PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 635 
resistance R and self-induction L, as was shown long ago by Sir WiLLiAm 
THomson, the discharge will be oscillatory if RaG =. The variation of the 
current is given by 
e-™ sinnt 
h eS ae 
where M=s7, M=/TxX—Tp- 
If we take the second coil of the differential telephone in experiment 5, 
R=15 (ohms), L=-004 (earth-quad.), X=-3 microfarad, 
: m 1 (R59R405 
m=1-9 x 10°, 5-= 5 /8298°105 
= 4585. 
The frequency therefore corresponds to a note well within the limits of 
hearing, and since — is not very small, a number of oscillations would take 
place before the currents were much damped. A note due to a free oscillation 
of this kind might therefore just have been heard in experiment 5. Of course 
the problem is in reality not quite so simple as the above, owing to the 
influence of the neighbouring coil. An exact solution could easily be given if 
there were experimental data that could be relied on to test it. It is simply a 
matter of the roots of a cubic equation. 
I made a somewhat simpler experiment by alternately charging a microfarad 
by means of three Le Clanché cells, and discharging it through a telephone 
whose self-induction was about ‘004 (earth-quad.). The sound of the discharge 
could be heard very well, whether the resistance of the circuit was 25 ohms or 
10,000; but the character of the sound was very different, according as large or 
small resistances were used. The nature of the difference may be approximated 
to by pronouncing the words pop and pink; the former representing the sound 
with large, the latter that with smali resistances. It would appear, therefore, 
that a certain high note is actually heard when the resistance is small, which 
is absent with large resistances. But this question is one for better musical 
ears than mine, and it is, moreover, an acoustical as well as an electrical 
question; for high notes of the kind are heard on simply tapping the ferrotype 
plate of the telephone with a pencil, so that this note might not be due to an 
electrical oscillation at all, but merely a free vibration of the plate exerted by 
the impulse arising from the magnetic action of the momentary current. 
Since the above was written, I have seen the description of an experiment 
by RéntcEN which bears on this subject, the significance of which he clearly 
points out. The current in the primary of an induction coil was interrupted, 
and the sound observed in a telephone inserted in the secondary with or 
