154 MR W. J. M. RANKINE ON THE 
The equilibrium of a vapour in contact with its liquid depends on three con- 
ditions. 
First, The total elasticity of the substance in the two states must be the 
same. 
Secondly, The superficial atomic elasticity must vary continuously ; so that 
if at the surface which reflects light there is an abrupt change of density (which 
seems almost certain), there must there be two densities corresponding to the 
same superficial-atomic elasticity. 
Thirdly, The two forces, which act on each stratum of vapour parallel to the 
surface of the liquid, namely, the preponderance of molecular attraction towards 
the liquid, and the difference of the superficial-atomic elasticities at the two sides 
of the stratum, must be in equilibrio. 
Close to the surface of the liquid, therefore, the vapour is highly condensed. 
The density diminishes rapidly as the distance from the liquid increases, and at 
all appreciable distances has a sensibly uniform value, which is a function of the 
temperature and of certain unknown molecular forces. 
The integration of a differential equation representing the third condition of 
equilibrium, indicates the form of the approximate equation. 
ioe Paes Re OI) 
The coefficients of which have been determined empirically by three experi- 
mental data for each fluid. For proofs of the extreme closeness with which the 
formulz thus obtained agree with experiment, I refer to the Journal in which 
they first appeared. 
I annex a table of the coefficients for water, alcohol, ether, turpentine, petro- 
leum, and mercury, in the direct equation, and also in the inverse formula, 
Ja wer - We. RN) 
by which the temperature of vapour at saturation may be calculated from the 
pressure. In the ninth and tenth columns are stated the limits between which the 
formulze have been compared with experiment. 
For turpentine, petroleum, and mercury, the formula consists of two terms 


only, 
Log P=a—2 2 ea) 
the small range of the experiments rendering the determination of y impossible. 
Se 
