192 Mr. J. T. Riley on Capillary Phenomena. 



sents the attraction of a plane surface, since ~=- vanishes 



TT 



when b becomes infinite. The expression K — -r also repre- 

 sents the attraction exerted on the canal by a segment cut 

 from the sphere by a plane to which the canal is perpen- 

 dicular, since all the sphere behind the plane is at too great a 



TT 



distance to have any effect. In a similar way, K + -=~ repre- 

 sents the action of a sphere upon an infinitely slender canal 

 internally perpendicular to its surface. 



He then applies this result to determine the action of any 

 curved surface upon an internal column of fluid enclosed in 

 an infinitely slender canal perpendicular to any point of this 

 surface. If E, and R' be the principal radii of curvature at 

 this point, he obtains for the attraction the expression 



K+ * H tt-4> 



Gauss * uses the principle of virtual velocities. He forms 

 an expression for the sum of the potentials arising from the 

 mutual action between pairs of particles. This expression 

 consists of three parts, corresponding to the action of gravity, 

 the mutual action between the particles of the fluid, and the 

 action between the particles of the fluid and the particles of 

 the solid or fluid in contact with it. The condition that the 

 system may be in equilibrium is that this expression shall 

 have a minimum value. 



Poisson f maintains that the density of the fluid is not 

 uniform, but that there is a rapid variation of density near 

 the surface. He obtains an equation of the capillary surface 

 similar to that of Laplace, but asserts that K is very small 

 instead of very great. 



Many physicists, unwilling to grant the possibility of a 

 negative pressure in a liquid, and confronted with the fact 

 that capillary elevations and depressions occur in vacuo just 

 as in the atmosphere, adopt the result of Laplace, and consider 

 that a plane surface exerts a considerable pressure on the 

 interior liquid. Thus in Everett's edition of Deschanel 

 (6th ed. p. 133) we find the following statement: — " We 

 cannot conceive of negative pressure existing in the interior 

 of a liquid, and we are driven to conclude that the elevation 

 is owing to the excess of pressure caused by the plane 



* Principia Generalia Theorice Figurce Fluidorum in Statu ^quilibrii. 

 t Nouvelle TMorie de V Action capillaire : Paris, 1831. 



