340 



SCIENCE 



[N. S. Vol. XLII. No. 1080 



Dr. H. G. Earle lias been appointed to the 

 chair of physiology in the University of Hong- 

 kong. 



DISCUSSION AND COBEESPONDENCE 

 MASS AS QUANTITY OF MATTER 



That the words " quantity of matter " are 

 of service in explaining the significance of 

 ■" mass " in dynamics has been assumed either 

 explicity or tacitly by many authorities, in- 

 cluding Newton, Maxwell, Kelvin, Tait and 

 Clifford, and this view is obviously held by 

 several of those who have contributed to the 

 recent discussion in Science. There are, 

 however, those who dissent from this view,^ 

 maintaining that the word mass as used in 

 dynamics has no meaning except that given to 

 it by the " law of acceleration " (Newton's 

 second law), and that the statement that "the 

 mass of a body is a measure of its quantity of 

 matter" contributes nothing to our under- 

 standing of the definition. My present object 

 is to call attention to a consideration which 

 appears to be lost sight of by those who take 

 this latter position. This consideration, stated 

 briefly, is that the mass of a hody is distributed 

 in a perfectly definite way among the individ- 



1 The dissenting view ia vigorously advocated by 

 Professor Huntington in his latest letter (Science, 

 July 30, 1915). It should be noted that this 

 question is aside from the question whether mass 

 should appear in the fundamental equations. 

 Whatever definition of mass may be adopted, the 

 fact remaius that the quantity ordinarily called 

 mass is a part of the fundamental data of dynam- 

 ics. That Professor Huntington's formulation 

 of principles obscures this fact is my chief reason 

 for dissenting from it. Further discussion of this 

 point by me would, however, be a reiteration of 

 what has been said in a former communication 

 (Science, April 23, 1915). Any reader who is 

 interested in Professor Huntington's reference to 

 my test-book on theoretical mechanics may find 

 by consulting the book that the explanation of the 

 laws of motion contained in it is substantially that 

 which I have recently favored in the pages of 

 Science; but it is my present belief that the notion 

 of quantity of matter might have been used more 

 effectively in this book, as well as in most other 

 text -books that are known to me. 



ual portions of matter of which the "body is 

 composed. 



Dynamics deals with the motions of bodies. 

 By a body we mean any connected aggregate 

 of matter. Without attempting to define mat- 

 ter, we recognize the applicability to it of the 

 notions that the whole is greater than any 

 part and the whole is equal to the sum of its 

 parts. These are quantitative notions; and it 

 will be seen that they are an essential part of 

 the notion of mass which we habitually use in 

 interpreting the second law of motion. 



Consider the following proposition : 



I. If two bodies be acted upon by equal 

 forces, the body having the greater mass will 

 have the lesser acceleration. 



According to one view this is merely an ar- 

 bitrary definition of the meaning of greater 

 and less as applied to mass; i. e., the state- 

 ment that "the mass of a body A is greater 

 than that of a body B " is held to mean noth- 

 ing more than that " i£ A and B be acted upon 

 by equal forces the acceleration of A will be 

 less than that of B." If, however, we are to 

 regard proposition I. as having any applica- 

 tion to actual physical bodies, it is easy to 

 show that it is not a mere definition, but a 

 partial expression of a physical law, enabling 

 us in certain cases to make predictions. Thus, 

 suppose material to be removed from a body A, 

 leaving a body B; we know that, if a certain 

 force be applied to A and an equal force after- 

 ward to B, the acceleration of B will be greater 

 than that of A; and the truth of this is recog- 

 nized because we know that B contains less 

 material than A. That is, in applying I. to 

 this case we associate with mass the notion of 

 quantity of matter. 



Consider now the following more definitely 

 quantitative proposition : 



II. If different bodies are acted upon by 

 equal forces, the resulting accelerations are in 

 the inverse ratios of the masses of the bodies. 



The interpretation we put upon this proposi- 

 tion becomes evident from a consideration of 

 particular cases. 



As a first illustration let J. be a body which, 

 when acted upon by a force F, has the accelera- 

 tion a; and suppose A to be divided into two 



