heredity--namely, how hormones or waste products from one part of the body
could differ from these from the same tissue in another part of the body.
If there were no special relation, hypertrophy of bone on one part of the
body such as the head, would merely stimulate the factor for the whole
skeleton in the gametocytes, and the result would merely be an increased
development of the whole skeleton. On the other hand, we have the evident
fact that a number of chromosomes formed apparently of the same substance,
by a series of equal chromosome divisions determine all the various
special parts of the complicated body. This is not more difficult to
understand than that every part of the body should give off special
substances which would have a special effect on the corresponding parts of
the chromosomes. We know that skin glands in different parts of the body
produce special odours, although all formed of the same tissue and all
derived from the epidermis. It seems not impossible that bones of
different parts of the body give off different hormones. If the factors in
the gametes were thus stimulated they would, when they developed in a new
individual, product a slightly increased development of the part which was
hypertrophied in the parent soma. No matter how slight the degree of
hereditary effect, if the stimulation was repeated in every generation, as
in the case of such characters as we are considering it undoubtedly was,
the hereditary effect would constantly increase until it was far greater
than the direct effect of the stimulation. We may express the process
mathematically in this way. Suppose the amount of hypertrophy in such a
case as the antlers to be _x,_ and that some fraction of this is
inherited. Then in the second generation the same amount of stimulation
together with the inherited effect would produce a result equal to
_x+x/n_. The latter fraction being already hereditary, a new fraction
_x/n_ would be added to the heredity in each generation, so that after _m_
generations the amount of hereditary development would be _x+mx/n_. If _n_
were 1000, then after 1000 generations the inherited effect would be equal