Becembee 24, 1915] 



SCIENCE 



905 



while, but the students will forget it, just as 

 the students do who are told that we may take 

 as our unit of mass that mass to which unit 

 force (1 pound) gives unit acceleration, and 

 are asked to inspect that more modern baby 

 the slug, alias gee-poimd, which will also be 

 forgotten. 



Why not teach that the unit of force is that 

 force (1 pound) which gives to unit quantity 

 (1 pound) of matter (call it weight or mass 

 as you will) an acceleration of 32.1740 feet 

 per second, or the force with which a pound of 

 matter is attracted to the earth at a standard 

 locality? That baby was pretty old before the 

 poimdal and the slug were born, and now as 

 a strong man is about to attend their funeral. 



Professor Huntington, July 30: 



(P. 158) Professor Hoskins's method presup- 

 poses as a matter of common knowledge the diffi- 

 cult concept of mass or inertia, while my method 

 postpones the introduction of this concept until 

 the student is in a position to define it in terms 

 of the simple concepts of force and acceleration. 



(P. 159) Mass as a factor in the determination 

 of motion means the constant ratio of force to 

 acceleration, and whatever the words quantity of 

 matter convey to a beginner's mind they certainly 

 can not convey this desired idea of mass and in- 

 ertia until after the ideas of force and accelera- 

 tion and the idea of constancy of their ratio for 

 a given body has been accepted. 



If FT=.MV, then FT/V = F/A; F = 

 MY/T=MA; T=ilf 7/ J'= Momentum/Force; 

 y == i?T/ilf ^ Impulse/Mass. Mass no more 

 means the ratio of force to acceleration than 

 force means the time-rate of the increase of 

 momentum, or that time means the ratio of 

 momentum to force, or that velocity means the 

 ratio of impulse to mass. These equations are 

 merely algebraic statements of numerical 

 equality. Not one of them is a definition. 

 Moreover, they are not true, if mass and force 

 are both measured in pounds or in kilograms. 

 They are true in the C.G.S. system, in which 

 force is measured in dynes and mass in 

 grams, and also in the hybrid systems in 

 which force is in poundals and mass in 

 pounds, or force in pounds and mass in slugs. 

 They are also true if it is understood that M 

 is just a symbol for Wh- 32.1740, W being 



weight, the word weight being defined as both 

 the force which gravity exerts on a body where 

 g = 32.1740 and the quantity of matter in 

 pounds as determined by weighing it on an 

 even balance scale. 



There is no difficulty whatever in the begin- 

 ner's mind in the " concept " of weight with 

 this double definition; his difficulty begins 

 when he is told by the text-books and the 

 teachers that weight is a variable quantity 

 changing with locality, and that mass accord- 

 ing to some writers means quantity of matter 

 in slugs, by others it means ratio of force to 

 acceleration, by others that it means the con- 

 stant ratio of a variable weight (force of 

 gravity) on a body to a variable value of g, 

 and by still others that it is the same thing as 

 inertia. 



(P. 164) The awkward attempt to make mass 

 the fundamental unit and force the derived unit 

 has been practically abandoned in the accepted 

 terminology of pure science. Why should it not 

 be abandoned in elementary teaching? 



Certainly it should be abandoned, and so 

 also should be abandoned the equally awkward 

 attempt to make mass a derived unit, the ratio 

 of force to acceleration. As Professor Hoskins 

 says in his footnote (page 610, April 23) : 



Professor Huntington 's statement that the mass 

 concept is a "derived concept both historically 

 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 authorities 

 from Newton down. 



Everybody (writers of text-books on me- 

 chanics and some teachers not excepted until 

 they get into " pure science " and become 

 metaphysical) knows that neither force nor 

 quantity of matter are derived concepts; both 

 are elementary and fundamental concepts. As 

 I said six years ago in my article on " The 

 Teaching of Elementary Dynamics in the 

 High School ":i 



Matter. — A stone is suspended by an elastic cord 

 from a nail driven into a projecting shelf. The 

 stone is a piece of matter. . . . Quantity of mat- 

 ter determined by weighing on an even balance 

 scale. The weight of the stone is W pounds. 



1 Science, Dec. 24, 1909. 



