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LVIL Force-Transformation, Proper Time, and FresneVs 

 Coefficient. By Prof. Frederick Slate *. 



FOR electronic conditions, Xewtonian dynamics and 

 relativity based on a Lorentz transformation are 

 reducible to parallelism as mathematical schemes. The 

 former introduces variable effective inertia where the 

 latter treats inertia essentially as constant f. Moreover, 

 relativity's method here can be assigned to widely inclusive 

 grounds. Any attempt at a detailed physics by resolving 

 further the data of energetics must countenance some 

 flexible factoring of energy and of energy-flux in its 

 tentative dynamics. Lagrange's equations are known to 

 admit such alternatives ; and no cogent reason exists for 

 bounding the range of that proper freedom by their 

 algebraic type %. As an implication of the present analysis, 

 we achieve a broader outlook, the gain of whose perspective 

 is worth seeking. 



" Let an energy-transfer (TV) of calculable amount be 

 associated with a working speed (v) at the close of an 

 interval (0, v), the frame being one among a "legitimate 

 group. " An interval like (?*, v) is covered by a difference. 

 Then it is mathematically permissible to express (TV) 

 variously as a doubled kinetic energy (2E), and to prepare 

 thus for corresponding mechanical analogues. Accordingly, 

 write a series of equivalents ; not exhaustive, but meant to 

 exemplify useful forms : 



!/*')0 2 )=(/*7) (« 2 )- • • (1) 



The first parentheses in each factoring separate an assumed 

 inertia-coefficient from a squared velocity; auxiliary velo- 

 cities (vvz, nz, c, etc.) are then one inherent feature of 

 any such series. The last two members employ a reduction 

 to standard (or terminal) velocity § ; (??ij) is a constant; 



* C om mimic ate d by the Author. 



+ Slate, Phil. Mag. vol. xxxix. p. 43o ; vol xl. p. 31 ; vol. xli. p. 96. 

 These papers are cited as (I.), (II.), (III.). 



J Generalized velocity and momentum are defined, and have "been 

 used practically, to realize this possibility. Incidentally, Abraham's 

 early success in extending Lagrange's equations to the electron may 

 find partial explanation here {Theorie der Elektrizitat, vol. ii. p. 177 

 (1908)). 



§ Introduced at eq. (9) of (III.). Notice also eq. (10, 11. 12) and the 

 application in eq. (20, 21). 



