Here however, we may freely confess that we are for the present on the
uncertain ground of suggestion and conjecture; and so must we remain,
in regard to many other simple and symmetrical organic forms, until
their form and dynamical stability shall have been investigated by the
mathematician: in other words, until the mathematicians shall have
become persuaded that there is an immense unworked field wherein they
may labour, in the detailed study of organic form.
――――――――――
According to Plateau, the viscidity of the liquid, while it helps to
retard the breaking up of the cylinder and so increases the length of
the segments beyond that which theory demands, has nevertheless less
influence in this direction than we might have expected. On the other
hand, any external support or adhesion, such as contact with a solid
body, will be equivalent to a reduction of surface-tension and so will
very greatly increase the {240} stability of our cylinder. It is for
this reason that the mercury in our thermometer tubes does not as a
rule separate into drops, though it occasionally does so, much to our
inconvenience. And again it is for this reason that the protoplasm in
a long and growing tubular or cylindrical cell does not necessarily
divide into separate cells and internodes, until the length of these
far exceeds the theoretic limits. Of course however and whenever it
does so, we must, without ever excluding the agency of surface tension,
remember that there may be other forces affecting the latter, and
accelerating or retarding that manifestation of surface tension by
which the cell is actually rounded off and divided.
In most liquids, Plateau asserts that, on the average, the influence
of viscosity is such as to cause the cylinder to segment when its
length is about four times, or at most from four to six times that
of its diameter: instead of a fraction over three times as, in a
perfect fluid, theory would demand. If we take it at four times, it
may then be shewn that the resulting spheres would have a diameter
of about 1·8 times, and their distance apart would be equal to about
2·2 times the diameter of the original cylinder. The calculation is
not difficult which would shew how these numbers are altered in the
case of a cylinder formed around a solid core, as in the case of
the spider’s web. Plateau has also made the interesting observation
that the _time_ taken in the process of division of the cylinder is
directly proportional to the diameter of the cylinder, while varying
considerably with the nature of the liquid. This question, of the time
occupied in the division of a cell or filament, in relation to the
dimensions of the latter, has not so far as I know been enquired into
by biologists.
――――――――――
Public-domain text, read in full here on John Shaqi.
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