CHAPTER V.

SEQUEL TO THE EPOCH OF KEPLER. RECEPTION, VERIFICATION, AND EXTENSION OF THE ELLIPTICAL THEORY.

Sect. 1.-Application of the Elliptical Theory to the

Planets.

THE extension, to the other planets, of Kepler's discoveries concerning the orbit of Mars, obviously offered itself as a strong probability, and was confirmed by trial. This was made in the first place upon the orbit of Mercury; which planet, in consequence of the largeness of its eccentricity, exhibits more clearly than the others the circumstances of the elliptical motion. These and various other supplementary portions of the views to which Kepler's discoveries had led, appeared in the latter part of his Epitome Astronomia Copernicanæ," published in 1622.

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The real verification of the new doctrine concerning the orbits and motions of the heavenly bodies was, of course, to be found in the construction of tables of those motions, and in the continued comparison of such tables with observation. Kepler's discoveries had been founded, as we have seen, prin

cipally on Tycho's observations. Longomontanus (so called as being a native of Langberg in Denmark,) published, in 1621, in his "Astronomia Danica," tables founded upon the theories as well as the observations of his countryman. Kepler' in 1627 published his tables of the planets, which he called "Rudolphine Tables," the result and application of his own theory. In 1633, Lansberg, a Belgian, published also "Tabula Perpetuæ;" a work which was ushered into the world with considerable pomp and pretension, and in which the author cavils very keenly at Kepler and Brahe. We may judge of the impression made upon the astronomical world in general by these rival works, from the account which our countryman Jeremy Horrox has given of their effect on him. He had been seduced by the magnificent promises of Lansberg, and the praises of his admirers, which are prefixed to the work; and was persuaded that the common opinion which preferred Tycho and Kepler to him was a prejudice. In 1636, however, he became acquainted with Crabtree, another young astronomer, who lived in the same part of Lancashire. By him Horrox was warned that Lansberg was not to be depended on; that his hypotheses were vicious, and his observations falsified or forced into agreement with his theories. He then read the works and adopted the opinions of Kepler; and after some hesitation which he felt at

1 Rheticus, Narratio, p. 98.

the thought of attacking the object of his former idolatry, he wrote a dissertation on the points of difference between them. It appears that, at one time, he intended to have offered himself as the umpire who was to adjudge the prize of excellence among the three rival theories, of Longomontanus, Kepler and Lansberg; and, in allusion to the story of ancient mythology, his work was to have been called "Paris Astronomicus;" we easily see that he would have given the golden apple to the Keplerian goddess. Succeeding observations confirmed his judgment: and the "Rudolphine Tables," thus published seventy-six years after the Prutenic, which were founded on the doctrines of Copernicus, were for a long time those universally used.

Sect. 2.-Application of the Elliptical Theory to the Moon.

THE reduction to rule of the motions of the moon was a harder task than the formation of planetary tables, if accuracy was required; for the moon's motion is affected by an incredible number of different and complex inequalities, which, till their law is detected, appear to defy all theory. Still, however, progress was made in this work. The most important advances were due to Tycho Brahe. In addition to the first and second inequalities of the moon (the equation of the centre, known very early, and the evection, which Ptolemy had discovered)

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Tycho proved that there was another inequality, which he termed the variation, which depended on the moon's position with respect to the sun, and which at its maximum was forty minutes and a half, about a quarter of the evection. He also perceived, though not very distinctly, the necessity of another correction of the moon's place depending on the sun's longitude, which has since been termed the annual equation.

These steps concerned the longitude of the moon ; Tycho also made important advances in the knowledge of the latitude. The inclination of the orbit had hitherto been assumed to be the same at all times; and the motion of the node had been supposed uniform. He found that the inclination increased and diminished by twenty minutes, according to the position of the line of nodes; and that the nodes, though they regress upon the whole, sometimes go forwards and sometimes go backwards.

Tycho's discoveries concerning the moon are given in his "Progymnasmata," which was published in 1603, two years after the author's death. He represents the moon's motion in longitude by means of certain combinations of epicycles and eccentrics. But after Kepler had shown that such devices are to be banished from the planetary system, it was impos

› We have seen (Book III, p. 228), that Aboul-Wefa, in the tenth century, had already noticed this inequality; but his discovery had been entirely forgotten long before the time of Tycho, and has only recently been brought again into notice.

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sible not to think of extending the elliptical theory to the moon. Horrox succeeded in doing this; and in 1638 sent his essay to his friend Crabtree. It was published in 1673, with the numerical elements requisite for its application added by Flamsteed. Flamsteed had also (in 1671 and 2) compared this theory with observation, and found that it agreed far more nearly than the "Philolaic Tables" of Bullialdus, or the "Carolinian Tables" of Street (Epilogus and Tabulas.) Halley, by making the centre of the ellipse revolve in an epicycle, gave an explanation of the evection, as well as of the equation of the centre.

Modern astronomers, by calculating the effects of the perturbing forces of the solar system, and comparing their calculations with observation, have added many new corrections or equations to those known at the time of Horrox; and since the motions of the heavenly bodies were even then affected by these variations as yet undetected, it is clear that the tables of that time must have shown some errors when compared with observation. These errors much perplexed astronomers, and naturally gave rise to the question, whether the motions of the heavenly bodies really were exactly regular, or whether they were not affected by accidents as little reducible to rule as wind and weather. Kepler had held the opinion of the casualty of such errors; but Horrox, far more philosophically, argues against this opinion, though he allows that he is much embarrassed by