610 



SCIENCE 



[N. S. Vol. XLI. No. 1060 



though we must also recognize that any gen- 

 eral method of comparing quantities of matter 

 must employ either the laws of dynamics or 

 some other physical law in which the same 

 body-constant is significant. 



Reflection iipon what is really involved in 

 the Newtonian laws soon shows, indeed, that 

 the provisional definitions of force and mass 

 are quite inadequate as a basis for a strictly 

 logical explanation of the laws. It has long 

 been recognized by writers who have attempted 

 to formulate fundamental principles with full 

 logical rigor that the definitions of both force 

 and mass are implicitly involved in the laws of 

 motion themselves.^ An analysis of the strict 

 logical import of the Newtonian system would, 

 however, be quite unintelligible to beginners, 

 and a recognition of the soundness of such 

 an analysis is no reason for dispensing with 

 the aid of the more tangible notions of quantity 

 of matter" and push or pull. 



While the method advocated by Professor 

 Huntington is in my opinion sound in its 

 essential features, the explanation of it in the 

 paper' to which he refers seems to encourage 

 the erroneous notion that the laws or facts of 

 terrestrial gravity form a part of the principles 

 of dynamics. Although the definition of 



5 ProhaWy the most adequate formulation of 

 the Newtonian laws from the point of view of 

 strict logic is that given by W. H. Macaulay 

 (Bull. Am. Math. Sac, July, 1897). Mr. Macau- 

 lay's analysis makes it clear not only that the defi- 

 nitions of mass and force are implicitly contained 

 in the laws themselves, but that the law of accel- 

 eration and the law of action and reaction can not 

 be treated as independent, and further that the 

 question of a base for estimating acceleration is 

 of fundamental importance, since the laws, if true 

 for one rigid base, will not be true for another 

 which has any motion except a uniform transla- 

 tion with respect to the first. 



6 Professor Huntington 's statement that the 

 mass concept is " a derived concept, both histor- 

 ically and practically" is hardly true in any sense 

 in which it is not also true of force. At all 

 events mass in the sense of quantity of matter has 

 been treated as fundamental by many high au- 

 thorities from Newton down. See the opening 

 paragraph of the "Principia. " 



7 Bull. S. F. E. E., June, 1913. 



standard weight quoted above is of course quite 

 independent of gravity, in the paper it is given 

 the form of a gravity definition : " The stand- 

 ard weight of a body is the force of gravity on 

 that body in the standard locality." The 

 reader is likely to miss the significance of the 

 qualifying statement made elsewhere in the 

 paper that the standard locality is any locality 

 where g has the value 32.1Y40 ft./sec.= — a 

 statement which makes the reference to locality 

 and to the force of gravity wholly irrelevant 

 as regards the real meaning of the quantity 

 called standard weight. 



It is to be feared, also, that the definition 

 of " force of gravity " given in the paper en- 

 courages vagueness rather than definiteness in 

 the force concept. The conception of force as 

 a push or pull, exemplified by the pull which 

 stretches a spring, is a very definite one. It 

 loses its definiteness, however, unless the fact 

 is kept in mind that there is always some hody 

 that does the pushing or pulling. When, there- 

 fore, it is said that a body is acted upon by a 

 certain force, it is always pertinent to ask hy 

 what hody this force is exerted. How is this 

 question to be answered in the case of the 

 " force of gravity " as defined in the paper ? 

 The definition is as follows: 



By the ' ' force of gi'avity " on a body, we mean 

 simply the unseens force which gives the body, 

 when allowed to fall freely from rest, in vacuo, in 

 the given locality, the observed acceleration g. It 

 is equal and opposite to the force required to sup- 

 port the body in that locality. 



The question hy what hody this force of 

 gravity is exerted is not answered in the 

 paper, and an attempt to supply the answer 

 leads to the conclusion that the definition is 

 inconsistent with the conception of force as 

 a push or pull exerted upon a hody hy another 

 hody. The " observed acceleration g " has a 

 component that is not due to force at all, but 

 to the fact that our base for estimating accel- 

 eration is the rotating earth. The body is not 

 acted upon by a push or pull that is "equal 

 and opposite to the force required to support 

 the body " ; if it were, a supported body would 

 have no acceleration, while in fact it has an 



sis the word "unseen" here intended to imply 

 tliat there are forces which are visible? 



