150 PROCEEDINGS OF THE AMERICAN ACADEMY. 



mined from a statical hysteresis diagram. The same phenomenon 

 appears when an electromagnet with finely laminated core has a sec- 

 ondary coil. The closing on itself of a secondary coil wound on the core 

 of an electromagnet when a current is being established in the primary 

 will, therefore, expedite at first the rise of this current, but the area over 

 the current curves ought to be the same in the two cases, and we must 

 expect, therefore, the building-up time to be somewhat longer when the 

 secondary coil is closed than when its circuit is broken. 



It is to be expected, of course, that the curves which show the march 

 of the current in the primary circuit will be noticeably different in form 

 when the secondary circuit is closed and when it is open ; for this is 

 often the fact in the case of two neighboring circuits which have fixed 

 self and mutual inductances {L^, L^, 31) if one of them containing an 

 electromotive force E be suddenly closed at the time ^ == 0, while the 

 other, which contains no electromotive force, is closed. Here 





(21) 



where ?\, ro are the resistances of the circuits and I^, I^ the currents in 

 them. 



If . A = ^^, and f. = ^^, 



where S=ULo-M\ Q = r.- L^ + r^- U, B-=Q--A7\-n- 8; 

 Ii^-7r^[B-^e^'{r,-L,-n-L, + E) +ie>''(r,-L,-rvL,-B)l (22) 



I, = ^^[e'" - e^'l (23) 



flU = -^, a.d /(^-/,).. = ^. (2,) 



Figure 44 illustrates a typical case where ^S* is positive : the heavy 

 line shows the current in the primary circuit when n == 3 ohms, r^, = 

 2 ohms, L^ = 3 henries, L2 = 2 henries, 31 = ^/6/S henries, jE\ = 12 

 volts, when the secondary is closed ; the lighter curve shows the rise of 

 the current in the same circuit when the secondary circuit is open. 



