to _x_. This, it is true, would not be a very rapid increase. But it is
possible that the fraction _x/n_ would increase, for the heredity might
very well consist not only in a growth independent of stimulation, but in
an increasing response to stimulation, so that _x_ itself might be
increasing, and the fraction _x/n_ would become larger in each generation.
The death and loss of the skin over the antler, originally duo to the
laceration of the skin in fighting, has also become hereditary, and it is
certainly difficult to conceive the action of hormones in this part of the
process. All we can suggest is that the hormone from the rapidly growing
antler, including the covering skin, is acting on the corresponding factor
in the gametocytes for a certain part of every year, and then, when the
skin is stripped off, the hormone disappears. The factor then may be said
to be stimulated for a time and then the stimulus suddenly ceases. The
bone also begins to die when the skin and periosteum is stripped off, and
the hormone from this also ceases to be produced.

The annual shedding and recrescence of the antler, however, is only to be
understood in connexion with the effect of the testicular hormone.
According to my theory there are two hormone actions, the centripetal from
the hypertrophied tissue to the corresponding factor in the gametocytes,
and the centrifugal from the testis to the tissue of the antler or other
organ concerned. The reason why the somatic sexual character does not
develop until the time of puberty, and develops again each breeding season
in such cases as antlers, is that the original hypertrophy due to external
stimulation occurred only when the testicular hormone was circulating in
the blood. The factor in the gametocytes then in each generation acted
upon by both hormones, and we must suppose that in some way the result was
produced that the hereditary development of the antler in the soma only
took place when the testicular hormone was present. It is to be remembered
that we are unable at present to form a clear conception of the process