SEQUEL TO THE EPOCH OF KEPLER. 455 



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 excel- 

 lence among the three rival theories of Longomon- 

 tanus, 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 Kep- 

 lerian 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 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 de- 

 tected, appear to defy all theory. Still, however, 

 progress was made in this work. The most impor- 

 tant advances were due to Tycho Brahe. In addi- 

 tion to the first and second inequalities of the moon 

 (the Equation of the Center, known very early, and 

 the Ejection which Ptolemy had discovered), Tycho 

 proved that there was another inequality, which he 



