308 STAFF COMMANDER EVANS AND MR. A. SMITH ON THE MAGNETIC 
direction making an angle a with the axis, p being the radius of the sphere, is 
1 + 
4ir 
~3 : rr 
(3 cos 2 a — 1) to North , 
„3 
F 3 sin a cos a from axis. 
47T r 3 J 
1+ ¥* 
Hence, at the pole, but outside the sphere , it is 
8?r 
J x 
——7 t”F to North. 
1+ T* 
At the equator, and anywhere inside the sphere, it is 
4.<7T}£ 
F to South. 
The sphere, therefore, acts on external particles precisely as an infinitely small magnet 
of moment . n 3 F held in the direction of the lines of force. 
Here we may pause to observe the very remarkable fact that while the effect of a thin 
rod or plate magnetized in a direction parallel to itself is nearly proportional to z, the 
effect of a plate magnetized at right angles to its plane, or of a solid sphere, is almost 
independent of the value of z. 
Thus, taking Webee’s observations, the values of z for steel and soft iron are nearly 
5 and 36. A soft iron rod or thin plate magnetized in the direction parallel to itself 
would therefore have more than seven times the effect of a steel rod or plate of the same 
dimensions ; but in the case of spheres the proportion of the effects would be 
5 . 36 954 . .993 
5-24 ' 36’24 * yy0 
= 24 26 nearly; 
or the effect of the hardest steel sphere is within 4 per cent, of the effect of a similar 
sphere of soft iron, and within 5 per cent, of the effect of a similar sphere of a substance 
infinitely susceptible of induction, and hammering such a sphere would make no per- 
ceptible difference in its effect. 
At the equator outside, and anywhere in the interior, the force of the sphere, as we 
have said, is 
4t»1 
xF 
to South; 
1 + • 
