418 Dr. Silvanus Thompson on 



specimen, or the rate (per unit of magnetizing force) at 

 which the magnetization was proceeding ; and this would at 

 every stage be proportional to the probable number of groups 

 that were coming into alignment, and to the magnitude of 

 the aligning force. The expression would thus assume the 

 form 



d33 (tiy 7V> 



<m ' 



where a and b are constants, the one denoting the maximum 

 value of cffi/cflfe, the other the particular value of f£ at which 

 that maximum is reached. The difficulty of integrating this 

 expression is not the only objection to it ; for it would at 

 best give only the ascending curve of magnetization, and 

 additional assumptions would need to be made before it could 

 be adapted to express the descending branch. 



§ 2. Hysteresis loops, as found by experiment, can how- 

 ever be considered from a wholly different standpoint. 

 Whatever the law connecting 33 and $?, the area enclosed by 

 the loop measures the amount of energy lost in the iron in 

 the cycle of magnetic operations ; the value, in ergs per 



cubic centimetre, being -r- [ 33 . (fik. Let it be assumed that 



4?r J 

 the variations of $? are such that 33 passes from the value 



+ 1$i to — 33 x and back, through a regular cycle of values 

 according to the expression 



33 = B : cos 6 ; 



then, in general, the variations of ?l, though they go through 

 a cycle, will not be capable of being expressed by any such 

 simple form, otherwise the shape of the hysteresis loop would 

 be simply an ellipse, or, in the limiting case, a straight line. 

 The fact that the magnetizing current (and therefore the 

 magnetizing force) in choking coils and transformers does 

 not follow a simple sine or cosine function is well known to 

 all electrical engineers. In these instruments, if worked 

 from a source of alternating electromotive force in which the 

 wave-form of the supply is a pure sine-curve, the wave-form 

 of the flux in the core, and therefore of the flux-density 33 in 

 the core, will also be a pure sine-curve having a lag of exactly 

 90° with respect to the impressed voltage curve. Or if the 

 impressed voltage is expressed by the equation 



V = V sin 0, 



the flux-density will be given by the equation 



33 = — B cos 6. 



