1892.] NUMERICAL VARIATION IN TEETH. 103 



this method of investigation is not merely a good one, but perhaps 

 the best open to us. 



The reason, then, is this. We 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 con- 

 sideration must be hereafter attempted, the matter cannot be 

 discussed here. We 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 homolog- 

 ous 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 maxi- 

 mum 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 anxj given form are either present or 

 absent ; and the business of the homologist is then to determine 

 which ill 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 



