New Reading of Relativity. 35 



equation (4) are of necessity carried with it into all combina- 

 tions that accent it. With its aid, standard dynamics and 

 O.G.S. measure have led straight to these results for the 

 frame (F). They are formally identical with what relativity 

 would allow, for parallel conditions ; though demanding for 

 them also wider validity. Emphasize that (m ) being a 

 special value here, its identification with " Minkowski mass " 

 requires constancy in the latter*. Modifications of equa- 

 tion (4) on this score or on others can be introduced, but 

 they are not of immediate concern. It can remain plastically 

 true, if held open to revision by further experimental success. 

 The equivalence of consolidations in equation (5) through 

 addition and through multiplication is a feature with notable 

 consequences f . 



What proves to be one main thread of the subsequent 

 analysis joins on to an elementary problem, whose results we 

 quote in part. Consider a straight path, constant propelling- 

 force (P) and mass (wii)* aR d a resistance (R) proportional 

 to (r 2 ). There is a terminal speed (t^). With notation and 

 detail 



P R 7 „ „ a 



— = a; —=kv 2 ; *'i=t; 

 mi m i * 



the equation of motion 



.p. -r> dv P — R dv ,_. 



dt nil dt v 



by simple recasting yields the forms 



r = ... 2_^'n ; K= ^2 — 3 7/,-; ' ' ' \P) 



'1 



v*dt' vf-rfdt 



p_ dv niiV 2 dv P _ dv v 2 dv 



~ mi Jt + r : 2 - ? dt ; m x " dt + V^tf dt' ' ( J) 



But equations (7) apply legitimately to net field-action com- 

 bining a constant propelling field (a), and an automatically 

 excited resisting field (/.'t? 9 ), the acceleration being then 

 characteristically independent of the " body coefficient " (mi). 

 And any actual physical linkage of («, k), when (k) changes 



* See note \, p. 32 ; and cf. Silberstein, p. 194. 



t Among- others this : it favours grafting- forms due to variable inertia 

 upou a root-idea of constant (m ). Relativity's " complex " of force has 

 the magnitude of (T ) : e. g., for the tensor of its quarternion ; which the 

 so-called " rest-system " then renders coincident with a u Newtonian ' 1 

 tore.-. Cf. Silberstein, pp. 193-4. The same thought applies at equa- 

 tion (11) below. 



1)2 



