192 MESSRS. A. M. WORTHINGTON AND R. S. COLE 



Explanation of the Flutings. 



The fact thus established experimentally, that the surface of a smooth sphere must 

 be rigid if the film is to envelope it closely, suggests what seems a satisfactory 

 explanation of the flutings. For it suggests that, even while the film is exceedingly 

 thin, the flow is of the kind demanded by POISEUILLE, in which the liquid next to the 

 solid has no motion relative to the solid, while the velocity farther away increases 

 with the distance from the surface. Since the sphere is descending while the film is 

 rising, there must be a strong viscous shear in the liquid impeding its rise. If by any 

 fortuitous oscillation a radial rib arises, this will be a channel in which the liquid, 

 being farther from the surface, will be less affected by the viscous drag ; it will 

 therefore be a channel of more rapid flow and diminished pressure, into which, 

 therefore, the neighbouring liquid will be drawn from either side. Thus a rib once 

 formed is in stable equilibrium, and will correspond to a jet at the edge of the rim. 

 This explains the persistence of the ribs when once established, and we may attribute 

 their regular distribution to the fact that they first originate in the spontaneous 

 segmentation of the annular rim at the edge of the advancing sheath. This 

 explanation receives unexpected confirmation in the appearance of the lop-sided 

 splashes of Series XX., in which we see, firstly, that the flutings are absent from that 

 part of the sheath which has left the sphere, and, secondly, we see how much higher 

 in every case the continuous film has risen in that part which has left the sphere than 

 in the part which has clung to it, and has been hindered by the viscous drag. 

 Especially is this the case in fig. 3, Series XXVI. (see p. 196), where the liquid was 

 pure glycerine. The effect of the viscous drag is, in fact, most marked in the most 

 viscous liquid. 



Influence of the Constants of the Liquid. 



Finally, in confirmation of the general argument, we have the fact that with a 

 liquid of small density and surface tension, such as Alexandra oil, a much smaller 

 velocity of impact with a highly polished sphere is required to give " rough " splash 

 than with water, a liquid of greater density and surface tension, the reason being 

 without doubt that the tangential velocity due to the impact is greater with the less 

 dense liquid, as, indeed, is proved to be the case by the greater height to which the 

 surrounding sheath is thrown up, and the smaller the surface tension the less will be 

 the abatement of velocity on account of work done in extending the surface. 



[Added January 11, 1900. The constants of the Alexandra oil employed in the 

 experiments were as follows : Specific Gravity, 0'840 ; Surface Tension, 2 '8 9 grams 

 per metre (= surface tension of water X 0'383) ; viscosity = viscosity of water at the 

 same temperature X 2 '607. Experiments shortly to be described show that the 

 addition to 51 vols. of water of as much as 6 vols. of glycerine, which must have 

 largely increased the viscosity, produced little difference in the splash, except in 



