1505 
If the steps ¢ are not infinitesimal, this simple way of calculation 
cannot be applied any longer. In that case we write the series 
M=2(M, — M, + M,...—Ms,) — M, = 
2mh?w* | 1 = 1 L NN 1 | 
ata. (Eee) (Beast) Ap 
2mhwf 1 1 1 | mh*w? 
—— | — - +... 4- —— =U Se eee 
EER ee ple. DA 
1 
By using the properties of the gamma-functions we can expand 
o o 
= 
Oe : ; JF, 
the series in square brackets in ascending powers of gas however 
i 2e 
the result is rather complicated I shall not write it down here. 
c. We may also suppose the external field to be produced by 
a current which decreases as a damped oscillation, as is the case 
with the discharge current of a condensator. Then we may write 
A, = H, .e—-— if x is the period and & the damping. This gives 
Hie 
Mn = M E = nl he | ; 
Va bis 
If now Ho, is still just somewhat greater than /, so that we may 
put Ho, = h, we obtain 
/ 
lh? 
Sn 
Eee 
1 
[1 — e2ke 1 etks |, — Pp ke] —m+ 
om i? se 
I m + =) (e2"= — 1) 
oe eke $1 
For very small damping this becomes 
h? 
M = mkt (: IS ) j 
HEL? 
If on the contrary 2,4; differs only very little from /, so that 
we can put Hs, — h, M becomes negative and equal to 
h? 
m ( 1 — — (ek) 
Eee 
en En 
e2kr TEN 
4 h? 
For very small damping this becomes J/ = — mkr (1 — = If 
1 
Hop nia Hop 5 ° N 
h=— 5 >» M is approximately zero. Generally however and 
principally when the damping is rather great so that e.g. Hs, is 
considerably higher than /, while //, 
h, M will have a certain value, either positive or negative. In such a 
41 18 somewhat smaller than 
