374 MAGNETIC INDUCTION. 



The force is sensibly zero at the equator, and at the pole its value 

 is three times that of the force of the field. 

 If the coefficient p- is near unity, and we put 



we get in like manner 



3 



In the interior of a hollow sphere, the force is 



9/x 

 If the coefficient /* is very great, we may write 



i 



If the coefficient /* is very near unity, and we again put /A = i + a, 

 we have 



I -- E -- :I _ 2 _ a2(l _ /8) . 



* 9 



A small magnetised needle introduced into the sphere would 

 determine there a new induced layer, which would be superposed on 

 the first, and the distribution of which can be easily calculated, for 

 the external action of such a needle is equal to that of a uniformly 

 magnetised sphere ; but the action of this new layer will always be 

 parallel to the magnetic axis of the needle, and will not influence its 

 direction. The oscillations of this needle depend then only on the 

 resultant actions of the external field, and on the layers induced by 

 the field itself. 



