Energy and Relativity. ' 105 



equations (8, 26, 27) are in one aspect mere algebraic 

 variations. Nevertheless, it should arrest attention that 

 the last term in equation (27) is now transferred among 

 positive contributors to energy-ilux, instead of figuring as 

 a negative quota of resistance. The type prescribed for the 

 first member of equation (1 (6)) is better maintained; separate 

 record is now entered, however, for each branch of a com- 

 posite process *. 



Equating the alternative mated pairs of terms in the total 

 derivative of equation (25 j provides another direct con- 

 nexion with equations (6, 7), and the possible rearrangements 

 of the four items present fair substitutes for some of 

 relativity's energetics. Omitting those details as nearly 

 obvious, follow up the more vital comparison which parallels 

 that of equations (19, 22). On usual assumptions, electro- 

 magnetic energy, its time-derivative, and the assignment of 

 -activity to magnetic energy and to electric energy are j" : 



M>=Wt'W;Ii'-i5(Md=T. + ;|; ] 



(I /M , r-?rm dv m /c 2 + v 2 \dv~\ Vm / c 2 + v 2 \ dv n I 



it (Mi) = v b di + i {t=?) Jt\ + v U {?--■?) dt J \ 



dv m /e 2 + v 2 \dv~] mv dv 



v m (r + v z \dv~\ mv a 

 t A ~ 2 \c 2 — v 2 )dt}~~ 4 a 



• • (29) 



Examine more narrowly the second member and the third 

 of the last equation. The former is co-ordinated instructively 

 with the subdivisions in the bracketed member of equal ions 

 (18) which Abraham's electron fits. One stabilized asso- 

 ciation of magnetic activity and power is common ; and so 

 is the type of the (electric) remainder, if ((dm/dt)^) displaces 

 (dm/dt). The last member of equations (29) adheres to the 

 primary conception of equations (1) to (7) ; the final sub- 

 tractive term harmonizes with their supposition of partial 

 conversion into other energy-forms of work done by (P). 

 The kinetic energy of any "weight-mass" (mi) must be 

 rated mechanical. Perhaps the current doctrine that the 



* The last two members of equation (28) and the verifications under 

 equation (24) give the foundation for a previous claim (I.), first lines o\' 

 p. 436. 



| See, for example, Richardson's ' Electron Theory of Matter' (1914) 

 pp. 217 sqq. 



