CHABACTEB OE THE AEMOUB-PLATED SHIPS OE THE EOTAL NAVY. 309 
this force therefore would, within 5 per cent, in the case of a steel sphere, and within 
1 per cent, in the case of a soft iron sphere, neutralize the effect of the earth’s magnetism. 
5. Spherical Shell. 
~Let p be the radius of the outer surface, q of the inner. 
There will be a distribution of free magnetism on the outside similar to that on the 
sphere, but in the case of the shell 
, 8tt / , o 3N 
I=xF L-± 7 3 . 
47 r 87r c, /, q 3 
1+4 "+t-s x ( 1_ ^. 
There will be a similar distribution of free magnetism, but of the opposite kind, in 
the interior surface, such that if I' represent the amount of blue magnetism on a unit of 
surface at the north pole of the interior surface, 
I'=*F 
4tt 87T 2 / q 3 \ 
1+4 ” + s"T x ( 1_ ?) 
Hence for an external particle the coefficient will be 
1 1 
K-) 
II 
-s 
1 
, „ 4.7T 8t r 
i+^'+T'T 
P / 
l-l 
47 r 
1 + T“ 
p ~ 87T7C 
nearly, if x be large and 1 — ^ small. 
If 1— ^ be infinitely small, the intensity both outside and inside at the North end 
is = 1 + • F, or the same as in a plate, as might be expected. 
Mr. Barlow found that in a shell of y^th o: 
the effect was -f that of a solid sphere, whence 
1 
150 2 
150 8ttx 
112-5 
or x— 
7T 
= 35-8, 
which agrees closely with the previous results. 
