430 OF CAPILLARY ATTRACTION AND THE COHESION OF FLUIDS. 



is equal to the observed altitude of the lowest point of the meniscus, 

 increased by one third of the radius of the tube, or which is the same 

 thing, by one sixth of the diameter ; the value of the constant quantity, 

 can therefore only be determined by experiment, and accordingly we 

 find, that various accurate observations have been made for the purpose 

 of assigning the value of this element; the mean of which, according 

 to M. Weitbrecht, gives 



hence, finally, we obtain 



#r=.0214. (315). 



541 . The equation (315), it may be remarked, is general for cylindrical 

 tubes, if the elevated column of fluid is terminated by a hemispherical 

 meniscus, and the practical rule which it supplies, is simply as follows. 



RULE. Divide the constant fraction .0214 by the radius of 

 the capillary tube, and the quotient will express the mean 

 altitude to which the Jluid rises above its natural level. 

 If it be required to determine the highest point to which the fluid 

 particles ascend, it will be discovered, by adding to the mean altitude 

 two thirds of the radius of the tube, or one sixth of the diameter. 



542. EXAMPLE. The diameter of a cylindrical tube of glass, is .06 of 

 an English inch ; now, supposing it to be placed in a vertical position, 

 with its lower extremity immersed in a vessel of water ; what is the 

 mean altitude to which the fluid will ascend, and what is the altitude 

 of the highest particles ? 



Since, according to the question, the diameter of the tube is .06 

 of an inch, the radius is .03 or half the diameter ; consequently, by 

 the rule, the mean altitude to which the water rises, is 

 h' =.. 0214 -~ . 03 0.713 of an inch, 

 and therefore, the point of highest ascent, is 

 0.713 4- .02 =z 0.733 of an inch. 



543. If the mean altitude of the fluid is given, the radius of the tube 

 can easily be found from equation (315), for it only requires the con- 

 stant number .0214 to be divided by the given altitude ; but when the 

 observed altitude, or the distance between the surface of the fluid in 

 the vessel, and the lowest point of the meniscus is given, the radius 

 can only be determined by the resolution of an adfected quadratic 

 equation ; for by equation (314), we have 



i**4- Ar-zz.0214, 



