100 Prof. F. Slate on Electronic 



Then tangential force and power are expressible gene- 

 rally as 



rr _d , . dfjb dE d . d/J , . 



T = It ( m ,v^v 1Jt ; 2 Tt = Jt („W) = lY Jf . . (10). 



Also activity enters into the forms, since //,% = ??i 2 v 2 , 

 * T / dfi' dv 2 \ 2 dfi' d'Vo 



=Vt v- n "w =Vt W ■ • (11) 



The last member, vanishing for constant inertia, affords 

 some general measure for that rate of conversion — mechani- 

 cal energy into other modes. The first of equations (II) is 

 the plain equivalent of 



A=9 dE_dEdV dE 1/ A , ^dv 2 ' 

 dt £)v 2 dt 



dV_l( WdvA 



dt-2\ A+ fadt)' ■ (1 - } 



the partial derivative being taken with (m 2 ) stationary at its 

 epoch-value. When (m 2 ) is constant, this partial becomes 

 total ; the principle of vis viva appears. Under a fictitious 

 supposition of such constancy, the last member may be 

 viewed as containing contribution from some (pseudo) 

 potential to the work of other external force. For any 

 epoch when (/x = 0) there are particular coincidences which, 

 like equations (2'.\) below, have bearing upon the use of 

 rest-frames. 



An additional suggestion from the algebra associated with 

 terminal velocity is to utilize a kinetic estimate of future 

 action as potential energy, according to the conditions, for 

 intervals beginning at rest and at (r) : 



) V h dt } V = 2 ol ) ™ lV dv= ^ ^ 



(13) 



Then 



m l V ' 2 , TT TT C^l dv _r V ™ BUl ds 



_ 2 _ +Ul =D„ ; , _^_ =nh _ = l i; eT]= ___. 



• • • (14) 



which prepares the way for a possible consolidation with 

 electrostatic potential energy. 



