p = t ⁄ r + t ⁄ r′.
Now if
r < r′, t ⁄ r > t ⁄ r′.
Therefore, in order to produce the small increment of pressure p, it is easier to do so by increasing t ⁄ r than t ⁄ r′; 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 “rippling” 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,—that 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 greatest curvature.
| Fig. 87. Nodosaria scalaris, Batsch. | Fig. 88. Gonangia of Campanularians. (a) C. gracilis; (b) C. grandis. (After Allman.) |
The longitudinal wrinkling of the flask-shaped bodies of our Lagenae, and of the more or less cylindrical cells of many other Foraminifera (Fig. [87]), is in complete accord with the above theoretical considerations; but nevertheless, we soon find that our result is not a general one, but is defined by certain limiting conditions, and is accordingly subject to what are, at first sight, important exceptions. For instance, when we turn to the narrow neck of the Lagena we see at once that our theory no longer holds; for {262} the wrinkling which was invariably longitudinal in the body of the cell is as invariably transverse in the narrow neck. The reason for the difference is not far to seek. The conditions in the neck are very different from those in the expanded portion of the cell: the main difference being that the thickness of the wall is no longer insignificant, but is of considerable magnitude as compared with the diameter, or circumference, of the neck. We must accordingly take it into account in considering the bending moments at any point in this region of the shell-wall. And it is at once obvious that, in any portion of the narrow neck, flexure of a wall in a transverse direction will be very difficult, while flexure in a longitudinal direction will be comparatively easy; just as, in the case of a long narrow strip of iron, we may easily bend it into folds running transversely to its long axis, but not the other way. The manner in which our little Lagena-shell tends to fold or wrinkle, longitudinally in its wider part, and transversely or annularly in its narrow neck, is thus completely and easily explained.
An identical phenomenon is apt to occur in the little flask-shaped gonangia, or reproductive capsules, of some of the hydroid zoophytes. In the annexed drawings of these gonangia in two species of Campanularia, we see that in one case the little vesicle {263} has the flask-shaped or unduloid configuration of a Lagena; and here the walls of the flask are longitudinally fluted, just after the manner we have witnessed in the latter genus. But in the other Campanularian the vesicles are long, narrow and tubular, and here a transverse folding or pleating takes the place of the longitudinally fluted pattern. And the very form of the folds or pleats is enough to suggest that we are not dealing here with a simple phenomenon of surface-tension, but with a condition in which surface-tension and stiffness are both present, and play their parts in the resultant form.
