234 SIXTH KEPORT — 1836. 



the observed velocitj' of sound and that which Newton derived 

 from the law of Mariotte (amounting to nearly a sixth of the 

 whole), has given rise to researches and experiments of a very 

 interesting nature, in which the philosophers of France have 

 chiefly signalized themselves. The first attempts to account for 

 this difference were unavailing. Newton did not succeed. Euler 

 supposed that as the Newtonian formula was obtained by neg- 

 lecting powers of the velocity of the aerial particles higher than 

 the first, the difference was attributable to an imperfect approxi- 

 mation. But Lagrange showed that the velocity of propagation 

 in the hypothetical fluid, of which the pressure varies in the 

 same proportion as the density, is the same for large excursions 

 of the vibrating particles as for small. Lagrange also remarked 

 that he could explain the discordance between the theory and 

 experiment by supposing the pressure of the air to increase 

 more rapidly than its density, but was deterred from arguing on 

 this supposition, as he considered it contradicted by the law of 

 Mariotte. The true solution was reserved for Laplace, who 

 first remarked that the excess of the experimental velocity above 

 the theoretical was owing to the development of heat and pro- 

 duction of cold which accompanies every very sudden compres- 

 sion and dilatation of the air, and which was not taken into ac- 

 count in the theory. This may perhaps be considered the most 

 successful explanation of a natural phaenomenon that has been 

 given in modern times. The cause assigned was a vera causae 

 one that may be presented to our senses, and therefore perfectly 

 intelligible. A very common experiment by which a combus- 

 tible substance is inflamed by the sudden compression of air, 

 leaves no room to doubt of the reality of the development of 

 heat under the circumstances contemplated in the theory. This 

 explanation was known to be Laplace's a considerable time be- 

 fore its author published anything expressly in writing respect- 

 ing it. An article by M. Biot in the Journal xle Physique, 

 1802, and the memoir of M. Poisson on the Theory of Sound*, 

 which was written in 1807, contain, I believe, the first applica- 

 tions of analysis to Laplace's Theory. Anterior to such appli- 

 cation it is necessary to make some supposition for the purpose 

 of connecting the effect of the developed heat with the other 

 elements of the problem. That which Biot and Poisson adopte<l 

 is thus expressed by the latter : — " In the propagation of sound, 

 the compression or dilatation which takes place successively in 

 the whole extent of the mass of air being very small, we may re- 

 gard the augmentation or diminution of temperature due to this 



• Journal (Ic I'Ecole Pohjtechniqiie, cah. xiv. 



