90 PTOLEMY
which is of universal application, may, we think -- regard being paid to its place in the _Almagest_ -- be justly attributed to Hipparchus. It is the first law of the "philosophia prima" of Comte.n1 We find in the same page another principle, or rather practical injunction, that in investigations founded on observations where great delicacy is required we should select those made at considerable intervals of time in order that the errors arising from the imperfection which is inherent in all observations, even in those made with the greatest care, may be lessened by being distributed over a large number of years. In the same chapter we find also the principle laid down that the object of mathematicians ought to be to represent all the celestial phenomena by uniform and circular motions. This principle is stated by Ptolemy in the manner which is unfortunately too common with him, that is to say, he does not give the least indication whence he derived it. We know, however, from Simplicius, on the authority of Sosigenes,n2 that Plato is said to have proposed the following problem to astronomers: "What regular and determined motions being assumed would fully account for the phenomena of the motions of the planetary bodies?" We know, too, from the same source that Eudemus says in the second book of his History of Astronomy that "Eudoxus of Cnidus was the first of the Greeks to take in hand hypotheses of this kind,"n3 that he was in fact the first Greek astronomer who proposed a geometrical hypothesis for explaining the periodic motions of the planets -- the famous system of concentric spheres. It thus appears that the principle laid down here by Ptolemy can be traced to Eudoxus and Plato; and it is probable that they derived it from the same source, namely, Archytas and the Pythagoreans. We have indeed the direct testimony of Geminus of Rhodes that the Pythagoreans endeavoured to explain the phenomena of the heavens by uniform and circular motions.n4
Books iv., v. are devoted to the motions of the moon, which are very complicated; the moon in fact, though the nearest to us of all the heavenly bodies, has always been the one which has given the greatest trouble to astronomers.n5 Book iv., in which Ptolemy follows Hipparchus, treats of the first and principal inequality of the moon, which quite corresponds to the inequality of the sun treated of in the third book. As to the observations which should be employed for the investigation of the motion of the moon, Ptolemy tells us that lunar eclipses should be preferred, inasmuch as they give the moon's place without any error on the score of parallax. The first thing to be determined is the time of the moon's revolution; Hipparchus, by comparing the observations of the Chaldaeans with his own, discovered that the shortest period in which the lunar eclipses return in the same order was 126,007 days and 1 hour. In this period he finds 4267 lunations, 4573 restitutions of anomaly, and 4612 tropical revolutions of the moon less 7½° q.p.; this quantity (7½°) is also wanting to complete the 345 revolutions which the sun makes in the same time with respect to the fixed stars. He concluded from this that the lunar month contains 29 days and 31' 50" 8'" 20"" of a day, very nearly, or 29 days 12 hours 44' 3" 20'". These results are of the highest importance. (See ASTRONOMY.) In order to explain this inequality, or the equation of the centre, Ptolemy makes use of the hypothesis of an epicycle, which he prefers to that of the eccentric. The fifth book commences with the description of the astrolabe of Hipparchus, which Ptolemy made use of in following up the observations of that astronomer, and by means of which he made his most important discovery, that of the second inequality in the moon's motion, now known by the name of the "evection." In order to explain this inequality he supposed the moon to move on an epicycle, which was carried by an eccentric whose centre turned about the earth in a direction contrary to that of the motion of the epicycle. This is the first instance in which we find the two hypotheses of eccentric and epicycle combined. The fifth book treats also of the parallaxes of the sun and moon, and gives a description of an instrument called later by Theon the "parallactic rods" devised by Ptolemy for observing meridian altitudes with greater accuracy.
The subject of parallaxes is continued in the sixth book of the Almagest, and the method of calculating eclipses is there given. The author says nothing in it which was not known before his time.
Books vii. , viii. treat of the fixed stars. Ptolemy verified the fixity of their relative positions and confirmed the observations of Hipparchus with regard to their motion in longitude, or the precession of the equinoxes. (See ASTRONOMY.) The seventh book concludes with the catalogue of the stars of the northern hemisphere, in which are entered their longitudes, latitudes, and magnitudes, arranged according to their constellations ; and the eighth book commences with a similar catalogue of the stars in the constellations of the southern hemisphere. This catalogue has been the subject of keen controversy amongst modern astronomers. Some, as Flamsteed and Lalande, maintain that it was the same catalogue which Hipparchus had drawn up 265 years before Ptolemy, whereas others, of whom Laplace is one, think that it is the work of Ptolemy himself. The probability is that in the main the catalogue is really that of Hipparchus altered to suit Ptolemy's own time, but that in making the changes which were necessary a wrong precession was assumed. This is Delambre's opinion; he says, "Whoever may have been the true author, the catalogue is unique, and does not suit the age when Ptolemy lived; by subtracting 2°40' from all the longitudes it would suit the age of Hipparchus; this is all that is certain."n6 It has been remarked that Ptolemy, living at Alexandria, at which city the altitude of the pole is 5° less than at Rhodes, where Hipparchus observed, could have seen stars which are not visible at Rhodes; none of these stars, however, are in Ptolemy's catalogue. The eighth book contains, moreover, a description of the milky way and the manner of constructing a celestial globe; it also treats of the configuration of the stars, first with regard to the sun, moon, and planets, and then with regard to the horizon, and likewise of the different aspects of the stars and of their rising, culmination, and setting simultaneously with the sun.
The remainder of the work is devoted to the planets. The ninth book commences with what concerns them all in general. The planets are much nearer to the earth than the fixed stars and more distant than the moon. Saturn is the most distant of all, then Jupiter and then Mars. These three planets are at a greater distance from the earth than the sun.n7 So far all astronomers are agreed. This is not the case, he says, with respect to the two remaining planets, Mercury and Venus, which the old astronomers placed between the sun and earth, whereas more recent writers n8 have placed them beyond the sun, because they were never seen on the sun.n9 He shows that this reasoning is not sound, for they might be nearer to us than the sun and not in the same plane, and consequently never seen on the sun. He decides in favour of the former opinion, which was indeed that of most mathematicians. The ground of the arrangement of the planets in order of distance was the relative length of their periodic times; the greater the circle, the greater, it was thought, would be the time required for its description. Hence we see the origin of the difficulty and the difference of opinion as to the arrangement of the sun, Mercury, and Venus, since the times in which, as seen from the earth, they appear to complete the circuit of the zodiac are nearly the same -- a year.n10 Delambre thinks it strange that Ptolemy did not see that these contrary opinions could be reconciled by supposing that the two planets moved in epicycles about the sun; this would be stranger still, he adds, if it is true that this idea, which is older than Ptolemy, since it is referred to by Cicero,n11 had been that of the Egyptians.n12 It may be added, as strangest of all, that this doctrine was held by Theon of Smyrna,n13 who was a contemporary of Ptolemy or somewhat senior to him. From this system to that of Tycho Brahe there is, as Delambre observes, only a single step.
We have seen that the problem which presented itself to the astronomers of the Alexandrian epoch was the following: it was required to find such a system of equable circular motions as would represent the inequalities in the apparent motions of the sun, the moon, and the planets. Ptolemy now takes up this question for the planets; he says that "this perfection is of the essence of celestial things, which admit of neither disorder nor inequality," that this planetary theory is one of extreme difficulty, and that no one had yet completely succeeded in it. He adds that it was owing to these difficulties that Hipparchus who loved truth above all things, and who, moreover, had not received from his predecessors observations either so numerous or so precise as those that he has left had succeeded, as far as possible, in representing the motions of the sun and moon by circles, but had not even commenced the theory of the five planets. He was content, Ptolemy
n1 Système de Politique Positive, iv. 173.
n2 This Sosigenes, as Th. H. Martin has shown, was not the astronomer of that name who was a contemporary of Julius Caesar, but a Peripatetic philosopher who lived at the end of the 2d century A.D.
n3 Brandis, _Schol. in Aristot. edidit Acad. Reg. Borussica (Berlin, 1836), p. 498.
n4 [Eisagoge eis ta phainomena], c.i. in Halma's edition of the works of Ptolemy, vol. iii. ("Introduction aux Phénomènes Célestes, traduite du Grec de Geminus," p. 9), Paris, 1819.
n5 This has been noticed by Pliny, who says, "Multiformi haec (luna) ambage torsit ingenia contemplantium, et proximum ignorari maxime sidus indignantium" (N.H., ii. 9).
n6 Delambre, Histoire de l'Astronomie Ancienne, ii. 264.
n7 This is true of their mean distances; but we know that Mars at opposition is nearer to us than the sun.
n8 Eratosthenes, for example, as we learn from Theon of Smyrna.
n9 Transits of Mercury and Veuus over the sun's disk, therefore, had not been observed.
n10 This was known to Eudoxus. Sir George Cornewall Lewis (_An Historical Survey of the Astronomy of the Ancients_, p.155), confusing the _geocentric_ revolutions assigned by Eudoxus to these two planets with the _heliocentric_ revolutions in the Copernican system, which are of course quite different, says that "the error with respect to Mercury and Venus is considerable"; this, however, is an error not of Eudoxus but of Cornewall Lewis, as Schiaparelli has remarked.
n11 "Hunc [solem] ut comites consequuntur Veneris alter, alter Mercurii cursus" (_Somnium Scipionis, De Rep._, vi. 17). This hypothesis is alluded to by Pliny, N. H., ii. 17, and is more explicitly stated by Vitruvius, _Arch._, ix. 4.
n12 Macrobius, _Commentarius ex Cicerone in Somnium Scipionis_, i. 19.
n13 Theon (Smyrnaeus Platonicus), _Liber de Astronomia_, ed. Th. H. Martin (Paris, 1849), pp. 174, 294, 296. Martin thinks that Theon, the mathematician, four of whose observations are used by Ptolemy (_Alm._, ii. 176, 193, 194, 195, 196, ed. Halma), is not the same as Theon of Smyrna, on the ground chiefly that the latter was not an observer.
