420 
DR. W. S. TUCKER AND MR. E. T. PARIS ON 
Assuming, as in the case when the microphone axis is vertical, that the relation 
between U and (dd can be put in the form 
sr = $K+a{Tj-v (> y+b{xj-v 0 y, 
we find that a fair agreement is obtained when 
£Et 0 = +0*02 
a — — 0 ‘ 3 
b = +0*0007 
V 0 = +0-25 
that is, 
Sli = 0‘02 —0'3 (U— 0'25) 2 + 0'0007 (U-0-25) 4 . 
Points calculated from this formula when U = 0, ± 1, etc., are shown, by the crosses 
in fig. 16. It will be seen that the fit is not so good as in the case when the microphone 
was held vertically (fig. 10), and also that the experimental curve is not quite symmetrical 
about the line U = V 0 = 0 -25 when U is small. It is, however, difficult to obtain reliable 
readings of the resistance of the grid when the microphone axis is horizontal or nearly 
so, and the above formula appears to represent the experimental results sufficiently 
well for the present purpose. It may be written 
SU = +0-15U-0-3U 2 —0-00035U 3 + 0-0007U 4 , 
and by putting U sin pt in place of U, and disregarding the terms in U 3 and U 4 , it can be 
seen that the three principal effects to be expected when the microphone is exposed to 
a sound-wave of suitable frequency are 
SR! = — 0 ‘ 15U 2 , 
dR 2 = + 0‘15U sinpb 
£R 3 = + 0 ‘ 15U 2 cos 2 pt. 
If these are compared with the corresponding expressions in § 6, it will be seen that 
for a given value of U the magnitude of the steady resistance change and the amplitude 
of the octave are reduced in the proportion 15/23, but that the amplitude of the 
fundamental vibration is reduced to .15/119 of its value when 0 = 0. Although, 
therefore, all these effects are diminished when the microphone is laid horizontally, it 
is the fundamental vibration which suffers the most. So far the deductions made from 
the results of the experiments with steady air-currents are in accordance with 
observation. 
For values of 6 between 0 and ^, curves intermediate in form between those in figs. 10 
and 16 are obtained. When 0 is greater than 0, V 0 no longer represents the velocity 
