This contracting power of a liquid surface is greatly affected by the introduction of impuri ties into the surface and by changes in tempera ture. Soapy water has less contracting power than pure water; and the motions of bits of camphor or of sodium or potassium on the sur face of water are explained by the unequal rates of pollution of the surface at various points of the solid and the consequent unequal alterations in the surface forces, which thus pull the solid Lit around in a most random path. If the temperature is raised, the surface forces decrease, as is shown by the fact that the height to which water stands in a glass tube decreases as the temperature increases.
These contracting tendencies of a liquid surface are due to the action of the minute particles of the surface: there are evidently forces holding these particles together. The force acting across a line of unit length is called the `surface-ten sion,' and it may be proved that if there is a spherical surface of radius r, there will be a contracting pressure given by the formula p = 2T/r where T is the surface tension of the liquid. Thus, to keep a soap-bubble of radius r from contracting, it is necessary to blow into it with a pressure 4 T/r, because there are two con tracting surfaces in a soap-bubble. Further, if
the liquid stands in a tube of small bore at a height it above the general level of the liquid, the hydrostatic pressure due to this height must be counterbalanced by the contracting pressure of the concave surface of the water in the tube. This hydrostatic pressure is pgh, where p is the density of the liquid. and y is the acceleration of a falling body. (See Ill•ntosTAncs.) hence, pgh = 2T/r 0-p or h - pyr where r is the radius of the tube at the point at the top of the column of water, because, strictly speaking, r is the radius of the spherical concave surface of the water, and this equals the radius of the tube at this point if the liquid wets the tube. Therefore, it is entirely immaterial what the radius of the tube is at other points below; the height h remains the same.
For most interesting and instructive descrip tions of capillary phenomena, consult Boys, .Soup Bubbles, and Bow to Blow Them (New York, 1900).