Page:Proceedings of the Royal Society of London Vol 69.djvu/209

Rh It is true that the geometrical relations of members in Successive Series are not included in the term Symmetry,* hut the distinction is largely one of degree, and the transition from one to the other is of frequent occurrence. Similar organs may l>e repeated in one species in radial series, while in an allied species the same organs by differentiation of an axis stand in succession to each other, as every naturalist knows.

Professor Pearson writes (p. 291) : " When we ascertain the sources of variation in the individual, then we shall have light on the problem of fraternal resemblance." May we not also say that when we ascer- tain the conditions of asymmetrical division we shall have light on the problem of fraternal variation ?

I introduce this reference to my own method of expression partly to show how far I am in agreement with Professor Pearson on a main point, and partly to emphasise the significance which the analogy between Repetition and reproduction gains by the reference to Symmetry.

Theoretical considerations in mathematical form are put forward by Professor Pearson as tending to the belief that the numerical value for homotypic correlation will, on an average of cases, approximate to the average value found for fraternal correlation.

The reasoning is beyond me, but I gather that the argument, by the introduction of appropriate assumptions, amounts to a proof that if the characters of the offspring, as measured by their deviations, depend on those of the germ-cells of the parents, then the characters of the repeated parts (or undifferentiated like parts) formed by that offspring will similarly depend on those of the germ-cells ; and it would then be expected that the correlation between those repeated parts of the sscme individual would be similar in intensity to that between the germ-cells of its parents. Whether the assumptions are justifiable I am noB able to judge, as I do not properly understand them.

The resemblance or correlation between " undifferentiated like parts " is, then, regarded as a phenomenon similar to the correlation between brothers. The latter correlation has been investigated by Professor Pearson in a number of heterogeneous cases, and has been found to vary from '1973 to '6934, where is zero and 1 denotes complete correlation.! The mean value approaches '45. He pro-

on the artificial production of Double Monsters, we must regard the relation between Homologous Twins as of the same nature as that subsisting between the right and left halves of a bilateral organism.

conceptions, but to do this at present is premature. When it becomes necessary to do so I anticipate that the largely analogous phenomena of rhythmical vibra- tion will provide ready metaphors from which to construct a terminology well adapted to denote the various phenomena of Merism.
 * It would be easy to suggest terms better adapted to the expression of these

t Both here and in the coefficients of " homotyposis" reasons are given for sup- posing that some of the greater departures from the mean may be explained away.