160 THE GEEEK ASTEOXOMY. 



to the student, that every place on the earth's surface might alike 

 be considered as the centre of the celestial motions. But if this was 

 true with respect to the motions of the fixed stars, was it also true 

 with regard to those of the sun and moon ? The displacement of the 

 sun by parallax is so small, that the best observers among the ancients 

 could never be sure of its existence ; but with respect to the moon, tho 

 case is different. She may be displaced by this cause to the amount 

 of twice her own breadth, a quantity easily noticed by the rudest pro- 

 cess of instrumental observation. The law of the displacement thus 

 produced is easily obtained by theory, the globular form of the earth 

 being supposed known ; but the amount of the displacement depends 

 upon the distance of the moon from the earth, and requires at least one 

 good observation to determine it. Ptolemy has given a table of the 

 effects of parallax, calculated according to the apparent altitude of the 

 moon, assuming certain supposed distances ; these distances, however, 

 do not follow the real law of the moon's distances, in consequence 

 of their being founded upon the Hypothesis of the Eccentric and 

 Epicycle. 



In fact this Hypothesis, though a very close representation of the 

 truth, so far as the positions of the luminaries are concerned, fails alto- 

 gether when we apply it to their distances. The radius of the epicycle, 

 or the eccentricity of the eccentric, are determined so as to satisfy 

 the observations of the apparent motions of the bodies ; but, inasmuch 

 as the hypothetical motions are different altogether from the real 

 motions, the Hypothesis does not, at the same time, satisfy the obser- 

 vations of the distances of the bodies, if we are able to make any such 

 observations. 



Parallax is one method by which the distances of the moon, at 

 different times, may be compared ; her Apparent Diameters afford 

 another method. Neither of these modes, however, is easily capable 

 of such accuracy as to overturn at once the Hypothesis of epicycles ; 

 and, accordingly, the Hypothesis continued to be entertained in spite 

 of such measures ; the measures being, indeed, in some degree falsified 

 in consequence of the reigning opinion. In fact, however, the imper- 

 fection of the methods of measuring parallax and magnitude, which 

 were in use at this period, was such, their results could not lead to 

 any degree of conviction deserving to be set in opposition to a theory 

 which was so satisfactory with regard to the more certain observations, 

 namely, those of the motions. 



The Eccentricity, or the Radius of the Epicycle, which would satisfy 



