432 OF CAPILLARY ATTRACTION AND THE COHESION OF FLUIDS. 



In this position, the whole weight of the elevated fluid, and the 

 united efforts of the attractive forces, are in equilibrio among them- 

 selves, and the problem requires the height to which the fluid rises, 

 when the powers of gravitation and attraction become equal to one 

 another ; for this purpose, 



Put b zr the horizontal breadth of the planes by whose attraction 



the fluid is elevated, 



d =. ab, the perpendicular distance between the planes, 

 li zz e n, the distance between the lowest point of the meniscus 



and the surface of the fluid, 



h' zz ev, the mean altitude of the fluid, or the height at which 

 it would stand, if the meniscus were to fall down and 

 form a level surface, 

 TT zz the ratio of the circumference of a circle to its diameter, 



and 



m zz the magnitude of the volume of fluid raised. 

 Then, if the constants <, 0', S and g denote as before, the magnitude 

 of the elevated volume will be found as follows. 



546. By the principles of mensuration, the solidity of the fluid 

 parallelopipedon, whose breadth is b, thickness d, and height h, is 

 expressed by bdh; and the solidity of the fluid meniscus whose 

 section is grnsf, is equal to the difference between a semi-cylinder 

 and its circumscribing parallelopipedon, the length being equal to 

 bj and the diameter equal to d, the distance between the attracting 

 planes. 



Now, the solidity of the circumscribing parallelopipedon is |6d 8 , 

 and the solidity of the semi-cylinder is J6eP?r; consequently, the 

 solidity of the meniscus, is 



to which if we add the solidity of the uniform solid, the whole magni- 

 uid becomes 

 m bdh -\- \bd\1 TT). 



tude of the elevated fluid becomes 



But the periphery of the fluid which is elevated between the planes, 

 is manifestly equal to 2( + d) ; consequently, by substituting this 

 value of the periphery for dir in equation (311); and for m, let its 

 value as determined above be substituted, and we shall obtain 

 {bdh+lbd\1-Tr}}Zg=i1(b+d)(<l<t> f), 

 and dividing both sides by b$g, it becomes 



\ 



vr 



