pattern of symmetrical folds. If the surface thus thrown into folds be that of a cylinder, or any other figure with one principal axis of symmetry, such as an ellipsoid or unduloid, the direction of the folds will tend to be related to the axis of symmetry, and we might expect accordingly to find regular longitudinal, or regular transverse wrinkling. Now as a matter of fact we almost invariably find in the Lagena the former condition: that is to say, in our ellipsoid or unduloid cell, the puckering takes the form of the vertical fluting on a column, rather than that of the transverse pleating of an accordion. And further, there is often a tendency for such longitudinal flutings to be more or less localised at the end of the ellipsoid, or in the region where the unduloid merges into its spherical base. In this latter region we often meet with a regular series of short longitudinal folds, as we do in the forms of Lagena denominated L. semistriata. All these various forms of surface can be imitated, or rather can be precisely reproduced, by the art of the glass-blower46.
Furthermore, they remind one, in a striking way, of the regular ribs or flutings in the film or sheath which splashes up to envelop a smooth ball which has been dropped into a liquid, as Mr Worthington has so beautifully shewn47.
In Mr Worthingtonãs experiment, there appears to be something of the nature of a viscous drag in the surface-pellicle; but whatever be the actual cause of variation of tension, it is not difficult to see that there must be in general a tendency towards longitudinal puckering or ãflutingã in the case of a thin-walled cylindrical or other elongated body, rather than a tendency towards transverse puckering, or ãpleating.ã For let us suppose that some change takes place involving an increase of surface-tension in some small area of the curved wall, and leading therefore to an increase of pressure: that is to say let T become Tã₤+ã₤t, and P become Pã₤+ã₤p. Our new equation of equiôÙlibôÙrium, then, in place of P =ã₤Tã₤ãã₤rã₤+ã₤Tã₤ãã₤rÿ£¢ãý becomes
and by subtraction,
Now if
Therefore, in order to produce the small increment of pressure p, it is easier to do so by increasing tã₤ãã₤r than tã₤ãã₤rÿ£¢ãý; that is to say, the easier way is to alter, or diminish r. And the same will hold good if the tension and pressure be diminished instead of increased.
This is as much as to say that, when corrugation or ãripplingã of the walls takes place owing to small changes of surface-tension, and consequently of pressure, such corrugation is more likely to take place in the plane of r,ãthat is to say, in the plane of greatest curvature. And it follows that in such a figure as an ellipsoid, wrinkling will be most likely to take place not only in a longitudinal direction but near the extremities of the figure, that is to say again in the region of