450 Sir W. Thomson on the Equilibrium of Vapour 



Now, in the space occupied by vapour, the pressure is less at the 

 higher than at the lower of two points whose difference of levels 

 is h, by a difference equal to ah. And there is permanent equi- 

 librium between vapour and liquid at all points of the free sur- 

 face. Hence the pressure of vapour in equilibrium is less at a 

 concave than at a plane surface of liquid, and less at a plane 

 surface than at a convex surface, by differences amounting to 



T<T 



per unit difference of curvature. That is to say, if & denote 



the pressure of vapour in equilibrium at a plane surface of liquid, 

 and p the pressure of vapour of the same liquid at the same tem- 

 perature presenting a curved surface to the vapour, we have 



- and — being the curvatures in the principal sections of the 



surface bounding liquid and vapour, reckoned positive when con- 

 cave towards the vapour. 



; In strictness, the value of a to be used in these equations, (1) 

 and (2), ought to be the mean density of a vertical column of 

 vapour extending through the height h from the plane of refer- 

 ence. But in all cases to which we can practically apply the 

 forumlse, according to present knowledge of the properties of 

 matter, the difference of densities in this column is very small, 

 and may be neglected. Hence, if H denote the height of an 

 imaginary homogeneous fluid above the plane of reference, which, 

 if of the same density as the vapour at that plane, would pro- 

 duce by its weight the actual pressure va t we have 



^ff 



Hence, by (1) and (2), 



p. 



0-4)- (3) 



For vapour of water at ordinary atmospheric temperatures, H 

 is about 1,300,000 centimetres. Hence, in a capillary tube 

 which would keep water up to a height of 13 metres above the 

 plane level, the curved surface of the water is in equilibrium with 

 the vapour in contact with it, when the pressure of the vapour is 

 less by about yoou of its own amount than the pressure of vapour 

 in equilibrium at the plane surface of water at the same tempe- 

 rature. 



For water the value of T at ordinary temperatures is about "08 

 of a gramme weight per centimetre ; and p, being the mean of 

 a cubic centimetre, in grammes, is unity. The value of a for 

 vapour of water, at any atmospheric temperature, is so small that 

 we may neglect it altogether in equation (1). In a capillary 



