6
THE ESSEX NATURALIST
Mathematical treatments are not foreign to Presidential
Addresses to this Club, but perhaps I should reassure you. My
mathematics never reached even the sixth-form level, so that
the geometrical conceptions I am about to discuss are, there-
fore, all of the simplest.
In solid objects that vary in size but not in form, three-
dimensional aspects, such as volume, vary as the cube, and
two-dimensional aspects, such as area, vary as the square of
the linear measurements.
Thus on doubling the dimensions of a fruit-body the volume
and, therefore, the weight of the cap is increased eight times,
whilst the cross-sectional area of the stipe which bears that
weight is increased only four times (Fig. 3). We might,
Fig. 3. Diagram to show how, in the structure like a toadstool, doubling
the linear dimensions doubles the ratio of cap volume to cross-sectional area.
of stipe.
therefore, expect adjustments of form with change of size,
otherwise the larger fruit-bodies would have stipes that are too
thin and the smaller ones' stipes too stout for the job in hand.
This is the so-called "principle of similitude." It is well
known in animals. We have only to consider an elephant and
a deer. Magnify a deer to the size of an elephant and it would
simply collapse. Reduce an elephant to the size of a deer and
you have a ridiculous beast with leg's far too thick for its body.