CHAPTER XVII. 



CURVILINEAR MOTION. 



SUPPOSE three equal bodies at the vertices of an 

 equilateral triangle. Their mutual attraction upon 

 one another must result in their traveling each along 

 a straight line, to a point within the triangle equally 

 distant from the several vertices. Each, without moving 

 directly toward either of the others, yet moves in such 

 direction as to meet them both by the shortest line. 



If, however, we take a more complex case, we shall 

 have a very different result. Even three unequal bodies, 

 and the more if not symmetrically grouped, must pre- 

 sent a wholly new set of relations. So intricate, 

 indeed, are the relations thus presented that " the prob- 

 lem of the three bodies " is one upon which, as Whewell 

 assures us, mathematicians have long exercised their 

 highest powers.* 



The precise quantitative determinations of this and 

 other complex quantitative problems we must, indeed, 

 leave to the mathematicians. All that will be neces- 

 sary for our present purpose will be to trace the 

 quantitative characteristics of the motion arising in 

 such case as that which is actually presented in the 

 concrete world. And for the sake of simplicity, let 

 us assume the concrete case of the relations existing 

 between the earth, the sun and the moon, severally. 



* "History of the Inductive Sciences," 3d (N. Y.) Ed., I., 367. 

 170 



