238 A Short History of Astronomy [CH. IX. 



then its positions when not very far from the sun would 

 be almost the same as if it moved in an elongated ellipse 

 (see fig. 73), and consequently it would hardly be possible 

 to distinguish the two cases. Newton accordingly worked 

 out the case of motion in a parabola, which is mathemati- 

 cally the simpler, and found that, in the case of a comet 

 which had attracted much attention in the winter 1680-1, 

 a parabolic path could be found, the calculated places of 

 the comet in which agreed closely with those observed. 

 In the later editions of the Prindpia the motions of a 

 number of other comets were investigated with a similar 



FIG. 73. An elongated ellipse and a parabola. 



result. It was thus established that in many cases a 

 comet's path is either a parabola or an elongated ellipse, 

 and that a similar result was to be expected in other cases. 

 This reduction to rule of the apparently arbitrary motions 

 of comets, and their inclusion with the planets in the same 

 class of bodies moving round the sun under the action 

 of gravitation, may fairly be regarded as one of the most 

 striking of the innumerable discoveries contained in the 

 Prindpia. 



In the same section Newton discussed also at some 

 length the nature of comets and in particular the structure 

 of their tails, arriving at the conclusion, which is in general 

 agreement with modern theories (chapter xin., 304), that 



