The fact thus established experimentally, that the surface of a smooth sphere must be rigid if the film is to envelop it closely, suggests also a satisfactory explanation of the flutings. For we know from other researches on the motion of liquids,[J] that a layer of liquid actually in contact with a solid can have no motion relative to the solid, but must move with it. Thus in the film or sheath which rises over and envelops the sphere, the layer of liquid next to the solid must be moving downwards with it, while the outermost layers at least are moving upwards; thus there must be a strong viscous shear in the film 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 forced 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 quite accords with the appearance of such figures as Fig. 6 of page 91 and Figs. 1 and 2 of page 113, in which, firstly, we see 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. 2, Series XIV (p. 105), where the liquid was pure glycerine. The effect of the viscous drag is, in fact, most marked in the most viscous liquid, and it is also in the viscous liquid that the ribs are most strongly marked. INFLUENCE OF THE NATURE OF THE LIQUID EXPLAINED. Finally, in confirmation of our explanation, we have the fact that with a liquid of small density and surface-tension, such as paraffin oil, a much smaller velocity of impact with a highly polished sphere suffices to give a "rough" splash than with water, a liquid of greater density and surface-tension, the reason being without doubt that the tangential velocity given by the impact is greater with the lighter liquid, as, indeed, is proved to be the case by the greater height to which the surrounding sheath is thrown up. The surface-tension also being smaller, the less is the abatement of velocity on account of work done in extending the surface. FOOTNOTES: [I] See _Nature_, vol. xxix., January 31, 1884. [J] See Whetham on "The Alleged Slipping at the Boundary of a Liquid in Motion." _Phil. Trans. Roy. Soc._, Vol. 181 (1890). CHAPTER X CONCLUSION