546 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



cores made of very finely divided soft iron, the hysteresis diagram is 

 extremely narrow, so that the inductance may be considered to be a 

 definite function of the current strength, we may 

 represent two different states of the circuit by 

 lines like OFR and OKS of Figure 4. It is 

 then easy to see that in this case also a sudden 

 change from one state to the other when the 

 current had the value OD = C^ would leave the 

 induction flux through the circuit momentarily 

 unchanged while the current fell to OE = Ci, 

 and the point which represents the state of the 

 circuit would suddenly move from F to K. 



Figure 4. The line 

 O F K S represents the 



If, at any instant, the total flux of magnetic 

 induction through any simple circuit, which 

 growth of the induction may or may not contain iron, is N (maxwells), 

 flux in a magnet with jf ^. jg ^^^ resistance of the circuit in ohms, 

 nnely divided core when /-y ,i , • j z^ j.l. i- i 



the inductance of the ^' ^^^ ^^^^^°* ^" amperes, and L, the applied 

 circuit is suddenly in- electromotive force m volts, 

 creased. 



„ 1 dN ^ , , 



iS'-— «-^^==rC; (10) 



10« dt 



or 



dN 



dt 



= W 



(f-"). 



(11) 



and if the final value (^/r) of the current be denoted by C\ and the 

 change in N during the time interval tx to t^ by iVi,2, 





(12) 



If, now, C be plotted against the time (as in an oscillograph diagram) 

 in a curve s (Figure 5) in which / centimeters parallel to the axis of 

 abscissas represent one second, and an ordinate m centimeters long one 

 ampere, the curve will have a horizontal asymptote (CY) at a distance 

 (KG) corresponding to E/r amperes from the time axis, and, if OK 

 represents the time ti and OL the time t^, the area FGDC, or A 1,2, ex- 

 pressed in square centimeters, is equal to 





C)dt, 



(13) 



