If, then, there be no reason to doubt that Thales predicted the phenomenon in question, we can hardly fail to admit that his method was borrowed; and borrowed, in all probability, from Chaldea. For it is sufficiently clear that nothing but a very long series of observations, conducted with care and regularity, could enable any man to arrive at this knowledge; such observations, as we have no reason for supposing to have been made in Greece at these early times; while, on the other hand, we have seen that the Chaldeans were in possession of a period which enabled them to predict pretty accurately the recurrence of eclipses.

*

Again, if we admit that Thales explained the causes and predicted the occurrence of eclipses of the sun, we can hardly doubt that he was able to do the same with regard to those of the moon. Eudemus, indeed, according to Anatolius, attributes the discovery of the causes of the moon's light and her eclipses to Anaximenes, one of the successors of Thales. In general, we may remark, that it is very difficult to determine, amid conflicting testimony, to which of the philosophers of these times particular discoveries are to be referred, though there is a general agreement as to the doctrines taught in the Ionian and Pythagorean schools. Thus Pliny refers the discovery of the obliquity of the ecliptic to Anaximander,-Plutarch to Pythagoras, or Enopides of Chios, Eudemus to some author whom he does not name, but different from all of these, and who fixed it at 24°. But Thales, who is said to have written on the length of the tropical year, and on the position of the solstices and equinoxes §, could hardly have been ignorant of the fact of the obliquity, even if he were not, as seems likely, the author of this ancient valuation. Again, the invention of the gnomon is attributed by Diogenes Laertius || to Anaximander,—and by Pliny ¶ to Anaximenes,-while Herodotus, with much more probability, says it was borrowed from the Babylonians **.

It is

* See the passage quoted above, chap. lii. With regard to Thales, we may observe, that Themistius, in a passage quoted by Fabricius, Bibliothec. Græc. vol. i. p. 239, says, that Anaximander was the first person who published any of the doctrines of Thales, this latter having written nothing him. self. This would tend to confirm the view taken in the text, that the pretended discoveries of

truly unfortunate, that in attempting to investigate the doctrines of these ancient philosophers, we are compelled to have recourse to authors whose ignorance of astronomy too often makes their accounts unintelligible. Thus Diogenes tells us, that Thales found the magnitude of the moon to beth part of the sun; a statement clearly absurd, if meant to apply, as it evidently must, to their apparent diameters. But a passage of Apuleius* shows us the real meaning of the determination so grossly misunderstood by Diogenes. Thales, he tells us, determined the magnitude of the sun in parts of its own orbit: now,

th part of a great circle is 30': the real diameter of the sun may be taken at a mean not far from 32'; so that we see the measure of Thales was a good approximation for those early times.†

We have stated above, that the constellations of the zodiac do not seem to have been known in Greece before the time of Thales. In fact, Eudemus, whose early date and astronomical knowledge make his testimony of great weight, states that they were invented by Enopides of Chios, a Pythagorean philosopher, generally placed considerably after the time of Thales. However, that they were not of Greek origin, seems highly probable, let them have been introduced into that country when they may. To establish this, it is not necessary to insist upon the zodiacs discovered in Egypt, since their antiquity has been disputed; but from the testimony of ancient authors, it is clear that the zodiac of Chaldea and Egypt was identical with that of Greece; and no doubt can remain as to which was borrowed from the other. The Syntaxis of Ptolemy establishes this identity in the case of Chaldea and Greece. In the planetary observations of the Chaldeans, quoted in that work, the place of the planet in the Chaldean zodiac is first given, and then reduced to the Greek: though the respective constellations did not quite coincide in space, yet the names are always identical, except in one instance, where it appears that the Chaldeans gave the name of the Balance

Anaximander and Anaximenes consisted in the publication of what they had learnt from Thales. • Florid.

V. Montucla, vol. i. p. 106. Bailly, Astron. Anc. p.441.

Pliny refers the invention to Cleostratus of Tenedos, a philosopher rather posterior to Thales, but before the time to which Enopides is usually referred, V. Hist. Nat. ii. 8,

to the constellation called by the Greeks the claws of the Scorpion. From a fragment quoted by Delambre †, it seems that the Egyptians also named the claws of the Scorpion the Balance.

To this we may add the very curious circumstance, that the zodiac of India is nearly identical with that of Greece: and Humboldt has shown, in a very interesting memoir, that the twelve Indian signs are taken from among the twentyseven lunar mansions, or constellations of the lunar zodiac, mentioned in the first and second chapters of this Treatise §.

Nothing, perhaps, is more remarkable,-and, if we refuse to admit the oriental origin of Greek science, more inexplicable, than the circumstance of the true doctrine of the motion of the earth having been promulgated in the schools of Pythagoras || and Thales. That this was the case with regard to the former, is well known; and it is generally supposed that Philolaus, the successor of Pythagoras, was the first to teach it openly T. But there are some reasons for supposing that it had been among the doctrines professed at an earlier period by Anaximander. Eudemus, whom we have frequently had occasion to quote, affirms, in the most express terms, that this was the system of Anaximander**. If this be true, it is as probable that this philosopher merely published what he had heard from his master, as (in the case of Philolaus and Pythagoras ++. Cicero, on the authority of Theophrastus, attributes this system to Hicetas of Syracuse; and this is partly confirmed by Plutarch §§. It certainly was embraced by some very eminent men, such as

about 450 B.C.

Fabric. Bibliothec. Græc. 1. c. Delambre grossly mistranslates this passage. Astron. Anc., vol. i. p. 15. It is but fair to state, that Simplicius places Anaximander among those who conceived the earth to be in the centre of the universe. De Cœlo, lib. ii.

tt Plutarch de Placit. Phil. iii. 11, certainly informs us that Thales placed the earth in the centre of the universe; his testimony, however, cannot be conclusive, when unsupported by any other. :: Quæst. Academ, iv. 39.

§ De Placit. Phil, iji. 13,

it

Archytas of Tarentum, Timæus Locrus, and, in later times, Aristarchus of Samos*. Others, as Heraclides of Pontus, and Ecphantus, admitted, we are told, merely the earth's diurnal revolution on its axist. One cannot help feeling some surprise, that after the true system of the world had once been promulgated,-when it had been adopted by a numerous school, and some of the most distinguished astronomers, should have fallen subsequently into comparative oblivion. No doubt the ancients had not the same decisive proof of the motion of the earth that we have in the aberration of the fixed stars; and the infinite distance of these bodies, which is a necessary consequence, may have staggered many of them. But the fact in question is principally to be attributed to the widespreading influence of the Peripatetic school, whose founder, Aristotle, had strenuously combated the Pythagorean doctrines .

It is a circumstance by no means to be overlooked, that Pythagoras had travelled, according to the testimony of all his biographers, into Egypt and the East, and some say that he penetrated as far as India §. Some corroboration of this circumstance might be found in his metaphysical doctrines, evidently borrowed either from India or Egypt; but to confine ourselves merely to astronomy, we may notice opinions analogous to those known to have existed in the countries we have mentioned. We have seen the belief of the Chaldeans about comets, according to the account of Apollonius Myndius: the Pythagorean doctrine on this subject bears the greatest analogy to it. These philosophers supposed comets to be bodies as ancient as the universe, revolving round the sun, and visible only in a certain part of their orbit. Yet this sublime conception shared the fate of the system of the earth's motion. The Peripatetics were reason; and for eighteen centuries, it once more triumphant over truth and was almost universally admitted that these bodies were simply meteors engendered in the terrestrial atmosphere.

The philosophical ideas of the Pytha

goreans about the nature of comets and the system of the world, render us not averse to admit that they taught, as is affirmed by some authors, the plurality of worlds; that they believed the fixed stars to be so many suns, each the centre of a system similar to our own. If, on the one hand, this idea is found to be ascribed to them only by some very ignorant authors, on the other, it may be observed, that the notion itself is much too sublime to have emanated from such unphilosophical sources. What is to be deeply regretted is, that to these just and beautiful theories the Pythagoreans should have added fanciful and extravagant speculations upon numbers, harmony, and the dimensions of the celestial orbits. One of these fanciful ideas has given rise to the celebrated notion of the music of the spheres; it would seem that Pythagoras fancied he perceived an analogy between the distances of the planets and the divisions of the octave in music. But the passage in which this doctrine is explained by Pliny + appears to contain some mistake, for as he has stated it, it is incompatible with the Pythagorean system of the motion of the earth; and even putting this out of the question, with another opinion attributed to Pythagoras by Pliny himself; namely, that the morning and evening stars are the same. From the way in which Pliny expresses himself on this last point, one would be led to believe that Pythagoras was aware that Venus and Mercury revolved round the sun. This doctrine we have before seen had its origin in Egypt; but on that account is, perhaps, the more likely to have formed one of the alleged discoveries of the Samian philosophers.

The arrangement of their calendar

• Plutarch de Plac. Phil. ii. 15. Achilles Tatius Isagoge.

Hist. Nat. ii. 22. Cf. Censorinum de die Natalio.

ii. 8. Cf. Diog. Laert. in Pythagorâ. We have studiously omitted any mention of various absurd opinions attributed to the philosophers of the Ionian and Pythagorean schools by some of the later writers of antiquity. These stories are always either at variance with what we know from more ancient and authentic sources, or they arise from some palpable misunderstanding of the narrator. It would be a waste of time to discuss all the absurdities of this nature to be found in Plutarch,—an author whose inaccuracy, careless ness, and inconsistency are not yet properly appreciated. A recent historian of astronomy has drawn largely, and almost exclusively, from him in his sketch of the notions of Thales, Pythagoras, and their successors, V. Delamb., op. cit. Notions Générales.

unintelligible and absurd in themselves; or lastly,

was a subject with which the astronomers of Greece were occupied, with various success, during several centuries. The difficulties arose from the perseverance with which they attempted to conciliate the motions of the sun and moon. The month being determined by a lunar, and the year by a solar, revolution, they must soon have perceived that the former was not contained any integral number of times in the latter. Their object, then, was to find a number of years, or period, at the end of which a restitution would be effected, and the beginning of the month and the year again correspond. This problem was more difficult than they seem to have imagined; for, in the first place, the two revolutions are, strictly speaking, incommensurable; and secondly, the moon's mean motion is subject to a secular acceleration, which even if, an accurate period could be found, would, in the course of time, render it inexact. However it was not impossible to find some practical solution which would be tolerably accurate for a time of no very great length, and to this object their attention was directed.

The first period of the kind alluded to was one of eight years, proposed by Cleostratus of Tenedos*. To understand its advantages and defects, it is necessary to observe that the Greek lunar year was composed of 354 days, divided into twelve months, alternately of 29 and 30 days. Cleostratus proposed, in the course of the eight years, to insert three intercalary months, of 30 days each, at the end of the third, fifth, and eighth years respectively. He thus got a period of 2922 days, comprising 99 lunar revolutions. But, in reality, 99 lunar revolutions are performed in somewhat more than 2923 days, 12 hours; so that at the end of the period there was an error of 36 hours on the place of the moon.

Various methods were proposed to rectify this defect, but none with much success till we come to the time of Meton. This astronomer immortalized himself by the invention of a new cycle, which, taking into account the accuracy compared with the number of years contained in the period, may be considered as the most perfect ever proposed. For it is clear that it is one of the great merits of a cycle of this kind, intended

Censorinus, c. 18.

† V. Gemin, Isagog.c.6.

for the purposes of civil life, to comprise as small a number of years as possible. The cycle of Meton was composed of 19 lunar years, in which seven months of 30 days were intercalated; namely, in the 3d, 6th, 8th, 11th, 14th, 17th, and 19th years. Besides this, some alteration was made in the distribution of the ordinary months: instead of having them alternately of 29 and 30 days, there were 110 only of the former, and 125 of the latter, in the period. To judge of the accuracy of the Metonian cycle, we must consider that 19 solar years comprise very nearly 6939 days, 14 hours 25 minutes; and 235 lunar revolutions comprise 6939 days, 16 hours nearly; so that at the end of this time the moon was only about two hours behind the sun. The cycle of Meton comprising 6940 days, after one period the sun had already commenced his revolution nine hours and a half, the moon seven hours and a half*. The great accuracy and convenience of this invention procured it universal approbation; it was adopted throughout Greece, and obtained the name which it still bears of the golden number. The first cycle began in the year 432 B.C.

Callippust about a century later proposed to remedy the slight defect of the cycle of Meton, by subtracting one day every 76 years. This was done by changing, after four periods of 19 years, one of the months of 30 days into one of 29. Callippus thus got a period of 76 years, comprising 27759 days. Now we may estimate that 940 revolutions of the moon make 27758d, 18h, 6, 76 revolutions of the sun 277584, 9h, 42m. The error on the place of the moon then was 5b, 54; on the sun 14h, 18m. It was the accumulation of this error that entailed the necessity of the Gregorian reform to be explained in a subsequent part of this treatise. The first Callippic period began in the year 330 B.C.

The above-mentioned are the only periods that have been in civil usage; but Hipparchus appears to have composed one of four Callippic periods or 304 years, at the end of which he subtracted a day. By reference to what has been said, it will be seen that this will almost destroy

any error on the moon's place, though it will leave one of more than a day on that of the sun. However this period never seems to have been much used even among astronomers; Ptolemy though a follower and admirer of Hipparchus, employs in preference that of Callippus.

The celebrity of Eudoxus of Cnidus, rather than his real merits, induce us to say a few words of him in this place. It is difficult to say upon what the astronomical reputation of this philosopher is founded. He was the friend and contemporary of Plato, and a distinguished geometer, but his merits, whether as an observer or a theorist in astronomy, appear to be very equivocal. He composed a description of the sphere which enjoyed great celebrity among the ancients, but it would seem from the poem of Aratus which was founded upon it, and from the commentary of Hipparchus, to have been but a rough and inaccurate production. It has been supposed by Newton and others, that Eudoxus merely copied the description of a sphere long anterior to his own time; but we rather lean to the opinion of Delambre, who seems to have shown pretty clearly that the positions on the sphere of Eudoxus are essentially inaccurate, and cannot be made consistent by a reference to any other time whatever.

Eudoxus is said to have studied thirteen years in Egypt*. Seneca informs us that he brought from that country into Greece, the theory of the five planets+; this, if true, can only allude to some very rough approximation to their motions, as we know that Hipparchus was obliged to abandon the consideration of this subject from the want of sufficient observations. We owe few thanks to Eudoxus for a physico-mathematical hypothesis, which, having been adopted by the Peripatetics, spread through their influence, and became the received doctrine on these points, till the final overthrow of the school of Aristotle in the sixteenth century. He conceived that each planet had a sort of firmament composed of several concentric solid spheres, whose different motions modified each other, so as to represent the motion of the planet. Thus, in the case of the sun,

Strabo, lib. xvii. 29. † Quæst. Nat. vii. 3. Aristot. Metaph. xi. 8. Cf. Simplicium de Cœlo, lib. ii.