622 PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 
tested by so delicate an instrument as the differential telephone. Along with 
any resistance Q” we must always introduce a certain residual self-induction M”. 
The general formule (6), (7), (8), and (9), enable us to correct our experi- 
mental results. The following may be conveniently used in place (7), (8), (9), 
to which they are equivalent, 
" Q’-Q' } 
M — 2Q M ) » ° . . . (1.) 
Gag 
N-M=-GqgM’, .°. . .. @Q) 
we Oe ee 
In practice, however, we may in most cases proceed as follows. Since M” is 
very small compared with M’, (9) gives approximately N=M-+ M”. 
N and Mare adjusted accordingly. Then either X or M’ is adjusted, taking 
Q” always =Q’, until there is approximate silence. Lastly, Q” is increased 
concurrently with residual adjustment of M’ or X, as the case may be, until 
absolute silence is obtained. 
CASE oF MULTIPLE ARC WITH INDUCTION. 
It will be noticed that by equation (9) the coefficients of induction in the 
multiple arc are combined like resistances. An interesting case, which brings 
this out still better, is that where we have in one circuit of the differential 
telephone a multiple arc, each branch of which has induction. This case is 
obtained from last by putting X=o in the conditions derived from (5). We 
thus get 
4(—\/7 
R=Qt+gy 
QM" + QM +(Q—R)(M'+M") +(Q'+ Q”)(M—N)=0, 
N=M+ rinate 
Using the first and last, the second of these gives 
uM 
Q — QO” = 
In other words, the time constants of the two branches of the multiple arc must 
be equal, and the resistances and coefficients of induction of the two circuits of 
the telephone must be equal, the inductions being combined by the same law 
as the resistances. 
