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XXXIX.— CUEIOUS CONSEQUENCES OF A WELL-KNOWN 

 DYNAMICAL THEOEEM. By G. JOHNSTONE STONEY,. 

 M.A., D. Sc, F.K.S., a Vice-President of the Society. 



[Read, January 19, 1887.] 



There is a well-known theorem in the science of Dynamics, re- 

 lating to a system of bodies in motion, which may act on each 

 other, but are not acted on by any external force. The theorem 

 in question is, that if at any instant the velocities of the several 

 bodies of the system be reversed, without any other change being 

 made (i. e. without altering either their masses or the laws accord- 

 ing to which they attract or otherwise act on one another), then 

 will all the bodies of the system retrace their steps, traversing in 

 the reverse direction the same paths which they had previously- 

 described, and in such manner that any position through which 

 any one of these bodies had passed in its onward progress, at a 

 certain time before the reversal, will be repassed with the same 

 velocity, but in the opposite direction, at the same interval of time 

 after the reversal. 



Now, if we regard the universe as a dynamical system, it is 

 exactly such a dynamical system as this theorem presupposes. 

 Its several parts act on one another, but are not subjected to any 

 other forces. And it is of interest to study what would be the 

 result if such a reversal as the theorem supposes were to take place 

 throughout the whole universe. "We must, of course, suppose that 

 the reversal affects all the motions of the universe, not only its 

 molar motions, but its molecular motions also; and not only the 

 motions of its ponderable matter, but also the motions of the ether. 



In order to be in a position to study the effects, let us first 

 suppose that we are spectators of this far-reaching change, without 

 being ourselves affected by it — that we are, from an intellectual 

 standpoint, as it were outside the great system whose future 

 history we want to trace, simply observing everything that takes 

 place, and not in any way interfering with it, nor ourselves in any 

 way transformed by the change. 



