ON THE MATHEMATICAL THEORY OF FLUIDS. 237 



quantity expressed by 1 + - — "- -at— is equal to the ratio of 



the specific heat under a constant pressure to the specific heat 

 under a constant volume. From the reasoning of M. Poisson 

 we may therefore infer, that for the theoretical explanation of 

 the excess of the velocity of sound over the Newtonian determi- 

 nation one assumption only is absolutely necessary, viz., that 

 the changes of temperature produced by sudden small variations 

 of density are, for a given temperature of the air, proportional 

 to those variations ; but if the consideration of specific heats be 

 introduced, that it is necessary also to suppose the small varia- 

 tions of absolute heat to be proportional to the corresponding 

 variations of temperature. 



Mr. Ivory has written on this question some things well de- 

 serving of notice. In a paper before referred to* he deduces 



the velocity of sound from the formula ^. ~ "^ , which 



P "^ P 



he had previously arrived at by considerations already stated, 

 and finds it equal to V V m^ ^ being the velocity obtained ac- 

 cording to the law of Boyle and Mariotte. This is the same 

 value that is given by other methods, since the index ?« is the 

 ratio of the specific heats. When the above equation is em- 

 ployed with reference to the variation of density in the atmo- 

 sphere and to astronomical refractions, the value of in that best 

 accords with phfenomena is nearly r25, as we have seen, in- 

 stead of 1'375. This seems to prove that the law of nature is 

 not expressed under all circumstances by the same formula, and 

 that one which applies very well to sudden changes of density 

 of the air in motion is inapplicable to those that are permanent, 

 like the variations of density of the atmosphere at rest depend- 

 ing on the height above the earth's surface. 



Afterwards, in 1827t, Mr. Ivory applied to the problem a 

 different kind of reasoning on the following principles. First, 

 it was admitted that equal quantities of absolute heat produce 

 equal increments of volume : secondly, that the rise of tempe- 

 rature is proportional to the increment of volume according to 

 the indications of the air thermometer : thirdly, that the abso- 

 lute heat is etjual to the sum of the latent heat, and the heat of 

 temperature. From which it follows that the increment of 

 latent heat is also proportional to the increment of volume ; 

 hence if v be the volume when the temperature is 0, v' the volume 



* Phil. Mag., vol. 66, p. 12. 



t Phil. Mag. and Annals, vol. i. pp. 91 and 251. 



