310 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



quantity of electricity which flows in the test coil. Of course, the in- 

 duced current may last with an extremely feeble intensity for a long 



iY j? time, but in any practical case 



it is easy to set a limit of time 

 after which no sensible flow will 

 occur. 



If A is the throw which would 

 be caused by an instantaneous 

 discharge of Q units of electric- 

 ity through a galvanometer at 

 the beginning of motion, A' the 

 throw caused by an instantane- 

 ous discharge of \ Q units at the 

 beginning and another discharge 



SECONDS. 



FlGUKK M. 



Figure M shows two reverse current ^°, ^ °., \ ~ i . °T 



rvpsfnr „, tornHiai mMm *t. Th P final of * Q umts seconds later, and 



curves for a toroidal magnet. The final 

 strength of the current was the same in 

 both cases, but the applied electromotive 



A" the throw due to a steady 

 current of Q/t units intensity 



force was twice as great in the case of the lasting from t — to t = r, then 

 curve B as in the case of the curve A. A , {& ^ ^ ^„ and ^ ^ 



turn is less than A. Occasionally one encounters an induction 

 current which has a form much like that indicated in Figure N by 

 the curve KLG, and we shall find it interesting to determine the 

 ratio A" /A for one or two practical cases. It is well to notice that 

 the second member of (42) depends only upon the ratios X = a/p and 



FlGUKK N. 



S = t/T, and not at all upon the other constants of the instrument; 

 for if we write z = pt and I=/(t) = </> (z), we shall find that 



i2tt6 



/VZ7T6 /»2tt5 



I <f> ( z ) • e Xe • cos z • dz I <f> (z) ■ e\s • sin z • dz 

 = ^-s=s- - 0= — -r=r- — , (47) 



p'ln6 



jo *&' dz 





