"The astionomci discoveis that gcometiy, a pme abstraction of the human mind, is the measure of planetaiy motion "
19 In the earlier penod of Greek history one of the chief functions expected of astionomers was the pioper regulation of the calendar The Greeks, like earlier nations, began with a calendar based on the moon. In the time of Hesiod a year consisting of 12 months of 30 days was m common use, at a later date a year made up of 6 Ml months of 30 days and 6 empty months of 29 days was mtioduced To Solon is attributed the merit of having introduced at Athens, about 594 bc, the piactice of adding to every alternate year a "full55 month Thus a penod of two yeais would contain 13 months of 30 days and 12 of 29 days, 01 738 days in all, distributed among 2 5 months, giving, for the average length of the year and month, 369 days and about 29] days respectively. This airangement was furthei impioved by the introduction, probably during the 5th century b c, of the octaeteris, or eight-year cycle, m three of the years of which an additional "full" month was introduced, while the remaining years consisted as before of 6 " full55 and 6 " empty" months By this arrangement the average length of the year was leduced to 365] days, that of the month remaining neaily unchanged As, however, the Greeks laid some stress on beginning the month when the new moon was first visible, it was necessary to make from time to time arbitiaiy alterations in the calendar, and considerable confusion i2X
resulted, of which Aristophanes makes the Moon complain m his play The Clouds, acted m 423 b c.
u Yet you will not maik youi days As she bids you, but confuse them, jumbling them all sorts of ways And, she says, the Gods m chorus shower reproaches on her head, When, in bitter disappointment, they go supperless to bed, Not obtaining festal banquets, duly on the festal day "
20 A little later, the astronomer Meton (born about 460 bc) made the discovery that the length of 19 yeais is very neaily equal to that of 235 lunar months (the difference being m fact less than a day), and he devised accordingly an arrangement of 12 years of 12 months and 7 of 13 months, 125 of the months m the whole cycle being "full" and the others "empty" Nearly a centuiy later Ccilhppits made a slight improvement, by substituting m every fourth period of 19 years a "full" month foi one of the " empty " ones. Whether Meton's cycle, as it is called, was introduced for the civil calendar or not is unceitam, but if not it was used as a standard by reference to which the actual calendai was from time to time adjusted The use of this cycle seems to have soon spread to other paits of Greece, and it is the basis of the present ecclesiastical rule for fixing Easter The difficulty of ensuring satisfactory correspondence between the civil calendar and the actual motions of the sun and moon led to the practice of publishing from time to time tables (napawrjyfj.aTa) «-not unlike our modern almanacks, giving for a series of years the dates of the phases of the moon, and the rising and setting of some of the fixed stars, together with predictions of the weather Owing to the same cause the early wnteis on agriculture (eg Hesiod) fixed the dates for agricultural opeiations, not by the calendar, but by the times of the rising and setting of constellations, % e the times when they first became visible before sunrise or were last visible immediately after sunset—a practice which was continued long after the establishment of a fairly satisfactory calendar, and was appai ently by no means extinct in the time of Galen (2nd century a d.)
21 The Roman calendar was m early times even more confused than the Greek There appeals to have been
Giegory XIII introduced therefore, in i582, a slight change; ten days were omitted from that year, and it was arranged to omit for the future three leap-years m four centuues (viz in 1700, 1800, 1900, 2100, etc, the yeais 1600, 2000, 2400, etc , remaining leap-years) The Gregorian Calendar, 01 liew Style, as it was commonly called, was not adopted in England till 1752, when 11 days had to be omitted, and has not yet been adopted m Russia and Gieece, the dates there being now 12 days behind those of Western Europe
23. While their oriental predecessors had confined themselves chiefly to astronomical observations, the eailiei Greek philosophers appear to have made next to no observations of importance, and to have been far moie interested m inquiring into causes of phenomena Thales, the founder of the Ionian school, was credited by latei writers with the introduction of Egyptian astronomy into Greece, at about the end of the 7th century bc , but both Thales and the majority of his immediate successors appear to have added little or nothing to astronomy, except some rather vague speculations as to the foim of the earth and its relation to the rest of the world On the other hand, some real progress seems to have been made by Pythagoras * and his followers Pythagoras taught that the earth, m common with the heavenly bodies, is a sphere, and that it rests without requnmg support m the middle of the universe Whether he had any real evidence in support of these views is doubtful, but it is at any late a reasonable conjecture that he knew the moon to be bright because the sun shines on it, and the phases to be caused by the greater or less amount of the illuminated half turned towards us, and the curved form of the boundary between the bright and dark portions of the moon was correctly interpreted by him as evidence that the moon was spherical, and not a flat disc, as it appears at first sight Analogy would then piobably suggest that the earth also was spherical However this may be, the belief in the spherical form of the earth never disappeared from
* We have little definite knowledge of his life. He was bom m the earlier part of the 6th century bc, and died at the end of the same century or beginning of the next,
Greek thought, and was m later times an established part of Greek systems, whence it has been handed down, almost unchanged, to modern times This belief is thus 2,000 years oldei than the belief 111 the lotation of the earth and its 1 evolution louncl the sun (chapter iv ), doctrines which we are sometimes inclined to couple with it as the foundations of modern astionomy.
In Pythagoras occuis also, peihaps foi the first time, an idea which had an extremely important influence on ancient and mediaeval astionomy Not only weie the stars supposed to be attached to a crystal spheie, which revolved daily on an axis thiough the earth, but each of the seven planets (the sun and moon being included) moved on a spheie of its own The distances of these spheres from the earth were fixed in accoidance with certain speculative notions of Pythagoras as to numbers and music, hence the spheres as they revolved produced harmonious sounds which specially gifted persons might at times heai this is the origin of the idea of the music of the spheres which recurs continually in mediaeval speculation and is found occasionally in modern literature At a latei stage these spheies of Pythagoras weie developed into a scientific repiesentation of the motions of the celestial bodies, which remained the basis of astronomy till the time of Kepler (chaptei vn)
24 The Pythagorean JPhtlolaus, who lived about a century later than his master, introduced for the fhst time the idea of the motion of the eaith he appears to have legarded the earth, as well as the sun, moon, and five planets, as 1 evolving round some central fire, the earth lotating on its own axis as it 1 evolved, appai ently 111 oider to ensuie that the central fiie should always remain invisible to the inhabitants of the known parts of the earth That the scheme was a purely fanciful one, and entirely diffeient from the modern doctnne of the motion of the earth, with which later writers confused it, is sufficiently shewn by the invention as pait of the scheme of a purely imaginary body, the counter-earth (amx^V), which brought the numbei of moving bodies up to ten, a sacred Pythagorean number The suggestion of such an important idea as that of the motion of the eaith? an idea so repugnant to umnstructed common sense, although piesented m such a crude form, without any of the evidence required to wm general assent, was, however, undoubtedly a valuable contribution to astronomical thought It is wTell worth notice that Coppemicus m the great book which is the foundation of modern astionomy (chapter iv, § 75) especially quotes Philolaus and othei Pythagoreans as authorities for his doctrine of the motion of the earth
Three other Pythagoreans, belonging to the end of the 6th century and to the 5th century b c , Hicetas of Syracuse, Hercichtus, and Ecphantus, are explicitly mentioned by later writers as having believed in the rotation of the earth.
An obscure passage m one of Plato's dialogues (the Timaeus) has been mteipreted by many ancient and modern commentators as implying a belief m the lotation of the eaith, and Plutaich also tells us, paitly on the authority of Theophrastus, that Plato in old age adopted the belief that the centre of the universe was not occupied by the earth but by some better body *
Almost the only scientific Greek astronomer who believed m the motion of the earth was Aristarchus of Samos, who lived in the fust half of the 3rd century b c , and is best known by his measuiements of the distances of the sun and moon (§ 32) He held that the sun and fixed stars were motionless, the sun being m the centre of the sphere on which the latter lay, and that the earth not only rotated on its axis, but also described an orbit lound the sun Sekucns of Seleucia, who belonged to the middle of the 2nd century bc, also held a similar opinion Unfor tunately we know nothing of the giounds of this belief m either case, and their views appear to have found little favour among their contemporaues or successors.
It may also be mentioned m this connection that Aristotle (§ 27) clearly realised that the apparent daily motion of the stars could be explained by a motion either of the stars or of the earth, but that he rejected the latter explanation
25 Plato (about 428-347 bc) devoted no dialogue especially to astronomy, but made a good many references
" Theophrastus was born about half a eentuiy, Plutarch neaily five centuries, later than Plato, to the subject 111 various places He condemned any careful study of the actual celestial motions as degrading rather than elevating, and apparently regaided the subject as worthy of attention chiefly on account of its connection with geometiy, and because the actual celestial motions suggested ideal motions of gieater beauty and interest This view of astronomy he contrasts with the popular conception, according to which the subject was useful chiefly foi giving to the agriculturist, the navigator, and otheis a knowledge of times and seasons ! At the end of the same dialogue he gives a shoit account of the celestial bodies, according to which the sun, moon, planets, and fixed stais revolve on eight concentric and closely fitting wheels or circles lound an axis passing thiough the earth Beginning with the body neaiest to the eaith, the order is Moon, Sun, Mercury, Venus, Mars, Jupitei, Saturn, stars The Sun, Mercury, and Venus are said to peiform then revolutions m the same time, while the other planets move more slowly, statements which shew that Plato was at any rate aware that the motions of Venus and Mercury are diffcient from those of the other planets. He also states that the moon shmes by reflected light received from the sun
Plato is said to have suggested to his pupils as a worthy pioblem the explanation of the celestial motions by means of a combination of uniform cnculai or spherical motions Anything like an accurate theory of the celestial motions, agieeing with actual obseivation, such as Hipparchus and Ptolemy afteiwaids constructed with fair success, would hardly seem to be in accordance with Plato s ideas of the true astronomy, but he may well have wished to see established some simple and haimomous geometrical scheme which would not be altogether at variance with known facts
26 Acting to some extent on this idea of Plato's, Eudoxm of Cniclus (about 409-356 bc) attempted to explain the most obvious peculiarities of the celestial motions by means of a combination of uniform circular motions He may be regarded as repi csentative of the tiansition from speculative
* Rrpitbhc, VIL 529, 530, to scientific Greek astronomy As m the schemes of several of his predecessors, the fixed stais lie on a sphere which revolves daily about an axis through the earth, the motion of each of the othei bodies is produced by a combination of other spheies, the centre of each sphere lying on the surface of the preceding one Foi the sun and moon three spheres were m each case necessary one to produce the daily motion, shared by all the celestial bodies, one to pioduce the annual or monthly motion in the opposite direction along the ecliptic, and a third, with its axis inclined to the axis of the preceding, to produce the smaller motion to and from the ecliptic Eudoxus evidently was well aware that the moon's path is not coincident with the ecliptic, and even that its path is not always the same, but changes continuously, so that the third spheie was m this case necessary 3 on the other hand, he could not possibly have been acquainted with the minute deviations of the sun from the ecliptic with which modern astronomy deals Either therefore he used enoneous observations, 01, as is more probable, the sun's third sphere was introduced to explain a purely imaginary motion conjectured to exist by " analogy " with the known motion of the moon For each of the five planets four spheres were necessary, the additional one serving to produce the variations m the speed of the motion and the reversal of the direction of motion along the ecliptic (chapter i, § 14, and below, § 51) Thus the celestial motions were to some extent explained by means of a system of 27 spheres, 1 for the stars, 6 foi the sun and moon, 20 foi the planets There is no clcai evidence that Eudoxus made any serious attempt to arrange either the size or the time of revolution of the spheres so as to produce any precise agreement with the observed motions of the celestial bodies, though he knew with considerable accuracy the time required by each planet to return to the same position with respect to the sun, m othei words, his scheme represented the celestial motions qualitatively but not quantitatively On the other hand, there is no reason to suppose that Eudoxus regarded his spheres (with the possible exception of the sphere of the fixed stars) as material, his known devotion to mathematics rendeis it probable that m his eyes (as m those of most of the scientific Gieek astronomers who succeeded him) the spheres were mere geometrical figures, useful as a means of resolving highly complicated motions into simpler elements Eudoxus was also the first Greek recorded to have had an observatory, which was at Cmdus, but we have few details as to the instruments used or as to the observations made. We owe, however, to him the first systematic description of the constellations (see below, §42), though it was probably based, to a large extent, on rough observations borrowed from his Gieek predecessors or from the Egyptians He was also an accomplished mathematician, and skilled in various other blanches of learning.
Shortly afteiwards Calhppus (§ 20) further developed Eudoxus's scheme of revolving spheres by adding, for leasons not known to us, two spheres each for the sun and moon and one each foi Venus, Mercury, and Mars, thus bringing the total number up to 34.
27 We have a tolerably full account of the astronomical views of Aristotle (384-322 b c), both by means of incidental references, and by two treatises—the Meteorolo^ica and the Be Coelo—though another book of his, dealing specially with the subject, has unfortunately been lost. He adopted the planetary scheme of Eudoxus and Callippus, but imagined on " metaphysical grounds " that the spheres would have certain disturbing effects on one another, and to counteract these found it necessaiy to add 22 fresh spheies, making 56 111 all At the same time he treated the spheres as matenal bodies, thus converting an ingenious and beautiful geometncal scheme into a confused mechanism/' Anstotle^s spheies weie, however, not adopted by the leading Greek astronomeis who succeeded him, the systems of Hippaichus and Ptolemy being geometncal schemes based on ideas more like those of Eudoxus.
28 Aristotle, m common with other philosophers of his time, believed the heavens and the heavenly bodies to be sphencaL In the case of the moon he supports this belief by the aigument attributed to Pythagoias (§ 23), namely that the obseived appeaianccs of the moon'm its seveial
* Confused, because the mcchamcal knowledge ot the time was quite unequal to giving any explanation of the way m which these fepheies acted on one another.
phases are those which would be assumed by a spherical body of which one half only is illuminated by the sun. Thus the visible portion of the moon is bounded by two planes passing nearly through its centie, perpendicular respectively to the lines joining the centre of the moon to those of the sun and earth In the accompanying diagram, which repiesents a section through the centres of the sun
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