Mr. W. R. Browne on Action at a Distance. 131 



in appearance, contains so many errors that I can hardly 

 believe I have read it aright. In the first place, he con- 

 siders my paper as valuable in pointing out metaphysical 

 difficulties, whereas my only allusion to metaphysics was in 

 repudiating the metaphysical notion that action at a distance 

 is a priori inconceivable. 



Secondly, he is fatally wrong in his statement of the prin- 

 ciple of the conservation of energy. The work done on a body 

 B is not " measured by the product of the force exerted into 

 the distance moved through in the direction of the force;" on 

 the contrary, it is measured by the product of the resistance 

 into the distance moved through against that resistance. Sup- 

 pose we have a weight A of 1 ton acting on a smaller weight 

 B over a pulley. Will Dr. Lodge assert that the work done 

 by A, when it has fallen through 1 foot, is precisely the same 

 whether the weight of B is 1 cwt. or 19 cwt. ? 



Thirdly, Dr. Lodge talks of equal and opposite forces, and 

 of equal and opposite works. What he means by these terms, 

 except that the motion due to such forces or works is in oppo- 

 site directions, I am unable to divine ; and yet that is the 

 point he is trying to disprove. That there can be no transfer 

 of energy due to motion of two bodies in the same direction, 

 is shown in a moment. First, let the velocities of the two 

 bodies be equal, and impress upon them a velocity equal and 

 opposite to this common velocity. This, by the second law of 

 motion, will in no way affect the case. But the two bodies 

 are now reduced to rest; and Dr. Lodge will not assert, I 

 presume, that any transfer of energy is taking place between 

 them. Secondly, let the velocities be different, and let them 

 be V-f v and V — v. Impress on both a velocity — V ; then 

 the bodies are left with velocities +v and — v ; that is, with 

 velocities tending in opposite directions. 



Fourthly, Dr. Lodge is obviously in error in assuming that 

 when the earth pulls a stone, any work whatever is done 

 upon either. This is at once apparent from the fact that 

 there is no resistance to the motion (neglecting, of course, 

 the friction &c. of the air). All that happens is, that in 

 each case a certain quantity of potential energy is turned 

 into actual energy. The total energy of each remains the 

 same, and no transference whatever takes place between 

 them. 



K2 



