456 HISTORY OF FORMAL ASTRONOMY. 



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, ac- 

 cording to the position of the line of nodes ; and 

 that the nodes, though they regress upon the whole, 

 sometimes go forwards and sometimes go back- 

 wards. 



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 



3 We have seen (Chap, in), 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. 



