256 Mr. W. J. M. Rankine on Pressures of Saturated Vapours. 

 ment of the formula (1) produces a series in terms of the powers 

 ofi. 



T 



The differences between the two formulae appear to me to be 

 the followdng. 



The formula (1) is deduced from certain reasonings as to rela- 

 tions between the pressure of vapour and its total heat of evapo- 

 ration (which reasonings it would be premature for me to discuss 

 after so brief an examination of them as I have yet been able to 

 make), and it contains essentially but three independent coeffi- 

 cients ; so that all the coefficients of its development must be 

 functions of the first three. 



The formula (2) was rather suggested by, than deduced from, 

 certain hypothetical views as to the condition of a vapour at and 

 near the surface of its liquid ; with respect to which views 1 may 

 refer to the Transactions of the Royal Society of Edinburgh, 

 vol. XX., and the Philosophical Magazine for December 1851 and 

 December 1854. In this formula the number of independent 

 coefficients to be determined empirically is indefinite, although 

 three coefficients have been found to give a sufficiently close 

 agreement with such experiments as have yet been made. On 

 this point see § 10 of a paper in the Philosophical Magazine for 

 December 1854. The computation of the coefficients is a very 

 easy process. 



I may observe, that, from the following principle in the theory 

 of thermo-dynamics (Phil. Trans. 1854, part 1), — 



Latent heat of evaporation of unity of weight of a fluid 



= T .-J— (V —V) 



dr 



(expressed in units of work at the rate of 772 foot-pounds 

 per Fahrenheit-unit of heat), where v and V are the volumes 

 of unity of weight of the fluid in the liquid and vaporous 

 states respectively, -- 



it is easily deduced that if the vapour be a perfect gas, 



l0geP = «-p^^{(*-K)l0g,T + ^}, . . (3) 



in which Tq, Pq, Vq refer to a fixed standard absolute tempera- 

 ture, K is the dynamical specific heat of the vapour under con- 

 stant pressure (or the mechanical work required to heat unity of 

 weight of it one degree under constant pressure by friction), A; 

 that of the liquid, and a and c are constants to be found empi- 

 rically. But as few saturated vapours arc even approximately^ 



