Form and function
We have limited ourselves to considering
man, only one among the primates. So let us look at other
primates. The siamang is a relatively small species, the gorilla
a large one. The illustration depicts them at about the same
size. One of the striking features is that the diameter of
the long bones does not seem to be proportionate to the length
of the long bones. The gorilla is much heavier than the siamang.
If body weight weight were to increase as length cubed, and
cross-sectional area of a bone in arm or leg as length squared,
then the static load of the bone per unit of area would not
be constant but increase linearly with body size. That would
only work if the bone became structurally stronger. However,
the skeleton is not only subject to static loads, it should
also be able to cope with elastic stresses. Think of the forces
that tend to bend and stretch, or create a torque, that occur
during running and jumping, getting up from a kneeling or
a squatting position, or are exerted during skiing. On that
account the gorilla needs a more robust skeleton than a siamang.
It turns out that in nature species of the same family are
scaled in such a manner that they are capable of dealing with
comparable elastic stresses. This can only be achieved if
the relationship between the length and the square of diameter
are constant across species. One can also apply this to the
branching of trees. The derivation of this law of 'elastic
similarity' is due to McMahon; it can e.g.
be found in 'TA McMahon, JT Bonner - On Size and Life, Scientific
American Library, New York, ISBN 0-7167-5000-7'.
Conclusion
Form and function must be adapted to static and elastic loads. The requirements are not the same for neonates, toddlers, children or adults within a species. Hence appropriate dimensional growth is an absolute requirement for optimal function of the individual, and hence for the survival of the species.