282 Mr Sang on the Theory of Capillary Action 



at the two orifices C and L. But, 6 being the inclination of the 

 surface at L to the horizon ; K the attractive force at C ; the 

 quantity of fluid at L, subjected to the attraction, is propor- 

 tional to the secant of 6, and therefore the whole attraction is 

 K sec 6. But of this force one portion is acting in the direction 

 of the canal, the other against its sides. The former of these 

 two is as the cosine of 6, and hence the compression caused in 

 the canal is K sec i. cos 6 or K itself. The fluid therefore is 

 (as indeed is demonstrated in the third section of the subject- 

 paper) in equilibrium with respect to the force of cohesion; but 

 it is not so in respect to that of gravity, so that the equilibrium 

 cannot take place unless the surface LMC is horizontal. 



The same conclusion might have been deduced from the 

 consideration of the equilibrium of a particle of fluid situated at 

 the point L. Such a particle is acted on only by two forces ; 

 that of gravity, and the cohesion of the fluid ; now the latter of 

 these is already perpendicular to the surface, wherefore no equi- 

 librium can exist, unless the other also is perpendicular to it, 

 that is, unless the surface at L be horizontal. 



The above reasoning appears to me sufficiently conclusive ; 

 yet, as the method differs considerably from that which has oc- 

 casioned these remarks, it may not be improper to consider the 

 subject in the same light with our author. 



Let, then, MLK represent a small por_ 

 tion of the inclined surface, LP a vertical 

 plane ; a particle placed at L is attracted 

 by the whole fluid with a force K, whence 

 that portion of this force produced by the 

 wedge MLP, is ^K — ;| K sin « ; and 

 the part due to the wedge PLK is 

 1 K -f J K sin tf. After establishing, in 

 the most distinct manner, this proposi- 

 tion, he proceeds : 



" Returning now to the canal below the vertical plane PL, 

 and the level surfaci- of the fluid, let 6 denote the inclination of 

 the curve at L to the horizon ; the canal would be in equili- 

 brium with respect to the corpuscular forces that act upon it, if 

 the attractions upon all its vertical sides were equal. But, ac- 

 cording to what has just been investigated, the upper end is at- 

 tracted by the fluid beyond the vertical plane PL, with a force 



