Force- Transformation and Proper Time. 653 



{£) must be in general a variable ratio. Whereas no parti- 

 cular factoring can modify the total energy-flux (dW/dt), 

 •certain coordinating conventions will reserve some latitude 

 about details under eacli adoption of factors. A momentum 

 (Q) involves inertia (m), velocity (V), and tangential force 

 (T), while (E) is invariant* : 



2E.=-Qi/; QeWj T=j t (mv'). . . (2) 



Kegarding (E) as a function of (m, v') ; and defining 



i\ = zv ; Qjl = m 1 v i ; Q 2 = fi'e = fiv ± ; . . (3) 



the indispensable connexions among the group derived from 

 equation (1) can be symbolized by 



dW_ dE / -dKdm\ 



The definite (constant) inertia (mx) is uniquely linked 

 with (Tj), for which alone the partial (dE/dm) vanishes, 

 and the principle of vis viva remains valid in the sense 

 belonging to rigid dynamics. The force (T 2 ) is unique 

 otherwise; its partner being (Y), the complementary partial 

 (dE/di/) is suppressed. There is a second unpartitioned 

 absorption of energy, also into kinetic form, but with an 

 accompanying variable inertia (//). This may be viewed 

 as another sense of the vis viva principle. The recurrence 

 of (c^d/n^dt), with differing plausible values for (ji'\ has 

 made itself noticeable throughout previous developments 

 regarding electronic energy f . 



The two abbreviated forms in equation (4), together with 

 the two general members, yield the following relations 

 among others : 



V 1 



,/ dv' ,dm\ m . ,„ dm m , dv 



This amounts to establishing a transition between two 

 activities (energy-fluxes), derived in turn from a variable 

 inertia and from one that is constant. Either value of the 



* Cf. (III.), p. 102 ; and eq. (12, 18). 



f See (HI.) passim ; it is plainly one goal of relativity's combinations. 

 An important effort to construct a physical meaning for this expression 

 is added by Sir J. J. Thomson, Phil. Mag. June 1920, p. 079. 



