Alternative View of Relativity. 437 



In this aspect of "Einstein's theorem," which equations 

 (13) in effect reproduce with altered meaning, it furnishes 

 a rule for making compensations in activity, for disturbed 

 value caused by passing over to a new frame (U). It is 

 self-evident how the procedure can be reversed, correcting 

 thus a distorted estimate in (F) of observations (or measure- 

 ments) made in (U). Reading then the established rule for 

 superposition of colinear " Lorentz transformations" in this 

 novel sense, any linked succession of repeated distortions 

 from original data can be traced through our frames (U), 

 and the net compensation at any stopping-point determined. 

 The proof is simple that the net effect (disturbance) is nil 

 whenever the chain is a closed one. 



Passing from activity to a similar analysis for tangential 

 force, differentiate the first of equations (13) as a beginning. 

 This gives 



S=k)(i-3]1(V).. . . d5) 



Hence, quoting the easily proved connexion 



M^h^> • • • ^ 



= 7F) 7(k0 ^" ' (17) 



We are brought thus to what is formally identical with 

 the " transformation of Minkowski-f orce " (K) : 



Y (»)(i-"-)t, = ( 7 („)T:); 



[T.=K(F); 7 («)T;. 3 K'(U)}, . (18) 



not overlooking that Minkowski's "proper time" (and not 

 " local time") replaces fluxion-time (t). All of this illuminates 

 vividly the corresponding statements according to the method 

 of relativity, and is readily seen to put in hand a complete 

 control for a new aim of the whole system of calculative 

 detail that flies the flag of "non-Newtonian mechanics." 

 The particulars of that restoration to the older allegiance 

 need not concern us here, beyond showing how the work- 

 equation is equally tractable. 



Let the interval begin at (v=zu). Then for the apparent 



