22 



SCIENCE 



[N. S. Vol. XLIV. No. 1123 



Why will a large ship, moving toward a wharf 

 with a motion hardly perceptible, crush with great 

 force a boat intervening? 



Because the great mass and weight of the vessel 

 compensates for its want of velocity. 



Which shows that the author of this famous 

 hook did not discriminate between mass and 

 weight in a case where weight as force does 

 not enter. 



This confusion of mass and weight can not 

 be helped by pseudo-definitions which attempt 

 to evade the essentially kinetic nature of the 

 mass concept. As is well known, Newton, in 

 the " Principia," defined mass as the product of 

 density and volume, and equivalent to quantity 

 of matter. Neither of these statements has 

 any value, as neither brings out the essential 

 fact that a body subject to acceleration dis- 

 plays a constant characteristic property, which 

 is the core of Newton's own treatment of the 

 problem of accelerated motion. Another more 

 recent definition states that mass is the result 

 obtained by weighing with a balance scale. 

 This can not help a student very much. The 

 balance scale was known for centuries before 

 Newton, and had mass been so easily defined it 

 would hardly have been left for him to dis- 

 cover the fact of its existence and importance. 

 The fact is, that mass is a concept of kinetics, 

 not to be reached at all by static experiments, 

 and not to be clearly discovered by kinetic ex- 

 periments affected by friction. It came into 

 science by way of Mars and the moon, and was 

 then read into terrestrial experience. The 

 " balance scale " gives us mass not directly, but 

 by interpretation, even as does the Jolly bal- 

 ance. It is not always true that " in physics 

 sensible people define things the way they do 

 them." 



Students in general seem to have no serious 

 difficulty with the equality of push and counter- 

 push, of friction and counter-friction, of ac- 

 tion and reaction. Trouble does come up in 

 the identification of actions and reactions, and 

 in the realization that these always act upon 

 different things, in opposite directions in the 

 same straight line. 



As illustrations, take two quotations, the first 

 from Wells's " Natural Philosophy," of the 

 sixties, the other from a recent book: 



The centrifugal force is that force which impels 

 a body moving in a curve to move outward or fly 

 off from a center. The centripetal force is that 

 force which draws a body moving in a curve toward 

 the center, and compels it to move in a bent, or 

 curvilinear course. In circular motion the centri- 

 fugal and centripetal forces are equal, and con- 

 stantly balance each other. If the centrifugal 

 force of a body revolving in a circular path be 

 destroyed, the body will immediately approach the 

 center; but if the centripetal force be destroyed, 

 the body will fly off in a straight line, called a 

 tangent. 



Suppose the horse drawing a sled increases his 

 speed. Two reactions now oppose the pull applied 

 to the sled. One, friction, opposes the slipping of 

 the sled over the ground; the other, due to inertia, 

 opposes increase of speed. These two together 

 are equal and opposite to the pull exerted on the 

 sled. 



These are only cases of confusion such as 

 come up in every physics or mechanics class- 

 room; centrifugal and centripetal forces bal- 

 ancing each other in circular motion, both act- 

 ing on the same thing ; friction and the " vis 

 inertia; " are the reactions to the pull exerted 

 by a horse. 



When one has endeavored to point out the 

 nature of a difficulty, it is natural to ask him 

 for the remedy. I am not pretending that I 

 have found remedies for the difficulties men- 

 tioned above, some of which seem to be im- 

 posed upon us by the constitution of our minds 

 and the environment in which the race has 

 grown up. The only thing to do is to make 

 every endeavor to break up the satisfaction of 

 the student with the concepts which he has 

 unconsciously formed, to try to contrive stri- 

 king experiments which shall, for example, 

 make plain that something more than the 

 notion of weight is needed for their explana- 

 tion, and, especially, to familiarize him with 

 the concept acceleration and the various ways 

 of arriving at its value, theoretically and prac- 

 tically. The teacher has almost to strive 

 against instinct in the treatment of the laws of 

 motion, and some people can never be expected 

 to grasp them. 



Willard J. Fisher 



New Hampshire College 



