ATMOSPHERE AND THE ACOUSTIC EFFICIENCY OF FOG-SIGNAL MACHINERY. 251 
that it agrees roughly with the value K = 2 - 50 cm. for an aperture of diameter 2'50 cm. in an infinitely 
extended thin plate. Reference to fig..2 of § 11 shows that the length of the resonator at position 0 is 
not determinate owing to the fact that the face opposite the aperture is not plane. The distance from the 
mica diaphragm to the aperture is 11 • 5 cm., not very different from the value of h 0 required to satisfy 
the theoretical formula (i.). For purposes of approximating to the pitch of such resonators for purposes 
of design, the theoretical formula (v.) may be employed. 
It should be noted that, according to the theoretical formula (v.), the resonance frequency exhibits the 
same temperature coefficient as the velocity of sound as given by (vi.). In designing an instrument for 
use in connection with fog-signals, where the temperature is liable to large fluctuations, the resonance 
should not be too sharp. 
The results of Table I. are shown graphically in fig. (i.). The continuous curve drawn through the 
observed points is calculated according to formula (v.). 
Fig. (i.). Pitch calibration curve of adjustable resonator of Webster phonometer. 
(iii.) Determination of Phonometer Resonance Curve with Respect to Sound-Waves 
Generated by the Diaphone. 
At distances from the fog-signal greater than 1000 feet the note of the diaphone appeared to be 
remarkably pure as far as could be judged by the unaided ear.* At lesser distances, especially within the 
angle of the resonator, the note was somewhat rougher, while close at hand (50 to 100 feet) a curious 
crackling sound, somewhat like that emitted when a large sheet of paper is being crumpled up, might be 
heard at the same time. Behind the resonator, in the acoustic shadow of the fog-signal buildings, the 
note, while still very loud, was comparatively pure. In order to study the behaviour of the phonometer, 
with respect to the intense waves emitted by the diaphone, a series of readings was taken at a control 
station behind the resonator at a corner of the balcony of the fog-signal engineer’s residence (marked S in 
Chart 1 of Appendix II.). The end of the diaphone trumpet was just visible from the phonometer. A 
few preliminary observations indicated that the diaphone note seemed to have the best quality at a mean 
pressure (between the beginning and end of the two 3-second blasts) of 19’7 lbs./sq. in. During the 
entire test the pressure fluctuated very slightly from this value. Readings were taken with the resonator 
in different positions. In the following table the mean of observations taken on several blasts are given. 
The maximum readings occurred at resonator position 8'0. According to Table I. the pitch of the 
diaphone note at the above pressure may be taken at 175 complete vibrations per second. The entire set 
* See footnote, p. 247. 
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VOL. CCXVIII.—A. 
