244 DR. LOUIS YESSOT KING ON THE PROPAGATION OF SOUND IN THE FREE 
This result enables us to calculate the rate at which energy is being propagated 
away as sound, and hence, in conjunction with equation (45), gives us a measure 
of the acoustic efficiency of the diaphone measured at the vertex of the conical 
resonator. As the method is not entirely free from sources of error inherent in the 
temperature measurements, the efficiency thus determined will be referred to as 
the “apparent efficiency.” As far as can be judged these sources of error are for the 
most part eliminated by taking temperature differences with the diaphone sounding 
and silent, so the apparent efficiency is probably not very different from the true 
value. 
(iii.) Discussion of the Father Point Tests. 
The observations described under Appendix III. were taken on a diaphone actually 
in service so that no alterations could be made in the disposition of the apparatus to 
allow of the x’ealization of the most satisfactory conditions for carrying out the tests. 
The results derived therefrom must, therefore, be regarded as the best available 
under the circumstances. The characteristics of the diaphone are shown graphically 
in figs, (i.) to (iv.) of Ajjpendix III. It is interesting to notice that the acoustic 
efficiency is at a maximum at an operating pressure of about 20 lbs. per square inch,, 
not very different from that at which fog-signal engineers have found by experiment 
that the note is most smooth and penetrating. It may be inferred from the trend 
of the curves that at very low pressures the acoustic efficiency would probably be of 
the order of one or two parts in a thousand, as has been found by Webster to be 
the case for musical wind instruments operated by air. at a pressure of a few inches 
of Avater. 
The conditions under which sound-waves are generated by the alternate opening 
and closing of the ports in the diaphone piston are too complex to allow of an 
estimate being made of the wave-form in the resonator. This aspect of the subject 
should, howeA^er, be dealt with experimentally by the oscillating valve method. We 
are unable at the present moment to understand definitely the part played by the 
formation of the discontinuity in preventing a greater proportion of energy to be 
propagated to a distance as sound-Avaves. In its application to fog-signal waA*es, the 
problem is greatly complicated by propagation in three dimensions, the divergence 
tending to retard the tendency to the formation of a discontinuity with the resulting 
dissipation of energy. The effect of confining the sound-wave to a conical trumpet 
tends to enhance the formation of a discontinuity. The superiority of the short 
trumpets employed in practice would seem to be due to the fact that conditions are 
so adjusted that, while the advantage of resonance is obtained, discontinuity does not 
form before the Avave has emerged into the free atmosphere, when more rapid 
divergence precludes the further possibility of discontinuity taking place. The fact 
that in a siren the wa\~e is carried forward by air moving with considerable velocity 
would tend to retard the formation of the discontinuity and probably increase the 
