ATMOSPHERE AND THE ACOUSTIC EFFICIENCY OF FOG-SIGNAL MACHINERY. 265 
No. 14. September 20, 1913. Table 14 and Chart 14. 
Note the tendency to the formation of a “ silent zone ” (observations 30 to 33), and the enormously 
improved conditions of sound propagation during a temporary calm (observations 48 to 70). 
Chart 14. Acoustic survey, September 20, 1913. 
(iii.) Discussion of Results of Acoustic Surveys. 
(1) Acoustic Gradients. 
It will be evident from an inspection of the charts we have just described that, even on the most 
favourable days, the atmosphere is so far from homogeneous that the propagation of sound according to 
the inverse-square law is an approximation of the roughest kind. It is of considerable interest, however, 
to compare the actual observed gradient of phonometer readings with the theoretical gradient calculated 
from the acoustic output of the diaphone, assuming ideal conditions of sound propagation. If j 8p j be the 
pressure amplitude at a distance r sufficiently great compared to a wave-length, the ratio of flow of energy 
across unit area of wave-front is very approximately given by 
[dW/dt] = 1 8p j 2 /{2ap 0 ) .(i.) 
Expressing the fact that the entire flow of energy across a hemisphere of radius r is equal to the acoustic 
output at the diaphone, we have 
2-n-r 2 x |Sp| 2 /(2«po) = (acoustic output).(ii.) 
If d is the phonometer reading in mm., we have from the known constant of the instrument 
1 8p J =0'708d .(iii.) 
From a knowledge of the pressure of air operating the diaphone, we may obtain a rough estimate of the 
acoustic output from the results of the thermal tests 1 or 3 described in Appendix III. 
