32 KANSAS UNIVERSITY QUARTERLY. 
The large letters represent complex quantities or vectors and the 
small letters denote real or scalar quantities: r denotes the resist- 
ance and x the reactance of a branch, i. e. x=Lo— where w is 
2 times the frequency of alternation. 
It is the purpose of this paper to apply the method outlined 
above to the solution of problems involving alternating currents in 
the branches of a Wheatstone’s Bridge. 
Let the branches of a Wheatstone’s Bridge be represented in 
Fig. 1, where the branches are numbered (1); @)5 <2 ee )yaae 
the arrows indicate assumed instantaneous directions of currents 
and electromotive forces. Branch (5) contains the galvanometer or 
telephone, and (6) the impressed E. M. F; a battery, to be closed 
after the galvanometer circuit is closed; or the secondary of an in- 
duction coil, with telephone in (5). 
Kirchhoft’s laws give the six equations: 
I1,+I,—I,=0 
L— l,l), —s 
I,+1,—l,=0 
be aA Sp <0) [1] 
Z,1,—Z,1,+Z,1,=o 
Lil oa 2 a, be 
The condition for no current in the galvanometer is I,—o, 
which gives fi DSO wien Oe tn 
I O San oO, KO" fom! 
G Pater sor iyvict =i, || 
| 
a ar ree LC 
Zee 7, sO) SO, sO) OM 
O 2, 0. Z,E, Z, 
Dye ih rr 
oe ene GtNariete, 1 ae 
i = aa SS a ==) [i 
I I O fe) Oil, | 
i) Geen OC) aro 
OC} Ome wl I Qt 
0)" "0, Z,—Z,--Z, ) 0 
Zi oh. OO iZe oR! 
pe Zp O Z, O Z| 
ZgZ3—Z,1Z,4 [3] 
