I 



318 Prof. A. Schuster on Magnetic Precession. 



r denoting time 



or 



dr Sir a 



This equation will determine the rate of increase of the 

 system of currents due to a given system of forces of corre- 

 sponding type. 



In the system of currents with OQ as axis, we may take 



IT 



the current-intensity I, at the points at which «=-^, to be 



the variable, which is now to be considered a function of the 

 time t. We also take 1' to be the corresponding variable of a 

 "system of similar currents having OR as axis. Introducing, 

 the forces due to the rotation of the sphere, we find that 



— =— col 



dr Swat ' 



<a__ 3 p 



dr Swat 



From which we deduce 



I = 1 cosI2t, 



I' = I sin XI t, 

 where H= ^— — , and I is the initial value of I. fl is the 



07T at 



angular velocity with which the whole system of currents 

 revolves. 



5. The rate of rotation of a system of currents in a 

 rotating spherical sheet which has been determined in the 

 simplest case, can also be calculated when the distribution 

 of currents is of a more complicated character. Let there 

 be a current function a<& on a sphere of radius a from 

 which the current- intensities are derived, so that if uq and u-e 

 are the currents in the direction of the axes of X and Y 

 respectively : 



d& d<P 



dy dx 



Introducing polar coordinates and taking dx — adS 7 

 dy = a sin 0d(f>, we find as in the previous paragraph that 

 the electric forces ^P E and "SPg acting towards the south and 



