'658 Prof. F. Slate on Force- Transformation, 



to work out. Consider first in (F) the force (K x ) and its 

 activity (Ai)'-: 



d 2 x cLv 



; Kj = mi -yy= y(vo)Ti ; Ax= -j- 2 ^ = 7(r )r 1 T ] 



Keeping equations (], 4) in view, determine the work (W^ 

 dor an interval (u, v ) : 



Jo <it \e -V <r— « / 



(9 9 \ 



C 2 -1' 2 C 2 -W 



= miC- 



= 



0/ / 

 6-(/X - 



-/V) 



= w 



-w 



[* 



= 7(j 



.)]■ 



(23) 



2 



c 2 

 '-*- 2 



= Wt] 



9 

 W— 



-r 2 

 u 2 ~ 



— »i 



i*l 



(24) 



C 





Therefore 



9 



9 »0 



1 c 2 — V 



which might be rated a trivial identity, did not our purpose 

 •connect it profitably with equations (6, 18)*. Denote 

 by (R') the product of the real terms in equation (6), 

 by (R") the product of the imaginary terms, and by (R{) 

 their sum Then for present values (R' + R") is seen to 

 ivpeat the first member of equation (24). Hence ^R,/^ o = 0, 

 .and referring to equation (7) also, 



dt o \y(r )> dt„\y(v„)) Ut Vy(r<>) ) ' [ ,„. % 



d I W \ , 2 dm' N dv„ ( - ' <• J 



Without elaborating every detail, this outline goes far 

 •enough to be convincing : it retraces essentially the "step up 

 and step down" with the factor (7(7*0)) which reaches 

 Newtonian activity in relativity's procedure — attainable 

 brevity or directness is not for the moment an issue. The 

 repetition with quantities belonging to a frame (U) is 

 so nearly routine that it is omitted. On any line of 

 analysis, the decision lies in the resistance problem, whether 

 at transfer a reduction factor shall be applied to values first 

 written for (F) or for (U). The turning-point is located in 



* Moreover, this " invariant function " is plainly an offshoot from 

 the fundamentals of the resistance problem. 



