and the Conservation of Energy . 137 



in it. The law deduced is thus not a law of the conservation, 

 but of the transference of energy. Obviously, with the 

 assumptions which seem to me to have been employed, the 

 complete law of conservation might have been deduced. But 

 the conservation of energy during residence in the body could 

 not have been proved without the explicit employment of the 

 two assumptions involved in the definition of energy. 



In a second version * of the above argument, Newton's 

 third law and contact-action are the only assumptions made ; 

 but the conclusion drawn is not a law of the conservation of 

 energy in the sense of working-power. The definition of 

 energy in this argument is quite different from that of the 

 earlier paper : — " Energy is that which a body loses when it 

 does work ; and it is to be measured as numerically equal to 

 the work done." There is here no reference to working- 

 power. Loss of energy is simply a synonym for work done 

 by, and gain of energy for work done on. The conservation 

 of energy which Prof. Lodge claims to have deduced is there- 

 fore the conservation of the work done on two bodies during 

 mutual action, which is of the same nature as the conservation 

 of their momentum, and is quite consistent with the non- 

 conservation of their working-power. 



(2) Generality and Axiomatic Character of 

 Prof. Lodge's Law. 



It will be obvious that, as Prof. Lodge's definition of energy 

 is different from the ordinary definition, his law of conserva- 

 tion cannot be the same as that ordinarily enunciated under 

 the same name. He says himself it is u probably a slight 

 (very slight) extension " of the ordinary law |. We have 

 seen, however, that in deducing it he assumes the ordinary 

 law, the third law of motion and universal contact-action. It 

 is therefore merely the form which the ordinary law takes 

 in the particular case of contact-action with equal reaction. 



This conclusion is borne out by a consideration of the 

 definition of energy quoted above. Work done and the 

 working-power of a body having been so defined \ as to make 



* Phil. Mag. [5] vol. xix. (1885) p. 483. 



f Ibid. vol. xi. ( 1881) p. 533. 



% " Whenever a body exerting a force moves in the sense of the force it- 

 exerts, it is said to do work ; and whenever a body exerting a force 

 moves in the sense opposite to that of the force it exerts, it is said to have 

 work done upon it, or to do anti-work, the quantity of the work being 

 measured in each case by the product of the force into the distance moved 

 through in its own direction." " The working-power of a body is mea- 

 sured by the average force it can exert, multiplied by the range or distance 

 through which it can exert it." Ibid. vol. viii. (1879) p. 278. 



