In Mr Worthington’s 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 “fluting” in the case of a thin-walled cylindrical or other
elongated body, rather than a tendency towards transverse puckering, or
“pleating.” 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 _T_ + _t_, and _P_ become _P_ + _p_. Our new equation of
equilibrium, then, in place of _P_ = _T_/_r_ + _T_/_r′_ becomes
_P_ + _p_ = (_T_ + _t_)/_r_ + (_T_ + _t_)/_r′_,
and by subtraction,
_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.
[Illustration: Fig. 87. _Nodosaria scalaris_, Batsch.]
[Illustration: Fig. 88. Gonangia of Campanularians. (_a_) _C.
gracilis_; (_b_) _C. grandis_. (After Allman.)]
Public-domain text, read in full here on John Shaqi.
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