ON THE MATHEMATICAL THEORY OF FLUIDS. 239 



the above relation between ji and p, Mr. Ivory infers (p. 255) 

 that the ratio of the specific heats is not a constant ratio for 

 large variations of density and temperature*. 



The principle on which the effect of moisture contained in the 

 air is introduced into the theoretical determination of the velocity 

 of sound, is derived from Dalton's theory of mixed gases. If 

 two quantities, v, v', of two gases under the same pressure p, 

 and of the same temperature 9, be put into a space v + v', the 

 gases will penetrate into each other and become perfectly mixed , 

 so that the proportional parts will be everywhere the same in 

 the same space. Also the temperature and pressure of the mix- 

 ture will be jy and 9, the same as those of the constituents. 

 From these facts, established by experience, may be derived by 

 reasoning as Poisson has done in the second of his papers in vol. 

 xxiii. of the Annates de Chi?n. et Phys., p. 348, the following 

 law, which experience also confirms : — '* The pressure of a mix- 

 ture of gases and vapours will always be the sxim of the pres- 

 sures which these fluids would support separately at the same 

 temperature, and the same in volume as the mixture." The 

 atmosphere in its usual state is a mixture of dry air and vapour 

 of water. It is found that the maximum of aqueous vapour 

 formed in a vacuum at the temperature 18°" 75 C, is measured 

 by the barometric height O^'OIG, and by the preceding law the 

 same height of the barometer would measure the elastic force of 

 vapour formed at the same temperature in diy air of the ordinary 

 pressure 0'"'76, and increase the pressure to 0°'*776, since the 

 maximum of vapour, that is, the greatest quantity which the 

 given temperature allows to be formed, is the same in the two 

 cases. Gay-Lussac has inferred from his experiments, that if 

 aqueous vapour covild be raised from the tension 0™*016 to 

 0'"'76 without liquifying, its density would be to that of dry air, 

 under the same pressure and at the same temperature, as 5 to 8. 

 Hence in general, if D be the density of dry air, D' that of moist 

 air under a given barometric pressure h, and at a given tempe- 



* An equivalent relation between^ and q may be obtained in another man- 

 ner, which I have adverted to in a communication to the No. of the Phil. Mag. 

 and Annals for May, 1S30, and have since developed more fully in a paper re- 

 cently read before the Cambridge Philosophical Society ; viz. by assuming the 

 velocity of propagation of sound to be constant when the temperature is given, 

 and then joining with the usual equations of fluid motion, a general expression 

 for uniform propagation, which may be arrived at independently of the consi- 

 deration of temperature. When the resulting equation between p and q is used 

 for finding the velocity of propagation, it gives an expression agreeing with that 

 obtained on the supposition of a constant ratio of the specific heats, when the 

 condensations and rarefactions are small, but diverging from it as they become 

 larger. 



