218 Mr. C. V. Boys on a 



the ring is a direct measure of any total change in the strength 

 of the field in which it lies, no matter by what law it changes 

 in strength. If at the end of any rapid change the field 

 remains of any strength, the motion of the ring will be rapidly 

 stopped by the well-known damping action, of which I shall 

 have more to say later. If, however, the field sinks to zero, 

 or nearly so, the momentum acquired can be measured and the 

 original intensity determined. 



The current induced in the ring will of course react on the 

 field and bend the lines of force in such a manner as to hinder 

 their passing through its edge, that is to delay the change of 

 included field-intensity ; but the impulse is independent of 

 the time or the manner in which the field changes, so it can- 

 not be effected to any extent by this cause. 



Since the impulse given to the disk during any element of 

 time is 



__7rr 3 sHsin2« dK 



the total impulse while H changes between and H will be 

 __7r?^H 2 sin2« 



If the moment of inertia of the disk be M, and the torsional 

 value of the supporting wire be T, the angular velocity o> 

 generated will be 



7rr 3 6'H 2 sin 2a 



•= ps — ' 



and the throw of the ring will be 



£_ 7r?* 3 sH 2 sin 2a 



~ 8/VMT 



The action on a disk may be considered as the sum of the 

 actions on the several elementary rings of which it is com- 

 posed, for there cannot be any tendency for any part of the 

 currents to cross over the elementary circles. The impulse 

 therefore on a disk of radius r and thickness s will be 



7rr*sW sin 2a 

 l 62p l 



and the impulse on a disk of radius r 2 with a concentric hole 

 of radius r x will be 



ttsH 2 sin 2a / . . x 



— 327— «- r ' ) - 



