and tlie Conservation of Energy. 



assume a law of the conservation of working-power 

 deduce contact-action. 



The energy of which he assumes the conservation is ( 

 in the same way as in the second version of his deduction ui 

 the law of conservation : — A body " is said " to have lost or 

 gained an amount of energy numerically equal to the work 

 done by or on it respectively. There is no reference to 

 working-power. What he assumes, therefore, is the conser- 

 vation of the work done on two bodies during their mutual 

 action. 



The conclusion drawn is that " the two bodies must move 

 over precisely the same distance in the same sense," which is 

 action at constant distance, not contact-action. Nor does 

 the assertion that they are " practically 3 ' the same make it 

 contact-action . 



It is obvious, however, that if the conclusion reached above 

 is sound, viz., that Prof. Lodge's law of the conservation of 

 energy is the ordinary law expressed for the particular case 

 of action with equal reaction at constant distance, action at 

 variable distance must be incompatible with it and the third 

 law of motion. 



The argument to show action at a distance to be incom- 

 patible with the law of the conservation of energy alone is as 

 follows *: — " If it were possible for two bodies exerting stress 

 on one another to move over unequal distances, then it would 

 be possible to obtain work without the anti-work, and thus 

 to get a new source of energy (technically called the per- 

 petual motion) ; but, as a fact of experience, it is not possible." 

 Clearly, in the case supposed, there would be a new source of 

 energy as defined by Prof. Lodge. But a new source of 

 energy as thus defined does not imply the perpetual motion. 

 For in such a case there would be working-power which 

 could not be called energy according to the definition ; and 

 the ordinary law of the conservation of energy tells us that, 

 provided the stress supposed to act were independent of the 

 velocities of the bodies acted upon, the change produced 

 during the motion in this portion of the working-power of 

 the system would be such as to render the perpetual motion 

 impossible. 



No attempt is made, in the papers cited above, to show 

 action at a distance to be incompatible with Newton's third 

 law of motion alone, although it is asserted f that the incom- 

 patibility may be proved. 



* Phil. Mag. [5] vol. viii. (1879) p. l>79. 

 t Ibid. vol. xi. (1881) p. 36. 



