PEIRCE. — MANNER OF GROWTH OP A CURRENT. 523 



The Effect of Variation in the Permeability of the Core 

 of an Electromagnet upon the Manner of Growth of a 

 Current in the Coil. 



We may add to the foregoing theoretical discussion of the effects of 

 Foucault currents in a solid core the permeability of which has a fixed 

 value, a few words upon the manner in which a current might be 

 established in the coil of the magnet described in this paper if there were 

 no eddy currents in the core, as, of course, there really would be in an 

 actual case, unless the core were divided. 



After the form of the dotted curve D P in Figure 4 had been deter- 

 mined with considerable accuracy (the observations of different days 

 agreeing with each other almost exactly), the curve was plotted on a very 

 large scale by means of a needle point upon thin sheet zinc and an accu- 

 rate template was then cut out ; with the help of this and a metal straight- 

 edge, I measured as carefully as I well could the slope (A) of this curve 

 for a large number of different values of the current (i) . Since 2.823 X 10 9 

 times an ordinate of the D P curve shows the total flux (F) through 

 the coil for a current represented by the corresponding abscissa in 

 amperes, then, if there were no eddy currents in the core and no time-lag 

 in the magnetization of the iron, the building up of a current in the coil 

 under the given circumstances on the application of a steady voltage E 

 in a circuit of total resistance r ohms would be dominated by the ecpuation 



E— ri= 28.23\-^ t (38) 



(or) ^.= (28.23) jA_, (39) 



in which the second member is now a known function of i. I plotted 

 this function and determined by aid of an Amsler's Planimeter the values 

 of t for a number of values of i in the actual case, where E was 84.0 and 

 r = 13.55. Figure 9 shows the building-up curve (Q) which this process 

 yields, and also the actual curve 13 carefully reproduced from an oscillo- 

 graph record. 



If we were to define the inductance of the magnet in a condition repre- 

 sented by a point R on the dotted line DP in the statical hysteresis 

 diagram, as the ratio of the total flux which then passes through the coils 



13 J. and B. Hopkinson, The Electrician, September 1892; J. Hopkinson, Wilson 

 and Lydall, Proceedings Royal Society, Vol. 53. 



