in Conducting Sheets and Solid Bodies. 19 



0=co cos Kt; and therefore we may write the couple 



For a thin shell, p is large, and the damping is regular. 

 Secondly, for a solid sphere, 



a d<p 0/ 



And, as before, we have approximately, if 

 P = A r n Y s n cos s<fr, 



the real part of which corresponds to an angular velocity 

 &) cos Kt. In fact, to our degree of approximation the whole 

 solution is the same as before, with cocos Kt written for co. 



For a sphere whose moment of inertia about a diameter is 

 I, in a uniform field whose magnetic force is F, we have the 

 equation of motion 



I rf +m< ^ + 15^ flF i =0 ' 

 where 



m = K 2 I ; 

 therefore -i^I 2 * 



£ = 0* 15<71 cos**, 



when the damping is small. So that the vibrations decay 

 owing to electromagnetic action at logarithmic rate -. , , 



Tji2 1O0\L 



which is equal to ^ , where d is the density of the sphere. 



bcrad 



F 2 



If we write 7, - = \, we have the general solution 



baad ° 



^ = coe~ kt cos £\//e 2 — X 2 ; 



thus the motion will just cease to be vibrational when \=/e, L e. 

 when 



F 2 =6<mZ*;. 



For copper, taking « = 3 centim., <7=1640, d=8'8j and 

 ac = t 1 q, which is thus our first order of small quantities, we find 



F = 160, nearly, 



or about 340 times the Earth's magnetic force. 



2 



