1 64 THE VARIATION OF ANIMALS IN NATURE 



area investigated, as his work is centred on the analysis of the 

 correlations in each species in each colony. But he states 

 (p. 68) that ' the mean altitude and mean diameter of C. 

 cravenensis always exceed those of C. rugosa . . . individually 

 their altitude ranges may overlap to some extent, but their 

 diameter ranges hardly ever . . . doubtful cases (shells of un- 

 certain specific identity) are rare.' From this one may infer, 

 though without a definite measure, that the correlations between 

 length and width and between shortness and narrowness are 

 marked enough to render it easy to decide at once to which 

 species a shell must be assigned. Within the range of each 

 species, however, the correlations are low, in a selected series 

 of colonies (p. 68) never exceeding o • 50 and sinking as low as 

 OT, the mean being for rugosa 0-31, and for cravenensis 0-39. 

 This is interesting as showing that, though the two species 

 tend to reveal two regularly contrasted characters, the latter 

 do not maintain an absolute identity of association within the 

 species. 



Alkins (1921) and Alkins and others (1921) also studied 

 the correlation of various proportion-indices in Sphaerium 

 lacustre, corneum and pallidum. They find that in all three 

 species the correlation of length and width, length and thick- 

 ness, and width and thickness has a high value, never falling 

 below 0-9. In S. lacustre and S. corneum length and width are 

 certainly diagnostic. 



We owe to Sumner (see his summary, 1932, and bibliography 

 of a long series of papers) a valuable study of interracial 

 diagnostic characters in the deer-mouse (Peromyscus) . He states 

 (1928, p. 183) that ' there is no general tendency for the 

 elements which distinguish one race from another to vary 

 together within the single race.' He does not state what the 

 figure for the total range of variation is, but from this paper 

 and a later one (1929) we may infer that the distinctive 

 interracial correlations may be fairly well marked : indeed in 

 the forms dealt with in the latter paper the amount of inter- 

 mediacy is very slight (I.e. p. 112). He sums up the situation 

 in his final review as follows : ' Interracial correlations, so 

 far as these concern the length of body parts, are altogether 

 erratic. While within single populations certain parts (e.g. 

 tail and foot) tend to vary together in their relative size, such 

 concomitant variation may or may not be encountered when 



