34 Prof. F. Slate on a 



by a product of inertia and acceleration *. Equation (1) 

 does not calculate the same value of (T ) from the second 

 member, when (v ) alone is altered there= Neither are 

 values of the acceleration equal for differing (# ) but equal 

 assigned (m, T ). This equation of motion is not fully in- 

 variant thus in either aspect of its double function. But 

 even under other conditions that do satisfy the " Newtonian 

 transformation," the freedom due to its force-invariance 

 should not be overrated. Not only do kinetic energy, 

 momentum, activity, change with velocity-values, but since 

 the relative path is affected, so also is the distribution of the 

 same total acceleration into its tangential and normal parts. 

 Therefore entire continuity across transfers among " legiti- 

 mate frames " will require some composite scheme. The 

 fuller scope of invariance for relatively fixed frames can be 

 worked in here ; at times with less than explicit credit for its 

 help, as will be seen later. 



Inquiry is still limited to progressive rectilinear motion of 

 an electronic particle (m), in part because this case makes 

 vital contacts and gives cues for less particular suppositions. 

 To lay out its province for relativity gradually by induction 

 runs truer to scientific form in any event ; we are not 

 declaring a creed. 



Adopting the " deformable electron " brought forward by 

 Lorentz and supported by experimental data, the rule is 

 taken over : 



dm mv dm mv. 



m = mo —--' . (4) 



o 



dv c 2 — v 2 ' dt c 2 —Vo 2 ' </ & 



Retain : 



(Z 2 \~" 

 1 ~7j '' m ° ~ Wvo==0 ; c - li A' h t-speed in (F). 



Then all the work may go into field-structure, as we noted, and 

 equations (1, 2, 3) become, if v o = (v) at £ = 0, 



T — "V + *=#) if =»'t 2 W Tt = m °rM Tt ; • (5) 



Ao = C 'W' W « = c2m o(7(^)-7(")o) (6) 



Whatever physical particulars record themselves through 



* Silberstein, p. 195 ; Laue, p. 5 ; illustrating the need of some such 

 remark. 



