530 Mr. Rankine on the Centrifugal Theory of Elasticity, 



(26.) The empirical formiilai (24), representing the experi- 

 ments of M. Regnanlt on the compressibility of carbonic acid 

 gas, atmospheric air, and hydrogen at certain temperatures, give 

 for these temperatures the values of a function which is theo- 

 retically expressed by 



CnMP_ CA CnMf(D) 

 tD "^""■^ "^ tD ^"^^f 



It is evident, that supposing the value of — =r— for any given 



density to be known by experiment, and that of A to be calcu- 

 lated from the value of the coefficient E, or from the empirical 

 formulae (25) and (26), the corresponding value of the function 



— i^ — - may be determined by means of equation (27). 



By this method I have obtained the following empirical for- 

 mulae for calculating the values of that function : — 



For Carbonic Acid, 



D ~ nW 

 where log h = 3- 1083932. 

 For Atmospheric Air, 



^M/(D) _ / D^y 

 D ~ ^ \nM/ ' 

 where log ^ = 3-8181545. 



As only one value of — -^ — - for hydrogen can at present be 



ascertained, it is impossible to determine a formula for that gas. 

 The single value in question is — 



For Po=l atmosphere, ^^^^^^ ='01059. . . (29) 



(27.) I now proceed to determine theoretically, from the data 

 which have already been obtained, the mean coefficients of dilata- 

 tion at constant pressure, between 0° and 100° of the Centigrade 

 scale, for the three gases under consideration, at various pressures. 



Let E' represent the coefficient required ; Sq and Si the re- 



nM. 

 spective values of ^jir- for 0° and 100° under the pressure P, that 



is to say, the volumes occupied by the weight wM at those tem- 

 peratures ; Aq and Aj, /q and /j, the corresponding values of A 



(38) 



