s*ct. iv.] DISSERTATION SECOND. 119 



which revolved westward, more slowly than the sphere of 

 the fixed stars. These spheres must be transparent, or 

 made of some crystalline substance, and hence the name of 

 the crystalline spheres, by which they were distinguish- 

 ed. This system, though it grew more complicated in 

 proportion to the number and variety of the phenomena 

 observed, was the system of Arislotle and Eudoxus, and, 

 with a few exceptions, of all the philosophers of anti- 

 quity. 



But when the business of observation came to be regu- 

 larly pursued ; when Timocharis and Aristillus, and their 

 successors in the Alexandrian school, began to study the 

 phenomena of the heavens, little was said of these orbs ; and 

 astronomers seemed only desirous of ascertaining the laws 

 or the general facts concerning the planetary motions. 



To do this, however, without the introduction of hypo- 

 thesis, was certainly difficult, and probably was then impossi- 

 ble. The simplest and most natural hypothesis was, that 

 the planets moved eastward in circles, and at a uniform rate. 

 But when it was found that, instead of moving uniformly 

 to the eastward, every one of them was subject to great 

 irregularity, the motion eastward becoming at certain pe- 

 riods slower, and at length vanishing altogether, so that the 

 planet became stationary, and afterwards acquiring a mo- 

 tion in (he contrary direction, proceeded for a time toward 

 the west, it was far from obvious how all these appear- 

 ances could be reconciled with the idea of a uniform circu* 

 lar motion. 



The solution of this difficulty is ascribed to Apollonius 

 Pergseus, one of the greatest geometers of antiquity. He 

 conceived that, in the circumference of a circle, having the 

 earth for its centre, there moved the centre of another 

 circle, in the circumference of which the planet ac- 

 tually revolved. The first of these circles was called 



