CIRCULAR COILS OF RECTANGULAR SECTION. 429 



and from Table II. 



A = (1 + 4xOU3125- 16x0-0009766) a, 

 = ri09375a. 



R = (1 + 4 x 0-0078125-16 x 0-0008647-64 x 0-0000069) r, 



= l'016973r. 

 so 



,= log. 



. 



"1 '016973 



(where <f> is given in Table I.) 



= log, 4 + ^ + 0-086965, 

 = 2-973259, 



and 



(8A 

 log^-2 = 4 irax T07970. 

 L\ 



LORENZ'S exact formula gives 



L = 4 T ax T08137. 



Thus the error in this case is 1 part in 650. 



When the comparison is made in less extreme cases we find the agreement with the 

 Lorenz formula very close. 



Thus when the length of the solenoid is equal to its radius () either of the methods 

 of this paper give 



L = 207453a, 

 while LORENZ'S formula gives 



L = 207463a, 



showing an error of 1 part in 20,000, and when the length of the solenoid is half the 

 radius we obtain 



L = 28'85332rt, 

 as against the Lorenz value 



L = 28'85335a, 



showing an error of only about 1 part in 1,000,000. 



