and the Observed Velocity of Sound in Air and Gases. 3 



tion*. Indeed, as this assumption is necessary in order to ren- 

 der the equation integrable, and as it requires that the magnitude 

 of the displacements of the molecules of air is infinitely small in 

 comparison with the length of the wave, there certainly was some 

 ground for suspecting the admissibility of the assumption, and 

 consequently for doubting the rigorous exactness of the result- 

 ing expression for the velocity of sound. But the more rational 

 and satisfactory explanation of this discrepancy was reserved for a 

 later period, and may be considered the legitimate offspring of 

 the great development of the science of thermotics which cha- 

 racterized the close of the last century. The bearing of these 

 discoveries on the problem of the propagation of sound did not 

 escape the sagacity of Laplace. The known extrication of heat 

 during the condensation of gases, furnished this illustrious phy- 

 sicist with a force which is momentarily developed in the vibra- 

 tions of a gas, and which, augmenting the ratio of the elasticity 

 to the density, necessarily increases the velocity of the generated 

 pulse. Accordingly, about the beginning of the present century, 

 he suggested this disengagement of heat during the wave-motion 

 as the true cause of the perplexing discrepancy. In the year 

 1807, M. Poisson first put Laplace's suggestion in a distinct 

 mathematical form, in a remarkable " Memoir on the Theory of 

 Sound"-}-. Finally, in 1816, Laplace himself announced the 

 following theorem as the result of his physico-mathematical 

 researches in relation to this problem • namely, " The velocity 

 of sound is equal to the product of the velocity which is given 

 by the Newtonian formula, by the square root of the ratio of the 

 specific heat of air under constant pressure, to its specific heat 

 under constant volume"!. 

 ^S- Since this period, although a large number of the most dis- 

 tinguished physical philosophers have regarded this extension of 

 the Newtonian theory as having exhausted the problem of the 

 propagation of sound, yet great obscurity and uncertainty seems 

 to have been attached to it by eminent English mathematicians 

 and physicists. Some have unhesitatingly denied the necessity 

 as well as the validity of Laplace's explanation of the discrepancy 

 between theory and fact, and have endeavoured to deduce for- 

 mulae for the velocity of sound which dispense with the disen- 

 gagement of heat during the wave-motion, and which neverthe- 

 .less give results sufficiently accordant with experiment. While 

 some have questioned the correctness of the mathematical pro- 



* Herschel's " Treatise on Sound," Encyc. Metrop. articles 55 and 67. 



t " Memoire sur la Theorie du Son," in the Journal de VEcole Poly- 

 technique, vol. vii. (cahier 14) p. 360 et seq. Paris, 1808. 



% Annales de Chimie et de Physique, vol. iii. p. 238. Paris, 1816. Also 

 Mecanique Celeste, vol. v. book 12. pp. 96 and 123. Paris, 1825. 



B2 



