542 
PROFESSOR H. LAMB ON ELECTRICAL 
x_*_ 1= 
n/x + n +1 
x„ 
(95), 
approximately. The currents in the sphere are then given by 
2? rip 2?i + l .p? ( d d \ 
— -:—ry h/w—z — X„, v=&c., w=& c. . 
p np, + n +1 \y dz dy 
■ (96). 
’ 1 3 principal part of the disturbance in the field, due to the presence of the sphere, is 
given by 
n(n + l)(fi — 1) d R 2n+1 
«i= . &i=&c., c 1= &c. 
»/x + w + l dx r 2 “ +1 
(97). 
These terms express the effect of the induced magnetization of the sphere. The 
effect of the induced currents is (under the circumstances supposed) small in com¬ 
parison. 
Next let us take the case of Ht large. It is to be noticed that owing to the occur¬ 
rence of the factor /x in (93) this condition is satisfied by very much smaller values of 
the frequency than the case of a non-magnetizable substance. We then have 
W . / 7 \ &V 
WX'=‘ ' 
In + l.^ n (hr) 
47r ' v //V Ait 2n + + (f 1 — V)n^r n {ldK) 
The factor of X» is by (70) 
2n + l 
&V 
R\« +1 
Att n{p — 1) + ikll \ r 
approximately. If we assume 
gq(r—Ti)+ig(r— K) 
n(p —l) + gTt=D cos e 
<yR=D sin e 
(98) , 
(99) , 
this may be written 
_ 271 + 1 .SV. V” +1 e? (r-E)+i { j(/-E) + ? -e } 
2tt D \r 
. ( 100 ). 
From this result we draw conclusions similar to those of § 5. The depth v within 
which the maximum intensity of current falls to 1/e of its surface values is 
"= 2 ”ll= V.Up 
In the case of iron we have, using the same data as before, i/='078 centim. for a 
frequency of 4000, or v^='78 for a frequency of 40. The value of v is thus, for the 
