The problems thus raised are unsolved, but they do not look insoluble. The solution may be nearer than we have thought. In a study of the geometry of differentiation, germinal and somatic, there is a way of watching and perhaps analyzing what may be distinguished as the mechanical phenomena of heredity. If any one could in the cases of the Picotee and the Bizarre Carnation, respectively, detect the real distinction between the two types of distribution, he would make a most notable advance. Any one acquainted with mechanical devices can construct a model which will reproduce some of these distinctions more or less faithfully. The point I would not lose sight of is that the analogy with such models must for a long way be a true and valuable guide. I trust that some one with the right intellectual equipment will endeavor to follow this guide; and I am sanguine enough to think that a comprehensive study of the geometrical phenomena of differentiation will suggest to a penetrative mind that critical experiment which may one day reveal the meaning of spontaneous division, the mystery through which lies the road, perhaps the most hopeful, to a knowledge of the nature of life. FOOTNOTES: [1] In saying this we make no assumption as to the particular cell-division at which differentiation occurs. This may be one of the maturation-divisions, or it may perhaps be much earlier. [2] From the recent discoveries of Erwin Baur we are led to surmise that in the flowering plants the sub-epidermal layer, or some of its elements, may legitimately be regarded as a similar germ-substance, continuous in Weismann's sense. [3] These fraternal twins, which show no special resemblance to each other, are like the multiple births of other animals, and there is no disposition for them to be of the same sex. In the sheep, for example, statistics show that the frequency of pairs of twins, male and female, is approximately double that of the frequency of pairs, both male or both female, as it should be if the sex-distribution were fortuitous. For instance Bernadin (_La Bergerie de Rambouillet_, 1890, p. 100) gives the following figures for twin-lambs in Merinos: both male, 87; both female, 83; sexes mixed, 187. The 9-banded Armadillo (_Dasypus novemcinctus_), in which the young born in one litter are said to be always of one sex, is the only known exception in Vertebrates, and is presumably a genuine case of normal polyembryony (see especially, Rosner, _Bull. Ac. Soc. Cracovie_, 1901, p. 443, and Newman and Patterson, _Biol. Bull._, XVII, 1909, p. 181), and an important paper lately published by H. H. Newman and J. T. Patterson, _Jour. Morph._, 1911, XXII, p. 855. [4] A good collection of evidence as to disease in homologous twins was lately published by E. A. Cockayne, _Brit. Jour. Child. Diseases_, Nov., 1911. [5] Cp. Windle, B. C. A., _Jour. Anal. Phys._, XXVI, p. 295.