68 POPULAR LECTURES AND ADDRESSES. 



the height of any point, P, of the free surface above 

 a certain plane of reference, which I shall call for 

 brevity the plane level of the free surface. This 

 will be sensibly the actual level of the free surface 

 in regions, if there are any, with no part of the 

 edge (or bounding line of the free surface where 

 liquid ends and solid begins) at a less distance 

 than several centimetres. Lastly, let r and r' be 

 the principal radii of curvature of the surface at P. 

 By Laplace's well-known law, we have, as the 

 equation of equilibrium, 



(p-r)// = T(i + l.,). . (I). 



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 /z, by a difference equal 

 to a/i. And there is permanent equilibrium between 

 vapour and liquid at all points of the free surface. 

 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 per unit difference 



p-a 



of curvature. That is to say, if e denote the pres- 

 sure of vapour in equilibrium at a plane surface of 

 liquid, and p the pressure of vapour of the same 

 liquid at the same temperature presenting a curved 

 surface to the vapour, we have 



f =a> -^(7 + ?)- (2) - 



