428 OF CAPILLARY ATTRACTION AND THE COHESION OF FLUIDS. 



f=i dirty, 

 which being substituted for /and/' in equation (310), gives 



m$g = dir('2<l> f). (311). 



This is the general equation that expresses the force by which the 

 water is raised in a cylindrical tube, and its application to particular 

 cases will be exemplified by the resolution of the following problems. 



PROBLEM LXIX. 



538. In a cylindrical capillary tube of a given diameter, the 

 top of the elevated column is terminated by a hemisphere : 



It is therefore required to determine the height to which 

 the 1 fluid ascends above its natural level. 



Let abed be a section passing along the axis of a very small 

 cylindrical tube, of whioh the diameter is 

 ab; let the tube be vertically immersed in 

 the fluid whose surface is IK, and suppose 

 that in consequence of the immersion, the 

 fluid rises in the tube to e on a level with 

 the surface IK, and from thence it is at- 

 tracted by the glass in the tube, together 

 with the mutual action of its own particles, 

 until it arrives at ab, where it forms the 

 spherical meniscus abfg, and in which 



position, the weight of the elevated column is in equilibrio with the 

 attractive forces. 



Now, the problem demands the height to which the fluid rises in 

 the tube in consequence of the attraction, and on the supposition 

 that its diameter is very small. 



Put r = am, the radius of the interior surface of the tube, 



h =n en, the height of the uniform column, or the distance 



between the surface of the fluid and the lowest point 



of the spherical meniscus, 

 A'n: ev, the mean altitude, or the height at which the fluid 



would stand, if the meniscus were to fall down and 



form a level surface, 



TT the ratio of the circumference to the diameter, and 

 m i= the magnitude of the whole elevated column. 



