

Energy and Relativity. 99 



'The identifications Vi = c, m\ = »i , bring the first of equations 

 (7) into formal parallel with results adopted for the Lorentz 

 electron and enlarged for legitimate frames in relativity, 

 with (m = y(v)m ) replacing (ml). One basic proposition of 

 our treatment is thereby corroborated ; but also the question 

 is opened, in how far (m) is & physical quantity. Conceding 

 the physics of equation (1 (b)) to be artificial, an admixture 

 •of fiction in the subsequent dynamics is unavoidable. Nor 

 is it dangerous, unless pseudo-values cause misconception of 

 the physical process *. 



Return to equation (3), and observe the possible general 

 reading of this work as a kinetic energy, measurable by a 

 changing multiple of (m^ at a standard speed (i^). The 

 multiple is invariant under all choices of (~) ; yet the 

 influence of (z) elsewhere may leave its determination an 

 important detail for each separate application resting on 

 equations (1, 3, 4). The vogue of the contractile electron 

 .has led to particularizing 



dv dv \ 



zmi Tt = m dt- ■ ■ ' (8) 



But the unique advantage of that choice remains a matter 

 for deeper inquiry ; at least one alternative will be con- 

 sidered presently, as well as the foundation on which decision 

 must stand. 



The permanent factor (vj) is a resource in making certain 

 forms valid indifferently, whether inertia be constant or 

 variable, after standardizing all momentum and kinetic 

 energy at the terminal velocity by appropriate reductions. 

 Define two " reduced inertias " (/a, jjl) corresponding to any 

 (m 2 , y 2 ) by 



fiv 1 =m 2 v 2 ; /j!v l 2 =m 2 V2 2 ; showing fi = — p. . (9) 



These reductions are similar to those of force-moment and 

 moment of inertia in relation to axial distance. Further, 

 it is evident how they expand the idea of equations (5, 6), 

 and move toward making broadly representative what was 

 invented more specially for the Lorentz electron. 



* See (II.), p. 36. The same thought recurs at equations (22, 27) 

 below. The reminder is in place, perhaps, that no pretension to close 

 .any such issue is here intended. On the contrary, the aim everywhere 

 is to open some escape, where earlier conclusions might be fallaciously 



■ confident. 



H 2 



