Fig. 41.—Coppernican explanation of the seasons. From the De Revolutionibus.
In fig. 41 A, B, C, D represent the centre of the earth in four positions, occupied by it about December 23rd, March 21st, June 22nd, and September 22nd respectively (i.e. at the beginnings of the four seasons, according to astronomical reckoning); the circle F G H I in each of its positions represents the equator of the earth, i.e. a great circle on the earth the plane of which is perpendicular to the axis of the earth and is consequently always parallel to the celestial equator. This circle is not in the plane of the ecliptic, but tilted up at an angle of 23-1∕2°, so that F must always be supposed below and H above the plane of the paper (which represents the ecliptic); the equator cuts the ecliptic along G I. The diagram (in accordance with the common custom in astronomical diagrams) represents the various circles as seen from the north side of the equator and ecliptic. When the earth is at A, the north pole (as is shewn more clearly in fig. 42, in which P, P′ denote the north pole and south pole respectively) is turned away from the sun, E, which is on the lower or south side of the plane of the equator, and consequently inhabitants of the northern hemisphere see the sun for less than half the day, while those on the southern hemisphere see the sun for more than half the day, and those beyond the line K L (in fig. 42) see the sun during the whole day. Three months later, when the earth’s centre is at B (fig. 41), the sun lies in the plane of the equator, the poles of the earth are turned neither towards nor away from the sun, but aside, and all over the earth daylight lasts for 12 hours and night for an equal time. Three months later still, when the earth’s centre is at C, the sun is above the plane of the equator, and the inhabitants of the northern hemisphere see the sun for more than half the day, those on the southern hemisphere for less than half, while those in parts of the earth farther north than the line M N (in fig. 42) see the sun for the whole 24 hours. Finally, when, at the autumn equinox, the earth has reached D (fig. 41), the sun is again in the plane of the equator, and the day is everywhere equal to the night.
Fig. 42.—Coppernican explanation of the seasons. From the De Revolutionibus.
83. Coppernicus devotes the first eleven chapters of the first book to this preliminary sketch of his system; the remainder of this book he fills with some mathematical propositions and tables, which, as previously mentioned ([§ 74]), had already been separately printed by Rheticus. The second book contains chiefly a number of the usual results relating to the celestial sphere and its apparent daily motion, treated much as by earlier writers, but with greater mathematical skill. Incidentally Coppernicus gives his measurement of the obliquity of the ecliptic, and infers from a comparison with earlier observations that the obliquity had decreased, which was in fact the case, though to a much less extent than his imperfect observations indicated. The book ends with a catalogue of stars, which is Ptolemy’s catalogue, occasionally corrected by fresh observations, and rearranged so as to avoid the effects of precession.[53] When, as frequently happened, the Greek and Latin versions of the Almagest gave, owing to copyists’ or printers’ errors, different results, Coppernicus appears to have followed sometimes the Latin and sometimes the Greek version, without in general attempting to ascertain by fresh observations which was right.
84. The third book begins with an elaborate discussion of the precession of the equinoxes (chapter II., [§ 42]). From a comparison of results obtained by Timocharis, by later Greek astronomers, and by Albategnius, Coppernicus infers that the amount of precession has varied, but that its average value is 50″·2 annually (almost exactly the true value), and accepts accordingly Tabit ben Korra’s unhappy suggestion of the trepidation (chapter III., [§ 58]). An examination of the data used by Coppernicus shews that the erroneous or fraudulent observations of Ptolemy (chapter II., [§ 50]) are chiefly responsible for the perpetuation of this mistake.
Of much more interest than the detailed discussion of trepidation and of geometrical schemes for representing it is the interpretation of precession as the result of a motion of the earth’s axis. Precession was originally recognised by Hipparchus as a motion of the celestial equator, in which its inclination to the ecliptic was sensibly unchanged. Now the ideas of Coppernicus make the celestial equator dependent on the equator of the earth, and hence on its axis; it is in fact a great circle of the celestial sphere which is always perpendicular to the axis about which the earth rotates daily. Hence precession, on the theory of Coppernicus, arises from a slow motion of the axis of the earth, which moves so as always to remain inclined at the same angle to the ecliptic, and to return to its original position after a period of about 26,000 years (since a motion of 50″·2 annually is equivalent to 360° or a complete circuit in that period); in other words, the earth’s axis has a slow conical motion, the central line (or axis) of the cone being at right angles to the plane of the ecliptic.
85. Precession being dealt with, the greater part of the remainder of the third book is devoted to a discussion in detail of the apparent annual motion of the sun round the earth, corresponding to the real annual motion of the earth round the sun. The geometrical theory of the Almagest was capable of being immediately applied to the new system, and Coppernicus, like Ptolemy, uses an eccentric. He makes the calculations afresh, arrives at a smaller and more accurate value of the eccentricity (about 1∕31 instead of 1∕24), fixes the position of the apogee and perigee (chapter II., [§ 39]), or rather of the equivalent aphelion and perihelion (i.e. the points in the earth’s orbit where it is respectively farthest from and nearest to the sun), and thus verifies Albategnius’s discovery (chapter III., [§ 59]) of the motion of the line of apses. The theory of the earth’s motion is worked out in some detail, and tables are given whereby the apparent place of the sun at any time can be easily computed.
The fourth book deals with the theory of the moon. As has been already noticed, the moon was the only celestial body the position of which in the universe was substantially unchanged by Coppernicus, and it might hence have been expected that little alteration would have been required in the traditional theory. Actually, however, there is scarcely any part of the subject in which Coppernicus did more to diminish the discrepancies between theory and observation. He rejects Ptolemy’s equant (chapter II., [§ 51]), partly on the ground that it produces an irregular motion unsuitable for the heavenly bodies, partly on the more substantial ground that, as already pointed out (chapter II., [§ 48]), Ptolemy’s theory makes the apparent size of the moon at times twice as great as at others. By an arrangement of epicycles Coppernicus succeeded in representing the chief irregularities in the moon’s motion, including evection, but without Ptolemy’s prosneusis (chapter II., [§ 48]) or Abul Wafa’s inequality (chapter III., [§ 60]), while he made the changes in the moon’s distance, and consequently in its apparent size, not very much greater than those which actually take place, the difference being imperceptible by the rough methods of observation which he used.[54]