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LXIV. Intelligence and Miscellaneous Articles. 



CURIOUS CONSEQUENCES OF A WELL-KNOWN DYNAMICAL 

 THEOREM. BY G, JOHNSTONE STONEY, M.A., D.SC, F.R.S.* 



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 aether. 



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. 



To such a spectator the past history of the universe would 

 repeat itself in reverse order, and many of the conditions under 

 which it would do so would appear to him very strange. The 

 bird which was shot to-day by the sportsman, and which is now 

 lying in his kitchen, will, if the reversal of the universe were to 

 take place at this instant, be restored by the keeper to the game- 

 bag, will be carried by him, walking backwards, to the place 

 where the pointer had fetched it in, where he will take it out, and 

 lay it on the ground. Thence the dog will lift it in his mouth, 

 and, trotting backwards, will reach the spot where the bird fell, 

 where, however, it will now rise to the height at which it was shot, 

 from which it will fly away backwards unharmed. Meanwhile, 

 the vapours into which the powder had been dissipated will stream 

 back into the barrel of the fowling-piece, and condense themselves 



* Reprinted, by permission, from the " Scientific Proceedings " of the 

 Royal Dublin Society of the 19th January, 1887. 



