6(iA 



ON TIIK COIIESIOX OF FLUIDS, 



vcctiii>n1e, ami S being 50^, the term afj'- 

 bccoines=4, and makes the negative part 

 of tiie forimila greater thaa the positive. 

 Wlien Mr. Lnphice investigates the relation 

 of the curvature and of the marginal depres- 

 sion to the diameter of tlie tuhe, he simply 

 -considers the whole surface as spherical ; but 

 even on this supposition his formula is by no 

 in(>ans the most accurate tiiat may be found, 

 and begins to be materially incorrect even 

 when liie diameter of the tube amounts to 

 one fifili of an inch only. The formula, 

 which I have already given in this paper, is 

 sufliciently accurate, until the diameter be- 

 comes equal to half an inch ; but I shall 

 hereafter mention another, whieii comes 

 much nearer to the truth in all cases, 



" The comparison of these results shows the true 

 causeofthe ascfiitor depression of fluid's in capillary tubes, 

 which is inversely proportional to their diameters. If we 

 imagine an infinitely narrow inverted siphon to have one 

 of its branches placed in the axis of the tube of glass, and 

 the other terminating in the general horizontal sur&ce of 

 the w;iter in the vessel, the action of the water in the tube 

 on the first branch of the siphon will be less, en account of 

 the concavity of its surface, than the action of the water of 

 the vessel on the second ; the fluid must therefore ascend in 

 the tube, in order to compensate for this difference ; and, 

 as it has been shown, that the difference of the two actions 

 is inversely proportional to the diameter of the tube, the 

 elevation of the fluid above the general level must follow 

 the same law. 



" If the surface of the fluid within the tube is convex as 

 in the case of mercury contained in a tube of glass, its ac- 

 tion on the inverted siphon will be greater than that of the 

 fluid in the vessel ; the fluid must therefore be depressed in 

 the tube, in proportion to the difference, that is, inversely 

 in proportion to the diameter of the tube. 



" It appears therefore, that the immediate attraction 

 of a capillary tube has no other effect on the elevation or 

 depression of the fluid contained in it, than so far as it de- 

 termines the inclination of the first portion of the surface of 

 the fluid, when it approaches the sides of the tube : and 

 that the concavity or convexity of the surface, as well as 

 the magnitude of its curvature, depends on this inclination. 

 The frictionof the fluid, against the sides of the tube, may 



increase or diminish a little the currature of its surface, as 

 we continually observe in the mercury of the barometer : 

 and in this case, the capillary effects are increased or dimi- 

 liished in the same proportion. These effects are also very 

 sensibly modified by the cooperation of the forces derived 

 from the concavity and convexity of two different surfaces. 

 It will appear hereafter, that water may be raised, in a 

 given capillary tube, to a greater height above its natural 

 level in this manner, than when the tube is immersed in a 

 vessel filled with that fluid." 



It would perhaps be more correct to say in 

 this case "above its apparent level ": for 

 the real horizontal surface must here be con- 

 sidered as situated above the lower orifice of 

 the tube, the weight of the portion of the 

 fluid below it being as much supported by 

 the convexity of the surface of the drop, as 

 if it were contained in a vessel of any other 

 kind. 



" The fluxional equation of the surface of a fluid, in- 

 closed in a capillary space of any kind, which may be re- 

 ferred to an axis of revolution, leads to this general result, 

 that if a cylinder be placed within a tube, so that its axis 

 may coincide with that of the tube, the fluid will rise in 

 this space to the same height, as in a tube of which the ra- 

 dius is equal to this distance. If we suppose the radii of 

 the tube and of the cylinder to become infinite, we obtain 

 the case of a fluid contained between two parallel vertical 

 planes, placed near each other. The conclusion is con- 

 fixmed in this case by the experiments which were made 

 long ago in the presence of the Royal Society of London, 

 under the inspection of Newton, who has quoted them in ■ 

 his Optics; that admirable work, in which this profound 

 genius, looking forwards beyond the state of science in his 

 own times, has suggested a variety of original ideas, which 

 the modern improvements of chemistry have confirmed. 

 Mr. Haiiy has been so good as to make, at my request, 

 some experiments on the case which constitutes the oppq. 

 site extreme, that is, with tubes and cylinders of a veiy 

 smsU diameter, and he has found the conclusion as correct 

 in this case, as in the former." 



If indeed we may be allowed to place any 

 confidence in the fundamental principle of 

 an equable tension of the surface of the fluid, 

 an equal length of the line of contact of the 

 solid and fluid supporting in all cases an 



