L78 



EEDINGS OF CHE AMERICAN A.I ADEMY. 



TABLK IX. 



m,'/ = 0.44168 

 ninh = 3.858 

 m s b = 7.0:]0 

 mj, = 10.183 

 w 5 6 = 13.331 



log &? = 0.79077 



log 3 3 - = 8.1946 

 log /3 4 2 = 3.5164 

 logj8 6 a = 3.7504 



BijJ = 0.78082 



m 2 - = 69.627 

 m,« = 197.672 



m 4 2 = 414.708 

 ;«;- = 710.884 



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 

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

 of a second. Let </> represent the first term of (So), then 



4>o = 



but 



400 7r/7 e -C176S< 

 (0.78032X0.20508) * 

 400 



2499.55, 



(0.78032X0.20508) 



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



(88) 





If there were no eddy currents in the iron, the total induction llu.x 

 through the rods which make up the core would be 



0' = wpaHPg, 



(89) 



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

 time t, we should have 



,///' _ »• . HI 



iB '>=- a .c>=- 



and 



where 



and 



tit 1 jtN 



h = w/4 7r-.V-V/-/x = 6.332573 + 



In the case under consideration we should have very nearly 



0' = 25OOx# o e-*- 882CT8< 



(90) 

 (91) 



(92) 



(93) 

 (94) 





