314 



SCIENCE 



[N. S. Vol. XLIII. No. 1105 



a "1 lb. -weight" in a given locality; this 

 means, primarily, that the force required to 

 support the given body, in the given locality, 

 is equal to the force required to support the 

 "1 lb. weight" in that locality; hence, by a 

 simple inference, the force required to support 

 the given body in the standard locality vpill be 

 equal to the force required to support the " 1 

 lb. weight " in the standard locality ; but the 

 force required to support the "1 lb. weight " in 

 the standard locality is guaranteed to be " 1 

 lb."; hence the force required to support the 

 given body in the standard locality — ^that is, 

 the " standard weight " of the body — is also 

 lib. 



11. Finally, if the standard weight of a body 

 is hnown, the dynamical properties of the body 

 are wholly determined. For example, if we 

 wish to find the acceleration, a, produced by 

 any force F in a body whose standard weight 

 is W„ we have merely to substitute the given 

 values in the equation F/W,, = (z/g„ and solve 

 for a. 



In other words, the simple principles enu- 

 merated above — ^principles the truth of which 

 has not been called in question — form a com- 

 plete and satisfactory foundation for the solu- 

 tion of elementary problems in dynamics. It 

 should be particularly noted that no restric- 

 tions whatever are imposed on the choice of 

 the fundamental units of force, length and 

 time; and that the only datum that we need 

 to know in advance concerning any body that 

 enters a problem is a single, readily determined 

 force, namely, the standard weight of the body. 



n. Let us now turn to Professor Hoskins's 

 method, and inquire what items one of the 

 very best of the modern text-book writers re- 

 gards it as necessary to add to these familiar 

 principles. 



In his article in Science for April 23, 1915, 

 page 608, he says : 



The method most intelligible to the beginner ia 

 to introduce at the outset the body-constant which 

 was called by Newton mass or quantity of matter, 

 and to make the fundamental principle . . . the 

 following: (a) A force acting upon a body other- 

 wise free would give it, at every instant, an ac- 

 celeration proportional directly to the force and 

 inversely to the mass of the body. 



His fundamental equation is therefore 



a _ F m' 

 a' ~ F' m' 



which is immediately thrown, by a perfectly 

 arbitrary restriction on the choice of units, 

 into the final form: F=.ma. 



It will be noticed that this method of Pro- 

 fessor Hoskins, and most other authors, in- 

 volves four fundamental concepts, namely, 

 force, length, time and mass ; while my method 

 involves only three, namely, force, length and 

 time. My chief objection to this complication 

 is not merely that the fourth concept, mass, is 

 superfluous, as a fundamental concept, but 

 also that this concept is, at this stage, exceed- 

 ingly ill-defined. Nowhere in Professor Hos- 

 kins's papers can one find a clear-cut statement 

 of what he really intends the student, at the 

 outset, to understand by mass. If he means 

 merely that m is a quantity proportional to 

 F/a, and m' a quantity proportional to F'/a', 

 which relations are consistent with his funda- 

 mental equation, of course no one could object 

 to this use of symbols ; but the compound quan- 

 tity F/a, or W/g, which is properly called the 

 inertia of the body, can surely not be under- 

 stood " at the outset," before the elements out 

 of which it is built up have been grasped ; and 

 this is clearly not Professor Hoskins's inten- 

 tion. 



His several attempts to point out certain 

 rather vague analogies between the concept of 

 mass or inertia and certain other concepts,' 

 have altogether failed to provide a satisfactory 

 justification for his use of mass as a term the 

 meaning of which can be presupposed at the 

 outset, for nowhere does he really define the 

 term, and nowhere does he squarely meet the 

 objections which I have raised to this pro- 

 cedure. 



A further objection to the equation F = ma, 

 which I have dwelt upon at length elsewhere,'' 

 is in regard to the question of imits. The 

 choice of units which the use of this equation 

 compels is needlessly complicated and quite 



■ 6 L. M. Hoskins, Science, September 10, 1915. 

 'See especially Science, July 30, 1915, page 

 160. 



