CAPILLARY ACTION 57 of the solution, and to form a thin skin on the outer face of the bubble. In 1787 Monge 1 asserted that "by supposing the adher ence of the particles of a fluid to have a sensible effect only at the surface itself and in the direction of the surface it would be easy to determine the curvature of the surfaces of fluids in the neighbourhood of the solid boundaries which contain them ; that these surfaces would be linteariae of which the tension, constant in all directions, would be everywhere equal to the adherence of two particles, and the phenomena of capillary tubes would then present nothing which could not be determined by analysis." He applied this principle of surface-tension to the explanation of the apparent attractions and repulsions between bodies floating on a liquid. In 1802 Leslie 2 gave the first correct explanation of the rise of a liquid in a tube by considering the effect of the attraction of the solid on the very thin stratum of the liquid in contact with it. He does not, like the earlier specu lators, suppose this attraction to act in an upward direction so as to support the fluid directly. He shows that the attraction is everywhere normal to the surface of the solid. The direct effect of the attrastion is to increase the pres sure of the stratum of the fluid in contact with the solid, so as to make it greater than the pressure in the interior of the fluid. The result of this pressure if unopposed is to cause this stratum to spread itself over the surface of the solid as a drop of water is observed to do when placed oo a clean horizontal glass plate, and this even when gravity opposes the action, as when the drop is placed on the under surface of the plate. Hence a glass tube plunged into water would become wet all over were it not that the ascending liquid film carries up a quantity of other liquid which coheres to it, so that when it has ascended to a cer tain height the weight of the column balances the force by which the film spreads itself over the glass. This explana tion of the action of the solid is equivalent to that by which Gauss afterwards supplied the defect of the theory of Laplace, except that, not being expressed in terms of mathematical symbols, it does not indicate the mathe matical relation between the attraction of individual par ticles and the final result. Leslie s theory was afterwards treated according to Laplace s mathematical methods by James Ivory in the article on capillary action, under the heading " Fluids, Elevation of," in the supplement to the fourth edition of the Encyclopaedia Britannica, published in 1819. In 180i Thomas Young 3 founded the theory of capillary phenomena on the principle of surface-tension. He also observed the constancy of the angle of contact of a liquid surface with a solid, and showed how from these two prin ciples to deduce the phenomena of capillary action. His essay contains the solution of a great number of cases, including most of those afterwards solved by Laplace, but his methods of demonstration, though always correct, and often extremely elegant, are sometimes rendered obscure by his scrupulous avoidance of mathematical symbols. Having applied the secondary principle of surface-tension to the various particular cases of capillary action, Young proceeds to deduce this surface-tension from ulterior prin ciples. He supposes the particles to act on one another with two different kinds of forces, one of which, the attrac tive force of cohesion, extends to particles at a greater distance than those to which the repulsive force is confined. He further supposes that the attractive force is constant throughout the minute distance to which it extends, but 1 Mtmoires de tAcad. des Sciences, 1787, p. 506.
- Philosophical Magazine, 1802, vol. xiv. p. 193.
s Essay on the "Cohesion of Fluids," Philosophical Tmnsactions, 1803, p. 65. that the repulsive force increases rapidly as the distance diminishes. He thus shows that at a curved part of the surface, a superficial particle would be urged towards the centre of curvature of the surface, and he gives reasons for concluding that this force is proportional to the sum of the curvatures of the surface in two normal planes at right angles to each other. The subject was next taken up by Laplace. 4 His results are in many respects identical with those of Young, but his methods of arriving at them are very different, being con ducted entirely by mathematical calculations. The form into which he has thrown his investigation seems to have deterred many able physicists from the inquiry into the ulterior cause of capillary phenomena, and induced them to rest content with deriving them from the fact of surface- tension. But for those who wish to study the molecular constitution of bodies it is necessary to study the effect of forces which are sensible only at insensible distances ; and Laplace has furnished us with an example of the method of this study which has never been surpassed. Laplace investigates the force acting on the fluid contained in an infinitely slender canal normal to the surface of the fluid arising from the attraction of the parts of the fluid outside the canal. He thus finds for the pressure at a point in the interior of the fluid an expression of the form where K is a constant pressure, probably very large, which, however, does not influence capillary phenomena, and therefore cannot be determined from observation of such phenomena ; H is another constant on which all capillary phenomena depend; and R and R are the radii of curvature of any two normal sections of the surface at right angles to each other. In the first part of our own investigation we shall adhere to the symbols used by Laplace, as we shall find that an accurate knowledge of the physical interpretation of these symbols is necessary for the further investigation of the subject. In the Supplement to the Theory of Capillary Action, Laplace deduces the equation of the surface of the fluid from the condition that the resultant force on a particle at the surface must be normal to the surface. His explana tion, however, of the rise of a liquid in a tube is based on the assumption of the constancy of the angle of contact for the same solid and fluid, and of this he has nowhere given a satisfactory proof. In this supplement Laplace gives many important applications of the theory, and compares the results with the experiments of Gay-Lussac. The next great step in the treatment of the subject was made by Gauss. 5 The principle which he adopts is that of virtual velocities, a principle which under his hands was gradually transforming itself into what is now known as the principle of the conservation of energy. Instead of calculating the direction and magnitude of the resultant force on each particle arising from the action of neighbour ing particles, he forms a single expression which is the aggregate of all the potentials arising from the mutual actiorTbetween pairs of particles. This expression has been called the force -function. With its sign reversed it is now called the potential energy of the system. It consists of three parts, the first depending on the action of gravity, the second on the mutual action between the particles of the fluid, and the third on the action between the particles of the fluid and the particles of a solid or fluid in contact with it. 4 Mecanique Celeste, supplement to the tenth book, published ill 1806. 8 Principia generalia Theorist Figures Fluidorum in staiu (Gottingen, 1830), or Werke, . 29 (Gottingen, 1867).
V.