VIII. On the spontaneous segmentation of a liquid annulus

Abstract

In seeking an explanation of the appearance of a definite number of lobes in the liquid annulus which is formed at a certain stage of the splash of a drop that has fallen vertically on to a horizontal plate, I was led to make some experiments on the spontaneous segmentation of such an annulus lying on a plate with a view to ascertaining whether the relation that exists between the dimensions of the annulus and the number of drops into which it will spontaneously split, is the same as for a straight cylinder of liquid under similar conditions. Finding that the relation was the same, it then occurred to me that by liberating an annulus in air without contact with any solid, a direct experimental proof might fee obtained of the law of segmentation of a free cylinder. It has been shown mathematically in various ways, and experimentally by M. Plateau, that the equilibrium of a free cylinder of any liquid, under the influence of surface tension only, becomes unstableas soon as the length exceeds π times the diameter; and it has been regarded as a necessary consequence of this that such a cylinder, if once realised, will spontaneously split into as many equal and equidistant spheres as π times the diameter is contained in the length.