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PROCEEDINGS OF THE AMERICAN ACADEMY. 



would be 0.5 • Cq, if the change in the inductance had been instan- 

 taneous. 



Figure 8 shows in TW the relative changes in the current in this 

 circuit from t =^ to t = 7] when T is one tenth of a second, and in 

 TZ the changes when T is one one-hundredth of a second. If the 

 change were instantaneous the course of the current in one tenth of a 

 second would correspond to the line TRU. 



Figure 8. If in a certain inductive circuit, without iron, the inductance 

 be instantaneously doubled, the course of the current in the next tenth of 

 a second will be TRU. TW shows the current if the doubling be brought 

 about by a continuous change going on at a constant rate during the whole 

 interval. TZ shows on a different time scale, the course of the current for a 

 hundredth of a second, if during this interval the inductance be changed at a 

 constant rate which results at the end in its being doubled. 



We may next consider the somewhat less simple circuit indicated in 

 Figure 9a, consisting of three parallel branches each of which has self- 

 inductance, but no two of which have mutual inductance. Let r, Vi, r^ 

 be the resistances of the branches, L, Li, Lo their inductances, E, Ei, E^ 

 the constant electromotive forces of the generators in them, and C, Ci, Ci 

 the currents. At the time t = 0, when the currents and the inductances 

 have given values, let the inductances begin to change according to 

 given laws each of which can be expressed by an equation similar to (1), 

 and let them attain, at the time J\ other given values, which they 



