June 30, 1916] 



SCIENCE 



927 



The solution of such problems involves the 

 use of a principle equivalent to the following : 

 The mass of a body is equal to the sum of the 

 masses of the individual portions of matter 

 composing it. Professor Himtington doubt- 

 less accepts this principle (even if disapprov- 

 ing the language in which it is expressed) ; 

 but nothing equivalent to it seems to be either 

 expressed or implied in the eleven propositions 

 given by him as suiEcient. It is not merely 

 that the word " mass " is not used ; the term 

 " standard weight " which replaces it is not 

 defined or explained in such a way as to cover 

 the above principle; there is no intimation 

 that standard weight is the measure of an 

 additive property^ of matter — that the stand- 

 ard weight of a hody is the sum of the stand- 

 ard weights of its partsJ But if this is not an 

 upon by the force F', and a second body has the 

 acceleration a" when acted upon by the force F"; 

 a body formed by combining the two would have 

 what acceleration when acted upon by a force F1 

 For example, the addition of 1,000 tons to the 

 load carried by a 5,000-ton vessel would have what 

 effect upon the acceleration of the vessel when 

 starting from rest with a given propeller action? 



' Of additive properties which are invariable and 

 possessed by all matter there are two : inertia 

 and gravitation. These furnish two independent 

 methods of making exact quantitative compari- 

 sons of different portions of matter. It is be- 

 lieved to be a fact that the two methods give re- 

 sults in exact agreement, but the basis of this belief 

 is, and must be, precise experiment, as was ex- 

 plicitly recognized by Newton (although Mr. Kent 

 apparently expects boys to learn it by watching 

 the grocer weigh sugar). Comparing quantities 

 of matter by weighing would involve only the 

 property of gravitation if the earth were at rest; 

 because of the earth's rotation it involves also the 

 property of inertia. (The word inertia is here 

 used in a quantitative sense for lack of a less ob- 

 jectionable term.) 



' Proposition 9 includes the statement that 

 standard weight is ' ' characteristic of the given 

 body, ' ' and proposition 3 the statement that ' ' if 

 any material is added to or taken away from the 

 body it ceases to be the same body"; but there is 

 no intimation that the addition of matter to a 

 body may not produce a body of less standard 

 weight than the original body. 



essential part of the principles of dynamics as 

 actually interpreted in solving problems, I 

 would be glad to know how it can be dispensed 

 with in the case of the particular problem 

 stated above. 



The point which Professor Huntington's 

 method of statement evades is brought out 

 clearly also by the following citations from 

 former articles in Science : 



Professor Huntington's view:^ The state- 

 ment : " Body A has three times the mass of 

 body B " is precisely equivalent to the state- 

 ment : " Body A requires three times as much 

 force as body B to give it a specified accelera- 

 tion." 



Ordinary view as understood by me :' The 

 statement that " body A has three times the 

 mass of body B " means more than that " body 

 A requires three times as much force as body 

 B to give it a specified acceleration " ; it means 

 that the material contained in body A might 

 be made into three bodies, each of which would 

 require the same force as body B to give it a 

 specified acceleration. 



If the latter view is correct, it shows clearly 

 the appropriateness of the words " quantity of 

 matter " as a brief definition of mass.^" If it 

 is not correct, I would again ask how it is pos- 

 sible to solve problems such as the one given 

 above. 



If a proposition expressing the fact that the 

 standard weight of a body is equal to the sum 

 of the standard weights of its parts is added to 

 Professor Huntington's eleven numbered state- 

 ments, the scheme becomes indeed logically 

 " suiEcient " as an explanation of the funda- 

 mental equation of motion. It is also, of 

 course, logically redundant, all that part refer- 

 ring to gravity being irrelevant as regards the 

 real meaning of the laws of dynamics. This 

 redundancy is not necessarily objectionable 



8 Science, July 30^ 1915, p. 159. 



Science, September 10, 1915, p. 341. 



lO'The significance of the words quantity of 

 matter in dynamics was discussed in a former 

 communication (Science, September 10, 1915). 

 A fuller analysis is given in an article published 

 in the American Mathematical Monthly, February, 

 1916. 



