630 PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 
If A?€ denote the square of the amplitude of 2 , 
AZ 5 ¥ L+Y , 
then 
if 2 
(x — Nn?) +S82n? 
aE BH Be 
2 
(2 oss 
~ (ayn?) + (B— one 
Experiment 4.—Here the neighbouring circuit consists simply of the other 
coil of the differential telephone. From the way the coils are wound, we have 
approximately M=N=L. To get the case where there is no condenser, we 
put X=o. We thus get, denoting by G and &, the values when the neigh- 
bouring circuit is open and closed respectively, 
(a x 3) Le +k 
RE Soles 
e L2n?2 alt R2 
Thus the effect of closing the neighbouring coil through an inductionless resist- 
ance is the same as if we increased the self-induction of the main circuit by the 
: R 
fraction q° 
The intensity of all tones is therefore diminished, and more diminished, the 
less the resistance through which the neighbouring coil is closed. 
The higher tones are much more deadened than the lower, so that the 
quality of the sound is flattened. 
The following table shows the theoretical value of : for different frequen- 
1 
cies. If m be the number of vibrations per second, then »=27m, and we have 
roughly, for R=20, S=15, L=-004 (the units being ohms and earth quadrants). 
Name of , Gi 
Note. mM. n, 
C 66 Lye" 1:03 
b 503 107 Po) 
ri 1592 108 4:5 
ev 5033 10° 5S 
Experiment 5.—If the second coil be closed through a resistance having a 
self-induction N’, then we must put N=N’+L, M=L. The above formule, 
