Energy and Relativity. 101 



The specification that (P) should account completely for 

 the influx of energy makes equations like 



5=P; W=$Pds; .... (15) 



one a total derivative and the other integrable. But after 

 having recognized that forces (P) can present themselves 

 through partial derivatives of momentum, a discrimination 

 about time-integral is seen to be needed there. Before clear 

 physical indications have fitted together acceptable values of 

 momentum and of energy, tentative factorings of (P) place 

 it in either class as a derivative of momentum. Note how 

 the complete activity (wF) is compatible with these groupings 

 and others : 



/ i\ 2 dv\ _ I m^r \dv 

 lh W-v 2 It) ~ W-v'Jdt 



V s/ Vl 2 -v 2 ) V V v/^v 2 dt J \vx-v) U + v dt J 



The last member is guided by equations (10) ; the third, 

 .fourth, and fifth members make (P) a partial derivative. 

 The supplement to (P) changes with the possible pair 

 ( m 2 5 v 2) segregated ; that is, according to the more plausible 

 selection of momentum (or quasi-momentum). This flexi- 

 bility is added to that afforded by the zero-parenthesis and 

 arbitrary factor in equations (7) and elsewhere. In effect, 

 a liberal leeway in quantitative adjustment to experimental 

 data is permitted, while equation (1) is retained as proto- 

 type *. One turning-point is found to be the discovery of a 

 " scale-factor " (z) that meets some condition connectable 

 with the. energetics of equations (11) ; when (v 2 , m 2 , T) are 

 furnished otherwise ; for example, making 



In determining the physical elements for a cycle of 

 problems to which the sequence of equations (1) to (16) 

 ■can be adapted, the unifying feature being the terminal 

 velocity (r t ), some margin of independent choice at equa- 

 tions (1, 16) and at equations (3, -1, 7) can be foreseen. 

 * Compare previous remark on this matter, (II.)? V- 35. 



