and other Conceptions of Biology. 205 



of correlation. The diversity due to differentiation may exhibit a 

 "homogeneous chance distribution," as, for example, in my illustra- 

 tion of the crab's claws. We have only to suppose that the " mode " 

 of the population falls on a form with claws approximately equal, and 

 to take the simplest case that the frequency of both right-handed 

 fH left-handed differentiation is inversely proportional to the magni- 

 tude of the differentiation, a state of things common enough in 

 nature. 



As a matter of fact even in the case of Nigella (p. 320) differentia- 

 tion was detected not by the seriations, but by common observation. 

 When the differentiation has been once detected, its influence can 

 be seen in the seriations. This is a mere accident. If the material 

 had happened to contain a certain proportion of a second race with a 

 "mode "on 10 or 13 and a secondary "mode" on 8 a condition 

 familiar in plants (from F. Ludwig's beautiful researches) the 

 differentiation might have been completely masked in the seriations.* 

 As it is, the seriations alone contain nothing which prove the existence 

 of differentiation. We happen to know otherwise that high numbers 

 are associated with centrals and lower numbers with laterals. This 

 is not revealed by the seriations. For all they show, the irregular 

 distribution might be due to ordinary discontinuous variation obeying 

 the laws which F. Ludwig has shown such distributions commonly 

 obey. 



We can feel nothing but admiration for those statistical methods 

 which, as perfected by Professor Pearson, are yielding many useful 

 results not otherwise attainable, yet their limitations must be constantly 

 remembered. But even if the differentiation could be discovered by 

 these means, in eliminating it we should have arbitrarily excluded a 

 class of facts which ought to have been included in calculating averuyc 

 homotyposis, or the correlation due on an average of cases to indi- 

 viduality. In determining the average correlation between brothers 

 we must bring to account the continuous and the discontinuous alike : 

 so in the average of homotypic correlations must be included both the 

 differentiant and the normal alike. 



To state the issue in a word : it appears that the attempt to exclude 

 differentiation by definition must constantly fail in practice and is 

 inadmissible in theory. 



* I strongly suspect that something of this kind may actually exist in the case 

 of Shirley Poppies. 



