166 Dr. J. Hopkinson. [Mar. 10 r 



Fig. 1. 



from this curve in equations (5) and (6), and so obtain the valuer 

 of x and y to a higher degree of approximation. If the values of & 

 were expressed by Fourier's theorem in terms of the time, we should 

 find that the action of the iron core introduced into the expression 

 for x and y, in addition to a term in cos (27r£/T) which would occur if 

 a and x were proportional, terms in sin (27r£/T) and terms in sines- 

 and cosines of multiples of 27rt/T. It is through the term in 

 sin (27r£/T) that the loss of energy by hysteresis comes in. 



A particular case, in which to stay at a first approximation would 

 be very misleading, is worthy of note. Let an attempt be made to 

 ascertain the highest possible values of a by using upon a trans- 

 former a very large primary current, and measuring the consequent 

 mean square of potential in the secondary circuit by means of an 

 electrometer, by the heating of a conductor, or other such device. 

 The value of a will be related to the time somewhat as indicated by 

 ABCDEFG in fig. 2 ; for simplicity assume it be as in fig. 3 ; the 



Fig. 2. 



