A SELECTIVE HOT-WIRE MICROPHONE. 
409 
in fig. 10. In all such experiments, where U did not exceed 5 cms. per second, it was 
found that the result could be expressed within the errors of the experiment by a formula 
of the type 
sb = m 0 -\-a(u-v„y+b{u-v {) y. 
In the above experiment the resistance was measured under the condition that the 
electric current carried by the grid was the same with and without the air-current. 
In many experiments, however, the cooling of the grid will be accompanied by an 
increase of electric current, which tends to restore the temperature to its initial value. 
The extent to which this takes place depends of course on the particular circuit in which 
the microphone is used, but in most cases its effect will not be very marked, owing to 
the dead resistance in series with the microphone. 
In a second experiment, performed with a grid of similar type to that used in the 
first experiment, the resistance was measured for various values of U by rebalancing 
the bridge with the resistance R, so that the heating current did not remain quite 
constant but increased or decreased according as the grid was cooled or heated. The 
resistance Rh was 240 ohms. It was found that the resistance-velocity curve had the 
same character as that in the first experiment, and up to velocities of 5 cms. per second 
the change in resistance could be quite adequately represented by an expression of the 
above type. 
It is convenient to write the expression for AR in the form 
SB = -2V 0 (a + 2bY 0 2 ) U + (a + 6bV 0 2 ) U 2 -46Y (J U 3 + 6U 4 . 
If the values of a, b and V 0 determined in the above experiment are inserted we get 
SBv = 1 ’ L9U —0‘46U 2 —0’022U 3 + 0'0044bJ 4 , 
so that if U is not much greater than 1 cm. per second, ^R is given by the first two terms 
to within 2 or 3 per cent. 
In applying these results to the case of oscillating air-currents, we shall at first suppose 
that U is so small that the third and fourth terms are negligible. If it is assumed that 
the resistance of the grid at any instant is the “ equilibrium " value which it would take 
up if the instantaneous velocity were maintained, then the changes in resistance produced 
by an alternating air-current U sin pt will be given by 
rlR = — 2V 0 (rt + 26Y 0 2 ) U sin pt 
+ {a + 6bV 0 2 ) U 2 sin 2 pt 
= l(a + 66Y, 2 )U 2 
— 2Y 0 (a + 26V 0 2 ) U siny>£ 
—\ (ct + 6&Y 0 2 )U 2 cos '2pt. 
