Page:Proceedings of the Royal Society of London Vol 69.djvu/214

200 distinction rests on fallacy 1 The reality of the problem as defined by Professor Pearson depends on the assumption that there is an absolute distinction between differentiation and variation among repeated parts, and its solubility depends on the assumption that this distinction can be perceived. The proviso that such a distinction is to be observed stultifies the whole inquiry. So far are we from being able to perceive this distinction, that we may even doubt whether variation among repeated parts can take place except as differentiation. If the idea of variation is to be extended to the case of differences between repeated parts it must inevitably include differentiations among them.

But, unless differentiation can always be detected or always reckoned for, the average value of the homotyposis coefficient will have no more natural significance than would the average variability of all organisms measured by their " Standard Deviation " from their various means, or the average size of living cells, or the average weight of all ponderable bodies.

I now proceed to a different point, in a sense the converse of the former. Professor Pearson perceives that the correlation between " undifferentiated like parts " has an analogy with the resemblance or correlation between brothers. But does he recognise that variation between brothers is comparable not merely with variation between repeated parts, but also with differentiation, and with predominantly orderly variation among such parts 1 The phenomena in a colonial or social form will clearly illustrate this principle. Ova and spermatozoa may be treated as "undifferentiated like parts " so long as their varia- tions, judged by the resulting offspring, are sensibly irregular. Can we recognise differentiation among them as distinct from variation ? Certainly we sometimes can. In determining the correlation of con- fraternities, the parentage enables us to distinguish the fraternal groups correctly, and consequently a fraternal correlation may be truly deter- mined. For to do so we are not compelled to distinguish differentiation from variation.

But I put it that the parallel Professor Pearson is seeking is im- properly instituted in his paper. He compares the homotyposis of " undift'erentiated like parts " with the correlation between brothers. He ought to compare it with the correlation between undifferentiated like brothers. As it is, he is trying to find for homotypes what he would be trying to find if he set about a determination of the average value of fraternal correlation for fraternal groups of like members taken from families composed of differentiated members. Such an attempt would immediately necessitate a distinction between differentiation and varia- tion. Had his comparison been correctly instituted, Professor Pearson could hardly have failed to discover the fallacy on which I submit his reasoning is based.

Let me state a case in illustration. In most species of Ants females