612 PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 
it is abundantly sensitive to the differences of the induction of the so-called 
inductionless coils of resistance boxes, 2.é., it can deal with induction coefficients 
of the order 0001 earth quadrant.* 
I propose to construct by means of the differential telephone, a scale of 
induction coefficients. This may be done as follows:—Suppose in fig. 1 
that the two coils, 8 and 6, are fixed on the stems. Let v be a small coil of 
arbitrary induction coefficient v, and suppose y to be another coil of the same 
resistance, but wound so as to have very little, say no, induction. a, the fellow 
coil to 8, is placed so that there is no mutual induction between the pair; v is 
put in the branch along with these, and x in the other branch. If the resist- 
ances were equal before, they will still be equal; then y is placed on the stem 
and slid to a position x, where for which there is silence. 
If N be the sum of the individual self-inductions of y and 6 (which is always 
the same), and v, double their coefficient of mutual induction when y is at 2, 
M the constant sum of the individual self-inductions of a and 8, then we have 
M+v=N +»p,. 
v and x are now removed, and a placed on the stem and slid along till there is 
a balance, a mark is made on the stem for this position and lettered 1. 
Then 
M+p,=N +, 
=M+v, 
ie aes 
Now put v and x in as before, and slide down y until there is a balance ; 
then take them out and slide down a till there is again a balance, and mark 
this position 2. 
Then 
M+p,+v=N+y», 
=N+,, 
me me 
pa =2u; 
and so on, 
We thus graduate the stem into parts, each of which corresponds to an 
increase v of the self-induction of the circuit.. Similarly we can graduate the 
other stem. It is then easy to interpolate and get a continuous scale. Lastly, 
we can, by a single observation, reading both stems, find the small difference 
M—N in terms of v. 
* The self-induction coefficients of the primary and secondary of a middling-sized Ruhmkorff's 
coil, when expressed in the same unit, run to from ‘01 to ‘1, and from 50 to 100 respectively. 
