67 
of Edinburgh, Session 1869 - 70 . 
But in all cases to which we can practically apply the formulas, 
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 homo- 
geneous fluid above the plane of reference, which, if of the same 
density as the vapour at that plane, would produce by its weight 
the actual pressure w, we have 
■zat 
°* = H ' 
Hence by (1) and (2) 
p “*( 1 “h) ■ • • (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 j-oVoth of its own amount than the pressure of vapour in 
equilibrium at a plane surface of water at the same temperature. 
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 tube thoroughly 
wet with water, the free surface is sensibly hemispherical, and 
therefore r and r' are each equal to the radius of the inner surface 
of the liquid film lining the tube above the free liquid surface; we 
have, therefore, 
h = -08 x - . 
r 
Hence, if h - 1300 centimetres, r = -00012 centimetres. There can 
be no doubt but that Laplace’s theory is applicable without serious 
modification even to a case in which the curvature is so great (or 
radius of curvature so small) as this. But in the present state of 
our knowledge we are not entitled to push it much further. The 
molecular forces assumed in Laplace’s theory to be “ insensible at 
sensible distances,” are certainly but little, if at all, sensible at 
distances equal to or exceeding the wave lengths of ordinary light. 
This is directly proved by the most cursory observation of soap 
