234 DR. LOUIS YESSOT KING ON THE PROPAGATION OF SOUND IN THE FREE 
For any given adjustment of the phonometer the breadth of this band is proportional 
to the amplitude of vibration of the centre of the diaphragm, therefore to the 
compression of the air in the resonator, and finally to the compression in the sound¬ 
wave in the atmosphere outside. 
The conversion of the measured width of this luminous band (referred to as the 
“ phonometer reading ”) into the pressure amplitude of the sound-wave expressed in 
absolute units requires the determination of the “constant” of the instrument. 
This is accomplished in several ways by Prof. Webster. The most convenient 
method of determining the “constant” is by taking simultaneous measurements of 
the amplitude of the waves from a constant source of sound by means of the 
instrument to be calibrated and by a “ standard phonometer.” In the latter 
instrument the amplitude of vibration of the diaphragm is measured directly by an 
interference method combined with a stroboscopic arrangement for observing the 
fringes. From the mathematical theory of the motion of the diaphragm vibrating 
under the influence of aerial vibrations in the resonator, it is possible to express the 
compression in the sound-wave outside the instrument in terms of the phonometer 
reading, making use of separately determined inertia, elastic and damping constants 
of the vibrating system. 
Through the courtesy of Prof. Webster, a phonometer specially designed for the 
Father Point tests was constructed under his immediate supervision, and was 
successfully employed under the severe practical conditions met with. An account 
of experiments carried out with the Webster phonometer in connection with the 
measurement of sound from the diaphone is given in Appendix I., where further 
details relating to its manipulation and characteristics are given. 
§12. On the Influence of Meteorological Conditions on the Propagation 
of Sound. 
(i.) Introduction. 
The capricious behaviour of sound-waves propagated in the open atmosphere has 
been attributed to the existence of innumerable discontinuities of temperature, 
density and humidity, and to refraction by gradients of wind-velocity.* 
It has long been known that the retarding effect of the earth’s surface on the 
velocity of the wind is to give rise to a velocity gradient. It was first pointed out by 
Stokes! in 1851, that as a result, a sound-wave travelling against the wind will have 
its wave-front continually tilted upwards, so that the sound tends to pass over the 
* An excellent summary, with an extensive bibliography of the work of previous observers, is given 
by Bateman, “ The Influence of Meteorological Conditions on the Propagation of Sound,” ‘ Monthly 
Weather Review,’ 42, May, 1914, pp. 258-265. 
f STOKES, ‘Brit. Assoc. Rep.,’ 1857, p. 22; or ‘Mathematical and Physical Papers,’ vol. IV., p. 110. 
See also Rayleigh’s ‘ Sound,’ 1896, vol. II., p. 132. 
