]892.] NUMERICAL VARIATION IN TEETH. 115 



One or both of these propositions may be true. If the division of 

 the other three first premolars were as complete as that of the 

 left P^ there would be no indication of their origin. But if it is 

 possible for a premolar to represent or to be represented by two 

 premolars, without any risible indication of its double nature, may 

 not the same be true of the premolars of other forms ? May it not 

 be true of teeth generally ? And if it is true, how are the homologies 

 of teeth to be determined ? Nevertheless teeth are alm^ost preemi- 

 nently amenable to this kind of treatment. They have been studied 

 with immense care. The facts which they present, and on which 

 their homologies are to be determined, are remarkably compact, and 

 of all Series of Multiple Parts they offer the best chance. But ex- 

 amined in the light of a knowledge of the facts of Variation, that 

 process is found to be capable of occurring in a way which precludes 

 the possibiHty of carrying out an analysis of the relation between 

 the parts and suggests that such relationship need not necessarily 

 exist at all. This subject cannot now be discussed further ; but if 

 any one wishes to realize the difficulties suggested by the Variations 

 of which instances have been given, let him read some good dis- 

 cussion of dental homologies, as, for example, Thomas's excellent 

 paper ^, with these cases in his mind, and as he reads let him ask 

 himself what margin is left for the occurrence of phenomena like 

 this. Such schemes as that alluded to, though they have done a 

 most useful work, and though they are ingenious, logical, and orderly, 

 are orderly because they are made without regard to the ways of 

 Variation, which is arbitrary and capricious and follows no order 

 that we have yet devised. 



An illustration will perhaps help to make clear the point at issue. 

 The received view of homology supposes that a varying form is 

 derived from the normal much as a man might make a wax model 

 of the variety from a wax model of the type, by small ad- 

 ditions to, and subtractions from, the several parts. This may, 

 to our imaginations, seem, perhaps, the readiest way by which 

 to make the varying form if we were asked to do it ; but 

 the natural process differs in one great essential from this. For 

 in nature tlie body of the varying form has never been the body 

 of its parent and is not formed by a plastic operation from it ; 

 but in eacli case the body of the offspring is made again from the 

 beginning, just as if the wax model had gone back into the melting- 

 pot before the new model was begun. 



The present system of Homology must probably be retained as a 

 basis of notation, imperfect though it is and though it is founded ou 

 a misconception of essential facts. It is likely that many will be 

 disposed to doubt the reality of this misconception, and I can only 

 ask that they should suspend judgment until the whole evidence can 

 be produced. In the meantime tbis summary of facts and conclusions 

 is put forward, together with a few " Prerogative Instances," in the 

 hope that some one may be thereby attracted to a most powerful 

 and fascinating method of zoological research. 



1 Phil. Trans. 1887, vol. ckxviii.B, p. 443. 



