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It is, in fact, always possible to choose a system of epicycles in such a way as to make either the direction of any body or its distance vary in any required manner, but not to satisfy both requirements at once. In the case of the motion of the moon round the earth, or of the earth round the sun, cases in which variations in distance could not readily be observed, epicycles might therefore be expected to give a satisfactory result, at any rate until methods of observation were sufficiently improved to measure with some accuracy the apparent sizes of the sun and moon, and so check the variations in their distances. But any variation in the distance of the earth from the sun would affect not merely the distance, but also the direction in which a planet would be seen; in the figure, for example, when the planet is at P and the sun at S, the apparent position of the planet, as seen from the earth, will be different according as the earth is at E or E′. Hence the epicycles and eccentrics of Coppernicus, which had to be adjusted in such a way that they necessarily involved incorrect values of the distances between the sun and earth, gave rise to corresponding errors in the observed places of the planets. The observations which Coppernicus used were hardly extensive or accurate enough to show this discrepancy clearly; but a crucial test was thus virtually suggested by means of which, when further observations of the planets had been made, a decision could be taken between an epicyclic representation of the motion of the planets and some other geometrical scheme.
Fig. 49.—The alteration in a planet’s apparent position due to an alteration in the earth’s distance from the sun.

91. The merits of Coppernicus are so great, and the part which he played in the overthrow of the Ptolemaic system is so conspicuous, that we are sometimes liable to forget that, so far from rejecting the epicycles and eccentrics of the Greeks, he used no other geometrical devices, and was even a more orthodox “epicyclist” than Ptolemy himself, as he rejected the equants of the latter.57 Milton’s famous description (Par. Lost, VIII. 82-5) of

“The Sphere
With Centric and Eccentric scribbled o’er,
Cycle and Epicycle, Orb in Orb,”

applies therefore just as well to the astronomy of Coppernicus as to that of his predecessors; and it was Kepler (chapter VII.), writing more than half a century later, not Coppernicus, to whom the rejection of the epicycle and eccentric is due.

92. One point which was of importance in later controversies deserves special mention here. The basis of the Coppernican system was that a motion of the earth carrying the observer with it produced an apparent motion of other bodies. The apparent motions of the sun and planets were thus shewn to be in great part explicable as the result of the motion of the earth round the sun. Similar reasoning ought apparently to lead to the conclusion that the fixed stars would also appear to have an annual motion. There would, in fact, be a displacement of the apparent position of a star due to the alteration of the earth’s position in its orbit, closely resembling the alteration in the apparent position of the moon due to the alteration of the observer’s position on the earth which had long been studied under the name of parallax (chapter II., § 43). As such a displacement had never been observed, Coppernicus explained the apparent contradiction by supposing the fixed stars so far off that any motion due to this cause was too small to be noticed. If, for example, the earth moves in six months from E to E′, the change in direction of a star at S′ is the angle E′ S′ E, which is less than that of a nearer star at S; and by supposing the star S′ sufficiently remote, the angle E′ S′ E can be made as small as may be required. For instance, if the distance of the star were 300 times the distance E E′, i.e. 600 times as far from the earth as the sun is, the angle E S′ E′ would be less than 12′, a quantity which the instruments of the time were barely capable of detecting.58 But more accurate observations of the fixed stars might be expected to throw further light on this problem.

Fig. 50.—Stellar parallax.

CHAPTER V.
THE RECEPTION OF THE COPPERNICAN THEORY AND THE PROGRESS OF OBSERVATION.
“Preposterous wits that cannot row at ease
On the smooth channel of our common seas;
And such are those, in my conceit at least,
Those clerks that think—think how absurd a jest!
That neither heavens nor stars do turn at all
Nor dance about this great round Earthly Ball,
But the Earth itself, this massy globe of ours,
Turns round about once every twice twelve hours!”

Du Bartas (Sylvester’s translation).

93. The publication of the De Revolutionibus appears to have been received much more quietly than might have been expected from the startling nature of its contents. The book, in fact, was so written as to be unintelligible except to mathematicians of considerable knowledge and ability, and could not have been read at all generally. Moreover the preface, inserted by Osiander but generally supposed to be by the author himself, must have done a good deal to disarm the hostile criticism due to prejudice and custom, by representing the fundamental principles of Coppernicus as mere geometrical abstractions, convenient for calculating the celestial motions. Although, as we have seen (chapter IV., § 73), the contradiction between the opinions of Coppernicus and the common interpretation of various passages in the Bible was promptly noticed by Luther, Melanchthon, and others, no objection was raised either by the Pope to whom the book was dedicated, or by his immediate successors.

The enthusiastic advocacy of the Coppernican views by Rheticus has already been referred to. The only other astronomer of note who at once accepted the new views was his friend and colleague Erasmus Reinhold (born at Saalfeld in 1511), who occupied the chief chair of mathematics and astronomy at Wittenberg from 1536 to 1553, and it thus happened, curiously enough, that the doctrines so emphatically condemned by two of the great Protestant leaders were championed principally in what was generally regarded as the very centre of Protestant thought.

94. Rheticus, after the publication of the Narratio Prima and of an Ephemeris or Almanack based on Coppernican principles (1550), occupied himself principally with the calculation of a very extensive set of mathematical tables, which he only succeeded in finishing just before his death in 1576.

Reinhold rendered to astronomy the extremely important service of calculating, on the basis of the De Revolutionibus, tables of the motions of the celestial bodies, which were published in 1551 at the expense of Duke Albert of Prussia and hence called Tabulæ Prutenicæ, or Prussian Tables. Reinhold revised most of the calculations made by Coppernicus, whose arithmetical work was occasionally at fault; but the chief object of the tables was the development in great detail of the work in the De Revolutionibus, in such a form that the places of the chief celestial bodies at any required time could be ascertained with ease. The author claimed for his tables that from them the places of all the heavenly bodies could be computed for the past 3,000 years, and would agree with all observations recorded during that period. The tables were indeed found to be on the whole decidedly superior to their predecessors the Alfonsine Tables (chapter III., § 66), and gradually came more and more into favour, until superseded three-quarters of a century later by the Rudolphine Tables of Kepler (chapter VII., § 148). This superiority of the new tables was only indirectly connected with the difference in the principles on which the two sets of tables were based, and was largely due to the facts that Reinhold was a much better computer than the assistants of Alfonso, and that Coppernicus, if not a better mathematician than Ptolemy, at any rate had better mathematical tools at command. Nevertheless the tables naturally, had great weight in inducing the astronomical world gradually to recognise the merits of the Coppernican system, at any rate as a basis for calculating the places of the celestial bodies.

Reinhold was unfortunately cut off by the plague in 1553, and with him disappeared a commentary on the De Revolutionibus which he had prepared but not published.

95. Very soon afterwards we find the first signs that the Coppernican system had spread into England. In 1556 John Field published an almanack for the following year avowedly based on Coppernicus and Reinhold, and a passage in the Whetstone of Witte (1557) by Robert Recorde (1510-1558), our first writer on algebra, shews that the author regarded the doctrines of Coppernicus with favour, even if he did not believe in them entirely. A few years later Thomas Digges (?-1595), in his Alae sive Scalae Mathematicae (1573), an astronomical treatise of no great importance, gave warm praise to Coppernicus and his ideas.

96. For nearly half a century after the death of Reinhold no important contributions were made to the Coppernican controversy. Reinhold’s tables were doubtless slowly doing their work in familiarising men’s minds with the new ideas, but certain definite additions to knowledge had to be made before the evidence for them could be regarded as really conclusive.

The serious mechanical difficulties connected with the assumption of a rapid motion of the earth which is quite imperceptible to its inhabitants could only be met by further progress in mechanics, and specially in knowledge of the laws according to which the motion of bodies is produced, kept up, changed, or destroyed; in this direction no considerable progress was made before the time of Galilei, whose work falls chiefly into the early 17th century (cf. chapter VI., §§ 116, 130, 133).

The objection to the Coppernican scheme that the stars shewed no such apparent annual motions as the motion of the earth should produce (chapter IV., § 92) would also be either answered or strengthened according as improved methods of observation did or did not reveal the required motion.

Moreover the Prussian Tables, although more accurate than the Alfonsine, hardly claimed, and certainly did not possess, minute accuracy. Coppernicus had once told Rheticus that he would be extravagantly pleased if he could make his theory agree with observation to within 10′; but as a matter of fact discrepancies of a much more serious character were noticed from time to time. The comparatively small number of observations available and their roughness made it extremely difficult, either to find the most satisfactory numerical data necessary for the detailed development of any theory, or to test the theory properly by comparison of calculated with observed places of the celestial bodies. Accordingly it became evident to more than one astronomer that one of the most pressing needs of the science was that observations should be taken on as large a scale as possible and with the utmost attainable accuracy. To meet this need two schools of observational astronomy, of very unequal excellence, developed during the latter half of the 16th century, and provided a mass of material for the use of the astronomers of the next generation. Fortunately too the same period was marked by

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