522 Mr. Rankine on the Centrifugal Theory of Elasticity, 

 and consequently 



¥«-T (12o) 



Therefore 



Temperature is a function of universal constants, and of the vor- 

 tical vis viva of the atomic atmospheres of so much of the substance 

 as would, in the condition of perfect gas, fill unity of volume under 

 unity of pressure at some standard temperature. 



The equation (12a) further shows, that in any two perfect gases, 

 the respective values of the quotient of the pressure by the density 

 corresponding to the same temperature, bear to each other a con- 

 stant ratio for all temperatures, being that of the values of the 



coefficient b ~. 

 M 



Therefore the pressure of a perfect gas at a given density, or 

 its volume under a given pressure, is the most convenient mea- 

 sure of temperature. 



Let Vq represent the elasticity of a perfect gas of the density 

 D at the temperature of melting ice, P that of the same gas at 

 the same density, at a temperature distant T degrees of the ther- 

 mometric sca'e from that of melting ice, and C a constant coeffi- 

 cient depending on the scale employed ; then the value of T is 

 given by the equation 



P— P 

 T=C^-p^^ 



or "^ y (13) 



T+C=C^ 



The value of the constant C is found experimentally as follows : 

 — Let Pj represent the elasticity of the gas at the temperature of 

 water boiling under the mean atmospheric pressure, Tj the num- 

 ber of degrees, on the scale adopted, between the freezing- and 

 boiling-points of water; then 



and 



^0 





(14) 



C is in fact the reciprocal of the coefficient of increase of elas- 

 ticity with temperature, or the reciprocal of the coefficient of 

 dilatation, of a perfect gas at the temperature of melting ice. 



(17.) As it is impossible in practice to obtain gases in the 

 theoretical condition referred to, the value of C can only be 

 obtained by approximation. From a comparison of all M. Reg- 

 nault's best experiments, I have arrived at the following values, 

 which apply to all gaseous bodies. 



