REPORT ON CAPILLARV ATTRACTION. 263 



conducts to the inference, that the surface of the fluid approaches 

 so much the nearer to that of a sphere as the diameter of the 

 tube is smaller. Hence it immediately follows that the surfaces 

 in tubes of different small diameters will be similar portions of 

 spherical surfaces, if at their jimcture with the interior surfaces 

 of the tubes they make with them the same angle. This angle 

 will appear to be independent of the diameter of the tube, from 

 the consideration that the extent of the sphere of activity of the 

 attraction of the tube is altogether imperceptible ; so that even 

 in a tube of very small bore, we may regard the action of the 

 cylindrical surface on the superficial fluid elemejits contiguous 

 to it, the same as if it were a plane*. Hence if Z» = the radius 

 of the fluid sui-face, and h its mean altitude above the horizon- 



TJ 



tal level of the exterior fluid, then R = R' =■ h, and — ■=. g qh. 



But in different tubes the surfaces of the fluid being similar seg- 

 ments of spherical surfaces, b evidently varies as the diameter 

 of the tube. Therefore h varies inversely as this diameter. 

 Such is the explanation according to Laplace's theory of what 

 may be looked upon as the principal phsenomenon of capillary 

 attraction. 



If the surface of the interior fluid were convex, as it is known 

 to be when a capillary glass tube is dipped in mercury, then if 

 we suppose for a moment all below the tangent plane at any 

 point to be fluid, the effect of the attraction on a canal terminat- 

 ing at this point perpendicularly to the surface, will only be 

 just equal to the action of the fluid on the other extremity, 

 where it terminates at the exterior horizontal level. If now we 

 subtract the fluid between the tangent plane and the surface, 

 which tends to draw the canal upwards, the resulting inequality 

 of action must be counterbalanced by the hydrostatic pressure 

 arising from a depression of the fluid in the tube. The mean 

 depth to which the fluid will be depressed may be shown, as in 

 the case of concavity, to vary inversely as the diameter of the 

 tube. 



From all this reasoning Laplace concludes that the attraction 

 of capillary tubes influences the elevation or depression of the 

 fluids they inclose, only by determining the inclination of the 

 fluid surface to the contiguous surface of the tube, on which in- 

 cUnation the concavity or convexity of the fluid surface depends, 

 as well as the magnitude of its radius. He consequently speaks 



* M. Gauss, wlio first remarked that the reason here assigned by Laplace 

 for the constancy of the angle of contact is vague and insufficient, has given a 

 more satisfactory demonstration, which we shall have occasion to speak of in a 

 subsequent part of the Report. 



