OF CAPILLARY ATTRACTION AND THE COHESION OF FLUIDS. 429 



Then, by the principles of mensuration, it is manifest that the 

 inner circumference of the tube is 2r7r, and the solidity of the 

 uniform column whose height is en, becomes r*/nr; now, the solidity 

 of the meniscus ganbf, is obviously equal to the difference between 

 the cylinder abfg and its inscribed hemisphere an b. 



But by the rules for the mensuration of solids, we know that tl>e 

 solidity of the cylinder abfg is r 8 7r, and that of the inscribed hemi- 

 sphere is fr 3 7r ; consequently, the solidity of the meniscus is 



r s 7r fr 3 7r = r 8 7r, 

 which being added to the solidity of the uniform column, gives 



wzrr 2 /i7r -f- T^TJ 

 from which, by collecting the terms, we get 



Now this is equivalent to the solidity of a cylinder, whose radius is 

 r and altitude evrz h' ; consequently, we have 

 m = r*K (h + r) zz rV h' ; 

 whence it appears, that 



h' = h + ir. (312). 



539. Instead of din the equation (3 11), let its equal 2r be substituted, 

 and instead of m in the same equation, let its equivalent h'r^ir be 

 introduced, and we shall obtain 



h' r 9 TT $g = 2r TT (20 0'), 

 and from this, by casting out the common factors, we get 



A' r 30 = 2(20 A 

 and dividing by 5#, it becomes 



Now, since the symbols <j>, 0', 3 and g are constant for the same 

 fluid and material, it follows that the whole expression is constant ; 

 hence, the height to which the fluid rises, varies inversely as the 

 radius of the tube. 



540. Instead of h' in the equation (313), let its equivalent (h -f- r) 

 in equation (312) be substituted, and we shall obtain 



" ' 



2(2<6 0') 

 Hence it is manifest, that the constant quantity -'- , is 



equal to the mean altitude of the fluid multiplied by the radius of the 

 tube ; and it has been shown in equation (312), that the mean altitude 



