REPORT ON CAPILLARY ATTRACTION. 275 



common statical problems there are two kinds of equations of 

 equilibrium, those in which pressures and tensions are involved, 

 and those which result when forces of this kind are eliminated. 

 The force corresponding to the convexity or concavity of the 

 fluid surface in capillary tubes is of the nature of a tension, and 

 may be kept out of view in finding the conditions of the equi- 

 librium of the forces which suspend or depress the fluid column. 

 For this pm-pose it will be necessary to pay regard only to the 

 action of the tube on the parts of the fluid contiguous to it, and 

 to the action exerted on the raised or depressed column con- 

 tained within the tube by the rest of the fluid. The former, as 

 Laplace shows, resolves itself into the attraction of a ring of the 

 tube immediately above the extreme upper edge of the fluid, 

 and an equal attraction of a like ring at the lower extremity of 

 the tube; and the latter, into the attraction of the upper ex- 

 tremity of a tube of the fluid, supposed to be a continuation of 

 the solid tube, and attracting with the proper action of the fluid 

 on itself. The first two forces tend to raise the fluid, the other 

 to depi-ess it. If the total upward force be called 2q'§c, and the 

 downward force qgc, both being proportional to c the contour, 

 it will hence appear that {2q' — q) §c := the weight of fluid raised. 

 If 2q' = q, there is no elevation ; a result which, as we know, 

 may be obtained in a very different manner. 



The preceding expression for the weight of the elevated 

 column being equated to that previously obtained, gives 



XT 



2q' — q =. — cos $. 

 Now it is shown satisfactorilyin the former treatise*, that when 



q' ■= q, & = : SO that q = — , This equality is also proved 



z 



by Laplace in an independent manner. It hence follows that 



o' 2 g 



— = cos-—, which equation, if 9' and q be assumed to be m 



the proportion of the densities of the sold and fluid, is the same 

 as that first obtained by Dr. Young. 



consequence the elevated column may be conceived to be contained in an 

 aqueous tube. Leslie, in a paper containing some original and ingenious views 

 on Capillary Atti-action, {Phil. Mag., vol. xiv. 1802, p. 193,) objects to the 

 principle of Jurin's explanation, and attributes the rise of the fluid solely to its 

 perpendicular pressure against the surface of the tube occasioned by the tube's 

 attraction. By this consideration he finds the height to be inversely as the dia- 

 meter. No doubt, as Leslie appears to have first observed, the rise is depen- 

 dent on a particular state of pressure at the surface of contact of the solid and 

 fluid, and according as this is greater or less than a certain pressure, there will 

 be a rise or depression. 

 •Art. 12. p. 48. 



T 2 



