23G SIXTH REPORT — 183G. 



between the theoretical and observed velocities of sound. The 

 result of the compai'ison, first made by Laplace, was, that the 

 theoretical determination fell short of the observed value by 

 7"'*5. A difference of this kind was to be expected, as it was 

 impossible to perform the experiment so rapidly that some of 

 the developed heat would not escape througii contact of the air 

 with the containing substances. The ratio of the specific heats, 

 as obtained by MM. Clement and Desormes, is 1-354. Gay- 

 Lussac, on repeating their experiment with great care, and un- 

 der circumstances a little different, fovmd 1*37'', which brings 

 the observed and theoretical velocities something nearer, but 

 the latter still falls short of the other. 



The mathematical theory* of Laplace is prefaced by certain 

 theoretical considerations respecting free and latent heat, and 

 the mutual action of the molecules of bodies and their caloric ; 

 which are subsequently introduced into the investigation for de- 

 termining the velocity of soundf . It is proper, however, to 

 observe that the solution of this problem is not necessarily con- 

 nected witii any considerations either of latent heat or of speci- 

 fic heats. This is sufficiently apparent from what M. Poisson 

 has written on the subject. In the first of two excellent papers 

 (contained in the volume of the Amiules de Chimie et de Phy- 

 sique for 1823), which place in a simple point of view all that 

 has been most satisfactorily established with reference to the 

 question before us, this autlior deduces the velocity of sound, 

 by means of the usual experimental data, from the formula ob- 

 tained in his Memoir on the theory of soimd, which, as was 

 said before, rests on the single assumption that the increment 

 of temperature is proportional to the condensation, without em- 

 ploying any additional hypothesis whatever, and without any 

 mention of specific heats or of latent heat. In the same paper 

 lie goes on to show, by adopting the definition of specific heat 

 stated above, and by further supposing that for small changes 

 of temperature the absolute quantity of heat gained or lost is 

 proportional to the rise or fall of the thermometer, that tlie 



* Mecanique Celeste, liv. xii. chap. iii. 



f Laplace has also supposed (liv. xii. chap. iii. art. 7,) that LL 



d ^^ 



= (1 — /3) —S. , g being the density of the gas, c the free caloric which has a 



sensible effect on the thermometer, and /3 a positive constant. This equation is 



not deduced from anterior considerations. It follows from it that — = — fi ~i 



c - ' 



and consequently that the free caloric increases as the density diminishes. 



J 



