670 



ox THE COHESIOV OF I'LUIDS. 



those of Claiiaut, whose steps he has fol- 

 lowed; and that the expression, which he has 

 derived from them, as indicating the condition 

 of equilibrium of the surface of a fluid incUn- 

 ed to that of a solid, implies, by including an 

 impossibility, that such an equilibiiuiu can- 

 not subsist. This equation requires that the 

 attraction of the fluid, contained between the 

 surface and its extreme tangent, be more 

 than equal to the difterence of the attraction 

 of the two rectangular portions composing the 

 flat solid, and one similar portion of the fluid, 

 reduced only in the ratio of the sine of the 

 angle occupied by the termination of the 

 fluid, to the radius : but it is very evident 

 that *he action of the portion of 'the fluid, 

 thus cut off by the tangent, must be utterly 

 evanescent, in comparison with the other 

 forces concerned, especially if we cousiiier 

 that the surface of the fluid, as well as that of 

 the tube, within the distance " of liic sphere 

 of activity of the attraction" is, to use Mr. 

 Laplace's terms, " almost absolutely plane." 

 There can therefore he no equilibrium upon 

 these principles, when the density of the solid 

 is greater or less than half that of the fluid, 

 unless the surface of the fluid have a common 

 tangent with that of the solid: while, on the 

 other hand, when the densities are in this pro- 

 portion, the surface will remain in equilibrium 

 in any position ; the action of the fluid being 

 always proportional to the chord of its angu- 

 lar extent, and composing, when coiiibined 

 with that of. the solid, a result perpendicular 

 to the surface. If Mr. Laplace had attempted 

 to confirm or to confute my reasoning, re- 

 specting the mutual attractions of solids and 

 fluids, he would probably have discovered 

 the insufficiency of these principles, and 

 would perhaps have been induced to admit 

 my explanation of the foundation of the laws 



of superficial cohesion, as derived from the 

 combination of an attractive with a repulsive 

 force, varying according to a different law. 



■ " If the intensity of the attraction of the tube for the 

 fJuid exceeds that of the attraction of the fluid for its own 

 particles, I think it probable that, in this case, the fluid, at- 

 taching itself firmly to the tube, forms of itself an interior 

 tube, which alone raises the fluid, so as to make its surface 

 a concave hemisphere. It may reasonably be conjectured, 

 that this is the case with water and with oils, in tubes of 

 glass. 



" The elevation of fluids between two vertical planes, 

 which form very small angles with each other, and their 

 discharge through capillary siphons, present a variety of 

 phenomena, which are so many corollaries from my 

 theory. On the whole, if any person will take the trouble 

 of comparing it with tlie numerous experiments which have 

 been made on capillary action, he will see that the results 

 of these experiments, when made with proper precaution, 

 may be deduced from it, not by vague considerations, 

 which always leave the subject in uncertainty, but by a se- 

 ries of geometrical arguments, which appear to me to re- 

 move every doubt respecting the truth of the theory. I 

 wish that this application of analytical reasoning, to one 

 of the most curious departments of natural philosophy, 

 may be thought interesting by mathematicians, and may 

 induce them to make further attempts of a similar nature. 

 Besides the advantage of adding certainty to physical sci- 

 ences, such investigations tend also to the improvement of 

 the mathematics themselves, since they frequently require 

 the invention of new methods of calculation." 



It must be confessed that, in this countrv.the 

 cultivation of the higher branches of the ma- 

 thematics, and the invention of new methods 

 of calculation, cannot be too much recom- 

 mended to the generality of those who apply 

 themselves to natural philosophy ; but it is 

 equally true, on the other hand, that the first 

 mathematicians on the continent have exert- 

 ed great ingenuity in involving the plainest 

 truths of mechanics in the intricacies of 

 algebraical formulas, and in some instances 

 have even lost sight of the real state of an 

 investigation, by attending only to the sym- 

 bols, which they have employed for express- 

 ing its steps. 



