New Reading of Relativity. 47 



Equation (14) records the special value of (T„') for that 

 rest-frame to which relativity concedes unique prominence 

 through a coincidence in magnitude for the two force-types 

 ("Minkowski" and "Newton") and a peculiar " rest- 

 acceleration. r Analysis of the transition from (F) to a 

 rest-frame (R) in those aspects detects three stages : 



(a) (/hanging Minskowski-force into Newton-type. 

 (/>) Cancelling a factor (y 2 (u)); or Qy 2 (v)) transiently 



undistinguished from it; with some freedom 

 among assignable reasons, 

 (c) Restoring the magnitude (y 3 (V) dv/dt) ; now as 

 acceleration in (R) under the sliding-scale of 

 units for time and length. 



A mathematically colourless regrouping of factors led to the 

 important quantities (v c \ v r ) of equations (18, 25); its con- 

 venience has wide range. But such fully interchangeable 

 forms are often unequal I}' accommodated to physics. Equa- 

 tion (5) presents in effect this same rest-acceleration as 

 incidental to a (probably fictitious) fusion of force-items. 

 Only an inflexible view about constant inertia can force upon 

 relativity the result of (c) as an acceleration. In comparison, 

 is the latter not artificial? What is worse, it is superficial 

 as well, if it obscures that inclusion of rest-frames in the 

 *? shift process " common to many coordinate-systems and 

 describable as a parameter-variation *. In that feature, it 

 enforces the thought attached to equations (10, 11), and 

 prompts a directer interpretation of rest-frame calculations, 

 though the formal results stand uncorrected. 



VCe build upon a more general relation for any frame (U) 

 and specify a momentum (Q L ) determined from a velocity (v x ) 

 and an inertia (m^ through 



Qi = m 1 y^i)v 1 = (m 1 y(u))v 1 =:7n 1 (y{ii)v l ). . . (42) 



This introduces the same weighting factor as equations (30, 

 31, 33) and it is written out to suggest a double possibility : 

 associating (y(u)) Ay ith either (mi) or (v{). Regarding (Qj) 

 as a function oE (u, v{), its exact differential and its total 



* For the elaboration of this idea see Slate, * Fundamental Equations 

 of Dynamics' (1918); Index, under "Shift," Shift-rate." Nothing but 

 unformed habit bars embracing in the same scheme continuous change 

 in the unit-magnitudes. Other seed-thoughts of the present paper are 

 to be found at pp. 38-43; p. 211 ; where the need of equations (I, 2, 3) 

 is emphasized. 



