New Reading of Relativity. 41 



symmetrically, for equivalent activities now " internal " to 



(tv/*«)T.'=«.T.; (22) 



where the factors in the second member are first any pair 

 that satisfy the equality. Then equation (20) repeats in the 

 form 



Vo 'T ' = r(u)T ( ,(v c -y). • . . (23) 



Since (T„) is a force in (F) at the speed (r c ), equation (5) 

 holds ; so 



T„ = » W 3 (rjJ (24) 



Both equations (22, 23) are satisfied when (r c ) is determined 

 by the conversion rule that pursues the track of relativity : 



v e = i ; t'o = ; y(u)(v c — it) = r ; 



^T(rJ) = ^(r^.. (25) 

 And provable corollaries of this assumed value are 



T.-(l + ^)"T.' ; T.'= 7 «(«)T.(l-^) ; 



I.'-^VM^ (26) 



The mathematics fixes upon equation (23) as committing us 

 already to the consequences in equation (26), by requiring 

 for consistency that (r c ) which equation (25) calculates. 

 The symmetry of (F, U) postulated by relativity is in fact 

 seen to lnrk in equation (23). The logical sequence may be 

 reversed and begin by superposing the third of equations (26) 

 upon equation (5). Whatever is hypothetical in equation (23) 

 is reflected in equation (26), and rice versa. 



It would not be overbold analogy, as the outcome thus 

 far shows, to anticipate through the second form of equation 

 (16) the factor that " reduces " from (U) to (F). In the 

 view of: local action, (T , T ', T a , T a ') of an electromagnetic 

 statement would involve effective strengths of a "motionless 

 field" (F-space, medium), and of a " convected field " (U- 

 space, medium). But whereas physics has long labelled (Wj) 

 without hesitation " apparent/' the notation here need not 

 be stressed hastily with similar decision. When relations 

 are ascertained clearly between mathematical sequences whose 



* Connect equation (10) with this invariance, and one similar in 

 equations (19). 



