A Short History of Astronomy by Arthur Berry (best novels for students .TXT) π
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33. Among the important contributions of the Greeks to astronomy must be placed the development, chiefly from the mathematical point of view, of the consequences of the rotation of the celestial sphere and of some of the simpler motions of the celestial bodies, a development the individual steps of which it is difficult to trace. We have, however, a series of minor treatises or textbooks, written for the most part during the Alexandrine period, dealing with this branch of the subject (known generally as Spherics, or the Doctrine of the Sphere), of which the Phenomena of the famous geometer Euclid (about 300 B.C.) is a good example. In addition to the points and circles of the sphere already mentioned (chapter I., §§ 8-11), we now find explicitly recognised the horizon, or the great circle in which a horizontal plane through the observer meets the celestial sphere, and its pole,17 the zenith,18 or point on the celestial sphere vertically above the observer; the verticals, or great circles through the zenith, meeting the horizon at right angles; and the declination circles, which pass through the north and south poles and cut the equator at right angles. Another important great circle was the meridian, passing through the zenith and the poles. The well-known Milky Way had been noticed, and was regarded as forming another great circle. There are also traces of the two chief methods in common use at the present day of indicating the position of a star on the celestial sphere, namely, by reference either to the equator or to the ecliptic. If through a star S we draw on the sphere a portion of a great circle S N, cutting the ecliptic β N at right angles in N, and another great circle (a declination circle) cutting the equator at M, and if β be the first point of Aries (Β§ 13), where the ecliptic crosses the equator, then the position of the star is completely defined either by the lengths of the arcs β N, N S, which are called the celestial longitude and latitude respectively, or by the arcs β M, M S, called respectively the right ascension and declination.19 For some purposes it is more convenient to find the position of the star by the first method, i.e. by reference to the ecliptic; for other purposes in the second way, by making use of the equator.
34. One of the applications of Spherics was to the construction of sun-dials, which were supposed to have been originally introduced into Greece from Babylon, but which were much improved by the Greeks, and extensively used both in Greek and in mediaeval times. The proper graduation of sun-dials placed in various positions, horizontal, vertical, and oblique, required considerable mathematical skill. Much attention was also given to the time of the rising and setting of the various constellations, and to similar questions.
35. The discovery of the spherical form of the earth led to a scientific treatment of the differences between the seasons in different parts of the earth, and to a corresponding division of the earth into zones. We have already seen that the height of the pole above the horizon varies in different places, and that it was recognised that, if a traveller were to go far enough north, he would find the pole to coincide with the zenith, whereas by going south he would reach a region (not very far beyond the limits of actual Greek travel) where the pole would be on the horizon and the equator consequently pass through the zenith; in regions still farther south the north pole would be permanently invisible, and the south pole would appear above the horizon.
Further, if in the figure H E K W represents the horizon, meeting the equator Q E R W in the east and west points E W, and the meridian H Q Z P K in the south and north points H and K, Z being the zenith and P the pole, then it is easily seen that Q Z is equal to P K, the height of the pole above the horizon. Any celestial body, therefore, the distance of which from the equator towards the north (declination) is less than P K, will cross the meridian to the south of the zenith, whereas if its declination be greater than P K, it will cross to the north of the zenith. Now the greatest distance of the sun from the equator is equal to the angle between the ecliptic and the equator, or about 23-1β2Β°, Consequently at places at which the height of the pole is less than 23-1β2Β° the sun will, during part of the year, cast shadows at midday towards the south. This was known actually to be the case not very far south of Alexandria. It was similarly recognised that on the other side of the equator there must be a region in which the sun ordinarily cast shadows towards the south, but occasionally towards the north. These two regions are the torrid zones of modern geographers.
Again, if the distance of the sun from the equator is 23-1β2Β°, its distance from the pole is 66-1β2Β°; therefore in regions so far north that the height P K of the north pole is more than 66-1β2Β°, the sun passes in summer into the region of the circumpolar stars which never set (chapter I., Β§ 9), and therefore during a portion of the summer the sun remains continuously above the horizon. Similarly in the same regions the sun is in winter so near the south pole that for a time it remains continuously below the horizon. Regions in which this occurs (our Arctic regions) were unknown to Greek travellers, but their existence was clearly indicated by the astronomers.
36. To Eratosthenes (276 B.C. to 195 or 196 B.C.), another member of the Alexandrine school, we owe one of the first scientific estimates of the size of the earth. He found that at the summer solstice the angular distance of the sun from the zenith at Alexandria was at midday 1β50th of a complete circumference, or about 7Β°, whereas at Syene in Upper Egypt the sun was known to be vertical at the same time. From this he inferred, assuming Syene to be due south of Alexandria, that the distance from Syene to Alexandria was also 1β50th of the circumference of the earth. Thus if in the figure S denotes the sun, A and B Alexandria and Syene respectively, C the centre of the earth, and A Z the direction of the zenith at Alexandria, Eratosthenes estimated the angle S A Z, which, owing to the great distance of S, is sensibly equal to the angle S C A, to be 7Β°, and hence inferred that the arc A B was to the circumference of the earth in the proportion of 7Β° to 360Β° or 1 to 50. The distance between Alexandria and Syene being known to be 5,000 stadia, Eratosthenes thus arrived at 250,000 stadia as an estimate of the circumference of the earth, a number altered into 252,000 in order to give an exact number of stadia (700) for each degree on the earth. It is evident that the data employed were rough, though the principle of the method is perfectly sound; it is, however, difficult to estimate the correctness of the result on account of the uncertainty as to the value of the stadium used. If, as seems probable, it was the common Olympic stadium, the result is about 20 per cent. too great, but according to another interpretation20 the result is less than 1 per cent. in error (cf. chapter X., Β§ 221).
Another measurement due to Eratosthenes was that of the obliquity of the ecliptic, which he estimated at 22β83 of a right angle, or 23Β° 51β², the error in which is only about 7β².
37. An immense advance in astronomy was made by Hipparchus, whom all competent critics have agreed to rank far above any other astronomer of the ancient world, and who must stand side by side with the greatest astronomers of all time. Unfortunately only one unimportant book of his has been preserved, and our knowledge of his work is derived almost entirely from the writings of his great admirer and disciple Ptolemy, who lived nearly three centuries later (§§ 46 seqq.). We have also scarcely any information about his life. He was born either at Nicaea in Bithynia or in Rhodes, in which island he erected an observatory and did most of his work. There is no evidence that he belonged to the Alexandrine school, though he probably visited Alexandria and may have made some observations there. Ptolemy mentions observations made by him in 146 B.C., 126 B.C., and at many intermediate dates, as well as a rather doubtful one of 161 B.C. The period of his greatest activity must therefore have been about the middle of the 2nd century B.C.
Apart from individual astronomical discoveries, his chief services to astronomy may be put under four heads. He invented or greatly developed a special branch of mathematics,21 which enabled processes of numerical calculation to be applied to geometrical figures, whether in a plane or on a sphere. He made an extensive series of observations, taken with all the accuracy that his instruments would permit. He systematically and critically made use of old observations for comparison with later ones so as to discover astronomical changes too slow to be detected within a single lifetime. Finally, he systematically employed a particular geometrical scheme (that of eccentrics, and to a less extent that of epicycles) for the representation of the motions of the sun and moon.
38. The merit of suggesting that the motions of the heavenly bodies could be represented more simply by combinations of uniform circular motions than by the revolving spheres of Eudoxus and his school (Β§ 26) is generally attributed to the great Alexandrine mathematician Apollonius of Perga, who lived in the latter half of the 3rd century B.C., but there is no clear evidence that he worked out a system in any detail.
On account of the important part that this idea played in astronomy for nearly 2,000 years, it may be worth while to examine in some detail Hipparchusβs theory of the sun, the simplest and most successful application of the idea.
We have already seen (chapter I., Β§ 10) that, in addition to the daily motion (from east to west) which it shares with the rest of the celestial bodies, and of which we need here take no further account, the sun has also an annual motion on the celestial sphere in the reverse direction (from west to east) in a path oblique to the equator, which was early recognised
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