138 Prof. J. G. MacGregor on Contact- Action 



their denotation identical with their ordinary denotation, pro 

 vided the third law of motion hold, energy is defined quali- 

 tatively as being the working-power of a body, and quanti- 

 tatively as being measured by the work done in producing it. 

 The ordinary definition of energy is working-power simply, 

 whether that power be possessed by a body or a system, its 

 measure being the work the body or system can do. Prof. 

 Lodge's energy will therefore be identical with energy in the 

 ordinary sense only in cases in which his work done and his 

 working-power are identical with ordinary work done and 

 ordinary working-power, and in which the working-power of 

 a system is ihe sum of the working-powers of the bodies of 

 which it consists. Now this latter condition requires that the 

 actions between the bodies of the system shall occur only at 

 constant distance. For if the actions might occur at variable 

 distance, a part of the working -power of the system would be 

 potential working-power which could not be said to be pos- 

 sessed by the bodies singly. The former condition is satisfied 

 if the third law of motion hold. Hence Prof. Lodge has so 

 defined energy as to make its denotation identical with the 

 ordinary denotation only in cases of action with equal reaction 

 at constant distance. 



Prof. Lodge asserts also that his law is " fully as axiomatic 

 as" the ordinary law*. Mere assertion, however, cannot 

 make two propositions equally axiomatic. They must be 

 proved to be so. And the test is very simple. If they are 

 applicable with equal generality in the investigation of djma- 

 mical phenomena, they are equally axiomatic ; if not, they are 

 not. Now, if there be actions in nature which are not actions 

 at constant distance, Prof. Lodge's law is not applicable to 

 them, while the ordinary law is. Even if it be admitted that 

 all actions in nature are contact-actions, there are many 

 groups of phenomena which, in the present state of our 

 knowledge of them, cannot be investigated on the hypothesis 

 of contact-action. The early stages of their investigation 

 must be conducted by the aid of the fiction of action at a 

 distance ; and in such stages Prof. Lodge's law is not applic- 

 able, while the ordinary law is. Hence Prof. Lodge's law 

 is not so general in its applicability as the ordinary law. 



(3) Deduction of Contact- Act ion. 



In Prof. Lodge's argument to prove the incompatibility of 

 action at a distance with the third law of motion and the law 

 of the conservation of energy |, he seeems to me neither to 



* Phil. Mag. [5] vol. xi. (1881) p. 533. 

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



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