246 Prof. J. G. MacGrregor on the 



Maxwell's version of Newton's argument*, which he regards 

 as " a deduction of the third law of motion from the first/' 

 may, as I showed in my Address (p. 12), be attacked on two 

 grounds. First, it assumes that the attraction between the 

 mountain and the remainder of the earth is the only stress 

 between them, ignoring the stress at their surface of contact, 

 an inequality in the action and reaction of which might ob- 

 viously neutralize the " residual force " due to the assumed 

 inequality in the action and reaction of the attraction. 

 Secondly, the conclusion, thus illogically obtained, is not the 

 third law of motion. For the former asserts the equality 

 and opposition of the action and reaction of the stress between 

 two parts of a body, to which body, as a whole, the first law 

 has been assumed to apply, while the latter makes the same 

 assertion for two bodies, to each of which the first law is 

 applicable. That this criticism is sound becomes especially 

 apparent, if w r e reflect that when dealing with rotation and 

 strain we must regard the laws of motion as applicable to 

 particles or elements, the first and second laws being held to 

 apply to each particle, and the third law to the stresses 

 between pairs of particles. Maxwell's deduced law would 

 apply only to the actions and reactions of the stresses between 

 the parts of single particles which, as Prof. Lodge says 

 (p. 11), are " not worth troubling about." It would tell us 

 nothing about the stresses between pairs of particles, and 

 would thus be of no use in the solution of dynamical 

 problems. 



Prof. Lodge's version of Newton's argument : — " Jam the 

 bodies apart with a rigid obstacle, then you have reduced 

 their action to contact action " &c._, (p. 10), is so condensed 

 that it is hard to analyse. But it is easy to see that its first 

 statement is incorrect. For when we "jam the bodies 

 apart" we do not reduce their action to contact action. The 

 attraction continues. We have simply introduced, in addi- 

 tion, two contact stresses. The premisses, therefore, being 

 thus faulty, the conclusion cannot be warranted. 



Prof. Lodge appears to have abandoned the deduction of 

 the third law from the first in its usual form. a Whether," 

 he says, " it is deducible from the first law or not may be 



* " If the attraction of any part of the earth, say. a mountain, upon 

 the remainder of the earth, were greater or less than that of the re- 

 mainder of the earth upon the mountain, there would be a residual force 

 acting upon the system of the earth and the mountain as a whole, which 

 would cause it to move off with an ever-increasing velocity through in- 

 finite space. This is contrary to the first law of motion, which asserts 

 that a body does not change its state of motion unless acted upon by- 

 external force " (' Matter and Motion ', Arts. lvii. and lviii.). 



