* 8 9 , 90] The Motion of the Planets j 2 1 



that the stationary points must exist, but shews how to 

 calculate their exact positions. 



89. So far the theory of the planets has cnly been 

 sketched very roughly, in order to bring into prominence 

 the essential differences between the Coppernican and the 

 Ptolemaic explanations of their motions, and n.; account 

 has been taken of the minor irregularities for which Ptolemy 

 devised his system of equants, eccentrics, etc.-, nor of the 

 motion in latitude, i.e. to and from the ecliptic. Copper- 

 nicus, as already mentioned, rejected the equant, as being 

 productive of an irregularity " unworthy " of the celestial 

 bodies, and constructed for each planet a fairly complicated 

 system of epicycles. For the motion in latitude dis- 

 cussed in Book VI. he supposed the orbit of each planet 

 round the sun to be inclined to the ecliptic at a small 

 angle, different for each planet, but found it necessary, in 

 order that his theory should agree with observation, to 

 introduce the wholly imaginary complication of a regular 

 increase and decrease in the inclinations of the orbits of 

 the planets to the ecliptic. 



The actual details of the epicycles employed are of no 

 great interest now, but it may be worth while to notice that 

 for the motions of the moon, earth, and five other planets 

 Coppernicus required altogether 34 circles, viz. four for the 

 moon, three for the earth, seven for Mercury (the motion 

 of which is peculiarly irregular), and five for each of the 

 other planets ; this number being a good deal less than 

 that required in most versions of Ptolemy's system : 

 Fracastor (chapter in., 69), for example, writing in 1538, 

 required 79 spheres, of which six were required for the 

 fixed stars. 



90. The planetary theory of Coppernicus necessarily 

 suffered from one of the essential defects of the system of 

 epicycles. It is, in fact, always possible to choose a system 

 of epicycles in such a way as to make either the direction of 

 any body or its distance vary in any required manner, but 

 not to satisfy both requirements at once. In the case of the 

 motion of the moon round the earth, or of the earth round 

 the sun, cases in which variations in distance could not 

 readily be observed, epicycles might therefore be expected 

 to give a satisfactory result, at any rate until methods of 



