56 



SCIENCE 



[N. S. Vol. XLII. No. 1071 



Dr. Albert H. Wright, instructor in neu- 

 rology and vertebrate zoology in Cornell Uni- 

 versity, has been promoted to be assistant pro- 

 fessor of zoology. Arthur A. Allen has been 

 appointed assistant professor of ornithology in 

 the college of agriculture. 



DISCUSSION AND COBBESPONDENCE 



ELEMENTARY MECHANICS 



To THE Editor op Science: Four or five 

 years ago we received several letters from our 

 physics friends criticizing our discussion of 

 Newton's laws of motion. One of these criti- 

 cisms related to our use of the term " un- 

 balanced force." If action and reaction are 

 always equal and opposite they must balance 

 each other, as some people seem to think, or 

 in other words, it must be impossible for a 

 body to be acted upon by an unbalanced force ! 



We swear by the God of Simplicity ! A mule 

 pulls forward on a cart with a force A, and 

 the ground pulls backwards on the cart with 

 a force B. I£ A and B are equal, the cart is 

 acted on by balanced forces; but if either is 

 greater than the other, the forces are un- 

 balanced and the cart gains or loses velocity. 

 The force with which the mule pulls on the cart 

 and the necessarily equal and opposite force 

 with which the cart pulls backwards on the 

 mule can not balance each other because they 

 do not act on the same body. Tou can not 

 keep a thief from setting your pocketbook in 

 motion by hanging tenaciously to a lamp post ! 

 and yet the ideas of action and reaction which 

 are soberly held by many of our most pretenti- 

 ous teachers of mechanics mean exactly that 

 when reduced to intelligible terms! Some of 

 those who make a mess of action and reaction 

 are like the Missouri purist who would wish 

 to invent a fancy way of saying that Iowa is 

 north of Missouri in order to avoid a verbal 

 battle with the man from Iowa who insists 

 that Missouri is south of Iowa. 



Another matter has entered into the recent 

 discussion of elementary mechanics in Science, 

 namely, the question as to the fundamental 

 equations of dynamics. Professor Huntington^ 

 is certainly wrong in claiming that the funda- 



1 SdENOE, February 5, 1915. 



mental facts of ISTewton's second law are cov- 

 ered by the statement that the acceleration of 

 a given body is proportional to the accelerating 

 force. 



It is very important to distinguish clearly 

 between the conventional content and the ex- 

 perimental content of Newton's second law of 

 motion concerning the accelerating eileet of 

 an unbalanced force. There are two^ more 

 or less distinct points of view concerning this 

 matter as follows: 



1. We may adopt the stretch of a spring as 

 the basis of force measurement. Then to a 

 fair degree of accuracy experiment shows that 

 the acceleration of a given body is proportional 

 to the accelerating force; and experiment also 

 shows that the acceleration which is produced 

 by a given unbalanced force is inversely pro- 

 portional to the mass of the accelerated body. 

 In this statement the mass of the body is 

 understood to be the result obtained by weigh- 

 ing a body on a balance scale. 



2. We may agree to consider one force as 



- Some physicists are inelined to a third point 

 of view which makes nearly the entire content of 

 Newton's second law conventional. The ratio of 

 two forces is defined as the ratio of the accelera- 

 tions produced by the respective forces when 

 they are made to act, one at a time, on a given 

 body (experiment only can show that the ratio 

 so measured is the same whatever body be used) ; 

 and the ratio of the masses of two bodies is de- 

 fined as the inverse ratio of the accelerations pro- 

 duced in the respective bodies by a given force 

 (experiment only can show that the ratio so meas- 

 ured is the same whatever force be used). From 

 this point of view it is considered as a discovery 

 that the ordinary centuries-old balance scale can 

 be used to measure materials! 



Consider any operation which always yields the 

 same numerical result when applied to a given 

 batch of sugar, but which yields a different nu- 

 merical result when applied to a part of the 

 batch. Such a numerical result can be used as a 

 measure of the quantity of sugar, and if any 

 such operation yields an invariant numerical re- 

 sult of extreme precision that particular opera- 

 tion should be taken as the quantitative definition 

 of mass, if mass is to mean quantity of matter; 

 but we should never forget that the adoption of 

 any particular measure is essentially arbitrary. 



