1306 
and as wa, =w, + (2n—1) a, wong = wv, + Anw, 
face ole 
Hu = 
5 w, + (2n—1)w , w, + 2nw 
and further 
h? h? fw, + (2n—-1) wi? 
Mo, =) A A 
(H2,—H,)° De p= A fw, <b (2n—1) of? 
h? h* we, +- Zn" 
Me 4 =m) 1 =| ==) 1 ~-- 
. (Hani + Ho) IFE + H, (w, +5 2na)i? 
Now we have 
M=2(M, — M,+ M,—...— Ma) — M, +2 Map = 
= ie We, EE EE + 2mh? = Liaw COEN 
n=0 VE Ie H, Ge, i + 2nw)}? aa Le E-H, „he, TE (2n Doi] 
(TE Slime w 2p 
— m| 1 — —————__| + 2m| i - - 
(FE + w,H,) ES ay Wo) 44 H HE 
If the steps w are small, we can replace the sums by integrals 
which gives 
2p W2p+2 
Vu mh? (> wedw ; mh? | we dw 
5 eed ee + fH, w)? wo) (fE—H,w)? 
wi Wa 
bw,” hw? att 
—_m| 1 — ———____ | + 2m] 1 2) 
LE (fE + w, H,)’ (fE 4 En Wad H ) 
For the calculation of this expression we shall suppose H, to be 
small with respect to the magnetic force of the alternating current, 
which must be the case as Jong as 2 H, <|Hor| — Hana: where we 
suppose the difference of Hs, and H2,4; to be small with respect 
to each of these quantities. In the expansion we therefore omit the 
terms with powers of //, higher than the first. Further we shall 
neglect w with respect to the resistances ww. So we obtain 
jj hw? “opt WH, 4 , 
M=m)\ 1 ri EP a. ap BE (w pl — W, ) 5 
By introducing the above derived boundary-condition, w,=— 
jEw 4 RA 
== SE and by putting 2,14; = w‚, which is allowed, as the 
OUR 
Ww 
— at the most, we find 
Wip 
error caused by it will be 
1) Making use of the properties of gamma-functions we may also in this 
= 
I 
, : : : if 
case expand the summations in ascending negative powers of ‚ where the 
steps w must he treated no longer as infinitesimal. 
