394 ANNALS NEW YORK ACADEMY OF SCIENCES 



evolve into useful, functional, structures ; as the horns of titanotheres, the 

 accessory cusps {e. g., mesostyle, metastylid, etc.) in the molar teeth of 

 Eocene Perissodactyls. These rectigradations appear independently in 

 different families during different stages of evolution. They constitute 

 striking examples of parallelism or convergence in closely related fami- 

 lies. Were they due to "a remote hereditary control", t. e., to a delayed 

 manifestation of a hereditary tendency in the generalized ancestral stock 

 (Osborn), or were they merely similar adaptations or responses, appear- 

 ing in similar materials, subjected to similar stimuli ? From his studies 

 on the mechanical interaction of the upper and lower grinding teeth, the 

 speaker concluded that the appearance of new cusps was always condi- 

 tioned in part by mechanical relations, but he did not take this as a proof 

 of the Lamarckian hypothesis. 



III. The matter of rectigradations was intimately connected with 

 Causes of Convergence and Parallelism, a topic forming part of the gen- 

 eral problem of reproduction, growth and adaptation in the individual 

 and in the race, and necessitating a brief consideration of Lamarckism 

 versus Natural Selection. From the uniformity of reaction shown in 

 parallelism and convergence, i. e., from the fact that similar adaptations 

 had occurred independently in many groups and at different times, it 

 seemed apparent that somehow the line of progressive adaptation has 

 been determined, in part, by the character of the environment or by the 

 nature of the interaction of one part upon another. 



Notwithstanding the case of the blind cave fishes, the Lamarckian hy- 

 pothesis of the direct transmission of acquired characters was obviously 

 insufficient to explain all cases of progressive adaptation (especially those 

 of the "lock and key" type), and it had been rejected by most authorities. 

 It had, indeed, been shown that in some cases the direct action of the 

 environment upon the soma or body of the parent had modified the germ 

 cells so that the offspring departed from the normal type. Such a se- 

 quence may be represented by the symbol A^ #->• o ^->- A^^, where A* 

 represents the parent (A) as modified by the environmental stimulus (a), 

 represents the germ cells, and A^^ the modified offspring. Direct trans- 

 mission of an acquired character might then be represented by the symbol 

 A* ^-> o ^->- Ai^ ; but the reality of this sequence is generally denied by 

 experimentalists. The apparent transmission of acquired characters may 

 sometimes have resulted from a sort of convergent evolution between 

 parent and offspring. For example, the extremely long legs of the colt 

 may conceivably be due not to the direct transmission of the effects of 

 exercise from parent to offspring but to the parallel or convergent inci- 

 dence of selection, operating independently upon both adults and off- 



