154 MR W. J. MACQUORN RANKINE ON THE DENSITY OF STEAM. 



15. So far as it is possible to represent those differences by anything like a 

 formula, they agree in a rough way with a constant excess of about 027 of a cubic 

 foot in the theoretical volume of one pound of steam above the experimental 

 volume ; and this also represents in a rough way the difference between the 

 curves, whose ordinates express respectively the results of the theoretical formula 

 and those of an empirical formula deduced from the experiments, so far as those 

 curves, as shown in a plate annexed to the paper referred to, extend through the 

 limits of actual experiment on steam, above 212°. 



16. As the principles of the mechanical theory of heat may now be considered 

 to be established beyond question, it is only in the data of the formula that we 

 can look for causes of error in the theoretical calculation. I shall now consider 

 those data, with reference to the probability of their containing numerical errors. 



I. Total Heat of JEvapo7'atio7i. — It is very improbable that this quantity, as 

 computed by M. Eegnault's formula, involves any material error. 



II. Sensible Heat of the Liquid Water. — The empirical formula from which 

 this quantity is computed was determined from experiments by M. Reqnault, 

 which agree extremely well amongst themselves. (For the investigation of the 

 formula, see " Trans. Royal Soc. Edin.," vol. xx. p. 441). The subtraction of the 

 sensible heat from the total heat leaves the latent heat, upon which the increase 

 of volume depends ; hence, to account for an error in excess of the formula for 

 the volume by means of an error in the computation of the sensible heat, it must 

 be supposed that the specific heat of liquid water above 212° increases much more 

 rapidly than M. Regnault's experiments show, so as to produce a correspond- 

 ingly more rapid diminution in the latent heat of evaporation. It is easily com- 

 puted, for example, that to account for an error in excess of 0*27 of a cubic foot 

 in the volume of one pound of steam at 266°, by an error in defect in the sensible 

 heat, we must suppose that error to amount to about 24 British thermal units per 

 pound of water ; but such an error is altogether improbable. 



III. Absolute Temperature. — The position of the absolute zero may be con- 

 sidered as established with a degree of accuracy which leaves no room for any 

 error sufficient to account for the differences now in question. 



dP 



IV. Function r-r-. — The same may unquestionably be said of this function; 



which represents the mechanical equivalent of the latent heat of evaporation of 

 so much water as fills one cubic foot more in the vaporous than in the liquid 

 state. 



