

Proper Time, and Fresnel's Coefficient. 661 



for the weighting factor (y(u)), and remembering (dt = dt r ), 

 the last equality stands in exact parallel with 



T.'= m l7 (r,) §+0'o"«) i o ( m ^^V- ' ( 34) 



Next use (*;, k') with those multiples (Kp,. K P ', K„', KJ of 

 (T , T a , To', T fl ') which have been subjected to a " Minkowski 

 transformation "; they are all of the same type as (T ) itself f. 

 The combinations disclose another phase of symmetry : 



dv ' dv ' ) 



Cl<-o wl | 



dv dv Y (35) 



«'Ku'=7Ci*>*i7(wi)'^; * K « == i( u ) m M v o)-£-°- 



Since y(X).= 7(V), ^' lie common factor y(-«) signalizes again 

 the fully reciprocal relations of (F, U) to transfer back and 

 forth. The effect otherwise of (/c, «') is to cancel from each' 

 force's companion the term depending on variable inertia t. 

 Put together equations (17, 33, 34), bringing out once -more 

 the vital divergence from relativity through employing 

 a time-variable uniformly in all frames. Whatever the 

 influence in other directions of such comparisons, they 

 will not prejudice judgment to undervalue the mental 

 vision which detected this fitness of local (or distorted) 

 time to restore an invariance in magnitude, as well as 

 preserve a mathematical type. 



By drawing upon the sequence of equations (17), the 

 original equation (9) can be employed to recalculate 

 for transfers among frames (U). That repetition passed over 

 as nearly self-evident, new conclusions remain to extract 

 from the comment attached to equation (5), that coordinates 

 one activity (vj 1\) with an adjustable set of activities 

 («' T). To grasp its full scope, and to weigh habitually all 

 its alternatives, may tend to clear perplexing or obscure 

 questions, when the energy is assigned in advance, to which 

 that equation shall be accommodated. Exhaustive inquiry 



* Laid down by war of fundamental premise in (II.), e( I- (I-)- 



f See (II.), p. 43. They will not be confused with "Minkowski 



forces," like ^sT,, s'T/) in eq. (13) above. 



X Returning closely to the assumption of (II.), p. 37. This point 



gains in importance, when the intimate bearing of Fresnel's coefficient 



upon the physical action is conceded. 



Phil. Mag. S. 6. Vol. 41. No. 244. April 1921. 2 X 



