310 STAFF COMMANDER EVANS AND MR. A. SMITH ON THE MAGNETIC 
The coefficient for the force on a point in the interior of the spherical shell is 
-T(I-I') 
An 
8?r / 1 ^ 
— x| 1 5 
= -F 
i_£ + A 
p 8nx 
nearly, when z is large and 1 small ; and the Avhole directive force in the interior 
will in that case be 
1 + 
tH) 
and therefore if the shell be thick it will be nearly zero, the residual force being inversely 
as the thickness ; if the shell be thin, the loss of force will be nearly proportional to the 
thickness. < 
6. Infinite cylinder , magnetized at right angles to its length. 
Radius = jp. 
The intensity of red magnetism on a point in the surface at an angle a from North is 
_ xF cos « 
i= 27TX+1 ‘ 
The effect on a red particle at a distance r, r making an angle a with the North and 
South axis of a perpendicular section, is 
— ■ ~FScos2« 
2ttx + 1 r z 
. to North, 
Z7TX-}-l r* 
fin 2os . . . to East. 
7. Infinite cylindrical shell. 
External radius jp, internal radius g. 
The distribution of free magnetism will be similar to that on the solid cylinder, 
except that, as in the case of a spherical shell, the free magnetism on the interior sur- 
face will be of the opposite kind to that at corresponding points of the external surface. 
For the external surface (red at North), 
I=*F 
1 + 2nx j 
(*- 
p*) 
1 
1 + 4ttx + 4ttV- | 
(i. 
1) 
