the Conservation of Force. 



121 



acting on one another with, forces depending on their relative 

 positions is due partly to their motion and partly to their re- 

 lative positions/' we are told that " the part which is due to 

 their relative position depends on the work which the various 

 forces would do if the bodies were to vield to the action of 

 those forces." (Ibid. p. 91 ) 



Suppose that we have two equal bodies, P, Q, which, under 

 the influence of their mutual attractions, varying inversely as 

 the distance squared, describe similar and equal ellipses about 

 their common centre of gravity, Gr, supposed at rest. If, at a 

 given instant, P occupying the position in the figure moves 

 towards A, we shall have Q in the line P Gr produced moving 

 towards a. 



In order to find in this case " the work which the various 

 forces would do if the bodies were to yield to the action of 

 those forces," we must resolve the attractive force on each 

 body in a direction parallel to the direction of its motion, since 

 " the whole effect ... of work . . . depends on the part of the 

 force which is in the direction of motion" (p. 90). 



In the case before us it is evident that throughout portions 

 of each orbit, amounting in the whole to one half, the force on 

 either body parallel to its motion, will act in the direction of 

 its motion ; while in the other portions, also amounting col- 

 lectively to one half, it will act in the direction opposite to the 

 direction of motion. 



But we are elsewhere informed (p. 89) that " if the force 

 acts on the body in the direction opposite to the motion . . . 

 the force, instead of doing work on the body, will be a resist- 

 ance which the body in its motion overcomes ;" and as work 

 is done when resistance is overcome (p. 87), it follows that the 

 work which is done under such circumstances is done not by 

 the force but by "the body in its motion" — or, to use some- 

 what plainer English, by the momentum with which the body 

 is for the time being endowed. 



It is evident, therefore, that in the case we have just been 



