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RELATION OF THE LAW OF GRAVITATION 



TO THE 



PRINCIPLE OF THE CONSERVATION OF ENERGY j 



WITH A PROOF OF THE NECKSSARY TRANSFORMATION OF THE FORCE OF GRAVITY, AT A CERTAIN 

 LIMIT, FROM A FORCE OF ATTRACTION TO ONE OF REPULSION. 



BY THE REV. GEORGE PaXTON YOIJNG, M.A., 

 Professor of Metaphysics and Ethics, University College, Toronto. 



I purpose in this paper to show that, if the principle of the Con- 

 servation of Energy be accepted, the force of gravitation, which, at 

 ordinary sensible distances, is one of attraction, must necessarily 

 undergo transformation,, at a certaia limit, into a force of I'epulsion, 

 and to indicate a higher law, under which the law of the attraction 

 of bodies, according to the inverse square of the distance, falls. 



1. — Preliminary Statement of the General Concbptiow on which the Solution of 

 THE Problem Proceeps. 



The principle of the Conservation of Energy implies that, in a 

 given finite material system, there is a definite amount of energy ; 

 exactly so much, and no more ; an amount which, if not dissipated 

 on the one hand, or augmented ah extra on the other, remains 

 unaffected by the actions of the bodies in the system on one another. 

 Hence, no law of mutual action between the bodies of the system, 

 which would give rise to an indefinitely great velocity, can operate 

 without limitation ; for, energy means capacity for doing work ; and 

 the work done upon a given mass of matter is estimated by half the 

 product of the mass by the square of the velocity ; therefore, an 

 indefinitely great velocity could not be produced unless at the expen- 

 ditiire of an indefinitely great amount of enei'gy. 



Let us apply this to the case of the law of gravitation, according 

 to which, two particles, whose masses are m and n, attract one 

 another with a force inversely proportional to the square of the dis- 

 tance. Two such particles, falling towards one another from rest, 

 would, if the law of gravitation continued to hold good without 

 limitation, acquire indefinitely great velocities as they approached 

 indefinitely near to one another ; in other words, an indefinitely great 



