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LV. On the Theoretical Shape of Large Bubbles and Drojos, 

 ivith other Allied Problems. By Allan Ferguson, B.Sc. 

 (Lond.'), Assistant Lecturer in Physics in the University 

 College of North Wales, Bangor*. 



[Plate VIII.] 



OF the various methods that have been proposed, from 

 time to time, for the measurement of capillary con- 

 stants, those which depend on the measurement of the 

 dimensions of bubbles and drops hold an important place. 

 The results obtained by the practice of these methods are 

 not, however, free from uncertainty, and it forms one of the 

 objects of the present paper to point out how some sources 

 of error may be avoided. Formulae are also developed by 

 the use of which it is hoped that reliable measurements of 

 surface-tensions may be made by studying the form and 

 dimensions of drops and bubbles of all sizes. 



In a recent paper j the writer has pointed out a method 

 by which the first integral of the differential equation of the 

 capillary surface in external contact with a cylinder of large 

 radius may be obtained. The methods there employed may 

 also be used to determine the approximate shape of large 

 bubbles and drops. 



The classical investigation on this subject is that of 

 PoissonJ ; the analysis given below is more simple and 

 direct, but leads to results which are in substantial agree- 

 ment with Poisson's, although, as the analysis will show, 

 the small correcting term in the expression for the diameter 

 of a large bubble or drop differs slightly from that given by 

 Poisson. 



A very close method of approximation to the outline of the 

 capillary surface under gravity is that developed by Bashf orth 

 and Adams §, but the labour involved in the development 

 renders it almost prohibitive as a practical method. It is 

 hoped that the results of the present analysis will point to 

 methods that are both reliable and reasonably rapid. 



Let us take, then, as our first problem, the determination 

 of the depth (q) of a large bubble of radius r } as shown in 



* Communicated by Prof. E. Taylor Jones. 



t Phil. Mag. Dec. 1 912, pp. 837 seqq. 



t i Nouvelle Theorie de Taction capillaire/ pp. 212 seqq. 



§ Bashforth and Adams, ' Capillary Action.' (Camb. Univ. Press.) 



