ON THE THEORY OP CAPILLARY ATTRACTION. JQQ 



in like manner, by the action of the space u g) -rr^ u, equal 

 to, and described in the same manner as, ofp d o. 



Now, suppose both sides of the section of the tube to re- 

 volve round the axes a b, a ^; the cyli d cal annulus 

 generated by e r is urged upwards by the action of the 

 annulus generated by the circular space ofp d o; and that 

 generated by s f by that generated hy u (p r. I ;. If we re- 

 present the action of the annulus generated by ofp d o hy 

 2 r, that of the annulus generated by ot ip tj- ^ w will be 2 r. 



By reasoning in the same manner with re pect to all other 

 cylindrical annuli within the sphere of action of the tube, 

 and taking the sum of all the actions, it is plain, that the 

 excess of the mass of the fluid in the leg A B over that in 

 the leg E F is as 2 r — 2 r. 



But now, supposing all other things to remain the same, 

 conceive the diameter of the tube to vary. A canal e r, at 

 the same distance from the si;le, in tubes of different 

 diameters, will be equally attracted by all of them : for 

 that part of the surface of the tube, which attracts the 

 canal, is so small (by the hypothesis) that it may be con- 

 sidered as plane whatever be the tube's diameter. 



Therefore, while the diameter of the tube varies, as the 

 number of equal columns in a cylindrical annulus of given 

 breadth, at a given distance from the tube, but within the - 

 reach of its action, varies quam proxime as the diameter of 

 the tube, while the force urging upwards each separate 

 column is constan , it is easy to see, by collecting as before 

 the sum of the forces acting on different annuli, that the 

 excess of the mass in the leg A B over that in E F is as the 

 diameter of the tube. 



By combining both parts of the proposition, and sup- 

 posing the diameter of the tube, and the attractions of its 

 two ends to va y together, the excess of the mass in A B 

 over that in E F will be as (2 r- — 2 r) X diameter. 

 QED. 



Cor. 1st. It is plain from the above demonstration, that Cotollarj I, 

 the mass of fluid, supported by a capillary tube, depends 

 not in the smallest degree on the figure c a d of its surface, 

 so that, if it were posside for us to make this surface take 

 any other cow eivahle figure ^ the same mass of fluid would 



Vol. XXVII— Oct. 1810. K still 



