as applied to Gases and Vapours. 535 



between tlie limits Xq and a?^ the result obtained is 



r^-E = -nd..X (34) 



'^PO P ^^0 



Had we a complete knowledge of the laws of molecular forces 

 in the solid, liquid and gaseous states,, this equation, taken in 

 conjunction with the two conditions previously stated, would be 

 sufficient to determine formulae^ for calculating the total elasti- 

 city, and the respective densities of a liquid and its vapour when 

 in contact in a limited space, at all temperatures. 



(33.) In the absence of that knowledge, I have used equation 

 (34), so as to indicate the form of an approximate equation suit- 

 able for calculating the elasticity of vapour in contact with its 

 liquid, at all ordinary temperatures, the coefficients of which I 

 have determined empirically, for water and mercury, from the 

 experiments of M. Regnault, and for alcohol, sether, turpentine, 

 and petroleum from those of Dr. Ure. 



It has been shown (equation 19) that the superficial atomic 

 elasticity is expressible approximately in terms of the density 

 and temperature for gases by 



P 



=p'i^y^^{p^c^b)y 



where the function F is a very rapidly convergmg series, m 

 terms of the negative powers of the absolute temperature, the 

 coefficients being functions of the density. It is probable that 

 a similar formula is applicable to liquids, the series being less 

 convergent. 



It follows that the density is expressible approximately in 

 terms of the superficial atomic elasticity by 





the function <l> being also a converging series in terms of the 

 negative powers of the absolute temperature, and the coefficients 

 being functions of p. 



Making this substitution in the first side of equation (34), and 



abbreviating <I> Ip, p—i) into <I>, we obtain the following 



result : — 



/*Pi , 1 T /*Pl J 



Po '^Xl+*) 





(log,;,.-log.;,„-^'" dp . ^(i:p^) 

 ■'<fe.X;. . (35) 



