On Central Forces and the Conservation of Energy. 35 



In its peculiar sensitiveness to the visible part of the spec- 

 trum selenium seems, so far as our present knowledge goes, 

 to stand almost, if not quite, alone*. 



Riverstone Lodge, Southfields, 

 Wandsworth, S.W. 



V. On Central Forces and the Conservation of Energy. By 

 Walter K. Browne, M.A. y M. Inst. C.E, late Fellow of 

 Trinity College, Cambridge^. 



IT is well known that the ordinary proof of the principle 

 known as the Conservation of Energy assumes the forces 

 acting to be Central Forces^; but the intimate connexion ex- 

 isting between these two facts — the existence of Central 

 Forces and the Conservation of Energy — has not, so far as I 

 am aware, been thoroughly examined. I shall here attempt 

 to show that the two necessarily imply each other; so that not 

 only is the Conservation of Energy true if the system is a 

 system of central forces, but the Conservation of Energy is 

 not true if the system is any thing but a system of central 

 forces. 



For the sake of simplicity I will confine myself to the case 

 of two particles, and suppose them so far apart, in proportion 

 to their dimensions, that each may be treated as if concentrated 

 at its centre of gravity. Let the particles be A and B, and 

 consider the motion of B with reference to A as fixed. Sup- 

 pose B to be moving away from A, and to be acted upon by a 

 moving force due to the action of A. Let it move from a dis- 

 tance a to a distance a + 6, and let F be the resolved part of 

 the moving force in the line AB. Then the energy exerted 

 by B during this motion in overcoming the attraction of A is 

 represented by 



>a + b 



Fdx. 



j: 



Let v x be B's initial velocity, m its mass. Then at the end of 

 the motion vi will be reduced to v, where v is given by the 



* So far as regards Dr. Moser's application of his theory to the carbon 

 photophone of Messrs Bell and Tainter, I entirely agree with him ; my 

 own experiments showing conclusively that the effects are due to heat 

 only. But the best carbon cells are vastly inferior in their action to those 

 of selenium. 



t Communicated by the Physical Society, having been read at the 

 Meeting on November 11, 1882. 



X This is recognized explicitly by Clausius, l Mechanical Theory of 

 Heat,' p. 16. 



D2 



