Magnetic Induction in Iron and other Metals. 459 



tan r = - — , . . . (19) 



rL — 7rr + z sin — ■ 



if we put y __ 87rc 



oft"' 



By help of (19) I drew curves on squared paper to show 

 the connexion of tan 6 r and Z for the values r = l, r=3, r = 5; 

 the curves are of course hyperbolas. In this way was found 

 a value of 6 r which, when substituted in (15), enables a value 

 for x to be determined such that the epochs obtained from 

 the experimeutal curve of Dr. Ewing could be most nearly 

 reproduced. 



The nearest approximation I could get was 



Z=22, ^=5°-4 3 3 =2°-l, 6> 5 = 1°-1, and a = l-33. 



Thus, when these respective values of x and 6 r are sub- 

 stituted in (15), we get as the harmonic constituents: — 



-1-33 s/ * - / o_ \ 



-1-33 4/^ / fr- \ 



D 3 e V -sin(^H-15°-3) 



Moreover, if we substitute in (18) the value of Z just 

 given, we can find D r . Thus 



Di = cx 1*214; 

 D ;3 =rx0-4; 

 D 5 = cx 0-223. 



Also, if we identify the calculated amplitudes of the 

 harmonic constituents with those found from the experimental 

 curve, we have 



-1-33. /~" 



D l€ V 180 =1521; 



—1-33 /'^ 



D 3 e V 180=468 ; 

 -r- 33 \/So=273. 



33 V 



J), e ' i8U sin 



ISO 



