Hypotheses of Dynamics. 249 



fore the conclusion which ought to be drawn is not even 

 expressed in the same words as the third law. It is also just 

 as obvious that even if the conclusion drawn had been war- 

 ranted, though expressed in the same words as the third law 

 it would not have been the same law, because the term reaction 

 would be used in entirely different senses in the two laws. 



That the above efforts to deduce the third law from the 

 first or second should thus prove futile need not surprise us. 

 For the second law gives us a quantitative statement as to 

 the effect which is produced in a particle by a force; while 

 the third tells us that forces always occur as one-sided aspects 

 of stresses, and gives us the relation between the two forces 

 of which every stress consists. Had these laws been recog- 

 nized as being thus complementary to one another, efforts to 

 deduce either from the other would have been seen before- 

 hand to be doomed to failure *, and the above dreary 

 refutations would not have been called for. 



(4) Prof. Lodge's Deduction of his Law of Conservation. 



Though Prof. Lodge still holds (pp. 11 & 14) that the 

 conservation of energy (as defined by him) " can be deduced 

 from Newton's third law and from the denial of action at a 

 distance," and indeed gives a new version of this deduction, 

 he admits that his deduction applies only to conservation 

 during transfer, and that conservation during residence or 

 " storage " is incapable of deduction f. How he reconciles 



* This seems, at first sight, not to agree with what Mach says 

 (Mechanik, p. 226) after having referred to the subject matter of New- 

 ton's first and second laws, viz. : — " The third law contains apparently 

 something new. We have already seen, however, that without the cor- 

 rect conception of mass it is unintelligible, and that on the other hand, 

 through the conception of mass, which itself can be obtained only 

 through dynamical experiences, it is rendered unnecessary." As, accor- 

 ding to the ordinary interpretation, the idea of mass is given in terms of 

 force by the second law, Mach would seem to hold that the third law is 

 not independent of the second. This is not the case, however. Mach 

 had previously shown that if we interpret Newton's second law by the 

 aid of his definitions, this law does not give us a clear conception of 

 mass. He himself obtains the conception, without reference to force, by 

 an appeal to experience, which takes the place of the appeal made in the 

 third law and thus renders it unnecessary. 



f After dismissing, with some hesitation, the " plausible " method of 

 establishing a law of nature by appeal to definition, he suggests that 

 conservation during storage should be adopted as an axiom ; but he does 

 not meet the argument given in my Address to show, that if we retain 

 Newton's laws, it is illogical to employ the law of conservation as an 

 axiom, and that if we adopt the latter law as an axiom, Tait's suggestion 

 {Ency. Brit. , Art. Mechanics, § 299) is the only logical one, viz., that 

 Newton's laws should be abandoned and the law of transference of 

 energy adopted instead. 



Phil. Mag. S. 5. Vol. 36. No. 220. Sept, 1893. S 



