Page:Proceedings of the Royal Society of London Vol 69.djvu/219

Rh 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 average homotyposis, or the correlation due on an average of cases to individuality. 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.