SEQUEL TO THE EPOCH OF HIPPARCHUS. 161 



the inequality of the motions of the moon, would, in fact, double the 

 inequality of the distances. The Eccentricity of the moon's orbit is 

 determined by Ptolemy as y 1 ^ of the radius of the orbit ; but its real 

 amount is only half as great ; this difference is a necessary conse- 

 quence of the supposition of uniform circular motions, on which the 

 Epicyclic Hypothesis proceeds. 



We see, therefore, that this part of the Hipparchian theory carries 

 in itself the germ of its own destruction. As soon as the art of celes- 

 tial measurement was so far perfected, that astronomers could be sure 

 of the apparent diameter of the moon within ^ or 3L of the whole, 

 the inconsistency of the theory with itself would become manifest. 

 We shall see, hereafter, the way in which this inconsistency operated ; 

 in reality a very long period elapsed before the methods of observing 

 were sufficiently good to bring it clearly into view. 



Sect. 3. — Methods of Observation of the Greek Astronomers. 



We must now say a word concerning the Methods above spoken of. 

 Since one of the most important tasks of verification is to ascertain 

 with accuracy the magnitude of the quantities which enter, as ele- 

 ments, into the theory which occupies men during the period ; the 

 improvement of instruments, and the methods of observing and ex- 

 perimenting, are principal features in such periods. We shall, there- 

 fore, mention some of the facts which bear upon this point. 



The estimation of distances among the stars by the eye, is an ex- 

 tremely inexact process. In some of the ancient observations, how- 

 ever, tftis appears to have been the method employed ; and stars are 

 described as being a cubit or two cubits from other stars. We may 

 form some notion of the scale of this kind of measurement, from what 

 Cleomedes remarks, 4 that the sun appears to be about a foot broad ; 

 an opinion which he confutes at length. 



A method of determining the positions of the stars, susceptible of 

 a little more exactness than the former, is the use of alineations, al- 

 ready noticed in speaking of Hipparchus's catalogue. Thus, a straight 

 line passing through two stars of the Great Bear passes also through 

 the pole-star ; this is, indeed, even now a method usually employed to 

 enable us readily to fix on the pole-star ; and the two stars j3 and a of 

 Ursa Major, are hence often called " the pointers." 



* Del. A. A. i. 222, 

 Vol. I.— 11 



