Twenty years ago in describing the facts of Variation, argument was necessary to show that these phenomena had a special value in the sciences of Zoology and Botany. This value is now universally understood and appreciated. In spite however of the general attention devoted to the study of Variation, and the accumulation of material bearing on the problem, no satisfactory or searching classification of the phenomena is possible. The reason for this failure is that a real classification must presuppose knowledge of the chemistry and physics of living things which at present is quite beyond our reach.

It is however becoming probable that if more knowledge of the chemical and physical structure of organisms is to be attained, the clue will be found through Genetics, and thus that even in the uncoordinated accumulation of facts of Variation we are providing the means of analysis applicable not only to them, but to the problems of normality also.

The only classification that we can yet institute with any confidence among the phenomena of Variation is that which distinguishes on the one hand variations in the processes of division from variations in the nature of the substances divided.

Variations in the processes of division are most often made apparent by a change in the number of the parts, and are therefore called Meristic Variations, while the changes in actual composition of material are spoken of as Substantive Variations. The Meristic Variations form on the whole a natural and fairly well defined group, but the Substantive Variations are obviously a heterogeneous assemblage.

Though this distinction does not go very far, it is useful, and in all probability fundamental. It is of value inasmuch as it brings into prominence the distinct and peculiar part which the process of division, or, more generally, repetition of parts, plays in the constitution of the forms of living things.

That there may be a real independence between the Meristic and the Substantive phenomena is evident from the fact both that Meristic changes may occur without Substantive Variation, and that the substances composing an organism may change without any perceptible alteration in its meristic structure. When the distinction between these two classes of phenomena is perceived it will be realised that the study of genetics has on the one hand a physical, or perhaps more strictly a mechanical aspect, which relates to the manner in which material is divided and distributed; and also a chemical aspect, which relates to the constitution of the materials themselves. Somewhat as the philosophers of the seventeenth and eighteenth centuries were awaiting both a chemical and a mechanical discovery which should serve as a key to the problems of unorganised matter, so have biologists been awaiting two several clues. In Mendelian analysis we have now, it is true, something comparable with the clue of chemistry, but there is still little prospect of penetrating the obscurity which envelops the mechanical aspect of our phenomena. To make clear the application of the terms chemical and mechanical to the problem of Genetics the nature of that problem must be more fully described. In its most concrete form this problem is expressed in the question, how does a cell divide? If the organism is unicellular, and the single cell is the whole body, then the process of heredity is accomplished in the single operation of cell-division. Similarly in animals and plants whose bodies are made up of many cells, the whole process of heredity is accomplished in the cell-divisions by which the germ-cells are formed. When therefore we see a cell dividing, we are witnessing the process by which the form and the properties of the daughter-cells are determined.

Now this process has the two aspects which I have called mechanical and chemical. The term "Entwicklungsmechanik" has familiarised us with the application of the word mechanics to these processes, but on reflexion it will be seen that this comprehensive term includes two sorts of events which are sometimes readily distinguishable. There is the event by which the cell divides, and the event by which the two halves or their descendants are or may be differentiated. It is common knowledge that in some cell-divisions two similar halves, indistinguishable in appearance, properties, and subsequent fate, may be produced, while in other divisions daughter-cells with distinct properties and powers are formed. We cannot imagine but that in the first case, when the resulting cells are identical, the division is a mechanical process by which the mother-cell is simply cut in two; while in order that two differentiated halves may be produced, some event must have taken place by which a chemical distinction between the two halves is effected.[1] In any ordinary Mendelian case we have a clear proof that such a chemical difference may be established between germ-cells. The facts of colour-inheritance for instance prove that germ-cells, otherwise identical, may be formed possessing the chromogen-factor which is necessary to the formation of colour in the flowers, or destitute of that factor. Similarly the germ-cells may possess the ferment which, by its action on the chromogenic substance, produces the colour, or they may be without that ferment. The same line of argument applied to a great range of cases. Nevertheless, though differences in chemical properties are often thus constituted by cell-divisions, and though we are thus able to make a quasi-chemical analysis of the individual by determining and enumerating these properties, yet it is evident that the distribution of these factors is not itself a chemical process. This is proved by the fact that similar divisions may be effected between halves which are exactly alike, and also by the fact that the numbers in which the various types of germ-cells are formed negative any suggestion of valency between them. The recognition of the unit-factors may lead—indeed must lead—to great advances in chemical physiology which without that clue would have been impossible, but in causation the chemical phenomena of heredity must be regarded as secondary to the physical or mechanical phenomena by which the cells and their constituents are divided and separated. When therefore we speak of the essential phenomena of heredity we mean the mechanics of division, especially, though not, as we shall see, exclusively, of cell-division; and in the relation between the two halves of the dividing cell we have the problem presented in what seems to be its simplest form.

In attempting to form some conception of the processes by which bodily characteristics are transmitted, or—to avoid that confusing metaphor of "transmission"—how it comes about that the offspring can grow to resemble its parent, continuity of the germ-substance which in some animals is a visible phenomenon,[2] gives at least apparent help. An egg for example on becoming adult develops in certain parts a particular pigment. The eggs of that adult when they reach the appropriate age develop the same pigment. We have no clear picture of the mechanism by which this process is effected, but when we realise that the pigment results from the interaction of certain substances, and that since all the eggs are in reality pieces of the same material, it seems, unless we inquire closely, not unnatural that the several pieces of the material should exhibit the same colours at the same periods of their development. The continuity of the material of the germs suggests that there is a continuity of the materials from which the pigment is formed, and that thus an actual bit of those substances passes into each egg ready at the appropriate moment to generate the pigment. The argument thus outlined applies to all substantive characteristics. In each case we can imagine, if we will, the appearance of that characteristic as due to the contribution of its rudiment from the germ tissues.

When we consider more critically it becomes evident that the aid given by this mental picture is of very doubtful reality, for even if it were true that any predestined particle actually corresponding with the pigment-forming materials is definitely passed on from germ to germ, yet the power of increase which must be attributed to it remains so incomprehensible that the mystery is hardly at all illuminated.

When however we pass from the substantive to the meristic characters, the conception that the character depends on the possession by the germ of a particle of a specific material becomes even less plausible. Hardly by any effort of imagination can we see any way by which the division of the vertebral column into x segments or into y segments, or of a Medusa into 4 segments or into 6, can be determined by the possession or by the want of a material particle. The distinction must surely be of a different order. If we are to look for a physical analogy at all we should rather be led to suppose that these differences in segmental numbers corresponded with changes in the amplitude or number of dividing waves than with any change in the substance or material divided.

Phenomena of Division

I have said that in the division of a cell we seem to see the problem in its simplest form, but it is important to observe that the problem of division may be presented by the bodies of animals and plants in forms which are independent of the divisions between cells. The existence of pattern implies a repetition of parts, and repetition of parts when developed in a material originally homogeneous can only be created by division. Cell-division is probably only a special case of a process similar to that by which the pattern of the skeleton is laid down in a unicellular body such as that of a Radiolarian or Foraminiferan. Attempts have lately been made to apply mathematical treatment to problems of biology. It has sometimes seemed to me that it is in the geometrical phenomena of life that the most hopeful field for the introduction of mathematics will be found. If anyone will compare one of our animal patterns, say that of a zebra's hide, with patterns known to be of purely mechanical production, he will need no argument to convince him that there must be an essential similarity between the processes by which the two kinds of patterns were made and that parts at least of the analysis applicable to the mechanical patterns are applicable to the zebra stripes also. Patterns mechanically produced are of many and very diverse kinds. One of the most familiar examples, and one presenting some especially striking analogies to organic patterns, is that provided by the ripples of a mackerel sky, or those made in a flat sandy beach by the wind or the ebbing tide. With a little search we can find among the ripple-marks, and in other patterns produced by simple physical means, the closest parallels to all the phenomena of striping as we see them in our animals. The forking of the stripes, the differentiation of two "faces," the deflections round the limbs and so forth, which in the body we know to be phenomena of division, are common both to the mechanical and the animal patterns. We cannot tell what in the zebra corresponds to the wind or the flow of the current, but we can perceive that in the distribution of the pigments, that is to say, of the chromogen-substances or of the ferments which act upon them, a rhythmical disturbance has been set up which has produced the pattern we see; and I think we are entitled to the inference that in the formation of patterns in animals and plants mechanical forces are operating which ought to be, and will prove to be, capable of mathematical analysis. The comparison between the striping of a living organism and the sand-ripples will serve us yet a little farther, for a pattern may either be formed by actual cell-divisions, and the distribution of differentiation coincidently determined, or—as visibly in the pigmentation of many animal and plant tissues—the pattern may be laid down and the pigment (for example) distributed through a tissue across or independently of the cell-divisions of the tissue. Our tissues therefore are like a beach composed of sands of different kinds, and different kinds of sands may show distinct and interpenetrating ripples. When the essential analogy between these various classes of phenomena is perceived, no one will be astonished at, or reluctant to admit, the reality of discontinuity in Variation, and if we are as far as ever from knowing the actual causation of pattern we ought not to feel surprised that it may arise suddenly or be suddenly modified in descent. Biologists have felt it easier to conceive the evolution of a striped animal like a zebra from a self-coloured type like a horse (or of the self-coloured from the striped) as a process involving many intergradational steps; but so far as the pattern is concerned, the change may have been decided by a single event, just as the multitudinous and ordered rippling of a beach may be created or obliterated at one tide.

Fig. 1. Tusk of Indian elephant, showing an abnormal segmentation.

This point is well illustrated by the tusk of an Indian elephant which I lately found in a London sale-room. This tusk is by some unknown cause, presumably a chronic inflammation, thrown up into thirteen well-marked ridges which closely simulate a series of segments (Fig. 1). Whatever the cause the condition shows how easily a normally unsegmented structure may be converted into a series of repeated parts.

The spread of segmentation through tissues normally unsegmented is very clearly exemplified in the skates' jaws shown in in Fig. 2. The right side of the upper figure shows the normal arrangement in the species Rhinoptera jussieui, but the structure on the left side is very different. The probable relations of the several rows of teeth to the normal rows is indicated by the lettering, but it is evident that by the appearance of new planes of division constituting separate centers of growth, the series has been recast. The pattern of the left side is so definite that had the variation affected the right side also, no systematist would have hesitated to give the specimen a new specific name. The other two drawings show similar variations of a less extensive kind, the nature of which is explained by the lettering of the rows of teeth.

Fig. 2. Jaws of Skates (Rhinoptera) showing meristic variation.
(For a detailed discussion see Materials for the Study of Variation, p. 259.)

This power to divide is a fundamental attribute of life, and of that power cell-division is a special example. In regard to almost all the chief vital phenomena we can say with truth that science has made some progress. If I mention respiration, metabolism, digestion, each of these words calls to mind something more than a bare statement that such acts are performed by an animal or a plant. Each stands for volumes of successful experiment and research, But the expression cell-division, the fundamental act which typifies the rest, and on which they all depend, remains a bare name. We can see with the microscope the outward symptoms of division, but we have no surmise as to the nature of the process by which the division is begun or accomplished. I know nothing which to a man well trained in scientific knowledge and method brings so vivid a realisation of our ignorance of the nature of life as the mystery of cell-division. What is a living thing? The best answer in few words that I know is one which my old teacher, Michael Foster, used to give in his lectures introductory to biology. "A living thing is a vortex of chemical and molecular change." This description gives much, if not all, that is of the essence of life. The living thing is unlike ordinary matter in the fact that, through it, matter is always passing. Matter is essential to it; but, provided that the flow in and out is unimpeded, the life-process can go on so far as we know indefinitely. Yet the living "vortex" differs from all others in the fact that it can divide and throw off other "vortices," through which again matter continually swirls.

We may perhaps take the parallel a stage further. A simple vortex, like a smoke-ring, if projected in a suitable way will twist and form two rings. If each loop as it is formed could grow and then twist again to form more loops, we should have a model representing several of the essential features of living things.

It is this power of spontaneous division which most sharply distinguishes the living from the non-living. In the excellent book dealing with the problems of development, lately published by Mr. Jenkinson a special emphasis is very properly laid on the distinction between the processes of division, and those of differentiation. Too often in discussions of the developmental processes the distinction is obscured. He regards differentiation as the "central difficulty." "Growth and division of the nucleus and the cells," he tells us, are side-issues. This view is quite defensible, but I suspect that the division is the central difficulty, and that if we could get a rationale of what is happening in cell-division we should not be long before we had a clue to the nature of differentiation. It may be self-deception, but I do not feel it impossible to form some hypothesis as to the mode of differentiation, but in no mood of freest speculation are we ever able to form a guess as to the nature of the division. We see differentiations occurring in the course of chemical action, in some phenomena of vibration and so forth: but where do we see anything like the spontaneous division of the living cell? Excite a gold-leaf electroscope, and the leaves separate, but we know that is because they were double before. In electrolysis various substances separate out at the positive and negative poles respectively. Now if in cell-division the two daughter-cells were always dissimilar—that is to say, if differentiation always occurred—we could conceive some rough comparison with such dissociations. But we know the dissimilarity between daughter-cells is not essential. In the reproduction of unicellular organisms and many other cases, the products formed at the two poles are, so far as we can tell, identical. Any assumption to the contrary, if we were disposed to make it, would involve us in difficulties still more serious. At any rate, therefore, if differentiation be really the central difficulty in development, it is division which is the essential problem of heredity.

Sir George Darwin and Professor Jeans tell us that "gravitational instability" consequent on the condensation of gases is "the primary agent at work in the actual evolution of the universe," which has led to the division of the heavenly bodies. The greatest advance I can conceive in biology would be the discovery of the nature of the instability which leads to the continual division of the cell. When I look at a dividing cell I feel as an astronomer might do if he beheld the formation of a double star: that an original act of creation is taking place before me. Enigmatical as the phenomenon seems, I am not without hope that, if it were studied for its own sake, dissociated from the complications which obscure it when regarded as a mere incident in development, some hint as to the nature of division could be found. It is I fear a problem rather for the physicist than for the biologist. The sentiment may not be a popular one to utter before an assembly of biologists, but looking at the truth impersonally I suspect that when at length minds of first rate analytical power are attracted to biological problems, some advance will be made of the kind which we are awaiting.

The study of the phenomena of bodily symmetry offers perhaps the most hopeful point of attack. The essential fact in reproduction is cell-division, and the essential basis of hereditary resemblance is the symmetry of cell-division. The phenomena of twinning provide a convincing demonstration that this is so. By twinning we mean the production of equivalent structures by division. The process is one which may affect the whole body of an animal or plant, or certain of its parts. The term twin as ordinarily used refers to the simultaneous birth of two individuals. Those who are naturalists know that such twins are of two kinds, (1) twins that are not more alike than any other two members of the same family, and (2) twins that are so much alike that even intimate friends mistake them. These latter twins, except in imaginative literature, are always of the same sex.

It is scarcely necessary for me to repeat the evidence from which it has been concluded that without doubt such twins arise by division of the same fertilised ovum. There is a perfect series of gradations connecting them with the various forms of double monsters united by homologous parts. They have been shown several times to be enclosed in the same chorion, and the proofs of experimental embryology show that in several animals by the separation of the two first hemispheres of a dividing egg twins can be produced. Lastly we have recently had the extraordinarily interesting demonstration of Loeb, to which I may specially refer. Herbst some years ago found that in sea water, from which all lime salts had been removed, the segments of the living egg fall apart as they are formed. Using this method Loeb has shown that a temporary immersion in lime-free sea water may result in the production of 90 per cent. of twins. We are therefore safe in regarding the homologous or "identical" twins as resulting from the divisions of one fertilised egg, while the non-identical or "fraternal" twins, as they are called, arise by the fertilisation of two separate ova.[3]

In the resemblance of identical twins we have an extreme case of hereditary likeness[4] and a proof, if any were needed, that the cause of individual variation is to be sought in the differentiation of germ-cells. The resemblance of identical twins depends on two circumstances, First, since only two germ-cells take part in their production, difference between the germ cells of the same individual cannot affect them. Secondly the division of the fertilised ovum, the process by which they became two instead of one, must have been a symmetrical division. The structure of twins raises however one extremely significant difficulty, which as yet we cannot in any way explain. The resemblance between twins is a phenomenon of symmetry, like the resemblance between the two sides of a bilaterally symmetrical body. Not only is the general resemblance readily so interpreted, but we know also that in double monsters, namely unseparated twins, various anatomical abnormalities shown by the one half-body are frequently shown by the other half-also.[5] The two belong to one system of symmetry. How then does it happen that the body of one of a pair of twins does not show a transposition of viscera? We know that the relation of right and left implies that the one should be the mirror-image of the other. Such a relation of images may be maintained even in minute details. For example if the same pattern of finger-print is given by the fingers of the two hands, one is the reverse of the other. In double monsters, namely unseparated twins, there is evidence that an inversion of viscera does occur with some frequency. Evidence from such cases is not so clear and simple as might be expected, because as a matter of fact, the heart and stomach, upon which the asymmetry of the viscera chiefly depend, are usually common to the two bodies. Duplicity generally affects either the anterior end alone, or the posterior end alone. The division is generally from the heart forwards, giving two heads and two pairs of anterior limbs on a common trunk, or from the heart backwards, giving two pairs of posterior limbs with the anterior body common. In either case, though the bodies may be grouped in a common system of symmetry, neither can be proved to show definite reversal of the parts. To see that reversal recourse must be had to more extreme duplications, such as the famous Siamese Twins. They, as a matter of fact, were an excellent instance of the proposition that twins are related as mirror-images, for both of them had eleven pairs of ribs instead of the normal twelve, and one of them had a partial reversal of viscera.[6] (KÜchenmeister, Verlagerung, etc., p. 204.)

If anyone could show how it is that neither of a pair of twins has transposition of viscera the whole mystery of division would, I expect, be greatly illuminated.[7] At present we have simply to accept the fact that twins, by virtue of their detachment from each other, have the power of resuming the polarity which is proper to any normal individual. It was nevertheless with great interest that I read Wilder's recent observation[8] that occasionally in identical twins the finger-print of one or both the index-fingers may be reversed, showing that there is after all some truth in the notion that reversal should occur in them.

There is another phenomenon by twinning which, if we could understand it, might help. I refer to the free-martin, the subject of one of John Hunter's masterpieces of anatomical description. In horned cattle twin births are rare, and when twins of opposite sexes are born, the male is perfect and normal, but the reproductive organs of the female are deformed and sterile, being known as a free-martin. The same thing occasionally happens in sheep, suggesting that in sheep also twins may be formed by the division of one ovum; for it is impossible to suppose that mere development in juxtaposition can produce a change of this character. I mention the free-martin because it raises a question of absorbing interest. It is conceivable that we should interpret it by reference to the phenomenon of gynandromorphism, seen occasionally in insects, and also in birds as a great rarity. In the gynandromorph one side of the body is male, the other female. A bullfinch for instance has been described with a sharp line of division down the breast between the red feathers of the cock on one side and the brown feathers of the hen on the other. (Poll, H., SB. Ges. Nat. Fr., Berlin, 1909, p. 338.) In such cases neither side is sexually perfect. If the halves of such a gynandromorph came apart, perhaps one would be a free-martin.

The behaviour of homologous twinning in heredity has been little studied. It does not exist as a normal feature in any animal which is amenable to experiment, and we cannot positively assert that a comparable phenomenon exists in plants; for in them—the Orange, for example—polyembryony may evidently be produced by a parthenogenetic development of nucellar tissue. It is possible that in Man twinning is due to a peculiarity of the mother, not of the father. It may and not rarely does descend from mother to daughter, but whether it can be passed on through a male generation to a daughter again, there is not sufficient evidence to show. The facts as far as they go are consistent with the inference which may be drawn from Loeb's experiment, that the twinning of a fertilized ovum may be determined not by the germ-cells which united to form it, but by the environment in which it begins to develop. The opinion that twinning may descend through the male directly has been lately expressed by Dr. J. Oliver in the Eugenics Review (1912), on the evidence of cases in which twins had occurred among the relations of fathers of twins, but I do not know of any comprehensive collection of evidence bearing on the subject.

Besides twinning of the whole body a comparable duplicity of various parts of the same body may occur. Such divisions affect especially those organs which have an axis of bilateral symmetry, such as the thumb, a cotyledon, a median petal, the frond of a fern or the anal fin of a fish. From the little yet known it is clear that the genetic analysis of these conditions must be very difficult, but evidence of any kind regarding them will be valuable. We want especially to know whether these divisions are due to the addition of some factor or power which enables the part to divide, or whether the division results from the absence of something which in the normal body prevents the part from dividing. Breeding experiments, so far as they go, suggest that the less divided state is usually dominant to the more divided.[9] The two-celled Tomato fruit is dominant to the many-celled type. The Manx Cat's tail, with its suppression of caudal segmentation is a partial dominant over the normal tail. The tail of the Fowl in what is called the "Rumpless" condition is at least superficially comparable with that of the Manx Cat, and though the evidence is not wholly consistent, Davenport obtained facts indicating that this suppressed condition of the caudal vertebrae is an imperfect dominant.[10]

Some evidence may also be derived from other examples of differences which at first sight appear to be substantive though they are more probably meristic in ultimate nature. The distinction between the normal and the "Angora" hair of the Rabbit is a case in point. We can scarcely doubt that one of the essential differences between these two types is that in the Angora coat the hair-follicles are more finely divided than they are in the normal coat, and we know that the normal, or less-divided condition, is dominant to the Angora, or more finely divided.

Fig. 3. I, II, III, various degrees of syndactyly affecting the medius and annularis in the hand; IV, syndactyly affecting the index and medius in the foot. (After Annandale.)

In the case of the solid-hoofed or "mule-footed" swine, the evidence shows, as Spillman has lately pointed out,[11] that the condition behaves as a dominant. The essential feature of this abnormality is that the digits III and IV are partially united. The union is greatest peripherally. Sometimes the third phalanges only are joined to form one bone, but the second and even the first phalanges may also be compounded together. Here the variation is obviously meristic and consists in a failure to divide, the normal separation of the median digits of the foot being suppressed.

Fig. 4. Case of complete syndactyly in the foot. II and III, digit apparently representing the index and medius. c² + c³, bone apparently representing the middle and external cuneiform; cb, cuboid; c¹, internal cuneiform. (After Gruber.)

Webbing between the digits, in at least some of its manifestations, is a variation of similar nature. The family recorded by Newsholme[12] very clearly shows the dominance of this condition. The case is morphologically of great interest and must undoubtedly have a bearing on the problems of the mechanics of Division. In discussing the phenomena of syndactylism I pointed out some years ago that the digits most frequently united in the human hand are III and IV, while in the foot, union most frequently takes place between II and III.[13] In Newsholme's family the union was always between II and III of the foot, except in the case of one male who had the digits III and IV of the right hand alone webbed together. There can be little doubt that the geometrical system on which the foot is planned has an axis of symmetry passing between the digits II and III, while the corresponding axis in the hand passes between III and IV. Union between such digits may therefore be regarded as comparable with any non-division or "coalescence" of lateral structures in a middle line, and when as in these examples such a condition is shown to be a dominant we cannot avoid the inference that some concrete factor has the power of suppressing or inhibiting this division. Figs. 3 and 4 illustrate degrees of union between digits in the human hand and foot.

It is not in question that various other forms of irregular webbing and coalescence of digits exist, and respecting the genetic behaviour of these practically nothing is as yet known. Such a case is described by Walker,[14] in which the first and second metacarpals of both feet were fused in mother and daughter, and several more are found in literature. Contrasted with these phenomena we have the curious fact that in the Pigeon, Staples-Browne found webbing of the toes a recessive character. The question thus arises whether this webbing is of the same nature as that shown to be a dominant in Man, and indeed whether the phenomenon in pigeons is really meristic at all. There is some difference perceptible between the two conditions; for in Man there is not so much a development of a special web-like skin uniting the digits as a want of proper division between the digits themselves, and in extreme cases two digits may be represented by a single one. In the Pigeon I am not aware that a real union of this kind has ever been observed, and though the web-like skin may extend the whole length of the digits and be so narrow as to prevent the spread of the toes, it may, I think, be maintained that the unity of the digits is unimpaired. For the present the nature of this variation in the pigeon's feet must be regarded as doubtful, and we should note that if it is actually an example of a more perfect division being dominant to a less perfect division, the case is a marked exception to the general rule that non-division is dominant to division.

Reference must also be made to the phenomenon of fasciation in the stems of plants. As Mendel showed in the case of Pisum this condition is often a recessive. The appearances suggest that the difference between a normal and a fasciated plant consists in the inability of the fasciated plant to separate its lateral branches. The nature of the condition is however very obscure and it is equally likely that some multiplication of the growing point is the essential phenomenon.[15]

Stockard's interesting experiments[16] illustrate this question. He showed that by treating the embryos of a fish (Fundulus heteroclitus) with a dilute solution of magnesium salts, various cyclopian monstrosities were frequently produced. These have been called cases of fusion of the optic vesicles. I would prefer to regard them as cases of a division suppressed or restricted by the control of the environment. Conversely, the splendid discovery of Loeb, that an unfertilised egg will divide and develop parthenogenetically without fertilisation, as a consequence of exposure to various media, may be interpreted as suggesting that the action of those media releases the strains already present in the ovum, though I admit that an interpretation based on the converse hypothesis, that the medium acts as a stimulus, is as yet by no means excluded.

In these cases we come nearest to the direct causation or the direct inhibition of a division, but the meaning of the evidence is still ambiguous. I incline to compare Loeb's parthenogenesis with the development (and of course accompanying cell-division) of dormant buds on stems which have been cut back.

It is interesting to note that sometimes as an abnormality, the faculty of division gets out of hand and runs a course apparently uncontrolled. A remarkable instance of this condition is seen in Begonia "phyllomaniaca", which breaks out into buds at any point on the stem, petioles, or leaves, each bud having, like other buds, the power of becoming a new plant if removed. We would give much to know the genetic properties of B. phyllomaniaca, and in conjunction with Mr. W. O. Backhouse I have for some time been experimenting with this plant. It proved totally sterile. Its own anthers produce no pollen, and all attempts to fertilise it with other species failed though the pollen of a great number of forms was tried.

Recently however we have succeeded in making plants which are in every respect Begonia phyllomaniaca, so far as the characters of stems and leaves are concerned. These plants, of which we have sixteen, were made by fertilising B. heracleifolia with B. polyantha. They are all beginning to break out in "phyllomania." As yet they have not flowered, but as they agree in all details with phyllomaniaca there can be little doubt that the original plant bearing that name was a hybrid similarly produced. The production of "phyllomania" on a hybrid Begonia has also been previously recorded by Duchartre.[17] In this case the cross was made between B. incarnata and lucida. The synonymy of the last species is unfortunately obscure, and I have not succeeded in repeating the experiment.

Fig. 5. Piece of petiole of Begonia phyllomaniaca. The proximal end is to the right of the figure.

From these facts it seems practically certain that the condition is one which is due to the meeting of complementary factors. At first sight we may incline to think that the phyllomania is in some way due to the sterility. This however cannot be seriously maintained; for not only is sterility in plants not usually associated with such manifestations, but we know a Begonia called "Wilhelma" which is exactly phyllomaniaca and equally sterile, though it has no trace of phyllomania. This plant arose in the nurseries of MM. P. Bruant of Poitiers, and has generally been described as a seedling of phyllomaniaca, but from the total sterility of that form this account of its origin must be set aside.

Fig. 6. Two right hind feet of polydactyle cats. II shows the lowest development of the condition yet recorded. The digit, d¹, which stands as hallux is fully formed and has three phalanges. Both it and the digit marked d² are formed as left digits. In the normal hind foot of the cat the hallux is represented by a rudiment only.

I shows a further development of the condition. In this foot there are six digits. d¹ has two phalanges, but both it and d² and d³ are shaped as left digits. Thus d³, which in the normal foot would be shaped as a right digit, is transformed so as to look like a left digit.

The phenomenon in this case can hardly be regarded as due to the excitation of dormant buds, for it is apparent on examination that the new growths are not placed in any fixed geometrical relation to the original plant. They arise on the petiole, for example, as small green outgrowths each of which gradually becomes a tiny leaf. The attitude of these leaves is quite indeterminate, and they may point in any direction, some having their apices turned peripherally, some centrally, and others in various oblique or transverse positions (Fig. 5). These little leaves are thus comparable with seedlings, in that their polarity is not related to, or consequent upon that of the parent plant. They have in fact that "individuality," which we associate with germinal reproduction.

There are many curious phenomena seen in the behaviour of parts normally repeated in bilateral symmetry which may some day guide us towards an understanding of the mechanics of division. A part like a hand, which needs the other hand to complete its symmetry, cannot twin by mere division, yet by proliferation and special modifications on the radial side of the same limb, even a hand may be twinned. In the well known polydactyle cats a change of this kind is very common and indeed almost the rule. When extra digits appear at the inner (tibial) side of the limb, they are shaped as digits of the other side, and even the normal digit II (index) is usually converted into the mirror-image of its normal self. The limb then develops a new symmetry in itself. Nevertheless it is not easy to interpret these facts as meaning that there has been some interruption in the control which one side of the body exercises over the other. The heredity of polydactylism is complex but there is little doubt that the condition familiar in the Cat is a dominant. In some human cases also the descent is that of a dominant, but irregularities are so frequent that no general rule can yet be perceived. The dominance of such a condition is an exception to the principle that the less-divided is usually dominant to the more-divided, a fact which probably should be interpreted as meaning that divisions are of more than one kind.

Among ordinary somatic divisions, whether of organs, cells, or patterns of differentiation, the control of symmetry is usually manifested. There is however one class of somatic differentiations which are exceptionally interesting from the fact that they may show a complete independence of such geometrical control. The most familiar examples of these geometrically uncontrolled Variations are to be seen in bud-sports. The normal differentiation of the organs of a plant is arranged on a definite geometrical system, which to those who have never given special attention to such things before, will often seem surprisingly precise. The arrangement of the leaves on uninjured, free-growing shoots can generally be seen to follow a very definite order, just as do the flowers or the parts of the flowers. If however bud sports occur, then though the parts included in the sports show all the geometrical peculiarities proper to the sport-variety, yet the sporting-buds themselves are not related to each other according to any geometrical plan.

A very familiar illustration is provided by the distribution of colour in those Carnations that are not self-coloured. The pigment may, as in Picotees, be distributed peripherally with great regularity to the edges of the petals; or, as in Bizarres and Flakes, it may be scattered in radial sectors which show no geometrical regularity. Now in this case the pigments are the same in both types of flower, and the chemical factors concerned in their production must surely be the same. The difference must lie in the mechanical processes of distribution of the pigment. In the Picotee we see the orderly differentiation which we associate with normality; in the Bizarre we see the disorderly differentiation characteristic of bud-sports. The distribution of colour in this case lies outside the scheme of symmetry of the plant.

Such a distribution is characteristic of bud-sports, and of certain other differentiations in both plants and animals, which I cannot on this occasion discuss. Now reflexion will show that these facts have an intimate bearing on the mechanical problems of heredity. For first in the bud-sports we are witnessing the distribution of factors which distinguish genetic varieties. We do not know the physical nature of those factors, but if we must give them a name, I suppose we should call them "ferments" exactly as Boyle did in 1666. He is discussing how it comes about that a bud, budded on a stock, becomes a branch bearing the fruit of its special kind. He notes that though the bud inserted be "not so big oftentimes as a Pea," yet "whether by the help of some peculiar kind of Strainer or by the Operation of some powerful Ferment lodged in it, or by both these, or some other cause," the sap is "so far changed as to constitute a Fruit quite otherwise qualify'd."[18] We can add nothing to his speculation, and we believe still that by a differential distribution of "ferments" the sports are produced. All the factors are together present in the normal parts; some are left out in the sport. In an analogous case however, that of a variegated Pelargonium which has green and also albino shoots, Baur proved that the shoots pure in colour are also pure in their posterity. There can be no doubt that the sports of Carnations, Azaleas, Chrysanthemums, etc., would behave in the same way.

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.