156 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



rt„ 



e L - 



¥ 



r ^-h 



If, however, the resistance of the circuit at the outset had been 

 (r + h) and if after the final value of the current /o for this resistance 



had been estabHshed, the 

 extra resistance had been 

 suddenly removed from the 

 circuit, the current curve 

 from that instant on would 

 have followed the equation 



rtf ]^ _rt/_ 



r 



or, smce 



E 



rtn 



^0 = 7(1-^ "^)' 



It is clear, therefore, that 

 in the case of a circuit of 

 this kind the last (upper) 

 portion of a step curve of 

 the form U (Figure 4) will 

 have exactly the same shape 

 as the corresponding part of 

 the V curve, although the 

 lower portions may be very 

 different. 



If in the case also of a 

 circuit which has one or 

 more finely divided iron 

 cores the flux of induction 

 through the circuit can be 

 considered as a single val- 

 ued (given) function of the 

 current strength when the 

 magnetic state of the iron at the outset is given, the upper portion of a 

 curve of the f^type (Figure 4) belonging to the circuit will be identical 

 with the corresponding i^art of a curve of the V type. We need con- 

 sider only a U curve with one intermediate step. If the induction {N) 



AMPERES. 



Fig ORE 



J/ is a portion of a statical hysteresis dia- 

 gram for a certain transformer under an excita- 

 tion of 1812 ampere turns. Nis, a similar curve 

 obtained from a reverse current oscillogram. 



