116 Prof. Langberg on the influence of Capillary Attraction upon 



value by means of which T can be calculated, when H is known 

 from observation. 



If we admit that which is in itself very probable, namely that 

 the generating curves of the capillary surfaces raised by all 

 wetted cylinders of whatever radii are similar, or even (what in 

 this case is alone essential) that the radius of curvature of the 

 generating curve at its highest point bears a constant proportion 

 to the ordinate of that point, then we have 



p : p" : : H : H", 

 or 



where p denotes the radius of curvature answering to the height It, 

 p" that answering to the height H". If, now, r{ = p'), the radius 

 of the cylinder, be infinite, that is to say, when a plane surface 

 is placed upright in a liquid, equation (3) can be integrated 

 without difficulty, and we find* 



p"=iH"andp=UI; 

 so that from (3) we have 



h=4,|-D=h(-"). 



or 



m= T7 (4) 



r 

 If, then, r and H are determined by measurement, mi = -r ) 



can be easily calculated. 



In order to test how far the above hypotheses arc correct, 

 Hagen measured the height H for discs of different radii, and 

 thereby discovered that the difference between the observed and 

 calculated heights fell within the limits of error of observation. 

 Having made several experiments with floating cylinders, I have 

 arrived at the same conclusion. 



Equation (4) may therefore, it seems, be applied with confi- 

 dence. If in this manner m, and thereby T, be determined, the 

 downward force exerted by the body of water elevated by the 

 disc may easily be calculated. The weight of the fluid cylinder 

 abop = \i'rrr'^k, and the force exerted by the above-mentioned ten- 

 sion = 27rrT; wherefore, the whole downward force being denoted 

 by G, we have 



G = H7rr^/c + 27rrT (5) 



* " On Fluid Surfaces," Poggendorff' s Annalen, vols. Ixvi. and Ixxvii. 



