84 Prof. G. Quincke on the Constants of 



If we call co the angle which the last element of the fluid sur- 

 face, where it meets the solid, makes with the vertical solid 

 bounding wall, 



dz 



\^r) = cot co . I rm I = cos co 



a=-~'-(oTiv):, 



and equation (4) becomes 

 _W 11 



2ttv 



(6) 



The weight of the fluid per unit of length of the circumference 

 of the cylinder which is lifted above the horizontal level is 



XT 



— cos co ; i. e. it is independent of the radius of the cylinder, and 



depends only on the nature of the fluid and of the enclosing solid 

 wall. The equation is also true for cylinders not hollow ; and 

 every vertical wall may be considered approximately a part of 

 such a hollow or solid cylinder. 



In fluids which wet the solids (i. e. where the last element of 

 the fluid layer is vertical) co is 0, and 



The weight of a fluid sustained per unit of length of the line of con- 

 tact (which is the line of intersection of the vertical wall and the 

 capillary surface) is a constant quantity, and measures the mutual 

 attraction of the particles of the given fluid — that is, is its cohe- 

 sion- or capillarity-constant. 



Since Poisson's time, the quantity 



a ~Mg~Mg (8) 



is frequently called the constant of capillarity. The advantage 

 is, that when it is divided by the inner radius it gives the mean 

 elevation above the horizontal level to which a fluid which wets 

 the solid ascends. The elevation of a fluid which wets a plane 

 vertical wall, or the rise of the highest point of the curved fluid 

 surface over the horizontal level, is «. 



4. Equation (7) is true also for drops which are formed at 

 the mouth of a vertical pipe, on the assumption that, in con- 

 sequence of the gradual accession of new fluid, the same pres- 

 sure is found in the interior fluid, at the mouth of the pipe, as in 

 a level fluid surface. The drop goes on increasing till co = 0, or 

 till the highest element of the fluid is vertical, and then it falls off. 

 If the radius of the cylinder on which the drop is formed be very 

 small, the weight of the portion of fluid which remains hanging 



