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ON THE COHESIOJfx of FLUIDS. 



supposerlto c.vijt, even if its presence were 

 not inferred from the effects of capillary 

 action. " Attempts!' have certainly been 

 made, to explain the equality of the ascent; 

 of a fluid between the two planes, and in a 

 tube of wiiic-h the radius is equal to their dis- 

 tuiice-; Mr. Leslie has made sueli an attempt, 

 and with perfect success ; but, if I am not 

 nii'^takeii, the same explanation had been 

 given long before. 



" Clatraut supposes, that a capillary tube may exert a 

 sensible aciion on an infinitely narrow column of thefluiii, 

 situated in the axis of the tube. In this respect, I am 

 obliged to differ from him, and to agree with Haultsbee, 

 and with many other philosophers, in thinking, that capil- 

 lary action, like refractive powers, and the forces of chemi- 

 cal affinities, is only sensible at imperceiitible distances. 

 Hauksbee has observed, that when the internal diameters 

 of several capillary tubes are equal, the water rises in them 

 to the same height, whether they are very thin or very 

 thick. The cylindrical strata of glass, which are at a sen- 

 sible distance from the interior surface, do not therefore 

 contribute to the ascent of the water, although each of 

 them, taken separately, would cause it to rise above its 

 natural level. It is not the interposition of the strata which 

 they surround, that prevents their action on tlie water ; for 

 it is natural to suppose, that the force of capillary attrac- 

 tion is transmitted through the substance of all material 

 bodies, in the same manner as that of gravitation ; this 

 action is, therefore, only prevented, by the distance of the 

 fluid from these strata; whence itfollows, that the attraction 

 of glass for water is only sensible at insensible distances. 



" Proceedini; upon this principle, I have investigated the 

 action of a fluid mass, terminated by a portion of a con- 

 cave or convex spherical surface, upon a fluid column with- 

 in it, contained in an infinitely narrow cylindrical cavity 

 or tube, directed towards the centre of the surface. By this 

 action I mean the pressure, which the fluid contained in 

 the tube would exert, in consequence of the attraction of 

 the whole mass, upon a flat ba^s, situated within the tube, 

 perpendicular to its sidi%, and at any sensible distance from 

 Jhe external surface, taking this basis for unity. I liave«hown 

 that this action is either smaller or greater than if the sur- 

 face were plane, accordingly as it is either concave or con- 

 vex. The algebraical formula, which expresses it, consists of 

 two terms : the first, which is mucli larger than th'e second, 

 «*j)rsS5(;s the action of thejnass supposed to he terminated 



by a plane .surface ; and I coneeive that this force is the 

 cause of the suspension of mercury in the tube of a baro- 

 meter, at a height two or three times greater than that 

 which is derived from the pressure of the atmosphere, of 

 the refractive powers of transparent bodies, of cohesion, 

 and of chemical affinities in general. The second term ex- 

 presses that part of the attraction, which is derived from the 

 curvature of the surface, that is, the attraction of the me- 

 niscus comprehended between that surface and the plane 

 which touches it. This action is either added to the fot- 

 raer, or subtracted from it, accordingly as the surface is con- 

 vex or concave. It is inversely proportional to the radius 

 of the spherical surface ; and it is indeed obvious, that, the 

 smaller the radius is, the greater is the meniscus near the 

 point of contact. This second term expresses the cause of 

 capillary action, which differs, in this respect, from the 

 chemical affinities represented by the first term." 



It is indeed so " obvious," that the menis- 

 cus, which constitutes the difference be- 

 tween a curve surface and a plane one, is 

 inversely proportional to the radius of cur- 

 vature, that the complicated calculations, 

 which have led Mr. Laplace to this conclu- 

 sion, must be considered as wholly superflu- 

 ous. The attraction of the meniscus upon 

 the evanescent column must be confined to 

 the edge which immediately touches the co- 

 lumn, extending only to an insensible dis- 

 tance on each side ; and the situation of all 

 the particles in this infinitely thin edge of 

 the meniscus, with respect to the column, 

 being similar, whatever the curvature may be, 

 it is evident that their joint action must be 

 proportional to their number, that is, to the 

 curvature of the surface. 



" From these conclusions, relating to bodies wliich are 

 terminated by sensible portions of a spherical surface, I de- 

 duce this general theorem. Whenever the attractive force be- 

 comes insensible at any sensible distance, the action of a 

 body, terminated by a curved surface, on an internal column, 

 of infinitely small diameter, and perpendicular to the sur- 

 face at any point, is equal to the half sum of the actions, 

 which would be exerted on the same column by two spheres, 

 having for their radii the largest and the smallest of the 

 radii of curvatute at the given point." 



