CHAEACTEE OE THE AEMOUE-PLATED SHIPS OE THE EOYAL NAVY. 307 
2. An infinitely thin plate of finite dimensions magnetized longitudinally. 
If F be the component of the earth’s magnetism in the plane, and perpendicular to 
any part of the edge, we shall have a distribution of red magnetism on the northern edge 
of the plate, of blue magnetism on the southern ; and if m be the thickness of the plate, 
then the force exerted by a part of the blue edge of length ds, or a red particle at a 
distance r, will be 
mds 
and the effect of the whole edge will be given by ordinary integration. Such a plate 
may in fact be considered as a collection of thin iron rods laid side by side, parallel to 
the direction of the component of the earth’s force which we are considering. 
3. An infinite plate of finite thickness magnetized perpendicularly. 
Let F be the component of the earth’s force perpendicular to the plate. 
The northern surface of the plate will have a distribution of red free magnetism, the 
southern surface of blue ; the amount of each on an element of surface —dS being 
1+47TX 
<zs. 
Each surface will exercise a force in a direction perpendicular to the plate of - F 
on a red particle anywhere situate. 
Hence the effect of the one surface, in the case of an external particle, will be to 
neutralize the effect of the other. 
On an internal particle, both surfaces acting in the same direction, the force will be 
Al TX „ 
— I to South. 
1+47 rx 
4. Sphere. 
The distribution of free magnetism on the surface of a sphere will of course be sym- 
metrical with regard to two poles and an axis parallel to the direction of dip, the free 
magnetism being red in the northern half of the sphere, blue in the southern ; the 
amount on a unit of surface at either pole will be 
I * — y 
I + Itt* ’ 
and at a point at the extremity of a radius making an angle a with the axis 
I cos u = — % — - . F cos a. 
1+f™ 
The effect on a red particle at a distance r from the centre of the sphere, and in a 
