ATMOSPHERE AND THE ACOUSTIC EFFICIENCY OF FOG-SIGNAL MACHINERY. -J67 
eddy motion may be deduced.* The gradient of temperature and water-vapour content should also be 
observed if possible. 
(2) Distribution of Sound over Circular Courses. 
From the phonometer observations taken over circular courses it is possible to compare at different 
distances the energy flux across portions of zones of spheres near the surface of the sea, subtending a small 
angle 89 (in a vertical plane) at the fog-signal station and a horizontal angle </> on either side of the axis 
of the diaphone trumpet. If [dW jdt] is the flux of energy across unit area of a spherical wave-front at a 
distance r, the total flux of energy across the surface just referred to is given by 
11r 2 [dW Jdt\ sin Odd d <\>.(iv.) 
Making use of (i.) we have, since sin 9 is very nearly unity, 
energy flux — f 1 8p j 2 df .(v.) 
2 ap 0 J -<j> 
Since the phonometer readings were taken at approximately equal intervals over the circular courses, the 
integral in (v.) may be written 2</>[jSpj 2 ], where [ {| 2 ] = (0 • 70S) 2 [d 2 ] is the mean square of the 
pressure amplitude between the angles ± </>. The value of 89 is chosen somewhat arbitrarily as the angle 
subtended by a vertical height of 40 feet at a distance of one nautical mile. Within the solid angle thus 
constituted is contained the sound which may be serviceable as a warning to ships. Inserting numerical 
values in (v.), we have, expressing the distance R in feet, 
energy flux = 3‘47 x 10 -3 . (R/1000)-.2</> x [d 2 ] watts.(vi.) 
It is of some interest to compare the energy flux thus observed with the theoretical value calculated 
from the acoustic output of the diaphone, assuming that the sound is equally distributed in all 
directions throughout a hemisphere and that conditions of propagation are ideal. In these circumstances 
we have 
theoretical energy flux sin 9 89 (2 f/2ir) x (acoustic output), 
or for purposes of numerical calculation, expressing the acoustic output in H.P., we have, inserting the 
value 89 = 40/6080, 
theoretical energy flux in watts = (2</>/2ir) x4'9x (acoustic output in H.P.) . . . (vii.) 
The acoustic output corresponding to the air pressure operating the diaphone is obtained from the results 
of the thermal tests tabulated in Appendix III. Before September 13, the acoustic outputs are determined 
from test 1 and after September 16 from test 3, as the valves admitting air to the diaphone were 
readjusted in the interval. The results of the acoustic surveys taken over circular courses are tabulated 
below. 
* The linear liot-wire anemometer, adapted to take continuous records, would appear to be suitable for this purpose 
(King, L. V., ‘ Phil. Mag.,’ vol. 29, April, 1915, pp. 556-577). 
N 
VOL. OCXVIII.-A. 
