Measuring the Surface- Tension of Liquids. 403 



maximum of weight is noticeable as the frame is raised, just 

 before the true double-film is formed. This maximum can be 

 found very exactly, and is made the basis of a third method 

 of measuring surface-tension. 



An equation to the capillary curve is found in the expres- 

 sion of the fact, that the vertical component of the surface- 

 tension at any point is equal to the weight of liquid raised 

 above the level surface, by the curved surface, from the level 

 up to a perpendicular through that point. That is to say, 

 taking a section of the capillary elevation of unit thickness 

 (%• 6), 



T sin «=#/>] ydx, (!) 



where 



a = the angle made by the tangent with axis of x (the 

 level surface) ; 



T = the surface-tension, in dynes per centim. ; 



p = the liquid density ; 



g = the constant of gravitation. 



If c 2 = 4T/gp, then 



dx c 2 



— = — cos «. 



dot ty 



And since tan a = dy/dx, 



dy c 2 . 

 .*. -f- = 7-sina. 

 dot Ay 



Integrating, 



cosa= ^ — ; {*) 



. dy ± V 1 — cos 2 « + 2y \^c 2 —y 2 



.'. -f- = tana= = ^=-^ — -. 



dx cos a c z — ly z 



Integrating again, 



c, c+^c 2 —y 2 /-= g n 



±x= 2 g y - V c 2 -y 2 + C. 



Taking the origin so that the axis of y is tangent to the curve, 

 when x = 0, y 2 = c 2 /2, from (2), and therefore 



+ *= §log C+ " V ~ y2 - V C ^T+ | { ^2-log(V2 + l)}.(3) 



Ay a 



Suppose a horizontal circular cylinder of density p, whose 

 diameter may be neglected in comparison with its length, to 

 be suspended from one arm of a balance and to be in equili- 

 brium just below the surface of a liquid, of density p, which 

 wets it. When the cylinder is raised through a distance h, 



2E2 



