50 



Mr. A. M. Worthington on the 



[Dec. 18, 



once realised, will spontaneously split into as many equal and equi- 

 distant spheres as nr times the diameter is contained in the length. 

 Thus, if n be the number of drops, 

 I the length, 



and d the diameter or thickness of the cylinder, the law of 

 segmentation is expressed by the formula 



n= 1 



M. Plateau has endeavoured to supply an experimental proof of. 

 this by liberating a cylinder of mercury, extended between two 

 amalgamated wires, on a glass plate, but he found that the frictional 

 contact with the plane surface along the length of the cylinder 

 diminished the number of drops, probably because the limits of 

 stability are extended by friction : thus, when the cylinder of mer- 

 cury rested on a glass plate, the limit of stability appeared to be 

 extended to 61 times the diameter, this being the average distance 

 apart at which the drops were formed. So that the law became 



n— - , and it was ouly by observing- the effect of simultaneous 



contact with a vertical as well as a horizontal plate that a rough 

 estimate could be made of the influence of friction on the number of 

 drops. 



By the method of liberation in air that is described in the latter 

 half of this paper all friction is avoided, and the results show a close 

 accordance with theory. 



I will first describe experiments with reference to an annulus lying 

 on a plate. It may be well at the outset to remark that an annulus is 

 not, like a cylinder, a figure of equilibrium for a liquid, there being 

 excess of pressure on the outside ; this excess, however,, will diminish 

 as the radius of the annulus increases, — as, in fact, it approximates to 

 a cylinder. The excess, moreover, will not be a large fraction of the 

 total surface-pressure, if, as in the case we have to deal with, the 

 thickness of the annulus is small in comparison with its width : thus 

 in the figure — 









\VlL 





mm 



III 





the principal radii of curvature at A are r and (R-f r) and at B are r 

 and -(R-r) r 



