CAPILLARY TUBES, ^ ^5\ 



canal would exercise, by virtue of the attraction of the entire Laplace's theo- 

 mass, upon a plane base situated in the interior of the canal, '7 "^'^'^f f^'^'^' 



' ' ' tion and de- 



perpendicular to its sides, at any sensible distance whatever prcssion of 



from the surface, that base bein^ taken for unity. I show '^^'*^! ''v ""ff *^ 



' '^ •' effect or attrac- 



that this action is less or greater than if the surface were plain ; tion which is 

 less if the surface be concave; greater if the surface be con- j^^^^I^^^ *^^^'^" 

 vex. Its analytical expression is composed of two terras; 

 the first much greater than the second, expresses the action of ^ 

 the mass -terminated by a plain surface, and I think that on 

 this term depend the phenomena of the adherence of bodies to 

 ■each other, and of the suspension of the mercury in a baro- 

 meter tube, at an elevation which is three or four times greater 

 than would arise fi'om the pressure of the atmosphere. The 

 second term expresses that part of the action which is due to 

 the sphericity of its surface : it is positive or negative, accord- 

 ingly as the surface is convex or concave. I shew that in each 

 case this term is in the inverse ratio of the radius of the 

 spherical surface. Thence I conclude the general theorem, 

 namely, that in all the laws wherein the attraction is not sensi- 

 ble but at insensible distances, the action of a body, termina- 

 ted by a curve surface, on an interior canal infinitely narrow 

 and perpendicular to that surface in any point whatever, is 

 equal to half the s^im of the actions on the same canal, of two 

 spheres which should have for their radii the greatest and the 

 smallest of the radii osculators of the surface at that point. By 

 means of this theorem and the laws of the equilibrium of fluids, 

 we may determine the figure which a fluid mass animated by 

 gravity or weight must take. I shew that in a cylindrical tube 

 of considerable diameter, the section of the surface of the 

 fluid, by a vertical plane, is a curve of the genus of those 

 which geometers have called elastic, and which are formed by 

 an elastic plate or blade bended by weights ; this results from 

 the circumstance, that in that section, as in the elastic curve, 

 the force due to the curvature is reciprocal to the radius oscu- 

 lator. If the tube be very narrow, the surface of the fluid ap- 

 proaches the more to that of a spherical segment as the diame- 

 ter of the tube is smaller, I afterwards prove, that in diffei*- 

 ent tubes of the same matter, these segments are nearly ahke; 

 whence it follows that the radii of their surfaces are very nearly 

 proportional to the diameters of the tubes. This similitude of 

 K k 2 the 



