100 On the Earth's Magnetic Field. 



The electrostatic potential due to the ring of doublets is 



AV=2irANw sin«^- T £r.P»M . P»(0). 



On replacing N by nydady in order to obtain the potential 

 due to the ring o£ cross-section ydctdy we obtain, on inte- 

 grating from a=0 to a = 7r and from j/ = () to ;/ = «. the 

 potential due to I lie whole sphere, in the form 



V=2»im&T rr.S-I.P.W{»i.+T.'}, 



where 



P 77 " , f "" d 



I /( — j sin 2 a . P 7l (a)rf«, En = 1 sin a. cos a. ^ .1' 



Jo » » ca 



On evaluating these integrals we obtain, for the polarization 

 F at the equator and on the surface. 



47rF=-^,=2-27™*7i. 

 aou 



{{')) The magnetic field due to a sphere in which the a& 



the molecular magnets are orientated in favour of the 

 direction of the axis of rotation. 



In terms of the notation on page 94 we find for the 

 moment per c.c. 



M =jnm. 



This corresponds to a sphere magnetized parallel to the axis 

 of rotation, and lo an intensity jnm. The case is thus one 

 ol'a uniformly magnetized sphere, and the magnetic potential 

 at the point, r . 6 is 



„ 1 " z ■ 



12= ., 7T 2 jnm co< r. 



n 4 a*. . ., 



1 1 ~ ^ 7T - inrn sin v. 

 .) r ' 



Physical Laboratory, 



I'l, •■ I ni\ ersitv of Sheffield, 



Mnrch L3, L912, 



