Dr. 0. J. Lodge on Action at a Distance. 37 



" work," and B to have work done upon it — the work done in 

 each case being measured by the product of the force exerted 

 into the distance moved through in the direction of the force ; 

 and A is said to have lost an amount of " energy " numerically 

 equal to the work done by it, and B is said to have gained an 

 amount of energy equal to the work done upon it. But there 

 is no loss or gain of energy on the whole ; so the energy is 

 simply transferred from A to B by the act of work; or the work 

 done by B upon A is equal and opposite to the work done by 

 A upon B. 



Now, if these premises are granted, it follows at once, since 

 the forces (F) are equal and opposite, and the works (Fs) are 

 also equal and opposite, that the distances (s) must be equal 

 but not opposite; that is, that the two bodies must move over 

 precisely the same distance and in the same sense ; which 

 practically asserts that they move together and are in contact, 

 so long as the action is going on. 



All this is utterly at variance with what happens when the 

 earth pulls a stone, or when a magnet attracts a piece of iron, 

 or when a gun fires a bullet. The distances moved through 

 by the two bodies are by no means the same, and are even in 

 opposite senses ; so that, so far from energy being transferred 

 from one body to the other, some energy is gained by both 

 bodies, though very little by the larger one. 



Hence, admitting the premises, we are bound (and of course 

 perfectly willing) to conclude that the gun does not fire the 

 bullet, but that the powder fires both the bullet and the gun : 

 the gun, in fact, has no direct action on the bullet at all, it 

 does not touch it ; it is the powder which is in contact with 

 each, does work on each, and communicates some of its energy 

 to each. 



But we are equally bound to conclude that the earth has no 

 direct action on the stone, nor the magnet on the iron, but 

 that the medium surrounding both presses them together : it 

 is in contact with each, does work on each, and communicates 

 some of its energy to each. The nature of this medium and 

 of its contact happen to be both utterly unknown ; but other- 

 wise the three cases are analogous. 



I could illustrate my meaning more fully by examining 

 these examples in greater detail or by taking others ; but I 

 believe it to be unnecessary. I may, however, be permitted 

 to refer Mr. Browne to a short paper on Energy which appeared 

 in the Philosophical Magazine for October 1879. 



University College, London. 



