500 fT. W. Glbbs — Equilibrium of Heterogeneous Substances. 



Sz and Sz, which indicate respectively the displacements of the solid 

 and the fluid, may have different values, but the components of 

 these displacements which are normal to the surfiice must be equal. 



F'rom this equation, among other particular conditions of equilib- 

 rium, we may derive the following — 



d5 = g{r)d.z, (681) 



[compare (614),] which expresses the law governing the distribu- 

 tion of a thin fluid film on the surface of a solid, when there are no 

 passive resistances to its motion. 



By applying equation (680) to the case of a vertical cylindrical tube 

 containing two different fluids, we may easily obtain the well-known 

 theorem that the product of the perimeter of the internal surface by 

 the difference ?'— ?" of the superficial tensions of the upper and lower 

 fluids in contact with the tube is equal to the excess of weight of the 

 matter in the tube above that which would be there, if the boundary 

 between the fluids were in the horizontal plane at which their pres- 

 sures woidd be equal. In this tlieoi'em, we may either include or 

 exclude the weight of a film of fluid matter adhering to the tube. 

 The proposition is usually applied to the column of fluid in mass 

 between the horizontal plane for which p'=zp" and the actual 

 boimdary between the two fluids. The superficial tensions s' and 5" 

 are then to be measured in the vicinity of this column. But we may 

 also include the weight of a film adhering to the internal surface of 

 the tube. For example, in the case of water in equilibrium with its 

 own vapor in a tube, tlie weight of all the water-substance in the 

 tube above the plane p'=p", diminished by that of the water-vapor 

 which would fill the same space, is equal to the perimeter multiplied 

 by the difterence in the values of 5 at the top of the tube and at the 

 plane p'z=p". If the height of the tube is infinite, the value of ? at 

 the top vanishes, and the weight of the film of water adhering to the 

 tube and of the mass of liquid water above the plane p'=^p" dimin- 

 ished by the weight of vapor which would fill the same space is 

 equal in numerical value but of opposite sign to the product of the 

 perimeter of the internal surface of the tube multiplied by ?", the 

 superficial tension of liquid water in contact with the tube at the 

 pressure at which the water and its vapor would be in equilibrium at 

 a plane surface. In this sense, the total weight of water which can 

 be supported l)y the tube per unit of the perimeter of its surface is 

 directly measured by the value of — ? for water in contact with the 

 tube. 



