PEIRCE. — CHANGES IN INDUCTANCES OF ELECTRIC CIRCUITS. 



545 



the system with a parting push which reduces its. own velocity to zero 

 and speeds its late companions on their way ; then, if C is the velocity 

 of the moving mass, E the accelerating force, and r(J the retarding 

 force, the equation of motion will be d{LC)/dt = E— rC, that is, (2). 



-rv 



Figure 2. 



If, when its velocity is C^, the mass of such a system be instantane- 

 ously changed from L^ to Li, the principle of the conservation of mo- 

 mentum in impact shows that if C\ is the velocity immediately after 

 the impulsive change, L^Cq = LiCi. 



The conventional diagram shown in Figure 2 indicates the nature 

 of this simple mechanical problem. L^ is a mass furnished with a stiff 

 vane of such a size as to make the air resistance (which is proportional 

 to the velocity) equal to r units when the mass is moving with unit 

 velocity. L^ is urged to the right by the constant force E and is re- 

 tarded by a force rv. A slack inextensible 

 string connects Lq with another mass Li — L^, 

 and when the string becomes taut, the im- 

 pulsive change in the velocity of Lq corre- 

 sponds to the change in the current in the 

 inductive circuit when the inductance is 

 impulsively changed from Lq to Ly 



If the induction flux, N, in a circuit which 

 contains no iron be plotted against the cur- 

 rent, the resulting locus is a straight line 

 through the origin, the slope of which is 

 the self-inductance of the circuit. If, then, 

 the lines (OH, OV, Figure 3) corresponding 

 to Xj and Lx be drawn, and if when the ris- 



Figure 3. The line OFTV 

 represents the change of 

 the induction flux Hnked 

 with a circuit without iron, 

 when the inductance is 

 suddenly increased. 



ing current has attained the value C^, the 

 inductance be supposed to change suddenly 

 to Zi, the induction flux through the circuit 

 preserves its value unchanged while the cur- 

 rent falls from Cq to Ci, and the point in the diagram which gives the 

 state of the circuit moves from F to T. 



If, as is approximately the case with some circuits which have open 



VOL. XLVI. — 35 



