where c stands for velocity (celerity), p for pressure, and d for density. When waves of sound are transmitted through air, the air is compressed in parts and rarefied in parts, in such a manner that compression follows rarefaction very rapidly, that part which is compressed at one instant being rarefied at the next, compressed again at a third, and rarefied at a fourth, and so on. Laplace was the first to point out that during such rapid changes of pressure as occur while a sound-wave is passing, the pressure will not rise proportionally to the density, as would be the case if Boyle’s law were followed; for on sudden rise of pressure the temperature of the compressed portion of the gas will be increased; and, correspondingly, on sudden fall of pressure, the wave of compression having passed, the temperature will fall. He showed that instead of two pressures being inversely proportional to their two volumes, under such circumstances, as they are according to Boyle’s law, or

p=v1,
p1 v

they must be inversely proportional to the volumes raised to a power, the numerical expression of which is the ratio of the specific heats of the two gases, γ, thus:

p= (v1 )γ;
p1 v

or as

v1 : v :: d : d1 ,

The ratio of the two specific heats can therefore be determined by finding the velocity of sound in the gas, and by noting at the same time its density and its pressure.

To determine the velocity of sound in a gas, it is not necessary to adopt the plan which has been successfully carried out with air; that is, to make a sudden sound at one spot and to measure the interval of time which the sound takes to travel to another spot some miles distant. There is a simpler method, depending on the fact that the lengths of the waves of compression and rarefaction are proportional to the velocity of the sound. So that, knowing the velocity of sound in air, the velocity in any other gas may be found by determining the relative length of the sound-waves in air and in that gas.