486 
M,' = Mz cos wt — My sin wt = 
wakes: é |» . (o—s)+(@ + s)isin wt et ‘ (w +s) —(w —s)isin a 
mt] (o +8) (0 + 2)"] 
Part of the function between the | | is independent of f, part of 
it depends periodically on ¢ with frequency w. As @ has nothing 
to do with s (usually w is much greater than s) we can take the 
mean of this part with respect to the time’); the formula then 
reduces to: 
Sw —s Bos 
1 aa 
M,' = est . 
A 
In the same way we find: 
al 
iq E (21) 
3o—s ; Ss 
: — —————=, 2 a 
dep : 2 2) 
My S: elst . — - TT ls ZAREN | — 
| Ae Ce A (+9) On 
Finally : 
ML = gist “ a ok 
mn,” 
Resulting moment in the direction of 4: 
M = M,'. cosa + My .cos B + BE cos sf = 
3W—s 30+ 
s 
„| ot (eos a+ cos" 8) —— (cosa + cos") 
Ee 2 ls 2cos” Bs 
m (w—s) [n,2—(w EPT | (w +8) [n, =_(w 43)?] nan 2 —s 
The mean of this quantity for all possible directions of ie sys 
system is: 
5 ee he A 3wW—s Bos 2 
M=— est, - : 99 
a en len 
(as: 
me — none 9 1 
08" = Ch B == eas, 7 —— — 
9 
J 
For the index of refraction we have the formula: 
N,.M 
n?—| = 42 — 
ian gist 
(N,: number of molecules per cc.) 
Hence: 
: Pe 30 —s Jos (23) 
i Tt eae (w —s) nen (w+s)[n, TE Ae ns? 
1) Depue (l. e. S. 15) expresses this in a somewhat different way: in his 
formulae the axes of « and x’ make the angle a for ¢ = 0, hence he has everywhere 
wt-++2 instead of wf. Then the mean is taken for all values of the phase-angle 
z, Which gives the same result. 
