( 677 ) 
§ 10. The necessity of retaining this term may also be seen in the 
following way. In the fundamental equations (4) the coordinates are 
already taken relative to axes, moving with the medium, but the 
local time has not yet been introduced. We shall now do this, so 
that our independent variables become x, y, z and tf. We shall 
distinguish by accents the differential coefficients with respect to 
x, Y, 2, for a constant ¢’ from the corresponding differential coeffi- 
cients, taken for a constant ¢. We shall likewise denote by Div' and 
Rot’ operations, in which the new differentiations occur in the same 
way as the original ones in the operations, represented by Div and Rot. 
The formulae of transformation are 
dr Ke d EN 
de \da/ ae!’ 
a. a 
Ones 
and, if 9% be any vector, 
i . 
Rot I= Rot. UF [Up] « (21) 
6 
Using these, and introducing instead of D the new vector 
1 
J ’ =, Sha a . q e Ld ° hd . . 22 
we may write for the first four of the equations (4) 
Div' D' = 0, 
Dio’ §' = 0, 
Rot! 5 = An D', 
Rot) € = — fy. 
These formulae have the same form as those which, for a body 
at rest, determine €, D and 5, as functions of w, y, 2 and ¢; the 
rotation of the plane of polarization will therefore be independent of 
the translation, if the connexion between D' and € in one, and that 
between D and € in the other case correspond to each other in the 
same way. Now, if, according to (7), we put for the body at rest 
ili . 
oO oO 
or 
1 ; 
D— €=—¢—1 Ree, 
An c? 0 OG 
the said agreement requires for the moving system 
1 1 ) 
EE Se RG 
An c? Gr. o? 
