﻿418 Mr. A. Ferguson on Photographic 



h being the vertical distance from the " free " surface to the 

 point in question, R and R' the principal radii of curvature 

 of the surface of the drop at any point of the surface in a 

 horizontal plane passing through P. In particular, if the 

 point P be taken at the vertex of the drop, we have 



2T 



and measurements of h and R will serve to determine T. 



The central idea of such a method possesses, of course, no 

 novelty. In a lecture given at the Poyal Institution *, 

 Lord Kelvin showed a simple apparatus by means of which 

 approximate measurements might be made, but in the 

 calculation appended thereto the drop is treated as hemi- 

 spherical, i. e. the two principal radii of curvature are treated 

 as constant and equal in value at any point on the surface, a 

 condition only approximately fulfilled when the drop is very 

 small. 



The main object of the present paper is to test the validity 

 of various equations which may be obtained, empirically or 

 otherwise, to fit the contour of the meridional section, 

 especially in the neighbourhood of the vertex. For a know- 

 ledge of the equation to the section enables one to calculate 

 the principal radii of curvature at any point, and hence 

 to deduce the surface tension in terms of known quantities. 



For small drops such an equation can be obtained by 

 following a method first proposed by Laplace f, in which the 

 differential equation of the meridional curve is integrated by 

 assuming that a circle, of radius c, can be determined, whose 

 ordinate, for a given abscissa, differs from that of the meri- 

 dional curve by a small quantity whose square is negligible. 

 The investigation of Laplace refers to the shape of the 

 curved surface inside a cylindrical capillary tube, but, writing 

 the equation of the surface in the form 



nstead of 



Id . h—y 



Id, . n h + y 



- -j- Usinfl) = — ^ 

 x ax a A 



* Proc. Roy. Inst. vol. xi. part iii. 



t Laplace, Mecanique Celest. Supp. to Bk. x. ; and Minchin, 'Hydro- 

 statics,' Chap. viii. 



