|2g •« THE THEORY or CAPILLART ATTRACTION. 



canal is not urged either way, except by those parts of the 

 tube which are situate near the surface of the fluid. 



For, from /, any particle of the tube, set oiF / wi, / n, 

 equal to one another, and of any length less than the radius 

 of the sphere of action of the particle. 



If this particle urges the canal in one direction by its ac- 

 tion at ;n, it urges it equally in the contrary direction by 

 its action at w*. 



We will now see what action the canal sustains near the 

 surface c e d. With a radius ef^ equal to that of the sphere 

 of action of the particles, and with the point e for a centre, 

 describe the circular arc oj'p. 



The canal e ris urged upwards by the resolved action of 

 those particles of the section of the tube contained in the 

 space ofp do; and if this space be divided into two equal 

 parts, by the horizontal line e f, the action of the part 

 above this line draws the canal as much upwards as that of 

 the lower part does. For from any point g, in the lower 

 part, draw g Ct g h equal to one another ; the action of g 

 on the part e h urges the canal neither upwards nor down- 

 wards ; for its action on any point above h is counteracted by 

 its action on another point at the same distance below c. 

 But there are particles below /*, and within the sphere of 

 action of gy as at ky on which it exercises an unbalanced 

 action tending to draw the canal upwards. Next, suppose 

 <", in the upper part of the space ofp d o, similarly situate 

 to g in the lower. Draw e i, which will be parallel to g A, 

 and will evidently draw upwards that part of the canal below 

 e, as much as g draws upwards the part below h. 



The other end e f, of the canal en mt, is urged upwards, 



* This is so plain, that one is astonished to find Mr. la Place, in 

 his second method, making the chief part of the force, which elevates 

 the fluid, reside at the junction of the two tubes. See " Supplement 

 « la Thiorie de V Action Capillaire,''' p. l6. Clairaut also, in a theory, 

 to which it has been lately the fashion to give very undeserved praise, 

 falls into the same erwur. "Figure de la Terre," p. 11 9. The false 

 proposition, that a mass with a plane surface presses a slender column 

 within it downwards, to which most of Mr. la Place's errours may be 

 traced, has Clairaut for its original author. Haiiy- has the same 

 tigure, and nearly the same words. 



