136 Prof. J. Gr. MacGregor on Contact-Action 



o 



of this view is published. But in the edition of his book on 

 Elementary Mechanics which bears the date 18D2, he reaches 

 this conclusion in the following way (p. 56) : — " It [Newton's 

 third law] is deducible from the first law of motion (see Max- 

 well, ' Matter and Motion ') , for if the forces exerted by two 

 parts of the same body on each other were not equal and 

 opposite, they would not be in equilibrium ; and consequently 

 two parts of the same body might, by their mutual action, 

 cause it to move with increasing velocity for ever, the possi- 

 bility of which the first law denies. We have already shown 

 that the first law is a special case of the second, and now we 

 have deduced the third from the first ; hence all are really 

 included in the second, which is therefore excessively im- 

 portant/'' That the first law is a special case of the second 

 ijs obvious ; but that the third is deducible from the first in 

 the above way I have elsewhere * endeavoured to disprove. 

 It is not necessary to repeat the discussion here ; for it will 

 probably be sufficient to point out that the equality and oppo- 

 sition of the action and reaction of two parts of the same body 

 do not constitute the third law of motion, that law asserting 

 the equality and opposition of the action and reaction between 

 two bodies, to each of which the first law applies. That this 

 criticism is sound becomes especially obvious if we reflect 

 that the laws of motion, as fundamental hypotheses of dy- 

 namics, must be held to apply to particles, not to extended 

 bodies ; and the above argument is clearly inapplicable to a 

 particle. 



The unacknowledged assumptions are thus not deducible, at 

 least have not been deduced, from those admittedly used. 

 Now the law of the conservation of energy, as ordinarily 

 enunciated, may be deduced from these two assumptions alone. 

 Hence, in the argument under consideration, Prof. Lodge 

 assumes the ordinary law of the conservation of energy in 

 addition to the third law of motion and universal contact- 

 action. 



(b) The following is the conclusion which he draws : — 

 a Hence the energy gained by the first body is equal to the 

 energy lost by the second ; or, on the whole, energy is 

 neither produced nor destroyed, but is simply transferred from 

 the second body to the first." This states only that energy 

 is conserved during transference, and says nothing as to its 

 fate after transference to the first body, and during residence 



t In an Address on the fundamental hypotheses of Dynamics, read at 

 the last Meeting of the Royal Society of Canada, and to be published in 

 vol. x. of its Transactions. See abstract in i Science,' vol. xx. (1892) 

 p. 71. 



