CAPILLARY ACTION. 



25? 



the demonstrations which vou did me the honour to insert Capillary ac- 

 in your 76th nuiuber. The area of the triangle A £ C ^'^^^ ^*^ ^"^^^*^ 

 (Vol. XVill, PI. I, Fig. 8), which shows the magnitude of 

 "the cohesive force at C, is proportional to the square of the 

 line A C, representing the distance to which the force of co- 

 liesion extends; and if the same number of particles be con- 

 densed into any smaller space, the force will remain the 

 same, and it will still be proportional to the square of the 

 number of particles concerned ; or, in other words, to the 

 square of the density of the substance. The same remark 

 is also applicable to the tension of the common surface of 

 two lifjuids, or of a liquid and a solid; and this determina- 

 tion of the force ought perhaps to have been employed in 

 the investigation of '* the angle of contact of a solid with a 

 fluid"; but it is very singular that the result of this investi- 

 gation will 'be precisely the same, whether we proceed on the 

 supposition of a tension proportional simply to the difference, 

 or to the square of the difference of the densities. Thus if 

 the density of the fluid C B E (Fig. 6) be called «, that of 

 the solid B, b, and that of a second fluid, supposed to oc- 

 cupy the space C B A, c; if the tension be simply propor- 

 tional to the difference of density, we may call the force 

 acting in the direction B A, b — c, in the direftion B E, 

 a — bf alid the difference of these, 2 b — c — c, must be equal 

 to the force /« — c in B C, reduced to the direction B H, and 

 must be represented by the line B H, if a — c be represent- 

 ed by B C or \ B, A H being 2 6—2 c; or if A E be called 

 a — c, A H will be b — c. Now if, instead of b — c, a — 6, 

 and a — c, we take their squares, the difference of the first 

 twQ will be c c — a a — 2 ^ c -f 2 a bzz^lb [a—c) — [a a—c c) 

 " (2 b — ("a -f cj) . (a — t), which is to {a — c)^ as 2 b — a — c 

 to a — c, and B H will be to B C in the same proportion as 

 before." It is obvious that when there is only one fluid, and 

 c — o, AH must be to A E as 6 to «, upon either supposi- 

 tion. 



The two suppositions are however not indifferent with re-» 

 spect to many other cases of the actions of capillary, forces, ■ 

 Ihus if two liquids be capable of perfectly wetting a tube, 

 supposing both of them to be contained in it at the same 

 time, the whole weight supported by the force of capillary 



actioiv 



