322 Royal Society. 



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 ^ of the whole heat emitted in the case 

 of carbonic acid, and ^J^ 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 

 expansion and compression determined by Regnault, are applied to 

 give a more precise evaluation. 



IV. An absolute scale of temperature, that is, a scale not founded 

 on reference to any particular thermometric substance or to any 

 special qualities of any class of bodies, is founded on the following 

 definition : — 



If a physical system be subjected to cycles of perfectly reversible 

 operations and be not allowed to take in or to emit heat except in loca- 

 lities, at two fixed temperatures, these temperatures are proportional to 

 the whole quantities of heat taken in or emitted at them respectively 

 during a complete cycle of the operations. 



ITie principles upon which the unit or degree of temperature is to 

 be chosen, so as to make the difference of temperatures on the abso- 

 lute scale, agree with that on any other scale for a particular range 

 of temperatures. If the difference of temperatures between the 

 freezing and the boiling-points of water be made 100° on the new 

 scale, the absolute temperature of the freezing-point is shown to be 

 about 273°" 7 ; audit is demonstrated that the temperatures from the 

 freezing-point on the new scale will agree very closely with Centi- 

 grade temperature by the standard air- thermometer ; quite within 

 the limits of the most accurate practical thermometry when the tem- 

 perature is between 0° and 100° Cent., and very nearly if not quite 

 within these limits for temperatures up to 300° Cent. 



V. An empirical formula for the pressure of air in terms of its 

 density, and its temperature on the absolute scale, is investigated, by 

 using forms such as those first proposed and used by Mr. Rankine, 

 and determining the constants so as to fulfill the conditions (1) of 

 giving the observed cooling effects, (2) of agreeing with Regnault's 

 observations on expansion by heat, and (3) of agreeing with Regnault's 

 experimental results on compressibility at a particular temperature. 



