Fisr. 1. 



316 Prof. A. Schuster on Magnetic Precession. 



— 2pcoi& cos 6 and 2fjum^ cos 6. These forces are of the 

 nature of electric forces, and their effects may be calculated 

 if the components of i are known. 

 3. In the simplest and most 

 important case, the currents are 

 such as to produce a magnetic field 

 identical on the outside with that 

 of a uniformly magnetized sphere, 

 the axis of magnetization passing 

 through the equator. Let Q 

 (fig. 1) be the axis of magnetiza- 

 tion. The currents will all lie in 

 planes at right angles to that axis. 

 If A S is a portion of such a current 

 and we write : 



a, for the arc QS or Q A ; 

 <f), for the angle SPA; 

 6, for the colatitude P A ; 

 a, for the radius of the sphere ; 

 the current function will be 



al cos a = la cos <f> sin 6. 

 Hence the component currents are : 

 Easterly component 



= -^ Icos 



a> 



(2)' 



<£sin#= — I cos <f>cos6 . . 



Southerly component 

 j 

 = -= — -a j , — I cos (f>sin#= — I sin 6. . 



These are components of currents per unit length of linear 

 cross-section at any point ; to obtain current-densities we 

 must divide by t, the thickness of the shell through which we 

 imagine the currents to flow. If we write % and ^e for 

 the electric forces acting towards the south and east 

 spectively, we have therefore 



^ s = -2^1 . cos 2 6 cos (f>/t, 

 M/j, = 2ftft)I cos 6 sin tj>/t. 

 Now 



re- 



2 cos' 2 6 cos <f> 



and 



2 cos 6 sin <fi =cos 6 sin <f> — 



cos <f> (1 + cos 2(9) = cos <f> + -tq (i cos $ sin 26), 



d 



sin 6 d<f> 



(i cos <j> sin 20). 



