596 



SCIENCE 



[N. S. Vol. XXXIX. No. 1008 



underlying the new meclianics as a survey of 

 his article.'- 



M. Langevin begins his discussion with the 

 statement that the idea of mass has been the 

 fundamental concept of mechanics since the 

 time of Newton, and that it may be intro- 

 duced in three different ways which correspond 

 to three aspects of inertia. We may define 

 mass as the coefficient of proportionality of 

 force to change of velocity as derived from 

 the formula, force equals mass times accelera- 

 tion (F =■ ma) ; as capacity for impulse or 

 quantity of motion, from the formula, momen- 

 tum equals mass times velocity (0 = mv); 

 as capacity for kinetic energy, from the for- 

 mula, kinetic energy equals one half mass times 

 velocity squared (u' = ^mt)^). 



Rational mechanics, to be consistent, re- 

 quires that there must be perfect equality 

 among these three definitions of mass, and 

 that the mass of any portion of matter must 

 remain absolutely invariable for all velocities 

 and for all changes of the body, whether due 

 to physical, chemical or mechanical agents. 



By inertia we ordinarily mean the property 

 which matter possesses of tending to preserve 

 its state of rest or of uniform motion in a 

 straight line; that is, matter resists any 

 change of motion in such a way that an ex- 

 ternal action or force is necessary to change 

 the quantity or the direction of a motion. 

 Newton based mechanics on this constant 

 proportion between force and change of mo- 

 tion, or acceleration; and he defined mass to 

 be the constant of this proportion. He thus 

 assumes that mass, determined in any other 

 manner, will give a consistent result with his 

 ■definition. 



And since the time of Newton, every trea- 

 tise on physics has begun with this assump- 

 tion, that inertia is the fundamental property 

 of matter, in the sense that it can not be ex- 

 pressed in simpler terms. Indeed, for more 

 than two centuries, it has been held to be the 

 essential doctrine of mechanics, that a phys- 

 ical phenomenon was satisfactorily explained 

 only when it was reduced to a type of motion. 



1 P. Langevin, ' ' L 'inertie de 1 'energie et ses 

 consequenees, " Le Journal de Physique, July, 

 1913. 



governed by the laws of this rational mechan- 

 ics, and particularly by the law of inertia. 



But now, after a searching criticism of the 

 postulates of mechanics, many physicists have 

 come to the conclusion that inertia is not a 

 fundamental property of substance, and they 

 claim to have proved that it can be reduced to 

 simpler terms by the laws of eleetromagnetism, 

 which show evidence of being simpler and 

 more fundamental than the laws of dynamics. 



First, because it can be proved that inertia 

 is not invariable, since the quantity of mass, 

 as measured by the three definitions given 

 above, ceases to be the same when the velocity 

 of matter is not small compared to the veloc- 

 ity of light. 



Furthermore, although for small velocities 

 the three definitions of mass agree and assign 

 to a given portion of matter a definite initial 

 or " stationary " mass, m„, yet even this initial 

 mass depends on the physical and chemical 

 state of the system and also varies for each 

 change of state which is accompanied by an 

 interchange of energy with an outside body. 



This evidently means that, if a body radi- 

 ates heat, light or electro-magnetic waves to 

 other bodies, or if a body unites with another 

 to form a new chemical compound, then the 

 mass of the body in each case changes. The 

 relation between this change of mass and the 

 change of energy is found to be a very simple 

 one, as the change of mass equals the change 

 of energy divided by the velocity of light 



squared, or v 



m — m' = -. 



w — w 



It follows because of the law of the conserva- 

 tion of energy that in a system of bodies whose 

 separate parts mutually exchange energy, the 

 masses of the separate parts vary, but the 

 total mass of all the parts added together re- 

 mains constant, if the system as a whole does 

 not change its total quantity of energy. Thus 

 the law of conservation of mass is merged into 

 the more fundamental law of conservation of 

 energy. 



The inadequacy of mechanics became appa- 

 rent when physicists attempted, without suc- 

 cess, to explain electro-magnetic and optical 

 phenomena from the accepted mechanical laws. 

 We now see, as Professor Einstein has shown 



