the Foundations of Dynamics. 9 



The well-known other objection, that a statement of the first 

 law is unnecessary because it is only a special case of the second, 

 rests on a different footing. Thomson and Tait have pointed out 

 that it acts as a definition of equal intervals of time. Prof. 

 MacGregor denies that the first law gives us any more useful 

 definition of time than the second does ; but seeing that every 

 clock is an attempt at a uniform mover, and that the second 

 law is concerned with the more complex notion of accelera- 

 tion rather than with the simple idea of velocity, I do not 

 imagine that he will seriously adhere to this view : and there- 

 fore, fully admitting the obvious fact that the first law is a 

 special case of the second, I still hold that its separate state- 

 ment is desirable, because it is so simple, and because it does 

 afford a clear practical definition of the mode of measuring 

 time. But were this its intended meaning it could have been 

 expressed more straightforwardly. Newton probably con- 

 sidered it as a qualitative statement introductory to his second 

 law : and as such it is entirely suitable. 



None of the objectors to the first law have the slightest 

 doubt of its truth, — that is what makes their contentions so 

 practically futile ; it would appear that it is too simple to 

 please them ; they seem to wish to complicate its statement 

 so as to make it look more like the difficult things with which 

 they are accustomed to deal. I feel convinced that many 

 mathematicians mistrust a simple statement in English, and 

 hardly conceive that such a language can really express an 

 important law ; their trained ability to deal with difficult con- 

 ceptions leads them, as I think, astray. 



I am not quite clear what the word logomachy means, but 

 much of the discussion which has been bandied about con- 

 cerning the statement of the first law seems to me to be 

 rightly designated by some such opprobrious or perhaps 

 complimentary epithet. 



When Dr. MacGregor goes on to consider the third law, 

 and to deny that it can properly be regarded as a deduction 

 from the first, he is urging a very minor matter, if what 1 

 have said concerning axioms has any truth in it. Still the 

 question has some interest. Whether it is deducible from 

 the first law or not may be held to depend on how general 

 the terms are in which that law has been stated. If it 

 can be axiomatically asserted that the centre of mass of a 

 rigid system moves uniformly until an external force acts on 

 the system, and also that the system does not begin to spin, 

 then the third law is established. For since zero accelera- 

 tion means zero force, it follows that all the internal forces 

 add up to zero, and have no moment ; and since the system 



