216 DR. LOUIS YESSOT KING ON THE PROPAGATION OF SOUND IN THE FREE 
first been investigated by Topler and by Boltzmann, # who determined a value 
|s| = 6'5 x 10 -8 for the maximum condensation in a musical note of pitch n = 181, and 
of sufficient intensity to be just audible. The matter was discussed considerably later 
by Rayleigh, t Wien,| and more recently by Webster. § who made use of an absolute 
“ phonometer ” of the type described in Part II. of the present paper. These 
experimenters agree in obtaining for the maximum condensation values of the 
same order as that given above. Inserting this value in the formulae of § 2, we 
obtain for the numerical characteristics of just audible sound-waves of pitch 181, 
\s | = 6'5 x 10~ 8 , 1 dp | /po — 9’2 x 10~ 8 , j ^! = 1‘9 x 10 -fi cm., |^j = 2'2xl0 -3 cm./sec., 
while \_dW/dt] = l'O x 10~ 4 ergs per sec./cm 2 . 
It will be seen in Part II., from the results of an efficiency test on a powerful 
fog-signal apparatus, that the above quantities may be many thousand times greater 
when calculated for the sound-waves generated at the vertex of the conical siren 
trumpet. 
The efficiency of sources of sound with reference to fog-signals seems to have 
first been discussed by Rayleigh || in connection with the Trinity House experiments 
conducted at St. Catherine’s Point, Isle of Wight, in 1901.11 Actual measurements 
of the acoustic output of musical instruments were carried out as early as 1902 by 
Webster, ## making use of his absolute phonometer. Various experiments agreed 
in assigning efficiencies of the order of two or three parts in a thousand to several 
varieties of wind instruments operated by pressures of a few inches of water, while 
an electrically-driven sound generator was constructed having an efficiency of as much 
as five parts in a thousand. 
It is interesting to make use of the preceding data in connection with the sound¬ 
waves generated by fog-sirens operating under normal atmospheric conditions. The 
“ diaphone ” described in Part II. gave a signal of six seconds duration each minute : 
pitch, n = 174 ; air consumption, 14‘8 cubic feet per second at a pressure of 23 lbs./ 
sq. in., representing a total available rate of expenditure of energy (calculated 
adiabatically) during the blast of 35 H.P. In exceptionally calm weather the signal 
was just audible at a distance of 10 nautical miles (18*4 km.). At this distance the 
flux of energy across a square centimetre of wave-front (regarded as. a plane wave) 
is given by 
[< dWldt-] = W\s\ 2 Po .(16) 
* Topler and Boltzmann, ‘Ann. Phys. Chem.,’ 141, pp. 321-352 (1870). 
t Rayleigh, ‘Roy. Soc. Proc.,’ 26, pp. 248-249 (1877); ‘Scientific Papers,’ vol. i., p. 328; ‘Theory 
of Sound,’ vol. II., p. 432 (1896). 
\ Wien, ‘Ann. Phys. u. Chem.,’ 36, pp. 834-857 (1889). 
§ Webster, ‘Boltzmann Memorial Volume,’ pp. 866-875 (J. A. Barth, Leipzig, 1904). 
|| Rayleigh, ‘Phil. Mag,,’ 6, pp. 289-305, 1903; ‘Scientific Papers,’vol. v., p. 126. 
If ‘ Report of Trinity House Fog-Signal Committee on Experiments Conducted at St. Catherine’s 
Point, Isle of Wight ’ (Darling and Son, London, 1901). 
** Webster, loc. tit., p. 872. 
