August 7, 1908] 



SCIENCE 



183 



constant. Until now, mass has been attrib- 

 uted to a body in the full sense of locating 

 the mass entirely within the volume of the 

 body, and measuring it by means of phenom- 

 ena exhibited there. The essential property 

 of mass may be put as its power to store 

 energy in the kinetic form, receiving and re- 

 taining the energy passively; that is, ac- 

 quiring and losing it only under the control 

 of external influence. J£ we distinguish be- 

 tween " real mass " and " effective mass " in 

 ordinary mechanics', they have in common the 

 passive storage of kinetic energy, definite in 

 amount for a given value of speed; but in 

 using the latter, we assign to the body a cer- 

 tain amount of kinetic energy that is in fact 

 not stored there. This part of the energy is 

 obtainable through the body, perhaps, but not 

 precisely from it. It happens that the ef- 

 fective mass is constant, imder the conditions 

 supposed to govern equations (2) and (3) ; 

 but that type of supposition does not limit the 

 entire range of the conception. This is evi- 

 dent from equation (4) in which m^ may be 

 variable. Neither is it essential, when we 

 enter the field of generalized dynamics, that 

 the storage of energy connected with inertia 

 is demonstrably of a nature that would be 

 described accurately as kinetic. The energy 

 must indeed be stored; that is, be conserva- 

 tively regainable; and this storage must be of 

 passive character in the sense explained above 

 — not accompanied by anything corresponding 

 to resilience, nor automatically convertible like 

 potential energy. These two conditions are 

 sufficient as well as necessary ; and the storage 

 of energy ascribed to electromagnetic mass 

 being in fact parallel with kinetic energy to 

 this necessary extent, only one vital inquiry 

 remains. This is concerned with what we may 

 call the location of the energy. The general- 

 ized inertia will be effective rather than real, 

 in proportion as the energy absorbed is not all 

 stored in the body to which it is assigned con- 

 ventionally; but is distributed throughout 

 some region — or field — surrounding that body. 

 And it is not excluded, as a limit, that the 

 fraction of the total energy to be found within 

 the boundary of the body itself is a negligible 

 part of the whole. 



It is of course nothing more than a com- 

 monplace to remark that the energy here in 

 question, in the case of an ordinary electric 

 circuit, is dispersed through a field, though 

 the inertia is spoken of figuratively in asso- 

 ciation with the conducting track. It is also 

 true that the factor L in equation (5) may be 

 variable. But the electromagnetic theory of 

 electrons is built on models supplied by finite 

 circuits; and the more novel aspects of that 

 theory modify nothing that is for our present 

 purpose essential. Without going further into 

 detail, it is sufficiently evident that the mass 

 of an electron is " effective " ; part of it, or 

 perhaps all, attaching really to the electron's 

 own magnetic field — of indefinite extent — 

 though attributed to the diminutive bulk of 

 the electron itself. In writing out dynamical 

 equations for application to electrons, there- 

 fore, the inertia belonging to the region out- 

 side the boundary of an electron will register 

 its influence on the equation of motion for the 

 electron itself in a force-term, according to 

 the general scheme of equation (4), the elec- 

 tron being the channel for transmission of 

 energy to or from the medium. And if it 

 should be finally established that the inertia 

 of the electron proper is negligible or zero, 

 the transmission would then be of perfect 

 efficiency, corresponding to the condition 

 X=^B ia the text above. And on that sup- 

 position, again speaking of the equation of 

 motion for the electron itself, the application 

 of d'Alembert's principle becomes merely for- 

 mal, since the terms corresponding to " forces 

 of inertia " have vanished, leaving a zero of 

 force in the first instance, instead of a zero re- 

 sulting from the introduction of an equilibrant. 

 The term B may indeed be read as a " kinetic 

 reaction," but in a modified sense; it is no 

 longer a reaction excited immediately in the 

 electron by whatever applies the force X, but 

 is the reaction of the medium against the 

 attempt to move the electron according to 

 certain laws. The term B may be more or 

 less approximately proportional to the accel- 

 eration of the electron; and differently pro- 

 portional for different types of acceleration. 

 Hence arises the idea that the electromagnetic 

 mass of an electron is not constant. 



