No. 548] SHORTER ARTICLES AND DISCUSSION 495 



the very nature of biological changes to be reversible, or recur- 

 rent in each generation. Only by limiting the idea of evolution 

 to changes in the underlying mechanism of transmission could 

 the specification of irreversibility be made to apply. 



Nor is there justification for considering biological evolution 

 under the caption of discontinuous systems. Variations, in the 

 sense of changes of expression of characters, are often discon- 

 tinuous, but this does not mean that evolution is discontinuous. 

 Some biologists have supposed that new characters constitute 

 new species, but in reality we have to think of the old species 

 as developing the new characters instead of the characters 

 originating the species. As long as species are considered only 

 in a statistical or biometrical sense, the existence of different 

 species will appear to rest on evidence of mathematical discon- 

 tinuity. But for any truly biological purposes such discon- 

 tinuity must be considered as a result of evolution, rather than 

 as a condition or cause of evolution. All characters, in the 

 evolutionary sense of the word, are first presented as differences 

 among the members of species. Such differences are always 

 variable, or alternative in expression, which is another way of 

 saying that they are reversible; that is, they appear and dis- 

 appear, or are expressed in various degrees, in the different in- 

 dividuals belonging to the same specific group. 



The phenomena of mutation represent discontinuity among 

 members of the same species, rather than differences between 

 species. Natural species seldom have the same kinds of differ- 

 ences as mutative variations. The theory that species originate 

 by mutative changes of characters is well calculated to deceive 

 Physicists and biometricians who are not familiar with the facts 

 of diversity in natural species. Ortmann diagnosed the diffi- 

 culty with the mutation theorv by saying that DeVries does not 

 know what a species is. Familiarity with species is seldom .-nn- 

 sidered as a necessary qualification for the study of evolution 

 and heredity. Indeed, most of our physiological and mathe- 

 matical biologists have dismissed species as something too in- 

 definite for their purposes. They prefer to begin with a 

 definition that can be stated in exact terms and turn.-d into 

 figures or formula?. The casual choice of words like irreversible 

 or discontinuous becomes fraught with a vast importance, seldom 

 litigated by any appreciation of the fact that most of the 

 la nguage of biology is merely descriptive and comparative, and 

 he nce to be understood only in relative senses. 



H ^ cut through a tree top it will appear that the branches 

 ar * discontinuous, but if we follow individual branches this 



