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different temperatures with a theoretical result derived according to 

 the general dynamical theory from an empirical formula for the 

 pressure of carbonic acid in terms of its temperature and density, 

 which was kindly communicated by Mr. Rankine to the authors, 

 having been investigated by him upon no other experimental data 

 than those of Regnault on the expansion of the gas by heat and its 

 compressibility. 



Experiments were also made on hydrogen gas, which, although 

 not such as to lead to accurate determinations, appeared to indicate 

 very decidedly a cooling effect amounting to a small fraction, per- 

 haps about yg-, of that which air would experience in the same cir- 

 cumstances. 



The following theoretical deductions from these experiments are 

 made : 



I. The relations between the heat generated and the work spent 

 in compressing carbonic acid, air and hydrogen, are investigated 

 from the experimental results. In each case the relation is nearly 

 that of equivalence, but the heat developed exceeds the equivalent 

 of the work spent, by a very small amount for hydrogen, consider- 

 ably more for air, and still more for carbonic acid. For slight 

 compressions with the gases kept about the temperature 16, this 

 excess amounts to about -fa of the whole heat emitted in the case 

 of carbonic acid, and ^-Q in the case of air. 



II. It is shown by the general dynamical theory, that the air ex- 

 periments, taken in connexion with Regnault's experimental results 

 on the latent heat and pressure of saturated steam, make it certain 

 that the density of saturated steam increases very much more with 

 the pressure than according to Boyle's and Gay-Lussac's gaseous 

 laws, and numbers are given expressing the theoretical densities of 

 saturated steam at different temperatures, which it is desired should 

 be verified by direct experiments. 



III. Carnot's function in the " Theory of the Motive Power of 

 Heat" is shown to be very nearly equal to the mechanical equivalent 

 of the thermal unit divided by the temperature from the zero of the 

 air-thermometer (that is, temperature Centigrade with a number equal 

 to the reciprocal of the coefficient of expansion added), and correc- 

 tions, depending on the amount of the observed cooling effects in the 

 new air experiments, and the deviations from the gaseous laws of 



