Alternative View of Relativity. 435 



analysed cases, the second integral corresponds to changes 

 of internal energy ; which may be nearly reversible (elastic 

 distortions) or practically irreversible (heat due to collision). 

 Adaptation to the electronic conditions must follow up the 

 former alternative. Before going further, remark that these 

 two items, though primarily separated in equation (5), may r 

 bd united by some artificial device : either the actual molar 

 energy may be attributed to internal energy and recorded as 

 such; or the internal energy may be entered fictitiously as 

 additional (molar) kinetic energy. Both coalescences are 

 only " book-keeping," exemplified also in the " two specific 

 heats " of a gas. Relativity will be found to have exploited 

 this open chance in handling energy-equations. 



It is vital to the suppositions of equations (2) that the 

 -activity must be affected by the term (udmjdt). Granting 

 that the force is (T ), we should recognize in a frame (U) 

 only (IV) and an activity 



K f =v'^ = {v^ii)ll a ^{v-ii)(T -u d ~\. . (6) 



Or intermediately, on any grounds recognizing (T ) at 

 invariant value, 



A"=(»- M )T =(«-«)(T < ,' + u^=«'T <1 '+m-'J. (7) 



Retaining the frame (F), adopt for it next the experi- 

 mentally suggested law for (m) : 



dm mv 



dm mv dv 







~dv ~ c 2 ^ 2 ' 



It ~7^v 2 dt 



■ ■ (») 



Writing 

 m = [m]v=o for the frame (F); and for any argument (z) 



■7(2)= (l — — 2 ) ; (c) being light-speed in (Fj ; straight- 

 forward algebra yields 



T = m^)(l+ ? -^ 2 )|' = m o7 '(tOj; (9) 



rT„=c^ ; W = c°m (y(v) - 7 (r.)) = sj/$ + [E]. (10) 



Noteworthy is the automatic vanishing of kinetic-energy 

 change from the result. This harmonizes with the claim that 

 electronic inertia is entirely electromagnetic as a corolla rv 

 of equations (8). The work would then be absorbed entirely 



2 F2 



