1080 
from which we find the solution 
uw Mt +n. 
Further it follows from these equations that p and y are periodic 
functions of the time, so that the system is stable. 
If Pest, Qe’ and Reist are the components of the electric force 
Hest in the beam of light, M,, 1, and M. those of the electric moment 
of the molecule, both respectively along the X-, Y-, Z-axis of the 
rotating system of coordinates and if 
Dia Ok g=P—71Q, 
we find the relations: 
e? ie’ ; piet 
M=" sin(, jd Ee 
m e e 4 
(s+M) -+ —— —(s—M)? + —— 
( ) Amr? Gai) EED 
es gie” pie i 
M,=— cos(9, + Mt) == —_— pi(s+M jt = ss ei(s—M )t 
7 Mm 3 
—(s-+ ML —— —(s- MY +- —~ 
re) 4imr* ( ) WS, 
ge? R : 
M, = — ——____— est 
m 3/8 e? 
Ene abe 
1l6mr* 
From this we find for the mean moment M of the molecule (in 
the supposition that for all molecules r and J/ have the same value): 
Bn ih 8 1 1 2 
fe, 
7 22 313 
erp BM 2 & 
= —s* enen 
4mr* 16mr® 
Amr? 
The index of refraction is then determined by 
s( —_—M? )+ 4e 
a Sa Ne? 1 Amr? | 1 s? 
SE EE RO I aa ZT . 
3m A Ee Wij ee 3Y Be? sy de? 3 
4mr* 4mr* 16 m7? 16 mr?) - 
e? 
Now, while giving to — the value that belongs to cathode rays, 
m 
we are still free to choose a value for 7 and M and we may do 
this in such a way that the equation changes into that of J. Kocu: 
n= tr 1S 6T 042908. M08 32: 
Indeed, if we put: 
« = 16 m7’, wes zede — xy. 
