FERROMAGNETIC DISTORTION OF A WAVE 



333 



h^^J{P + Qy 



4:PQ sin2 ^-—^ t 



X cos 



p + q , J P - Q p - 



(9) 



which is sometimes more convenient. The envelope of the wave is 

 represented by the two branches of the radical. If its magnitude does 

 not change much between adjacent maxima and minima of the wave, 

 these extremes lie close to the points of tangency between the wave 

 and its envelope ; the latter condition is the one necessary in order that 

 the envelope may be used to evaluate the extreme magnetizing force Hj. 

 This force acquires its values at the reversal points, which are situ- 

 ated at the zeros of dli/dt. Put into a form like equation (9) by the 

 same transformations as were used above, this derivative is 



yj = - <{pp + Qqy 



4PpQq sin2 st 



where 2r = p -{- q, 2s 

 only at 



X sin 

 = P - 

 rt + tan-i 



^' + '^"-'(iw^^"^') 



(10) 



q. Except when k = 1, this vanishes 

 \ - K 



1 + K 



tan st 



J^< 



(ii: 



j integral or null. Substituting equation (11) into equation (9) yields 

 the magnetizing force at the jth reversal from ^ = : 



H, = V(P + (2)' - 4PQ sin^ st 



• , , / 1 - k 



X cos jTT + tan~^ 



tan st — tan" 



1 - 



tan st 



1 + k / "" \l -\- K 



letting k = Q/P. Upon combining the arc tangents this becomes 



//. = pV(1 + /^)' - 4/fe sin2 5/ 



X 



cos JTT — tan ^ 



2{k — k) tan st 



(1 + y^)(l + k) + (I - k){l - k) tan2 st 



(12) 



According to equation (12) the magnetizing force and its envelope 

 are tangent at reversal points provided the arc tangent is always zero. 

 This it is if ^ = k, a trivial solution. By certain choices of these two 

 parameters, however, it is possible to keep the angle between any 

 reversal point and the nearest extreme of the magnetizing force from 

 exceeding any prescribed limit. The maximum value of the angle in 



