Other methods depending directly on the fundamental equation

Other methods depending directly on the fundamental equation. Direct measurement of the radius of curvature of a surface, by methods similar to those used in determining the radius of curvature of mirrors, has been applied by C. T. R. Wilson1 and C. V. Boys 2 simultaneous measurement of the pressure on both sides of the surface gives the surface tension at once by (2). No convenient instrument has been designed for rapid measurement of surface tensions, on this principle, however. 

For drops where this curvature cannot be neglected, Verschaffelt3 and others have given approximate formulae for the calculation of the surface tension from h and the diameter Dorsey4 and Porter6 have applied Bashforth and Adams s calculations, and Porter s results are given in a form so simple that the surface tension can be calculated in a few minutes from the observations. 

The method is independent of the angle of contact between the liquid and the plate, provided that this is not so variable as to distort the bubbles or drop seriously from the form of a figure of revolution about a vertical axis, to which alone the calculations apply. With bubbles under a plate, it is almost necessary to use very slightly concave plates, or it becomes impossible to retain the bubble in position.6 A measuring microscope with a very good vertical travel is desirable for the measurement of h, and it should also be capable of horizontal 

Very great precautions must be taken against accidental contamination of the surface, which cannot be renewed except by removing the bubble or drop, and replacing it by a new one. The method has recently proved useful with metals, and in studying the slow changes of surface tension which take place in solutions of some colloidal electrolytes. 

The exact calculation of the weight of liquid lifted, in terms of the surface tension and density, is difficult and requires usually special solutions of the fundamental equation of Capillarity, for figures which often are not figures of revolution. The pull may reach a maximum some distance before the object is completely detached and the measurement of this maximum is considered more satisfactory than that of the pull at the moment of detachment.7 In most cases, however, the pull is applied by means of a torsion balance, and the upward motion of the object cannot be checked after the maximum pull is past, so that the detachment takes place almost immediately the maximum pull is reached. 

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