522 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Suppose that in the case of the solenoid the resistance (w ! ) of the coil 

 alone, per centimeter of the length of the core, is such that when there is 

 no outside resistance in the coil circuit, s is 2.5, and let us study the effect 

 upon the manner of growth of O, of adding resistance wound non- 

 inductively to the coil circuit to such an amount (w") per unit of length 

 of the core that s becomes 1. 



From (35), we get 



Vrrs (->t 



-tSttto- (37) 



C^ a *H1 + s' 2 n 



and Tables VI and VIII show that the second member of this equation is 

 greater for every value of t after the beginning when s is 2.5 than when 

 * is 1, whatever the value of xi may be. The first member denotes the frac- 

 tional part of the final current which the actual current has at the time t 

 still to attain ; if, then, the intensity of the final current (6^ = Ejw) be 

 fixed, and if the current be built up in the coil circuit, first, when w = w' 

 and s = 2.5 and the value of E is correspondingly low ; and second, when 

 w = w' + w', s = 1, and E has a correspondingly high value, the actual 

 current will lag behind the final current by a smaller amount at every 

 instant in the second case than in the first. Again, if E be fixed and if 

 different values be given to w so that C^ has different values the actual 

 current lags behind the final current by a smaller fraction of the latter at 

 every instant when 5 is 1 than when s = 2.5, that is when w is large than 

 when w is small. 



The quantity s, when the geometrical conditions are fixed, is inversely 

 proportional to w, but is independent of/*, as is also n; a 2 is, however, 

 inversely proportional to /x, and for two different values of ll, e~ aH would 

 have the same numerical value at times which are to each other as these 

 values of jx. It is sufficiently well proved that the effective permeability 

 of the iron core of an electromagnet, when a current is rising rapidly in 

 the coil, is not always the same as the permeability belonging to the 

 instantaneous value of the current as determined from a statical hysteresis 

 diagram. If in any case where w is fixed the effective value of /x. should 

 be greater or smaller for an increase in the value of the applied voltage 

 E, the growth of the current would be relatively retarded or accelerated. 

 We shall find it well to return to this subject later on. 



