New Reading of Relativity. 33 



indeterminateness now ; while the fullest employment of 

 their united suggestions must mark the sanest course in 

 adjudicating questions there, or in regard to gravitation. In 

 that interest, this paper turns solely to detecting simple links 

 of interrelation between the two methods. Whatever yokes 

 standard dynamics and relativity for joint service based on 

 complete reciprocal consistency — this the new line of approach 

 seeks. Preferential choice may nevertheless remain open to 

 individual opinion ; or indeed it may prove to shift with the 

 class of problem in hand. Some resettlement of rating in 

 this quarter is scarcely avoidable, because the extension to 

 variable inertia certainly upsets at least one allegation. The 

 fact looms up at once that the rigid dynamics (of Einstein's 

 theory) becomes now a convergence -point of two more general 

 forms, under approximations through dm/dt=0 ; c = c© ; 

 respectively. It is not tenable that broader Newtonian 

 dynamics itself reduces directly from relativity by neglecting 

 in the latter terms that contain powers of (1/c) *. 



Those expressions for tangential force, activity, and work 

 laid down in the previous paper lie then at the heart of 

 the matter. For convenience we quote them, with minor 

 changes : — 



t & /r\\— d d'\, dm 



T ° = dt^=dt( mVo ^ m M^ Vo T{l ; ' ' « 



*°~ lol °-dt\ 2 ) + i < l ° dt ' W 



W ^ v T dt=[V]+i\ r »- "dt. 

 Jo *=* Jo at 



(3) 



The subscript letter (o) tags a quantity, here and elsewhere, 

 as " observed," or as calculated without artifice from ob- 

 servations. The equations are written for one standard 

 frame (F), always for standard signs and in C.G.S. measure. 

 Plainly (Q ) symbolizes momentum, and (E ) kinetic energy. 

 So long as the dynamical process mirrors quantitatively one 

 of pure mechanics, nothing hinders a mixed reading for (m); 

 it can cover narrow weight-mass and inclusive inertia, with 

 (Q , E ) read to correspond. 



In equations (2, 3), the "Principle of vis viva" has gone 

 by the board, along, with an exclusive measurement of force 



* Of. Siiberstein, p. 115; Lane, Das Relativitatsprinzip, p. 157 j and 



others. 



Phil. Mag. Ser. G. Vol. 40. No. 235. July 1920. D 



