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Show 1892.] NUMERICAL VARIATION IN T E E T H . 103 this method of investigation is not merely a good one, but perhaps the best open to us. The reason, then, is this. W e assume that the transition from one form to another takes place by Variation. If, therefore, we can see the variations, we shall see the precise mode by which Descent is effected. Now the problem of Descent includes the problem of Homology, and, therefore, in any case of supposed Homology between organs the ideally best proof or disproof of such a supposition is to be had by appeal to the facts of Variation. For the statement that an organ of one form is homologous with the organ of another form means that there is between the two some connexion of Descent, and that the one organ has been formed by modification of the other or both by modification of a third. The precise way in which this connexion exists is not defined, and, indeed, has scarcely ever been considered, and though such a consideration must be hereafter attempted, the matter cannot be discussed here. W e must be content for the present with the belief that in some undefined way there is a relationship between homologous parts, and that this is what we mean when we affirm that they are homologous. In the case of the homologies of Teeth, we are concerned with the application of this belief or principle to the case, not of a single organ, but to Multiple Parts arranged in Series. If, then, the whole series of teeth in one form is homologous with the whole series in another, we have now to consider how far we can extend the principle to the case of individual members of the two series. This is the question which is again and again arising with regard to Multiple Parts, but there are still no general principles by which it may be decided. But though no one has told us the steps by which the Numerical Variation of teeth proceeds, there is nevertheless a received view by which it is sought to interpret the phenomena, and though there are several schemes upon which the homologies of teeth are defined, all are alike based upon one principle, which may be stated as follows. It is believed that in the case of mammals, perhaps excluding the Cetacea, the series of teeth consisted originally of some maxim u m number from which the formulae now characteristic of the several forms have been derived by successive diminution. On this view the series is believed to be always composed of definite and individual members, ivhich in any given form are either present or absent; and the business of the homologist is then to determine which in each case is present and which absent. This hypothesis, of course, involves a definite conception of the mode in which Variation works, and it is most important to realize this clearly. For if it is true that each member of the Series of Teeth has in every form an individual and proper history, it follows that if we had before us the whole series of ancestors from which the form has sprung, we should then be able to see the history of each tooth distinctly and severally in the jaws of each of these progenitors. In such a series the rise of one individual tooth and the decline of |