130 DISSERTATION SECOND. [paiiti. 



or Ptolemy. These ancient astronomers determined the 

 longitude of the fixed stars by referring their places to 

 those of the moon, the longitude of which, for a given 

 time, was known from the theory of her motions. Thus 

 they were forced to depend on the most irregular of all 

 the bodies in the heavens, for ascertaining the positions of 

 the most fixed, those which ought to have been the basis 

 of the former, and of so many other determinations. Tycho 

 made use of the planet Venus instead of the moon, and 

 his method, though more tedious, was more accurate than 

 that of the Greek astronomers. His catalogue contained 

 the places of 777 fixed stars. 



The irregularities of the moon's motions were his next 

 subjects of inquiry. The ancienis had discovered the in- 

 equality of that planet depending on the eccentricity of 

 the orbit, the same which is now called the equation of the 

 centre. * Ptolemy had added the knowledge of another 

 inequality in the moon's motion, to which the name of the 

 evection has been given, amounting to an increase of the 

 former equation at the quarters, and a diminution of it at 

 the times of new and full moon. Tycho discovered another 

 inequality, which is greatest at the octants, and depends 

 on the difference between the longitude of the moon and 

 that of the sun. A fourth irregularity to which the moon's 

 motion is subject, depending wholly on the sun's place, was 

 known to Tycho, but included among the sun's equations. 

 Besides, these observations made him acquainted with the 

 changes in the inclination of the plane of the moon's orbit ; 

 and, lastly, with the irregular motion of the nodes, which, 

 instead of being always retrograde at the same rate, are 

 subject to change that rate, and even to become progres- 



1 The allowance made for any such equality, when the place 

 of a planet is to be computed for a t given time, is called an 

 equation in the language of astronomy. 



