New Reading of Relativity. 45 



the initial inertia were (m ! = j(a)m ), which continuity of 

 value with our assumptions for the standard (F) would make 

 it. The result that one vital difference hidden under identical 

 kinematics in (F, U) is due to altered inertia affecting work 

 provoked early comment. In one dynamical analysis of 

 relativity, it was shrewdly proposed as a chief postulate *. 

 The accompanying pairs of interchanges between (v ' + i/ y 

 » , Vo) and (vj, v c , v c — a) must certainly not be ignored. 

 Yet the commonsense reason for those is also one key to 

 Einstein's redefined simultaneousness. The same value of 

 fluxion time (t) as an argument in time functions defines 

 Newtonian simultaneous values of them. In this meaning, 

 the auxiliary (vj) and the observed (v ) are simultaneous ; 

 also (v c , v '). In addition, simultaneous observations in 

 (F, U) would of necessity be recorded as (v , i? — u), or as 

 (vj + u, v '). It is clear that a pair of such observable data 

 (VeZ + w, v ') would not realize, for instance, the simplicity of 

 equations (26), if (v '-\-u) were substituted for (i\.) there. 

 But if time-slip (lag or lead) between straightforward C.G.S. 

 observations in (F, U) be regulated under a known law of 

 velocity-change, the paired values (v c , vj) requisite for sim- 

 plicity are also attainable as observed. The same thought 

 coordinates equation (13) [Newton] and equation (21) 

 [Einstein]. Further, because this "propagated simul- 

 taneousness 55 and the Newtonian allowance for "apparent 

 force" establish identical reduction factors; for Newtonian 

 velocity and for Einstein's force-law respectively ; it seems 

 fairly proven that the two systems of procedure are effectively 

 alternative — for the electronic case discussed. 



The reciprocal relations between the dynamics of the 

 standard frame (F) and that formulated for any one frame 

 of the group (U) are to this extent conclusively settled. It 

 remains to examine how much of such reciprocity persists, 

 when neither of the compared frames is (F). This will 

 confront the conditions where relativity can do best service 

 through its simplifications. Choose then two comparison 

 frames (U', U") with origins (0'. 0") and with translations 

 [u ', u") relative to (F), still colinear with (v ) of course. 

 Denote observed velocities of (m) now b}' (y, v\ v"), so that 

 v = v >+ ll '= v " + u " ; v '-. v " =u "— u \ m (35) 



A reasonable notation for other quantities will also distinguish 

 them by accents. Thus simultaneously for (m): 



T,/ = T „(l-$); T.» = T„(l-!£). . . (36) 



* Frank, Wied. Ann. (1912) vol. xxxix. p. 093. 



