224 DR. LOUIS YESSOT KING ON THE PROPAGATION OF SOUND IN THE FREE 
If R be the gas-constant, we have p^p x = R0i. In terms of the specific heat of air 
at constant pressure and volume, C p and C v , we have R = J (C p — C„), where J is the 
mechanical equivalent of heat. Since y = CJC V we have R = JC„ (y— l), so that (42) 
may be written 
w = JC v m0 1 [1 ~{p 0 /pi)~] = JC v rh (©j -0 O ) .(43) 
The portion of the air-consumption (M—m) due to leakage performs no external work 
(except the negligibly small amount done against intramolecular attraction represented 
by the Joule-Thomson effect), and thus passes through the siren without change of 
temperature, but mixes with the effective air to give a temperature 0 at some distance 
from the siren ports, sufficiently far downstream for eddies to have died down and the 
flow to have become regular except for the motion of the medium due to sound¬ 
waves. In these circumstances, as there is no rate of loss of heat, 0 is given by 
C w M0 = C„m0 o + C„ (M—to) 0j, 
or 
M (0 X — 0) = m(0!-0 0 ). 
We thus have for the rate at which external work is propagated away as sound 
from the siren the expression 
w = JC„M (0,-0), .(44) 
in which M and (0j —0) are experimentally measurable quantities. As a standard 
of comparison we shall adopt an ideal siren having no “leakage” and operating 
according to the cycle described. Replacing m by M in the first of equations (43), 
the acoustic output of such a siren may be written 
w = jcjae 1 [i-(ft/p 1 )'r].(45) 
In terms of this standard we may write for the “ acoustic efficiency ” of the siren the 
expression 
w _ (0 X — 0) 
^ e, [i-(ft/AA 
(46) 
The results of tests on an actual siren (a “ diaphone ”) based on the above theory are 
described in Appendix III., together with the precautions to be observed in carrying 
out the necessary temperature measurements. 
The theory of the present section enables us to estimate the acoustic output of 
types of fog-signal apparatus in which the compressed air is utilized to produce 
sound in other ways than by escape through siren ports intermittently opened and 
closed. For instance, by a suitable arrangement of valves as in a compressed-air 
rivetter, or in the “ driving head ” of the piston of the diaphone, it might be feasible 
to cause a piston to vibrate through a large amplitude in a cylinder opening out into 
a conical resonator, thus realizing the type of apparatus considered theoretically 
