At the same time it is perfectly true that _all_ changes of form,
inasmuch as they necessarily involve changes of actual and relative
magnitude, may, in a sense, be properly looked upon as phenomena of
growth; and it is also true, since the movement of matter must always
involve an element of time[81], that in all cases the rate of growth
is a phenomenon to be considered. Even though the molecular forces
which play their part in modifying the form of an organism exert an
action which is, theoretically, all but instantaneous, that action is
apt to be dragged out to an appreciable interval of time by reason of
viscosity or some other form of resistance in the material. From the
physical or physiological point of view the rate of action even in such
cases may be well worth studying; for example, a study of the rate of
cell-division in a segmenting egg may teach us something about the work
done, and about the various energies concerned. But in such cases the
action is, as a rule, so homogeneous, and the form finally attained is
so definite and so little dependent on the time taken to effect it,
that the specific rate of change, or rate of growth, does not enter
into the _morphological_ problem.
To sum up, we may lay down the following general statements. The form
of organisms is a phenomenon to be referred in part to the direct
action of molecular forces, in part to a more complex and slower
process, indirectly resulting from chemical, osmotic and other forces,
by which material is introduced into the organism and transferred from
one part of it to another. It is this latter complex phenomenon which
we usually speak of as “growth.” {54}
Every growing organism, and every part of such a growing organism, has
its own specific rate of growth, referred to a particular direction.
It is the ratio between the rates of growth in various directions by
which we must account for the external forms of all, save certain
very minute, organisms. This ratio between rates of growth in various
directions may sometimes be of a _simple_ kind, as when it results in
the mathematically definable outline of a shell, or in the smooth curve
of the margin of a leaf. It may sometimes be a very _constant_ one, in
which case the organism, while growing in bulk, suffers little or no
perceptible change in form; but such equilibrium seldom endures for
more than a season, and when the _ratio_ tends to alter, then we have
the phenomenon of morphological “development,” or steady and persistent
change of form.
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