534 Mr. Rankine on the Centrifugal Theory of Elasticity, 



liquid, the density of vapour is sensibly uniform, the layers close 

 to that surface are probably in a state of condensation by attrac- 

 tion, analogous to that of the earth's atmosphere under the in- 

 fluence of gravity. 



Professor Faraday has expressed an opinion, founded on his 

 own experiments and those of MM. Dulong and Thenard, that 

 a state of condensation exactly resembling that which I have 

 described is produced in gases by the superficial attraction of 

 various substances, especially platinum, and gives rise to chemi- 

 cal actions which have been called catalytic. 



To express this third condition algebraically, let the boundary 

 between the liquid and the vapour be conceived to be a plane of 

 indefinite extent, perpendicular to the axis of a? ; and let positive 

 distances be measured in a direction from the liquid towards the 

 vapour. 



Let X, x + dx represent the positions of two planes, perpen- 

 dicular to the axis of x, bounding a layer whose thickness dx is 

 very great as compared with the distance between two atomic 

 centres, but very small as compared with any perceptible distance, 

 and let a portion of the layer be considered whose transverse 

 area is unity. 



Let p represent the mean density of the layer. Then it is 

 acted upon by a force 



—pXdx, 



the resultant of the actions of all the neighbouring atoms, which 

 has the negative sign, because it is attractive towards the liquid, 

 X being a function of the position of the layer in question, and 

 of the densities and positions of all the neighbouring layers. 

 The superficial atomic elasticity behind the layer being p, and 



in front of it j9 + ~ dx, it is also acted on by the force 



-^dx- 

 dx"^^' 



hence its condition of equilibrium is 



S+''X=0 (33) 



In order to integrate this equation, so as to give a relation 

 applicable at perceptible distances from the surface, let Xq, Xy 

 represent the positions of two planes perpendicular to the axis 

 of X, the former situated in the liquid, the latter in the vapour, 

 and so far asunder that the densities beyond them are sensibly 

 uniform, and equal respectively to Dq for the liquid and D, for 

 the vapour, the corresponding superficial atomic elasticities being 

 Pq and;?|. TJien dividing equation (33) by /?, and integrating 



