The well-known Azaleas Perle de Ledeburg, President Kerchove, and Vervaeana are familiar illustrations. Perle de Ledeburg is predominantly white, but it has red streaks in some of its flowers. It not very rarely gives off a self-red sport. This is evidently due to the development of a bud in a red-bearing area of the stem. The red in this plant is not under "geometrical control." Many plants have white flowers with no markings, but if the red markings are geometrically ordered differentiations, no self-coloured sports are formed. The case of Vervaeana is a good illustration of this proposition. It has white flowers with red markings arranged in an orderly manner on the lower parts of the petals, especially on the dorsal petals. This is one of the Azaleas most liable to have red sports, and at first sight it might seem that the sport represented the red of the central marks. Examination however of a good many flowers shows that irregular red streaks like those of Perle de Ledeburg occur, about as commonly as in that variety. Vervaeana in fact is Perle de Ledeburg with definite red markings added, and its red sports obviously are those branches the germs of which came in a patch of the stem bearing these red elements. That this is the true account is rendered quite obvious by the fact that the red of the sport is a colour somewhat different from that of the definite marks, and that these marks are still present on the red ground of the sporting flowers.
It will be understood that these remarks apply to those cases in which the production of sports is habitual or frequent, and I imagine in all such examples it will be found that there are indications of irregularity in the distribution of the differentiations such as to justify the view that they are not under that geometrical control which governs the normal differentiation of the parts. The question next arises whether these considerations apply also to the production of a bud-sport as a rare exception, but by the nature of the case it is not possible to say positively whether the appearance of an exceptional sport is due to the unsuspected presence of a pre-existing fragment of material having a special constitution, or to the origin, de novo, of such a material. For instance one of the garden forms of Pelargonium known as altum is liable perhaps once in some hundreds of flowers to have one or two magenta petals. The normal colour is a brilliant red; and as we may be fairly sure that this red is recessive to magenta the interpretation would be quite different according as the appearance of the magenta is regarded as due to the presence of small areas endowed with magentaness, or to the spontaneous generation of the factor for that pigment. Either interpretation is possible on the facts, but the view that the whole plant has in it scarce mosaic particles of magenta seems on the whole more consistent with present knowledge.
In Pelargonium altum the enzyme causing the magenta colours must be distributed in very small areas, but a case in which the magenta is similarly arranged in a much coarser patchwork may be seen in the Pelargonium "Don Juan," which often bears whole trusses or branches of red flowers upon plants having the normal dominant magenta trusses. In most cases there is little doubt that though the magenta flowered parts can "sport" to red, the red parts could not produce the magenta flowers.
The asymmetrical, or to speak more precisely, the disorderly, mingling of the colours in the somatic parts is thus an indication of a similarly disorderly mixing of the factors for those colours in the germ-tissues, so that some of the gametes bear enough of the colour-factors to make a self-coloured plant, while others bear so little that the plant to which they give rise is a patchwork. If this view is correct we may extend it so far as to consider whether the fineness or coarseness of the mixture visible in the flowers or leaves may not give an indication of the degree to which the factors are subdivided among the germ-cells. We know very little about the genetic properties of striped varieties. In both Antirrhinum and Mirabilis it has been found that the striped may occasionally and irregularly throw self-coloured plants, and therefore the striping cannot be regarded simply as a recessive character. On the other hand in Primula Sinensis there are well-known flaked varieties which ordinarily at least breed true. Whether these ever throw selfs I do not know, but if they do it must be quite exceptionally. The power of these flaked plants to breed true is, I suspect, connected with the fact that in their flowers the coloured and white parts are intimately mixed, this intimate mixture thus being an indication of a similarly intimate mixture in the germ-cells. It would be important to ascertain whether self-fertilised seed from the occasional flowers in which the colour has run together to join a large patch gives more self-coloured plants than the intimately flaked flowers do.
The next fact may eventually prove of great importance. We have seen that in bud-sports the differentiation is of the same nature as that between pure types, and also that in the sporting plant this differentiation is distributed without any reference to the plant's axis, or any other consideration of symmetry. Now among the germ-cells of a Mendelian hybrid exactly such characters are being distributed allelomorphically, and there again we have strong evidence for believing that the distribution obeys no pattern. For example, we can in the case of seeds still in situ perceive how the characters were distributed among the germ-cells, and there is certainly no obvious pattern connecting them, nor can we suppose that there is an actual pattern obscured.
Of this one illustration is especially curious. Individual plants of the same species are, as regards the decussations of their leaves and in other respects, either rights or lefts. The fact is not emphasized in modern botany and is in some danger of being forgotten. When, as in the flowers of Arum, some Gladioli, Exacum, St. Paulia, or the fruits of Loasa, rights and lefts occur on the same stem, they come off alternately. But if, as in the seedlings of Barley the twist of the first leaf be examined, it will be seen to be either a right-or left-handed screw. An ear of barley, say a two-row barley, is a definitely symmetrical structure. The seeds stand in their envelopes back to back in definite positions. Each has its organs placed in perfectly definite places. If these seeds were buds their differentiations would be grouped into a common plan. One might expect that the differentiations of these embryos would still fall into the pattern; but they do not, and so far as I have tested them, any one may be a right or a left, just as each may carry any of the Mendelian allelomorphs possessed by the parent plant, without reference to the differentiation of any other seed. The fertilisation may be responsible, but our experience of the allelomorphic characters suggest that the irregularity is in the egg-cells themselves.[19]
Germ cells thus differ from somatic cells in the fact that their differentiations are outside the geometrical order which governs the differentiation of the somatic cells. I can think of possible exceptions, but I have confidence that the rule is true and I regard it as of great significance.
The old riddle, what is an individual, finds at least a partial solution in the reply that an individual is a group of parts differentiated in a geometrically interdependent order. With the germ-cell a new geometrical order, with independent polarity is almost if not quite always, begun, and with this geometrical independence the power of rejuvenescence may possibly be associated.
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.