174 THE GREEK ASTRONOMY. 



the discoveries of Ptolemy, although separated by a long interval of 

 time ; for these discoveries were only made by Tycho Brahe in the 

 sixteenth century. The imperfection of astronomical instruments was 

 the great cause of this long delay. 



3. The Epicyclical Hypothesis was found capable of accommodating 

 itself to such new discoveries. These new inequalities could be repre- 

 sented by new combinations of eccentrics and epicycles : all the real 

 and imaginary discoveries by astronomers, up to Copernicus, were 

 actually embodied in these hypotheses ; Copernicus, as we have said, 

 did not reject such hypotheses ; the lunar inequalities which Tycho 

 detected might have boen similarly exhibited ; and even Newton 36 

 represents the motion of the moon's apogee by means of an epicycle. 

 As a mode of expressing the law of the irregularity, and of calculating 

 its results in particular cases, the epicyclical theory was capable of 

 continuing to render great service to astronomy, however extensive the 

 progress of the science might be. It was, in fact, as we have -already 

 said, the modern process of representing the motion by means of a 

 series of circular functions. 



4. But though the doctrine of eccentrics and epicycles was thus 

 admissible as an Hypothesis, and convenient as a means of expressing 

 the laws of the heavenly motions, the successive occasions on which 

 it was called into use, gave no countenance to it as a Theory ; that is, 

 as a true view of the nature of these motions, and their causes. By 

 the steps of the progress of this Hypothesis, it became more and more 

 complex, instead of becoming more simple, which, as we shall see, 

 was the course of the true Theory. The notions concerning the posi- 

 tion and connection of the heavenly bodies, which were suggested by 

 one set of phenomena, were not confirmed by the indications ot 

 another set of phenomena ; for instance, those relations of the epi- 

 cycles which were adopted to account for the Motions of the heavenly 

 bodies, were not found to fall in with the consequences of their ap- 

 parent Diameters and Parallaxes. In reality, as we have said, if the 

 relative distances of the sun and moon at different times could have 

 been accurately determined, the Theory of Epicycles must have been 

 forthwith overturned. The insecurity of such measurements alone 

 maintained the theory to later times. 37 



36 Principle, lib. iii. prop. xxxv. 



37 The alteration of the apparent diameter of the moon is so great that it cannot 

 escape us, even with very moderate instruments. This apparent diameter con- 

 'ains, when the moon is nearest the earth, 2010 seconds; when she is farthest ofl 



