circumference of each was supposed uniform. Lastly, it was 
 conceived that the motion of the centre of the epicycle in the circum- 
 ference of the deferent, and likewise the motion of the planet in that 
 of the epicycle, were in opposite directions; the first being towards 
 the east, and the scond towards the west. In this way, the change 
 
 * Although it is said that Pythagoras taught that the earth was a planet, and 
 that the sun was fixed in the centre of the planetary system ; thai the apparent 
 revolution of the heavens was produced by the diurnal revolution of the earth; 
 and that the apparent annual motion of the sun was occasioned by the earth- 
 moving round him like the other planets ; yet this doctrine was never taught 
 publicly, and in a very short time it was completely forgotten. 
 
 O 2 
 
148 OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, &C. 
 
 from progressive to retrograde, as well as the intermediate stationary 
 points, were readily explained. 
 
 But, notwithstanding the accomplishment of this important object, 
 and some further applications of the method of epicycles by Hip- 
 parchus, to account for the inequality of the sun's apparent motion 
 round the earth, no regular system of astronomy appears to have 
 been framed or taught by any individual till the appearance of the 
 celebrated Ptolemy, who has always been reckoned the prince of 
 ancient astronomers, not so much on account of being the founder of 
 the system which goes by his name, as for the number of observations 
 which he made, and the extent of his astronomical writings. 
 
 PTOLEMAIC SYSTEM. 
 
 Ptolemy supposed the earth to be fixed immoveably in the centre 
 of the universe, and that the sun, moon, and planets move round it in 
 the following order; viz. The Moon, Mercury, Venus, the Sun, 
 Mars, Jupiter, Saturn, as represented by the following figure. 
 
 P.M 
 
OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, &C. 149 
 
 Above these he placed the firmament of fixed stars, then two 
 crystalline spheres ; all of which were included in what he called 
 theprimum mobile, which was by some unaccountable means turned 
 round once in twenty-four hours, carrying all the rest along with it. 
 
 From this arrangement, in which the sun is placed between Venus 
 and Mars, it appears, that he was acquainted with the common dis- 
 tinction of inferior and superior planets. It appears, also, that the 
 arrangement of the planets in the above order, was made on consi- 
 dering the time which each of them required to perform a complete 
 circuit of the heavens ; hence we find the moon placed nearest t<? 
 the earth. Although he could explain the respective motions o 
 the planets round the heavens, from west to east, as well as their 
 diurnal motion round the earth, yet he was obliged to have recourse 
 to the epicycles of Apollonius to explain the apparent irregularities 
 in their motions, such as appearing to be stationary, retrograde, &c. 
 
 In order to account for the inclination of the respective orbits of 
 the planets to the ecliptic, it was said, that the deferent and epicycle 
 were in different planes from the ecliptic. And when any new and 
 anomalous motion was detected, another epicycle was immediately 
 added to explain the appearance. 
 
 In this way, by means of the most extravagant suppositions, and 
 complicated machinery, a system was at length formed, which ex- 
 plained, in a plausible but conjectural manner, most of the constant 
 phenomena of the heavens. But the awkward and complicated 
 machinery by which it is supported, when compared with the simpli- 
 city of the Copernican system, is almost sufficient to cause it to be 
 rejected. Besides the whole theory is entirely hypothetical ; and that 
 the existence of the agents employed to produce such mighty effects 
 has never been attempted to be proved. But, independent of these 
 objections, this system is now found to be at complete variance with 
 many of the modern discoveries which have been made, respecting 
 comets ; for the orbits of these bodies are known to cross those of the 
 planets in every direction ; a fact which is quite incompatible with 
 the existence of crystalline spheres. And the constant periodical 
 motions and appearances of the two interior planets, Mercury and 
 Venus, completely refute the whole system. For if this system were 
 true, these two planets could never be hid behind the sun, because 
 their orbits are included in his, according to Ptolemy's hypothesis. 
 These motions, too, would always be direct, and they would appear 
 as often in opposition to, as in conjunction with, the sun : but the con- 
 trary of all this takes place; for these two planets are just as often 
 behind the sun as before him appear as often to move backward as 
 forward and, instead of being seen at any time in that side of the 
 heavens which is opposite to the sun, they were never yet seen a 
 quarter of a circle distant from him ; which certainly proves that the 
 Ptolemaic system is contrary to what actually takes place in nature: 
 and yet it continued to receive the sanction both of the learned and 
 unlearned for nearly fourteen hundred years, without the truth of it 
 ever being publicly called in question. 
 
150 OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, &C. 
 
 COPERNICAN SYSTEM, 
 
 The celebrated astronomer Copernicus, was the person who gave 
 the death-blow to the system of Ptolemy, by conceiving the bold 
 pystem which removes the earth from the centre of the world, and 
 ascribes to it a two-fold motion,* 
 
 Copernicus was first led to turn his attention to the framing of a 
 new theory, from a perception of the complexity, or rather absurdity 
 of the doctrine of epicycles. In the early part of his life he began to 
 consider whether a more rational and satisfactory manner of account- 
 ing for the apparent motions of the heavenly bodies could not be 
 discovered, than that which was given by Ptolemy. By intense 
 application to the subject, and a few obscure hints obtained from the 
 ancients, he at last deduced a complete system, capable of solving 
 every phenomena in a more simple and satisfactory manner than was 
 ever done before, 
 
 In this system the sun is placed in the centre, and the planets 
 move round him in the following order; viz. Mercury, Venus, the 
 Earth, Mars, Jupiter, Saturn ; and far beyond the orbit of Saturn are 
 placed the fixed stars, which form the boundary of the visible 
 creation. f This is the system which is now generally received 
 by all modern astronomers, and the one upon which all the pheno- 
 mena, mentioned in the preceding pages, have been accounted for 
 and explained. 
 
 It may, perhaps, be proper to notice some objections which have 
 repeatedly been advanced against it, especially as these were not 
 noticed when treating of the annual and diurnal motions of the earth. 
 This we shall however defer till we have given a short account of 
 the Tychonic System ; because its author was one of the most inge- 
 nious and powerful opponents that ever appeared against the Coper- 
 nican System. 
 
 TYCHONIC SYSTEM. 
 
 Although the Copernican System was received by most men of 
 science then living, yet there were some who would never assent to 
 it. The motion of the earth was so contrary to what they were 
 always accustomed to hear on the subject, and, as they thought, to 
 appearances, that they could never agree to support such doctrine. 
 
 Among those who opposed the system of Copernicus, was Tyclio 
 Brahe, a Danish nobleman, who was born in the year 1546, and who 
 devoted the whole of his life to the study of astronomy. As he could 
 not entirely adopt the Ptolemaic system, being convinced that the 
 earth is not the centre about which the planets revolve, and being a 
 man of genius, he invented a new system, which was a kind of mean 
 between the Ptolemaic and the Copernican. 
 
 * The diurnal and annual. See pages 120 and 125. 
 t See page 13. 
 
OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, &C. 151 
 
 In this system, the earth is placed in the centre of the orbits 
 of the sun and moon ; but the sun is supposed to be the centre of 
 the orbits of the five primary planets then known. Thus, according 
 to Tycho Brahe, the sun and all the planets moved round the earth, 
 in order to save the earth from revolving on its axis once in twenty- 
 four hours ! 
 
 This System is represented by the following figure. 
 
 It must be allowed, that all the phenomena purely astronomical 
 may be accounted for on this hypothesis; and that the objections to 
 it are rather derived from physical and mechanical considerations, 
 than from the appearances themselves. It is simpler than the Ptole- 
 maic system, and free from its inconsistencies ; but it is more com- 
 plex than the Copernican, and in no respect affords a better expla- 
 nation of the phenomena. Its true place is between these two 
 systems ; an advance beyond the one, and a step short of the other. 
 If its author had lived before Copernicus, it would have been a step 
 in the advancement of knowledge ; but coming after him, it was a 
 step backward. 
 
 It is certainly not to his credit as a philosopher to have made this 
 retrograde movement, yet he is not altogether without apology. For 
 the physical arguments in favour of the Coperuican system could not 
 
152 OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, &C. 
 
 be supposed to have much weight in an age when the laws of motion 
 were unknown, and when it was not clearly understood that the sun 
 and planets had any effect on each other. Having already fully and 
 clearly established both the diurnal and annual motion of the earth, 
 and having advanced some other convincing arguments in favour of the 
 Copernican system, in the former part of this work, it would be 
 superfluous to enter into a formal refutation of the Tychonic system, 
 which is so different from that of the Copernican. 
 
 But as Tycho Brahe advanced a number of objections against the 
 Copernican system, and particularly that part of it which supposes 
 the earth in motion, we shall here notice a few of those objections 
 which appear to have the greatest weight, although the arguments 
 already advanced in support of the annual as well as the diurnal 
 motion of the earth, would be considered as equivalent to a demon- 
 stration by any person who was not previously prepossessed against 
 the possibility of such motions. 
 
 Tycho asked, how was it possible for a ball which was projected 
 perpendicularly up in the air, to fall down on the same spot from 
 which it was projected if the earth revolved on its axis ? In answer 
 to this objection, it will be sufficient to observe, that the atmosphere 
 which surrounds the earth revolves with it, having received the 
 same common motion, in the same direction ; and that every thing 
 on the earth revolves with it, and retains the same relative position. 
 It is rather astonishing that Tycho, and all those who have repeated 
 the same argument, in various forms, never observed that when balls 
 or billiards are played in a vessel sailing with the greatest velocity, 
 that the shock of the ball is there given with the same force the one 
 v/ay as the other ; and that when a stone is dropped from the top of 
 the mast, it falls just as near the foot of it when the vessel sails as 
 when she is at rest. But though this be the case, the stone has 
 actually been carried some distance, in the direction of the ship's 
 motion, from the point perpendicularly under that from which it was 
 dropt : and if a spectator in another vessel at rest were to observe the 
 stone during its descent, he would see it describe an oblique line, or 
 the diagonal of a parallelogram, the sides of which would be the 
 height of the mast, and the distance which the ship sailed during the 
 time of the stone's descent. The motion of the vessel is communi- 
 cated to the mast, to the stone, and to every thing on board, in such 
 a way, that every thing thrown or moved arrives at the same point, 
 and strikes with the same force, when the ship sails as when she is 
 at rest, provided it be thrown with the same velocity in the one case 
 as in the other. 
 
 The reason that the stone is seen to describe an oblique line, or 
 even to have any motion at all, is its meeting or passing other objects 
 in its descent which are known to be fixed. But as the earth meets 
 with no other object, there is nothing at a distance from it, nor on its 
 surface, which can by its situation, by its motion, or by its resistance, 
 make us perceive or feel either its annual or diurnal motion. All 
 bodies on or near the surface of the earth partake of the motion of the 
 earth itself, and are carried smoothly through the air with the same 
 
OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, tfcc. 153 
 
 velocity, and continue to preserve the same relative position with 
 respect to each other. 
 
 " The earth," said Tycho Brahe, to the followers of Copernicus, 
 " is a heavy inert mass, very ill adapted to motion, and seems only 
 fitted to be the fixed foundation of all stability ; and yet you wish to 
 make it a star, and travel about in the air ! That is too strange an 
 idea!" 
 
 But there is nothing in this remark of Tycho's which carries with 
 it the smallest degree of evidence against the motion of the earth. 
 Why not the earth move which is so much less than the sun, even 
 following the observations and demonstrations of Tycho himself? 
 Why should it be viler or grosser than the planets, which are round 
 like the earth, opaque and dark like it, when the sun does not shine 
 on them, and some of them much larger, even according to Tycho? 
 
 Another thing which shocked Tycho very much was the enormous 
 distance at which the fixed stars must be placed in the system of 
 Copernicus ; for the breadth of the earth's orbit is an insensible 
 point compared with their distance. "It is not probable," said he, 
 11 that the distance between Saturn and the fixed stars is seven hun- 
 dred times greater than the distance between Saturn and the sun, 
 without other stars being placed in the interval ! " But this distance 
 cannot be less, since it is found that the annual parallax of none of 
 the fixed stars amounts to two seconds of a degree. And as this is 
 the angle under which the earth's orbit appears when viewed from a 
 fixed star, if it be equal to the angle under which we see the star, it 
 follows that the star and orbit are equal in magnitude. 
 
 Now, as the parallax of the stars is so small as scarcely to amount 
 to one second, they must either greatly exceed the earth's orbit in 
 diameter, or be immensely distant fr.om the earth.* But if Tycho 
 had lived at the present day, he would not have advanced this objec- 
 tion against the motion of the earth ; for he would have learned that 
 the planet Uranus, as well as many of the comets, moved in orbits 
 which extend far beyond that of Saturn, and fill apart of that immense 
 space which appeared to him so inconceivable. He would have 
 known by the discovery of telescopes, that the apparent diameter of 
 stars of the first magnitude, does not amount to one second ; and of 
 course we are not under the necessity of supposing them so prodi- 
 giously great as if it amounted to two or three minutes, as he sup- 
 posed. And though it should be admitted that there exists an 
 immense interval void of stars and planets, and that the fixed stars 
 are incomparably greater than the sun, it proves nothing against the 
 system of Copernicus. 
 
 That the stars become nearer and smaller in the system of Tycho, 
 are things too vague to prove any thing in his favour ; because we 
 have no more knowledge respecting their real size than their true 
 distance. 
 
 Tycho also asked, how it was possible for the earth to preserve the 
 
 * According to Tycho, the apparent diameter of the stars of the first magnitude 
 was two or three minutes ! 
 
Io4 OF TftE PRINCIPAL SYSTEMS OF ASTRONOMY, &C. 
 
 parallelism of its axis during the whole of its revolution round the suri 
 or how one and the same body could have two different motions, 
 one of which transports the centre of the globe, and the other which 
 changes the position of its axis ? But although the axis continues to 
 maintain its parallelism during the whole of its annual revolution, 
 this is not a peculiar motion as Tyclio supposed, and forming a third 
 motion, in the sense which Copernicus views motion. It is a situation 
 natural to the axis, which does not change, for there is no cause to 
 make it change. 
 
 It is sufficient that the axis has once been directed to a particular 
 point in the heavens, for it still continues to be directed there, though 
 the earth itself be constantly moving forward in its orbit. There is 
 no physical nor mathematical reason from whence it can be concluded, 
 that* the axis would be perpendicular to the plane of the orbit, if the 
 earth had a motion on its axis there is no connection between these 
 two motions. 
 
 In the time that all parts of the earth are thrown from the same 
 side by a projectile force, they all acquire the same velocity, as well 
 as a parallel direction j but this change does not affect the parts with 
 respect to each other, nor in the least alter the position which they 
 ought to have* All parts receive the same impression ; there is a 
 perfect equilibrium between the superior and inferior parts ; and they 
 all preserve the motion of rotation which they had before, or each 
 particle moves in a direction parallel to that which it had when the 
 earth was at rest. 
 
 A body having begun to move round its axis, the two poles, or 
 the two immoveable points round which the body turns, receive the 
 same motion by impulse from the centre which produces the motion 
 of translation : and if they receive the same motion, there is no reason 
 for supposing that one of these points advances faster than the other ; 
 and as|the two make equal advances, they will necessarily be always 
 in a line parallel to that in which they were when they began to 
 move. 
 
 When a top turns upon a table by a rotatory motion, the table may 
 be moved either up or down, or from right to left, obliquely or circu- 
 larly, without occasioning any difference in the movement of the top. 
 The top may also be thrown in any direction whatever, and yet con- 
 tinue to turn on the same axis. A ball thrown from the mouth of a 
 cannon almost always turns round an axis, and although that axis 
 may sometimes be vertical, horizontal, or inclined, yet this depends 
 on the obstacles which it meets with in one or other of these direc- 
 tions before it leaves the mouth of the cannon. But as the earth 
 meets with no obstacle in its revolution, the axis always continues to 
 point in the same direction. 
 
 As the annual and diurnal motions of the earth are the foundation 
 of all astronomy, both physical and practical, we have been at parti- 
 cular pains to refute the objections which have been started against 
 these motions by the celebrated Tycho Brahe, because they are the 
 strongest philosophical arguments that have ever been urged against 
 the Copernican system. But had Tycho known what has been dis-* 
 
OF THE PRINCIPAL SYSTEMS OF ASTRONOMY, &C. 15& 
 
 covered since his death he would not have started many of the 
 objections which he has done against this system, 
 
 CARTESIAN SYSTEM, 
 
 The next system was the Cartesian. Its founder, Rhene Des 
 Cartes, flourished about the beginning of the 17th century. He 
 supposed that every thing in the universe was formed from very 
 minute bodies, called atoms, which had been floating in open space. 
 To each atom he attributed a motion on its axis ; and he also main- 
 tained that there was a general motion of the whole universe round 
 like a vortex, or whirlpool. In the centre of this vortex was the sun, 
 with all the planets circulating round him at different distances ; 
 those that were nearer the sun circulating faster than those at a greater 
 distance, as the most distant parts of a vortex or whirlpool are known 
 to do. Besides this general vortex, each of the planets had a parti- 
 cular vortex of its own, by which its satellites, if it had any, were 
 whirled round, and any other body that came within its reach. 
 
 This is the celebrated system of vortices, invented by Des Cartes. 
 The fabric, it must be confessed, is raised with great art and inge- 
 nuity, and is evidently the produce of a lively fancy and a ferule 
 imagination. But then, it can be considered only as a philosophical 
 romance, which amuses without instructing us ; and serves principally 
 to shew that the most shining abilities are frequently misemployed. 
 
 In this hypothesis, Des Cartes supposes extension to constitute the 
 essence of matter, and wholly neglects solidity, as well as the inertia 
 by which it resists any change in its state of motion or rest, which 
 principally distinguishes body from space ; and., consequently, the 
 doctrine of an universal plenum, deduced frontr this definition, is 
 founded upon false principles. 
 
 That there is such a thing as a vacuum in nattfre^or a space void 
 of body, may be demonstrated from various experiments. By means 
 of the air-pump, we can so far exhaust the air from a glass receiver, 
 that a piece of gold and a feather, let fall together, from the top of 
 the vessel, shall both descend equally swift, and come to the bottom 
 at the same time : which evidently shews, that, the air being taken 
 away, there remains no other matter sufficient to cause any sensible 
 resistance, or that in the least impedes or obstructs their passage. 
 
 It was said by many of the ancient philosophers, that nature abhors 
 a vacuum; and by means of this dogma, and others of a like nature, 
 they attempted to prove and illustrate the doctrine of an universal 
 plenum, like that of Des Cartes. But this is an assertion, unsup- 
 ported by facts, and too idle a notion to require any formal refutation : 
 and in nearly the same predicament are most of the other arguments 
 which have been used in defence of this doctrine. They are all 
 sufficiently exposed, not only by the Torricilian experiment, and the 
 nature of pumps in general, but likewise from the most obvious phe- 
 nomena of the constant and free motion of bodies, whether celestial 
 or terrestrial, which come continually under our inspection. 
 
 On the system of Des Cartes, and all others that depend on the 
 
156 HISTORY OF ASTRONOMY. 
 
 same principle, we may remark, that if the planets be carried round 
 the sun in vortices, the quantity of matter in the sun cannot affect 
 the velocity of the vortex, or the bodies immersed in it; consequently 
 the velocity might be the same though there were no central body 
 whatsoever. The quantity of matter in the sun, therefore, cannot 
 have the least effect in retaining the planets in their orbits. But the 
 quantity of matter in the sun does affect the planet, and is a material 
 element in its gravitation towards the centre of its orbit. It is there- 
 fore impossible that the action of a vortex, can have any effect what- 
 ever upon that gravitation. This argument is perfectly conclusive and 
 fatal to the system of vortices. But we may observe that this system 
 owed its downfall to another argument, equally if not still more 
 powerful; viz. that whenever you suppose the vortex so arranged 
 that it will explain one of those great facts in the planetary motions, 
 known by the name of Kepler's Laws, it becomes quite inconsistent 
 with the rest. 
 
 The vortices of Des Cartes have, therefore, ceased to afford any 
 satisfaction even to the most superficial reasoner, and are now only 
 known in the history of opinions; in which they will ever furnish a 
 most instructive chapter. 
 
 HISTORY OF ASTRONOMY. 
 
 No science in the world is of more value, or of higher antiquity* 
 than Astronomy. Its antiquity may be learned from what was 
 spoken by God himself at the creation of the world ; for he said 
 " Let the sun and the moon be for signs and for seasons," &c. 
 
 By this it is thought the human race never existed without some 
 knowledge of astronomy among them. It is said by some Jewish 
 Rabbins, that Adam was endowed with a knowledge of the 
 nature, influence, and uses of the heavenly bodies ; and Josephus 
 ascribes to Seth and his posterity an extensive knowledge of astro- 
 nomy. 
 
 It is supposed, by some writers, that Noah retired after the flood 
 to the north-east part of Asia, where his descendants peopled the 
 vast empire of China. " This," says Dr. Long, " may account for 
 the Chinese having so early cultivated the study of astronomy." But 
 the vanity of the Chinese has prompted them to pretend to a know- 
 ledge of this science almost as early as the flood itself. 
 
 To the emperor Hoang-ti, the grand-son of Noah, they attribute 
 the discovery of the Pole star and the mariner's compass. They 
 also say, that Confucius, their great philosopher, who lived 551 years 
 B. C. has recorded 36 eclipses ; but be this as it may, the Chinese 
 are allowed to have had a very early knowledge of astronomy. 
 
 Some authors say it had its origin among the Chaldeans, others 
 among the Hindoos, and some, with more probability, among the 
 Egyptians. Professor Playfair has given a learned and ingenious 
 dissertation on the astronomy of the Brahmins, in the second volume 
 
HISTORY OF ASTRONOMY. 157 
 
 of the Transactions of the Royal Society of Edinburgh, in which he 
 shews the great accuracy and high antiquity of the science among 
 them ; and he also shews that it is extremely probable that the Hin- 
 doos were among the first astronomers in the world. 
 
 But Thales of Miletus is considered as the first person that pro- 
 pagated any truly scientific knowledge of astronomy ; and it is said 
 he acquired his knowledge of the subject in Egypt. 
 
 Thales taught his countrymen the cause of the inequality of the 
 days and nights ; explained to them the theory of eclipses, and the 
 manner of predicting them ; and gave them an example of his art in 
 an eclipse of the sun, which happened soon after: he was born 640 
 years B. C. Anaximander was a pupil of Thales, and succeeded 
 him as head of the school of Miletus. It is said he had some idea of 
 the spherical shape of the earth ; he is also said to have been the 
 inventor of celestial globes, and of the orthographic projection of 
 maps. 
 
 He erected a gnomon at Sparta, by which he ascertained the 
 obliquity of the ecliptic, with the solstices and equinoxes. 
 
 Pythagoras was the next person who improved the science. He 
 founded a school in Italy for that very purpose. Seconded by his 
 earliest scholars, he clearly demonstrated the spherical shape of the 
 earth, which Anaximander had only conjectured. Pythagoras taught 
 that the sun was fixed in the centre of the planetary orbits, and that 
 the earth moved round it with the other planets the very system 
 which is taught at this day. This opinion he communicated only to 
 his pupils in secret ; for being repugnant to the received opinions of 
 that time, (and even appearances,) he did not wish to expose himself 
 to the derision and persecution of ignorance and fanaticism, which 
 would have been the inevitable consequence. For, about one hun- 
 dred years after his time, Anaxagoras was condemned to banishment 
 for saying that the sun was a mass of fiery matter. The measuring 
 of time being a principal object in astronomy, many efforts were 
 made by the ancients to determine accurately, and to compare with 
 each other, the motions of the sun and moon, on which this measure 
 universally depends. 
 
 Meton and Euctemon, two Greek astronomers, accordingly ap- 
 plied themselves to the study of this subject with great industry ; and 
 by sagaciously combining all the observations then known, formed a 
 luni-solar period, or cycle of 19 years. This cycle was adopted on 
 the 16th July, in the year 433 B. C. and is still in use. It is called 
 the Metonic cycle, after the inventor of it. In this discovery is 
 visible very extensive astronomical knowledge, and every appearance 
 of great accuracy. Such was its success in Greece, that the order 
 of the period was engraved in letters of gold, and at this day goes 
 by the name of the Golden Number. 
 
 Among the ancients, Eudoxus is particularly distinguished for his 
 
 knowledge, and also for his attention to astronomy. He built an 
 
 observatory at Cnidus, his birth-place, which was shown long after 
 
 his death. He invented a sphere, (which is called Eudoxus's sphere) 
 
 14 P 
 
158 HISTORY OF ASTRONOMY. 
 
 to show the rising and setting of the sun and raoon, &c. for the 
 climate of Greece. 
 
 He also composed two books on astronomy : the one was a des- 
 cription of the constellations, the other treated on the times of their 
 rising and setting. Aratus, by order of Antiochus, king of Macedon, 
 reduced all that was then known of astronomy into Greek verse* 
 anno B. C. 276. This poem is divided into two books, one of which 
 describes the sphere of Eudoxus ; the other gives rules for predicting 
 the weather. Both of these have reached us entire. 
 
 While astronomy made such great progress in Greece, it was 
 cultivated also by some of the Western nations of Europe. Pytheas* 
 a celebrated astronomer at Marseilles, observed in that city the 
 meridian altitude of the sun, at the time of the summer solstice, by a 
 gnomon for the purpose of determining the latitude of that place. 
 This man travelled to other parts of the globe, for the purpose of 
 observing the phenomena of nature. He mentions having visited an 
 island, which he calls Thule, where the sun rose presently after he 
 had set. As this is the case in Norway and Iceland, it is inferred 
 that he had reached those countries. 
 
 The same philosopher discovered that the Polar star is not pre- 
 cisely at the Pole itself. He likewise pointed out the connection of 
 the tides with the motion of the moon. 
 
 Alexander the Great, by his conquests, rendered great service 
 both to astronomy and natural philosophy. On these subjects 
 Aristotle wrote, by his order, a great number of books. In one of 
 these, entitled De Ccelo, he proves the spherical shape of the earth, 
 from the circular shadow it casts on the moon in eclipses, and also 
 from the difference of altitude observable on any of the fixed stars, in 
 travelling north or south. He wrote one called De Mundo, which 
 gives an account of the three quarters of the globe then known ; viz, 
 Asia, Africa, and Europe. 
 
 From this time, geography became, through its alliance with astro- 
 my, a real science. 
 
 Horace mentions that the earth had been measured before his 
 time; for he calls Archytas, who had been Plato's master, the 
 measurer of the earth. 
 
 But the first person who measured the earth by a method con- 
 sistent with the principles of geometry and astronomy, was Eratos- 
 thenes, librarian of the Alexandrian Museum. As this measurement 
 was performed in a somewhat curious manner, it may be gratifying 
 to the reader here to mention it, as it will serve to give some idea 
 how that has lately been performed in Europe. 
 
 Eratosthenes was informed, that, on the day of the summer sol- 
 stice, the sun was vertical at noon to the city of Syene, on the 
 borders of Ethiopia, under the tropic of Cancer. A well is parti- 
 cularly mentioned to have been illuminated to the bottom by the sun 
 at noon on the solstitial day. He knew likewise that Alexandria 
 and Syene were both under the same meridian. 
 
 From these data, by means of a concave hemisphere, with a stile 
 
HISTORY OF ASTRONOMY. 159 
 
 fixed in its centre, he found that the shadow of the meridian sun 
 paused by the stile at Alexandria, was one-fiftieth part of the whole 
 circumference. Hence he inferred, that the arc of the heavens 
 comprised between Alexandria and Syene must be the same ; and 
 that the distance between the two cities must likewise be a similar 
 arc, or one-fiftieth part of the circumference of the earth. On mea- 
 suring this distance, he found it to be 5000 stadia, which gave 
 250,000 stadia for the circumference of the earth. As there were 
 different stadia then in use, it is not well ascertained how many feet 
 a stadium contained. If it was the Egyptian stadium that was used, 
 this measurement exceeds the modern measures about a sixth part. 
 
 About the same time with Eratosthenes, flourished Aristarchus of 
 Samos, who has given a very simple method of determining the ratio 
 of the distance of the sun and moon from the earth, which, though 
 not very accurate, is yet ingenious. 
 
 Of all the ancient astronomers, no one has so much enriched the 
 science, or acquired so great a name, as Hipparchus, a native of 
 Nice in Bithynia, 142 B. C. 
 
 One of his first cares was to rectify the year, which before his 
 time was made to consist of 365 days six hours, which he found to 
 be a little too much. He also found that the sun was longer in tra- 
 versing the six northern signs of the ecliptic than the other half of it ; 
 and deduced from this the eccentricity of the solar orbit. 
 
 He likewise made similar remarks and calculations for the lunar 
 orbit. 
 
 From these data, he constructed tables of the motions of the sun 
 and moon, which are the first of the kind that are mentioned. 
 
 Hipparchus made another important discovery. He found that 
 the stars always preserved the same relative positions with respect 
 to each other ; but that they had all a trifling motion in the order of 
 the signs of the zodiac, which was about 48" in a year. He also 
 substituted a more complete mode of measuring the ratio of the 
 distance of the sun and moon from the earth, than the one given by 
 Aristarchus. He made use chiefly of parallaxes ; which is the 
 method now in use. On the disappearance of a very large star, he 
 set about numbering the stars, and to note down their configurations, 
 respective distances, &c. and gave a very good catalogue of them. 
 
 This immense labour laid the foundation on which the whole super- 
 structure of astronomy was to be raised, Jle was admired and 
 celebrated in all nations where learning was pursued. Hipparchus 
 was the first who applied this science to familiar purposes of the 
 greatest utility in geography, by determining the situation of places 
 by their latitudes and longitudes. 
 
 Cleomedes, who lived a little later than Hipparchus, has left a 
 work on the sphere, the periods of the planets, their distances and 
 magnitudes, with an accqunt of ancient eclipses, which he says he 
 derived the knowledge of from Pythagoras, Eratosthenes, and Hip- 
 parchus. This work is valuable, as it is the most ancient that has 
 reached us on the subject. 
 
 P 2 
 
160 HISTORY OF ASTRONOMY. 
 
 The next person that claims particular notice, was Julius Caesar, 
 who rendered an important service to the science of astronomy by 
 new-modelling the Roman calendar, B. C. 46 years. 
 
 Caesar appears to have been well versed in astronomy. He dis- 
 covered that autumn occupied the place of the winter months of the 
 calendar, and that winter occurred in the months of spring. He 
 invited the astronomer Sosigenes from Athens to Rome, to assist 
 him in correcting this disorder. They began by giving fourteen 
 months to the year of Rome, to re-establish the order of the seasons. 
 They likewise determined that the year should consist of 365 days 
 6 hours in future; but, as we shall afterwards see, this was making 
 the year too long by 11' 11" ; yet this was coming wonderfully near 
 the real length of the tropical year, considering the state of the science 
 at 'that time. This is still called the Julian year, out of compliment 
 to Julius Caesar. 
 
 Menelaus, a learned geometrician, A. D. 55, also distinguished 
 himself in astronomy, by the discovery of the principal theorems of 
 spherical trigonometry, which are applicable to the purposes of 
 astronomy. 
 
 Astronomy had begun to languish in the school of Alexandria, 
 when the celebrated Ptolemy made his appearance, in A. D. 140. 
 
 He was anativeofPelusium in Egypt, and, when very young, came 
 to Alexandria to study in that school. His principal work is enti- 
 tled the Almagest, an Arabic word which signifies the great collection. 
 It contains all the ancient observations and theories, to which his 
 own researches are added, and is considered as the most complete 
 collection of ancient astronomy that ever appeared. 
 
 Ptolemy embraced the common opinion, that the sun, moon, and 
 planets moved round the earth as their common centre. This system 
 continued to maintain its ground till the time of Copernicus, and has 
 descended from Ptolemy to the present day, under the name of the 
 Ptolemaic System. 
 
 Besides the Almagest, there exists another great work of Pto- 
 lemy's, his Geography, in which he determines the situation of 
 places by their latitude and longitude, according to the method of 
 Hipparchus. Ptolemy had the ambition, like Archimedes, to trans- 
 mit the remembrance of his labours to posterity by a public monument. 
 In the temple of Serapis, at Canopus, there is an inscription on 
 marble, in which are explained the hypothesis of his astronomical 
 system, such as the length of the year, the motions of the planets, 
 &c. If there have been men of greater genius than Ptolemy, there 
 is no man that ever collected a greater body of profound knowledge, 
 or more truly conduced to the progress of astronomy, considering the 
 age he lived in, and the time he wrote. 
 
 From Ptolemy to the time of the Arabs, no astronomer of the first 
 order is to be found amongst the Greeks, except, perhaps, Theon of 
 Alexandria, who wrote a learned commentary on the Almagest, 
 about the year 395. 
 
 Among the Arabs there have been many excellent astronomers. 
 
HISTORY OF ASTRONOMY. 161 
 
 As there was no science to which they devoted so much attention, 
 there were none in which they made so many discoveries. Their 
 Caliphs were particularly distinguished for their knowledge and 
 patronage of this science. They soon found that Ptolemy had stated 
 the obliquity of the ecliptic a little too great; and, after many obser- 
 vations, found it to be nearly what it is at present. 
 
 The Caliph Almansor the Victorious, who ascended the throne inf 
 754, ranks among the first of their astronomers. Haroun, his grand- 
 son, who reigned from 786 to 809, sent a present to Charlemagne of 
 a water clock, in the dial of which were twelve small doors, forming 
 the division of the hours. Each of these doors opened at the hour it 
 marked, and let out little balls, which, falling on a bell of brass, 
 struck the hours. The doors continued open till 12 o'clock, when 
 twelve little knights, mounted on horseback, came out together, 
 paraded round the dial, and shut all the doors. This clock at that 
 time astonished all Europe. 
 
 After Haroun, his son Al Maimon succeeded to the throne. He 
 also cultivated the study of astronomy. In his time there lived 
 several celebrated astronomers, among whom was Alfragan, who 
 composed several books on astronomy; and from his facility in cal- 
 culation, he was surnamed the Calculator. 
 
 Albategni was also among the greatest of the Arabian astronomers. 
 He found the year to contain only two minutes less then what it was 
 found to be by Dr. Halley six hundred years after. 
 
 After the Arabs had conquered the greater part of Spain, in the 
 year 1020, they built there many observatories to conduct their 
 observations. Alhazen, one of their astronomers, has left a treatise 
 on Optics, which contains the first established theory of refraction 
 and twilight which we have. 
 
 Among the Persians, also, there have been many eminent astro- 
 nomers. They made many observations to discover the real length 
 of the solar year, which they fixed at 365 days six hours. One of 
 their chief astronomers was the famous Ulugh Beg, grandson of 
 Tamerlane; he not only encouraged the sciences as a sovereign, but 
 was himself reckoned one of the most learned men of his age. To 
 determine the latitude of Samarcand, it is said he employed a quad- 
 rant, the radius of which was one hundred and eighty feet !* 
 
 He composed a catalogue of the stars, and several astronomical 
 tables, the most perfect then known in the east. He was assassi- 
 nated by his own son. 
 
 From the year 800 till the beginning of the fourteenth century, 
 almost all Europe was immersed in gross- ignorance. The only 
 people who paid any regard to science, was the Arabs that settled 
 in Spain, some of whom have been mentioned above. Profiting by 
 the books they had preserved from the wreck of the Alexandrian 
 
 * It is thought by many astronomers, that this must have been a gnomon in- 
 stead of a quadrant. 
 
162 HISTORY OF ASTRONOMY. 
 
 library, they cultivated and improved all the sciences, and particu- 
 larly astronomy, in which they had many able professors. 
 
 From the beginning of the ninth century to the year 1423, when 
 Purbachius appeared, there is no name that deserves to be mentioned 
 as contributing to the improvement of astronomy. Purbachius was a 
 man af great talents ; he began an Epitome of Ptolemy's Almagest, 
 but died before it war? completed. This was executed by his friend 
 and [pupil, John Muller, commonly called Regiomontanus. This 
 man made many observations, and collected the writings of many of 
 the ancient astronomers. He published ephemerides for thirty years 
 to come, wrote a theory of the planets and comets, and calculated a 
 table of signs and tangents for every degree and minute of the quad- 
 rant. He died in the year 1476. 
 
 Nicolas Copernicus j born 1473, rose next, and made so great a 
 figure in astronomy, that the true system discovered, or rather 
 restored by him, has been ever since called the Copernican System. 
 He revived the old system of astronomy taught by Pythagoras j 
 which had been set aside from the time of Ptolemy. His understand- 
 ing at once revolted against the explanations which that philosopher 
 had given of the motions of our planetary system ; and set about 
 correcting his mistakes, by laying the foundation of what is at this 
 day held to be the true system of the world. This system he gra- 
 dually improved by along series of observations, and a close attention 
 to the writings of ancient authors. His first grand work was printed 
 in 1543, under the care of Schoner and Osiander ; and he received a 
 copy of it only a few hours before his death, on the 23d May, 1543, 
 at the age of seventy years. 
 
 After the death of this great man, there were several astronomers 
 of considerable note, that greatly improved the science ; but the only 
 one that claims particular notice was Tycho Brahe, a Danish noble- 
 man, who was the inventor of a new system, a kind of semi-Ptolemaic, 
 which he vainly endeavoured to establish instead of the Copernican. 
 His numerous works shew that he was a man of great abilities ; and 
 it is to be regretted that he sacrificed his talents, artd perhaps his 
 inward conviction, to superstitious considerations. He restored the 
 earth to its fancied immobility, and made the sun and moon revolve 
 round it; but the planets he made to revolve round the sun, which 
 was a still more absurd hypothesis than that of Ptolemy. But we 
 ought to forgive this error, or rather weakness, in return for the many 
 observations and discoveries with which he enriched astronomy. 
 No man ever made more observations than Tycho Brahe. 
 
 Contemporary with Tycho fldurished several eminent astronomers, 
 among whom was the famous Kepler. To him we owe the true figure 
 of the orbits of the planets, and the proportions of the motions and 
 distances of the, various bodies which compose the solar system. 
 The three great Laws of Kepler may be said to be the foundation of 
 all astronomy. Kepler was born in 1 571 , and died in 1631. 
 
 Galileo was the next person who rendered any very important 
 services to astronomy. He was the first who applied the telescope 
 
HISTORY OF ASTRONOMY. 168 
 
 ta astronomical observations, and with it made many useful and 
 valuable discoveries. By the observations and reasoning of Galileo, 
 the system of Copernicus acquired a probability almost equivalent to 
 demonstration. By espousing the opinions of Copernicus, he drew 
 on him the vengeance of the Inquisition, who decreed that he should 
 pass his days in a dungeon ; but he was liberated after the expiration 
 of a year, on condition that he should never more teach or hold up 
 the Copernican as the true system of astronomy. He was born in 
 the year 1564, and died in 1642. 
 
 In spite of the Inquisition, or the passages in Scripture which were 
 always brought forward as objections to the motion of the earth, the 
 system of Copernicus gained ground every day. 
 
 Contemporary with Galileo were a number of astronomers, who 
 contributed to the progress of the science. Baron Napier published 
 his tables of logarithms in 1614. Bayer, also, obtaining great cele- 
 brity by the publication of his Uranometria, in which the stars were 
 designated by the letters of the Greek alphabet, which is still the 
 case on our celestial globes and planispheres. 
 
 Gassendi, a French philosopher, saw the planet Mercury on the 
 sun's disc, which was the first observation of the kind. A little after 
 this, in the year 1633, Mr. Horrox, an Englishman of very extraor- 
 dinary talents, discovered that Venus would pass over the disc of the 
 sun on the 24th November, 1639. This event he only mentioned to 
 one friend, a Mr. Crabtree; and these two men were the only persons 
 in the world who observed this transit, which was the first transit 
 of Venus that had ever been viewed by human eyes. Mr. Horrox 
 made many useful observations about this time, and had even formed 
 a new theory of the moon, so ingenious as to attract the attention of 
 Sir Isaac Newton. But the hopes of astronomers, from the abilities 
 of this extraordinary young man, were soon blasted, for he died in 
 the beginning of the year 1640, aged twenty-four years. 
 
 Hevelius, burgomaster of Dantzic, also rendered himself emi- 
 nent by his numerous and delicate observations. He founded an 
 observatory at Dantzic, and furnished it with a great many excellent 
 instruments, some of which were divided into so small divisions as 
 &. His observations on the spots of the sun, and on the nature of 
 comets, were very numerous ; and his catalogue of fixed stars, con- 
 taining the longitude of above 1888, was remarkable for its accuracy. 
 
 It is to him, also, we are indebted for the first accurate description 
 of the spots on the moon. 
 
 The improvement of the telescope continued to lay open new 
 sources of discovery. The celebrated Huygens constructed two 
 excellent telescopes, one of twelve feet in length, and the other 
 twenty- four, with which he discovered the fourth satellite of Saturn; 
 which he said afterwards led him to discover the ring that surrounds 
 that planet. Huygens was likewise the first person who applied 
 pendulums to clocks. He died in 1695, aged 66 years. 
 
 About this time the Royal Society of London, and the Royal 
 Academy of Paris, were establish^, each of which has produced 
 
164 HISTORY OF ASTRONOMY. 
 
 astronomers of the first order. The first person appointed to conduct 
 the observations at the royal observatory at Paris, was Dominic 
 Cassini, who soon after discovered the first, second, third, and fifth 
 satellites of Saturn. He also discovered that the planets Jupiter, 
 Mars, and Venus, turned round their axis in a manner similar to the 
 earth. He died in the year 1712. 
 
 The successive propagation of light, one of the most curious dis- 
 coveries in astronomy, was about this time made by Hoemer, a 
 Danish astronomer. This has ever since been accounted a most 
 essential element in astronomy, and must secure immortality to the 
 name of Roemer. 
 
 England, at all times, produced astronomers of the first order ; and 
 at this period it had to boast of Hook, Flamstead, and Halley. 
 
 Hook was born in 1635, and died in 1702. He was not only a 
 great observer in every branch of astronomy, but his inventive powers 
 have been exhibited in almost every branch of science. He was the 
 inventor of the Zenith Sector, an instrument which was used to deter- 
 mine whether or not the earth's orbit had any sensible parallax. He 
 gave the first hint of making a quadrant for measuring angles by 
 reflexion ; and he, in some measure, anticipated the discoveries of 
 Newton, by shewing that the motion of the planets resulted from a 
 projectile force, combined with the attractive power of the sun. 
 
 Flamstead was born 1646, and died in 1720. After the Royal 
 Observatory at Greenwich was finished, he was appointed by King 
 Charles II. to the management of it, with the title of Astronomer 
 Royal. He made a very great number of observations, which he 
 has recorded in his Historia Celestis, and in the Philosophical Trans- 
 actions. But the principal service he rendered astronomy, was by 
 forming a catalogue of 3000 fixed stars. 
 
 Flamstead was succeeded, in 1719, by Dr. Halley, the greatest 
 astronomer, says M. de la Lnnde, in England ; and Dr. Long adds, 
 " I believe he might have said the whole world/' He was sent by 
 King Charles II. to St. Helena, in order to form a catalogue of the 
 stars in the southern hemisphere, which was published in 1679. 
 While he was in the island of St. Helena, making this catalogue, he 
 had an opportunity of observing a transit of Mercury across the sun's 
 disc, by which he was enabled to point out the method of determining 
 the parallax of the sun. 
 
 On his way between Calais and Paris, he obtained a sight of the 
 famous comet that appeared in 1680, which suggested to him the idea 
 of writing a treatise on the subject of comets, in which he investigates 
 the orbits of these wandering bodies, and predicted the return of the 
 one that appeared in 1759, which is the only prediction of the kind 
 that ever was verified. It is said that during the nine years he was 
 at Greenwich, he made 1600 observations. Halley was acquainted, 
 either personally or by letter, with every astronomer of note in 
 Europe then living. He died in the year 1742, aged eighty-six years; 
 and was succeeded by Dr. Bradley, to whom we are indebted for two 
 of the most beautiful discoveries of which the science can boast the 
 
HISTORY OF ASTRONOMY. 165 
 
 aberration of light, and the nutation of the earth's axis. He also 
 made a great many observations, in order to discover if the fixed stars 
 had any sensible parallax. These observations are partly published, 
 and the remainder of them are in the hands of a Mr. Abraham Ro- 
 bertson, to whom their publication was entrusted. Bradley died in 
 the year 1762. 
 
 But to no individual is the science of astronomy more indebted than 
 to the celebrated Sir Isaac Newton. This great man was bom on 
 the 25th December, 1642, at Woolstrope in Lincolnshire. His dis- 
 coveries were not confined to astronomy alone ; for in mathematics 
 and natural philosophy he was equally great. His chief discovery in 
 astronomy was the law of gravitation, by which he was enabled to 
 account for some of the greatest phenomena in nature. His great 
 work the Principia, appeared in 1686. This work is one of the most 
 valuable books on physical astronomy that ever was published. His 
 discoveries are so numerous and important in this science, that the 
 solar system, or that restored by Copernicus, has received the appel- 
 lation of the Newtonian system. 
 
 In this country there have been several distinguished astronomers 
 since the time of Newton, among whom may be mentioned Dr. Long, 
 Dr. Keil, Dr. Bliss, Mr. Ferguson, Mr. Hadley, and Dr. Herschel ; 
 the latter of whom, for his many accurate observations, deserves to 
 be ranked among the first class of astronomers of any age or nation. 
 In the year 1781, on the 13th of September, he discovered the planet 
 Georgium Sidus. In the year 1787, he discovered two satellites 
 revolving round that planet; and in 1790 and 1794, he discovered 
 other two satellites. These discoveries of Herschel form a new era 
 in Astronomy. 
 
 Dr. Maskelyne, the late Astronomer Royal, has likewise rendered 
 very important service to the science. He was the first who proposed 
 to the Board of Longitude the publishing of an Ephemeris or Nautical 
 Almanack, which was begun in the year 1767. This almanack is 
 still continued annually, and has been of the utmost service to navi- 
 gation. 
 
 Dr. Maskelyne died a few years ago, and was succeeded by the 
 present Astronomer Royal, Mr. Pond, who is also a man of genius, 
 and promises to be of great service to astronomy. 
 
 On the continent also there have been many astronomers of great 
 talents since the time of Newton, particularly in France. Among 
 these, La Caille deserves to be mentioned with credit. He was born 
 in 1713, and in the year 1751 he undertook a voyage to the Cape of 
 Good Hope, for the purpose of perfecting the catalogue of the stars 
 in the southern hemisphere. After incredible labour and exertion, 
 he returned to Europe with a catalogue of 9800 stars, which were 
 comprehended between the south pole and the tropic of Capricorn. 
 In addition to these labours, La Caille calculated new tables of the 
 Sun, made observations on the parallax of Mars and Venus, on 
 atmospherical refraction, on the length of pendulums, and measured 
 a degree of the meridian during his stay at the Cape : he died in the 
 
166 HISTORY OF ASTRONOMY. 
 
 year 1762. Contemporary with La Caille lived several very eminent 
 astronomers, of whom may be mentioned Cassini, Bouguer, Conda- 
 mine, Maupertuis, and Clairaut, who were all employed soon after 
 this, in measuring degrees of the meridian in different parts of the 
 world. Professor Mayer, of Gottingen, deserves also to be men- 
 tioned, as contributing greatly to the improvement of the science, by 
 the excellent set of tables which he calculated for finding the place of 
 the moon, &c. These tables are now used in making the calculations 
 of the Nautical Almanack. His widow received 3000/. for them 
 from the British Government, on account of their great accuracy. 
 Mayer died in 1762, aged 41 years. ITAlembert also rendered great 
 service to astronomy by his indefatigable labours, particularly in 
 resolving the problem of the precession of the equinoxes. He died 
 1783. 
 
 Euler, one of the greatest geniuses and calculators that any age 
 or nation can boast of, ought to be associated with the history of 
 astronomy, as one of its most distinguished votaries and improvers. 
 By his many and accurate calculations, he has rendered the most 
 essential service, not only to astronomy, but to all the physical 
 sciences ; but his labours are too numerous to be detailed here. The 
 eighteenth century was distinguished by many other eminent astro- 
 nomers ; viz. Maclaurin, Simpson, Bernoulli, Lambert, Mason, Bos- 
 covich, De Lisle, Bailly, La Lande, &c. 
 
 The celebrated La Grange, who outlived most of his contempora- 
 ries, was born at Turin in 1736, and has enriched astronomy with 
 some of the most splendid discoveries of which it can boast. The 
 subjects of his researches in this science were, the theory of Jupiter's 
 satellites, the motions of the planets, and their action on each other, 
 which he determined with great accuracy. 
 
 As the labours of the most distinguished astronomers that have 
 appeared in the world have now been briefly noticed, and of whom 
 their labours are the only memorials that exist ; all that remains to 
 complete this short account of the improvements that have taken 
 place in the science, down to the present day, is to mention the 
 labours of a few individuals still alive. 
 
 La Place has also distinguished himself by his labours to improve 
 astronomy, particularly in solving the problem of the tides, in adding 
 some new corrections to the lunar tables, and some discoveries 
 respecting the precession of the equinoxes. He also ascertained the 
 mean depth of the sea to be four leagues. 
 
 The name of Troughton ought also to be mentioned ; for to nq 
 individual of the present age is practical astronomy more indebted 
 than to this distinguished artist. The great improvements he has 
 made upon astronomical instruments, has rendered his name cele- 
 brated in every country in Europe. There is scarcely an observatory 
 of note to be found that does not contain some of Mr. Troughton's 
 instruments. 
 
 The labours of Dr. Olbers, Harding, and Piazzi, will be noticed 
 in treating of the new planets. 
 
SUPPLEMENT 
 
 TO 
 
 ASTRONOMY 
 
 AS IT IS, COMPARED WITH WHAT IT WAS 5 
 
 CONTAINING, 
 
 THE USE OF ASTRONOMICAL INSTRUMENTS, 
 
 of computing tije Notes of tfie GTaUnlrar, 
 
 THE MAGNITUDES, PERIODS, AND DISTANCES OF THE SUN, MOON, 
 PLANETS, &c- 
 
 INTRODUCTION. 
 
 THE Work, to which the following pages fprm a Supplement, 
 being entirely confined to what may be termed the Descrip- 
 tive and Historical parts of Astronomy, it was thought it 
 might tend to make the work still more generally useful if it 
 contained a description of Astronomical Instruments, and a 
 short account of the Calendar. In order to accomplish this, 
 without interfering with the plan proposed for treating of 
 the various branches of Astronomy in a systematic and 
 popular manner, it was found that a Supplement was necesr 
 sary. This has therefore been added, and will be found to 
 form a very valuable addition to the Work itself. 
 
 The principal instruments used in the practical part of 
 Astronomy are not only represented by figures and described 
 at considerable length, but many other subjects connected 
 
INTRODUUCTION. 
 
 with Astronomy have been introduced, which could not have 
 been noticed in a work purely astronomical. Among these 
 will be found several interesting essays on Meteorology and 
 Physical Geography, accompanied with diagrams, which 
 cannot fail to render the subjects perfectly level to the un- 
 derstanding of the humblest inquirer after scientific infor- 
 mation. 
 
 An acquaintance with the Calendar, and the manner of 
 computing the common Notes of the year, is so useful to 
 every class of society, that the rules contained in the fol- 
 lowing pages, for effecting this, cannot fail to gratify all 
 who wish to possess the slightest acquaintance with As- 
 tronomy. 
 
 The manner of calculating most of the fundamental Ele- 
 ments employed in Practical Astronomy have been added, 
 with the view of rendering the work not only more complete, 
 but to induce the astronomical reader to enter more deeply 
 into this beautiful and highly interesting branch of the science. 
 To those who have made some progress in the study of As- 
 tronomy, and who are in some degree judges of works which 
 treat of the practical parts of the science, this will perhaps 
 be considered the most valuable part of the Work. 
 
ASTRONOMY, 
 
 AS IT IS KNOWN AT THE PRESENT DAY. 
 
 On Astronomical Tables. 
 
 IN constructing tables for computing, at any given instant, the places 
 of the sun, moon, and planets, the first step is to determine, from a 
 series of accurate observations, the time in which those bodies des- 
 cribe a space of 360, or perform a complete revolution round the 
 sun, or the primary planet. 
 
 When this important element is exactly ascertained, we can easily 
 find, by simple proportion, the space which the planet describes in 
 any number of years, months, days, minutes, or seconds, upon the 
 supposition that it moves uniformly, or describes equal spaces in 
 equal times in the circumference of a circle. This is called the 
 mean motion of the body. 
 
 The next thing to be settled is the epochs, or radical places of the 
 planet, which is nothing more than its longitude upon the supposition 
 of its motion being uniform, at certain epochs of time, from which 
 the calculations are supposed to commence. These epochs of time, 
 or mean longitudes, are generally put down in Astronomical tables 
 of the noon of the 1st of January of each year. These elements are 
 all which would be necessary for computing the longitude of a planet, 
 if it moved uniformly in a circular orbit ; but as all the bodies of the 
 solar system move in eliptical orbits round the sun, or their primary 
 planet, placed in one of their foci, we must next determine the form 
 of their orbits, or the nature of the elipse which they describe. This 
 may be done in the case of the sun and moon, by observing the va- 
 riations of their apparent diameters during a complete revolution ; 
 their distance from the earth being inversely proportional to the angle 
 they subtend. 
 
 The ratio of their greatest and least diameters is a measure of the 
 relation between their greatest and least distances, and consequently 
 enables us to ascertain the eccentricity of their orbits. The same re- 
 sults may be obtained by observing the spaces described by the 
 planets during equal intervals of time. As the areas described by 
 the radius vector of a planet are proportional to the times, equal 
 areas will correspond to equal angles, if the planet moves in a cir- 
 cular orbit. The observed inequalities, therefore, in the case of an 
 eliptic orbit, being the effect of the eccentricity of the orbit, will 
 
*2 ASTRONOMY, &C. 
 
 enable us to determine that important element. If we, therefore, 
 suppose that the real planet moves with different velocities in an 
 eliptical orbit, while a fictitious planet sets off from the peregee at the 
 same instant, and describes a circular orbit, with an uniform motion, 
 in the same time that the real planet describes the eliptical orbit, we 
 shall obtain a simple explanation of the inequalities arising from the 
 eliptical motion of the body. At no place of the orbit will these two 
 planets be together, but when they are in Peregee and Apogee, or 
 when the real planet is at its greatest and least distances from the sun. 
 
 The angular distance, at any time, between the real and fictitious 
 planet, is called the Equation of the Centre. 
 
 This is greatest when the fictitious planet is at that part of its orbit, 
 where a line drawn from it to the line of the Apsides forms a right 
 angle, or where the real planet is at its mean distance. From the 
 Perihelionto the Aphelion, the real planet will be before the fictitious ; 
 but from its Aphelion to its Perihelion, it will be behind the ficti- 
 tious planet. During the motion of the real planet from the Aphe- 
 lion to its Perihelion, the mean place has been farther advanced than 
 the true place ; and therefore the equation of the centre must be sub- 
 tracted from the mean longitude, to obtain the true longitude of the 
 planet; but from the Perihelion to the Aphelion it must be added, 
 because the mean place is behind the true. The equation of the 
 centre obviously depends on the mean anomaly of the planet, or its 
 distance from the apogee, which, in all the primary planets except 
 Venus, has a motion according to the order of the signs. By deter- 
 mining, therefore, the place of the apogee, and subtracting its longi- 
 tude from that of the planet, we obtain the mean anomaly of the 
 planet; with which, as an argument, we find from the Tables the 
 corresponding equation of the centre, which, applied to the mean 
 place of the planet, gives its longitude in an eliptical orbit. 
 
 This result would be the true place of the planet in its orbit, if its 
 motion were not influenced by any disturbing force ; but, owing to 
 the mutual action of the planets, their motions are sometimes acce- 
 lerated, and at others retarded; and therefore the longitudes of these 
 bodies must be still farther corrected. 
 
 Ih determining the places of the planets, we must compute also 
 their latitudes or distances from the ecliptic, which must evidently 
 depend On the distance of the planet from its node. As the nodes of 
 all the planetary orbits have a retrograde motion along the ecliptic, 
 the radical place of the node, or its position at any particular time, 
 must first be ascertained ; and its retrograde motion being known, we 
 can obtain the longitude of the node at any time, and consequently 
 the distance of the planet from the node. When the distance from 
 the node is 0, the latitude will be nothing ; and when the distance 
 from the node is a maximum, or 3 or 9 signs, the latitude is also a 
 maximum, Or equal to the inclination of the planet's orbit to the 
 ecliptic. 
 
 The places of the primary planets computed in the manner which 
 h here described, are evidently their heliocentric places, or their 
 places as seen from the sun. The geocentric place of the planet, or 
 
DOUBLE STARS. 3 
 
 its place as seen from the earth, may be readily found by the so- 
 lution of a triangle, formed by lines joining the sun and planet, the 
 sun and earth, and the planet and the earth. The angle at the sun 
 is equal to the difference between the heliocentric longitude of the 
 earth and the planet. One of the sides of the triangle is equal to the 
 distance of the earth from the sun, and the other is equal to the dis- 
 tance of the planet from the sun ; so that from these data, the angle 
 formed at the sun, or the difference between the geocentric place of 
 the sun, and the geocentric place of the planet, may be easily ob- 
 tained ; or we may obtain the angle formed at the planet, which is 
 the difference between its heliocentric and geocentric place. 
 
 On the Changes that have happened in the relative situation of 
 Double Stars. 
 
 THE late Sir W. Herschel remarks, that the affections of the 
 newly-discovered celestial bodies extend our knowledge of the con- 
 struction of the solar system, which is the one best known to us ; and 
 proceeds to support, by the evidence of observation, the opinion, 
 which he has before advanced, of the existence of binary sidereal 
 combinations, revolving round the common Uentre of gravity. Dr. 
 Herschel first considers the apparent effect of the motion of either of 
 the three bodies concerned, the two stars, and the sun with its at- 
 tendant planets ; and then states the arguments respecting the mo- 
 tions of a few only out of the fifty double stars, of which he has as- 
 certained the revolutions. The first example is Castor, or Alpha 
 Geminorum : here Dr. Herschel stops to show how accurately the 
 apparent diameter of a star, viewed with a constant magnifying 
 power, may be assumed as a measure of small angular distances ; he 
 found that ten different mirrors, of seven feet focal length, exhibited 
 no perceptible difference in this respect. In the case of Castor, no 
 change of the distance of the stars has been observed, but their an- 
 gular situation appears to have varied somewhat more than 45 since 
 it was observed by Dr. Bradley in 1759 ; and they have been found 
 by Dr. Herschel in intermediate positions at intermediate times. Dr. 
 Herschel allows that it is barely possible that a separate proper mo- 
 tion, in each of the stars and in the sun, may have caused such a 
 change in the relative situation, but that the probability is very deci- 
 dedly in favour of the existence of a revolution. Its period must be 
 a little more than 342 years, and its plane nearly perpendicular to 
 the direction of the sun. The revolution of Gamma Leonis is sup- 
 posed to be in a plane considerably inclined to the line in which we 
 view it, and to be performed in about 1200 years. Both these revo- 
 lutions are retrograde ; that of Epsilon Bootis is direct, and is sup- 
 posed to occupy 1681 years, the orbit being in an oblique position 
 with respect to the sun. In Zeta Herculis, Dr. Herschel observed, 
 in 1802, the appearance of an occultation of the small star by the 
 larger one ; in 1782 he had seen them separate ; the plane of the re- 
 volution must therefore pass nearly through the sun ; and this is all 
 
4 ASTRONOMY, &C. 
 
 that can at present be determined respecting it. The stars of Delta 
 Serpentis appear to perform a retrograde revolution in about 375 
 years : their apparent distance is invariable, as well as that of the 
 two stars which constitute Gamma Virginis, the last double star 
 which Dr. Herschel mentions in this paper, and to which he attri- 
 butes a periodical revolution of about 708 years. 
 
 On the great Corona, or Circles which sometimes surround the Sun 
 
 and Moon. 
 
 As it may be satisfactory to some of our readers to know the 
 opinion of so celebrated a Meteorologist as Mariotte on the cause of 
 the circular ring which sometimes appears round the sun and moon, 
 we shall present them with the following extract from his work on 
 Colours : 
 
 " Sometimes, when the air is pretty serene, a circle of about 45 
 diameter is seen round the sun or moon ; the colours are not in ge- 
 neral very lively, the blue is without, and the red within; their 
 breadth is nearly as in the common external rainbow. 
 
 " Explanation. I take for the cause of this appearance small 
 filaments of snow, moderately transparent, having the form of an 
 equilateral triangular prism. I conjecture that the smaH flat flakes 
 of snow which fall during a hard frost, and which have the figure of 
 stars, are composed of little filaments like equilateral prisms, parti- 
 cularly those which are like fern leaves, as is easily seen by the mi- 
 croscope. I have often looked at the filaments which compose the 
 hoar frost, that appears like little trees or plants in the cold mornings 
 of spring and autumn, and I have found them cut into three equal 
 facets ; and when viewed in the sunshine, they exhibited rainbow 
 colours. Now it is very propable that, before these little figures of 
 trees or stars are formed, there are floating among the thin vapours 
 in the air some of these separate prisms, which, when they unite, 
 form the compound figures. These little stars are very thin, and 
 very light, and the little filaments, which compose them, are still 
 more so, and may often be supported a long time in the air by the 
 winds : hence when the air is moderately filled with them, so as not 
 to be much darkened, many of them, whether separate or united, will 
 turn in every direction as the air impels them, and will be disposed 
 to transmit to the eye for some time a coloured light, nearly like to 
 that which would be produced by equilateral prisms of glass/' 
 
 On Meteoric Stones. 
 
 IT had long been conjectured by several persons in this country, 
 that the stones said to have fallen from the air, on different parts of 
 the earth, and lately analysed by Mr. Howard, might originally have 
 been emitted by lunar volcanos facing the earth ; and meeting with 
 little or no resistance from the moon's atmosphere, might have risen 
 to such a height, as to be more powerfully attracted by the earth than 
 
ASTRONOMICAL INSTRUMENTS. 5 
 
 by the moon, and, of consequence, to be compelled to continue their 
 course, until they arrived at the confines of our atmosphere, and were 
 again retarded by its resistance. 
 
 The idea has been lately renewed in France by Laplace; and the 
 inflammation and combustion of the stones has been attributed to the 
 intense heat which must necessarily be extricated by so great a com- 
 pression of the air, as would be produced by the velocity with which 
 these bodies must enter the atmosphere. 
 
 Mr. Biot has calculated, that an initial velocity, about five times 
 as great as that which a cannon ball sometimes receives, would be 
 sufficient for the projection of a body from a lunar volcano into the 
 limits of the earth's superior attraction, which are situated at nearly 
 one-ninth of the distance of the earth from the moon. 
 
 A body, entering the atmosphere with such a velocity, would soon 
 experience a resistance many thousand times greater than its weight, 
 and the velocity would therefore soon be very considerably lessened. 
 It may easily be shown, that a stone of moderate dimensions could 
 scarcely retain a velocity of above 200 feet in a second. With re- 
 spect, however, to the actual probability of the stones in question 
 having been projected from the volcanos of the moon, there will, per- 
 haps, long be a diversity of opinion ; and, in the absence of all ac- 
 curate knowledge on the subject, it would, perhaps, be unphiloso- 
 phicalto attempt to establish any theory respecting their origin. 
 
 Upon the Precision to be attained with Astronomical Instruments. 
 
 MR. AMICI, in a letter addressed to Baron Zach, affirms, that, on 
 a circle of 3 feet, one cannot, even with the aid of a vernier and 
 simple microscope, discern two or three seconds, even though the 
 instrument be mathematically divided with the utmost precision. 
 " To prove this," says he, " I draw upon a sheet of white paper 
 two thick vertical lines of ^ an inch, in such a manner, that the 
 right side of one is parallel with the left of the other. These two 
 lines may be considered as belonging, one to the limb of the instru- 
 ment, and the other to the vernier. I place this paper in a very 
 strong light, and I raise myself perpendicularly from it to the dis- 
 tance of 28 feet ; I look at these lines with one eye, and I see them 
 united as though there were but one line. Here then is the utmost 
 extent of my sight, at which I judge the lines to be joined, although 
 in reality there is a distance equal to their own length between them. 
 This limit expressed by the angle formed by the object in the eye of 
 the observer answers to 51 seconds ; but in a circle of 3 feet in dia- 
 meter, the arc of a second occupies 0-001 of a line ; and this arc 
 forms in the eye of an observer, furnished with a simple microscope, 
 of an inch focus, an angle of 17 seconds, consequently invisible 
 to me." 
 
 Mr. Amici closes his letter by remarking, that no astonishment 
 ought to be excited at the inaccuracies to which the most experienced 
 astronomers are subject, making a difference of from 1 to 5 seconds, 
 
 b 
 
6 APPARENT SIZE OF OBJECTS. 
 
 if due attention be paid to the errors which are likely to result from 
 the optical parallax between the divisions of the limb and those of 
 the vernier ; the inequalities of the lines which form those divisions 
 rendering their union equivocal and doubtful ; the reflexion of the 
 glasses; the unequal expansion of the metal ; and the irregularity of 
 the surface or levels. 
 
 Upon the apparent Size of Objects caused by the Refraction of Light 
 in passing through the Atmosphere. By JEAN MILE, Professor of 
 Physiology. 
 
 THE author, in a letter addressed to Mr. J. C. Skrodzki, Professor 
 of Physic at Varsovie, recalls to his recollection, that, after having 
 gone through the explanation of this well-known phenomenon, they 
 were mutually convinced of their insufficiency. He therefore pro- 
 poses an explanation founded upon the refraction of light, which 
 enables us to perceive objects situated beyond the limits of our at- 
 mosphere. This refraction not only enables us to see objects in a 
 situation different from their real position, but it also changes their 
 real size. This latter effect resembles the former in this, that the 
 nearer the objects are to the horizon, the greater is their apparent 
 size ; or, what amounts to the same thing, the greater their distance 
 from the zenith, so in proportion is their size. The rays of light which 
 traverse the air through a denser medium than itself, terminated by 
 plane or parallel surfaces, follow, in issuing from the latter, a direc- 
 tion parallel to their incidence. But it has been falsely concluded 
 in this case, that the object is seen under the same angle as though 
 the rays had only passed through one medium. The author affords 
 us eight successive theorems, which he links with each other, and 
 the last of which explains the phenomenon of the apparent size of 
 objects. 
 
 Theorem 1st. An object and the observer being situated in the air, 
 should the visual rays which pass from the one to the other traverse 
 an intermediate medium, terminated by plane surfaces, the visual 
 angle will become greater. 
 
 He gives a demonstration of this upon mathematical principles, 
 which would be too long to be inserted here. The following expe- 
 riment, however, will render his axiom perfectly comprehensible. 
 Procure a tin tube, three inches in diameter, and a yard in length, 
 the two ends of which must be closed with plain glass. The tube is 
 then to be placed in a horizontal position, and half filled with spirits 
 of wine, that is to say, to its central axis; and if an object then be 
 viewed through the tube, that half of the object which is seen through 
 the medium of the spirits of wine will appear to be much larger than 
 the half seen through the air alone. In general, the degree of aug- 
 mentation is in a direct ratio to the depth of the refracting medium, 
 and consequently depends in this instance upon the length of the tube. 
 
 Theorem 2d. The visual angle will never change, so long as the 
 rays from the surfaces are spherical ; and their radii will be respec- 
 
APPARENT SIZE OF OBJECTS. 7 
 
 lively equal to the distance of the eye to each of them ; in fact, the 
 eye being situate at the centre of the curves which terminate the me- 
 dium, the visual rays proceeding in the same direction will not be 
 subject to the slightest deviation. The object then will be seen under 
 the same angle. This may be proved by the following experiment. 
 A conical shaped tube of tin may be half rilled with spirits of wine, 
 as mentioned above, and each end enclosed with watch glasses of 
 different diameters, and then placing the eye in the direct centre of 
 the two spherical surfaces in the front of the tube. 
 
 Theorem 3d. The visual angle will become smaller when the radii 
 from the surfaces are spherical, and are respectively smaller accord- 
 ing to the distances of the eye from them. This may be easily proved 
 by the above-mentioned apparatus, by placing the eye at a greater 
 distance from the central point of the termination of the two spherical 
 surfaces. 
 
 Theorem 4th Is the converse of the preceding one ; that is to 
 say, the visual angle is greater when the radii from the surfaces, 
 are spherical, which terminate the refracting medium, and are respec- 
 tively greater than the distance between the eye and each of them. 
 This is also to be proved by the before-mentioned apparatus, by 
 placing the eye at a less distance from the tube than that between its 
 centre and the termination of its spherical surfaces. 
 
 Observation. Should the medium in which the eye is situated be 
 of greater density, the refraction will occasion phenomena directly 
 the contrary. This is the case with the objects placed beyond the 
 limits of our atmosphere. 
 
 Theorem 5th. The surfaces of the refracting medium being sphe- 
 rical, and their radii being equal to the distance of the eye from each 
 of them, the visual angle will not be changed. This would be the 
 case were the eye situated at the centre of the earth, which is physi- 
 cally impossible. 
 
 Theorem 6th. If the distance of the eye be greater than the radius 
 of the surface of the refracting medium, the visual angle will become 
 greater. This would be the case were an observer situated in such a 
 manner that the centre of the earth intervened between him and the 
 celestial bodies, which is physically impossible. 
 
 Theorem 7th. If the distance ot the eye be less than the radius of 
 the refracting surfaces, the visual angle would be less. This is what 
 always takes place, at least, when we look at the celestial bodies. 
 
 Theorem 8th. Although the heavenly bodies ought to appear 
 much smaller when seen from the surface of the earth, owing to the 
 refraction of light, still the degree of diminution of the visual angle 
 depends upon the greater or less extent of the refracting medium, 
 that is, the atmosphere ; the diminution of the visual angle, there- 
 fore, is less according as these limits are more extended. Hence it 
 results, that the heavenly bodies appear to us so much the larger, in 
 proportion as the limits of the atmosphere are extended. These bo- 
 dies, therefore, will increase in size in proportion to the increase of 
 their distance from the zenith ; for the nearer they approach the 
 horizon, the more extensive are the limits of the atmosphere, thougU 
 
8 METEORS, &C. 
 
 the observer must behold them when he is situated upon the surface 
 of the earth. We may hence perceive the reasons why, when the 
 sun is invisible, the densest clouds appear to be at the horizon ; why 
 the clouds which are driven by the wind towards the zenith decrease 
 in magnitude the higher they rise ; why, when the sun is momentarily 
 hid by the clouds, the rays appear to accumulate at the point where 
 he is situated, although, in reality, they are parallel to one another. 
 The explanation of the beautiful phenomenon of the Aurora Borealis 
 is capable also of receiving a slight modification. 
 
 Upon the Meteors which play round the Earth. 
 
 PROFESSOR MEINECKE, in a paper read to the Society of Natural 
 History at Halle, in Germany, proves, in various ways, the existence 
 of an inferior or subterrestial atmosphere. He considers himself borne 
 out by reasons, which he alleges to conclude with certainty, that an at- 
 mosphere which can penetrate to the depth of 20 geographical miles 
 is already compressed at a less depth, to a degree at which, without 
 being liquid, forms a fluid equivalent to water. Hence there results 
 to the interior parts of the earth an atmosphere, in comparison with 
 which the common atmosphere will appear to be of a very light de- 
 scription, which, as is known, is equal to a column of water 30 feet 
 high, or thereabouts. 
 
 It is to this mass of interior air, which pervades the pores of fos- 
 sils, exists in the cavities and abysses of the earth, and forms like- 
 wise a portion of the elementary parts of fossils, that Professor 
 Meinecke attributes the greater part of meteors ; while the mass of 
 light air universally disseminated in the form of a vapour, and which 
 is called atmosphere, contributes but in a very small degree to their 
 appearance. As he attributes the barometrical phenomena to the 
 subterrestial atmosphere, he denies at the same time the influence of 
 the moon upon the weather. 
 
 On the Change of the Place of the Fixed Stars. 
 
 IT appears from a paper by Mr. Pond, Astronomer Royal, lately 
 read before the Royal Society, that he thinks that his observations 
 lead to the conclusion that some variation, either continued or peri- 
 odical, takes place in the siderial system, which, producing but very 
 small deviations in a finite portion of time, has hitherto escaped 
 notice. The nature of this motion appears to be such, that the stars 
 are now mostly found a considerable quantity to the southward of 
 their computed places. With respect to the laws by which these 
 motions are governed, Mr. Pond admits that his observations are 
 not sufficiently exact to throw any light upon the subject. 
 
ASTRONOMICAL AND GALILEAN TELESCOPES. 
 
 Astronomical Telescope. 
 
 THE Astronomical Telescope which was invented by Kepler is 
 represented by the following figure. 
 
 It consists of two convex glasses placed in a tube ; the one next 
 the object is called the object-glass, and the one next the eye, as 
 B E, the eye-glass, which is always of a much less focal length than 
 the object-glass. The focal length of the object-glass is a little 
 greater than the tube into which it is screwed, and the eye-glass is 
 fixed into a small tube, which can be moved out and in at the other 
 extremity of the longer tube. When such an instrument is directed 
 to a distant object, and distinct vision obtained by adjusting the 
 tube containing the eye-glass, the magnified object is formed by the 
 rays ABC and DEC, which come from the extremities of the visi- 
 ble field through the middle of the object-glass, and produce an in- 
 verted image nearly in the principal focus of the eye-glass, through 
 which this image is viewed as by a simple microscope, and therefore 
 still remains apparently inverted. This, however is not considered a 
 disadvantage by astronomers, and therefore it has received the name 
 of the astronomical telescope. 
 
 In order to find the magnifying power, we must divide the focal 
 length of the object-glass by that of the eye-glass : this quotient is 
 consequently the greater as the focal length of the object-glass is 
 greater, and as that of the eye-glass is smaller ; but the power of the 
 instrument cannot be increased at pleasure by lessening the focal 
 length of the eye-glass, because the object-glass would not furnish 
 light enough to render the view distinct, if the magnifying power 
 were too great. 
 
 Galilean Telescope. 
 
 The Galilean Telescope received its name from its having been 
 first used by Galileo, and differs in no respect from the astronomical 
 telescope, excepting in the substitution of a concave eye-glass in 
 place of a convex eye-glass. This eye-glass is placed between the 
 object-glass and its principal focus, and receives the converging rays 
 before they form the image. 
 
 The magnifying power of this telescope will be equal to the focal 
 length of the object-glass divided by that of the eye-glass ; for the 
 extreme pencils which were formerly made to converge, are now 
 made to diverge. 
 
GALILEAN TELESCOPE. 
 
 This telescope possesses some advantages over the astronomical 
 telescope. 1st. It has the same magnifying power under a 
 shorter length, the length of the telescope being equal to the dif- 
 ference of the focal lengths of the object-glass and the eye-glass, 
 whereas in the astronomical telescope it is equal to their sum. 2d. 
 It gives us an erect view of the object without using three eye- 
 glasses, which must occasion a great loss of light, even if the lenses 
 are ground to a perfect figure. 3d. There is less absorption of 
 light, in consequence of the rays passing through a less thickness of 
 eye-glass ; and 4th, the vision is much more perfect ; a circumstance 
 which no doubt arises from the rays never coming to a positive focus, 
 and never crossing one another in a condensed state during the whole 
 of their progress through the instrument. For it cannot be doubted 
 that the rays of light, notwithstanding their extreme tenuity, interfere 
 with one another, and produce an indistinctness of vision. 
 
 The disadvantages of the Galilean telescope arise solely from its 
 limited field of view since the lateral pencils now diverge from the axis 
 of the lenses, the field of view depends solely on the diameter of the 
 pupil of the eye, and as this cannot be increased at pleasure, there 
 are no means of remedying this evil in the Galilean telescope. 
 
 The imperfections of the common refracting telescope with a single 
 object-glass, are so great, that in order to obtain a high magnifying 
 power, it is necessary to use object glasses of a great focal length, 
 such as those of Huygens, some of which were not less than 24 feet 
 in length** 
 
 It follows from the theory of aberration* arising from the spherical 
 figure of the surface, that the apparent indistinctness of a given 
 object seen through a refracting telescope, is directly as the area of 
 the object-glass, and inversely as the square of the focal distance of 
 the eye-glass. In like manner, it may be shown, that the apparent 
 brightness of a given object is directly as the square of the lineal 
 aperture of the object-glass, and inversely as the square of its mag- 
 nifying power. Hence, it follows, that in refracting telescopes of 
 different lengths, a given object will appear equally bright, and 
 equally distinct, when their linear apertures, and the focal distances 
 of the eye-glasses, are as the square roots of the focal distances of 
 their object-glasses, and consequently their magnifying powers will 
 be as the square roots of the focal distances of the object-glasses. 
 
 Upon these principles, we may compute the focal distance of ihe 
 eye-glasses suited to object-glasses of different focal lengths, pro- 
 vided we have once ascertained by experiment the highest magnify- 
 ing power that an object-glass of a given focal length will bear with 
 perfect distinctness. One of Huygen's best telescopes, 30 feet long, 
 had an aperture of three inches, with an eye-glass three inches and 
 three-tenths in focal length; and from this telescope, as a standard, 
 the editors of his Dioptrics computed the table given in p. 211 of 
 that work, and reprinted by Dr. Smith in the 148th page of the first 
 
 * This excellent astronomer while in England presented the Royal Society 
 with two object-glasses, one of which had a focal length of 120, and the other of 
 i23 feet* 
 
METEORS, OR FALLING STARS. 11 
 
 Volume of his Optics. It appears, however, from the Astroscopia Com- 
 peiidiari of Huygens, that he possessed a telescope superior even to 
 this, whose object-glass was 34 feet in focal length, and which had a 
 magnifying power of 163 times, with an eye-glass of 2 inches focal 
 length. 
 
 In order to render the common refracting telescope as perfect as 
 possible, without making it achromatic, the spherical aberration 
 should be reduced by grinding the exterior surface of the object-glass 
 to a radius equal to Jive-ninths of its focal length, and the interior 
 surface to a radius equal to Jive times its focal length. In the eye- 
 glasses, the radius of the surface next the object should be nine 
 times its focal length, and that of the surface next the eye, three- 
 fifths of the same distance. 
 
 When the object to which the telescope is directed is luminous, 
 such as the Sun, and Jupiter, and Venus, when they are near the 
 earth, considerable advantage may be derived from the use of red or 
 green eye-glasses ; or, if the telescope is large, from the interposition 
 of plane pieces of green and red glass. 
 
 On Meteors, or Falling Stars. 
 
 THESE bodies appear to be of different magnitudes, and even of 
 various forms, though this last circumstance may perhaps be the 
 effect of optical deception. In general they seem to be globular, 
 continuing visible only for a few seconds, and moving with great ve- 
 locity. Their course is on some occasions in a straight line, and on 
 others curvilineal, rendered more distinct by the tail or luminous train 
 which they leave behind them; and before disappearing they .are 
 sometimes separated into several smaller bodies, accompanied with 
 an explosion resembling thunder, more or less loud according to 
 their magnitude or distance. It was long supposed, and has now 
 been proved by the most incontrovertible evidence, that these explo- 
 sions are followed by a shower of solid bodies of a stony or metallic 
 substance, some of which have appeared luminous even in their descent 
 after the explosion, and have been taken up before they had time to 
 cool. This last phenomenon, indeed, is of comparatively rare oc- 
 currence. Thousands of small meteors, as various in magnitude and 
 brilliancy as the fixed stars, have been seen in all seasons, and in 
 almost every variety of weather, unaccompanied either with explo- 
 sions, or the deposition of solid substances ; nor is it certain that 
 even the larger and more luminous meteors, such as that of 1783, 
 described by Cavallo, or one in 1811, an account of which was given 
 by Professor Pictet in the Bibliotheque Britannique for May, 1811, 
 are always followed by a fall of meteoric stones. On the other hand, 
 these stones have sometimes been observed to fall after a loud detona- 
 tion, when no meteor was visible, though this may perhaps be ac- 
 counted for. from its having been obscured either by the superior 
 Jight of the sun, or the intervention of clouds. But however this 
 
12 METEORS, OR FALLING STARS. 
 
 may be, the appearance of large meteors, and the fall of meteoric 
 stones, or, as they have very improperly been called, aeroliths, are 
 phenomena that appear to be closely connected, and this is almost 
 all that is known upon the subject. Whether they are all of the 
 same origin, but varying in appearance, in consequence either of 
 their different distances, or of some peculiar state of the atmosphere, 
 or whether they are essentially different in their nature, are questions 
 to which, in the present state of metereological science, no answer 
 can be given. As prognostics of the weather, they have in general 
 been supposed to predict wind, as appears from various passages in 
 ancient authors ; and it is also commonly believed, that the wind 
 which follows will blow from the point of the compass towards 
 which the meteor is observed to move. One at least of the various 
 hypotheses which have been proposed to account for these pheno- 
 mena is interesting, inasmuch as it appears to explain, in certain 
 cases, the connection between the motion of the meteor and the di- 
 rection of the wind. 
 
 The hypothesis to which we allude, is that which ascribes meteors 
 to certain vapours arising from the earth, and becoming ignited in the 
 higher regions of the atmosphere. The origin of this opinion may 
 be traced to Aristotle ; but from the discoveries in chemistry, of 
 which that author was in a great measure ignorant, it has assumed, 
 in the hands of the modem philosopher, a more definite form. Halley, 
 and after him De Luc, has endeavoured, on this principle, to account 
 for some at least of the circumstances attending the appearance of 
 luminous meteors. The latter supposes that falling stars proceed 
 from a phosphoric fluid, ascending from some spot of the surface of 
 the earth, which becomes visible only when, by decomposition in the 
 higher regions, it takes fire, and light is disengaged. If such a fluid 
 can be supposed to rise in a continued column, without mixing with 
 the atmosphere, or being dispersed by wind, there is no difficulty in 
 conceiving how it may produce the appearance of a falling star. 
 When the upper extremity of the column has reached such a height 
 as to be in a great measure above the region of the clouds and mois- 
 ture, it may, from the dryness of the air, take fire spontaneously, as 
 phosphorus is known to do when exposed to the atmosphere in its 
 ordinary state ; and ignition having once commenced, it may be com- 
 municated backward to successive portions of the column, till it ar- 
 rives at a portion of the atmosphere sufficiently moist to extinguish 
 it, or at the same point where the column itself has been broken and 
 separated. In these circumstances, it is obvious that the appearance 
 would be precisely that of a falling star ; and Mr. Forster has inge- 
 niously applied the hypothesis to account for the apparent relation 
 between such phenomena and succeeding gales of wind. It has 
 been long known that different, and even opposite currents of wind, 
 may exist at different heights in the atmosphere at the same time ; 
 and the author just referred to, has found, from various experiments 
 and observations, that when the wind near the surface of the earth 
 changes, it frequently blows from the same point from which the 
 current above had previously blown. He observes, therefore, that 
 
ON PREDICTING THE WEATHER. 13 
 
 De Luc's hypothesis, though he is far from embracing it as satisfac- 
 tory, will sufficiently account for the relation above stated, by sup- 
 posing that the column of phosphoric fluid is bent, previous to igni- 
 tion, in the direction of the upper current ; so that, when ignition 
 commences, the luminous body moves towards the point from which 
 that current then proceeds, and from which the lower current is 
 afterwards to blow. It is a prognostication of \\ ind, then, only in so 
 far as it indicates a change that has already commenced in the higher 
 regions of the atmosphere, but which has not yet taken place near 
 the surface of the earth. 
 
 On Predicting the Weather, 
 
 FROM a very great number of meteorological observations, made 
 in England between the years 1677 and 1789, Mr. Kirwan has de- 
 duced the following probable conjectures of the weather : 
 
 1. That when there has been no storm before or after the vernal 
 equinox, the ensuing summer is generally dry, at least five times 
 in six. 
 
 2. That when a storm happens from any easterly point, either 
 on the 19th, 20th, or 21st of March, the succeeding summer is gene- 
 rally dry, four times in five. 
 
 3. That when a storm arises on the 25th, 26th, or 27th of March, 
 and not before, in any point, the succeeding summer is generally dry, 
 four times in five. 
 
 4. If there be a storm at S.W., or W.S.W., on the 19th, 20th, 
 21st, or 22d of March, the succeeding summer is generally wet, four 
 times in five. 
 
 To the above we shall add the following observations from the 
 Encyclopedia Britannica. 
 
 1. A moist autumn, with a mild winter, is generally followed by 
 a cold and dry spring, which greatly retards vegetation. 
 
 2. If the summer be remarkably rainy, it is probable that the 
 ensuing winter will be severe; for the unusual evaporation will have 
 carried off the heat of the earth. Wet summers are generally at- 
 tended with an unusual quantity of seed on the white thorn and dog- 
 rose bushes. Hence the unusual fruitfulness of these shrubs is a 
 sign of a severe winter. 
 
 3. The appearance of cranes, and birds of passage, early in au- 
 tumn, announces a very severe winter; for it is a sign that it has 
 already begun in the northern countries. 
 
 4. When it rains plentifully in May, it will rain but little in Sep- 
 tember, and vice versa. 
 
 d 
 
14 ON THE CONSTRUCTION OF THE HEAVENS. 
 
 5. When the wind is S.W. during summer or autumn, and the 
 temperature of the air unusually cold for the season, both to the 
 feeling and the thermometer, with a low barometer, much rain is to 
 be expected. 
 
 6. Violent temperatures, as storms or great rains, produce a sort of 
 crisis in the atmosphere, which produces a constant temperature, 
 good or bad, for some months. 
 
 7. A rainy winter predicts a sterile yeaj; a severe autumn an- 
 nounces a windy winter. 
 
 On the Construction of the Heavens, by the late Sir W. Herschel. 
 
 IN a paper on this subject read before the Royal Society, Sir 
 W. Herschel enumerates a great diversity of parts that enter into the 
 construction of the heavens. The first species are insulated stars ; 
 as such the author considers our sun, and all the brightest stars, 
 which he supposes nearly out of the reach of mutual gravitation ; for, 
 stating the annual parallax of Sirius at 1'', he calculates that Sirius 
 and the sun, if left alone, would be 33 millions of years in falling 
 together ; and that the action of the stars of the milky way, as well 
 as others, would tend to protract this time much more. Herschel 
 conjectures that insulated stars alone are surrounded by planets. 
 The next are binary sidereal systems, or double stars ; from the 
 great number of these which are visible in different parts of the 
 heavens, and the frequent apparent equality of the two stars, 
 Herschel calculates the very great improbability, that they should 
 be at distances from each other at all comparable to those of the 
 insulated stars : hence he infers, that they must be subjected to mu- 
 tual gravitation, and can only preserve their relative distances by a 
 periodical revolution round a common centre. In confirmation of 
 this inference, he states that many double stars have actually changed 
 their situation in a progressive course, the motion of some being 
 direct, and of others retrograde. The proper motion of our sun does 
 not appear to be of this kind, but to be rather the effect of some 
 perturbations in the neighbouring systems. The same theory is next 
 applied to triple, quadruple, and multiple systems of stars, and par- 
 ticular hypothetical cases are explained by diagrams. Some such 
 cases, Herschel is fully persuaded, have a real existence in 
 nature. The fourth species consists of clustering stars, and of the 
 milky way ; the stars thus disposed constitute masses, which appear 
 brighter in the middle, and fainter towards the extremities, being 
 perhaps collected in a spherical form. Groups of stars the author 
 distinguishes from these by a want of apparent condensation about a 
 centre of attraction : and clusters of stars, by a much more complete 
 compression near such a centre, so as to exhibit a mottled lustre, 
 almost resembling a nucleus. The eighth species consists of nebulas, 
 
ON THE USE OF THE TELESCOPE. 15 
 
 which probably differ from the three last species only in being much 
 more remote,; some of them, Herschel calculates, must be at so 
 great a distance, that the rays of light must have been nearly two 
 millions of years in travelling from them to our system. .The stellar 
 nebulae, or stars with burs, form a distinct species. A milky nebu- 
 losity is next mentioned, which may in some cases resemble other 
 nebulae, but in others appear to be diffused, almost like a fluid : the 
 author is not inclined to consider it as either resembling the zodiacal 
 light of the sun, or of a phosphorescent nature. The tenth species is 
 denominated nebulous stars ; these are stars surrounded with a 
 nebulosity like an atmosphere, of which the magnitude must be 
 amazingly great ; for the apparent diameter of one of them, described 
 in the catalogue, was 3'. The planetary nebulae are distinguished by 
 their equable brightness, and circular form, while their light is still 
 too faint to be produced by a single luminary of great dimensions. 
 When they have bright central points, Herschel considers them 
 as forming a twelfth species, and supposes them to be allied to the 
 nebulous stars, which might approach to their nature, if their 
 luminous atmospheres were very much condensed round the 
 nucleus. 
 
 On the Use of the Telescope. 
 
 THE late Sir W. Herschel has remarked, that, " In order to see 
 well with telescopes, it is required that the temperature of the 
 atmosphere and mirror should be uniform, and the air fraught with 
 moisture." Thus a frost after a thaw, or a thaw after a frost, will 
 impair the perfection of the focus : a telescope brought out of a warm 
 room into a cold air, or even directed through an aperture of any 
 kind, acts but imperfectly : windy weather is unfavourable to dis- 
 tinct vision, from a mixture of air of different temperatures : an 
 aurora borealis sometimes affects the distinctness of the view, as 
 well as the air ascending from the warm roof of a house : dampness, 
 fogs, and the neighbourhood of moisture, are very favourable to dis- 
 tinct vision with telescopes, except when a fog is so opaque as 
 totally to intercept it. Sir W. Herschel remarks, that some of these 
 obstacles are insuperable ; but that the effect of heat may sometimes 
 be remedied by the application of a heated body near the opposite 
 surface of the mirror. 
 
 Sir W. also observes, that the central part of a mirror produces a 
 greater aberration in the image of a fixed star than the whole 
 mirror, and the whole mirror a greater aberration than an annular 
 portion remote from the centre : and that this is true of all good 
 mirrors.* 
 
 * Some additional and useful remarks on the nature and application of the 
 telescope, by the same author, will be found at page 31 of this work. 
 
TABLE L 
 
 RIGHT ASCENSIONS and DECLINATIONS of the PRINCIPAL FIXED STARS, adapted to 
 the Beginning of the YEAR 1824. 
 
 Names of the Stars. 
 
 Mag. 
 
 Right 
 Ascension 
 
 Ann. 
 Var. 
 
 Declination. 
 
 nn. Var. 
 
 
 
 in Time. 
 
 add. 
 
 
 
 
 
 H. M. S. 
 
 S. 
 
 
 
 y Pegasus Algenib 
 
 2 
 
 4 11 
 
 3-1 
 
 14 12 20 N. 
 
 + 20 
 
 a Phoenix 
 
 2-3 
 
 17 34 
 
 3'0 
 
 43 15 10 S. 
 
 20 
 
 Cetus .. 
 
 2'3 
 
 34 44 
 
 3-0 
 
 18 57 16 S. 
 
 20 
 
 Andromeda Mirach 
 
 2 
 
 59 53 
 
 3-3 
 
 34 41 9 N. 
 
 + 19 
 
 a Eridanus " Achernar 
 
 1 
 
 1 31 8 
 
 2'2 
 
 58 7 58 S. 
 
 19 
 
 a Aries ARIETIS 
 
 2 
 
 1 57 16 
 
 3'4 
 
 22 37 34 N. 
 
 + 17 
 
 y Cetus 
 
 3 
 
 2 34 11 
 
 3*1 
 
 2 29 38 N. 
 
 + 16 
 
 a Cetus .. .. Menkar 
 
 2 
 
 2 53 5 
 
 3-1 
 
 3 23 41 N. 
 
 + 15 
 
 & Perseus .. .. Algol 
 
 Var. 
 
 2 56 46 
 
 3-8 
 
 40 16 15 N. 
 
 + 14 
 
 a Perseus 
 
 2 
 
 3 11 48 
 
 4-2 
 
 49 13 36 N. 
 
 -f 14 
 
 a Taurus .. ALDEBARAN 
 
 1 
 
 4 25 50 
 
 3-4 
 
 16 8 54 N. 
 
 + 8 
 
 a Auriga .. .. Capella 
 
 1 
 
 5 3 42 
 
 4-4 
 
 45 48 29 N. 
 
 + 5 
 
 Orion Rigel 
 
 1 
 
 565 
 
 2-9 
 
 8 24 40 N. 
 
 5 
 
 8 Taurus 
 
 2 
 
 5 15 11 
 
 3-8 
 
 28 26 59 N. 
 
 + 4 
 
 y Orion Bellatrix 
 
 2 
 
 5 15 42 
 
 3-2 
 
 6 10 59 N. 
 
 + 4 
 
 a Columba 
 
 
 5 33 18 
 
 2-2 
 
 34 10 20 S. 
 
 2 
 
 Orion 
 
 2-3 
 
 5 39 25 
 
 2-8 
 
 9 44 15 S. 
 
 2 
 
 a Orion Betelguese 
 
 1 
 
 5 35 39 
 
 3-4 
 
 7 21 59 N. 
 
 + 1 
 
 a Argo Navis .. .. Canopus 
 
 1 
 
 6 20 3 
 
 1-3 
 
 52 36 9 S. 
 
 + 2 
 
 a Canis Major .. Sirius 
 
 1 
 
 6 37 24 
 
 2-6 
 
 16 28 48 S. 
 
 + 4 
 
 Canis Major 
 rt Canis Major 
 
 2'3 
 23 
 
 7 1 15 
 7 17 8 
 
 2-4 
 2-4 
 
 26 7 14 S. 
 28 57 52 S. 
 
 + 5 
 
 + r 
 
 a Gemini .. .. Castor 
 
 1 
 
 7 23 22 
 
 3-8 
 
 32 15 56 N. 
 
 7 
 
 a Canis Minor Procyon 
 
 1-2 
 
 7 30 5 
 
 3-2 
 
 5 40 11 N. 
 
 , p 
 
 8 Gemini .. .. POLLUX 
 
 1 
 
 7 34 32 
 
 3-7 
 
 28 26 36 N. 
 
 8 
 
 Argo Navis 
 
 2 
 
 7 57 24 
 
 2-1 
 
 39 30 38 S. 
 
 + 10 
 
 v Argo Navis 
 
 2 
 
 848 
 
 1*8 
 
 46 49 11 S. 
 
 + 10 
 
 > Argo Navis 
 
 2 
 
 8 39 52 
 
 1-6 
 
 54 3 45 S. 
 
 + 13 
 
 Argo Navis 
 
 1 
 
 9 11 17 
 
 0-7 
 
 68 59 42 S. 
 
 -f 15 
 
 a Hydra Alphard 
 
 2 
 
 9 18 56 
 
 3-0 
 
 7 53 58 S. 
 
 -f 15 
 
 a Leo .. .. REGULUS 
 
 1 
 
 9 58 59 
 
 3-2 
 
 12 49 27 N. 
 
 17 
 
 Ursa Major 
 
 2 
 
 10 51 10 
 
 3-7 
 
 57 19 25 N. 
 
 19 
 
 a Ursa Major .. Dubke 
 
 1-2 
 
 10 52 47 
 
 3-8 
 
 62 41 57 N. 
 
 19 
 
 Leo Deneb 
 
 2 
 
 11 40 5 
 
 3-1 
 
 15 33 22 N. 
 
 - 20 
 
 a Crux 
 
 1 
 
 12 16 54 
 
 3-2 
 
 62 7 29 S. 
 
 + 20 
 
 y Crux 
 
 2 
 
 12 21 26 
 
 3-3 
 
 56 7 21 S. 
 
 + 20 
 
 Crux 
 
 2 
 
 12 37 30 
 
 3'4 
 
 58 43 33 S. 
 
 -f 20 
 
 a Virgo SPICA 
 
 1 
 
 13 15 56 
 
 3-1 
 
 10 14 19 S. 
 
 + 19 
 
 * Ursa Major .. Benetnach 
 
 2 
 
 13 40 36 
 
 2-4 
 
 50 11 42 N. 
 
 18 
 
 Centaurus 
 
 2 
 
 13 51 30 
 
 4-1 
 
 59 31 2 S. 
 
 + 18 
 
 a Draco 
 
 2-3 
 
 13 59 39 
 
 1-6 
 
 65 13 8 N. 
 
 17 
 
 a Bootes .. .. Arcturus 
 
 1 
 
 14 7 39 
 
 2-7 
 
 20 6 12 N. 
 
 19 
 
 a Centaurus 
 
 1 
 
 14 28 18 
 
 4-4 
 
 60 7 5 S. 
 
 + 16 
 
 a Libra Zubenesch 
 
 2-3 
 
 14 41 4 
 
 3-3 
 
 15 16 48 S. 
 
 + 15 
 
 Libra Zubenelg 
 
 2-3 
 
 15 7 34 
 
 3-2 
 
 8 43 38 S. 
 
 H- 14 
 
 a Corona Borealis .. Alphacca 
 
 2 
 
 15 27 15 
 
 2-5 
 
 27 18 47 N. 
 
 12 
 
 a Serpens 
 
 2 
 
 15 35 36 
 
 2-9 
 
 6 59 11 N. 
 
 12 
 
 a Scorpio .. .. ANTARES 
 
 1 
 
 16 18 37 
 
 3-6 
 
 26 1 50 S. 
 
 -f 9 
 
 a Hercules .. Ras Algethi 
 
 2 
 
 17 6 38 
 
 2-7 
 
 14 35 56 N. 
 
 4 
 
 a Serpentarius .. Ras AUiague 
 
 2 
 
 17 26 46 
 
 2-8 
 
 12 41 47 N. 
 
 . Q 
 
 y Draco Rastaban 
 
 2-3 
 
 17 52 31 
 
 1-4 
 
 51 30 48 N. 
 
 1 
 
 a Lyra Vega 
 
 1 
 
 18 30 59 
 
 2-0 
 
 38 37 33 N. 
 
 + 3 
 
 a Aquila .. .. ALTAIR 
 
 1-2 
 
 19 42 12 
 
 2-9 
 
 8 24 41 N. 
 
 + 9 
 
 a Pavo .. 
 
 1*2 
 
 20 11 40 
 
 4.8 
 
 57 17 19 S. 
 
 11 
 
 a Cygnus . Arided 
 
 1-2 
 
 20 35 26 
 
 2-0 
 
 44 39 21 N. 
 
 + 13 
 
 a Cepheus Alderaimin 
 
 3 
 
 21 14 22 
 
 1-4 
 
 61 50 31 N. 
 
 + 15 
 
 a Grux .. 
 
 2 
 
 21 57 6 
 
 3-8 
 
 47 48 11 S. 
 
 17 
 
 a Pisces Aus FOMALHAUT 
 
 1 
 
 22 47 54 
 
 3'3 
 
 30 33 10 S. 
 
 19 
 
 Pegasus .. Scheat 
 
 2 
 
 22 25 15 
 
 2-9 
 
 27 7 37 N. 
 
 + 19 
 
 a Pegasus .. MARCAB 
 
 2 
 
 22 56 
 
 3-0 
 
 14 15 42 N. 
 
 -f 19 
 
 a Andromeda .. Alpheratz 
 
 2 
 
 23 59 19 
 
 3-1 
 
 28 17 10 N. 
 
 + 20 
 
REMARKS ON THE MOON. 17 
 
 Remarks on different Hypotheses respecting the Moon, and various Phe- 
 nomena of that Planet. 
 
 WE make no apology for submitting to our readers the subjoined 
 extracts from a highly ingenious and interesting work, entitled 
 SELENOGNOSTIC FRAGMENTS, published by Dr. Gruithuisen, 
 whose name ranks deservedly high in the list of foreign astronomers. 
 
 No body in the starry heavens, observes the Doctor, in his intro- 
 duction, excites more general interest than the faithful satellite of the 
 earth : in fact, its surface presents, even to the naked eye, objects so 
 varied, that it instantly inspires the spectator with a wish to inspect 
 this unknown world, with the aid of a powerful telescope. But what 
 especially prompts us to study the physical properties and constitu- 
 tion of the moon, is the expectation of discovering an analogy com- 
 mon to all the great bodies of the universe, with respect to their or- 
 ganization. This, he adds, is what has hitherto been the foundation 
 of my celestial observations, being myself convinced that we shall 
 never attain to any excellence in the study of geognosy, till we have 
 discovered this analogy. It is with this intention that the author has 
 surveyed, examined, and studied many chains of terrestrial moun- 
 tains ; and it is with this view that he publishes the particular appear- 
 ances, which eight years observations have enabled him to remark 
 upon the surface of the moon. 
 
 To render his work more intelligible to his readers, the Doctor has 
 inserted a lithographic general map of this planet ; for which purpose 
 he has consulted Mayer's draught of the moon, and the special maps 
 given by Schroeter in his Selenographic Fragments. Nor has he neg- 
 lected to avail himself of his own observations. He likewise cites 
 the lunar map of Lambert, and refers to a memoir of that philosopher 
 in the first volume of the Berlin astronomical almanack. 
 
 Atmosphere of the Moon. Cassini, Louville, Bianchini, Carbone, 
 Euler, Kriiger, Boscovich, Ulloa, Dusejour, Wolf, and Halle, 
 maintain the existence of a lunar atmosphere; while Mayer, 
 Grandjean de Fouchy, De 1'Isle, and De la Hire, deny it. Without 
 dwelling upon the reasons and observations which, before the inven- 
 tion of achromatic telescopes have been alleged on both sides of the 
 questions, Doctor Gruithuisen confines himself to the direct proofs 
 drawn from the discoveries of Schroeter. The latter has calculated 
 the elevation of the twilight observed by him in repeated observa- 
 tions on the increasing moon. This elevation agrees in a surprising 
 manner with the theorem of Melanderhielm ; namely, that on the sur- 
 face of planets the density of their atmospheres is in proportion to the 
 squares of the weight of the bodies. This proportion had been sug- 
 gested to Newton by that of the squares of weights on the surface of 
 the moon, and the surface of the earth. In fact, this latter propor- 
 tion being as 1 to 28'40, is almost equal to the result of Schroeter, 
 who found that the lunar atmosphere is 28*94 times less dense than 
 our own. Hevelius, Deluc, and many other philosophers, have 
 thought that the air on the surface of planets was only ether con- 
 densed, and have considered ether, in its turn, as rarified air, an 
 
18 REMARKS ON THE MOON. 
 
 opinion, which, in a theoretical point of view, confirms the theorem 
 of Melanderhielm. 
 
 To attempt to combat this theory, adds our author, would have 
 the effect of entangling us in a multitude of inextricable difficulties; 
 for we must then affirm that ether and air have no communication to- 
 gether; that consequently they cannot mix, and that there is between 
 them a kind of barrier, as if our earth was enclosed in a globe of hol- 
 low glass : yet we know that all gases mingle together, which, 
 moreover, must happen from the pressure of our air upon ether, and, 
 reciprocally, on account of the rapid motion of the earth. It is to this 
 pressure that M. de Zach attributes the diurnal oscillations of the 
 barometer, observed at the equator by H umboldt. We should like- 
 wise be obliged to affirm, that as the air of planets is essentially dif- 
 ferent from ether, there can be no affinity between them, and conse- 
 quently that nobody can burn in ether for want of oxygen, a conclu- 
 sion not warranted by observations, since shooting stars and meteors 
 burn and shine at a height at which in general the presence of atmos- 
 pheric air is not supposed. For example, in 1795, Schroeter saw, 
 with his reflecting telescope of 20 feet long, a shooting star, the 
 height of which he estimated at more than four millions of miles. If 
 then it be admitted that each body of the universe, by the influence 
 of a weight proportioned to its bulk, forms out of ether, the atmos- 
 phere by which it is surrounded, then the moon must also borrow 
 from ether its portion, which becomes condensed and forms its at- 
 mosphere. The existence of water in the lunar atmosphere can no 
 longer be questioned, for clouds have been seen upon its surface, as 
 is proved by the almost innumerable observations of Schroeter, to 
 whose work the Doctor refers for more extensive details. 
 
 Organised Beings in the Moon. It is a remarkable circumstance, 
 observes M. Gruithuisen, that all those who only take what may be 
 termed a cursory survey of the moon through a telescope, consider it 
 as a desert and globe, upon which nothing lives or grows : on the 
 contrary, others who have explored its surface for many years, speak 
 of it, as if organised beings could not fail to exist there. 
 
 Shroeter conjectures the existence of a town towards the north of 
 murius (a lunar spot), and the canals which are observable towards 
 hyginus (another spot), and which, after disappearing in some places, 
 are again perceived in others (a thing, says Dr. G. of which I have 
 convinced myself), appear to him very advantageous for the com- 
 merce of the Selcnites: finally, he represents a part of the spot named 
 mare imbrium to be as fertile as Campania. 
 
 The ancients supposed the moon to be inhabited. Orpheus, Anax- 
 agoras, Xenophon, and Pythagoras, are of this opinion. Their 
 strength of reasoning compensated, in this instance, for their want of 
 telescopes : even Plutarch entertained the idea, that .the obscure 
 places on the moon's surface were seas, which could not reflect the 
 light of the sun. More recently, Kepler, Duhamel, and many others 
 have been of the same way of thinking respecting the existence of 
 the Selenites. Indeed, so general has this sentiment been, that 
 even the American savages have believed the moon to be inhabited. 
 
REMARKS ON THE MOON. 19 
 
 Iii latter times, some persons have considered the too great rare- 
 faction of the air as an insuperable obstacle to peopling the moon. 
 Without doubt, says our author, this circumstance would not fail to 
 alarm more than one philosopher of a delicate constitution, particu- 
 larly when he knows that neither raisins nor apricots are to be found 
 even on the Chimbora^o. Others, on the contrary, have not forgotten 
 that Mr. Guy-Lussac ascended, with his balloon, to a height greater 
 by 2000 feet than the height of that mountain. So that an inhabitant 
 of our globe, if placed in the lowest regions of the moon, might find 
 himself very ill at his ease, but not so much so as to cause his 
 death. 
 
 While speaking of the inhabitants of the moon, we may observe, 
 that some theorists have affirmed that no animated beings could 
 exist on that planet, but such as were capable of eating stones, do- 
 ing without drink, living on a scanty supply of air, and supporting 
 the extremes of heat and cold. These particulars, adds Mr. Gui- 
 thuisen, may be considered as a summing up of all the doubts that have 
 arisen on the question whether the planets are habitable or not. He 
 then discusses each of these points. He thinks he can confidently 
 affirm that the moon has vegetables and animals to serve for food to 
 its inhabitants : he even goes so far as to indicate some of their 
 genera and species. In the absence of wine, he continues, the Se- 
 Icnites have water, so that they possess the means of quenching their 
 thirst. They are likewise supplied with air in more than sufficient 
 quantity, only that this air is extremely rarefied. If we admit of 
 lakes and seas in the moon, why should they not contain shell and 
 other fish, and amphibious beings? And that man can accustom him- 
 self to a highly rarefied atmosphere, has been shewn by the aerial 
 ascent of M. Guy-Lussac, already referred to. According to Hum- 
 boldt, the atmosphere supports a column of quicksilver of only 
 twenty inches at Quito ; of eighteen inches at Micuipampa, and of 
 seventeen inches in the latitude of Antisana, all inhabited places 
 upon the earth, notwithstanding this rarefaction. Lastly, the Selen- 
 ites can face the cold and heat with the assistance of fire, which they 
 have the means of procuring in the former case ; and in the latter, by 
 means of the deep caverns, in whose coolness they can obtain refuge 
 from the heat. 
 
 Waters in the Mom. By these, says our author, I understand all 
 the springs, rivers, lakes, and seas. After having collected and 
 discussed at great length all the facts calculated to illustrate the 
 subject, he thinks he has a right to ask, who can now bring forward 
 any probable argument against the existence of lakes in the moon ? 
 But, he adds, lakes presuppose rivers, or at least simple rivulets 
 or springs, their existence is then sufficiently demonstrated. 
 
 Of the Lunar Structure. The interior structure of the moon is 
 probably not different from that which is common to all the bodies of 
 the universe ; namely, concentric beds formed by the accumulation of 
 successive strata. 
 
 Of the Exterior Structure or Constitution. This consists properly in 
 
20 OBSERVATIONS ON THE FIXED STARS. 
 
 the chains of mountains ; the caverns, the declivities and the acclivi- 
 ties are immediate consequences of this disposition. 
 
 We shall only add a few words relative to the lithographical map 
 which Doctor Gruithuisen has attached to his work, for the purpose 
 of facilitating the discovery of the points, which he more particularly 
 wishes to designate upon the face of the moon. To accomplish this, 
 he indicates their situation by their distance from two lines, which 
 may be said to represent the equator and the first meridian of the 
 moon, which we consider to be a felicitous and useful imitation of 
 terrestrial longitudes and latitudes. 
 
 On Professor Struve's Observations to determine the Parallax of the 
 fixed Stars. 
 
 OF the various attempts to discover the parallax of the fixed stars, 
 the observations of Professor Struve must be regarded as among the 
 best, and most judicious. 
 
 His object is, by means of an excellent transit instrument furnished 
 with seven wires, to determine the sum of the parallaxes of several 
 fixed stars, differing nearly 12 hours in right ascension from each other. 
 
 The results which he obtains, seem to verify a remark made by 
 Mr. Pond, that in proportion as any improvement takes place either 
 in our instruments or our processes, the resulting parallax becomes 
 proportionally less. 
 
 Of fourteen sets of opposite stars thus compared, Mr. Struve finds 
 seven, which give the parallax negative; this circumstance alone 
 should suggest great caution in attributing to the effects of parallax 
 the small positive quantities that are derived from the remaining 
 seven. Mr. Struve however is inclined to assign 0".16 of space as 
 the parallax of 8 Ursae Minoris, and 0".45 for the sum of the paral- 
 laxes of Cigni, and * TJrsae Majoris. His learned coadjutor, M. 
 Walbeck, who, it appears, has undertaken the calculations, is dis- 
 posed to attribute the greatest portion of this parallax to the smaller 
 star; a circumstance so improbable requires very strong evidence 
 for its support. 
 
 If we take the mean of the fourteen results as relating generally to 
 stars from the 1st to the 4th magnitude, jt will appear that the mean 
 sum of the parallaxes of two opposite stars is equal to 0".036 of space, 
 or the parallax of a single star equal to 0".018. 
 
 If any reliance can be placed on these observations, evWy at- 
 tempt to determine the parallax of these stars in declination must be 
 entirely hopeless ; since in this case we can only measure the shorter 
 axis of the Ellipse, and the uncertainty of refraction must amount, at 
 least, to twenty times the quantity we are in search of. 
 
FIGURE OF THE EARTH. 21 
 
 On the Method of Determining the Figure of the Earth by the 
 Pendulum. 
 
 THE method of determining the figure of the earth by means of the 
 pendulum, depends upon the variation of gravity at the earth's surface. 
 
 This subtile and pervading power, tends to communicate to bodies 
 exposed to its influence equal velocities in equal times. One of the 
 modifications of this action is the oscillation of the pendulum, which 
 is of longer or shorter dilation, according to the energy of the attrac- 
 tive force, and the square root of the length of the pendulum. If the 
 earth were an exact sphere, destitute of the motion of rotation, and 
 possessing the same density throughout its whole mass, the force of 
 gravity, by which bodies at its surface are drawn towards the centre, 
 would be uniform, and invariable in every latitude. But the elliptical 
 form of the earth destroys this uniformity, and causes the attractive 
 force at the poles to preponderate over that at the equator. This 
 inequality in the force, by which bodies at the surface of the earth 
 retain their positions, is augmented by the diurnal rotation, which, by 
 centrifugal tendency, impresses a greater disposition on bodies to 
 recede from the centre of the earth at the equator than at the poles, 
 where its effects cease to be felt. By the joint operation of these 
 two causes, one of which acts with a force proportional to the square 
 of the sine of the latitude, a sensible difference ought to be observed 
 in the velocity acquired by heavy bodies, in falling through the same 
 space, as we advance from the equator to the poles. An important 
 relation between the time of the vibration of a pendulum, and that of 
 the descent of a heavy body, according to which the lengths of 
 pendulums, vibrating ischronously, are directly as the force of 
 gravity, enables us to submit this conclusion to the test of experi- 
 ment. Newton long ago demonstrated, that if the earth were per- 
 fectly homogeneous, the same fraction, viz. 230 , would express both 
 the compression of the terrestrial ellipsoid, and the increase of gravity 
 from the equator to the poles. This conclusion, which was deduced 
 from the supposition of an uniform density, was afterwards modified, 
 with singular address, by Clairaut, who showed, that the two frac- 
 tions expressing the compression, and the increase of grvity, though 
 not exactly equal, must always together amount to . Assuming 
 the compression, therefore, to be eqnal to 3 } 2 , the increase of gravity 
 from the equator to the poles, or the indication of that increase, as 
 given by the length of the pendulum, should be 3*, 3 } 2 , or ^ nearly. 
 The correctness of this conclusion, if not completely established, is, 
 at least, to a certain extent, confirmed, by the experiments which have 
 been made with the pendulum in different latitudes. La Place having 
 selected fifteen of the best of these observations, and applied to them 
 the necessary corrections, on account of the resistance of the air, 
 difference of temperature, and elevation above the level of the sea, 
 deduced the following results, in which the length of the pendulum at 
 Paris is considered to be unity. 
 
22 
 
 FIGURE OF THE EARTH. 
 
 Latitude. 
 
 Length of 
 the Seconds 
 Pendulum. 
 
 Names of the 
 Observers. 
 
 Places of 
 Observation. 
 
 Equator 
 
 99669 
 
 Bouguer 
 
 Peru 
 
 9 32' 56" 
 
 99689 
 
 Ditto 
 
 Portobello 
 
 11 55 30 
 
 99710 
 
 Gentil 
 
 Pondicherry 
 
 18 
 
 99745 
 
 Campbell 
 
 Jamaica 
 
 18 27 
 
 99728 
 
 Bouguer 
 
 Petit Grave 
 
 34 7 15 
 
 99877 
 
 La Caille 
 
 Cape G. H. 
 
 43 35 45 
 
 99950 
 
 Darquior 
 
 Toulouse 
 
 48 12 48 
 
 99077 
 
 Liesganig 
 
 Vienna 
 
 48 50 
 
 1-00000 
 
 Bouguer 
 
 Paris 
 
 50 58 
 
 1-00006 
 
 Zach 
 
 Gotha 
 
 51 30 
 
 1-00018 
 
 
 London 
 
 58 14 53 
 
 1-00074 
 
 Mallet 
 
 Petersburgh 
 
 59 56 24 
 
 1-00101 
 
 Ditto 
 
 Ponoi 
 
 66 48 
 
 JL-00137 
 
 Grischow 
 
 Arensberg 
 
 67 5 
 
 1-00148 
 
 Mapertius 
 
 Tornea 
 
 The above results indicate obviously an increase of the force of 
 gravity from the equator towards the poles. La Place has shewn 
 that, in whatever way they are combined, it is impossible to avoid an 
 error of less than '00018, on the hypothesis of the variation of gravity 
 at the surface of the earth increasing as the squares of the sines of the 
 latitude from the equator to the poles. The expression for the ellipti- 
 city, which connects best the different equations of condition, is 38 J. 78 , 
 a result which accords in a very remarkable manner with the com- 
 pression deduced from the measures of the French mathematicians in 
 France, and at the equator. 
 
 It may be inferred from these experiments with the pendulum, that 
 the compression of the earth is greater than is compatible with the 
 supposition of an uniform density. The same anomalies, too, which 
 are discernible in the measurement of a degree of the meridian, and 
 which are undoubtedly owing to the dissimilar structure of the globe, 
 may be traced in the results of these experiments. The beautiful pro- 
 perty of the pendulum, first discovered by Huggens, that the centre of 
 oscillation and the point of suspension, are interchangeable with each 
 other, and which has been so happily applied by Captain Kater, to 
 determine the length of the seconds' pendulum, renders this mechani- 
 cal contrivance infinitely better fitted to ascertain the true figure of 
 the earth, than the complicated methods which were formerly em- 
 ployed for the same purpose. The facility with which the observations 
 may be made, and the certainty of the results with which they are 
 attended, may be expected to furnish much interesting information, 
 not only with respect to the general form of the globe, but also with 
 respect to its structure and composition in particular situations. 
 
TABLE. 
 
 TIME to be ADDED to the RIGHT ASCENSION of a STAR, to find the TIME of it* 
 PASSING the MERIDIAN on any day of the YEAR. 
 
 Days. 
 
 Jan. 
 
 Feb. 
 
 March 
 
 April 
 
 May 
 
 June 
 
 July 
 
 August 
 
 Sept. 
 
 Oct. 
 
 Nov. 
 
 Dec. 
 
 Days 
 
 
 h. in. 
 
 h. in. 
 
 h. m. 
 
 h. m. 
 
 h. m. 
 
 L. m. 
 
 h. m. 
 
 h. in. 
 
 h. m. 
 
 h. m. 
 
 h. in. 
 
 h. m. 
 
 
 1 
 
 5 14 
 
 3 2 
 
 1 12 
 
 23 18 
 
 21 37 
 
 19 25 
 
 17 20 
 
 15 15 
 
 13 19 
 
 11 31 
 
 9 35 
 
 7 31 
 
 1 
 
 2 
 
 5 10 
 
 2 58 
 
 1 8 
 
 23 15 
 
 21 23 
 
 19 20 
 
 17 16 
 
 15 11 
 
 13 16 
 
 11 28 
 
 9 31 
 
 7 27 
 
 2 
 
 3 
 
 5 6 
 
 2 54 
 
 1 4 
 
 23 11 
 
 21 20 
 
 19 16 
 
 17 12 
 
 15 8 
 
 13 12 
 
 11 24 
 
 9 27 
 
 7 23 
 
 3 
 
 4 
 
 5 1 
 
 2 50 
 
 1 1 
 
 23 7 
 
 21 16 
 
 19 12 
 
 17 8 
 
 15 4 
 
 13 8 
 
 11 20 
 
 9 23 
 
 7 18 
 
 4 
 
 5 
 
 4 57 
 
 2 46 
 
 57 
 
 23 4 
 
 21 12 
 
 19 8 
 
 17 4 
 
 15 
 
 13 5 
 
 11 17 
 
 9 19 
 
 7 14 
 
 5 
 
 6 
 
 4 52 
 
 2 42 
 
 53 
 
 23 
 
 21 8 
 
 19 4 
 
 17 
 
 14 56 
 
 13 1 
 
 11 13 
 
 9 15 
 
 7 9 
 
 6 
 
 7 
 
 4 48 
 
 2 38 
 
 50 
 
 22 56 
 
 21 4 
 
 19 
 
 16 56 
 
 14 52 
 
 12 58 
 
 11 9 
 
 9 11 
 
 7 5 
 
 7 
 
 8 
 
 4 44 
 
 2 34 
 
 46 
 
 22 53 
 
 21 
 
 18 56 
 
 16 51 
 
 14 48 
 
 12 54 
 
 11 6 
 
 9 7 
 
 7 1 
 
 8 
 
 9 
 
 4 39 
 
 2 30 
 
 42 
 
 22 49 
 
 20 56 
 
 18 52 
 
 16 47 
 
 14 45 
 
 12 50 
 
 11 2 
 
 9 3 
 
 6 56 
 
 9 
 
 10 
 
 4 35 
 
 2 26 
 
 39 
 
 22 45 
 
 20 52 
 
 18 47 
 
 16 43 
 
 14 41 
 
 12 47 
 
 10 58 
 
 8 59 
 
 6 52 
 
 10 
 
 11 
 
 4 31 
 
 2 22 
 
 35 
 
 22 42 
 
 20 49 
 
 18 43 
 
 16 39 
 
 14 37 
 
 12 43 
 
 10 55 
 
 8 55 
 
 6 47 
 
 11 
 
 12 
 
 4 26 
 
 2 18 
 
 31 
 
 22 38 
 
 20 45 
 
 18 39 
 
 16 35 
 
 14 33 
 
 12 40 
 
 10 51 
 
 8 51 
 
 6 43 
 
 12 
 
 13 
 
 4 22 
 
 2 14 
 
 27 
 
 22 34 
 
 20 41 
 
 18 35 
 
 16 31 
 
 14 29 
 
 12 36 
 
 10 47 
 
 8 47 
 
 6 39 
 
 13 
 
 14 
 
 4 18 
 
 2 10 
 
 24 
 
 22 31 
 
 20 37 
 
 18 31 
 
 16 27 
 
 14 26 
 
 12 32 
 
 10 44 
 
 8 43 
 
 6 34 
 
 14 
 
 15 
 
 4 13 
 
 2 6 
 
 20 
 
 22 27 
 
 20 33 
 
 18 27 
 
 16 23 
 
 14 22 
 
 12 29 
 
 10 40 
 
 8 39 
 
 6 30 
 
 15 
 
 16 
 
 4 9 
 
 2 2 
 
 17 
 
 22 83 
 
 20 29 
 
 18 23 
 
 16 19 
 
 14 18 
 
 12 25 
 
 10 36 
 
 8 35 
 
 6 25 
 
 16 
 
 17 
 
 4 5 
 
 1 58 
 
 13 
 
 22 20 
 
 20 25 
 
 18 18 
 
 16 15 
 
 14 14 
 
 12 22 
 
 10 32 
 
 8 30 
 
 6 21 
 
 17 
 
 18 
 
 4 
 
 1 55 
 
 9 
 
 22 16 
 
 20 21 
 
 18 14 
 
 16 11 
 
 14 11 
 
 12 18 
 
 JO 29 
 
 8 26 
 
 6 17 
 
 18 
 
 19 
 
 3 56 
 
 1 51 
 
 6 
 
 22 12 
 
 20 17 
 
 18 10 
 
 16 7 
 
 14 7 
 
 12 14 
 
 10 25 
 
 8 22 
 
 6 12 
 
 19 
 
 20 
 
 3 52 
 
 1 47 
 
 2 
 
 22 9 
 
 20 13 
 
 18 6 
 
 16 3 
 
 14 3 
 
 12 11 
 
 10 21 
 
 8 18 
 
 6 8 
 
 20 
 
 21 
 
 3 48 
 
 1 43 
 
 23 58 
 
 22 5 
 
 20 9 
 
 18 2 
 
 15 59 
 
 14 
 
 12 7 
 
 10 17 
 
 8 14 
 
 6 3 
 
 21 
 
 22 
 
 3 43 
 
 1 39 
 
 23 55 
 
 22 1 
 
 20 5 
 
 17 58 
 
 15 55 
 
 13 56 
 
 12 4 
 
 10 14 
 
 8 10 
 
 5 59 
 
 22 
 
 23 
 
 3 39 
 
 1 35 
 
 23 51 
 
 21 57 
 
 20 1 
 
 17 53 
 
 15 51 
 
 13 52 
 
 12 
 
 10 10 
 
 8 5 
 
 5 54 
 
 23 
 
 24 
 
 3 35 
 
 1 32 
 
 23 47 
 
 21 54 
 
 19 57 
 
 17 49 
 
 15 47 
 
 13 48 
 
 11 56 
 
 10 6 
 
 8 1 
 
 5 50 
 
 24 
 
 25 
 
 3 31 
 
 1 28 
 
 23 44 
 
 21 50 
 
 19 53 
 
 17 45 
 
 15 43 
 
 13 45 
 
 11 53 
 
 10 2 
 
 7 57 
 
 5 45 
 
 25 
 
 26 
 
 3 27 
 
 1 24 
 
 23 40 
 
 21 46 
 
 19 49 
 
 17 41 
 
 15 39 
 
 13 41 
 
 11 49 
 
 9 58 
 
 7 53 
 
 5 41 
 
 26 
 
 27 
 
 3 23 
 
 1 20 
 
 23 37 
 
 21 42 
 
 19 45 
 
 17 37 
 
 15 35 
 
 13 37 
 
 11 46 
 
 9 54 
 
 7 48 
 
 5 37 
 
 27 
 
 28 
 
 3 18 
 
 1 17 
 
 23 33 
 
 21 39 
 
 19 41 
 
 17 33 
 
 15 31 
 
 13 34 
 
 11 42 
 
 9 51 
 
 7 44 
 
 5 32 
 
 28 
 
 29 
 
 5 14 
 
 1 14 
 
 23 29 
 
 21 35 
 
 19 37 
 
 17 29 
 
 15 27 
 
 13 30 
 
 11 38 
 
 9 47 
 
 7 40 
 
 5 28 
 
 29 
 
 30 
 
 3 10 
 
 
 23*26 
 
 21 31 
 
 19 33 
 
 17 24 
 
 15 23 
 
 13 27 
 
 11 35 
 
 9 43 
 
 7 35 
 
 5 23 
 
 30 
 
 31 
 
 3 6 
 
 
 23 22 
 
 
 19 29 
 
 
 15 19 
 
 13 23 
 
 
 9 39 
 
 
 5 19 
 
 31 
 
WATER SPOUTS. 
 Water Spouts. 
 
 Remarkable Water-spout in France in 1823. In the arrondissemens 
 of Dreux and of Mantes, about 3 o'clock of the 26th of August, 1823, 
 a storm came on from the S.W., accompanied with a sudden and 
 powerful heat. A water- spout was seen not far from the village of 
 JBoncourt, having its broad base resting on the ground, and its sum- 
 mit lost in the clouds. It consisted of a thick and blackish vapour, 
 in the middle of which were often seen flames in several directions. 
 Advancing along with the storm, it broke or tore up by the roots, in 
 the space of a league, seven or eight hundred trees of different sizes, 
 and at last burst with great violence in the village of Marchepoy, one 
 half of the houses of which were instantly destroyed. The walls, 
 overturned to their foundations, rolled down on all sides ; the roofs, 
 when carried off, broke in pieces, and the debris were dragged to the 
 distance of half a league by the force of this aerial torrent. Some of 
 the inhabitants were crushed to pieces, or wounded by the fall of 
 their houses, and those who were occupied in the labours of the field, 
 were overthrown or blown away by the whirlwind. Hailstones as 
 large as the fist, and stones and other foreign bodies carried off by 
 the wind, injured several individuals. Carts heavily loaded were 
 broken in pieces, and their loads dispersed. Their axle-trees were 
 broken, and the wheels were found at the distance of 200 or 300 paces 
 from the spot where they were overturned. One of these carts, 
 which had been carried off almost bodily, was pitched above a tile- 
 kiln, which had been beaten down, and some of the materials of 
 which had been carried to a considerable distance. A spire, several 
 hamlets, and different insulated houses, were overthrown. Several 
 villages were considerably injured. The lower part of the water- 
 spout is supposed to have been about 100 toises in diameter. See 
 the Moniteur of the 31st October, where the account is signed by 
 M. Foucault, and the Bibl Univers. Oct. 1823, p. 133. 
 
 Water-spout near Genoa in 1823. In the communes of Quigliano 
 and Valeggia, in the province of Savona, a heavy rain fell on the 
 16th September, at 5 o'clock in the morning. It increased to such a 
 degree, that at 9 o'clock in the morning the country was inundated. 
 Towards noon there issued from a mountain situated in the parish of 
 Valeggia, a whirlwind of black smoke and fire. It first carried off 
 the roof of a house, in which two children were crushed to pieces, 
 and the parents wounded. The water-spout then advanced to the 
 opposite side of the mountain, called Magliolo ; crossed the river, 
 the waters of which it heaped up in an instant, though they were 
 much swelled ; carried off the roofs of two inhabited houses, and 
 advanced along the same mountain in the district of Quigliano, where 
 it dissipated itself near the Convent of Capuchins, situated in the 
 village. It tore up many large trees of all kinds, and committed 
 ravages, the extent of which is not yet known. The preceding 
 account was sent by the commandant of the province of Savona to 
 the governor of Genoa, in a letter, part of which is published in the 
 Moniteur of the 1st of October, and in the Bibl. Univers. Nov. 1823, 
 p. 135. 
 
OF THE RAINBOW. 25 
 
 Of the Rainbow. 
 
 THE phenomena of the rainbow consists, as every person knows, 
 of two bows, or arches, stretching across the sky, and tinged with 
 all the colours of the prismatic spectrum. The internal or principal 
 rainbow, which is often seen without the other, has the violet rays 
 innermost, and the red rays outermost. The external, or secondary 
 rainbow, which is much fainter than the other, has the violet colour 
 outermost, and the red colour innermost. Sometimes supernumerary 
 bows are seen to accompany the principal bows. 
 
 As the rainbow is never seen unless when the sun shines, and when 
 rain is falling, it has been universally ascribed to the decomposition 
 of white light by the refraction of the drops of rain, and their reflec- 
 tion within the drops. The production of rainbows by the spray of 
 water-falls, or by drops of water scattered by a brush or syringe, is 
 an experimental proof of their origin. 
 
 Let an observer be placed with his back to the sun, and his eye 
 directed through a shower of rain to the part of the sky opposite to 
 the sun. As the drops of rain are spherical particles of water, they 
 will reflect and refract the sun's rays, according to the usual laws of 
 refraction and reflection. Thus, in the following figure, where ssss 
 represent the sun's rays, and A the place of a spectator, in the centre 
 of the two bows (the planes of which are supposed to be perpendicu- 
 lar to his view), the drops a and b produce part of the inner bow by 
 two refractions and one reflection ; 
 
 and the drops c and d part of the exterior bow, by two refractions and 
 one reflection. 
 
 This holds good at whatever height the sun may chance to be in a 
 shower of rain ; if high, the rainbow must be low ; if the sun be low, 
 the rainbow is high : and if a shower happen in a vale when a spec- 
 tator is on a mountain, he often sees the bow completed to a circle 
 below him. So, in the spray of the sea, or a cascade, a circular rain- 
 
26 OF THE RAINBOW. 
 
 bow is often seen ; and it is but the interposition of the earth that pre- 
 vents a circular spectrum from being seen at all times, the eye being 
 the vertex of a cone, whose base (the bow) is in part cut off by the 
 earth. 
 
 It is only necessary, for the formation of a rainbow, that* the sun 
 should shine on a dense cloud, or a shower of rain, in a proper situa- 
 tion, or even on a number of minute drops of water, scattered by a 
 brush or by a syringe, so that the the light may reach the eye after 
 having undergone a certain angular deviation, by means of various 
 refractions and reflections, as already stated. The light which is 
 reflected by the external surface of a sphere, is scattered almost 
 equally in all directions, setting aside the difference arising from the 
 greater efficacy of oblique reflection : but when it first enters the 
 drop, and is there reflected by its posterior surface, its deviation never 
 exceeds a certain angle, which depends on the degree of refrangi- 
 bility, and is, therefore, different for light of different colours : and 
 the density of the light being the greatest at the angle of greatest devi- 
 ation, the appearance of a luminous arch is produced by the rays of 
 each colour at its appropriate distance. The rays which never enter 
 the drops produce no other effect, than to cause a brightness, or hazi- 
 ness, round the sun, where the reflection is the most oblique : those 
 which are once reflected within the drop, exhibit the common inter- 
 nal or primary rainbow, at the distance of about 41 degrees from the 
 point opposite to the sun : those which are twice reflected, the exter- 
 nal or secondary rainbow, of 52 degrees; and if the effect of the 
 light, three times reflected, were sufficiently powerful, it would 
 appear at the distance of about 42 degrees from the sun. The 
 colours of both rainbows encroach considerably on each other ; for 
 each point of the sun may be considered as affording a distinct arch 
 of each colour, and the whole disc, as producing an arch about half a 
 degree in breadth, for each kind of light ; so that the arrangement 
 nearly resembles that of the common mixed spectrum. 
 
 A lunar rainbow is much more rarely seen than a solar one ; but 
 its colours differ little, except in intensity, from those of the common 
 rainbow. 
 
 The appearance of a rainbow may be produced at any time, when 
 the sun shines, as follows; opposite to a window, into which the 
 sun shines, suspend a glass globe, filled with clear water, in such a 
 manner as to be able to raise it or lower it at pleasure, in order that 
 the sun's rays may strike upon it. Raise the globe gradually, and 
 when it gets to the altitude of forty degrees, a person standing in 
 a proper situation, will perceive a purple colour in the glass, and 
 upon raising it higher the other prismatic colours, blue, green, yellow, 
 orange, and red, will successively appear. After this, the colours 
 will disappear, till the globe be raised to about fifty degrees, when 
 they will again be seen, but in an inverted order; the red appearing 
 first, and the blue, or violet, last. Upon raising the globe to about 
 fifty-four degrees, the colours will totally vanish. 
 
 In the highest northern latitudes, where the air is commonly 
 loaded with frozen particles, the sun and moon usually appear sur- 
 rounded by halos, or coloured circles, at the distances of about 22 
 
ON THE LINE OF PERPETUAL CONGELATION. 27 
 
 and 46 degrees from their centres. Several new forms of halos and 
 paraselenae, or mock-moons, have been described by Captain Ross 
 and Captain Parry. And Captain Scoresby, in his account of the 
 Arctic Regions, has delineated an immense number of particles of 
 snow, which assume the most beautiful and varied crystallizations, 
 all depending more or less on ^six-sided combinations of minute par- 
 ticles of ice. 
 
 When particles of such forms are floating or descending in the air, 
 there can be no difficulty in deriving from them those various and in- 
 tricate forms which are occasionally met with among this class of 
 phenomena. 
 
 Halos are frequently observed in other climates, as well as in the 
 northern regions of the globe, especially in the colder months, and 
 in the light clouds which float in the highest regions of the air. The 
 halos are usually attended by a horizontal white circle, with brighter 
 spots, or parhelia, near their intersections with this circle, and with 
 portions of inverted arches of various curvatures; the horizontal circle 
 has also sometimes anthelia, or bright spots nearly opposite to the 
 sun. These phenomena have usually been attributed to the effect of 
 spherical particles of hail, each having a central opaque portion of a 
 certain magnitude, mixed with oblong particles, of a determinate 
 form, and floating with a certain constant obliquity to the horizon. 
 But all these arbitrary suppositions, which were imagined by Huy- 
 gens, are in themselves extremely complicated and improbable. A 
 much simpler, and more natural, as well as more accurate explana- 
 tion, which was suggested at an earlier period by Mariotte, had long 
 been wholly forgotten, till the same idea occurred to Dr. Young. 
 The explanation given by the last mentioned philosophers is, that 
 water has a tendency to congeal or crystallize in the form of a prism, 
 and that the rays of light passing through these prisms (which are 
 disposed in various positions,) by their own weight, are so refracted 
 as to produce the different appearances which halos and parhelia 
 have been observed to assume. 
 
 The colours which these phenomena exhibit, are nearly the same as 
 the rainbow, but less distinct ; the red being nearest to the luminary, 
 and the whole halo being very ill defined on the exterior side. Some- 
 times the figures of halos and parhelia are so complicated, as to 
 defy all attempts to account for the formation of their different parts ; 
 but if the various forms and appearances which the flakes of snow 
 assume, be considered, there will be no reason to think them inade- 
 quate to the production of all these appearances. 
 
 On the Line of Perpetual Congelation. 
 
 In consequence of the diminution of temperature which is experi- 
 enced as we ascend in the atmosphere, it is evident that in every 
 climate a point of elevation may be reached where it will be con- 
 tinually freezing. The altitude of the point above the surface of the 
 earth, will depend partly on the temperature of the lower regions of 
 the atmosphere, and partly on the decrement of heat belonging to 
 the column at the period of observation, Thus, near the equator, 
 it was observed by Bougner, that it began to freeze on the sides of 
 
28 
 
 ON THE LINE OF PERPETUAL CONGELATION. 
 
 the lofty mountain Pinchencha, at the height of 15,577 feet above 
 the level of the sea, whereas congelation was found by Saussure to 
 take place on the Alps at the height of 13,428 feet. By tracing a 
 line on the plane of the meridian, through the points at which it con- 
 stantly freezes, a curve is obtained, which has been denominated the 
 line of Perpetual Congelation. The height at which this curve inter- 
 sects a vertical line in the various latitudes, has been computed by 
 Kirwan, partly from observation, and partly from the mean tempera- 
 ture of the parallel, and the decrement of heat, as we ascend in the 
 atmosphere. The following table exhibits the result of his calcu- 
 lations ; and though it is constructed on the erroneous supposition, 
 that the mean annual temperature of the pole is 31, which, accord- 
 ing to the observations of Captain Scoresby and Captain Parry, 
 must be far beyond the truth, it is tolerably accurate for the more 
 accessible regions of the globe. 
 
 Mean Height of Line Mean Height of Line 
 
 Latitude. of Congelation. Latitude. of Congelation. 
 
 - - - 15,577 45 - - - 7,658 
 
 5 - - 15,457 50 - - - 6,260 
 
 10 - - - 15,067 55 - - - 4,912 
 
 15 - - , 15,498 60 - - - 3,684 
 
 20 - - - 13,719 65 - - - 2,516 
 
 25 - - - 13,030 70 - - - 1,557 
 
 30 - - - 31,592 75 - - - 748 
 
 35 - - - 10,664 BO - - - 128 
 40 - - - 9,016 
 
 These numerical relations will be best perceived at a glance, by 
 means of the following diagram : 
 H 
 
 14,000 
 
 Here E P represents the rectified meridian from the equator to the 
 pole, divided into intervals of 10 each; and the different perpendi- 
 culars or ordinates at the point 0, 10, 20, &c. represent the height 
 of the freezing point at the equator, and at latitude 10, 20, &c. to 
 the pole P. The curve H P, which has a contrary flexure about 60, 
 exhibits the general form of the line of Perpetual Congelation from 
 the equator to the pole. 
 
ON THE REGULATION OF PUBLIC CLOCKS. 29 
 
 On the manner of Regulating Public Clocks. By J. LlTTROW, 
 Director of the Observatory of Vienna. 
 
 Up to this time, says the Author, in our town and many others, 
 persons have been appointed for the express purpose of regulating the 
 public clocks : every one knows by experience in what manner they 
 discharge this duty. 
 
 The first thing to be desired is that public clocks should agree 
 better, if not with the heavens, at least with one another, to obviate 
 the possibility of mistakes arising in keeping appointments at any 
 given time. Undoubtedly it is sufficient for many persons if the town 
 clocks keep time tolerably together, whether right or wrong; but there 
 are likewise many others to whom it is of importance that they should 
 go correctly. In fact, if the principal church clock, by which the 
 others must be regulated, be bad (and the best clocks of this descrip- 
 tion are so, if compared with astronomical clocks), it will go some- 
 times too slow, sometimes too fast, and it will be necessary some- 
 times to put the other clocks-back, and sometimes forward, although 
 they are often better than the principal ones. It will be the same 
 with regard to private clocks, which, adds Mr. Littrow, must be con- 
 tinually adjusted, to make them agree with the principal town-clock, 
 by which all the others must be regulated. 
 
 Thus the public clocks, if we wish to establish systematic 
 order, ought not only to agree together, but the clock which serves to 
 regulate the others must go well, and correspond exactly to the great 
 celestial clock; this must be the second necessary condition. But 
 how is this conformity to be brought about ? The pretended regulating 
 clocks, or the common pendulums frequently used for that purpose, 
 are of no great utility, on account of their elevated situation, of their 
 being exposed to the influence of variations of temperature, and to the 
 high winds which cannot fail to agitate lofty towers, and of the oscil- 
 latory movement communicated by the bells, at the time of striking, 
 to the whole building. The solar dials of themselves are too small 
 and too imperfect, to expect from them the exactness necessary in 
 such a case. Meridians, besides various other inconveniences, are 
 of no use except when the sun appears precisely at noon. If, 
 which is not uncommon in our foggy months of winter, the sun is three 
 or four weeks concealed behind the clouds, at noon-time, even when 
 the rest of the day is fine, the poor superintendant of the clock-house 
 can no longer discern the time, and must remain inactive, even though 
 his clock should be so much out of order, as to be half an hour too 
 slow or too fast. In order to accomplish this object satisfactorily, 
 a signal should be given from an observatory, the only place in 
 which the time of the day can he known with certainty at every 
 instant. 
 
 To remedy this double inconvenience, and to regulate for the future 
 the town-clocks (of Vienna), he proposes that, commencing from the 
 1st of March, 1824, the precise moment of noon shall be coiuiuuni- 
 
 h 
 
30 ON THE REGULATION OF PUBLIC CLOCKS. 
 
 cated by a large bell, placed in the observatory for that purpose, in 
 the following manner. Two minutes before noon, the sound of the 
 bell shall give warning for some seconds to inform the superintendants 
 of the public clocks, and all the inhabitants of the town, that it is 
 time to go to their clocks and regulate them. Twenty-four seconds 
 before noon, the same bell to begin striking like a clock, one stroke 
 every two seconds, so that the twelfth and last stroke is the precise 
 moment of noon. Exactly at this last stroke, it shall be previously 
 arranged for the clock of St. Stephen's church to begin striking noon, 
 which will serve as a signal to regulate with axactness all the other 
 public clocks of the town and suburbs. Every inhabitant will like- 
 wise be able to avail himself of this opportunity to regulate his own 
 clock. 
 
 We think we ought, says M. Littrow, to add two remarks to the 
 preceding. The first relates to the persons to whom the execution of 
 the plan must be principally confided. They have often occasion to 
 know the time almost to a second, and the means which they have 
 hitherto employed effected their purpose badly, or not at all. We 
 are not speaking here of those who, like their predecessors in the last 
 century, make use of solar dials, and other methods equally defective ; 
 for such workmen, who are satisfied with knowing the time within a 
 few minutes, must not be confounded with real artists. But there are 
 men of this class, adds Mr. Littrow, and I myself know several, who 
 would rival the most celebrated artists of England, if they received 
 the necessary encouragements. Every English artist has an obser- 
 vatory in Ijis house for his own use ; it is with this great celestial 
 clock that he compares his instruments ; he corrects and rectifies his 
 work, till he is able to say, with a full conviction to every purchaser 
 who presents himself " It is ready, it is finished, it is complete." 
 
 Our author's second remark relates to the difference which exists 
 between what is called true time and mean time. He here enters 
 into a long digression on measuring time by the moon. The most 
 ancient nations regulated their weeks by this planet and its dif- 
 ferent phases. Many periods of unequal duration have been invented 
 to calculate centuries and ages, but men have been unanimous in 
 reckoning seven days to the week, the origin of which is lost in re- 
 mote antiquity. Doubtless at first sight, the moon appears, by its 
 continually changing disk, and its striking phases, to have been made 
 expressly to serve as a perpetual calendar : nevertheless, it will soon 
 be perceived, that, of all the heavenly bodies, it has the least right to 
 this prerogative. In fact the Jews, among whom the moon plays the 
 most important part, have the most confused chronology among the 
 moderns. There are no less than six different kinds of years in use 
 among them, and the learned alone can comprehend their calendar, 
 which in exceedingly complicated. But what shall we say of our 
 pwn ecclesiastical computation ? Are there many people, even among 
 the well-informed, who can tell what day Easter or Whitsuntide will 
 fall upon, in any year ? 
 
 If the moon is so ill adapted for regulating the calendar, we may 
 
ON THE REGULATION OF PUBLIC CLOCKS. 31 
 
 likewise observe that it is not from the sun we can expect an exact 
 division of the day into hours, minutes, &c. In fact, to adopt popular 
 language, the sun moves in an ellipse, in an oval curve. In winter, 
 he is nearer the earth than in summer, and he moves faster in the 
 former season than in the latter. This circumstance alone would 
 create an inequality in the length of the days, as well as in that of 
 the hours, minutes, &c. But there is besides another cause of ine- 
 quality. The sun moves in the ecliptic, whose plane makes an angle 
 of about 23 28' with that of the equator, and it is to this latter circle 
 that we refer the measure of time. In fact all our determinations on 
 this head are founded on the perfectly uniform rotation of the hea- 
 vens, or rather of the earth, around the axis of the world, that is to say, 
 around the axis of the equator, the direction of which is exactly from 
 south to north. Even were the sun to move uniformly in the ecliptic, 
 for instance, a degree each day, this degree, referred to the equator, 
 would hardly ever correspond to a degree of the latter circle, but 
 would be sometimes more, sometimes less. So that even the motion 
 of the sun at a constantly equal rate would be to no purpose ; his 
 motion would be unequal with respect to us, and could not serve to 
 determine the time exactly. 
 
 Since the true sun, that king of our days, that dispenser of light 
 and heat, so useful to form great periods of years and centuries, is so 
 little adapted to measure the day and its parts, astronomers have 
 chosen another sun, which assuredly has neither light nor heat, and 
 does not even exist in the heavens, but which is, for that very reason, 
 the better calculated to be the regulator of our clocks. This sun, 
 which is called the mean sun, to distinguish it from the true sun that 
 attracts the eye, moves uniformly in the plane of the equator, so that 
 it completes its annual course in the same time that the real sun tra- 
 verses the ecliptic by an unequal movement. When this mean sun 
 passes over the meridian of a place, we say that it is mean noon in 
 that place ; and often in the course of a year, there is more than a 
 quarter of an hour of difference between this mean noon, and the true 
 noon of the real sun. But as the mean solar days are always of the 
 same length, the mean noon will always be exactly given by the last 
 stroke of the observatory bell, as before explained. In this manner, 
 clocks will no longer be made to go against their nature, that is to say 
 irregularly, but without incessantly altering them, it will be sufficient 
 to see every noon if their movements be regular ; and the superin- 
 tendants of clocks, who have hitherto had no good method of verify- 
 ing the time to a second, will hereafter have an opportunity of ascer- 
 taining daily how far the movement of their pendulums is correct. 
 (Bui. de Sciences.) 
 
32 ON PREDICTING THE WEATHER BY THE BAROMETER. 
 
 On Predicting the Weather by the Barometer. 
 
 It is now a considerable time since the barometer was proposed 
 as a a proper instrument for predicting the weather; and hence it 
 obtained the name of weather glass. Accordingly, rules for this 
 purpose have been given by Dr. Halley, Dr. Hutton, Messrs. Pascal, 
 Patrick, Rowning, Changeux, de Luc, Clarke, Dalton, and many 
 others, from whose writings we have collected the following rules. 
 
 When the mercury in the barometer rises, it is a sign of fair wea- 
 ther, attended with heat, if in summer, but frost in winter. If the 
 mercury falls, it denotes rain, or wind, or perhaps both. 
 
 If the mercury rises suddenly during the time of rain, the ensuing 
 fair weather will not continue "long ; but if the rise is gradual, and 
 continues for several days, a continuance of fair weather may be ex- 
 pected. 
 
 If the mercury falls suddenly several divisions, it is a sign that the 
 succeeding rain will not be of long duration. But if the mercury 
 continues to fall regularly for several days, rain or wind, or perhaps 
 both, will be of considerable duration. 
 
 The mercury falling considerably in autumn, winter, or spring, in- 
 dicates gales of wind, commonly attended with rain, snow, or sleet; 
 but, in summer, it denotes rain, and probably thunder. The mercury 
 is low with high winds, and still lower if accompanied with rain. If 
 the mercury falls quickly in very warm weather, thunder showers may 
 be expected soon after. 
 
 If the mercury be in an unsettled and fluctuating state the weather 
 has the appearance of being very changeable. 
 
 If the mercury has been stationary during several days, its surface 
 must be carefully observed, to ascertain whether it is rising or falling. 
 For this purpose, let the exact figure of the surface of the mercury 
 be observed ; then shake the tube a little, and observe if the mercury is 
 more or less convex or concave. If it is more convex, it is a sign 
 the mercury is rising ; if the same as before, it is stationary ; but if 
 less, that it has attained its greatest altitude at that time, and will 
 fall soon. If the mercury was concave before the tube was shaken, 
 and more concave afterwards, the mercury is falling ; if of the same 
 concavity, or nearly so, it is stationary ; but if less concave it is 
 rising. 
 
 Between the tropics, there is . little variation in the height of the 
 mercury in the barometer ; and the more distant any place is from the 
 equator, the greater is the range of the mercury. Thus, at St. He- 
 lena, the extreme variation is very little ; at Jamaica it is only about 
 three tenths of an inch ; at Naples it seldom exceeds an inch. In 
 England the extreme range amounts to about 2^ inches ; and at Pe- 
 tersburgh to 3 J- inches nearly. 
 
ON ASCERTAINING THE LONGITUDE, &C. 3*3 
 
 On the. Methods proposed for ascertaining the Longitudes and Latitudes 
 of Places by Magnetical Instruments. 
 
 THE facility and readiness with which the longitudes and latitudes 
 of places upon the surface of the earth might be ascertained, by means 
 of magnetical instruments, if their performance could be depended 
 upon, has at various times brought forward the proposals of instru- 
 ments, and calculations made expressly for the purpose; but the ac- 
 tual experiments made on those plans have constantly shewn, that 
 both the instruments and the calculations are insufficient to answer 
 that object; and the principal reason of the failure is the uncertainty 
 of the motion of the magnetic poles of the earth, upon which the 
 variation of the compass principally depends. 
 
 That those poles (which may be considered to be the centres or 
 focuses of all the magnetic bodies contained in the earth) do not 
 remain fixed, but that they do actually move from place to place, is 
 sufficiently evinced by the results of accurate observations ; and no 
 modern writer seems to entertain a doubt about it. The variation of 
 the declination, or the change of variation, is principally attributed to 
 the motion of those poles ; but the difficulty consists in determining 
 whether this motion is regular or irregular, viz. whether it may, or 
 may not, be foretold by calculation, according to any rule what- 
 soever. 
 
 That nature is regular in her works, and that every natural opera- 
 tion depends upon adequate causes, no person, who is at all ac- 
 quainted with philosophy, can possibly deny. But when a certain 
 phenomenon depends upon the combination of a variety of causes, 
 some of which, and perhaps all of them, arR out of the reach of our 
 senses, and of calculation, we call it irregular or accidental; not for 
 want of a natural dependance upon adequate causes, but because we 
 are unable to discover and ascertain the laws of that dependance. 
 Thus we know that the temperature of the atmosphere in London de- 
 pends on the time of the year, on the point from which the wind 
 blows, on the clearness of the air, &c. yet no one can foretel the 
 precise degree of heat that will be indicated by the thermometer on a 
 particular day of the next year ; because, in the first place, we are 
 not acquainted with all the concurring causes, and secondly, because, 
 from the action of those causes upon each other, their ultimate effect 
 upon the body of the earth becomes the result of an immense and 
 incommensurable combination. 
 
 With respect then to magnetism, we must first endeavour to dis- 
 cover the causes which occasion the motion of the magnetic poles of 
 the earth ; and secondly, we must consider whether the effects of those 
 causes may or may not be subjected to calculation. 
 
 The projectors of the methods for ascertaining the longitude and 
 latitude by means of the variation compass, and of the dipping needle, 
 generally frame hypotheses of regular movements, and establish 
 upon them all their rules and calculations, and overlook the natural 
 causes of irregularity or uncertainty. But hypotheses that are not 
 founded upon a constant coincidence of effects, and especially when 
 
34 ON ASCERTAINING THE LONGITUDE, &C. 
 
 they are insufficient to account for all the phenomena, cannot be con- 
 sidered as guides in the investigation of future events. The magnetic 
 poles of the earth have been supposed to be four in number; though 
 they are at present generally, and more properly, thought to be only 
 two. They have been supposed to reside on the surface of the earth, 
 and to move upon it at a certain annual rate : They have been sup- 
 posed to be fixed to a sort of nucleus within the earth, and to move 
 along with it either from east to west, or from west to east : They 
 have been supposed to be in the atmosphere ; and in short, the con- 
 jectures have been very numerous; but let the hypothesis be what it 
 will, we have no reason to believe that their motion is so regular as 
 to be foretold, which will more evidently appear from the following 
 reasons. 
 
 In the investigation of natural properties, when they are out of the 
 reach of actual observation or calculation, the imagination must start 
 with, and be guided by the analogy of, established facts and laws; 
 otherwise the probability of being right vanishes entirely. Agreea- 
 bly to this rule, if we attempt to form conjectures relative to the mag- 
 netic poles of the earth, we must in the first place say, that as the 
 magnetic polarity has been found to be a property only of iron or 
 ferruginous bodies, therefore it is likely that the magnetic poles of the 
 earth reside not in the atmosphere, but in the ferruginous bodies con- 
 tained in the earth. Secondly, we have no reason whatever to believe 
 that the earth contains a moveable nucleus or kernel, but we know 
 that in a magnet, whether natural or artificial, the poles frequently 
 change their places, though the magnet has no nucleus ; and there- 
 fore the magnetic poles of the earth may be susceptible of motion 
 independent of a nucleus. Thirdly, it is natural to suppose that the 
 same causes, which have been found to alter the situation of the poles 
 of a magnet, act in the same manner upon the earth, and occasion 
 the motion of its poles. Those causes, and the method of manifest- 
 ing their effects, may be reduced to four ; viz. the action of one mag- 
 net upon the other; the action of heat and cold; the chymical alte- 
 ration or decomposition of the substance affected with magnetism ; 
 and, lastly, the mere mechanical derangement of parts. That all 
 those causes take place in the earth, nobody can deny ; and of course 
 it seems to be as evident, as the nature of the subject will admit of, 
 that the motion of the magnetic poles is governed by the concurrence 
 of all those causes. 
 
 So far we have considered only the motion of the magnetic poles 
 of the earth, which undoubtedly govern the general variation of the 
 magnetic needle; but if we also take into the account the local 
 causes, which have been indisputably found to affect the needle in 
 particular places, such as the vicinity of great tracts of land, pro- 
 montories, volcanos, &c. we must acknowledge that the prospect is 
 very discouraging, and the probability of our ever becoming able to 
 ascertain the longitude and latitude by means of magnetical instru- 
 ments, seems almost to vanish. In fact, when we examine the differ- 
 ent projects hitherto published, and compare their results, we find an 
 astonishing diversity as well among themselves, as between them and 
 actual observations. 
 
TABLE OF LATITUDES AND LONGITUDES. 
 
 TABLE 
 
 Of the Latitudes and Longitudes of the Principal Observatories in the 
 World, from the latest and most accurate Observations. 
 
 Names of Places. 
 
 Latitude. 
 
 Londitude. 
 
 In Degrees. 
 
 In Time. 
 
 
 52 22 17 N. 
 
 4 53 15 E. 
 6 37 30 W. 
 106 51 45 E. 
 13 22 15 E. 
 11 21 30 E. 
 8 48 E. 
 17 2 18 E. 
 10 32 E. 
 19 2 30 E 
 6 17 22 W. 
 7 34 E. 
 9 35 18 E. 
 8 24 42 W. 
 28 55 15 E. 
 12 35 6 E. 
 19 57 9 E. 
 18 38 5 E. 
 26 42 E. 
 13 43 1 E. 
 6 20 30 W. 
 3 10 21 W. 
 11 15 45 E. 
 9 22 15 E. 
 8 58 E. 
 4 16 OW. 
 10 44 E. 
 9 56 30 E. 
 000 
 6 7 55 W. 
 15 45 E. 
 12 21 45 E. 
 4 29 13 E. 
 8 54 15 E. 
 9 8 30 W. 
 5 47W. 
 3 42 15 W. 
 14 30 35 E. 
 8 28 E. 
 
 h. m. s. 
 19 33 E. 
 26 30 W. 
 7 7 27 E. 
 53 29 E. 
 45 26 E. 
 35 12 E. 
 1 8 9 E. 
 42 8 E. 
 1 16 10 E. 
 25 9W. 
 30 E. 
 38 21 E. 
 33 39 W. 
 1 55 41 E. 
 50 21 E. 
 1 19 49 E. 
 1 14 32 E. 
 1 46 48 E. 
 54 52 E. 
 25 22 W. 
 12 41 W. 
 43 3 E. 
 37 29 E. 
 35 52 E. 
 17 4W. 
 42 56 E. 
 39 46 E. 
 000 
 24 32 E. 
 1 3W. 
 49 27 E. 
 17 57 E. 
 35 37 E. 
 36 34 W. 
 23 W. 
 14 49 W. 
 58 2 E. 
 33 52 E. 
 
 Armagh 
 
 54 21 15 N. 
 6 9 S. 
 52 31 45 N. 
 44 30 12 N. 
 53 4 38 N 
 
 
 Berlin 
 
 
 Breslaw 
 
 51 6 30 N. 
 52 16 29 N. 
 47 29 44 N. 
 36 32 N. 
 52 12 43 N. 
 51 19 20 N. 
 40 12 30 N. 
 41 1 27 N. 
 55 41 4 N. 
 50 3 38 N. 
 54 20 48 N. 
 58 22 47 N. 
 51 2 50 N. 
 53 23 13 N. 
 55 57 57 N. 
 43 46 41 N. 
 47 25 40 N. 
 44 25 N. 
 55 51 32 N. 
 50 56 8 N. 
 51 31 50 N. 
 51 28 39 N. 
 43 7 2 N. 
 51 28 37 N. 
 51 20 16 N. 
 52 9 30 N. 
 53 8 30 N. 
 38 42 24 N. 
 51 30 49 N. 
 40 24 57 N. 
 35 53 N. 
 49 29 18 N. 
 
 
 Buda 
 
 Cadiz 
 
 Cambridge (St.M. Steeple) 
 Cassel 
 
 Coimbra 
 
 Constantinople (St.Sophia) 
 Copenhagen 
 
 
 Dantzic 
 
 Dorpat 
 
 
 Dublin 
 
 
 Florence 
 
 St. Gall (Switzerland) . . 
 Genoa 
 
 Glasgow 
 
 xotha (Seeberg) . . . 
 Gottingen 
 
 Greenwich 
 
 
 Kew 
 
 Leipsic 
 
 _<eyden 
 
 Lilienthal 
 
 .Jsbon 
 
 Condon (St. Paul's) . . 
 Madrid (Grand Square) . 
 Malta (Valetta) .... 
 Manheim 
 
TABLE OP LATITUDES AND LONGITUDES. 
 
 Names of Places. 
 
 Latitude. 
 
 Longitude. 
 
 In Degrees. | In Time._ 
 
 Marseilles ..... 
 Milan ....... 
 
 43 17 49 N 
 45 28 2 N 
 43 5 7 N 
 56 39 6 N 
 44 55 N 
 43 36 16 N 
 55 45 45 N 
 48 8 20 N 
 40 50 15 N 
 49 26 55 N. 
 51 45 39 N. 
 45 24 2 N. 
 38 6 44 N. 
 48 50 14 N. 
 39 54 13 N. 
 59 56 23 N. 
 43 43 11 N. 
 50 22 20 N. 
 50 48 3 N. 
 50 5 19 N. 
 49 53 N. 
 51 28 8 N. 
 41 53 54 N. 
 51 30 20 N. 
 59 20 31 N. 
 48 34 56 N. 
 43 35 46 N. 
 45 4 14 N. 
 59 51 50 N. 
 52 5 31 N. 
 45 25 32 N, 
 45 26 7 N. 
 48 12 40 N. 
 44 29 14 N 
 
 6 22 15 E 
 9 11 31 E 
 1 5-2 26 E 
 22 43 27 E 
 1 20 45 E 
 3 52 40 E 
 37 33 E 
 11 34 40 E 
 14 15 45 E 
 11 4 15 E 
 1 15 22W 
 11 51 32 E 
 13 22 E 
 2 20 15 E. 
 116 27 45 E 
 30 18 45 E. 
 10 24 E. 
 4 7 16W. 
 1 5 59 W. 
 14 25 15 E. 
 12 4 30 E. 
 18 45 W. 
 12 29 47 E. 
 36 OW. 
 18 3 30 E. 
 7 44 51 E. 
 1 26 30 E. 
 7 40 15 E. 
 17 39 E. 
 5 7 16 E. 
 12 20 59 E. 
 11 1 15 E. 
 16 22 45 E. 
 4 41 E. 
 11 21 E. 
 25 18 E. 
 
 h. m. s. 
 21 29 E. 
 36 46 E. 
 7 30 E. 
 1 34 54 E. 
 5 23 E. 
 15 31 E. 
 2 30 12 E. 
 46 18 E. 
 57 3 E. 
 44 17 E. 
 5 1W. 
 47 26 E. 
 53 28 E. 
 9 21 E. 
 7 45 51 E. 
 2 1 15 E. 
 41 36 E. 
 16 29 W. 
 4 24 W. 
 57 41 E. 
 48 18 E. 
 1 15W. 
 49 59 E. 
 2 24W. 
 1 12 14 E. 
 30 59 E, 
 5 46 E. 
 30 41 E. 
 1 10 36 E. 
 20 29 E. 
 49 24 E. 
 44 5 E. 
 1 5 31 E. 
 18 44 E. 
 45 24 E. 
 1 41 12 E. 
 
 Mirepoix ...... 
 
 Mittau 
 
 Moritauban 
 
 Montpellier ..... 
 
 
 Munich 
 
 
 
 
 
 Palermo ...... 
 
 Paris ....... 
 
 Pekin , 
 
 
 
 
 Portsmouth . . , 
 
 
 
 Richmond ..... 
 
 lome (College) . . . 
 Slough (Herschei's) . . 
 Stockholm ...... 
 
 
 Toulouse ...... 
 
 
 
 Utrecht 
 
 Venice (St. Mark's) . . 
 Verona ...... 
 
 
 
 Weimar ...... 
 
 50 59 12 N. 
 54 41 2 N. 
 
 Wilna 
 
ON THE OBLATE SPHEROID. 37 
 
 On the Method of determining the Flatness of the Oblate Spheroid in 
 France, by the comparison of an Arc of the Meridian with an Arc 
 of a Parallel. 
 
 THE two lines of curvature on the earth's surface at any place, 
 being well calculated to determine with precision the dimensions of 
 the oblate spheroid in that place, geometers and astronomers have 
 long wished that the great geodesic operations executed in Europe, 
 like those upon which the new system of French measures is founded, 
 should be immediately applied to the measurement of different arcs 
 of meridians and parallels, in order to acquire, by this means, a more 
 accurate knowledge of the real figure of the earth. 
 
 The trigonometrical labours undertaken by the French royal body 
 of geographical engineers, under the immediate direction of the war 
 department, and which are to serve as the skeleton of the new map 
 of that country, already furnish very valuable results for the solution 
 of the problem in question. For example : an arc of the parallel, 
 measured trigonometrically and astronomically, in the latitude of 45 
 degrees, extends from the tower of Cordovan into Piedmont, and 
 might even be continued to Fiume and farther. The observations on 
 longitudes made last year, by Colonel Brousseaud and the astro- 
 nomer Nicollet, by means of signals of fire, give the amplitudes of four 
 consecutive portions of this line, which embrace an extent of seven 
 degrees. They are connected with those made by Messrs. Plana 
 and Carlini, and other foreign philosophers a year before, upon the 
 same line beyond the Alps, and thus form a geographical union be- 
 tween France and Italy. 
 
 Another arc of the parallel, not less important, comprised between 
 Brest and Strasburg, the measure of which had been earnestly desired 
 by the illustrious La Place, author of the Mecanique Celeste, is al- 
 ready known geodesically. It is upon this line that reverberating 
 lamps have been constantly used for the purpose of ascertaining 
 whether angular observations in places but little elevated, agree toge- 
 ther better by night than*by day. It is also upon* this line, that a 
 trigonometrical survey has been effected by reciprocal and simulta- 
 neous observations from Paris to Brest; with the view either of deter- 
 mining exactly the absolute heights of the stations comprised between 
 these extreme points, or of connecting by these stations all the 
 secondary surveys intended to be afterwards undertaken for forming a 
 hydrographic map of France. 
 
 It is proposed this year to make observations on the longitude of 
 this second primordial line ; but in order to avoid the trouble of estab- 
 lishing temporary observatories in an open country, and above all, 
 the enormous expense which their construction would occasion, the 
 difference of longitude between the extremities of this axis, will, with 
 the assistance of chronometers placed at several intermediate points, 
 be obtained, by the rapid transmission, by means of gunpowder 
 signals, of the hours which will be counted, at the same instant of 
 time, at Brest, and at Strasburg. This very simple proceeding is 
 
 k 
 
38 ON THE OBLATE SPHEROID. 
 
 perhaps the best that can be employed to obtain promptly the total 
 amplitude of a great arc of parallel, not only because it is independent 
 of the errors which might result from the ordinary method of absolute 
 time determined at intermediate stations at *a short distance from 
 one another, but because it is not liable to the irregularities in the 
 diurnal movement of chronometers. Nevertheless, as it is of import- 
 ance to compare together different arcs of the same parallel, it will be 
 highly useful to ascertain separately the difference between the meri- 
 dians of Brest and Paris, and that between the meridians of Paris 
 and Strasburg. 
 
 The parallel of the 45th degree, of which we have just spoken, is 
 joined in one direction to one of the sides of the meridian of France, 
 and in the other to the base of Beccaria, near Turin, being verified 
 by the French geographical engineers, as well as by M. Plana, and 
 other Italian philosophers ; so that the method laid down by La 
 Place in the third Supplement to his " Analytical Theory of Proba- 
 bilities" might be easily applied for correcting in the most advan- 
 tageous manner this arc and its several parts, by the difference 
 existing between the entire base measured directly, and its length, as 
 deduced from the chain of triangles. 
 
 The calculations relative to the comparison of an arc of the parallel 
 with an arc of ihe meridian, are capable of being effected in a manner 
 analogous to that made use of for determining the oblateness of the 
 earth, by the measure of two arcs of meridians under different lati- 
 tudes. In fact, there exists a relation between the length of an arc 
 of the meridian, considered as elliptical, and the latitude of its extre- 
 mities; and this relation is essentially a function of the radius of the 
 equator, and of the oblateness of the earth. "In like manner, an arc 
 of the parallel in any given latitude, is a function of its amplitude, of 
 the radius of the equator, and of the same oblateness ; thus, proceed- 
 ing by the ordinary mode of elimination, we can obtain these two last 
 unknown quantities ; that is to say, the . dimensions of the oblate 
 spheroid at the point where the two combined arcs cut one another, 
 and consequently can ascertain whether the figure of this solid is the 
 same generally attributed to the whole earth, according to the com- 
 parison made of the arcs of meridians measured in France and at the 
 equator. 
 
 If the parts of the parallel thus examined are not proportional to 
 their amplitudes, it will be advisable to determine the spheroid which 
 corresponds best upon the whole with the observations of longitude, 
 and this by using the method of the smallest squares, invented by M. 
 Legendre, and demonstrated by M. Laplace to be the most advan- 
 tageous. In this case, conditional equations must be formed between 
 the errors to which observations are liable and the oblateness of the earth ; 
 and if among the smallest probable errors which affect the observation 
 of longitude, there should be any too considerable to be really attri- 
 butable to the observations, it may be concluded that the spheroid 
 sought is not that of revolution. The surest method will then be to 
 have recourse to the admirable theory given in the third book of the 
 Celestial Mechanics of La Place. 
 
OF THE AGENCY OF THE EARTH, &C. 39 
 
 The grand trigonometrical surveys undertaken to furnish materials 
 for the new topographical map of France, and the numerous obser- 
 vations of the pendulum carefully collected by the Board of Longi- 
 tude in that kingdom, concur to throw a new light upon the difficult 
 question of the figure of the earth. And it is to be earnestly hoped 
 that, in other countries besides France, similar exertions in favour of 
 science and public utility will be promoted and patronised. 
 
 On the Agency of the Earth in producing Meteors. 
 By Professor MEINECKE. 
 
 THIS gentleman, in a memoir read to the Natural Society of 
 Halle, proves, in various ways, the existence of a lower terrestrial 
 atmosphere; he thinks himself justified, by the reasons he alleges, in 
 concluding with certainty, that this atmosphere, which may penetrate 
 to a depth of twenty geographical miles into the interior of the earth, 
 is already compressed at a smaller depth, so that without being 
 liquid, it forms a fluid equivalent to water. Hence there results for 
 the lower terrestrial atmosphere a mass, in comparison of which, the 
 higher atmosphere, which is known to be equal in weight to a column 
 of water, about thirty feet high, appears very small. 
 
 It is to this mass of inferior air, contained in the pores of fossils, 
 in cavities, in abysses, and even constituting part of the elements of 
 fossils, that the professor attributes the greater part of meteors ; 
 while that insignificant mass of air, disseminated in the form of 
 vapour, and hitherto called the atmosphere, at most contributes but 
 slightly to their creation. As he attributes the barometrical pheno- 
 mena to the inferior atmosphere, he likewise denies the influence of 
 the moon upon the weather. 
 
 On the Colours of the Atmosphere. 
 
 IF the earth's atmosphere consisted of a medium unlimited, and 
 perfectly homogeneous, the sun and planets would shine in a firma- 
 ment of the most intense darkness, similar to what has been observed 
 by travellers on the elevated summits of the Alps and the Andes. 
 
 As the atmosphere, however, is of a limited extent, and composed 
 of strata of variable density, the light of the sun which falls upon it is 
 reflected in every direction, and reaches the surface of the earth with 
 that chaste tinge of blue, which forms such a fine relief to the yellow- 
 ish light of the heavenly bodies. 
 
 The blue colour of the sky was attributed by Fromondus, Otto 
 Guericke, Wolfius, and Muschenbroek, to a mixture of light and 
 shadow. Sir Isaac Newton and Bouguer, on the contrary, were of 
 opinion, that the particles of air reflect the blue rays more copiously, 
 and transmit the red. 
 
4O ON THE COLOURS OF THE ATMOSPHERE. 
 
 This explanation, which was then little better than a mere conjec- 
 ture, has been rendered highly probable by the experiments of Dr. 
 Brewster on the polarisation of light. 
 
 He observed that one of the images of certain parts of the sky, 
 formed by a doubly refracting crystal, was much bluer than the other, 
 and that the images changed their tints alternately. Upon the sup- 
 position, therefore, that the light of the sky consists of two portions 
 of light, one blue and the other nearly colourless, we may explain all 
 the phenomena which appear, when the light of the sky is examined 
 in different azimuths, and in different planes passing through the sun. 
 
 The phenomena of blue shadows, which have been so often observed, 
 arise from the illumination of the shadows of bodies by the blue light 
 of the sky, the parts without the shadow being illuminated by some 
 other light, such as that of the sun or of a candle. These coloured 
 shadows are generally seen with most distinctness at sun-rise and 
 sun-set, when the sun's light has a yellow tinge. 
 
 The colours of shadows illuminated by the sky, vary in different 
 countries, and with different seasons of the year, from pale blue to a 
 violet black ; and when there are yellow vapours in the horizon of 
 yellow light reflected from the lower part of the sky, either at sun- 
 rise or at sun-set, the shadows have a strong tinge of green, arising 
 from the mixture of these accidental rays with the blue tint of the 
 shadow. 
 
 The phenomena of coloured shadows are often finely seen in the 
 interior of a room. They arise from the blue light of the sky, and the 
 light reflected either from the furniture, or the painted walls of the 
 room. 
 
 M. Hassenfratz has written a very elaborate memoir on the subject 
 of coloured shadows, and has deduced the following conclusions from 
 his various experiments and observations. 
 
 1 That the shadows formed by the direct light of the sun and that 
 of the atmosphere, vary from a meadow green, to a violet black, in a 
 gradation through the blue, indigo, and violet ; and that the variation 
 depends on the intensity of the light of the sun, compared with that of 
 the atmosphere. 
 
 2. That the shadows formed in apartments by the light of the at- 
 mosphere and reflected lights, may present all the prismatic colours, 
 more or less changed by black. 
 
 3. That the shadows produced on a piece of pasteboard, illumi- 
 nated by artificial light, are reddish and blueish, more or less deep ; 
 and, that very probably, the blueish and reddish tints of the shadows, 
 depend on the proportion of hydrogen and carbon in the combustible 
 bodies. 
 
TABLE FOR REDUCING TIME. 
 
 TABLE 
 
 For Reducing Sidereal into Mean Solar Time. 
 
 Hours. 
 
 Equa. " 
 
 Min. 
 
 Equa. 
 
 Sec. 
 
 Equa. 
 
 
 III. S. 
 
 
 s. 
 
 
 S. 
 
 1 
 
 9-83 
 
 1 
 
 0-16 
 
 1 
 
 o-oo 
 
 2 
 
 19-66 
 
 2 
 
 0-33 
 
 2 
 
 o-oi 
 
 3 
 
 29-49 
 
 3 
 
 0-49 
 
 3 
 
 0-0 L 
 
 4 
 
 39-32 
 
 4 
 
 0-66 
 
 4 
 
 o-oi 
 
 5 
 
 39-15 
 
 5 
 
 0'82 
 
 5 
 
 0-01 
 
 6 
 
 58-98 
 
 6 
 
 0-98 
 
 6 
 
 0-02 
 
 7 
 
 1 08-81 
 
 7 
 
 1-15 
 
 7 
 
 0-02 
 
 8 
 
 1 18-64 
 
 8 
 
 1-31 
 
 8 
 
 0-02 
 
 9 
 
 1 28-47 
 
 9 
 
 1-47 
 
 
 
 0-02 
 
 10 
 
 1 38-30 
 
 10 
 
 1-64 
 
 10 
 
 0.03 
 
 U 
 
 1 48-13 
 
 11 
 
 1-80 
 
 11 
 
 0-33 
 
 12 
 
 1 57-96 
 
 12 
 
 1-97 
 
 12 
 
 0-03 
 
 13 
 
 2 07-78 
 
 13 
 
 2-13 
 
 13 
 
 0-04, 
 
 14 
 
 2 17-61 
 
 14 
 
 2-29 
 
 14 
 
 0-04 
 
 15 
 
 2 27-44 
 
 15 
 
 2'46 
 
 15 
 
 0-04 
 
 16 
 
 2 37-27 
 
 16 
 
 2-62 
 
 16 
 
 0-04 
 
 17 
 
 2 47-10 
 
 17 
 
 2-78 
 
 17 
 
 0-05 
 
 18 
 
 2 56-93 
 
 18 
 
 2-95 
 
 18 
 
 0-05 
 
 19 
 
 3 06-76 
 
 19 
 
 3-11 
 
 19 
 
 0-05 
 
 20 
 
 3 16-59 
 
 20 
 
 3-28 
 
 20 
 
 0-05 
 
 21 
 
 3 26-42 
 
 21 
 
 491 
 
 21 
 
 0-08 
 
 22 
 
 3 36-25 
 
 22 
 
 6-55 
 
 22 
 
 0-11 
 
 23 
 
 3 46-08 
 
 23 
 
 8-19 
 
 23 
 
 0-14 
 
 24 
 
 3 55-91 
 
 24 
 
 9-83 
 
 24 
 
 0-16 
 
 EXAMPLE. 
 
 Reduce 8 hours, 54 minutes, 18*5 seconds, Sidereal Time into Mean 
 
 Solar Time. 
 
 8 hours 
 50 minutes 
 
 Equa. 
 ditto 
 
 m. s. 
 1 18-64 
 08-19 
 
 4 minutes 
 
 ditto 
 
 0-66 
 
 18*5 seconds . 
 
 ditto 
 
 0-05 
 
 Sum 
 
 
 . 1 27-54 
 
 Given time 
 
 . 
 
 . 8h 54 18-50 
 
 Mean time required 
 
 8 52 50-96 
 
42 
 
 TABLE FOR REDUCING TIME. 
 
 TABLE 
 
 For Reducing Mean Solar into Sidereal Time. 
 
 Hours. 
 
 Equa. 
 
 Min. 
 
 Equa. 
 
 Sec. 
 
 Equa. 
 
 
 m. s. 
 
 
 s. 
 
 
 S. 
 
 1 
 
 9-86 
 
 1 
 
 0-16 
 
 1 
 
 o-oo 
 
 2 
 
 19-71 
 
 2 
 
 0-33 
 
 2 
 
 o-oi 
 
 3 
 
 29-57 
 
 3 
 
 0-49 
 
 3 
 
 o-oi 
 
 4 
 
 39-43 
 
 4 
 
 0-66 
 
 4 
 
 o-oi 
 
 5 
 
 49-28 
 
 5 
 
 0-82 
 
 5 
 
 o-oi 
 
 6 
 
 59-14 
 
 6 
 
 0-99 
 
 6 
 
 0-02 
 
 7 
 
 1 08-99 
 
 7 
 
 1-15 
 
 7 
 
 0-02 
 
 8 
 
 1 18-85 
 
 8 
 
 1-31 
 
 8 
 
 0-02 
 
 9 
 
 1 28-71 
 
 9 
 
 1-48 
 
 9 
 
 0-02 
 
 10 
 
 1 38-56 
 
 10 
 
 1-64 
 
 10 
 
 0-03 
 
 11 
 
 1 48-42 
 
 11 
 
 1-82 
 
 11 
 
 0-03 
 
 12 
 
 1 51-28 
 
 12 
 
 197 
 
 12 
 
 0-03 
 
 13 
 
 2 08-13 
 
 13 
 
 2-14 
 
 13 
 
 0-04 
 
 14 
 
 2 17-99 
 
 14 
 
 2-30 
 
 14 
 
 0-04 
 
 15 
 
 2 27 85 
 
 15 
 
 2 '46 
 
 15 
 
 0-04 
 
 16 
 
 2 37-70 
 
 16 
 
 2-63 
 
 16 
 
 0-04 
 
 17 
 
 2 47-56 
 
 17 
 
 2*79 
 
 17 
 
 0-05 
 
 18 
 
 2 57-42 
 
 18 
 
 2-96 
 
 18 
 
 6-05 
 
 19 
 
 3 07-27 
 
 19 
 
 3-12 
 
 19 
 
 0-05 
 
 20 
 
 3 17 13 
 
 20 
 
 328 
 
 20 
 
 0-05 
 
 21 
 
 3 26-98 
 
 21 
 
 4-93 
 
 21 
 
 0-08 
 
 22 
 
 3 36-84 
 
 22 
 
 6-57 
 
 22 
 
 0-11 
 
 23 
 
 3 46-70 
 
 23 
 
 8-21 
 
 23 
 
 0-14 
 
 24 
 
 3 56-55 
 
 24 
 
 9-86 
 
 24 
 
 0-16 
 
 EXAMPLE. 
 
 Reduce 8 hours, 52 minutes, 50-96 seconds, Mean Solar Time into 
 
 Sidereal Time. 
 
 m. s. 
 1 18*85 
 08-21 
 00-33 
 
 8 hours . 
 
 50 minutes 
 
 2 minutes 
 
 50-96 seconds 
 
 Sum 
 Given time 
 
 Equa. 
 ditto 
 ditto 
 ditto 
 
 00-14 
 
 4- 1 27-53 
 8h 52 50-96 
 
 Sidereal Time required 
 
 8 54 18-49 
 
OF THE REFLECTING TELESCOPE. 
 
 43 
 
 Of the Reflecting Telescope. 
 
 THE great difficulty of managing refracting telescopes when of 
 great length, and the impossibility of obtaining a higher magnifying 
 power than 500 times, even by making them 600 feet long, stimu- 
 lated philosophers to attempt a different mode of constructing teles- 
 copes, which they have effected by applying the principle of reflection, 
 instead of that of direct vision. By this means instruments of a much 
 shorter length answer the purpose much better ; for a reflecting teles- 
 cope, 6 feet long, will magnify as much as a refracting one 100 feet 
 long. 
 
 Gregorian Telescope. 
 
 THE first telescope of the reflecting kind, which was found to 
 answer the purpose, was invented by Dr. James Gregory, a Scots- 
 man, about the year 1661. 
 
 The instrument which he invented is represented by the following 
 figure. 
 
 A 
 
 At the bottom of the great tube TTTT is placed the large concave 
 mirror DUVF, whose principal focus is at m; and in its middle is a 
 round hole P, opposite to which is placed the small mirror L, concave 
 toward the great one ; and so fixed to a strong wire M, that it may 
 be moved farther from the great mirror, or nearer to it, by means of a 
 long screw on the outside of the tube, keeping its axis still in the 
 same line P m n, with that of the great one. Now, since in viewing 
 a very remote object, we can scarcely see a point of it but what is at 
 least as broad as the great mirror, we may consider the rays of each 
 pencil, which flow from every point of the object, to be parallel to 
 each other, and to cover the whole reflecting surface DUVF. But 
 to avoid confusion in the figure, we shall only draw two rays of a 
 pencil flowing from each extremity of the object into the great tube, 
 and trace their progress, through all their reflections and refractions, 
 to the eye/, at the end of the small tube tt, which is joined to the 
 great one. 
 
 Let us then suppose the object A B to be at such a distance, that 
 the rays C may flow from its lower extremity B, and the rays E from 
 its upper extremity A. Then the rays C falling parallel upon the 
 great mirror at D, will be thence reflected converging, in the direction 
 D G ; and by crossing at I in the principal focus of the mirror, they 
 
44 ON THE GREGORIAN TELKSCOPK. 
 
 will form the upper extremity I of the inverted image IK, similar to 
 the lower extremity B of the object A B : and passing on to the 
 concave mirror L, (whose focus is at ?i) they will fall upon it at g t 
 and be thence reflected converging, in the direction g N, because ym 
 is longer than yn; and passing through the hole 1? in the large 
 mirror, they would meet somewhere about r, and form the lower ex- 
 tremity d of the erect image ad, similar to the lower extremity B of 
 the object A B. But by passing through the plano-convex glass R 
 in their way, they form that extremity of the image at b. In like 
 manner, the rays E which come from the top of the object A B, and fall 
 parallel upon the great mirror at F, are thence reflected converging to its 
 focus, where they form the lower extremity K of the inverted image 
 IK, similar to the upper extremity A of the object A B ; and thence 
 passing on to the small mirror L, and falling upon it at A, they are 
 thence reflected in the converging state hO ; and going on through 
 the hole P of the great mirror, they will meet somewhere about q, 
 and form there the upper extremity a of the erect image ad, similar 
 to the upper extremity A of the object A B : but by passing through 
 the convex glass R in their way, they meet and cross sooner, as at a, 
 where that point of the erect image is formed. The like being under- 
 stood of all those rays which flow from the intermediate points of the 
 object, between A and B, and enter the tube at TT; all the inter- 
 mediate points of the image between a and b will be formed: and 
 the rays passing on from the image through the eye-glass S, and 
 through a small hole e in the end of the lesser tube 1 1, they enter the 
 eye/, which sees the image a d (by means of the eye-glass) under the 
 large angle ced, and magnified in length, under that angle from cto d. 
 
 In the best reflecting telescopes, the focus of the small mirror is 
 never coincident with the focus m of the great one, where the first 
 image IK is formed, but a little beyond it (with respect to the eye) 
 as at n: the consequence of which is, that the rays of the pencils will 
 not be parallel after reflection from the small mirror, but converge so 
 as to meet in points about qer; where they will form a larger upright 
 image than a d, if the glass R was not in their way : and this image 
 might be viewed by means of a single eye-glass properly placed be- 
 tween the image and the eye : but then the field of view would be 
 less, and consequently not so pleasant, for which reason, the glass 
 R is still retained, to enlarge the scope or area of the field. 
 
 To find the magnifying power of this telescope, multiply the focal 
 distance of the great mirror by the distance of the small mirror from 
 the image next the eye, and multiply the focal distance of the small 
 mirror by the focal distance of the eye-glass: then, divide the pro- 
 duct of the former multiplication by the product of the latter, and 
 the quotient will express the magnifying power. 
 
 One great advantage of the reflecting telescope is, that it will ad- 
 mit of an eye-glass of a much shorter focal distance than a refracting 
 telescope will ; and, consequently, it will magnify so much the more : 
 for the rays are not coloured by reflection from a concave mirror, if 
 it be. ground to a. true figure, as they are by passing through a convex- 
 glass, let it be ground ever so true. 
 
ASTRONOMICAL QUADRANT. 
 
 Astronomical Quadrant, 
 
 THE following figure represents the portable Astronomical Quad 
 rant mounted on an axis and pedestal. 
 
 The axis allows us to place the instrument in any vertical position* 
 and the pedestal, moveable in the axis of the circle E F, at the bot- 
 tom, permits us to place it in the direction of any azimuth, or towards 
 any point of the compass. 
 
 The limb A B is graduated into degrees and halves, numbered 
 from A. 
 
 Upon the radius C B is fixed a telescope, through which we view 
 any remote celestial or other object. This limb is elevated or de- 
 pressed by a rack and pinion. 
 
 The horizontal circle is graduated into quadrants of 90, and these 
 again into half degrees, and so on. 
 
 Til 
 
4Q ON OBSERVING WITH THE TELESCOPE. 
 
 The point Zero on the quadrant corresponds with Zero on the 
 nonius G, 
 
 The quadrant united to the pedestal moves round the limb by 
 means of rack-work and a pinion, F, and shews the position of the 
 place of the quadrant, and consequently of an object. 
 
 The rationale of this instrument is very obvious ; for by means of 
 it we can measure the angular distance of any celestial body in the 
 zenith, or at any altitude; or of any terrestrial object from any 
 other object in the horizon, 
 
 The former is effected by means of the graduated quadrant A B ; 
 and the graduated circle EF, accomplishes the latter process. To- 
 gether, these graduations enable us to determine both the altitude and 
 azimuth of a celestial object, since by the compass we can place the 
 instrument due north and south. 
 
 On Observing with the Telescope. 
 
 THE apparent magnitude of an object, viewed through a telescope, 
 may be measured, with great accuracy, by a scale or by two wires, 
 introduced at the place of the last image, reducing afterwards the 
 angle thus ascertained according to the magnifying power. Care 
 must, however, be taken to avoid as much as possible the distortion 
 which usually accompanies any curvature of the image ; and the 
 wires, one of which is sometimes made moveable, by means of a 
 micrometer screw, must be sufficiently illuminated to be distinctly 
 visible. Sometimes a scale is introduced, which, from the apparent 
 magnitude of a known object, such as that of a man of ordinary 
 height, or of a portion of a wall built witli bricks of the usual size, 
 enables us at ouce to read off its actual distance, which is expressed 
 on the scale in hundreds of yards. The angular magnitude of an 
 object, seen through a telescope, may also be found, by viewing at 
 the same time, with the other eye, either a scale, or any other object 
 of known dimensions, placed at a given distance : the lucid disc mi- 
 crometer of Dr. Herschel is employed in this manner for judging of 
 the magnitude of the celestial bodies. The divided object glass 
 micrometer affords another mode of measurement : the object glass 
 being divided into two semicircular portions, one of which slides on 
 the other ; each portion acts as a separate lens, and two images of 
 every part of the object being formed, the angular distance of any 
 two points is determined by bringing their images together, and mea- 
 suring the displacement of the moveable portion of the object glass, 
 which is required for procuring the coincidence. Sometimes, also, a 
 similar purpose isanswered by inserting a divided glass in the eye piece, 
 which is nearly on (he same principle, and which seems to be some- 
 what less liable to error. In a reflecting telescope of Cassegrain's 
 ponstruction, Mr. Jiamsden has also produced the same effect by 
 dividing the convex speculum, and causing a part of it to turn round 
 an axis. All these arrangements particularly deserve the attention 
 
OF THE TRANSIT INSTRUMENT' 47 
 
 of those who are employed in practical astronomy and in geography, 
 since the advancement of these sciences much depends on the accu- 
 racy of the telescopic and microscopic measures, which are performed 
 by means of optical instruments. 
 
 To Find the Rate of Time-keepers. 
 
 IF a Time-keeper could be so constructed as to go uniformly in every 
 season and climate, it would obviate all difficulty respecting the 
 longitude : and though perfect regularity of motion cannot be hoped 
 for in any mechanical contrivance, the want may be in some measure 
 supplied, particularly in short voyages, by ascertaining the rate of a 
 time-keeper; that is, by finding what it gains or loses daily, during a 
 series of observations. 
 
 The most general method, as well as the most accurate, of finding 
 the rate of a time-keeper, is by a transit instrument, the use of which 
 will be shewn in the next article. 
 
 In order to ascertain the mean daily rate of a watch, it should be 
 some days under trial, and the operation is performed either by taking 
 an arithmetical mean between the two extreme daily variations, or 
 between them all together ; the latter method seems the most correct : 
 but if the watch should materially alter its rate of going while 
 under trial, all the observations made before the alterations took 
 place must be rejected, and only those retained which were made 
 afterwards. The time generally allowed for ascertaining the mean 
 rate of a watch is about a month. 
 
 But some astronomers think that a rate deduced from a long series 
 of observations is best ; while others prefer the latest rate, taken from 
 a short trial. On such a nice point as this, little can be said with 
 certainty. If, however, the rate is found to be uniform, and the 
 watch be well adjusted for heat and cold, a few days may be sufficient 
 to determine its mean rate; but if this be not the case, several 
 months may be necessary. 
 
 With respect to the adjustment for climate, as well as the various 
 precautions necessary in the management of a time-keeper, the 
 maker's directions should be carefully followed. 
 
 Of the Transit Instrument. 
 
 A TRANSIT Instrument is a telescope placed in the meridian in 
 order to observe the times that the heavenly bodies pass this great 
 circle ; and thus (by the help of a sidereal clock) to find their right 
 ascensions ; and also, to determine the errors and rates of chrono- 
 meters. 
 
 Across the middle of the telescope is fixed an axis, at right angles 
 to it, the ends of which are tapered into pivots, which turn in notches 
 
48 OF THE TRANSIT INSTRUMENT. 
 
 made in a frame for this purpose. The axis must be perfectly level, 
 and placed east and west, that the telescope may turn in the plane 
 of the meridian. 
 
 In order to observe the instant that a celestial object passes the 
 meridian, there is placed in the telescope a system of wires, generally 
 consisting of five, equi-distant from each other, and perpendicular to 
 the horizon ; there is also an horizontal wire bisecting the rest. The 
 middle vertical wire is intended to coincide with the meridian ; and 
 the instant that any heavenly body passes this wire is called its 
 transit. The other parallel wires are intended to correct or verify the 
 observation ; which is done by taking a mean between the transits 
 over the first wire and the last, or over the second and fourth ; or, 
 what is reckoned most correct, a mean of the whole, which is called 
 the reduction of the wires. 
 
 There are five adjustments principally necessary to a transit instru- 
 ment, three of which regard the telescope, and two the axis. 
 
 1. The wires should be set perfectly vertical, which is proved by 
 observing that any distant object, cut by a wire, does not vary on 
 moving the instrument up and down, but keeps in the same position 
 over the wire ; otherwise, the wires must be turned about till the 
 adjustment is made. 
 
 2. The telescope should have noparallax. This is seen by bisecting any 
 distant object with the horizontal wire : and if, on moving the eye up 
 and down a little, the object should appear to separate from the wire, 
 the instrument is said to have a parallax, which must be corrected by 
 placing the object and eye glasses at such a distance asunder, that 
 their foci may meet in the point where the wires are fixed : but when 
 the object glass has been properly fixed by the instrument maker, the 
 observer has only to adjust the eye glass. 
 
 3. The telescope should be in collimation.* This is known by ob- 
 serving any object as cut by the meridian wire, and if, on reversing 
 the axis, the object remains cut in the same manner as before, the 
 instrument is in collimation ; otherwise, it must be corrected by means 
 of the two small screws in the sides of the telescope ; that is, by 
 easing one, and screwing up the other, until the error appears one 
 half diminished ; and again, by inverting the axis, and repeating the 
 operation, until the adjustment is properly effected. 
 
 4. To level the axis. This is done by means of a screw placed 
 under one of the notches, which raises or depresses that end of the 
 axis at pleasure ; and the true horizontal position is proved by a spirit 
 level. 
 
 5. To bring the telescope into the meridian. This is performed by 
 an horizontal screw, which moves one end of the axis backward or 
 forward as occasion requires; but to ascertain the meridian with 
 perfect accuracy is a problem of some difficulty as well as importance. 
 
 * The line of collimation (i. e. of aiming) is a right line passing from the in- 
 tersection of the meridian wire with the horizontal, to the centre of the object 
 glass. Or^ it may be defined a right line passing through the centre of the tele- 
 scope, and "perpendicular to its axis. 
 
ON THE ETHER OF NEWTON. 
 
 On the Ether of Newton. 
 
 WE have made the following extract from Su* I. Newton's works, 
 to shew that he was of opinion that there is an ethereal medium or 
 subtle elastic ether which pervades the universe : 
 
 *' To proceed to the hypothesis : first, it is to be supposed therein, 
 that there is an ethereal medium, much of the same constitution 
 with air, but far rarer, subtler, and more strongly elastic. It is not 
 to be supposed, that this medium is one uniform matter, but com- 
 pounded, partly of the main phlegmatic body of either, partly of 
 other various ethereal spirits, much after the manner that ajr is com- 
 pounded of the phlegmatic body of air, intermixed with various 
 vapours and exhalations : for the electric and magnetic effluvia, and 
 gravitating principle, seem to argue such variety,, 
 
 " Isiiot the heat (of the warm room) conveyed through the vacuum 
 by the vibrations of a much subtiler medium than air ? And is not 
 this medium the same with that medium by which it is refracted and 
 reflected, and by whose vibrations light communicates heat to 
 bodies, and is put into fits of easy reflection and easy transmission? 
 And do not the vibrations of this medium in hot bodies, contribute 
 to the intenseness and duration of their heat? And do not hot 
 bodies communicate their heat to contiguous cold ones, by the vibra- 
 tions of this medium propagated from them into the cold ones? 
 And is not this medium exceedingly more rare and subtile than the 
 air, and exceedingly more elastic and active ? And doth it not 
 really pervade all bodies ? And is it not by its elastic force, ex- 
 panded through all the heavens ? May not planets and cornets, and 
 all gross bodies, perform their motions in this ethereal medium ? 
 And may not its resistance be so small as to be inconsiderable ? For 
 instance ; if this ether (for so I will call it) should be supposed 
 700,000 times more elastic than our air, and above 700,1900 more rare, 
 its resistance would be about 600,000,000 times less than that of water. 
 And so small a resistance would scarce make any sensible alteration 
 in the motions of the planets in ten thousand years. If any one 
 would ask how a medium can be so rare, let him tell me how an 
 electric body can by friction emit an exhalation so rare and subtile, 
 and yet so potent? And how the effluvia of a magnet can pass 
 through a plate of glass, without resistance, and yet turn a magnetic 
 needle beyond the glass ?" 
 
 This is a quotation which has been many times made by those 
 philosophers who favour the undulatory theory of light, to show that 
 Newton was not confident in what is generally said to be his own 
 theory, namely, that light is a real substance. 
 
60 OF THE ACHROMATIC TELESCOPE. 
 
 Achromatic Telescope.* 
 
 Achromatic Telescopes differ only from those of the common 
 refracting kind, in the formation and combination of the glasses em- 
 ployed in their construction. 
 
 In viewing objects through a refracting telescope, which is not 
 furnished with an achromatic object glass, a kind of aberration is 
 produced, by the different refrangibilities of the various coloured rays 
 of light which form an infinite number of images, neither agreeing 
 perfectly in situation nor in magnitude, so that the objects are ren- 
 dered indistinct, by an appearance of colours at their edges : this im- 
 perfection, however, Mr. Dolland has in great measure obviated, by 
 his achromatic object glasses : the construction of which depends on 
 the important discovery, that some kinds of glass separate the rays of 
 different colours from each other much more than others, while the 
 whole deviation produced in the pencil of light is the same. Mr. 
 Dolland therefore combined a concave lens of flint glass, with a 
 convex lens of crown glass, and sometimes with two such lenses. 
 
 The following figure represents an achromatic telescope with a 
 triple object glass, and with Boscovitch's achromatic eye-piece, con- 
 sisting olf two similar lenses, one of which is every way three times 
 as great as the other, their distance being twice the focal length 
 of the smaller. 
 
 The concave lens of flint glass was sufficiently powerful to correct 
 the whole dispersion of coloured light produced by the crown glass, 
 but not enough to destroy the effect of its refraction, which was still 
 sufficient to collect the rays of light into a distant focus. For this 
 purpose it is necessary that the focal lengths of the two lenses should 
 be in the same proportion, as the dispersive powers of the respective 
 substances, when the mean deviations of the pencils are equal; that 
 is, in the case of the kinds of glass commonly used nearly in the 
 ratio of seven to ten. Sometimes, also, the chromatic aberration, 
 that is, the error arising from the different refrangibilities of the 
 different rays, is particularly corrected in an eye-piece, by placing a 
 field glass in such a manner, as considerably to contract the dimen- 
 
 * A lens or prism is said to be achromatic, if it form an image free from colour, 
 or if it refracts all the rays of white light to one locus. 
 
 A compound lens may be made achromatic, or nearly free from colours, if it 
 consists of two lenses formed of substances of different dispersive powers, the 
 one being convex and the other concave, and having their focal lengths propor- 
 tional to their dispersing powers. 
 
OF THE ACHROMATIC TELESCOPE. 
 
 51 
 
 sions of the image formed by the least refrangible rays, which is 
 nearest to the eye glass, and to cause it to subtend an equal angle 
 to the image formed by the most refrangible rays, this image being 
 little affected by the glass. 
 
 The following figure represents one of Mr. Dolland's achromatic 
 telescopes, supported in the centre of gravity, with its rack work 
 motions, and mounted on its mahogany stand, 
 
 
 the three legs of which are made to close up together by means of the 
 brass frame aaa, which is composed of three bars, connected toge- 
 ther in the centre piece by three joints, and also to the three legs of 
 the mahogany stand by three other joints, so that the three bars of 
 this frame may lie close against the insides of the legs of the mahogany 
 stand when they are pressed together, for the convenience of car- 
 
52 OF THE ACHROMATIC TELESCOPE. 
 
 The brass pin, under the rack work, is made to move round in the 
 brass socket b, and may be tightened by means of the ringer screw d, 
 when the telescope is directed nearly to the object intended to be 
 observed. This socket turns on two centres, by which means it may 
 be set perpendicular to the horizon, or to any angle required in 
 respect to the horizon, the angle may be ascertained by the divided 
 arc, and then made fast by the screw e. If this socket be set to the 
 latitude of the place at which the telescope is used, and the plane of 
 this arc be turned on the top of the mahogany stand, so as to be in 
 the plane of the meridian, the socket b being fixed to the inclination 
 of the pole of the earth, the telescope, when turned in this socket, 
 will have an equatorial motion, which is always very convenient in 
 making astronomical observations. 
 
 Fig. 2 in the plate, represents a stand to be used on a table, which 
 may be more convenient for many situations, than the large mahogany 
 stand. The telescope, with its rack work, may be applied to either 
 of the two stands, as occasion may require, the sockets on the tops 
 of both being made exactly of the same size. The sliding rods may 
 be applied to the feet of the brass stand, so that the telescope may 
 be used with the same advantages on one as on the other. 
 
 The tube A A may be made either of brass or mahogany, of three 
 and half feet long. The achromatic object glass of three and half 
 feet focal distance, has an aperture of two inches and three quarters. 
 
 The larger size is with a tube five feet long, and has an achromatic 
 object glass of three inches and one quarter aperture. 
 
 The eye tube, as represented by B, contains four eye glasses, to be 
 used for day, or any land objects. There are three eye tubes, as C, 
 which have two glasses in each, to be used for astronomical purposes. 
 These eye tubes all screw into the short brass tube at D. By turning 
 the button or milled head atf, this tube is moved out of the larger, 
 so as to adjust the eye glasses to the proper distance from the object 
 glass, to render the object distinct to any sight, with any of the dif- 
 ferent eye tubes. 
 
 The magnifying power of the three-and~half-feet telescope, with the 
 eye tube for land objects, is forty-five times, and of the five-feet for 
 land objects, sixty-five times. With those for astronomical purposes, 
 with the three-and-half-feet, the magnifying powers are eighty, one 
 hundred and thirty, and one hundred and eighty ; and for the five- 
 feet, one hundred and ten, one hundred and ninety, and two hundred 
 and fifty times. 
 
 Stained glasses, as g, are applied to all the different eye tubes, to 
 guard the eye in observing the spots on the sun. These glasses are 
 to be taken off when the eye tubes are used for other purposes. 
 
 The rack work is intended to move the telescope in any direction 
 required, and is worked by means of the two handles at h. When 
 the direction of the tube is required to be considerably altered, the 
 worm-screws which act against the arc and the circle must be dis- 
 charged : then the screw d being loosened, the pin of the rack work 
 move easily round in the socket 6. 
 
 For the more readily finding or directing the telescope to any 
 
OF THE MARINERS COMPASS. 
 
 53 
 
 object, particularly astronomical objects, there is a small tube or 
 telescope, called the finder, fixed near the eye-end of the large 
 telescope. At the focus of the object glass of this finder, there are 
 two wires, which intersect each other in the axis of the tube, and as 
 the magnifying power is only about six times, the real field of view- 
 is very large ; therefore any object will be readily found within it, 
 which being brought to the intersection of the wires, it will then be 
 within the field of the telescope. 
 
 In viewing astronomical objects, (and particularly when the greatest 
 magnifying powers are applied) it is very necessary to render the 
 telescope as steady as possible; .for that purpose there are two sets 
 of brass sliding rods, ii, as represented in the figure. These rods 
 connect the eye-end of the telescope with two of the legs of the stand, 
 by which any vibrations of the tube that might be occasioned by the 
 motion of the air or otherwise, will be prevented, and the telescope 
 rendered sufficiently steady for using the greatest powers. These 
 sliding rods move within one another with so much ease, as to admit 
 of the rack-work being used in the same manner as if they were not 
 
 applied. 
 
 Of the Mariner's Compass. 
 
 THE Mariner's Compass is an instrument by which a ship is 
 directed to any intended port. It is also of the greatest use in deter- 
 mining the bearing of one object from another. 
 
 The following figure is a representation of the card of a steering 
 compass, with the names of eight of the points marked ; the other 
 divisions indicate half points. 
 
54 OF THE MARINER'S COMPASS. 
 
 The circumference of the card of the compass is divided into 
 thirty-two equal parts, called points ; the interval between two ad- 
 jacent points is, therefore, equal to 11 15', and each point is subdi- 
 vided into quarters. In azimuth compasses, the circumference of 
 the card, besides the usual division into points and quarters, is also 
 divided into 360 degrees; and in some other compasses the quarter 
 of the circumference is divided into 96 equal parts, and hence each 
 division is 56| minutes. Four of the points of the compass, namely, 
 N. E. S.W. are called cardinal points, being the principal points, 
 and because the names of the others are derived from them. 
 
 To the under side of the card, and in the direction of its north and 
 south line, is attached a magnetic bar of hardened steel, of a rectan- 
 gular form, called the needle, by which means the north end of the 
 card is directed towards the northern part of the horizon ; and hence 
 the other points of the compass are directed towards the correspond- 
 ent points of the horizon. 
 
 The card and needle are suspended on an upright pin, called the 
 supporter, which is fixed to the bottom of a brass or wooden circular 
 box : and the whole is covered with a plate of glass to prevent the 
 wind from disturbing the card. The box has two pins, one on each 
 side diametrically opposite. These pins are let into a brass ring, 
 which is movable, in a square wooden box, on two pins at right 
 angles to the former ; by this contrivance, called jimbals, the card 
 remains nearly horizontal, although the ship should be considerably 
 agitated. Although the card be made to retain an horizontal position 
 at the place where the compass was constructed, yet, when it is 
 carried to any other place where the dip or inclination of the needle 
 is considerably different, it will no longer remain horizontal. In 
 order, therefore, to remedy this, one or two pieces of brass wire, with 
 sliding weights, are placed below the card ; and hence, by moving 
 one or both of these weights, the equilibrium of the card will be 
 restored. 
 
 Upon the inside of the circular box a black line is drawn vertically, 
 which line is usually called lubber's point. The compass should be 
 so placed in the binnacle, that the line, joining the centre of the 
 card and lubber's point, may be parallel to the ship's keel. 
 
 Before a compass is used it should be accurately examined. For 
 this purpose it will be necessary to observe if the magnetic axis of 
 the needle corresponds exactly with the north and south line of the 
 card. This may be easily examined if the needle is so constructed 
 as to be capable of reversion. Thus, let the needle be taken from 
 the card, and suspended on a pin, and carefully observe the direction 
 of its axis; reverse the needle, and again observe its direction; then 
 half the difference of these will be the magnetic axis of the needle ; 
 and this line ought to coincide with the meridian of the card. Other 
 methods might be proposed to determine the angular distance between 
 the meridian of the card and the magnetic axis of the needle ; the 
 easiest of which is by comparing it with a meridian line, truly 
 drawn on a plane ; for the difference between the direction of this meri 
 dian as shewn by the compass and the known variation is the error. 
 
DESCRIPTION OF HADtEY J S QUADRANT. 
 
 55 
 
 Description and Use of Hadley's Quadrant. 
 
 ONE of the most useful and convenient instruments for measuring 
 the altitude of a celestial object, is Hadley's Quadrant, which is 
 represented by the following figure. 
 
 The form of the instrument is an octagonal sector of a circle, and 
 contains 45; but, because of the double reflexion, the limb is divided 
 into 90. 
 
 AB, and AC, are the two radii, and BC the circle or limb, 
 which, together with the braces, P Q, form the octant, or frame of 
 
56 DESCRIPTION OF HADLEY'S QUADRANT. 
 
 the quadrant ; A is the index glass, H the fore horizon glass, and G 
 the back horizon glass, and E F the corresponding sight vanes ; 1 
 the coloured glass, the stem of which is put into the hole K, when 
 the back observation is usejl; and L is a pencil for writing down the 
 observation. 
 
 The altitude of any object is determined by the position of the 
 index on the limb, when, by reflection, that object appears in contact 
 with the horizon. 
 
 If the object whose altitude is to be observed be the sun, and if so 
 bright that its image may be seen in the transparent part of the fore 
 horizon glass> the eye is then to be applied to the upper hole in the 
 sight vane ; otherwise, to the lower hole : and, in this case, the 
 quadrant is to be held so that the sun may be bisected by the line 
 joining the silvered and transparent parts of the glass. The moon is 
 to be kept as nearly as possible in the same position, and the image 
 of a star is to be observed in the silvered part of the glass, adjacent 
 to the line of separation of the two parts. 
 
 There are two different methods of taking observations with the 
 quadrant. In the first of these the face of the observer is directed 
 towards that part of the horizon immediately under the sun ; and is 
 therefore called the fore observation. In the other method, the ob- 
 server's face is directed to the opposite part of the horizon, and con- 
 sequently his back is towards the part under the sun, and is hence 
 called the back observation. This last method of observation is to 
 be used only when the horizon under the sun is obscured, or rendered 
 indistinct by fog, or any other impediment. 
 
 This quadrant was first proposed by Newton, but improved, or 
 perhaps re-invented, by Hadley. Its operation depends on the effect 
 of two mirrors which bring both the objects of which the angular 
 distance is to be measured at once into the field of view ; and the 
 inclination of the speculums by which this is performed serves to 
 determine the angle. The ray proceeding from one of the objects is 
 made to coincide, after two reflections, with the ray coming imme- 
 diately from the other* ancl since the inclination f the reflecting 
 surfaces is then half the angular distance of the objects, this inclina- 
 tion is read off on a scale in which every actual degree represents two 
 degrees of angular distance, and is marked accordingly. There is 
 also a second fixed speculum placed at right angles to the movea- 
 ble one, when in its remotest situation, which then produces a 
 deviation of two right angles in the apparent place of one of the 
 objects, and which enables us, by moving the index, to measure any 
 angle between 80 and 90. 
 
 This operation is called the back observation ; it is however 
 seldom employed, on account of the difficulty of adjusting the spe- 
 culum for it with accuracy. The reflecting instrument originally 
 invented by Hooke was arranged in a manner somewhat different. 
 
OF THE CALENDAR. 67 
 
 OF THE CALENDAR. 
 
 ALTHOUGH we have completed the systematic part of this work, 
 we deem it necessary to add a short account of the Calendar, on 
 account of its great importance in regulating time, and preserving the 
 seasons and particular days to the same time of the year. And to 
 render the work as complete as possible, we shall also add the 
 method of performing the most interesting and important calculations 
 in Astronomy ; which we hope to do in a more simple and intelligible 
 manner than what is to be found in works which profess to treat of 
 this subject more fully than we intend to do. 
 
 Having already treated fully of the change of seasons and the 
 regulation of time, we shall only observe here, that the tropical year 
 exceeds the civil year, five hours, forty-eight minutes, forty-nine 
 seconds. Now if this difference were not attended to, the seasons 
 would soon happen in a different time of the year from what they do 
 at present. This circumstance was known long before the real length 
 of the year was ascertained ; and to prevent it from taking place, the 
 Romans inserted intercalary days ; but without much regularity, till 
 the time of Julius Caesar, who observed that the year was almost 6 
 hours longer than 365 days : he therefore added a day every fourth 
 year, which made that year 366 days. This intercalary day was 
 counted the 24th of February, and was called by the Romans, sexto 
 calendas Martias, or the sixth of the calends of March ; there was, 
 therefore, in that year two sixths of the calends of March, whence it 
 was called Bissextile. 
 
 To find Bissextile or Leap Year. 
 
 Rule. Divide the given year by 4; if nothing remain, that year 
 is leap year; but if 1, 2, or 3, remain, it is as many years after leap 
 year. 
 
 Example. Let it be required to find if the year 1825 be leap year, 
 or the 1st, 2d, or 3d after it ? 
 
 1825 -f- 4 rr 456 with a remainder of 1 ; 
 therefore it is the first after leap year. 
 
 Note. Even centuries not divisible by 4 are not reckoned leap 
 years, such as 1800, 1900, 2100, &c. ; but 2000, 2400, &c. are 
 reckoned leap years. 
 
 OF THE DOMINICAL LETTER. 
 
 It has long been customary to distinguish each day throughout 
 the year by one of the seven first letters of the alphabet ; viz. A, B, 
 C, D, E, Is G. The first, A, is affixed to the first day of January; 
 the next, B, to the second ; C to the third, and so on to the seventh, 
 G; then A to the eighth, B to the ninth, &c. to the end of the year. 
 By this means we know, that if any letter be prefixed to any day of 
 
 P 
 
58 OF THE CALENDAR. 
 
 the week, the same letter will represent the same day of the week 
 throughout the year. If the 1st day of January, marked by the letter 
 A, be a Sunday, all the other days of the year, which shall have the 
 letter A prefixed to them, will also be Sundays. If the 3d of January, 
 for which the letter C stands, be Sunday, then all the days of the 
 year, marked by that letter, will be Sundays, and for that reason it is 
 called the Dominical or Sunday Letter : the following letter will also 
 represent the Mondays, and so on with the others. 
 
 As a common year consists of 365 days, or 7 times 52, and one 
 more, it follows that the letter A, which we prefix to the first day of 
 the year, ought also to represent the last, and if it commenced on a 
 Sunday, it would end on Sunday, and of course the next year would 
 begin on a Monday, and the 7th would be Sunday, which is marked 
 by the letter G ; that letter will then be the Dominical letter, and as 
 this year began on Monday, it will therefore end with a Monday, and 
 the 3d year will begin on a Tuesday ; then the 6th of January, marked 
 F, will be Sunday, and that letter the Dominical letter for the year. 
 In the same way will E become the Dominical letter for the 4th 
 year, D the 5th, and so on in this retrograde order. 
 
 If every year consisted exactly of 365 days, in the course of seven 
 years, the same day of the month would fall on the same day of the 
 week ; but, as every 4th or leap year consists of 366 days, which is 
 equal to 7 times 52, and two more ; therefore if a leap year begin on 
 a Sunday, it will end on a Monday, and the following one will begin 
 on a Tuesday ; of course Sunday will fall on the 6th of January, and 
 F will be the Dominical letter for the year after Bissextile, sup- 
 posing A to have been the Dominical letter for Bissextile. 
 
 By means of Bissextile, the order of the Dominical letters is inter- 
 rupted every 4 years, but again returns after 4 times 7 or 28 years. 
 This is what is called the Solar Cycle, after which the days of the 
 month resume the same order as before. Because every Bissextile 
 consists of 366 days, the intercalary day is added to the end of Fe- 
 bruary, which, in that year, will have 29 days, and therefore the first 
 Dominical letter in March will fall a day sooner than in common 
 years, so that leap year will have two Dominical letters, the one 
 serving to the 29th of February, and the other the remainder of the 
 year. 
 
 It is supposed that the Solar Cycle commenced 9 years A. C., and 
 that it was leap year ; therefore to find what year of that Cycle any 
 proposed year is ; to the given year add 9, and divide the sum by 
 28, the remainder, if any, is the year of the Cycle, and the quotient 
 shows the number of Cycles since the birth of Christ : if nothing 
 remain, it is the 28th year of the Cycle. 
 
 Example. What year of the Solar Cycle is 1825? 
 
 1834 
 1825 + 9 = ~rg- zz 65 Cycles, and 14 remains, 
 
 which is the Solar Cycle. 
 
OF THE CALENDAR. $$ 
 
 ' ' . 
 
 To find the Dominical Letter. 
 
 Rule. To the given year of our Lord add its 4th part, neglecting 
 any remainders; divide the sum by 7, and the remainder taken from 8, 
 will be the index of the Dominical letter in common years, (remem- 
 bering that A is 1, B 2, C 3, &c.) but if nothing remain after dividing 
 by 7, then A is the Dominical letter in common years. 
 
 In leap ^years, to this letter is prefixed its preceding one. in the 
 retrograde order which these letters take, which becomes the Domi- 
 nical letter after the month of February. 
 
 Example. Required the Dominical letter for the year 1825 ? 
 
 Here, 1825 divided by 4 is 456, which added to 1825 is 2281, 
 and this divided by 7, leaves a remainder of 6, which taken from 8, 
 leaves 2 for the index of the letter ; therefore B is the Dominical 
 letter for that year. 
 
 OF THE GOLDEN NUMBER. 
 
 As it is well known that the periodical returns of the Sun and 
 Moon are constantly the same, and that the moon moves nearly 13 
 times faster than the sun, it follows, that, after a certain number of 
 revolutions, these two bodies will again be in conjunction in the same 
 place of the heavens. 
 
 A Greek astrononmer, named Meton, discovered, that the space 
 of time necessary to bring this phenomenon about was 19 years : this 
 period has, on that account, been called the Metonic Cycle ; and 
 was very much used by the ancients for determining the times of new 
 and full moon. For, according to that period, the new and full moon 
 ought to happen the same day, and at the same hour of the day, ac 
 the end of every 19 years. Therefore, if the day and hour of any new 
 or full moon be known in the interval of 19 years, all the new and 
 full moons, for the preceding and following years, will be known. 
 
 At the time of the Council of Nice, where the question of fixing the 
 Feast ofEaster was discussed, this cycle, of which they made so 
 much use, served as the foundation of their computations. They 
 had found by observation, that in the first year of the cycle the new 
 moons happened on the 23d of January, 21st February, 23d March, 
 &c. opposite to these days, in the calendar, they wrote 1. They had 
 also found, that, in the second of the cycle, the new moons happened 
 on the 12th January, 10th February, 12th March, &c. opposite these 
 they wrote 2 ; and so on for the other years of the cycle. By 
 this means the year of the cycle being given, they found, by inspec- 
 tion, all the new moons of that year, in the same column of the 
 calendar ; and, on account of the great use of those numbers, they 
 were written in characters of gold. Hence the year of the cycle has 
 received the name of the Golden Number. 
 
 To find the Golden Number. 
 
 Rule. To the given year add 1 ; divide the sum by 19. The 
 
 P2 
 
OF THE CALENDAR. 
 
 quotient is the number of cycles elapsed since the commencement of 
 the Christian era, and the remainder will be the golden number from 
 the last cycle. 
 
 Example. Required the golden number for the year 1825 ? 
 
 Then 1825 + 1 = - - - z= 96 cycles, and 2 remains, 
 1" 
 
 which is the golden number. 
 
 As the solar year exceeds the lunar year by 10 d 21 h 0' 11", or 
 nearly 11 days, these intercalary days are named the Epact. 
 
 The epact is nothing when the golden number is 1. It is 11 when 
 the golden number is 2; 22, or twice 11, when the golden number is 
 3; and when the golden number is 4, the epact is 3 times 11, or 33, 
 or rather 3, because, when the number is more than 30, the excess i* 
 called the epact. 
 
 To find the Epact 
 
 Rule. From the golden number of the given year subtract 1, mul- 
 tiply the remainder by 1 1, and divide the product by 30, if it exceeds 
 that number ; the remainder will be the epact. 
 
 Example. Required the epact for the year 1825, the golden 
 number being 2 ; 
 
 2 1 = 1 x 11 = 11, and therefore 1 is the epact. 
 
 If the epact, for any year, be subtracted from a mean lunation, or 
 29 d 12 h 44' 3", the remainder will be the mean new moon in January 
 for that year ; and as that month consists of 31 days, or a day and a 
 half more than a mean lunation, if to the epact we add this day and 
 a half, and subtract the sum from a mean lunation, as above, we shall 
 obtain the time of new moon in February ; and as that month, in 
 common years, consists of 28 days, the months of January and Fe- 
 bruary together make 59 days, or very nearly two lunations, the new 
 moon in March will therefore fall nearly at the same time of that 
 month, as in the month of January. By augmenting the epact in 
 this manner, by the excess of each month above a mean lunation, and 
 retrenching from that sum a lunation, or 29 d 12 h 44' 3", we shall have 
 the mean new moon for every month in the year. Likewise, by adding 
 half a lunation, or 14 d 18 h 22' to the day of new moon, we shall have 
 the day of full moon. But, to avoid fractions, we generally give 30 
 days to a lunation or synodic period, and add nothing to the epact for 
 January and 2 for February. For March we add 0, for April 2, for 
 May 2, June 3, July 4, August 5, September 7, October 8, Novem- 
 ber 9, and for December 10.* 
 
 This method will not differ above half a day from the time of the 
 true conjunction, and often agrees very nearly; therefore it may be 
 accounted sufficiently exact for ordinary purposes. In the same 
 manner, we add 15 days to have the day of the following full moon. 
 
 * These numbers are termed the numbers of the month. 
 
OF THE CALENDAR. 61 
 
 For example, the epact for 1814 was 9, which subtracted from 30, 
 leaves 21 for the day of new moon in January and also in March 
 For February, we add 2 to the epact, and take 11, the sum, from 30 
 and there remains 19, the day of new moon in February. For April, 
 we add 2, and take the sum from 30, and the day of new moon for 
 April is the 19th. For May, we add 2, and the new moon is the 
 19th, and so on. 
 
 As the epact of any year determines the number of days elapsed 
 from the last new moon to the first day of that year, if we wish to 
 know the moon's age on any day of any month, we only need to add 
 the number for that month, as given above, the epact, and day of the 
 month into one sum, and if it be less than 30 it be the moon's age on 
 that day, but if the sum exceed 30, that quantity must be retrenched. 
 
 To find the Time of the Moon's Southing. 
 
 As the moon, at a mean rate, comes to the meridian 49 minutes 
 later on any day than the preceding day, multiply her age by 49, and 
 the product is the time of her southing in minutes ; or multiply her 
 age by 4, and divide by 5, the quotient is the hours, and the remainder 
 multiplied by 12, the minutes when she is south, or on the meridian. 
 
 To find the Time of high Water at a known Place. Common Method. 
 
 Rule. To the time of the moon's southing add the time that it is 
 high water at the given place on the days of full and change, the sum, 
 if under 12, is the hour of high water in the afternoon of that day ; if 
 it exceed 12, subtract 12 h 24' ; from this again take 24 minutes, and 
 it will be the time of high water in the forenoon of the given day. It 
 is however necessary to remark, that this method is only an approxima- 
 tion, and may, on some occasions, be an hour, or even an hour and a 
 half, wrong. 
 
 CYCLES, EPOCHS, &C. 
 
 If we multiply the solar and lunar cycle together, that is 28 and 
 19, we shall have a third period of 532, which is called the Victorian 
 or Dionysian Period. At the end of the above number of years, not 
 only the new and full moons return to the same days of the months, 
 but to the same day of the week, and also the same Dominical 
 letters, and all the moveable feasts return in the same order. On 
 this account it is called the Great Pascal Cycle. 
 
 To find the year of the Victorian Period answering to a current 
 year, because the birth of Christ happened in the 457th year of that 
 period ; to the year of our Lord add 457 years, and divide the sum 
 by 532, the remainder will be the year of the period. 
 
 Example. Required what year of the Victorian Period the year 
 1825 was? 
 
 1825 +457 =rf = 4, and there remains 154, the year 
 oi the 532 
 
 Victorian Period. 
 
6'2 OF THE CALENDAR. 
 
 Besides the cycles of the sun and moon, the Romans employed 
 another cycle, which they called the Cycle of Indiction. It was a 
 period of 15 years, but had no respect to the movement of any of the 
 heavenly bodies. It is believed that it was established to exact 
 certain tributes or taxes of the provinces. 
 
 The Emperor Justinian ordered that it should be observed or no- 
 ticed in the public acts ; and the Popes still use it in their Bulls, and 
 they fix the commencement of it to the calends of January, but the 
 Romans gave it another epoch. The fourth year of this cycle cor- 
 responds to the first of the Christian era ; therefore, to find what year 
 of the cycle corresponds to any given year of the Christian era, add 
 3 to the given year, and divide the sum by 15, the remainder is the 
 year of Indiction. 
 
 Example. What year of the Indiction was the year 1825 ? 
 
 1825 + 3= =121, and 13 remains for the yea; of Indiction. 
 
 OF PERIODS AND EPOCHS. 
 
 The continued multiplication of the solar, lunar, and indiction 
 cycles, that is, 28, 19, and 15, gives what is called the Great 
 Julian Period* of 7980 years, which is supposed to have commenced 
 764 years before the creation, and that then the three cycles began 
 at the same time. It is not yet completed, and it comprehends all 
 the other periods, cycles, and epochs. There is not more than one 
 year in all the period that has the same number for the three cycles, 
 and therefore if historians had marked the three cycles in their annals 
 for every year, there could have been no dispute respecting the time 
 that any event happened. The birth of Jesus Christ took place in 
 the 4713th year of the Julian Period. Therefore, to find what year of 
 that period corresponds to any current year, add 4713 to the given 
 year, and the sum is the year of the Julian Period. In this manner, 
 the year 1825 will be found to be the 6538th year of the Great Julian 
 Period. 
 
 These are the principal periods ; but there are others less used, 
 such as the year of Jubilee among the Jews, which was composed of 
 seven years of Sabbaths, and returned in about 49 or 50 years. 
 
 The Olympiads among the Greeks, which consisted of four years ; 
 and the great Platonic Year, so celebrated among historians, which 
 contained the entire revolution of all the stars from the point from 
 whence they set out to the same again. 
 
 As there are in the heavens certain fixed points from which astro- 
 nomers begin their calculations, historians have also other fixed points, 
 which they call eras or epochs, from whence they set out in fixing 
 the time of any event. 
 
 The most ancient of these is the Creation of the World, the next 
 i* that of the Deluge, 2956 years before the birth of Jesus Christ ; 
 
 * From Julius Scaliger, its Inventor. 
 
OF THE CALENDAR. 64 
 
 the third is that of the Olympiads, which began in Greece 776 years 
 before Christ, in the 3938th year of the Julian period, the solar cycle 
 being then 18, the lunar cycle 5, and the Roman indiction 8. The 
 next remarkable epoch is that of the foundation of Rome towards 
 the end of the third year of the 6th Olympiad, 753 years before 
 Jesus Christ, in the 3961st year of the Julian Period, the cycle of 
 the sun being then 13, the cycle of the moon 9, and the indiction 1. 
 
 The next in order of time is that of Nabonassar, king of Babylon, 
 to famous in astronomy. It has been employed by Ptolemy, Alba- 
 tegnius, Alphonso, Copernicus, and many others, as the most proper 
 era for calculating the motions of the stars. It began, according to 
 Ptolemy, in the 4th of the calends of March, on a Friday, 747 years 
 before Jesus Christ, in the year 3967 of the Julian Period, the first 
 year of the 8th Olympiad, the solar cycle being 19, the lunar cycle 
 15, and the indiction 6. 
 
 After this epoch we have that of Alexander the Great, 424 Egyp- 
 tian years after the commencement of the era of Nabonassar, for 
 Alexander died at Babylon in the 33d year of his age, the first year 
 of the 1 14th Olympiad, on the 3d of the month Desii, according to 
 some historians, but according to others, on the 23d or 27th of the 
 Julian calendar, which is the 20th of May according to the one, and 
 the 9th or 23d June according to the other, and according to some 
 the 25th July. 
 
 But the astronomers who have employed those epochs, as Alba- 
 tegnius and others, fix it to the 12th of November, a Sunday at mid- 
 day, the first day of the Egyptian month Thoth, 324 years before 
 Jesus Christ, in the 4390th year of the Julian Period, 279 years before 
 the commencement of the Julian Epoch, and 424 complete Egyptian 
 years after the commencement of the era of Nabonassar. 
 
 The era of the Syrians and Chaldeans began in the reign of Seleu- 
 cus Nicator, who succeeded Alexander the Great, and reigned in 
 Syria and in part of Africa, after the death of Alexander the Great 
 The Julian epoch, adopted by Julius Caesar, began on the 1st of 
 January of the year of the Confusion, which is found to have been on 
 a Tuesday. This prince, seeing that the year established by Numa 
 Pompilius, the second king of Rome, consisted only of twelve lunar 
 months, aad that such a division of the year did not accord with the 
 sun, ordered, in the fourth year of his consulship, 708 years after the 
 foundation of Rome, in the 731st year of the Olympiads, 45 years 
 before the birth of Jesus Christ, that, in future, the year should con- 
 sist of 365 days 6 hours, which Was afterwards, and is still, called the 
 Julian Year. 
 
 The Spanish Era began in the reign of Augustus, in the 7th year of 
 the Julian Era, 38 years before Jesus Christ, 715 years after the 
 foundation of Rome, and in the 738th year of the Olympiads. It is 
 said it was occasioned by the division ef the empire. Spain was 
 given to Augustus, and when he first took possession, to render that 
 day memorable, it was fixed upon for an epoch, and computed from 
 afterwards, Ab Exordia Regni Augusti These four words were 
 afterwards abridged, and reduced to the initial letters. This, accord- 
 
04- OF FINDING THE LATITUDE OF A PLACE. 
 
 ing to some authors, was the origin of the word AER A, which now 
 serves to mark the epoch from whence years are reckoned. 
 
 The next epoch following in the order of time, the most renowned, 
 and the best known of any, is the Incarnation of our Lord Jesus 
 Christ, which, on that account, is called the Christian Era. 
 
 It began the first minute after the 31st December immediately after 
 his birth, which was on a Saturday, in the 4714th year of the Julian 
 Period, 753 years after the foundation of Rome, in the 747th year 
 of Nabonassar, and 324 years after the death of Alexander the Great, 
 the solar cycle being 10, the lunar cycle 2, and the Roman indic- 
 tion 4. 
 
 There are other periods less used, as that of the Emperor Diocle- 
 sian, beginning on the 21st April, in the 284th year of Jesus Christ, 
 and 4997 of the Julian Period. There is also the Epoch of the Ethio- 
 pians, of the Abyssinians, and of the Martyrs, because of the great 
 persecution that the Christians suffered in that reign. 
 
 There is also the Epoch of the Turks, which is called the Hegira, 
 and which began with the Flight of Mahomet from Mecca to go to 
 Gabriel, on Tuesday the 16th July, in the 622d year of the Christian 
 Era, at which time Mahomet preached and spread his fake doctrine. 
 
 That of the Persians is named the Jesdegird, from the name of 
 one of their kings, who died on Wednesday the 16th July, in the 
 632 year of the Christian Era. 
 
 The Jews, in their Calendar, reckon the creation of the world to 
 have taken place 3760 years before the Christian Era, 
 
 To Draw a Meridian Line. 
 
 UPON a plain board, set parallel to the horizon, describe several 
 concentric circles ; in the centre of these fix a gnomon, or stile, ex- 
 actly perpendicular to the plane of the board, and of such a height 
 as the shadow of it may fall upon the circumference of all the circles 
 at different times of the day : mark the point where the top of the 
 stile falls in the forenoon, which will be on the circumference of one 
 of the circles ; then watch the time when the shadow falls on the same 
 circle in the afternoon ; and a line drawn from the centre or stile 
 bisecting the distance between these points will be in the direction of 
 the true meridian. 
 
 The reason of several circles being drawn, is to observe the shadow 
 of the stile on any of them, in case the sun should not be shining out 
 in the afternoon, when he would throw a shadow on the same circle ; 
 and also to perform the same operation with each circle, in order to 
 ensure accuracy, by taking the mean of the observations. 
 
 The best time of the year for doing this, is about the time of the 
 summer solstice, when the daily difference of declination is least. 
 The reason of this opposition may easily be perceived for at equal 
 distances from the meridian, the suu will have equal altitudes, and, 
 *>f course, the shadow of any object will have the same length. 
 
OF FINDING THE LATITUDE OF A PLACE. 65 
 
 Of finding the Latitude of a Place. 
 
 THE latitude of any place is equal to the altitude of the pole above 
 the horizon of that place ; therefore the poles will appear in the ho- 
 rizon of a place which has no latitude, or that is on the equator. 
 
 This problem is nothing else, than finding the elevation of 
 the pole above the horizon ; but as there is no star exactly in the 
 pole of the heavens, take any star which is not more than 8 or 10 
 from the pole, and observe with a quadrant its greatest and least 
 meridianal altitudes; then if both observations are on the same side 
 of the zenith, half the sum of the altitude is the latitude. If the ob- 
 servations are on different sides of the zenith, half the difference of 
 the altitudes is the co-latitude. 
 
 Note. There will be about twelve hours between the observations. 
 
 Of the Magnitude of the Earth. 
 
 To find the magnitude of the earth is a problem of such importance 
 in astronomy, that it has been attempted by some of the ablest mathe- 
 maticians, in almost every age, since the days of Eratosthenes to 
 the present. The French mathematicians, by connecting a series of 
 triangles, have lately measured the distance from Dunkirk to For- 
 mentera, which corresponds to an arc of the meridian, of 12 22' 
 13"-395 ; and from this extensive base the circumference of the earth 
 is computed to be 24,855-42 English miles. 
 
 A degree of the meridian has been measured in different latitudes, 
 by several astronomers, in order to ascertain the true figure of the 
 earth, as well as to determine its magnitude. Mapertius, along with 
 some other mathematicians, measured a degree in Lapland, at lat. 
 66 20', and found it 57,438 toises. 
 
 Another, by La Hire, at latitude 49 22', which was found to be 
 57,074 toises. 
 
 Toises. 
 By Cassini and La Caille, at latitude 45 = 57050 
 
 By (Pennsylvania) lat. 39 =: 56888 
 
 By Bescovich . . . .43 = 56979 
 By Juan and Ulloa . . . 33 18' = 57037 
 By Dolumbert (France) . . 46 12' = 57018 
 
 By Bouguer (Equator) ... = 56753 
 
 By De la Condamini . . 56749 
 
 A T*ise is = 1-06577 fathoms. 
 
 By comparing these numbers with each other, and taking the 
 arithmetical mean of the whole, the equatorial axis is to the polar, as 
 230 to 228-92974, which is nearly what Sir I. Newton made it by 
 calculation long before. 
 
 From this it is plain the earth is not exactly spherical, but is a 
 kind of oblate spheroid, flattened at the poles. 
 
 This proportion makes the equatciial axis exceed the polar by 
 about 34 miles, but some think this statement rather exceeds the 
 truth, and give the compression at -j^j.^j 25*66 miles. 
 
66 TO FIND THE OBLIQUITY OF THE ECLIPTIC. 
 
 The method of performing the operation of measuring a degree 
 of the meridianal arc, and its corresponding arc of the earth's sur- 
 face, is abundantly simple in theory, although there is scarcely any 
 operation more difficult in execution. It is performed by measuring 
 a base line as nearly as possible in the direction of the meridian, then 
 finding exactly the difference of latitude between the extremities of 
 the base line. Then, as the difference of latitude or celestial arc is 
 to the measured base line, so is one degree of the celestial arc to tho 
 length of a degree of the earth's surface, in the same measure as the 
 base line was taken. 
 
 In a similar manner may the circumference of the earth's orbit be 
 obtained from knowing the sun's parallax : thus, 
 
 smd. semids. * 
 
 8-f" : 360 : 1 :: 149538, 
 the circumference of the earth's orbit. 
 
 To find the distance of the sun and earth; then 
 
 smds. semids. 
 
 3-1416x2 : 149538 :: 1 : 23799-8, 
 the earth's distance from the sun. 
 
 From the above dimensions of the earth, it appears that one degree 
 on the globe is nearly 69| English miles. 
 
 The length of a degree may be found, very nearly, by the follow- 
 ing theorem : 
 
 Let L = the latitude, then 60761 (295-75) co-sine 2 L* will be 
 the length of a degree. 
 
 Example. Required the length of a degree of the meridian, at 
 latitude 51? Here the co-sine of the latitude is -6293, which multi- 
 plied by 2, and by the number 295'75, gives 370, which subtracted 
 from 60761, leaves 60392 fathoms for the length of a degree of the 
 meridian, at latitude 51. 
 
 To find the Obliquity of the Ecliptic. 
 
 Rule. -LET the meridian altitude of the sun's centre be observed, 
 on the days of the summer and winter solstices ; the difference of 
 those altitudes will be the distance of the tropics ; and half that dis- 
 tance will be the obliquity of the ecliptic. 
 
 Rule 2. Or if the latitude of the place be known, the meridian 
 altitude of the sun, at the summer solstice, lessened by the co-lati- 
 tude, will give the obliquity of the ecliptic. 
 
 The obliquity of the ecliptic for the year 1825, is 23 27' 44". By 
 comparing ancient observations with what have lately been made, 
 it appears that the obliquity is decreasing at the rate of f" annually. 
 
 Remark. By this last rule the declination of a fixed star may 
 also be determined. 
 
 * The number 60761 is the radius of the globe, at latitude 45, in fathoms. 
 
TO FIND THE PERIODIC TIME OF A PLANET. 67 
 
 To find the Time of an Equinox. 
 
 AT a place, the latitude of which is known, let the sun's meridian 
 altitude be taken the day before the equinox is expected to happen, 
 and also the day after, then the difference between those altitudes, 
 and the co-latitude, will be the sun's declination on those .two days 
 when the altitudes were taken. 
 
 If either of the altitudes be equal to the co-latitude, that observa- 
 tion was made at the time of the equinox. If not proceed thus : 
 
 Let A B C be a portion of the equator, and D B E an arc of the 
 ecliptic, D the place of the sun at the first observation, E his place 
 at the secondhand B the equinoctial point ; also, A D the declination 
 at first observation, and E C at second ; then in the right-angled 
 spherical triangles, A B D and E B C, there are given the obliquity 
 of the ecliptic, and the declination A D and E C, to find the sides 
 D B and E B, which being found, are to be added together : then 
 say, D B -f E B is to D B, so is 24 hours to the time between the 
 first observation and the moment the sun entered the equinoctial 
 point. 
 
 To find the Periodic Time of a Planet. 
 
 THIS is best done when the planet has no latitude, or in the 
 ecliptic, it will then be in one of its nodes ; this time is to be care- 
 fully noted, and compared with the time when the planet has a like 
 position, both in latitude, longitude, right ascension, and the line of its 
 apsides. If the planet has only performed one revolution, the inter- 
 val betwixt the two observations will be the periodic time of the 
 planet ; but if it has performed more revolutions, the interval is to be 
 divided by the number of revolutions, and the quotient will be the 
 periodic time. From this it is evident, the greater the interval, or the 
 greater the number of revolutions, the more accurately will the pe- 
 riodic time of the planet be found. 
 
 In this manner the length of the tropical year is found to be 365 d 
 5 h 48' 48" ; the sidereal year 365 d 6 h 9' 11" ; and the anomalistic 
 year 365 d 6 h 14' 2". 
 
 The tropical year being shorter by 20' 23" than the sidereal, shows 
 that the sun has returned to the same point of the ecliptic, before he 
 
08 TO FIND THE RIGHT ASCENSION OF THE STARS. 
 
 has made one entire revolution with regard to the stars: conse- 
 quently, every point, of the ecliptic must have moved backward, or 
 in antecedentia, and this motion is called the precession or recession 
 of the equinoxes. 
 
 The quantity of the recession may be found as follows : 365 d 6 h 9' 
 11" : 360 :: 20' 23" : 50J" the recession of the equinoxes annually, 
 which maks one degree nearly in 72 years ; so that in about 2160 
 years these points change a whole sign in the zodiac, and in 25,920 
 years will go entirely round the heavens, and perform what is called 
 the grand celestial period. 
 
 A sidereal revolution being performed sooner by 5' 51" than the 
 anomalistic, shows that the line of the apsides has a motion in con- 
 sequentia ; for, 365 d 6 h 9' 11" : 365 d 6 h 14' 2" : 5' 51" : : 15", the 
 yearly quantity by which the sun's apogee is advanced with respect 
 to the stars : and as the equinoxes move 50|" in antecedentia, and 
 the apsides in 15" consequentia, their sum (65|") is the motion of 
 the apsides from the equinoxes. 
 
 The periodic time of the moon, (sometimes called a periodic or 
 lunar month,) is the time which she takes to revolve from any point 
 of her orbit to the same again is 27 d 7 h 43'. 
 
 A synodical month, or the time which the moon takes in passing 
 from one conjunction with the sun to another, is found to be 29 d 12 h 
 44' 2-8", being 2 d 5 h 1' 2*9" longer than the periodic month. 
 
 This difference arises from the earth's motion in her orbit ; for while 
 the moon is passing from one conjunction to another, the earth will 
 have advanced considerably in her annual course ; therefore, the 
 moon must advance as mnch more than one revolution as the earth 
 has done since the last conjunction, before she be again in conjunction 
 with the sun. 
 
 To find the Sun's place in the Ecliptic, or his Longitude. 
 
 HAVING the sun's declination and the obliquity of the ecliptic, his 
 longitude and right ascension can easily be found, and tables formed 
 which will give his place in the ecliptic, answering to his declination, 
 for every day in the year. Thus, to find the sun's longitude, the rule 
 or analogy is as follows : 
 
 As sine obliq. eclip. is to sine declination, so is radius to sine sun's 
 longitude. 
 
 To find the sun's right ascension the analogy is this : 
 
 As tan. ob. eclip. is to tan. declin. so is radius to co-sine right 
 ascension. 
 
 To find the Right Ascension of the Stars. 
 
 HAVING the sun's place in the ecliptic, and a well-regulated clock. 
 The clock being adjusted to sidereal time, when the sun is on the 
 meridian, point the hand to the moment from whence the time is to 
 be reckoned; and observe when the star comes to the meridian 
 
ON THE EQUATION OF THE CENTRE. 69 
 
 then mark the hour and minute that the hand shews on the clock* 
 The time described by it, turned into degrees and minutes of the 
 equator, will be the difference between the right ascension of the sun 
 and stars. This difference being added to the right ascension of the sun, 
 will give the right ascension of the star. The right ascension of one 
 star being known, that of any other may be obtained by it. This is 
 done by marking the time upon the clock, between the arrival of the 
 star at the meridian whose right ascension is known, and the other 
 star whose right ascension is to be found. This time, converted into 
 hours and minutes of the equator (or mean time), will be the difference 
 of right ascensions ; hence, by addition or subtraction, the right 
 ascension of the star required is found. 
 
 The right ascension and declination of any star being known, its 
 latitude and longitude may be found ; and hence, catalogues may be 
 formed of all the stars that are visible in the heavens. 
 
 To find the greatest Equation of the Centre.* 
 
 THE equation of the centre of any planet, means the difference of 
 the radius victor moving in a circle, and as moving in the planet's 
 orbit : or it is the difference between the true and mean anomaly. 
 And as these are no where the same, but when the planet is in its 
 perihelion or aphelion, their difference is called the equation to the 
 centre; which is greatest when the sun is at his mean distance from 
 the earth. Therefore, find the sun's longitude when he is at his 
 mean distances from the earth, which is about the beginning of Oc- 
 tober and the end of March ; then the difference of longitude will be 
 the sun's true motion in that interval of time. Find, also, his mean 
 motion for that interval of time : then half the difference between the 
 true and mean motions will be the greatest equation of the centre. 
 The sun's mean motion for any interval of time, may be found by 
 multiplying his daily motion, 59' 8"'985647 of a day, by the days and 
 parts of day in that interval. 
 
 Or say, 365 d 242264 : 360 : : a d : a; ; if the time be reckoned 
 from 1st of January, it will be the sun's mean anomaly; but if from 
 Aries, it will be his longitude, as under :f 
 
 Example. To find the greatest equation to the centre. 
 
 In the year 1824, October 1st, at 23 h 49' 12", mean time, the sun's 
 longitude was 6 s 9 32' 6", and in 1825, March 29th, at O h 4' 50", 
 mean time, his longitude was s 8 50"'27 ; therefore the true differ- 
 ence of longitude is 5 s 29 18' 27", and the interval is 178 d O h 15' 38", 
 now 365-242264 : 360 :: 178 d 01085648 : 175-45584 zz 175 27 
 20" mean motion ; and 179 18' 27"=5 S 29 18' 27" 
 
 175 27 20 
 2) 3 5L 7 
 
 1 55' 38" 
 The greatest equation to the centre, according to these observations, 
 
 * This is called the Keplerian Problem, 
 t Here a is the interval, and x the mean motion. 
 
70 OF SOLAR AND. SIDEREAL TIME, 
 
 To find the Equation of Time. 
 
 HAVING already given sorqe account of the difference between mean 
 and apparent time, we shall here show the manner of calculating that 
 difference. As we have already said, it arises from two causes, and 
 therefore consists of two parts, which being rightly put together forms 
 the absolute equation. One of these causes is the obliquity of the 
 ecliptic to the equator ; and the other is, the unequal motion of the 
 earth in her orbit. The greatest part of the equation is that which 
 arises from the former of these causes, and is found by converting the 
 difference between the sun's longitude and his right ascension into 
 time. His longitude and right ascension may both be found from 
 tables, or from his declination and the obliquity of the ecliptic, by 
 solving a right-angled spherical triangle, and hence their difference 
 or this part of the equation may be obtained. 
 
 That part of the equation arising from the unequal motion of the 
 earth, in different parts of her orbit, is found by taking the difference 
 of the mean and true anomalies, or the equation to the centre, and 
 converting it into time, which is the second part of the equation ; and 
 is to be added to, or subtracted from, the other part, according as 
 they have like or unlike signs, in order to form the absolute equation. 
 The proper sign is affixed to each of these quantities, by considering 
 whether the mean time is preceded by the apparent, or is preceded 
 by it. 
 
 While the earth is going from her aphelion to her perihelion, the 
 apparent time (depending on this cause) will be before the mean, and 
 therefore this part of the equation must be subtracted from the appa- 
 rent, in order to gain the mean time. But in the other semicircle of 
 her orbit it will be after it, and therefore must be added to gain the 
 mean. 
 
 From the 14th April to the 15th June, and from the 13th August 
 to the 23d December, that part of the equation depending on the ob- 
 liquity of the ecliptic, is also to be subtracted from the apparent (for 
 the apparent is then before the mean) ; but from the 15th June to the 
 31st August, and from the 23d December to the 14th April, it is to 
 be added to the apparent in order to gain the mean. 
 
 The earth's daily motion in apogee, or at her greatest distance 
 from the sun, is 57' 12" ; but in perigee, or at her nearest distance, 
 it is 61' 12". Accordingly, we have the summer longer than the 
 winter by eight days, for she is 8 days longer in passing through the 
 northern half of her orbit than the southern. 
 
 Of Solar and Sidereal Time. 
 
 A SIDEREAL day is the interval between two successive transits 
 of a star over the meridian. This interval is uniform, for all the fixed 
 stars, make their revolutions in equal times, owing to the uniformity 
 of the earth's diurnal rotation about its axis. 
 
TO FIND THE ECCENTRICITY OF THE EARTH'S ORBIT. 71 
 
 The sidereal clay is shorter than the mean solar day by 3' 56"-55. 
 This difference arises from the sun's apparent annual motion from 
 west to east, which leaves the star as it were behind. Thus, if the 
 sun and a star be observed on any day to pass the meridian at the 
 same instant, the next day, when the star returns to the meridian, the 
 sun will have advanced nearly a degree easterly, (which is his daily 
 portion of the ecliptic) and as the earth's diurnal rotation on its axis 
 is from west to east, the star will come to the meridian before the 
 sun ; insomuch, that, at the end of the year, it will have gained a day 
 on the sun, that is, it will have passed the meridian 3G6 times, while 
 the sun will have passed it but 365 times. 
 
 Now, as the sun appears to perform his revolution of 360 in a 
 year, or 365 d 5 h 48' 48" : 360 : : l d : 59' 8"-3, which is the space 
 the sun would describe in a day, if all the days were of an equal 
 length ; and this space reduced to s time is = 3' 56"-55, the excess of 
 a mean solar day above a sidereal day. 
 
 Hence, it appears that the earth describes about its axis an angle 
 of 360 59 / 8"-3 in a mean solar day, and an angle of 360 in a side- 
 real day; therefore, as 360 59' 8"-3 : 24 h :: 360 : 23 h 56' 4"-09, 
 the length of a sidereal day in mean solar tim,e, or the interval 
 between two successive transits of a star over the meridian. 
 
 Hence, the following general rule for converting sidereal into mean 
 time, and the contrary. 
 
 Rule. As 24 h : 23 h 56' 4"-09 : : any portion of sidereal time to 
 its equivalent in mean time. 
 
 And as 23 h 56' 4"-09 : 24 h : : any portion of mean time to its 
 equivalent in sidereal time. 
 
 To find the Eccentricity of the Earth's Orbit. 
 
 HAVING the greatest equation of the centre, we can easily find 
 the eccentricity of the earth's orbit by the following proportion : 
 
 As the diameter of a circle in degrees, 
 
 Is to the diameter in equal parts; 
 
 So is the greatest equation of the centre in degrees, 
 
 To the eccentricity in equal parts. 
 
 Example. The greatest equation of the centre, is 1 55' 33"-l 925833, 
 and the circumference of a circle whose diameter is 1, is 3- 141 5926 ; 
 then, 3-1415926 ; 1 : : 360 : 114-59 15609 equal the diameter; 
 andll4-5915609 : 1 :: 1-925833 : 00168061 eccentricity. Hence 
 1+ 0-0 168061 =1-01 6806, the aphelion distance ; and 
 10-016806 -983194, the perihelion distance. 
 The eccentricity of the earth's and moon's orbit may also be found 
 by observing the variations of the apparent diameter of the sun and 
 moon during a complete revolution, (by a micrometer) their distance 
 from the earth being inversely proportional to the angle which they 
 subtend. 
 
 The ratio of their greatest and least diameters is a measure of the 
 
72 TO FIND THE SUN'S MEAN ANOMALY. 
 
 relation between their greatest and least distances, and consequently 
 enables us to ascertain the eccentricity of their orbits. 
 
 Thus, if the diameter of the sun be found to measure 32' 35"-6 
 when the earth is in one part of her orbit; and 31' 31" when in the 
 opposite point (which is found to be the case on the 1st January and 
 1st July) then will the ratio of the diameter of the orbit be to the 
 eccentricit as 3$35"'Q 31' / 31 // =l / 4 // -6 and 64"-632 f 35"-6 + 31' 
 
 eccentricity as 3$35"'Q 31' / 31 // =l / 4 // -6 and 64"-6^_32 f 35"-6 + 31' 31 " 
 
 2 ' 2 
 
 ooo" 
 
 . _ = -0168 nearly what it was found to be above. 
 19233" 
 
 This method is more liable to error than the first. 
 
 . 
 
 To find the Time and Place of the Sun's Apogee. 
 
 THE apogee is that point of the orbit which is farthest from the 
 focus in which the sun is placed; this problem is therefore no more 
 than to determine at what time the planet is farthest from the sun. 
 
 By the decrease of the sun's apparent diameter, we can have an 
 idea when this happens, though other methods must be had recourse to, 
 when we wish to determine it accurately ; one of these is as follows : 
 On the day of two successive apsides, observe the sun's place and the 
 time. Then if the interval between those times be equal to the half 
 of 365 d 6 h 15' 28", and the difference of the sun's places be equal to 
 the half of 360 1' 6" (the space he describes in the above time), the 
 observations were made when the sun was in the apsides. 
 
 But if those observed intervals of time and place differ from the 
 above halves, take the difference between the interval of place and 
 180 0' 33". Then to the daily motion of the sun in apogee (which is 
 57' 12") the said difference and 24 h find the proportional time : which 
 proportional time and difference being applied to the time and places 
 of the apogeon observation, gives a time and place when it is 180 0' 
 33" distant from the observed perigeon place : now, if the interval 
 of these times be 182 d 15 h 7' 44^" the times and places of the apsides 
 are known. 
 
 But if the interval of time differs from 182 h 15 d 7' 44", say, as the 
 difference between the perigeon and apogeon daily motions, is to the 
 daily motion of the apogee, so is the difference of the interval of time 
 to a second correction of the time of the apogee ; which applied to the 
 apogeon time, corrected as above, will give the true time of the sun's 
 apogee. Also, to the last correction of time, find the proportional 
 motion of the sun's apogee, and apply it to the last corrected place of 
 the apogee, and the true place of the apogee will be obtained. 
 
 At any Given Time to find the Sun's Mean Anomaly. 
 
 THE time when the sun passes his aphelion being accurately as- 
 certained, the mean anomaly at any time may be found, by multiply- 
 
TO FIND THE SUN'S TRUE ANOMALY. 73 
 
 ing the sun's daily mean motion (which is 59' 8") by the number of 
 days, and parts of a day, which he is past his aphelion. 
 
 Or, as the time of a tropical revolution, or solar year, is to the 
 interval between the aphelion and given time, so is 360 to the 
 degrees of mean anomaly. 
 
 Or, from the tables of mean motions find the sun's mean motion 
 for the given time, and this will be the mean anomaly. 
 
 If the earth's orbit were circular, the sun's true place at any time 
 would be the same as shown by the tables of his mean motion ; or 
 the mean and true anomaly would always be the same. But the 
 earth moving in an elliptical orbit, its true anomaly will differ from its 
 mean, in every part of her orbit, except when she is in her perihelion 
 and aphelion, where they coincide. 
 
 To find the Sun's true Anomaly 
 
 HAVING the sun's mean anomaly, and the dimensions of the 
 earth's orbit, the eccentric anomaly may be found by the following 
 analogy : 
 
 As the aphelion distance 
 
 Is to the perihelion distance ; 
 
 So is the tangent of half the mean anomaly 
 
 To the tangent of an arc A ; 
 
 which arc being added to half the mean anomaly, gives the eccentric 
 anomaly. 
 
 The sun's eccentric anomaly, and the dimensions of the earth's 
 orbit being known, to find the true anomaly. 
 
 Rule. As tho square root of the aphelion distance 
 
 1 s to the square root of the perihelion distance ; 
 So is the tangent of half the eccentric anomaly, 
 To the Tangent of half the true anomaly. 
 
 To find the mean Anomaly from the true being given. 
 
 Rule. As the square root of the perihelion distance 
 Is to the square root of the aphelion distance ; 
 So is the tangent of half the true anomaly 
 To the tangent of half the eccentric anomaly. 
 
 And, As radius is to the sine of the eccentric anomaly, 
 So is the degrees in an arc equal in length to the eccentricity; 
 To the degrees, &c. in the arc of correction, which being added to 
 the eccentric anomaly, gives the mean anomaly. 
 
 q 
 
74 TO FIND THE DISTANCES OF THE HEAVENLY BODIES. 
 
 Greatest equation of the centre 1 55' 38" 
 Eccentricity in parts . - . '01682 
 Aphelion distance . . 1-01682 
 
 Perihelion distance . . -98318 
 
 The logarithm of the ratio of the square root of the aphelion dis- 
 tance to the perihelion distance is 0-00731 ; therefore, if this constant 
 log. be added to the log. tangent of f the true anomaly, it will give 
 the tangent of \ the eccentric anomaly. 
 
 And in the second proportion, the arc equal in length to the eccen- 
 tricity 1682, is also a constant quantity, which may be found as 
 follows: 100000 : 1682 :: 57'29578 : 0- 96375 eccentricity, the 
 log. of which is 9'98396, this added to the log. sine of the eccentric 
 anomaly, abating 10 from the indices of the sun, gives the log. of an 
 arc, the degrees, minutes, and seconds of which being added to the 
 eccentric anomaly, gives the mean anomaly. 
 
 To find the Distances of the Heavenly Bodies. 
 
 THE distances of the heavenly bodies are found by discovering 
 their horizontal parallaxes. The horizontal parallax of any body 
 has already been explained to be, the angle under which the semi- 
 diameter of the earth would appear if it were seen from that body, 
 and this is found out by various methods. 
 
 The parallax most wanted is that of the sun, by which his distance 
 from the earth may easily be found ; and from knowing this, the 
 true distances of the planets from the sun may be otained from their 
 relative distances, by the second law of Kepler. 
 
 Before the year 1761, the sun's parallax was always stated at 12|" ; 
 but in the above year, Dr. Halley discovered, by the transit of the 
 planet Venus across the sun's disc, that his parallax was only 8|" 
 which makes his distance much greater than it was then supposed to be. 
 
 Having his parallax, his distance is found by this analogy. 
 
 As Tan. Parallax . . 8"-6 =5*6227666 
 Is to Earth's semid. .1 rr 
 
 SoisRad. ... 90 = 10- 
 
 To dis. in Semid. Earth 23835 -lzi 4' 3772334 
 Semid. Earth . . . 3981 =3-6000000 
 Dist. in Eng. miles 94'897'172 ir: 7'9772334. 
 
 The nearer any object is to the earth the greater will be its paral- 
 lax ; for the semidiameter of the earth must then appear under a 
 greater angle. The moon being much nearer the earth than the sun, 
 her parallax is much greater : at a mean rate it amounts to 57' 26", 
 Her distance may be found by the same analogy as that given for the 
 sun above, which will be found to be about 240,000 miles. 
 
 When any object is in the horizon, its parallax is greatest, and it 
 diminishes as the altitude of the object increases. In the zenith it 
 will have no parallax. 
 
TO FIND THE DISTANCES OF THE HEAVENLY BODIES. 75 
 
 In most calculations, where the moon is concerned, it becomes 
 necessary to find her parallax in altitude ; this is done by saying, 
 
 As radius is to the horizontal parallax, so is the cosine of the alti- 
 tude to the sine of the parallax in altitude. 
 
 In the same manner may the distance of any planet be found, if its 
 parallax be known. 
 
 As the fixed stars have no sensible parallax, their distance can 
 only be guessed at ; for though Dr. Bradley made many attempts, 
 with the best of instruments, to discover the parallax of the star <v> 
 Draconis, he never could find its parallax to amount to a single 
 second. 
 
 The distances of Mercury and Venus may also be determined 
 by their greatest elongations from the sun. 
 
 Thus, let S be the sun, T the earth, A VB the orbit of Venus, 
 which suppose perfectly circular, let V represent the place of Venus, 
 at her greatest elongation, and join V T ; then in the triangle S T V, 
 right-angled at V, the angles, viz. the angle V, and the angle S T V, 
 the greatest elongation, and the side S T the earth's distance from the 
 sun are known, therefore, the side S V, Venus's distance from the 
 sun may be found, and the side TV, Venus's distance from the earth, 
 may also be found by plane trigonometry. 
 
 The distances of the superior planets may be determined by their 
 retrograde motions, and such of them as have satellites, by the 
 eclipses of those satellites. 
 
 q2 
 
76 TO FIND THE DISTANCES OF THE HEAVENLY BODIES. 
 
 Let I represent Jupiter, S the sun, and E the earth ; join S I, 
 and produce it to M ; then I M is the axis of his shadow, the posi- 
 tion of which is determined by the eclipses of the satellites, and 
 shews his heliocentric place. Join T I and produce it to N, 
 which will be the place of Jupiter when viewed from the earth. The 
 difference of these places gives the angle N I M, or T I S ; the elon- 
 gation of Jupiter when viewed from the earth atT ; or the angle ITS 
 is easily found by observation, consequently all the angles in the 
 triangle TI S are known, and also the side ST, the distance of the 
 earth from the sun ; therefore the sides SI and T I may both be 
 found, and thus the distance of Jupiter from the sun or the earth is 
 obtained. 
 
 In the same figure, let I represent any of the superior planets, or 
 any remote object of the system A, the point where the earth passes 
 between the sun S and object I, and let I T be a tangent drawn from 
 I to the earth's orbit, which suppose to be circular : then the earth 
 being at A, the object I will appear in the same place both to the 
 earth and sun ; but when the earth comes to T, supposing I to have 
 no motion, it will appear to the earth to have gone backward by the 
 arc that measures the angle T IS, or the angle which the earth's 
 distance from the sun subtends at the object I ; and this angle being 
 determined by observation, its sine will be to radius, as ST, the dis- 
 tance of the earth from the sun, to S I, the distance of the object from 
 the sun ; or as its co-sine to TI, the distance of the object from the 
 earth. 
 
 It is in this manner that the earth's annual parallax is used by 
 astronomers instead of the diurnal, in rinding the distances of remote 
 objects not belonging to the solar system ; the semidiameter of the 
 earth being so small in comparison of those distances that they have 
 found it necessary to substitute the semidiameter of her orbit instead 
 of it, which is called the annual parallax. 
 
OF THE SUN'S RISING AND SETTING. 
 
 To find the Periodic Time of a Planet. 
 
 THE times in which the planets perform their revolutions about the 
 sun are known by observation; therefore, having the distance of any 
 one of them from the sun, the distance of the ethers may be found by 
 Kepler's law. Thus, suppose the distance of the earth from the sun 
 to be 1, and it is required to find the distance of Mercury ; 
 
 365| 2 : I 3 : 88 2 : : V05805 = -87; and so of the others. 
 
 To find the Time of the Sun's Rising and Setting. 
 
 Rule. To the tangent of the latitude of the place, add the tangent 
 of sun's declination ; the sum, rejecting 10 from the index, will be the 
 logarithm co-sine of an arch, which reduced to time, at the rate of 
 15 to an hour, will be the time of the rising, when the declination is 
 of the same name with the latitude ; but the time of setting, when it 
 is of a different name. 
 
 Required the time of the sun's rising in latitude 52 12' N., on the 
 4th of May? 
 
 The sun's declination on the 4th of May is 15 64' N. which is there- 
 fore of the same name with the latitude. Hence, in the present 
 example : 
 
 Tan. 15 54' Log. 9-454628 
 Tan. 52 12 Log. 10-110318 
 
 Co-Sine 68 27' Log. 19-565046 
 
 Now, 68 27' converted into time is 4 hours 34 minutes nearly ; 
 which is the time of the sun's rising on the 4th of May, at latitude 52 
 12' N. 
 
 To find the Time of a Planet Rising and Setting. 
 
 IN the same manner may half the time of a star or planet's conti~ 
 nuance above the horizon be found ; but in order to find the time of its 
 rising, this time must be subtracted from the time of its passing the 
 meridian ; and to find the time of its setting, it must be added to 
 the time of its passing the meridian. 
 
 As the time of a planet's passing the meridian can easily be obtained 
 from an ephemeris, and the time of its half continuance above the 
 horizon by the above rule, it is unnecessary to give an example of 
 computing the time of a planet rising or setting. 
 
 The time of a fixed star's rising or setting is found exactly in the 
 same manner as that of a planet. 
 
78 REAL MAGNITUDES OF THE PLANETS. 
 
 To find the Time of a Star or Planet's passing the Meridian on any 
 Day of the Year, &c. 
 
 Rule. From the right ascension of the star* subtract the right 
 ascension of the sun, for the given day, and the remainder will be the 
 approximated time of the star's passing the meridian. If the star's 
 right ascension be less than the sun's, it must be increased by twenty- 
 four hours. 
 
 When the time of the star's passage over the meridian is less than 
 twelve hours, the time is P.M.; when greater, it will be as many hours 
 after 12 p. M. of the given day. 
 
 The approximate time of a planet's passing the meridian may be 
 found in the same manner, if its right ascension be known. 
 
 To find the Real Magnitudes of the Planets. 
 
 HAVING found, by observation, the apparent diameters of the 
 planets, either at their greatest or least distance from the earth, and 
 knowing previously the distance of the earth from the sun, and also 
 the distance of the planets, their real magnitudes may be found by a 
 simple calculation. Since the apparent diameters of distant bodies 
 vary inversely as their distances, it is easy to ascertain what must be 
 the apparent diameter of each of the planets viewed from the sun ; 
 or, what is better, the apparent diameter of each of the planets, viewed 
 at a distance equal to that of the sun from the earth. 
 
 Example. Venus's mean distance from the sun is known to be 
 about 68,000,000 miles, and the earth 95,000,000 miles ; ergo, when 
 Venus is in her inferior conjunction, or nearest to the earth, she is 
 only 27,000,000 million miles from the earth (for 9568=27). We 
 know, from observation, Venus's apparent diameter in this position is 
 60"; ergo, 27 : 60" : : 95 : 17" nearly diameter of Venus, viewed 
 at as great a distance from the sun as the earth, and the apparent 
 diameter of the earth at the sun is known to be 17"'5 (double 8'"73 
 the parallax); ergo, as 17"'5 : 7912 m : : 17" : 7686 miles, the real dia- 
 meter of Venus. In like manner, Jupiter in opposition has an appa- 
 rent diameter of 48", his mean distance about 490,000,000 miles ; 
 ergo, at that time his distance from the earth is 395,000,000 miles ; 
 ergo, 395 m : 48" : : 95 m : 199", the apparent diameter of Jupiter at 
 the distance of the earth from the sun. 
 
 To find his real diameter, we have only to say, 17"-5 : 7912 111 : : 
 199" : 89160 m . 
 
 The apparent diameter of the sun, as seen from the earth, is about 
 32' or 1920'; ergo, 17"'5 : 791 2 m : : 1920" : 870,000 m nearly. The 
 real diameter of the moon and the other planets may be found in a 
 similar manner : and hence their bulks may be easily calculated as 
 follows : 
 
 * See Table, page 10. 
 
OF THE MATTER IN THE SUN AND PLANETS. 19 
 
 The sun at his mean distance from the earth, subtends an angle 
 of 32' 12" = 1932", and the earth at the sun 17|", therefore the sun's 
 diameter is to the earth's diameter as 1932" to 17", or as 11 1 to 1 ; 
 and as spheres are to each other as the cubes of their diameters, 
 the bulk of the sun will be to the bulk of the earth as the cube of 111 J 
 to the cube of 1, or as 1386166 to 1. The earth's diameter, as seen 
 from the moon, subtends an angle of double the moon's horizontal 
 parallax, which being taken at 57' 26", or 3446", the earth's must be 
 1 54' 52", or 6892"; when the moon's horizontal parallax is as here 
 stated, her diameter subtends an angle of 31' 2" = 1862" ; therefore 
 the earth's diameter is to that of the moon's as 3446" to 1862", or as 
 3*7 to 1 ; and her bulk will be to the moon's as 49-4 to 1. 
 
 In this manner may the bulk of any of the planets be found : by 
 first finding what angle the planet subtends from the earth, and then 
 comparing its diameter with the earth's diameter. 
 
 Note. As Venus is seen, sometimes, on the sun's disc, which is 
 at the time she is in her inferior conjunction, or nearest to the earth, 
 it affords an excellent opportunity of measuring her apparent diameter. 
 
 The elements of the planets are 1st. long, ascending node ; 2d. 
 eccentricity of orbit; 3d. mean longitude, 1st January; 4th. mean 
 longitude perihelion ; 5th. secular variation of perihelion ; 6th. incli- 
 nation of orbit; 7th. sidereal revolution ; 8th. mean distance. 
 
 Method of finding the Mass of Matter in the Sun and Planets. 
 LET F and f denote the forces by which two bodies revole in circles, 
 whose radii are D and d in the periodic times P and p ; then, by the 
 
 D d 
 theory of central forces (Dynamics) F : f :: 2 : j^S' 
 
 Now in the case of the sun and planets, the force F is the amount 
 of the deflections of the revolving body to all the particles in the 
 central body, which, putting M for the mass of matter in that body, 
 
 M 
 will be expressed by v^ and similarly putting m for the matter in 
 
 the central body towards which the other body gravitates at the 
 
 m M m D d 
 
 distance d, T* therefore, jp : r^ : : p 2 : ~ and consequently 
 
 D 3 d 3 
 
 M : m : : 2 : 2 . Hence it appears, that the mass of matter in 
 
 the bodies that compose the solar system are directly as the cubes 
 of the mean distances of any bodies which revolve about them, and 
 inversely as the squares of the, times in which the revolutions are 
 performed. 
 
 The application of the above theorem to determine the quantity of 
 matter in the sun, taking the quantity of matter in the earth as unity. 
 The sun's distance in miles . . 93726900 
 The moon's distance . ... 240144 
 
 Earth's revolution in sidereal days . 365*25 
 Moon's sidereal revolution . . 27'322 
 
80 OF DETERMINING THE LONGITUDE. 
 
 Then by the formula : 
 
 240144 3 93726900 s tl 
 
 :: m = 1:M = *" matter w the 
 
 sun. Therefore M = 9372690 f * 27 ' 322 * = 332669 
 365-25 2 x 240144 s 
 
 But this must be increased about ^th, because the moon is here- 
 supposed to revolve about the centre of the earth, whereas she really 
 moves about their common centre, and on this account the gravitation 
 of the earth is estimated greater than it ought to be. 
 
 Thus increased, the quantity of matter in the sun may be reckoned 
 at 337422 times that of the earth. 
 
 However this cannot be considered as very accurate, as the sun's 
 distance from the earth is uncertain, it being deduced from his hori- 
 zontal parallax, which is said to be only about 8"'7 or 8"*8, and an 
 error of one-tenth of a second in the parallax will produce an error of 
 -3*3- of the whole, for the error will vary in a triplicate proportion. 
 
 In the same manner may Jupiter be compared with the earth ; by 
 comparing the gravitation of his nearest satellite with that of the 
 moon. By a calculation similar to the above, it appears that Jupiter 
 contains 313 times more matter than the earth. From the periodic 
 times and distances of the satellites of Saturn and Uranus, may also 
 be estimated the forces by which they gravitate; and hence it is 
 found, by calculation, that the former planet contains 103 times more 
 matter than the earth, and the latter 17 times as much. 
 
 The quantity of nfatter in those planets that have no satellites can 
 only be guessed from the effect they produce in disturbing the motions 
 of the other planets. The quantity of matter in the moon, however, 
 may be determined with greater certainty, by comparing together the 
 influence of the sun and moon in producing the tides, and the precession 
 of the equinoxes. Hence it is found that the moon is about T J ff of the 
 earth. The quantity of matter in each of the planets has already been 
 stated at page 145 of this Work, to which the reader may refer for 
 more information on this subject. 
 
 To determine the Longitude of Places on the Earth. 
 
 THIS is a problem of such great difficulty in practice, that, although 
 the efforts of some of the greatest mathematicians in JEurope have 
 been directed towards the invention of easy, practicable methods, yet 
 none has been hitherto discovered that is not liable to errors ; these 
 errors, it must be remarked, are not to be ascribed entirely to the 
 theory, (which is, at least, with respect to several of the methods, 
 accurate,) but to the practice, particularly when the observations for 
 determining the longitude are taken at sea. Still, however, when a 
 comparison is formed between the modern methods of solving this 
 problem, and those which were practised two centuries ago, it will 
 appear that very considerable advances have been made towards a 
 perfect s htion ; and these are probably, in great measure, to be 
 attribute^ to *^ verv handsome rewards which have been offered by 
 
OF DETERMINING THE LONGITUDE. 81 
 
 commercial nations to those who should propose the most accurate 
 and practicable way of attaining so desirable an end. 
 
 It may seem a matter of astonishment, that this question, which is 
 probably the most interesting that ever engaged the human attention, 
 is little more than to be able to tell what o'clock it is elsewhere ; for 
 the longitude is found by the comparison of local or relative time ; 
 and as the hour is easily found at the place of observation by alti- 
 tudes, the only difficulty is, to find the time at the same instant at 
 some other place whose longitude is known. Now as the sun, in his 
 daily course, passes over 360 degrees of longitude in 24 hours, he 
 passes over 15 degrees in one hour, and over any other space in this 
 proportion ; and therefore if the difference in time between any two 
 places be known, the difference of longitude is thence determined. 
 
 Hence, if a perfect time-keeper could be constructed, it would 
 obviate all difficulty on this subject, and render the longitude as 
 simple a problem as the latitude ; for such an instrument being set to 
 the time of any place whose longitude is known (suppose to that of 
 Greenwich Observatory, from whence we reckon our longitude) it 
 would preserve this time in all other parts of the world ; and, by com- 
 paring this chronometer with a clock or watch properly regulated for 
 the place of observation, the difference would show the longitude. 
 
 Notwithstanding the great degree of perfection to which time- 
 keepers have been brought, they cannot be supposed such infallible 
 guides to the longitude as the heavenly bodies : the advantage the 
 former have is, that of being at all times most easily consulted ; but 
 the prudent mariner will not trust to chronometers abne, though he 
 must use them as auxiliaries to his astronomical calculations ; for 
 such delicate and complicated pieces of mechanism wil be ever more 
 or less liable to be affected by the violence of motion, or the vicissi- 
 tudes of season and climate, and, like all other productions of human 
 art, must be subject to accident, disorder, and decay : whereas the 
 heavenly bodies are unchangeable ; these only are the unerring time- 
 keepers which exibit a true species of perpetual motion. 
 
 There are various methods of finding the longitude by celestial 
 observations, but all proceed upon the same principle, or tend to the 
 same object, which is to tell the time at Greenwich Observatory, and 
 this compared with the time at the place of observation, shews the 
 distance east or west from Greenwich, and of course shews the lon- 
 gitude of that place. 
 
 First method : By the sun's declination. Find the ceclination of the 
 sun at noon, from observations made upon him either at the meridian, 
 or three or four hours from it : take the difference between this com- 
 puted declination, and that for the noon of the same day at Green- 
 wich, as shewn by the Ephemeris ; from which take likewise the 
 daily difference of declination at that time, then employ the following 
 analogy : As the daily difference of declination, is to the difference 
 above found, so are 360 to the difference of longitude. But here a 
 small error in the computed declination, will cause a very considerable 
 one in the difference of longitude ; and as such an error must inevita- 
 bly arise from considering the change of declination, during a day, 
 as regular, this method is not to be recommended in practice. 
 
82 OF DETERMINING THE LONGITUDE. 
 
 Second method: By the moon's culminating. Seek in the Ephemeris 
 for the time of the moon's coming to the meridian on the given day, 
 and on the day following, and take the difference ; take also the dif- 
 ference between their times of culminating on the same day, as found 
 in the Ephemeris, and as observed ; then say, as the daily difference 
 in the Ephemeris, is to the difference between the times of southing 
 found by the Ephemeris and by observation, so are 360 to the differ- 
 ence of longitude. Here the moon's motion is supposed to be 
 uniform, which is not the case; therefore, since a small error in this 
 respect, or in the time of the moon's culminating, may occasion a 
 great error in the longitude, this method is no more to be recom- 
 mended in practice than the former. 
 
 Third method: By the distance between the moon and a known fixed 
 star, when both are on the meridian. Let one observer take the alti- 
 tude of the moon's centre when on the meridian (which may be done 
 by taking the altitude of the upper or lower limb, and allowing for 
 the semidiameter), and another the altitude of any such star in the 
 zodiac as then happens to be on or very near the meridian. Now the 
 right ascension of the moon will be equal to the right ascension of the 
 star, if they were on the meridian exactly together : but if they are 
 not on the meridian together, if their difference of culminating do not 
 exceed eight or ten minutes, the right ascension of the moon may be 
 found by adding or subtracting this difference to or from the right 
 ascension of the star, according as the moon culminates after or be- 
 fore the star. Then, knowing the day of the month, with the moon's 
 right ascension^ examine the Nautical Almanac, and find, by propor- 
 tion, at what time at Greenwich the moon had that right ascension. 
 Take also the difference between the meridional altitudes of the moon 
 and the star which is then on the meridian ; this difference (when 
 properly corrected for dip, refraction, and parallax) will be the differ- 
 ence of the declinations of the moon and star, whence, the declination 
 of the star behg known, that of the moon becomes known also. Then 
 find, by means of the Nautical Almanac, at what time on the given 
 day, the mooi had this declination : if the time thus found agree 
 either exactly or very nearly with the time deduced from the right 
 ascension, take the difference between half the sum of them, and the 
 time of the observation (determined by some of the methods before 
 referred to), for the difference of longitude in time, whence the longi- 
 tude in degrees, &c. may be found : but if the times thus deduced do 
 not correspond tolerably accurately, recourse must be had to some of 
 the following methods. 
 
 Fourth method : By eclipses of the moon. These eclipses are seen 
 at the same instant of absolute time in all parts of the earth : there- 
 fore, if in two or more distant places where an eclipse of the moon is 
 visible, the times of the beginning or ending are carefully observed ; 
 as also the times when any number of digits were eclipsed ; or, which 
 is better, the times when the earth's shadow began to touch, or to 
 leave any remarkable spot on the moon's face ; then will the difference 
 of the times when the observations of like kind were made, give the 
 difference of longitude between the places of observation. Or, in- 
 stead of comparing the observations at two different meridians, the 
 
OF DETERMINING THE LONGITUDE. 83 
 
 times of the beginning and end of the eclipse, as observed at the 
 place the longitude of which is required, may be compared with the 
 times of beginning and end at Greenwich, as given in the Nautical 
 Almanac, and the longitude may be deduced from the difference of 
 times as before : but the longitude thus found will not be so accurate 
 as that determined by two observations, because of the inaccuracy of 
 the lunar tables, and of the great difficulty of telling exactly the time 
 of the first and last contact of the earth's shadow with the moon's 
 limb. 
 
 Fifth method: By the eclipses of Jupiter's satellites.. The eclipses 
 of Jupiter's satellites afford one of the readiest, and for general prac- 
 tice one of the best, methods of determining the longitudes of places 
 at land : and whenever Jupiter is to be seen,* they might be applied 
 at sea, oftener than they would be wanted, if they could be observed 
 with sufficient accuracy in a ship under. sail. In order to find the 
 longitude of a place at land by an eclipse of one of Jupiter's satellites, 
 the following directions must be observed : On the day preceding 
 the evening on which it is proposed to observe the eclipse, note the 
 time it will happen at Greenwich, as given in the Nautical Almanac. 
 Let the estimated longitude of the place of observation be converted 
 into time, and, if eastward of Greenwich, added to the time of the 
 beginning of the eclipse, as given in the Nautical Almanac ; but if 
 the place be westward, subtracted ; and it will give the time nearly 
 when the eclipse is to be expected at that place. Begin to observe 
 twenty or thirty minutes sooner than the time thus estimated, and let 
 the instant when the eclipse begins or ends be noted, as shewn by a 
 watch previously regulated to mean time at the place of observa- 
 tion : then the difference between this time and the Greenwich time, 
 converted into degrees, will shew the longitude from Greenwich. If 
 the time at Greenwich be less than the time observed, the longitude 
 is cast; otherwise it is west. The best eclipses for finding the 
 longitude are those of the first satellite, because its theory is most 
 accurately settled ; but it should be observed, that its emersions are 
 not visible from the time of Jupiter's conjunction with the sun to the 
 time of his opposition; and the immersions are not visible from his 
 opposition to his conjunction. 
 
 A sixth method, is by the difference between the observed times of 
 the moon and a fixed star passing the meridian of each place. But 
 this method is attended with very considerable trouble in the calcula- 
 tion, and is not more accurate than the methods already noticed. 
 
 The last method we shall notice is that of observing the distance 
 between the moon and the sun, or a fixed star. This is one of the 
 most accurate methods which can be employed, and is peculiarly 
 adapted for determining the longitude at sea. It is, therefore, the 
 only astronomical method to which seamen have recourse to for this 
 
 * An eclipse will be visible in any place, if Jupiter be 8 or more above the 
 horizon, and the sun as much below it : whether this will or will not be the case 
 at any place where the observation is intended to be made, may be readily found 
 with sufficient accuracy by a celestial globe. 
 
84 OF THE NAUTICAL ALMANACK. 
 
 important purpose ; but our limits will not permit us to enlarge far- 
 ther upon it. 
 
 Variation charts have also been recommended ; but they cannot be 
 depended upon for any length of time, as the needle is constantly 
 changing its direction, and the law of its variation is still a secret. 
 
 Explanation and Use of the Nautical Almanac or Ephemeris. 
 
 THIS National Almanac is chiefly intended for nautical purposes, 
 but it is of the greatest use in all astronomical calculations. It was 
 begun in 1767, under the direction of the Board of Longitude, on the 
 recommendation of Dr. Maskelyne, who had the immediate conduct- 
 ing of it for many years. 
 
 All the calculations of the Ephemeris, except those of the 
 eclipses of Jupiter's satellites, are made according; to the apparent 
 time by the meridian of the Royal Observatory at Greenwich : and 
 the sun's, planets', and moon's places, with the particulars depending 
 on them, are computed to the instant of apparent noon, or that of the 
 sun's centre passing the meridian of Greenwich. 
 
 The day is here supposed, according to the method of astronomers, 
 to begin at noon, or twelve hours later than the civil day of the same 
 denomination, and to be counted up to twenty-four hours, or the 
 succeeding noon, when the next day begins. Thus the day of the 
 month and the hour of the day are the same in this method as in the 
 civil account at noon, and from noon till midnight; but from midnight 
 till noon they differ. 
 
 There are twelve pages for every month. The first column of the 
 first page of each month contains the day of the week expressed con- 
 cisely by the initial letter or letters; the second the day of the month; 
 the third column exhibits the Sundays and Festivals of the Church of 
 England, and other remarkable days; the last column shows at top 
 the moon's phases, or the times of new and full moon, and of the first 
 and last quarter or two quadratures with the sun ; beneath are con- 
 tained miscellaneous phenomena ; namely, eclipses of the sun and 
 moon, and occultations of planets or fixed stars not less than the 
 " fourth" magnitude, by the moon, which can be occultations any 
 where on the globe, between the latitudes of 60" north and 40 south ; 
 the entrance of the sun into the several signs, and any other re- 
 markable phenomena. 
 
 The stars are expressed by Bayer's characters of reference. The 
 conjunction of the moon or a planet with a star is denoted by prefix- 
 ing the character of the moon or planet to that of the star, the time 
 of the conjunction being placed immediately before. The case is the 
 same with respect to the occultation of a star or planet by the moon, 
 only this is further distinguished by the addition of im. or immersion, 
 to signify the disappearance behind the moon : and em. or emersion, 
 to signify the re-appearance of the same. Thus 8 d 16 !l 22' D 3" yf > 
 signifies that the moon will be in conjunction with the star S ^f on 
 the eighth day at J6 h 22', exclusive of parallax; and I0 (l D h 14' im. 
 ff n ; 10 d 10 h 23' em. signifies that the moon will eclipse e n on 
 
OF THE NAUTICAL ALMANACK. 85 
 
 the 10th day, the immersion being at 9 h 14, and the emersion at 10 h 
 23' apparent time at Greenwich. 
 
 The occultations set down are only those visible at Greenwich ; 
 the circumstances of which will commonly not differ very widely in 
 most parts of the kingdom ; but in very distant places they will differ 
 very much, owing to the change of the moon's parallax, or it may 
 become no occultation at all. The same may be said of eclipses of 
 the sun. 
 
 The two first columns of the second page of the month contain the 
 day of the week and month, as before ; next follow the sun's longi- 
 tude, right ascension in time, declination, and the equation of time 
 with its difference from day to day. 
 
 To find the sun's longitude at any time different from noon, propor- 
 tion must be made according to its daily increase : saying, as 24 h is to 
 the hour from noon reckoned by the meridian of Greenwich, so is 
 the daily variation of the sun's longitude to a fourth number; which 
 added to the sun's longitude at the preceding noon, gives the true 
 longitude at the given time. 
 
 If the time given be that of a meridian different from Greenwich, 
 it must be first reduced thereto, by adding or subtracting the differ- 
 ence of longitude turned into time at the rate of one hour to 15. 
 
 The surf's longitude serves also to compute the aberration of the 
 fixed stars and planets. 
 
 The sun's right ascension in time is useful to the practical astrono- 
 mer in regular observatories, who adjusts his clocks by sidereal time. 
 It is also useful to him for converting apparent into sidereal time ; 
 as suppose that of an eclipse of Jupiter's satellites, in order to know 
 at what time it may be expected to happen by his clock. For this 
 purpose the sun's right ascension at the preceding noon, together with 
 the increase of right ascension from noon, must be added to the appa- 
 rent time of the phenomenon set down in the Ephemeris. 
 
 The sun's right ascension in time serves also to compute the appa- 
 rent time of a known star passing the meridian : thus, subtract the 
 sun's right ascension in time at noon from the star's right ascension in 
 time, the remainder is the apparent time of the star's passing the me- 
 ridian nearly ; from which the proportional part of the daily mcrease 
 of the sun's right ascension for this apparent time from noon being 
 subtracted, leaves the correct time of the star's passing the meridian. 
 
 The sun's declination is necessary to find the latitude, whether at 
 sea or land, from his meridian altitude observed. It is also necessary 
 to calculate the apparent time from an observed altitude of the sun at 
 a distance from the meridian, the latitude being given ; or to compute 
 the time of the sun's setting or rising ; which, though a less accurate 
 method than the former of obtaining the time, may yet be useful when 
 that cannot be had. For any of these purposes the sun's declination 
 must be found to the time given nearly, reduced to the meridian of 
 Greenwich, making proportion according to the daily increase or 
 decrease, in like manner as was shown with respect to the sun's 
 longitude. 
 
 The equation of time is a correction, which added to, or subtracted 
 from the apparent time (according to its title at the top of the column) 
 
86 OF THE NAUTICAL ALMANACK. 
 
 gives equated or mean time, or that which should be shown by a good 
 clock or watch. 
 
 The equation of time being set down in the Ephemeris for noon 
 at Greenwich, proportion must be made according to the daily differ- 
 ence, to find what it should be at any given time reduced to the same 
 meridian, as in the preceding articles. The last column of this page, 
 containing the daily differences of the equation, is designed for this 
 purpose. 
 
 But when time-keepers are used at sea, the apparent time deduced 
 from an altitude of the sun must be corrected by the equation of time, 
 and the mean time found compared with that shown by the watch ; the 
 difference will be the longitude in time from the meridian by which 
 the watch was set, as near as the going of the watch can be depended 
 upon. 
 
 The time of the sun's semidiameter passing the meridian, page 3d, 
 serves to reduce an observation of a transit of the preceding or subse- 
 quent limb over the meridian to that of the centre, when only one was 
 observed. It signifies a portion of apparent time, or even mean 
 time, the difference being absolutely insensible upon so small an 
 interval. 
 
 From the time of the sun's semidiameter passing the meridian may 
 also be found the time of its passing the horizontal or vertical wire of 
 a quadrant or sextant, which on some occasions may have its use. 
 
 The semidiameter of the sun is necessary to reduce the observed 
 altitude of his upper or lower limb to that of the centre ; also to 
 reduce the observed distance of the moon's nearest limb from the 
 sun's nearest limb to the distance of the centres. It is also useful to 
 astronomers to verify or ascertain the exactness of the scale of their 
 micrometers, by comparison with the measure of the sun's horizontal 
 diameter. 
 
 The hourly motion of the sun is useful in computing solar and lunar 
 eclipses. The logarithm of the sun's distance is useful in the calcu- 
 lation of the places of the planets and comets. The place of the 
 moon's node signifies its mean longitude, and is necessary for finding 
 the equation of the equinoctial points both in longitude and right 
 ascension, the equation of the obliquity of the ecliptic, and the devia- 
 tions of the fixed stars in right ascension and declination. 
 
 The eclipses of Jupiter's satellites are set down on the lower part 
 of page 3d, and to mean time. They are well known to afford the 
 readiest, and for general practice the best method of settling the 
 longitudes of places at land; and it is by their means principally that 
 geography has been so much reformed since the invention of teles- 
 copes, and the construction of tables for calculating the time of their 
 happening. 
 
 The eclipses of Jupiter's satellites are observed by astronomers at 
 land, as well in order to provide materials for improving the theories 
 and tables of their motions, as for the sake of comparison with the 
 corresponding observations which may be made by persons in dif- 
 ferent parts of the globe, whereby the longitude of such places will 
 be accurately ascertained. It is indeed to be lamented that persons, 
 who visit distant countries, are not more diligent to multiply observa- 
 
OP THE NAUTICAL ALMANACK. 87 
 
 tions of this kind ; for want of which, the observations made by 
 astronomers in established observatories lose half their use, and the 
 improvement of geography is retarded. 
 
 The eclipses, carefully calculated and set down in the Ephemeris, 
 will serve to advertise them and observers in general of the times when 
 they should attend to these observations. 
 
 The immersions signify the instant of the disappearance of the satel- 
 lite by entering into the shadow of Jupiter; and the emersions sig- 
 nify the first instant of its appearance at coming out of the same. 
 They generally happen when the satellite is at some distance from 
 the body of Jupiter, except near the opposition of Jupiter to the sun, 
 when the satellite approaches nearer to his body. Before the oppo- 
 sition of Jupiter to the sun, the immersions and emersions happen on 
 the west side of Jupiter, and after the opposition on the east side ; 
 but if an astronomical telescope be used, which reverses objects, the 
 appearance will be directly the contrary. Before the opposition, the 
 immersions only of the first satellite are visible ; and after the oppo- 
 sition, the emersions only. The same is generally the case with 
 jespect to the second satellite ; but both the phenomena of the same 
 eclipse are frequently observable in the two outer satellites. The 
 immersions and emersions, marked with an asterisk in the Ephemeris, 
 are those visible at Greenwich. 
 
 The immersion or emersion of any satellite being carefully ob- 
 served in any place according to mean time, the longitude from 
 Greenwich is found immediately, by taking the difference of the ob- 
 servation from the corresponding time shewn in the Ephemeris, which 
 must be turned into degrees, &c. and will be east or west of Green- 
 wich, as the time observed is more or less than that of the Ephemeris. 
 
 Example. Suppose an emersion of the first satellite should be 
 observed at the Cape of Good Hope, April 16, 1805, at 13 h 25' 35" 
 mean time ; the time by the Ephemeris being 12 h 12' 2', the differ- 
 ence is l h 13' 33", whence the longitude of the Cape should be 18 
 23' 15" east of Greenwich, because the time supposed to be observed 
 at the Cape is more than that of the Ephemeris. 
 
 The longitudes and latitudes of the planets, page 4th, serve to show 
 where to look for them in the heavens, to enable persons less skilled 
 to distinguish them from the fixed stars. They also show when they 
 are in the most important points of their orbits, where it is most ma- 
 terial to observe them. 
 
 The 5th, 6th, 7th, 8th, 9th, 10th, and 1 Ith pages of each month 
 contain the moon's place, and all the circumstances retating to her 
 motion and her distancen from the sun and proper stars, from which 
 her distances should be observed for finding the longitude at sea. 
 For the sake of greater precision, the moon's longitude, latitude, 
 right ascension, declination, semidiameter, horizontal parallax, with 
 its proportional logarithm, are computed twice a day to noon and 
 midnight, and may readily be inferred to any intermediate time with 
 "he greatest exactness. 
 
 T he moon's longitude and latitude are used in computing the dis- 
 
 s from the sun and stars contained in the four last pages of the 
 
 is well as the appulses to stars pointed out in page 1st, and, 
 
8& OP THE NAUTICAL ALMANACK. 
 
 jointly with her parallax and semidiameter, are necessary for com- 
 puting the eclipses of the sun and moon, and the occultations of fixed 
 stars and planets by the moon. They also facilitate the calculation 
 of the longitude of any place from an observed eclipse of the sun, or 
 occupation of a star or planet by the moon. Or, if the longitude be 
 well known, the parallax and semidiameter serve to deduce the 
 moon's true place in the heavens from the observation, which, com- 
 pared with that given by the Ephemeris, shows the error of the tables 
 at the time. The moon's semidiameter and parallax are applied in 
 correcting almost all observations of the moon. The proportional 
 logarithms of the moon's parallax serve further to facilitate the calcu- 
 lations of parallaxes. 
 
 The moon's right ascension and declination are useful to compute 
 her altitude at any time, particularly at the observation of her distance 
 from the sun or a star, supposing it was neglected to be or could not 
 be observed properly ; which latter case may sometimes happen in 
 the night. The moon's declination, with her semidiameter and paral- 
 lax, serve for rinding the latitude by the meridian altitude of her 
 upper and lower limb observed at sea. The moon's right ascension 
 and declination also serve to compute the time from her altitude ob- 
 served at the observation of her distance from a star ; whence the 
 longitude may be inferred, though no altitude of the sun or a star was 
 taken for regulating the time. 
 
 The distances of the moon from sun and fixed stars, contained in 
 the 8th, 9th, 10th, and llth pages of the month, are set down to 
 every three hours of apparent time by the meridian of Greenwich, and 
 are designed to prevent the necessity of a calculation by seamen and 
 others who wish to determine the longitude by lunar observations. 
 
 The configurations of Jupiter's satellites, page 12th and last, exhi- 
 bit the apparent positions of the satellites with respect to each other, 
 and to Jupiter, at such an hour of the evening or night as they are 
 most likely to be observed, and serve to distinguish the satellites from 
 one another. Jupiter is distinguished by the mark O , and the satel- 
 lites by points with figures annexed ; the figure 1 signifying the first 
 satellite, 2 the second satellite, &c. When the satellite is approach- 
 ing towards Jupiter, the figure is put between Jupiter and the point; 
 and when the satellite is receding from Jupiter, the figure is put on the 
 other side of the point. The satellites are in the superior parts of 
 their orbits, or farthest from the earth, when they are marked to the 
 right hand or west from Jupiter approaching him ; or to the left hand 
 or east of Jupiter receding from him ; but are in the inferior parts of 
 their orbits, or nearest to the earth, when they are marked to the 
 right hand or west of Jupiter receding from him, or to the left or east 
 of Jupiter approaching him. The cipher O , sometimes annexed to 
 the figure of the satellite towards the margin, signifies that it is invi- 
 sible on the face of Jupiter; and the black mark $ signifies that it is 
 invisible, being eclipsed in Jupiter's shadow, or behind Jupiter 
 eclipsed by his body. 
 
 THE END. 
 
 Printed by Hodgson and Co. 10, Newgate-street. 
 
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