uilibrium. 



ON CAPILLARY ACTION. 295 



ratio of the specific gravity of the prism to that of the 

 fluid, the weight of the prism will be to that of the volume 



of fluid depressed as i k : qx ( 1-| ) By suitably di-oreq 



minishing i therefore, we may render the two weights equal, 

 and thus keep the prism at the surface of the fluid. From 

 the preceding principles too we may determine the diminu- 

 tion of weight of a body completely immersed in a vessel 

 filled with several fluids. 



If the end of a very slender tube be immersed perpendi- 

 cularly in a fluid, putting / for the radius of the cavity of 

 the tube, and q for the height to which the fluid is raised 

 above the level in it, we shall have, by my theory of ca- 

 pillary action, I q = ; w being the angle which the 



a. D 



surface of the interior fluid forms with that part of the 

 inner surface of the tube, which is in contact with it. 

 When the fluid is depressed below the level, this angle 

 exceeds a right angle, and then its cosine becomes negative, 

 as well as q : but <* is a constant quantity, which depends 

 only on the weight and action of the fluid on itself. By 



what precedes we have, — ? —~ = — -'• therefore we shall 

 gD 2 



. 2ax(2 ? -f') A . 



have cos. TO =- rr > C 1 *) 



g D 



But it has appeared in the theory quoted, that, ^ being 

 null, « is equal to two right angles : which may be con- 

 cluded likewise from the analysis I shall give in a supple- Resistance a 



J disk opposes to 



ment to that theory, on the resistance that a very large separation from 



circular disk, applied to the surface of a fluid, opposes to afluid - 

 its separation from the fluid. From this analysis it folloAvs, 

 that, i being the radius of the disk, supposed of the same 

 matter as the preceding tube, this resistance is equal to 

 gDxirxi'X Vl?XCOS.j«r ■ ^ ft ., ^ ft ^ 



be null, when ? is null, or when the disk has no action on 

 the fluid ; we shall then have cos. £ *r null, which gives 

 *rr=27r, and consequently cos. ^—-1: thus the equation 



CI) will eivee'=- , and consequently -^-= cos. * x § w. 



Hence 



