PEIRCE. — CHANGES IN INDUCTANCES OF ELECTRIC CIRCUITS. 5G5 



first braiicli tiiul no electroniotive forces in the other branches, so that 

 L = 0, L\ = 0, Ki = 0, anil any instantaneous change in the induc- 

 tances will leave 



j5^ 



o 



and (M(\ + LX.^ 



momentarily unchanged. 

 If in Figure 11 



F = Li- iM, 



Q = L + iV, 



Ji = U- 31, 



and if the vanes are of such 

 dimensions as to make the 

 air resistance ri, r, r^ when 

 the bodies to which they 

 are attached have unit ve- 

 locities, the e(iuations of 



motion of the mechanical system are of the form (32), if E is applied 

 upward to Q. 



Figure 2G illustrates a special case under this problem where ^' = 1, 

 ^1 = 20, 7-2 = 80, Zi = 2, Z2 = 3, il/ = 0, up to the time OC, when by 

 a sadden change in the conformation of the circuit, J/ is made equal 

 to 2. Before the change C'l = 1.986, C2. = 1.324 ; the change in M 

 leaves Ci momentarily unchanged but suddenly reduces C^ to zero. 

 After the impulse the currents are given by the equations 



Figure 25. 



C'l = 3 - 1.717 e-^-«5^' + 0.703 e-'^4.54u^ 

 C\ = 2 - 1.428 e-s-959' - 0.572 e-54.54u^ 



(33) 



very nearly. 



If in the arrangement shown in Figure 9e, the gap 0, which has 

 been closed by a stout wire, is suddenly opened, the current falls im- 

 pulsively to a value which keeps the induction flux through the battery 

 circuit momentarily unchanged. 



The mechanical system shown in Figure 27 is analogous to the elec- 

 trical circuit indicated in Figure 9f. The gap 0, which has been 

 closed, is supposed to be opened at a given signal. The spring S is the 

 analogue of the condenser K. 



