SEQUEL TO THE EPOCH OF KEPLER. 303 



mer, 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 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 offer himself as the umpire who was to adjudge the 

 prize of excellence among the three rival theories of Longomontanus, 

 Kepler, and Lansbeig ; and, in allusion to the story of ancient mythol- 

 ogy, his work was to have been called Paris Astronomicus ; we easily 

 see that he would have given the golden apple to the Keplerian god- 

 dess. Succeeding observations confirmed his judgment : and the Ru- 

 dolphine 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 of the Moon's motions to rule 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), 

 Tycho proved that there was another inequality, which he termed the 

 Variation, 2 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 Inclina- 

 tion of the Orbit had hitherto been assumed to be the same at all 



2 We have seen (chap, iii.), 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. 



