ATMOSPHERE AND THE ACOUSTIC EFFICIENCY OF FOG-SIGNAL MACHINERY. 249 
the immediate neighbourhood of a fog-signal generator are very large, there is no need for the magnifying 
effect of a resonator. In future experiments the difficulty just mentioned may be dispensed with by making 
use of a phonometer consisting only of a suitable diaphragm together with the optical system for 
determining its vibration amplitude. On account of these uncertainties the phonometer readings 
obtained on the various acoustic surveys are not reduced to pressure amplitudes. The recorded readings 
are, however, comparable among themselves for an instrument built to the exact dimensions of that 
employed in the present tests. While the phonometer readings at a distance may be accurately 
converted into pressure amplitudes, the variability of atmospheric conditions, even on a calm day, and the 
absence of any definite law of propagation make it impossible to utilize absolute readings except to a 
limited extent. In the tabulation of the observations obtained on the acoustic surveys described in 
Appendix II., and in their graphic representation in the accompanying charts, the results are given in 
terms of the phonometer readings, which may be reduced, if required, to pressure amplitudes by 
formula (iv.). 
A glance at the tabulated results of the acoustic surveys show that a phonometer reading of OT mm, 
corresponds to a signal which is feeble, but still sufficiently distinct to serve as a warning under ordinary 
conditions prevailing at sea. According to formula (iv.) this corresponds to a pressure amplitude, 
I Sp j = 0 - 071 dynes/cm. 2 = 7'0x 10~ s atmosphere. 
It is interesting to note that this is not far removed from the estimate j Sp | = 9 - 2 x 10 -s atmosphere 
for a just audible note of pitch 181 as determined by Topler and Boltzmann.* The sensitivity of the 
phonometer was thus very suitably adjusted for the purpose of fog-signal testing at great distances. 
(ii.) Calibration of Phonometer Resonator for Pitch. 
In order to employ the Webster phonometer in the measurement of sound, it is necessary to tune 
the resonator to the pitch of the note emitted by the diaphone. This is accomplished by pulling out 
the inner of the two telescoping cylinders shown in fig. 2, whose position with reference to the outer 
cylinder is indicated by means of a centimetre scale engraved on the former. Each “resonator position,” 
as defined by the scale reading, corresponds to a definite fundamental pitch. This was determined 
experimentally by running a small laboratory siren of the usual type by means of compressed air stored 
up in the tanks of the fog-signal apparatus.! By keeping a finger dipped in oil pressed against the 
revolving spindle of the siren the speed could be regulated and kept constant over a sufficient length of 
time to permit the speed of rotation to be accurately determined by means of a stop-watch. At each 
position of the resonator the siren was allowed to gain in speed while the image of the filament was 
carefully observed. Resonance was at once observed by widening of the image into a broad band. The 
siren was then held at this speed and the pitch determined in the usual way. As the pitch was allowed 
to increase to a value in the neighbourhood of 2000, a whole series of resonance frequencies was 
observed. There was no difficulty in selecting those corresponding to the fundamental frequencies of the 
resonator (n complete vibrations per second). It was found that resonance was obtained for frequencies 
of \n ; this was evidently due to the first harmonic of the complex note emitted by the siren. More 
difficult to explain were a series of several resonance frequencies unconnected with the resonator pitch in 
any simple way, but showing evidence of simple numerical relationships among themselves. As it was 
# Topler and Boltzmaun ‘Ann. Phys. Chem.,’ 141, 1870, pp. 321-352. Boltzmanx’s estimate is. probably a little too 
great. For a note of pitch 200 Wien gives | 5yj | =l'0x 10~ 9 atmosphere (quoted by Rayleigh, 1 Phil. Mag.,' 14, 1907, 
pp. 596-604, ‘ Scientific Papers,’ vol. v., p. 420). For a note of pitch 256 Webster gives | Sp j =8 '9 x 10~ 9 , agreeing fairly 
well vrith the value | Sp | = 6'0x 10 -9 obtained by Rayleigh for a note of the same pitch. 
t The siren is very unsatisfactory for the purpose of this determination owing to the presence in the note emitted of a 
very large number of high harmonics, whose frequencies may coincide with those of the high-pitched overtones of the 
diaphragm or of the resonator itself, giving rise to numerous spurious resonances. 
