as applied to Gases and Vapours. 527 



Supposing the value of ^p to be known, this equation 



affords the means of calculating the values of the function A cor- 

 responding to various densities, from those of the coefficient E as 

 given by experiment. 



As a gas is rarefied, -yrn- approximates to unity, A dimi- 

 nishes without limit, and the value of E consequently approxi- 

 mates to YT) the reciprocal of the absolute temperature at 0^ Cen- 

 tigrade. This conclusion is verified by experiment; and by 

 means of it I have determined the values already given, viz. 



C = 274F'6 Centigrade, and -i =-00364166 for the Centigrade 

 scale. -p. 



(24.) In order to calculate the values of ^p , I have made 



use of empirical formulae, deduced from those given by M. Reg- 

 nault in his memoir on the Compressibility of Elastic Fluids. 

 In M. Eegnault's formulae, the unit of pressure is one metre of 

 mercury, and the unit of density the actual density correspond- 

 ing to that pressure. In the formulae which I am about to state, 

 the unit of pressure is an atmosphere of 760 millimetres of mer- 

 cury, or 29*922 inches ; and the unity of density, the theoretical 

 density in the perfectly gaseous state at 0° Centigrade, under a 

 pressure of one atmosphere, which has been found from M. Reg- 

 nault's formulae by making the pressure =0 in the value of 



M/iP 



— YY"^. M. Eegnault^s experiments were made at temperatures 



slightly above the freezing-point, but not sufficiently so to render 

 the formulae inaccurate for the purpose of calculating the ratio 



in question, ^^. 



The formulae are as follows : — 



Supposing jjj^ given, 



C»MP . D ^jDy 



which, when T is small, or t nearly = C, gives an 

 approximate value of — tT"^- 

 Supposing Py given, 



which, when T is small, gives an approximate 

 value of 



> ' . (24) 



»MPo 



2N2 



