Page:Proceedings of the Royal Society of London Vol 69.djvu/210

196 poses in- this paper to find a numerical value for the average correla- tion between undifferentiated like parts of the same individual. A large series of heterogeneous cases of various organs in various plants have been investigated. The values found range from -1733 to 8607. Eeasons are put forward for excluding some of the highest and for doubting the validity of others, especially some of the lower ones. Eventually the average result -45 is again reached, taken on a series ranging from '1733 to "6311.

Professor Pearson attaches importance to the rather close similarity between the two average values. We are bound, therefore, to remark as a suspicious circumstance that the range of values is so wide, and that the average value should so nearly approach the mean of the whole possible range ; but upon this point I do not propose to dwell, preferring to deal with more general aspects of the problem.

Now Professor Pearson is attempting to measure to what extent there is a resemblance or correlation between repeated parts of one individual as compared with the same parts of different individuals of the same race : how much, that is, of the resemblance between repeated parts of an individual is due to its individuality 1 Further, how much on an average of many individuals may be expected to be due to individuality 1

For various sources of error Professor Pearson is well prepared. In his Malm material, for instance, he finds little correlation due to indi- viduality ; because, as he points out, his specimens may have been all or largely the vegetative product of one or few individuals. In some Mushrooms, on the contrary, he finds this correlation high, but he thinks that here individuality may partly be due to stages of growth, for his individuals were not all of similar age. In comparison with what/ follows these sources of error are trifling.

It will be remembered that the series of homotypes is to be undif- ferentiated. If differentiation exists and is not recognised the apparent homotyposis due to individuality will, as Professor Pearson perceives^ be immediately lowered. In order, therefore, that the inquiry should have significance, it is necessary that differentiation occurring between members of a series of parts should have a clear meaning as distinct from variation occurring amongst them ; and further, in order that the investigation should be carried through, we must be able to discrimi- nate such differentiation from variation. On critical consideration it will be apparent that neither of these postulates accords with the facts of nature. I cannot find that Professor Pearson has in any real way dealt with this difficulty. The practical difficulty he has perceived and in part met, but the more serious theoretical difficulty has, I think, escaped him. When fully understood, it will surely be seen to invalidate the whole argument.

Let us grant for the moment that differentiation of the parts can be