on the Mechanical Function of an SEther. 415 



the kinetic energy of a definite mass moving with given speed 

 varies according to the standard of rest arbitrarily chosen ; in 

 other words that energy is as arbitrary and relative as velocity ; 

 and the amount of work needed to confer a given velocity on 

 a body depends on how fast that body was already moving 

 [because (u + v) 2 — u 2 = v* + a term proportional to w~] , a datum 

 either meaningless or impossible to know. 



But further, even though ivork might be rigidly defined, 

 with reference to two bodies and their velocities relative to 

 their centre of mass, by a suitable statement of the third law 

 of motion, yet the same would not be true of energy, for it 

 is not expressible in terms of their relative motion, and is 

 therefore essentially arbitrary. Professor Newcomb takes 

 this as limiting the generality of the law of the Conservation 

 of Energy ; and says that it would promote sound philosophy 

 if the limitation were made clear. 



But I submit that it is more consonant with physical habit 

 to assume the law of conservation and to deduce its conse- 

 quences. Nothing that we know about energy points to its 

 being a relative thing ; it has all the marks of objectivity. 

 No one can really suppose that energy is destroyed or created 

 wholesale by a mere change in the origin or point of reckoning 

 for velocity. It is kinematically convenient to confer an 

 arbitrary velocity on an extensive system so as to bring some 

 body in it to rest, but it is not physically possible without 

 performance of work ; hence it would appear that there is a 

 real meaning in absolute velocity after all. Newton perceived 

 this, and his great scholium preceding the aziomata, though 

 it has been often criticised and misunderstood, is one of the 

 most interesting details of his philosophy. 



It was indeed the instinctive feeling of the race that absolute 

 motion had somehow a real meaning which caused the excite- 

 ment concerning Copernican views of astronomical movements, 

 as taught by Galileo and others. 



To show that conservation of energy, as accepted, demands 

 attention to absolute velocity, and that it is only the customary 

 neighbourhood of a practically infinite mass which has masked 

 the ambiguity, it suffices to take the simplest possible case ; 

 say the earth and a stone initially moving together with 

 absolute velocity u. Their absolute energy is E = | (M -f ni)u 9 , 

 their relative energy is nothing. 



Fire the stone in the same direction, with extra velocity v, and 

 let the earth recoil with velocity iv ; the absolute energy is now 

 Ej, such that E x — ~Ei = ^mv 2 -\- ^'hv 2 + (mv — Miv)u; and, since 

 the last term is zero, the gain of absolute energy is equal to 

 the gain of relative energy provided the imparted velocity he 

 reckoned from the centre of mass the only point whose velocity 



2 G2 



