ATMOSPHERE AND THE ACOUSTIC EFFICIENCY OF FOG-SIGNAL MACHINERY. 245 
power delivered to the free atmosphere. All these questions are of great importance 
in practice and constitute a practically unexplored field for future investigation. 
Some light may be thrown on the formation of the discontinuity by considering 
a harmonic plane wave propagated in a cylindrical tube having the cross-section 
(90 cm. 2 ) of the narrowest part of the conical resonator of the diaphone whose acoustic 
output was measured by the thermodynamical method. It will be noticed from 
Test 3 that the maximum power output is 2‘36 H.P. at a pressure of 19 1 pounds per 
sq. in A The air consumption is 13'3 cubic ft. per sec., which gives for the mean velocity 
of air over the 90 cm. 2 cross-section of the resonator the value 4'18 x 10 3 cm./sec. at 
the frequency n— 175. If we assume that the wave is initially harmonic (an 
assumption which sets a lower limit to the maximum compression) we may estimate 
the numerical characteristics of the equivalent sine-wave from the formulae of 
§ 1. We have [dW/dt] — 2'36 x 746 x 10 7 /90 = 1'95 x 10 8 ergs cm. -2 sec. -1 . Taking 
a = 3’32 x 10 4 cm./sec., p 0 = 1'29 x 10 -3 gr./cm. 3 , we obtain ap 0 = 42‘8. 
In terms of the pressure amplitude we have from formulae (7) j Sp j 2 = 2ap 0 [dW/dt], 
giving 
| Sp = 1'29 x 10 5 dynes/cm. 2 , J f | = 3'02 x 10 3 cm./sec. 
1^| = 274 cm. | Sp\/ Po = \s\ = 0*091 
According to formula (23) we are enabled to calculate that the distance x 1 which the 
wave will travel before discontinuity sets in, by identifying U of that formula with 
the above value of |^j. We thus find, for y = 1'40, 
296 cm. < x 1 < 327 cm. 
The estimate just derived leads the writer to believe that in actual fog-alarms 
the tendency to the forma,tion of a discontinuity in a distance comparable to the 
wave-length and to the axial length of the resonator plays an important part in 
determining the output of sound which is eventually transmitted to a distance. 
§ 14. Summary and Conclusions. 
The tests described in the present paper have demonstrated the successful use of 
the Webster phonometer as a simple and practical instrument for the measurement 
of the characteristics of pure-toned sound-waves of ordinary intensity. By carrying 
out acoustic surveys with this instrument, the propagation of fog-signal waves under 
varying conditions of wind and weather has been studied. The observations show 
that the wind is by far the most important factor affecting sound propagation. 
Many of these results may be interpreted in terms of Taylor’s theory of extinction 
of sound by the eddy structure of the atmosphere. From this point of view it may 
* [Added February 14, 1919.—From phonodeik records taken during the 1917 tests at 860 feet distance 
it was estimated that 25 per cent, of the total acoustic output is contained in the master tone of pitch 174. 
See footnote, p. 247.] 
2 K 2 
