1881.] 



On Pendent Drops. 



367 



Perhaps a statement of the physical circumstances under which the 

 drop develops and separates, in the light of the information afforded 

 by the tracings, may not be out of place here. 



The cohesion of a liquid, as is well known, manifests itself in a 

 uniform internal compression (A) which may conveniently be regarded 

 as transmitted from the surface, and, in addition, a surface tension 

 (T) which produces a further pressure proportional, at any point of 

 the surface, to the sum of the reciprocals of the principal radii of cur- 

 vature at that point, so that the total pressure at any point of the 

 surface may be written, 



\P P J 



The value of the last term may be positive or negative, according to 

 the nature of the curvature, but the total pressure must always be 

 positive, indeed the term A is always relatively very great. 



The surface acts in many respects like a membrane stretched uni- 

 formly in all directions, and in the case of a pendent drop, the liquid 

 within may be regarded as sustained by the tension of this skin. 



On ordinary hydrostatic principles the pressure must be the same 

 at all points in the same horizontal plane, from which condition the 

 •equation to the generating curve is at once obtained — 



V p / 



where the axes are those of the figure, D the weight of the unit 

 volume of the liquid, and c a constant expressing the pressure due to 

 curvature at the base of the drop where y=0. 



Fig. 2. 



If we take the radius of curvature in the plane of the paper as p, 



