Continuous and Discontinuous Variation 375 



a new state of equilibrium around a new mode. In some such 

 way as this, thought Galton, we can conceive of evolution as 

 a process of shifting the equilibrium or mode of a species, and 

 we could account at the same time for 



" (i) variability within narrow limits without preju- 

 dice to the purity of the breed; 



(2) partly stable sub- types; 



(3) the tendency, when much disturbed, to revert 

 from a sub-type to an earlier form; and 



(4) the occasional sports which may give rise to new 

 types." 



As a purely abstract description of the facts, Galton's 

 model may serve to reconcile the contradictory behavior of 

 living things, especially the paradox of permanence and 

 stability going hand in hand with perpetual change. This 

 is helpful, although it gives us no hint whatever as to just 

 what it is that happens in living substance to bring about the 

 observed results. 



Continuous and Discontinuous Variation 



It became increasingly difficult to reconcile the Dar- 

 winian explanation of evolution, natural selection, with the 

 assumption of progressive accumulation of imperceptible 

 variations. It finally became necessary to reexamine the 

 fundamental facts. As a beginning of this task William 

 Bateson assembled a large mass of data. Materials for the 

 Study of Evolution, in which are given hundreds of cases of 

 discontinuous variations — that is, variations that transcend 

 the normal fluctuations found in every species. 



The best material is found among traits in which the 

 specific character is represented by a numerical constancy 

 — for example, the number of digits on the hand or foot, 

 the number of ribs or vertebras, the number of petals or 

 carpels in a flower, the number of joints in a leg or a finger 

 (see Fig. 55). In such characters it is obviously impossible to 



