CAPILLARY ACTION. 



aid* the canal. He thus finds for the pressure at a point in the interior of 

 the fluid an expression of the form 



when A" u * conUnt pressure, probably very large, which, however, does not 

 influence capillary phenomena, and therefore cannot be determined from observa- 

 tion of such phenomena ; // is another constant on which all capillary phenomena 

 depend; and R and K are the radii of curvature of any two normal sections 

 ,/ the surface at right angles to each other. 



In the first part of our own investigation we shall adhere to the symbols 

 myrjl by Laplace, as we shall find that an accurate knowledge of the physical 

 intiTprvtation of these symbols is necessary for the further investigation of the 

 xubject. 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 expla- 

 nation, however, of the rise of a liquid in a tube is based on the assumption 

 I" 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*. 

 The principle which lie adopts is that of virtual velocities, a principle which 

 under liis 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 neighbouring particles, he forms a single expression which is the aggregate 

 of all the potentials arising from the mutual action between pairs of particles. 

 This expression lias 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 



een the particles of the fluid, and the third on the action between the 

 I "articles of the fluid and the particles of a solid or fluid in contact with it. 



The condition of equilibrium is that this expression (which we may for 

 the sake of distinctness call the potential energy) shall be a minimum. This 



Priitcipia gewmlia Theoria Figune Fluidorum in flatu jEquilibrii (Gottingen. 1830), or Werke, 

 T. 29 (Gottingw,, 1867). 



