40 Prof. F. Slate on a 



modified from the observed value (vj = v — 11) as equation (18) 

 denotes. Put into other words : Einstein's rule yields a 

 distorted speed in (U) which compensates exactly the dis- 

 tortion of force into (IV) from (T ). What may well be 

 called a process internal to (U) is made in so far indifferent 

 about the supposition of equal accelerations. Plainly the 

 same rule holds between (U) and any frame (F') fixed 

 relatively to the original (F) . But observe how our derivation 

 locates that compensation within the experimentally verified 

 scope of equation (4). As a matter of algebra, we obtain 

 the four forms : 



v «= — ^r v ° = f> 7"( M )( ?, c + w ) = ; 



1 _ UV ° 1 _L UVc 1 ^ 



c 2 c z c L 



They all connect some Newtonian velocity of (m) relative to 

 (0, 0') the origins of (F, U) with Einstein's specification of 

 it. None of these alternative aspects is released, however, 

 from its source in a strictly conventional expedient to the 

 same end, which is here just nakedly announced, but which 

 the Lorentz transformation has masked under the Einstein 

 variables. 



The completer activity (v T ) in (F), expressed also by 

 means of (v c \ T„') is 



A ~v o T o = y\u)T a Xvc' + u). • • . (20) 

 Therefore 



T, = 7»T a '(l+ "-f); y(«)T.'-*;%V(fl/). (21) 



Equations (13, 21) being demonstrated corollaries of equa- 

 tion (5), they are pivotal relations between the u observing- 

 frame" (F), and the auxiliary quantities (appearances) in a 

 comparison frame (U). 



Continuing, we may undertake to render equation (13) 

 more fully reciprocal between the frames (F, U). Instead 

 of depending upon observations in (F),let them be primarily 

 taken in (XT), the distinctive notation being (dv '/dt, v \ T '). 

 Correlate the force denoted by (T</) on the one hand with its 

 associated kinematics and on ihe other with a supposititious 

 partner (T ) in (F). The plan of equation (18) gives 



