64 



SCIENCE. 



[N. S. Vol. XXIII. No. 576. 



some of the characteristic differences be- 

 tween the fundamental principles of ordi- 

 nary mechanics and the modern electro- 

 magnetic theory. Is it necessary, then, to- 

 keep these two sciences distinct, or is it 

 possible to build them up on a common 

 foundation? Such a common foundation 

 is certainly desirable; and it will ultimately 

 amount to the same whether we try to gen- 

 eralize the principles of mechanics so as to 

 embrace the electromagnetic theory, or 

 whether we follow W. Wien° in deducing 

 the principles of mechanics as a particular 

 or rather limiting case from Maxwell's 

 equations. 



The question can be put in a somcAvhat 

 different form. There seem to be two 

 things underlying all the phenomena in the 

 physical world: the ether and matter. To 

 attain the unification of physical science, 

 shall we consider the ether as a particular 

 kind of matter 1 Or shall matter be inter- 

 preted electromagnetically 1 The . older 

 mechanics dealt exclusively with matter; 

 and when it first became necessaiy to intro- 

 duce the ether, this new medium was often 

 endowed with properties very much like 

 those of matter. The hydrodynamic anal- 

 ogy by which the apparent mass of the 

 moving charge was interpreted above illus- 

 trates this tendency. The physics of the 

 ether has, however, reached so full a de- 

 velopment that the properties of the ether 

 are now known far more definitely than 

 those of matter. These properties are con- 

 tained implicitly in the fundamental equa- 

 tions of Maxwell and Hertz which in their 

 essential features are adopted in the elec- 

 tron theory of Lorentz. 



In this theory the electromagnetic mass 

 of the electron is nothing but the self-induc- 

 tion of the convection current produced 

 by the moving electron. This mass de- 



° Ueber die Mfiglichkeit einer elektromagnet- 

 ischen Begriindung der Mechanik, Archives nier- 

 landaises (2), 5 (Lorentz Festschrift), 1900, pp. 

 Oti-107. 



pends on the velocity of the electron, or 

 rather on the ratio of this velocity to that 

 of light. Moreover, this mass, or inertia, 

 may be of two kinds: longitudinal, as op- 

 posing acceleration in the direction of mo- 

 tion, and transverse, as opposing accelera- 

 tion at right angles to the path. Any 

 variation in the velocity is transmitted as 

 a radiation through the ether with tlie 

 velocity of light. 



The electromagnetic energy does not 

 reside in the moving electron, but is dis- 

 tributed through the whole field, with the 

 volume density (I/Stt) (E^ + H^), if E and 

 H are the electric and magnetic vectors of 

 the field. In determining the rate of work 

 in any region we must take into account 

 not only the time-rate of change of this 

 energy in the region, but also the flux of 

 energy through its boundary, which has 

 the value (c/47r) E X H, per surface ele- 

 ment, c being the velocity of light. 

 . M. Abraham^ has shown that the fun- 

 damental equations of Lorentz 's theory 

 of electromagnetism can be given a form 

 that bears a striking resemblance to the 

 fundamental equations of ordinary me- 

 chanics. But he has pointed out at the 

 same time that in spite of this analogy of 

 mathematical form the real meaning of the 

 equations is essentially different from their 

 meaning in the older mechanics. The 

 underlying invariant quantity is not or- 

 dinary mass, but the electric charge of the 

 electron; mass, or inertia, is variable, de- 

 pending on the velocity; momentum and 

 energy are distributed through the field; 

 the flux of energy, given by Poynting's 

 radiation vector, is essential in determining 

 the rate of working of a system. All these 

 differences are ultimately due to the mod- 

 ern conception of the propagation of all 

 actions, not instantaneously, but in time, 

 through a medium. This idea, as seems to 



'' Annalen der Phi/sik. Vol. 10 (1903), pp. 105- 

 179. 



