ATMOSPHERE AND THE ACOUSTIC EFFICIENCY OF FOG-SIGNAL MACHINERY. 287 
(ii.) Measurement of Pressure and Air Consumption. 
Pressure was measured by a mercury gauge connected to the storage tanks. During the 6-second blast 
required for the resistance thermometers to take up their final temperatures, the mercury column fell 
through a measured distance from which the air consumption could be calculated. Let the pressure fall 
from pi to p \. If pi and p\ be the corresponding densities, we have by Boyle’s law 
Pi - Pi = (pi ~ Pi) R6i,.(i-) 
0i being the temperature of the air in the storage-tanks and R the gas constant. If we denote by M 
the rate of mass-flow of air during a blast of t seconds, and by Y the total value of the storage tanks, we 
have 
Mf = V ( P i - p\) .(ii.) 
Under standard conditions of pressure and temperature we have 
Po = PoRQo) .(iii-) 
so that from (i.), (ii.), and (iii.) we have for the rate of air consumption 
M8i = ( Pl - p\) Ye 0 . (iv 
Po Po t 
The volume of each of the storage tanks was calculated to be 282 cubic ft., so that 
Y = 846 cubic ft. = 2'39 x 10 6 cm. 3 . 
Throughout all the observations the duration of blast was t = 6 seconds. The pressure drop varied from 
4 to 12 cms., and could be read with ease to half a millimetre. Allowance was made at each observation 
for the rate at which the pressure was increasing during the 6 seconds owing to the continuous operation 
of the compressors. The temperature of the air in the tanks was taken at 15° C. throughout, a value 
observed during one of the tests by the resistance thermometers. The air consumption in cubic feet per 
second under standard conditions of pressure and temperature is then given by (iv.) in the form 
M (pi-p'i) 846 273° , 
— = r - 7 g x — X = I' /6 X (pi-pi) cubic ft./sec. 
6 288° 
(v.) 
The output of a siren of unit efficiency as determined by formula (45) is given by 
W = JC.M0, 
l ~(Polpi) y 
(vi.) 
Remembering that JCe(y- 1) = R = i?o/(po8o)> and making use of (iv.), we may write equation (vi.) in 
the form 
W = 
(pi-p'i) V 
yz 1 
l ~(PolPi) y 
t y-l 
If ( P i -p'i) be measured in centimetres of mercury, we have for numerical reduction 
• (Pi-P'i)x 13-6 x 981 2-39 xlO ti 
w =-eVoT-' x 7 ■ 46 x 10 9 
y-lu 
W = 17 • 8 x (pi~p'\) x 
y- 1 
1 - (po/pi) y 
l-(Po/pi) y 
H.P. . 
H.P. 
(vii.) 
In calculating the last factor we write for p x the mean pressure (above vacuum) between the beginning and 
end of the 6-second blast. 
