178 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



A mere inspection of these values shows that the value of ^ can be 

 computed with an accuracy much more than sufficient for any practical 

 purpose from the first two terms of the series (85), if t is as great as 

 xioth of a second, and from the first term alone if t is as great as 3^0 th 

 of a second. Let ^0 represent the first term of (85), then 



<^o = 



but 



400 ttZTq e-G-i768i 

 (0.78032)(0.20508)' 



400 



= 2499.55, 



(0.78U32)(0.20508) 

 which differs from 2500 by about ^V^h of one per cent only. 



(88) 



If there were no eddy currents in the iron, the total induction flux 

 through the rods which make up the core would be 



^' = TTfia-H' 



5) 



(89) 



and if O were the strength of the current in the exciting coil at the 

 time ty we should have 



^/,aW- "^ = -tvC' = ~l';S'' (90) 



and 



where 

 and 



dt 4 ttN 



h = w/4 7rWV/x = 6.332573 + 



(91) 



(92) 



In the case under consideration we should have very nearly 



0' = 2500 ttHo e-«-33^573< (93) 



4 ^NC = H', = H, e-e-3325T3/. (94) 



