410 
DR. W. S. TUCKER AND MR, E. T. PARIS ON 
The total change would therefore be made up of three parts :— 
(1) A steady drop in resistance given by dR^ = j (a + 6bY 0 2 ) IP. 
(2) A periodic change of resistance dR 2 = — 2V 0 (a + 2bY 2 ) U sin pi of the same 
frequency as the sound stimulating the resonator. 
(3) A periodic resistance change dR 3 = —|-(a+66Y 0 2 ) IP cos 2 pt of frequency twice 
that of the sound stimulating the resonator. 
The relative importance of these effects can be gauged by putting in the values of 
a, b, and V 0 previously found. This gives 
m, = — 0'23U 2 , 
<1R 2 = + U19U sinp£, 
dR 3 = + 0'23lP cos 2 pt. 
These resistance changes correspond to the three most obvious effects of a sound of 
suitable pitch upon the microphone. 
oRj is the effect made use of when the microphone is employed in a Wheatstone 
Bridge. Since it is proportional to IP, that is, to the energy of the vibration in the 
neck, it should be proportional to the intensity of the sound-wave stimulating the micro¬ 
phone. This is confirmed by the experiments described in § 7. 
()R 2 is the effect which causes the ripple on the heating current, and which can be made 
audible by the use of an amplifier. It will be seen that the amplitude of tiffs effect is 
proportional to U, and therefore to the amplitude of the sound affecting the microphone. 
The extent to which this is confirmed by experiment is described in § 7. It should also 
be noted that the amplitude of the effect is proportional to V 0 , the free convection 
current from the grid. It should therefore be possible to increase the loudness of the 
sound heard in the telephones by artificially increasing the steady air-current passing 
the grid. That this conclusion is correct can easily be demonstrated by gently heating 
the brass container with a flame so that a current of air is forced out past the grid. 
The existence of ffR 3 , which should produce a note in the telephones an octave above 
the fundamental, is not easy to demonstrate when the microphone is held vertically. 
It cannot of course be heard in the telephones because it is completely swamped by the 
fundamental. When, however, the microphone is tilted the octave becomes relatively 
more important, and is easily heard at certain angles. These effects are described 
in § 9. 
In order to discover what will occur in the case of very loud sounds, it will be necessary 
to use the more complete expression for ffR which involves the third and fourth powers 
of U. Thus, writing the relation between ffR and U for steady currents in the form 
£R - AU + YURfflP + ffTJ 4 , 
