﻿Measurements of Pendent Drops. 419 



where a 2 =T/gp, and proceeding on similar lines, we obtain 

 finally 



y 



. (f 



= C-y/c 2 -Z 2 + 5-3 log 



k 2 °* c+y C 2_^ 



The form of this resulting equation, however, containing, 

 as it does, a mixture of algebraic and logarithmic terms, 

 renders it somewhat unsuitable for numerical computations. 

 A similar objection applies to the method devised by 

 Prof. J. 0. Adams * for the calculation of the forms of 

 sessile drops of mercury, — *a method which consists in 

 " developing the increments of the coordinates in series 

 proceeding according to ascending powers of the increment 

 of the quantity chosen as the independent variable" f, and 

 which, whilst of a high order of accuracy, is, in numerical 

 work, laborious to a proportionate degree. It seemed, there- 

 fore, preferable to attempt to find an empirical equation 

 which should, in the neighbourhood of the vertex, at any 

 rate, fit sufficiently closely the outline of the meridional 

 section of the drop. 



An attempt to evaluate surface tensions in such a way 

 seems all the more desirable, as it frees one from the 

 necessity of troubling about that somewhat elusive quantity, 

 the "angle of contact." For liquids which wet the solid 

 with which they are in contact, it is safe to assume the angle 

 of contact to be zero, and for such liquids measurements of 

 the height of rise of the liquid in capillary tubes are 

 sufficiently exact ; for other liquids, the determination of 

 the angle of contact introduces an element of uncertainty, 

 and the " method of ripples/'' whilst avoiding the measure- 

 ment of contact-angles, possesses the disadvantage that the 

 equation for T is a cubic in X, the term in A, 3 being the most 

 important, so that a one-per-cent. error in the determination 

 of the wave-length involves an error of approximately three- 

 per-cent. in the value of the surface tension J. 



The apparatus used and method pursued in this paper 

 are as follows § : — 



* Baslifortli and Adams, ' Capillary Action ' (Unmb. Univ. Press. 

 1888). 



t Op. cit. p. 15. 



X Rayleign, Scientific Papers, vol. iii. p. 389 ; and Watson, Physical 

 lie view', May L901. 



§ Of Worthington, Proc. Roy. Soc. June L881, 



2 F 2 



