RICE: ALTERNATING CURRENTS IN WHEATSTONE’S BRIDGE. 35 
the condenser is shunted around only a part Aig, 3 
of the resistance in branch (1). If the re- 
sistance A to C—r, and Ato B=1', then 
Zg—I,—JXq 
Z,—Ts 
Zy—To 
, Le f , 
1 DSO eee aan a 4) 
Z,—',;—T1 hae Cr ames aD . 
Xe Ty 2 IL 
Substituting these values in equation [3] gives the two conditions 
Xe itr —0t =x, =n te) [14] 
12 
T,X 4Xe¢ Ty (Tel3—T yy) Pr yt, [15] 
And if the bridge is first balanced for continuous currents, equa- 
tion [15] reduces to 
12 
mie ae 
wir ’ 
Keely 
or putting in the values of x, and x, the relation becomes 
° 
Grr. 
I 1 4 
ao) 
Ss 
the one given by Rimington. In this case the bridge is first bal- 
anced for steady currents and then the point B is found so as to 
balance for variable currents, without repeated adjustments of re- 
sistances. 
To compare the mutual inductance of two coils, C and D, with 
the self-inductance of one of them, D, consider the arrangement 
indicated in Fig. 4, a Wheatstone’s bridge with an extra conductor 
from Ato B. _ Kirchheff’s laws give the seven equations: 
I,+1,—I,+I,=o0 
I,—I,—I,=o 
I,+1,—I,+I,=0 
Ze ZZ 0 
LN Zl g--Z lh |X lg 
Z1,+2Z,1,+2,1,=E+)xm I, 
Z,1,+Z,1,—Z,1I,=0 
The condition for I,=o, derived as in the preceding problems, is 
Pig, 
