correlation of these appendages. So long as differentiation regularly and conspicuously begins at a certain region we can exclude it. But suppose in some individuals it begins at one segment and in another at another, as it almost certainly would do, how should we know which specimens or which segments must be rejected as introducing a con- fusion through differentiation, and which must be included in reckoning homotypic variation ? If differentiation is irregular, will it not change the apparent homotypic correlation ?
Professor Pearson has determined the racial correlation for the lengths of the first phalanges of digits III and IV in women. It comes out high, '914,* as might fairly be expected by any one who had studied the meristic variations of digits. There is, of course, differentiation between these two digits, so that they may be said to be unsuitable subjects for determination of homotypic correlation of like parts. But if instead of Man, the digits III and IV had been studied in an Artiodactyle, say a Deer, the racial correlation would doubtless have been much nearer unity. In other words, these two digits in the Deer are approximately in the relation of bilateral symmetry about the median axis of the foot.
In this case the differentiation between the digits is low. They approach the homotypic condition, and their homotyposis could be measured. But a population may consist of some individuals in which there is a high correlation between these two digits III and IV, and others in which differentiation had begun or sensibly persisted. In such a population the racial correlation would be clearly reduced. But would not the homotypic correlation, as calculated, be changed also 1 Would Professor Pearson's method show to what extent incipient differentiation had introduced error in the determination of the homotypic correlation ?f
Yet another and even clearer illustration. The two claws of a Crab are a pair of homotypes. Their homotypic correlation in respect of any character, length for example, might be determined. Now there are species of crab in which the two claws are approximately equal or undifferentiated. On the contrary, in some species the right, in others the left, in others the right or left with varying frequency, is differentiated in size and other characters. Can it be decided in such a case which deviations from, or approaches to, bilateral symmetry are, <ix mriations, to be included in a determination of homotypic correla- tion, and which are to be rejected as due to changes in differen- tiation 1
On this rather wider view of the facts is it not manifest that the
- ' Grammar of Science,' 1900, p. 398.
f If Professor Pearson declares that such differentiation would be " statistically discoverable," he must assume that the differentiation would always affect the saw digit in the same direction, an assumption for which I can see no warrant.
