September 24, 1915] 



SCIENCE 



423 



the table would lead to the following generali- 

 zations. 



(a) If one force produces twice as much 

 acceleration as another force when acting on a 

 given body, then the one force produces twice 

 as much acceleration as the other force when 

 acting on any body whatever. 



(fc) If one body is accelerated twice as much 

 as another body under the action of a given 

 force, then the one body is accelerated twice as 

 much as the other body under the action of any 

 force whatever. 



The experimental fact (a) makes it conven- 

 ient to define the ratio of two forces as the 

 ratio of the accelerations they produce when 

 acting on a given body, because this ratio is 

 the same for aU bodies. 



The experimental fact (h) makes it conven- 

 ient to define the ratio of the masses of two 

 bodies as the inverse ratio of the accelerations 

 produced by a given force, because this ratio 

 is the same for all forces. 



MEASUREMENT VERSUS UNDERSTANDING 



Forty or fifty years ago, after the system of 

 electric and magnetic measurements had been 

 fuUy established, every physicist had come 

 near to a belief which was voiced by Sir 

 William Thomson when he said that " when 

 you can measure a thing you know all about 

 it," and this point of view reached its climax 

 in the days when physicists almost without ex- 

 ception believed that all subsequent develop- 

 ment in tlieir science would be to add signif- 

 icant figures farther and farther to the right 

 of the decimal point! This point of view has, 

 however, been swept away by the discoveries of 

 recent years, and yet its germ seems to cling 

 to some of the older phases of natural philos- 

 ophy, for it comes to life in nearly every one's 

 mind when any of the long-established prin- 

 ciples of physics are contemplated. This is 

 illustrated by nearly everything that has been 

 said of recent years concerning the laws of 

 motion. The measurement of force and the 

 measurement of mass seem to be mixed up in- 

 extricably with the experimental aspects of 

 the laws of motion in nearly every one's mind, 

 whereas, as it seems to us, the laws of motion 



appear in their simplest and most clearly intel- 

 ligible form when forces and masses (bodies) 

 are not measured but merely identified. Sir 

 William Thomson's statement certainly repre- 

 sents an obsolete point of view, which no doubt 

 Lord Kelvin would have admitted. Tou can 

 know a lot about a thing even if you can't 

 measure it, and if you can and do measure it 

 under widely varying conditions you can find 

 out a great deal more about it. But to be able 

 to measure a thing is, in the last analysis, 

 merely to have enough wit to read a clock, or 

 a yard stick, or to use a balance. 



Measurement versus understanding! It cer- 

 tainly does seem fair so to characterize the 

 difference between the natural philosophy of 

 forty years ago and the natural philosophy of 

 to-day ; and no one shows a keener insight into 

 the changing point of view than Karl Pearson^ 

 when he insists that after all physics, like bot- 

 any, is a descriptive science. 



INERTIA AND MASS. THE ESSENCE OF 

 mathematical PHYSICS 



The inverse ratio of the accelerations pro- 

 duced in two bodies by a given force is spoken 

 of above as the ratio of the masses of the two 

 bodies. Let us speak of this as the ratio of 

 inertias, and let us reserve the word mass to 

 designate the result obtained by weighing a 

 body on a balance. Then the quantitative 

 identity of mass and inertia is a discovery, 

 but it is by no means a discovery which should 

 make us ashamed of the balance as an instru- 

 ment of precision. 



Let us retain as the fundamental meaning of 

 the word mass the result of weighing on a 

 halance scale. Indeed, the laboratory man 

 would laugh at any one who pretended to do 

 otherwise; beware of the laugh of the labora- 

 tory man, he can satisfy the man from Mis- 

 souri ! 



Tes, but the ratio of inertias is a more abso- 

 lute thing than the ratio of masses because the 

 balance must be on earth ! But is it ? No one 

 can imagine a celestial operation which would 

 show the ratio of inertias of two lone bodies 

 without a third body of some kind acting. 



1 See Pearson 's ' ' Grammar of Science. ' ' 



