CAPILLARY ACTION. 565 



If four fluids, a, b, c, d, meet in a point 0, and if a tetrahedron ABCD 

 is formed so that its edge AB represents the tension of the surface of contact 

 of the liquids a and b, BC that of b and c, and so on; then if we place 

 this tetrahedron so that the face ABC is normal to the tangent at O to the 

 line of concourse of the fluids abc, and turn it so that the edge AB is normal 

 to the tangent plane at O to the surface of contact of the fluids a and b, 

 then the other three faces of the tetrahedron will be normal to the tangents 

 at O to the other three lines of concourse of the liquids, and the other five 

 edges of the tetrahedron will be normal to the tangent planes at to the 

 other five surfaces of contact. 



If six films of the same liquid meet in a point the corresponding tetra- 

 hedron is a regular tetrahedron, and each film, where it meets the others, has 

 an angle whose cosine is f. Hence if we take two nets of wire with 

 hexagonal meshes, and place one on the other so that the point of concourse 

 of three hexagons of one net coincides with the middle of a hexagon of the 

 other, and if we then, after dipping them in Plateau's liquid, place them 

 horizontally, and gently raise the upper one, we shall develop a system of 

 plane laminae arranged as the walls and floors of the cells are arranged in a 

 honeycomb. We must not, however, raise the upper net too much, or the 

 system of films will become unstable. 



When a drop of one liquid, B, is placed on the surface of another, A, 

 the phenomena which take place depend on the relative magnitude of the three 

 surface-tensions corresponding to the surface between A and air, between B 

 and air, and between A and B. If no one of these tensions is greater than 

 the sum of the other two, the drop will assume the form of a lens, the 

 angles which the upper and lower surfaces of the lens make with the free 

 surface of A and with each other being equal to the external angles of the 

 triangle of forces. Such lenses are often seen formed by drops of fat floating 

 on the surface of hot water, soup, or gravy. But when the surface-tension of 

 A exceeds the sum of the tensions of the surfaces of contact of B with air 

 and with A, it is impossible to construct the triangle of forces, so that equi- 

 librium becomes impossible. The edge of the drop is drawn out by the surface- 

 tension of A with a force greater than the sum of the tensions of the two 

 surfaces of the drop. The drop, therefore, spreads itself out, with great velocity, 

 over the surface of A till it covers an enormous area, and is reduced to such 

 extreme tenuity that it is ' not probable that it retains the same properties of 



