Inasmuch as Laplace's formula is a rigorous deduction from the physical hypotheses adopted, there is no way of escaping from his result but by calling in question the hypotheses themselves. Now the development of heat and cold by sudden condensation and rarefaction is not merely a hypothetical cause, the only evidence of whose existence is that it explains the phenomena, but is a well-known physical fact, proved by direct experiment. That in the case of small sudden condensations (positive or negative) the increase of temperature is ultimately proportional, cæteris paribus, to the condensation, will not, it is presumed, be called in question. The only way, then, of escaping from the conclusion that the velocity of sound is really increased by the cause assigned is, to suppose that the heat produced by condensation passes away so rapidly by radiation that the result is the same as though condensation and rarefaction were incapable of changing the temperature of air. The main object of the present communication is to examine the consequences of such a supposition, in order to make out whether it be tenable or not.

Let us take the case of an infinite mass of homogeneous elastic fluid, acted on by no external forces, and having throughout a uniform temperature, and consequently a uniform pressure, except in so far as the pressure, and consequently the temperature, are affected by small vibratory movements.