542 PROCEEDINGS OF THE AMERICAN ACADEMY. 



This paper discusses first, with the help of mechanical analogies, a few 

 simple and familiar cases of circuits without cores, with the purpose of 

 emphasizing some facts to be met with also when cores are present, and 

 then gives a number of diagrams obtained from the photographic 

 records of oscillographs in circuits which contained large electromagnets 

 some with solid and some with divided cores. Changes in the induc- 

 tances of a circuit which contains one or more electromagnets often 

 involve the moving of comparatively large masses of metal, and it 

 is obviously impossible to make such changes instantaneously even 

 though they may be carried out in intervals which are not long rela- 

 tively to the time constants of the circuit. In solid cores, also, eddy 

 currents tend to mask the effects of sudden changes in the conforma- 

 tion of the circuit, and this, with the fact that the susceptibihty of the 

 iron depends not only upon the intensity of the present excitation, but 

 also upon the past experiences of the metal, leads to considerable 

 differences in the magnetic behavior of a circuit according as it does 

 or does not "contain iron." The diagrams show these differences and 

 illustrate some typical conditions which arise in practical work. 



It is well known that the final flux of magnetic induction through 

 a solid iron core is not determined by the intensity of the excitation 

 alone even when its magnetic condition at the outset is given, but de- 

 pends in many cases upon the manner of application of the given 

 excitation, — whether it be made suddenly, by small steps at intervals, 

 or by slow, continuous rise. The diagrams are interesting in this con- 

 nection because they show that when the core is fairly well divided, 

 the forms of two distinct portions of a current curve, interrupted by a 

 sudden change of inductances, are often almost identical with corre- 

 sponding portions of two current curves obtained without any such 

 interruption, the one with the original inductances, the other with the 

 final ones. 



It may be well to consider briefly at the outset the very simplest case, 

 the familiar one of a single circuit, without iron, of fixed resistance, 

 r ohms, and of inductance originally equal to Zo henries, which contains 

 a constant electromotive force of E volts and is carrying at the time 

 ^ = 0, a current of Co amperes. At this instant {t. = 0) let the induc- 

 tance begin to change according to some law, and progressing always 

 in the same direction, let it attain at the time T the given value Li, 

 after which it shall remain constant. 



In order to illustrate graphically the effect of making the given 

 change in inductance in longer or shorter time intervals, it will be 

 convenient to use three rectangular axes for t, C, and T respectively, 



