414 
DR. W. S. TUCKER AND MR. E. T. PARIS ON 
what is the probable maximum value of U in the above experiment. It was found that 
the sound from the fork was certainlv inaudible to the unaided ear at a distance of 250 
«/ 
feet, this being probably rather an over-estimate of the distance at which the sound was 
just lost. Taking the amplitude of the sound at this distance to be 1 *27 X 10 -7 cms. 
(Rayleigh’s value for the minimum amplitude audible when the note is 256), we find 
that the amplitude of the sound at 12 feet from the fork is about 2 -7 X 10 -6 , so that 
the maximum value of velocity in the sound-wave does not exceed 0 -005 cm. per 
second, and the maximum velocity TJ of the air in the neck of the resonator will probably 
not be greater than 0 *3 cm. In this case the effect of the second term in the expression 
for (iRj is negligible. 
A second experiment performed on another occasion under almost identical conditions 
confirmed the results already obtained. The distances employed in this experiment, 
however, did not exceed 32 feet. 
(ii) Second Experiment .—The expression deduced in § 6 for the oscillatory resistance- 
change of the same frequency as that of the sound is 
m 2 = a'U (l +f G -, U 2 ^ sin pt , 
where £ - r is very small, so that, except for exceedingly loud sounds, 
CC 
c® 2 = a'U sin pt. 
In the case of experiments such as that just described, we may write 
£R, = — sin pt, 
r 
since £R 2 is proportional to the amplitude of the sound affecting the resonator. 
When an amplifier is used as a means of observing this effect, its working depends 
in the first place on the fluctuation of the current in the primary circuit. The effect of 
the small oscillatory resistance change in the microphone is to produce a “ ripple ” on 
the steady heating current, the amplitude of which to a first approximation is proportional 
to the amplitude of the oscillatory resistance change. Without considering the processes 
by which this ripple is amplified by the series of transformers and thermionic valves 
which constitute a transformer amplifier, we shall at once proceed to enquire by an 
experimental method whether the amplitude of the current on the output side of the 
amplifier is proportional to the amplitude of the sound affecting the microphone. It is 
perhaps scarcely necessary to point out that in such an experiment it cannot be assumed 
that the amplification is constant for different values of the amplitude of the ripple. 
For ripples of very small amplitude, however, it seems probable that the amplification 
may be sensibly constant over a moderate range. In spite of these difficulties, which 
make the interpretation of the observations somewhat obscure, the results obtained 
appear to be of sufficient interest to justify their inclusion in this paper. 
