

Proper Time, and FresneVs Coefficient. 657 



The results are patterned after a " f orce-invariance for 

 frames (U)." It is relevant to completed comparison, that 

 Newtonian dynamics and relativity control these similar 

 resources. Nevertheless, no such steps of algebraic mani- 

 pulation, subject mainly to notational consistency, can 

 acquire physical standing in either plan, except by the one 

 test. 



Under the supposition z=y(v ), we approach the assump- 

 tions for the Lorentz electron and the frame (F); but 

 retain as before a constant inertia (mj, whose ratio to 

 the standard (m ) can be assigned later. Resume from 

 preydous notation and values : 



Tx = m l7 3 (fo)$° ; T„ = "-% ; m'== m a M 5 vT, = c*^L *. ( 18 ) 



OLt )11^ 01X 



dd, from equations (12, 9) : 





dE _ 2 dm' . 1 dE __ 1 dE 



dt ~ C dr' <y(v ) dt ~ i\c ) dr ' 



dfj,' 



dt 



-«■*£=<>. (19) 



Whatever condition reduces to zero the first parenthesis in 

 equation (10) makes the difference (in! 1 — [jl) constant. This 

 requires 



v 2 ( r 2 \ 



mi z 2 = (m^ 2 ) -~ -f Cl ; ci = m^y 1 — -^ J = m l 



V fl [^7 2 W]. • (20) 



r urther, 



I f 2/ \ 1 \ 1U \ V o I C m \ V o 



p = mi (y\v )-l) = -fl—tf fl = fi'~ = * ; 



c — v ?! y c - — Vq 2 



jxc — ??ii7(r )r . . (21), 



The u transverse mass ,; and the momentum of relativity's 

 Lorentz electron emerge thus simply from general expressions 

 through an assumption regarding activity. Remark that 

 (l — Vo 2 jc 2 ) is an intrinsic factor in the resistance problem, 

 and in equation (20) ; its equality with (1/c 2 ) is introduced 

 by a condition open to revision. 



To class " multiple forces/'' like (~T 1 , c'T/) in equa- 

 tions (13), as being of "Minkowski" type suggests bringing 

 the original (I\, T\') under a " Newton " type ; indeed the 

 latter are part of normal Newtonian dynamics. The work 

 and the impulse of the two force-classes offer several points 



* The general bearing of the ''resistance problem" and its terminal 

 velocity is to be kept in mind : (II.), p. 35 ; (II 1.) passim, but especially 

 eq. (6, 22). Distinguish two uses of the symbol (v 1 ). 



