160 



SCIENCE 



[jST. S. Vol. XLII. No. 1074 



equivalent body) by some known force can 

 we predict what acceleration will be produced 

 in tbe body by any other force. In other 

 words, not until we have applied in some form 

 or other the principle expressed by the equa- 

 tion F/F' = a/a' can we arrive at any prac- 

 tical working knowledge of the mass or inertia 

 of the body, as a factor in the determination 

 of its motion. To say to the beginning stu- 

 dent: " Here is a body whose mass is so and so 

 much" simply begs the question, unless he 

 understands how this datum was obtained. 

 The mass or inertia of a body is like its 

 modulus of elasticity; it is physical property 

 to be discovered by experiment, not a meta- 

 physical something to be presiipposed as a 

 matter of common knowledge. 



In view of those considerations, I can not 

 agree with Professor Hoskins when he says 

 there is no reason for regarding the equation 

 F/F' = a/a' as more " fundamental " than the 

 various other equations mentioned in his 

 paper. The reason seems to me very obvious. 

 The statement of this equation presupposes 

 on the part of the reader a knowledge of 

 the meaning of only three fundamental terms, 

 namely: hody, force and acceleration; while 

 the statements of the other equations presup- 

 pose a knowledge not only of these three terms, 

 but also of a fourth term, mass. Since the 

 notion of lod}/ is obviously more elementary 

 than the notion of hody-having-a-given-mass, 

 the equation F/F' ^ a/a', which involves only 

 body and not mass, seems to me clearly more 

 fundamental than any of the other equations, 

 and (especially in the form F/W^a/g) 

 much more suitable as an introduction to 

 mechanics. 



II. A second point of difference between 

 Professor Hoskins and myself concerns the 

 questions of units. According to my method, 

 any units one pleases may be chosen for force, 

 length, and time, and all the other quantities 

 which occur in elementary mechanics are then 

 expressed systematically and naturally in 

 terms of these fundamental units. Hence, as 

 soon as the student has grasped the meaning 

 of the fundamental equation F/F' = a/a', he 

 can proceed at once to the solution of practical 



problems.* On the other method, the student is 

 unable to begin work on the simplest prob- 

 lems in rectilinear motion (such as those 

 treated on page 186 of Professor Hoskins's 

 " Theoretical Mechanics ") until after he has 

 mastered a long discussion of various arti- 

 ficially restricted systems of units, with their 

 unfamiliar names like the dyne and the 

 poundal (pages 177-186). This needless re- 

 striction on the choice of units is a serious 

 disadvantage to the beginner — a disadvantage 

 which results solely from the insistence on the 

 use of the equation F = ma as the funda- 

 mental equation of mechanics, and which dis- 

 appears altogether when the equation F/F'c=: 

 a/a' is employed. 



In further defense of my contention that the 

 system of units based on force, length, and 

 time is more convenient and more natural 

 than the system based on mass, length, and 

 time, I may add that this contention is strik- 

 ingly borne out by the usages of scientific 

 terminology. Even in the C. G. S. system, 

 which is understood to be based on the centi- 

 meter, the gram mass, and the second as the 

 fundamental units, the dyne force plays a more 

 important role in the naming of the derived 

 units than does the gram mass. For example, 

 the unit of power in this system is the dyne- 

 centimeter per second; the unit of pressure 

 the dyne per square centimeter, etc.; whereas 

 if the gram mass were consistently retained as 

 the fundamental unit, we should have to have 

 1 gram centimeter- per second^ as the unit of 

 power, and 1 gram per centimeter-second^ as 

 the imit of pressure! In other words, the 

 awkward attempt to make mass the funda- 

 mental and force the derived unit has been 

 practically abandoned in the accepted term- 

 inology of pure science. Why should it not 

 be abandoned also in elementary teaching?^ 



4 See my article in Science for February 5, 

 1915. 



5 We are not here concerned with the purely 

 technical question as to how the physical stand- 

 ards for the various units may best be preserved 

 to posterity. For purposes of elementary instruc- 

 tion, a standard spring balance representing a 

 unit of force is just as satisfactory as a standard 

 lump of metal representing a unit of mass, in spite 



