Energy and Relativity. 

 Begin with Abraham's value * 



: and therefore 



M-WElog(Sj)- 



vat [_v 2 c 2 —v 2 v s G \c — v j _\dt j 



103 



>ov 



J 



Establish a junction with equation (16) through its first 

 or its last form ; either shows (P) as the total derivative 

 of an auxiliary momentum 



. . . (20) 



The last member being already standardized at (c), the plan 

 of equations (9, 10, 11) gives 



P~ ^r 



MS3 J ^'W<^ 



fm Y c 2 v \ dv m x c , /c 4- u\ <iw 



i 



im 



dt 



(21) 



Mark how the last member returns to one leading idea of 

 equations (4, 6, 7). 



The scale-factor (s") that equalizes this rate of work- 

 conversion with what equation (19) demands is then 

 conditioned by 



. . . (22) 



In the last equation, due choice of the arbitrary ratio 

 (wq/wii) has reduced one coefficient to unity. The corre- 

 sponding activities in equations (6, 7, 22) exhibit, then, as 

 sole essential distinction the effective inertia whose time- 

 rate occurs in each one — a remarkably significant symmetry. 

 Why should it include the Lorentz electron without par- 

 ticularized values beyond {i\ = c \ m 1 ^-m )? The answer 



* Translated into our notation, but unaltered otherwise. The 

 quotation is from his ' Theorie der Elektrizitat,' vol. ii. (1908). 

 The chief equations referred to are (113, 113 c, 113 d, 117, 117 a, 

 117 6). The numbering of equations is fortunately unchanged through 

 a series of editions. Rest-mass (m ) coincides with the usage of 

 Lorentz-Minkowski, allowing for " rational units," etc. 



