factors or determinants might be stimulated by products circulating in the blood and derived from the parts of the soma corresponding to them. There is no reason to suppose that an exostosis formed on the frontal bone as a result of repeated mechanical stimulation due to the butting of stags would give off a special hormone which was never formed in the body before, but it would probably in its increased growth give off an increased quantity of intermediate waste products of the same kind as the tissues from which it arose gave off before. These products would act as a hormone on the gametocytes, stimulating the factors which in the next generation would control the development of the frontal bone and adjacent tissues. The difficulty of this theory is one which has occurred to biologists who have previously made suggestions of a connexion between hormones and 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_