CHARACTER OF THE ARMOTJR-PLATEE SHIPS OE THE ROYAL NAVY. 317 
or nearly, when * is large and 1 — ~ small, 
i_2 
l— i+— - 
p own 
Hence we see that the force of the shell will be half that of a sphere of equal 
external radius if * be 12 and the thickness of the shell be y-jjo of the semidiameter, 
or if *=24 and the thickness be 2-50 °f the semidiameter, or if *=36 and the thick- 
ness of the shell be 3-^0 of the semidiameter. 
Hence the effect of a tank ^th of an inch thick and 4 feet diameter would probably 
be about one-third that of a solid mass of the same dimensions. 
The effect of such a mass as a rifle-tower 4^ inches thick and 10 feet in diameter will 
be nearly the same as if it were of solid iron. Such a tower placed in front of a compass, 
as in the Warrior, will give a considerable +«, a — e of half the amount, and therefore 
increase \ and 3 D, and if the compass be neither much above nor below it, decrease the 
heeling error. 
Infinite cylinder magnetized perpendicularly to its length. 
A compass placed at a considerable height above the deck, near an iron mast or 
funnel, may be considered as acted on by a vertical cylinder or cylindrical shell of infi- 
nite length. If r be the distance of its centre from the centre of the compass, p and ^ 
the radii of the outer and inner surfaces of the cylinder, then when the cylinder is solid, 
M= 
2wk p 2 
1 + 2wn r 2 
and when the cylinder is hollow 
M= 2 ™ v 2 
1 + 2ww r 2 
( 1+2 w*y 
H) 
l + 4** + 4»V 
H) 
2wn p 2 p 
1 + 2 wn r 2 q 1 
p + 2wx 
nearly, if * is large and 1 — ® small. 
Also 
a = M, 
e = — M; 
hence * 
K = 1 , 
■ 2) = M; 
whence we get the remarkable result, that a long vertical cylinder or a cylindrical shell 
