FERROMAGNETIC DISTORTION OF A WAVE 



339 



can be made practically coincident with the corresponding maximum 

 in the magnetizing force. 

 Writing 



/ = T + X, (29) 



the lower-frequency component in the vicinity is expressible by the 

 Taylor's series 



Q cos qt = Q 



2! "^ 4! 



-Q 



q\ 



cos qr 



f]f q^ 

 3! "^ 5! 



sin qr. (30) 



Over one cycle of the higher frequency this component is very nearly 

 linear, so its variation in this range is 



— 4A = — ItkP sin qr. 



(31) 



Since r has been so chosen as to be an integral multiple of lir/p, when 

 equations (29) and (30) are substituted in the magnetizing force given 

 by equation (2) it becomes 



h = P cos p'K -\- Q cos qr — \Qq sin qr. 



(32) 



Its value referred to a new set of coordinates, B' , h' , with their origin 

 at the junction of the major and minor loops is 



h' = P(l + cos p\) - 2^(\ + 



p\ 



{^^) 



According to Madelung's findings previous minor loops will not 

 influence the one under consideration, so its lower branch will proceed 

 toward the upper tip of the major loop as indicated in Fig. 2. A 

 transformation of equation (1), simplified by the use of Rayleigh's 

 relation, then gives for this branch 



Bi — iJLoh' + vh'". 



The upper branch is 



Bi' = [/xo + 4KP - A)]/// - vh'\ 



(34) 



(35) 



The small portion of the major loop traversed during the last of the 

 cycle may be expanded in a Taylor's series 



B' = B' (0) + h 



,dB, 



dh 





+ 



(36) 



