ON THE MATHEMATICAL. THEORY OF FLUIDS. 235 



change of density as being^ proportional to it." By aid of this 

 consideration he arrives at the following equation : 



\/%M 



1 + T- 



(1 + «9)y/ 



in which a is the velocity of sound, g the force of gravity, g h 

 the pressure of the air on a unit of surface, when its density is D 

 and temperature 9, and «; the increment of temperature caused 

 by the sudden condensation y. At the time this memoir was 

 written no experiments had been made by which the rise of 

 temperature, caused by a given small and sudden condensation, 

 could be determined. M. Poisson therefore reverses the ques- 

 tion, and infers the increment of temperature fi-om the observed 

 velocity of sound. He finds that if the dilatation or compression 

 were ^\-^ of the M'hole volume, the temperature would be de- 

 pressed or elevated one degree of the centigrade thermometer. 

 In the volume of the Annales de Physique et de Chhnie for the 

 year 1816, Laplace published the following theorem without the 

 demonstration : " The velocity of sound is equal to the pi'oduct 

 of the velocity which the Newtonian formvila gives, by the square 

 rootof the ratio of the specific heat of air when the pressure is con- 

 stant to its specific heat when the volume is constant." The proof 

 was first given in the Connaissance des Terns for 1825, and after- 

 wards in the fifth volume of the M^canique Cdleste ; jjrevious 

 to which the experiment* of Clement and Desormes, before men- 

 tioned, had furnished the means of instituting a numerical com- 

 parison between the theoretical and the observed velocity of 

 sound. This experiment was in fact a practical imitation, as 

 near as could be, of what was supposed to take place in aerial 

 vibrations. If specific heat be defined to be the quantity of heat 

 required to raise the temperature 1° under given circumstances, 

 the datum furnished by the experiment is the ratio of the spe- 

 cific heat under a constant pressvu-e to the specific heat under a 

 constant volume. It is convenient to speak of it in these terms 

 though the consideration of specific heats is not absolutely ne- 

 cessary in this question, as we shall presently see. By whatever 

 terms it be denoted the datum is one which experiment alone can 

 furnish, and without it no numerical comparison can be made 



* See the Memoir in \he^ Journal de Physique, im'^o^emh^x, 1819. This 

 memoir, wliich was composed in competition for the prize awarded by the 

 French Institute in 1813 to MM. Delaroche and Berard, contains in addition 

 to the detail of experiments made with reference to the subject proposed by 

 the Institute, viz., the specific heat of gases, the views of the authors respecting 

 the absolute caloric of space and the absolute zero of caloric. 



