THE SUSPENDED-RING METHOD 185 



dipped below the surface and then carefully pulled vertically upwards 

 will drag with it a film of the liquid. If we assume that this film becomes 

 vertical before rupture takes place, then the downward pull P on the 

 ring must be equal to twice the product of mean circumference of ring 

 by surface energy. To the first approximation 



P = 4tRT 



To increase the accuracy, the exact dimensions of the ring and the 

 diameter 2r of the wire of which it is made must be taken into considera- 

 tion. On account of the incompleteness of the theory, Harkins, Young, 

 and Cheng [1926] have increased the reliability of the method to better 

 than 1 per cent by introducing an experimental correction factor F, so 

 that the working equation becomes 



T = mg ™ 



4wR 



To obtain an unknown surface energy the maximum pull in dynes to 

 raise the ring when the surface is on the point of rupture is obtained, 

 experimentally, as p = mg/^irR, where R is the mean radius of the ring. 

 The volume of the liquid V raised by means of the ring above the plane 

 surface of the liquid, which corresponds with the above maximum pull, is 

 V = m/(d — p), where d is the density of the liquid, p is the density of 

 air saturated with vapor of the liquid, and m is the mass of the raised 

 liquid. 



It was found that for the proper values of the ratio of R/r the correc- 

 tion factor F is determined by the value of R 3 /V. Hence, the values of 

 R, r, and the experimentally determined value of V being known, the 

 surface energy may be determined to a high degree of precision with the 

 aid of a table of these correction factors as 



T = p-F 



In the hands of du Nouy [1919] this method was brought to a high 

 degree of precision. He adopted a ring of platinum (10 per cent iridium) 

 which hangs from an inverted V frame of the same kind of wire fused to 

 the ring. This ring can be cleaned by simply heating it white hot. It is 

 suspended from the arm of a specially designed torsion balance, as in the 

 Cenco-du Notiy tensiometer (Fig. V-5). The wire ring is of circular 

 section about 0.3 mm in diameter with a mean circumference of 4 cm. 

 The torsion wire is made of steel piano wire of diameter 0.25 mm. The 

 liquid is placed in a shallow crystallizing dish or watch glass into which 

 the ring is allowed to dip. The pointer attached to the torsion wire 

 rotates over a fixed circular scale as the ring is raised to the point where it 



