248 DR, LOUIS VESSOT KINO ON THE PROPAGATION OF SOUND IN THE FREE 
Appendix I.—ON THE ACOUSTIC CHARACTERISTICS OF THE WEBSTER PHONOMETER 
AS EMPLOYED IN THE MEASUREMENT OF SOUND FROM THE DIAPHONE. 
(i.) Determination of Phonometer Constants. 
The detailed construction of the Webster phonometer employed during the Father Point tests is 
briefly described in § 11 and 15 illustrated in fig. 2. 
After the instrument had been employed in carrying out the measurements of sound from the 
diaphone as described in the present paper, the constants of the instrument were kindly determined by 
Prof. Webster himself at Clark University. Without going very far into the mathematical theory of 
the phonometer, which is to be considered by Prof. Webster elsewhere, it may be remarked that the 
free vibrations of the diaphragm may be represented by the differential equation 
mx + KX+fx = 0,.(i.) 
where m is the effective mass of the loaded diaphragm, k is the effective damping constant, and / is the 
effective stiffness of the diaphragm. According to the determination of Prof. Webster 
and 
m = O'891 grs., k = 14'0 dynes/(cm. per sec.), 
/ = 5 • 67 x 10 6 dynes/cm. 
The frequency n of the fundamental, given by 
2nn = [f/m- (/t/2ffl) 2 ]- 1 .(ii.,. 
gives n = 401 complete vibrations per second. 
The magnification of the optical system was determined by mounting an interferometer on the 
resonator side of the mica diaphragm, and by means of a stroboscopic arrangement measuring the 
displacement of the centre in terms of a wave-length of light while in actual vibration at frequency 175. 
At the same time the breadth of the luminous band in which the filament was drawn out was read in the 
usual way. In this way it was found that 1-scale division of the microscope eye-piece (1 mm.) 
corresponded to O'000120 cm. diaphragm displacement. 
The pressure amplitude in a sound-wave, j Sp j, is connected with the diaphragm displacement and 
resonator constants by formulae which have been developed theoretically (and verified experimentally) by 
Prof. Webster. According to his determinations, with the resonator in position 8, jSpj (expressed in 
dynes/cm. 2 ), is connected with the diaphragm amplitude j&rj (expressed in cm.) by the relation 
j&sj = 8'48 x 10~ 5 jopj...(iii.) 
Hence if d is the phonometer scale reading (double amplitude in mm.) we have |dx0'000120 = J Sx j, from 
which it follows that 
j Sp j = 0 • 708 x d dvnes/cm. 2 .(iv.) 
Prof. Webster states that the constants from which (iii.) was derived were tested by measuring in the 
open air the sound from a standard “phone” or sound generator at pitch 256. Agreements were 
obtained to within less than one per cent. 
There are difficulties in the way of applying (iv.), as determined for small intensities, to convert the 
larger readings (greater than 5 mm.) to pressure amplitudes, owing to the fact that in the latter case 
noticeable eddies are set up in the neighbourhood of the resonator aperture. For this reason it would be 
necessary to carry out a special series of experiments to determine the limits of error (if any) involved in 
measuring very powerful fog-signal waves by means of the phonometer. As the pressure amplitudes in 
