PEIRCE. — MAGNETIZATION IN IRON. 135 



If, however, when the primary current has its steady value, V/R, 

 and there are no currents in the secondary circuit, the primary resis- 

 tance be instantaneously changed from R to R', at the time ^ = 0, 

 there is no sudden change in the current in any branch, but for all 

 subsequent time, the constants are determined by the equations: — 



A+ B+ C+ D+ E+ ^ = ^-^' 



aoA + I32B + 72C + 82D + e2£ + 772^ = 

 asA + /Ssfi + 73C + 8sD + ezE + rjsH ^ 

 aa + l3f,B + T5C + 8,D + e,E + r„H = 



(7) 



and it is evident that every one of the quantities, A, B, C, D, E, H, I, 

 given by (7) has a value which bears to the corresponding value given 

 by (5) the ratio {R — R')/R', and the same relation holds between the 

 whole discharges through the galvanometer in the two cases. If the 

 gap be instantly opened so that R' is infinite, when the current in 

 the primary circuit is V/R and there are no secondary currents, the 

 galvanometer throw is equal, but opposite in sign, to the throw caused 

 by suddenly closing the gap when all the currents are zero. 



The electrokinetic energy for the coupled circuits is 



T=hL-P+M- lih + h+ h) + iVa(/o + 73 + hY 



+ |iV2 • h' + |A^3 • h' + hN^ih + hY + |A'5 • h, (8) 



so that the electrokinetic momenta are 



p =L-I+ M{h + h+ h) 



po= M-I+ Niih + h + h) + N2-l2 



p, = M'I+ A\{h + h+ h) + N^ih + h) + .V5/5 



(9) 



If, when I has the value I = V/R, and there are no other currents, the 

 gap be instantly opened, / suddenly drops to zero, and /o, I3, I5, which 

 were 0, suddenly acquire initial values which may be determined by 

 the fact that the electrokinetic momenta, po, ps, j^b, which before the 

 change were equal to Pq = MV/R, are not altered by the impulse. 

 After the gap is opened, the currents in the branches obey the system 

 of equations (2), but the initial values of these currents are to be 

 found from the equations 



