Mr. W. R. Browne on Action at a Distance. 379 



undulations from luminous ones. The first portion of the 

 word proposed, however, has so decided a meaning that no one 

 can imagine it to mean a production of luminous undulations, 

 but will immediately recognize it as meaning the production 

 of sonorous ones. 

 Bristol, April 4, 1881. 



LI. On Action at a Distance. By Walter R. Browne, 

 M.A., M. Inst. C.E., late Fellow of Trinity College, Cam- 

 bridge. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



I AM indebted to your courtesy for space to conclude (at 

 least as far as I am concerned) the controversy which has 

 arisen out of my paper on Action at a Distance. I will con- 

 fine myself to a very few w r ords as to the points at issue be- 

 tween myself and Dr. Lodge. 



The difficulty of understanding each other's position has 

 arisen from our employing the word Work in different senses. 

 Dr. Lodge, following modern works on Dynamics, defines 

 Work done as equivalent to Energy exerted, and as measured 

 by the product of the moving force and the distance through 

 which its point of application is moved. I, looking at the 

 matter from the point of view of Applied Mechanics, followed 

 the definition of Rankine, according to w 7 hich Work is done 

 only when there is a resisting force acting in the opposite 

 direction to the moving force ; and is measured by the pro- 

 duct of this resisting force and the distance through which its 

 point of application is moved*. I perhaps owe Dr. Lodge an 

 apology for not having seen this from the first ; but I will 

 not dwell longer on this or any other matters of mere per- 

 sonal controversy between us. 



It remains, finally, to give my reasons for rejecting the 

 remarkably short and simple argument by which Dr. Lodge 

 conceives that he has disposed for ever of the idea of Action 

 at a Distance. This argument! is as follows : — It first states 

 generally the law of the equality of Action and Reaction, 

 where tw r o bodies, A and B, act " directly and solely " on each 

 other with forces F, through distances s ; and then asserts that, 



* For this definition, and for a proof that Rankine did not include in his 

 Resistances the inertia of the body, I may refer to the following articles 

 in his ' Applied Mechanics,' first edition, 1858 : — page 477, arts. 511-514; 

 page 499, art, 549 ; and especially page 622, art. 689. 



t Phil. Mag. January 1881, p. 36. 



2E2 



