Isolation. 13 



adopting his term. Here it is enough to remark 

 that it answers to the generic term Isolation, with- 

 out reference to the kind of isolation as discriminate 

 or indiscriminate, homogamous or apogamous. On 

 the other hand, my Independent Variability is merely 

 a re-statement of the so-called "Law of Delboeuf/' 

 which, in his own words, is as follows : — 



One point, however, is definitely attained. It is that the 

 proposition, which further back we designated paradoxical, 

 is rigorously true. A constant cause of variation, however 

 insignificant it may be, changes the uniformity [of type] 

 little by little, and diversifies it ad infinitum. From the homo- 

 geneous, left to itself, only the homogeneous can proceed ; but 

 if there be a slight disturbance [" l^ger ferment "] in the 

 homogeneous, the homogeneity will be invaded at a single 

 point, differentiation will penetrate the whole, and, after 

 a time — it may be an infinite time — the differentiation will 

 have disintegrated it altogether. 



In other words, the '' Law," which Delbceuf has 

 formulated on mathematical grounds, and with express 

 reference to the. question of segregate breeding, 

 proves that, no matter how infinitesimally small the 

 difference may be between the average qualities of 

 an isolated section of a species compared with the 

 average qualities of the rest of that species, if the 

 isolation continues sufficiently long, differentiation of 

 specific type is necessarily bound to ensue. But, to 

 make this mathematical law biologically complete, it 

 ought to be added that the time required for the 

 change of type to supervene (supposing apogamy to 

 be the only agent of change) will be governed by the 

 range of individual variability which the species in 

 question presents. A highly stable species (such as 

 the Goose) might require an immensely long time for 



