CHARACTER OF THE ARMOUR-PLATED SHIPS OF THE ROYAL NAVY. 305 
neons, the result on all external bodies is precisely the same as that of a certain distri- 
bution of North and South magnetism on the surface of the iron. 
To avoid the ambiguity which arises from the use of the terms “ North” and “ South” 
magnetism, we shall speak of the magnetism of the north end of the needle and the 
southern hemisphere of the earth as red magnetism, of the south end of the needle and 
the northern hemisphere as blue magnetism. 
I. An infinitely thin rod. 
Let S be the area of a section of the rod, F the component of the earth’s force in the 
direction of the rod, and x a coefficient depending on the inductive capacity of the iron. 
Each end of the rod will have a quantity of free magnetism =«SF, the magnetism 
being red at the north end, blue at the south end of the rod. 
If x, y, z be the coordinates, r the distance of the blue end, A, y', z' the coordinates, 
/ the distance of the red end, l the length of the rod, X, Y, Z the components of the 
earth’s force, then the effect of the rod on a red particle at the origin is a force 
Towards x=xS (jp—ps) 
Y+ “- 77 -Z 
To war 
Towards 
ds y=x S (y-y) j : 
*-* x+ / 
iT+'-fl®, 
-X+S^Y 
If the rod be infinitely short, and x’ — x=dx, y' —y=dy, z 1 — z—dz, l=ds, then force 
Towards 
dsl~x (x dx y dy z ds 
1 2. 
r ds'rds ' r ds 
dx\(dx dy dz \ 
Towards y—x S- 
dx y 
ds 
+ 
1 d J) _M Jf x+§A+M 
r ds 1 r ds J risj yds 1 ds ' ds y 
Towards 
If the rod be in the plane of x, y and parallel to the axis of x, then z, dy and dz— 0, 
and force 
Towards x- 
Towards y = ^ 3fX, 
Towards 2 = 0. 
If the rod be in the axis of x, then x==r, and the force is 
2 y^X in the direction of -\-x. 
If the rod be in the axis of y , then #=0, and the force is 
^Tf X in the direction of — x. 
The. product «S£X is called the moment of the magnetic rod. 
2 t 2 
