410 PROCEEDINGS OF THE ACADEMY OF [1892. 



(4) The considerations which Dybowski (No. 3), Fleischmann 

 and Mahn advance as showing that the anterior end of the lower 

 molars is homologous with the posterior end of the upper ones and 

 vice versa, are derived from the resemblance of form in these parts 

 respectively and from the assumption that in Arvicola the cement 

 bands on the teeth are guides to homology. But for purposes of 

 morphological analysis, resemblance of form is of no value what- 

 ever, and as Mahn himself points out, the positions of the cement 

 bands in Arvicola is determined by the necessity of fixing the tooth 

 in the alveolus without undue compression of the cells of the per- 

 sistently functional enamel organ. How deceptive mere resem- 

 blance of form may be, is clearly shown by the facts of premolar 

 evolution already alluded to; viz., that in those genera which have 

 molariform premolars, there is the same apparent correspondence 

 between the outside of the upper and the inside of the lovver pre- 

 molars, as obtains in the molars. And yet, as will be more fully 

 shown in the sequel, this correspondence is entirely of form and not 

 of homology, for in both superior and inferior premolars the proto- 

 cone remains upon the external or buccal side of the crown. 



When the line of argument adopted by Fleischmann and Mahn is 

 pushed to the conclusion that the third lower molar is the homo- 

 logue of the first upper molar, it would certainly appear to be a 

 reductio ad absurdum of the considerations which lead to such a 

 result. On Mahn's principles the fourth upper premolar of 

 Castoroides, and not the first molar, may be proved to be homolo- 

 gous with the last inferior molar. If the equivalence of ^ and m* 

 means anything at all, it must imply that at some time in the early 

 history of the mammals, either the upper or lower series was turned 

 about, end for end, mj now occupying the place originally held 

 by ^^. Is such a thing conceivable? and if so, what are the steps 

 by which the change was brought about? Such a shifting could 

 not be effected by a partial rotation of the upper tooth in one direc- 

 tion and of the lower tooth in the opposite direction. 



The only safe method of determining the homologies of the various 

 cusps in the protean forms assumed by the mammalian molar and pre- 

 molar, is that of followiugoutstep by step the changes which take place 

 in well defined phyletic series. Even embryology, valuable as is the 

 assistance which it affords, must be used with great caution and in 

 a general rather than a special way. The shapes taken by embry- 

 onic teeth are seldom like anything which is known among fossil 



