284 Dr. Rankine on the Elasticity of Vapours. 



cal Journal for July 1849, viz. 



, b c 



where t denotes the absolute temperature, measured from the 

 absolute zero, 274° C. below melting ice, and a, b, and c are 

 determined from three data for each fluid. (For values of those 

 constants for various fluids, see also the Philosophical Magazine 

 for December 1854, and l A Manual of Prime Movers/ p. 237). 

 This formula, besides agreeing very closely with experiment at 

 all temperatures, gives the following results : — That every sub- 

 stance can exist in the state of vapour at all temperatures above 

 the absolute zero ; and that the pressure of saturation of every 

 vapour tends towards a limit as the temperature increases, — the 

 latter result being in accordance with the conclusion deduced 

 by M. Regnault from his experiments. 



6. It may be remarked that if vapours at saturation were 

 perfectly gaseous, it can be proved from the laws of thermo- 

 dynamics that their pressures of saturation would be given by 

 the formula 



hyp log,, = <i- j^ - ^ . hyp log t ; 



where c is the specific heat of the gas at constant volume, d its 

 specific heat at constant pressure, c" the specific heat of the 

 liquid, b the total heat of gasefication of the fluid at the abso- 

 lute zero, from which t is reckoned, and a a constant to be de- 

 termined by experiments on the pressure corresponding to a 

 given boiling-point. So far as I know, this proposition has not 

 before been published ; but its demonstration will be obvious to 

 any one acquainted with the principles of thermo-dynamics. 

 When the formula is applied to steam, it gives pressures agreeing 

 very closely with actual pressures of steam from 0° to 160° C. ; 

 but above the latter temperature the effect of the deviation of 

 the vapour from the perfectly gaseous condition becomes consi- 

 derable; so that at 220° C. the pressure given by the formula 

 for a perfect gas is about one-fiftieth part less than the actual 

 pressure. 



I am, Gentlemen, 



Your most obedient Servant, 



W. J. Macquorn Rankine. 

 Glasgow University, Feb. 18, 1865. 



P.S. — Since the above was written, I have seen the formula 

 proposed by Mr. Edmonds in the Philosophical Magazine for 

 March 1865. In the notation of the present paper, that formula 



