﻿52 Prof. G. A. Schott on the 



calculated for the electron with e = 4*65 . 10~ 10 E.S.U. and 

 e/cm = l'77 . 10 7 . When the new units are used we must 

 replace the factor m in (2), 2e 2 /3c in (3), c 2 m in (5), and 

 2ce 2 /3 in (6) and (7) by unity, the quantity ft in (2) and (5) 

 by v, and the velocity c in the expression <r — v 2 in (3), (6), 

 and (7) by unity. 



4. Introduction of a new time-variable. — Using the new 

 units we put * 



T=rv(i-^jji (8) 



We shall use an accent to denote differentiation with 

 respect to the new time-variable r, but for the sake of brevity 

 shall use the symbol w to denote the velocity relative to r. 

 Then we find in succession 



v=w,/(l -, 2 ) = 7 ^L- 2) , whence ^(1-r*) = ^^ 



w (ww )w 



• • _ w f/ ( ww")w + 3(ww') w' + w' 2 w _ 4(ww f ) 2 w 



v -(l + ^)^"" (l + ^ 2 ) 5/2 (1 + w 2 ) 7 ' 2 * 



Substituting these values in the expressions (2), (3), (5), (6),. 

 and (7), we find 



G = w, (9) 



T= v /(l + ^)-l, • (11) 



o ( ww _l^ = r . . . 02) 



R=w' 2 -^ (13) 



(ww') 2 

 1 + w* 



With these values the equation of motion (1) becomes 



w '_ w " + R w = Fi/(l + i<; 2 ). . . . (14) 



Similarly the equation of energy (4) becomes 



T'-T" + R(T + l)=(wF) (15) 



The curious similarity of form of the last two equations is 

 worthy of remark. 



* E. E. p. 292, 



