CAPILLARY CONSTANTS 437 



some two or three millimetres. But these difficulties may be 

 overcome by taking a magnified photograph of the bubble 

 illuminated by means of a pencil of light the rays of which are 

 accurately horizontal. From measurements of this photograph 

 the values of q and of r may be determined with a very high 

 percentage accuracy. The method possesses two other advan- 

 tages — it is accurately statical, and there is very little risk of 

 contamination of the surface of the bubble. 



Method (8), which depends on the photographic measure- 

 ment of bubbles or drops of any size, is suited to various special 

 cases, e.g. the determination of the surface-tensions of molten 

 metals. Suppose that a photograph of a bubble or drop has 

 been taken and that the co-ordinates of a number of points on 

 the outline have been determined. The equation of equilibrium 

 of any given portion of the bubble or drop can be written down 

 exactly in a form which contains the integrals 



/xdy, /x 2 dy, and yxydy 



taken between the appropriate limits. As we do not know 

 x as a function of y, the above integrals cannot be evaluated 

 algebraically. But by plotting out three curves between x and y, 

 x 2 andj/, and xy and y respectively on squared paper, the values 

 of the integrals can be determined with considerable accuracy 

 either by the planimeter or by square-counting. These values, 

 substituted in the original equation, then enable us to deter- 

 mine T. 



Two methods of a high order of exactness are tabulated 

 under the heading " capillary tubes." In the very ingenious 

 method due to M. Sentis, a pendent drop of the liquid is formed 

 at the end of a vertical capillary tube. The position of the 

 meniscus formed by the liquid in the tube is then noted, and the 

 maximum radius (r) of the pendent drop is measured. A beaker 

 of the same liquid is then placed on the head of a spherometer, 

 which is raised until the liquid in the beaker just touches the 

 vertex of the drop. The spherometer is now further raised 

 until the liquid in the capillary reaches its original level. If the 

 difference between the spherometer readings in the two positions 

 be h, then T is given by the equation 



T-?(*-g. 



The method is simple and very exact, and the only factor which 



