Petiole
Fig. 5.Piece of petiole ofBegonia 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 exactlyphyllomaniacaand 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 ofphyllomaniaca, but from the total sterility of that form this account of its origin must be set aside.
Petiole
Fig. 6.Two right hind feet of polydactyle cats.IIshows 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 markedd2are formed asleftdigits. In the normal hind foot of the cat the hallux is represented by a rudiment only.
Ishows a further development of the condition. In this foot there aresixdigits.d1has two phalanges, but both it andd2andd3are shaped as left digits. Thusd3, which in the normal foot would be shaped as a right digit, is transformed so as to look like aleftdigit.
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 geometricalsystem, 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 othercause," 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 variegatedPelargoniumwhich 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, andVervaeanaare 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 ofVervaeanais 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.Vervaeanain fact is Perle de Ledeburg withdefinitered 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, andI 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 ofPelargoniumknown asaltumis 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.
InPelargonium altumthe 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 thePelargonium"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 considerwhether 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 bothAntirrhinumandMirabilisit 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 inPrimula Sinensisthere 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 areintimatelymixed, 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 stillin situperceive 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, someGladioli,Exacum,St. Paulia, or the fruits ofLoasa, rights and lefts occuron 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 budstheir 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 twotypes 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.
Models may be and often have been devised imitating some of the phenomena of division, but none of them have reproduced the peculiarity which characterises divisions of living tissues, thatthe position of chemical differentiationisdetermined by those divisions. For example, models of segmentation, whether radial or linear, may be made by the vibration of plates as in the familiar Chladni figures of the physical laboratory, or by the bowing of a tube dusted on the inside with lycopodium powder, and in various other ways. The sand or the powder will be heaped up in the nodes or regions of least movement, and the patterns thus formed reproduce many of the geometrical features of segmentation. But in the segmentations of living things the nodes and internodes, once determined by the dividing forces, would each become the seat of appropriate and distinct chemical processes leading to the differentiation of the parts, and the deposition of the bones, petals, spines, hairs, and other organs in relation to the meristic ground-plan. The "ripples" of meristic division not merely divide but differentiate, and when a "ripple" forks the result is not merely a division but a reduplication of the organ through which the fork runs. An example illustrating such a consequence is that of the half-vertebrae of the Python. On the left side the vertebra is single (Fig. 7) and bears a single rib, but on the right side a division has occurred with the result that two half-vertebrae, each bearing a rib, are formed, one standing in succession to the other. We cannot, indeed, imagine any operation of physiological division carried out in such an organ as a vertebra, passing through a plane at right angles to the long axis of the body, which does not necessarily involve the further process of reduplication.
As the meristic system of distribution spreads through the body, chemical differentiations follow in its track, withsegmentation and pattern as the visible result. Could we analyse these simultaneous phenomena and show how it is that the places of chemical differentiation are determined by the system of division, progress would then be rapid. It is here that all speculation fails.
Figs.7 and 8.Two examples of imperfect division in the vertebræ of a python.I, the vertebræ147-150from the right side, showing imperfect division between the148thand149th. The condition on the left side of this vertebra was the same.II, the dorsal surface of vertebræ165-167. On the right side the166this double and bears two ribs, but on the left side it is normal and has one rib only.
Many attempts have been made to interpret the processes of division and repetition, in terms of mechanics, or at least to refer them to their nearest mechanical analogies, so far withlittle success. The problem is beset with difficulties as yet insurmountable and of these one must be especially noticed. In the living thing the process by which repetition and patterns come into being consists partly in division but partly also in growth. We have no means of studying the phenomena of pattern-formation except in association with that of growth. Growth soon ceases unless division takes place, and if growth is impossible division soon ceases also. In consequence of this fact that the final pattern is partly a product of growth, it can never be used as unimpeachable evidence of the primary geometrical relations of the members as laid down in the divisions.
In the last chapter in referring to the problem of repetition I introduced an analogy, comparing the patterns of the organic world with those produced in unorganised materials by wave-motion. In the preliminary stage of ignorance, having no more trustworthy clue, I do not think it wholly unprofitable to consider the applicability of this analogy somewhat more fully. It possesses, as I hope to show, at least so much validity as to encourage the belief that morphology may safely discard one source of long-standing error and confusion.
Those who have studied the structure of parts repeated in series will have encountered the old morphological problem of "Serial Homology," which has absorbed so much of the attention of naturalists and especially of zoologists at various periods. This problem includes two separate questions. The first of these is the origin in evolution of the resemblance between two organs occurring in a repeated series, of which the fore and hind limbs of Vertebrates are the prerogative instance. From the fact that these resemblances can be traced very far, often into minute details of structure, many anatomists have inclined to the opinion that the resemblance must originally have been still more complete, and that the two limbs, for instance, must have acquired their present forms by the differentiation of two identical groups of parts.
Similar questions arise whenever parts are repeated in series, whether the series be linear or radial, and, though less obviously, even when the repetition is bilateral only. In each such examplethe question arises, is the resemblance between the parts the remains of a still closer resemblance, or is differentiation original? Sometimes the view that these parts have arisen by the differentiation of a series of identical parts is plausible enough, as for example when the peculiarities of various appendages of a Decapod Crustacean are referred to modifications of the Phyllopod series. In application to other cases however we soon meet with difficulty, and the suggestion that the segments of a vertebrate were originally all alike is seen at once to be absurd, for the reason that a creature so constituted could not exist, and that, differentiation of at least one anterior and one posterior segment, is an essential condition of a viable organism consisting of parts repeated in a linear series. Between these two terminal segments it is possible to imagine the addition of one segment, or of a series of approximately similar segments; but when once it is realised that the terminals must have been differentiated from the beginning, it will be seen that the problem of the origin of the resemblance between segments is not rendered more comprehensible by the suggestion that even the intervening members were originally alike. Seeing indeed that some differentiation must have existed primordially it is as easy to imagine that the original body was composed of a series grading from the condition of the anterior segment to that of the posterior, as any other arrangement. The existence of a linear or successive series in fact postulates a polarity of the whole, and in such a system the conception of an ideal segment containing all the parts represented in the others has manifestly no place. The introduction of that conception though sanctioned by the great masters of comparative anatomy, has, as I think, really delayed the progress of a rational study of the phenomena of division. The same notion has been applied to every class of repetition both in animals and plants, generally with the same unhappy results. In the cruder forms in which this doctrine was taught thirty years ago it is now seldom expressed, but modified presentations of it still survive and confuse our judgments.
The process of repetition of parts in the bodies of organisms is however a periodic phenomenon. This much, provided we remain free from prejudice as to the nature and causation of the period or rhythm, we may safely declare, and a comparison may thus be instituted between the consequences of meristic repetition in the bodies of living things and those repetitions which in the inorganic world are due to rhythmical processes. Of such processes there is a practically unlimited diversity and we have nothing to indicate with which of them our repetitions should rather be compared.
Fig. 9.Osmotic growths simulating segmentation. (After Leduc.)
In some respects perhaps the best models of living organisms yet made are the "osmotic growths" produced by Leduc.[1]These curious structures were formed by placing a fragment of a salt, for instance calcium chloride, in a solution of some colloidal substance. As the solid takes up water from the solution a permeable pellicle or membrane is formed around it. The vesicle thus enclosed grows by further absorption of water, often extending in a linear direction, and in many examples this growth occurs by a series of rhythmically interrupted extensions. Some of the growths thus formed are remarkably like organic structures, and might pass for a series of antennary segments or many other organs consisting of a linear series of repeated parts. In admitting the essential resemblance between these "osmotic growths" and living bodies or their organs I lay less stress on the general conformation of the growths, which often as Leduc points out, recall the forms of fungi or hydroids, but rather on the fact that the interruptions in the development of these systems are so closely analogous to the segmentations or repetitions of parts characteristic of living things (Fig. 9). In the same way I am less impressed by Leduc's models of Karyokinesis, wonderful as they nevertheless are, for the division is here imitated by putting separate drops on the gelatine film. What we most want to know is how in the living creature one drop becomes two. The models of linear segmentation have the remarkable merit that they do in some measure imitate the process of actual division or repetition. So in a somewhat modified method Leduc, by causing the diffusion of a solution in a gelatine film, produced rhythmical or periodic precipitations strikingly reminiscent of various organic tissues, for here also the process of periodic repetition is imitated with success.
It is a feature common to these and to all other rhythmical repetitions produced by purely mechanical forces that there is resemblance between the members of the series, and that this similarity of conformation may be maintained in most complex detail. When however in the mechanical series some of the members differ from the rest we have no difficulty in recognisingthat these differences—which correspond with the differentiations of the organic series—are due to special heterogeneity in the conditions or in the materials, and it never occurs to us to suppose that all the members must have been primordially alike. For example, in the case of ripple-marks on the sand, which I choose as one of the most familiar and obvious illustrations of a repeated series due to mechanical agencies, if we notice one ripple different in form from those adjacent to it, we do not suppose that this variation must have been brought about by deformation of a ripple which was at first formed like the others, but we ascribe it to a difference in the sand at that point, or to a difference in the way in which the wind or the tide dealt with it. We may press the analogy further by observing that in as much as such a series of waves has a beginning and an end, it possesses polarity like that of the various linear series of parts in organisms, and even the formation of each member must influence the shape of its successor. Since in an organism the beginning and end of the series are always included, some differentiation among the repetitions must be inevitable. If therefore it be conceded, as I think it must, that segmentation and pattern are the consequence of a periodic process we realize that it is at least as easy to imagine the formation of such a series of parts having family likeness combined with differentiation as it would be to conceive of their arising primordially as a series of identical repetitions. The suggestion that the likenesses which we now perceive are the remains of a still more complete resemblance is a substitution of a more complex conception for a simpler one.
The other question raised by the problem of Serial Homology is how far there is a correspondence between individual members of series when the series differ from each other either in the number of parts, or in the mode of distribution of differentiation among them. Students, for example, of vertebrate morphology debate whether thenth vertebra which carries the pelvic girdle in Lizard A is individually homologous with then+xth vertebra which fulfils this function in Lizard B, or whether it is not more truly homologous with the vertebra standing in thenth ordinal position, though that vertebra in Lizard B is free.
In various and more complex aspects the same question is debated in regard to the cranial and spinal nerves, the branches of the aorta, the appendages of Arthropoda, and indeed in regard to all such series of differentiated parts in linear or successive repetition. Persons exercised with these problems should before making up their minds consider how similar questions would be answered in the case of any series of rhythmical repetitions formed by mechanical agencies. In the case of our illustration of the ripples in the sand, given the same forces acting on the same materials in the same area, the number of ripples produced will be the same, and thenth ripple counting from the end of the series will stand in the same place whenever the series is evoked. If any of the conditions be changed, the number and shapes can be changed too, and a fresh "distribution of differentiation" created. Stated in this form it is evident that the considerations which would guide the judgment in the case of the sand ripples are not essentially different from those which govern the problem of individual homology in its application to vertebrae, nerves, or digits.
The fact that the unit of repetition is also the unit of growth is the source of the obscurity which veils the process. When we compare the skeleton of a long-tailed monkey with that of a short-tailed or tailless ape we see at once how readily the additional series of caudal segments may be described as a consequence of the propagation of the "waves" of segmentation beyond the point where they die out in the shorter column, and we see that with an extension of the series of repetitions there is growth and extension of material.
The considerations which apply to this example will be found operating in many cases of the variation of terminal members of linear series. Some of these series, like the teeth of the dog, end in a terminal member of a size greatly reduced below that of the next to it. Even when there is thus a definite specialisation of the last member of the series it not infrequently happens that the addition, by variation, of a member beyond the normal terminal, is accompanied by a very palpable increase in size of the member which stands numerically in the place of the normalterminal.[2]So also with variation in the number of ribs, when a lumbar vertebra varies homoeotically into the likeness of the last dorsal and bears a rib, the rib placed next in front of this, which in the normal trunk is the last, shows a definite increase in development.
The consequences of such homoeoses are sometimes very extensive, involving readjustments of differentiation affecting a long series of members, as may easily be seen by comparing the vertebral columns of several individual Sloths[3](whetherBradypusorCholoepus) to take a specially striking example.
It may be urged that no feature as yet enables us to perceive wherein lies the primary distinction which determines such variation, whether it is due to a difference in the dividing forces or in the material to be divided. If for instance we were to imitate such a series of segments by pressing hanging drops of a viscous fluid out of a paint-tube by successive squeezes, the number of times the tube is contracted before it is empty will give the number of the segments, but their size may depend either on the force of the contractions or on the capacity of the tube, or on various other factors. Nevertheless in the case of the variation of terminal members, whatever be the nature of the rhythmical impulse which produces the series of organs, the elevation of the normally terminal member in correspondence with the addition of another is what we should expect.
If the organism acquired its full size first and the delimitation of the parts took place afterwards, there might be some hope that the resemblance between living patterns and those mechanically caused by wave-motion might be shown to be a consequence of some real similarity of causation, but in view of the part played by growth, appeal to these mechanical phenomena cannot be declared to have more than illustrative value. Similarly in as much as living patterns appear, and almost certainly do in reality come into existence by a rhythmical process, comparisons of these patterns with those developed in crystalline structures, and in the various fields of force are, as it seems to me, inadmissible, or at least inappropriate.
However their intermittence be determined, the rhythms of division must be looked upon as the immediate source of those geometrically ordered repetitions universally characteristic of organic life. In the same category we may thus group the segmentation of the Vertebrates and of the Arthropods, the concentric growth of the Lamellibranch shells or of Fishes' scales, the ripples on the horns of a goat, or the skeletons of the Foraminifera or of the Heliozoa. In the case of plant-structures Church[4]has admirably shown, with an abundance of detail, how on analysis the definiteness of phyllotaxis is an expression of such rhythm in the division of the apical tissues, and how the spirals and "orthostichies" displayed in the grown plant are its ultimate consequences. The problem thus narrows itself down to the question of the mode whereby these rhythms are determined.
It is natural that we should incline to refer them to a chemical source. If we think of the illustration just given, of the segmentation of a viscous fluid into drops by successive contractions of a soft-walled tube we can, I think, conceive of such rhythmic contractions as due to summations of chemical stimuli, somewhat as are the beats of the heart. But when we recognize the vast diversity of materials the distribution of which is determined by an ostensibly similar rhythmic process it seems hopeless to look forward to a directly chemical solution. That the chemical degradation of protoplasm or of materials which it contains is the source of the energy used in the divisions cannot be in dispute, but that these divisions can be themselves the manifestations of chemical action seems in the highest degree improbable.
We may therefore insist with some confidence on the distinction between the Meristic and the substantive constitution of organisms, between, that is to say, the system according to which the materials are divided and the essential composition of the materials, conscious of the fact that the energy of division is supplied from the materials, and that in the ontogeny the manner in which the divisions are effected must depend secondarily on the nature of the substances to be divided. Themechanical processes of division remain a distinguishable group of phenomena, and variations in the substances to be distributed in division may be independent of variations in the system by which the distribution is effected.
Modern genetic analysis supplies many remarkable examples of this distinction. When formerly we compared the leaves of a normal palmatifid Chinese Primula with the pinnatifid leaves[5]of its fern-leaved variety we were quite unable to say whether the difference between the two types of leaf was due to a difference in the material cut up in the process of division or to a difference in that process itself. Knowledge that the distinction is determined by a single segregable factor tends to prove that the critical difference is one of substance. So also in the Silky fowl we know that the condition of its feathers is due to the absence of some one factor present in the normal form. We may conceive such differences as due to change of form in the successive "waves" of division, but we cannot yet imagine segregation otherwise than as acting by the removal or retention of a material element. Future observation by some novel method may suggest some other possibility, but such cases bring before us very clearly the difficulties by which the problem is beset.
Primula Sinensis Leaves
Fig. 10.The palm-and fern type of leaf inPrimula Sinensis.The palm is dominant and the fern is recessive.
In another region of observation phenomena occur which as it seems to me put it beyond question that the meristic forces are essentially independent of the materials upon which they act, save, in the remoter sense, in so far as these materials are the sources of energy. The physiology of those regenerations and repetitions which follow upon mutilation supplies a group of facts which both stimulate and limit speculation. No satisfactory interpretations of these extraordinary occurrences has ever been found, but we already know enough to feel sure that in them we are witnessing indications which should lead to the discovery of the true mechanics of repetition and pattern. The consequences of mutilation in causing new growth or perhaps more strictly in enabling new growth to take place, are such that they cannot be interpreted as responses to chemical stimuli inany sense which the word chemical at present connotes. Powers are released by mutilation of which in the normal conditions of life no sign can be detected. All who have tried to analyse the phenomena of regeneration are compelled to have recourse to the metaphor of equilibrium, speaking of the normal body as in a state of strain or tension (Morgan) which when disturbed by mutilation results in new division and growth. The forces of division are inacessible to ordinary means of stimulation. Applications, for example, of heat or of electricity excite no responses of a positive kind unless the stimuli are so violent as to bring about actual destruction.[6]These agents do not, to use a loose expression, come into touch with the meristic forces. Changes in the chemical environment of cells may, as in the experiments of Loeb and of Stockard produce definite effects, but the facts suggest that these effects are due rather to alterations in the living material than to influence exerted directly on the forces of division themselves.
By destruction of tissue however the forces both of growth and of division also may often be called into action with a resulting regeneration. Interruption of the solid connexion between the parts may produce the same effects, as for example when the new heads or tails grow on the divided edges of Planarians (Morgan), or when from each half embryo partially separated from its normally corresponding half, a new half is formed with a twin monster as the result.
Often classed with regenerations but in reality quite distinct from them are those special and most interesting examples where the growth of apairedstructure is excited by a simplewound. Some of the best known of these instances are presented by the paired extra appendages of Insects and Crustacea. Some years ago I made an examination of all the examples of such monstrosities to which access was to be obtained, and it was with no ordinary feeling of excitement that I found that these supernumerary structures were commonly disposed on a recognizable geometrical plan, having definite spatial relations both to each other and to the normal limb from which they grew. The more recent researches of Tornier[7]and especially his experiments on the Frog have shown that a cut into the posterior limb-bud induces the outgrowth of such apairof limbs at the wounded place. Few observations can compare with this in novelty or significance; and though we cannot yet interpret these phenomena or place them in their proper relations with normal occurrences, we feel convinced that here is an observation which is no mere isolated curiosity but a discovery destined to throw a new light on biological mechanics. The supernumerary legs of the Frog are evidently grouped in a system of symmetry similar to that which those of the Arthropods exhibit, and though in Arthropods paired repetitions have not been actually produced by injury under experimental conditions we need now have no hesitation in referring them to these causes as Przibram has done.
At this point some of the special features of the supernumerary appendages become important. First they may arise at any point on the normal limb, being found in all situations from the base to the apex. Nor are they limited as to the surface from which they spring, arising sometimes from the dorsal, anterior, ventral, or posterior surfaces, or at points intermediate between these principal surfaces.
With rare and dubious exceptions, the parts which are contained in these extra appendages are only those which lieperipheral to their point of origin. Thus when the point of origin is in the apical joint of the tarsus, the extra growth if completely developed consists of a double tarsal apex bearing two pairs of claws. If they arise from the tibia, two complete tarsi areadded. If they spring from the actual base of the appendage then two complete appendages may be developed in addition to the normal one. We must therefore conclude that in any point on a normal appendage the power exists which, if released, may produce a bud containing in it a paired set of the parts peripheral to this point.
Arthropoda
Fig. 11.Diagrams of the geometrical relations which are generally exhibited by extra pairs of appendages in Arthropoda. The sections are supposed to be those of the apex of a tibia in a beetle.A, anterior,P, posterior,D, dorsal,V, ventral.M1,M2are the imaginary planes of reflexion. The shaded figure is in each case a limb formed like that of the other side of the body, and the outer unshaded figures are shaped like the normal for the side on which the appendages are. On the several radii are shown the extra pairs in their several possible relations to the normal from which they arise. The normal is drawn in thick lines in the center.
Next the geometrical relations of the halves of the supernumerary pair are determined by the position in which they standin regard to the original appendage. These relations are best explained by the diagram (Fig. 11), from which it will be seen that the two supernumerary appendages stand as images of each other; and, of them, that which is adjacent to the normal appendage forms an image of it. Thus if the supernumerary pair arise from a point on the dorsal surface of the normal appendage, the twoventralsurfaces of the extra pair will face each other. If they arise on the anterior surface of the normal appendage, their morphologically posterior surfaces will be adjacent, and so on.
These facts give us a view of the relations of the two halves of a dividing bud very different from that which is to be derived from the exclusive study of normal structures. Ordinary morphological conceptions no longer apply. The distribution of the parts shows that the bud or rudiment which becomes the supernumerary pair may break or open out in various ways according to its relations to the normal limb. Its planes of division are decided by its geometrical relations to the normal body.
Especially curious are some of the cases in which the extra pair are imperfectly formed. The appearance produced is then that of two limbs in various stages of coalescence, though in reality of course they are stages of imperfect separation. The plane of "coalescence" may fall anywhere, and the two appendages may thus be compounded with each other much as an object partially immersed in mercury "compounds" with its optical image reflected from the surface.
Supernumerary paired structures are not usually, if ever, formed when an appendage is simply amputated. Cases occasionally are seen which nevertheless seem to be of this nature. Borradaile,[8]for example, described a crab (Cancer pagurus) having in place of the right chela threesmallchelae arising from a common base, where the appearances suggested that the three reduced limbs replaced a single normal limb. From the details reported however it seems still possible that one of the chelae (that lettered F. I in Borradaile's figure) may be the normal one, and the other two an extra pair. The chela which I suspect to be the normal is in several respects deformed as well as beingreduced in size, and this deformity may perhaps have ensued as a consequence of the same wound which excited the growth of the extra pair. Its reduced size may be due to the same injury, which may quite well have checked its growth to full proportions.
Admitting doubt in these ambiguous cases it seems to be a general rule that for the production of the extra pair the normal limb should persist in connexion with the body. Moreover it is practically certain that in no case can asingle, viz. an unpaired, duplicate of the normal appendage grow from it. Many examples have been described as of this nature, but all of them may be with confidence regarded as instances of a supernumerary pair in which only the two morphologically anterior or the two morphologically posterior surfaces are developed. We have thus the paradox that a limb of one side of the body, say the right, has in it the power to form a pair of limbs, right and left, as an outgrowth of itself, but cannot form a second left limb alone.
A very interesting question arises whether it is strictly correct to describe the extra pair as a right and a left, or whether they are not rather two lefts or two rights of which one is reversed. This question did not occur to me when in former years I studied these subjects. It was suggested to me by Dr. Przibram. The answer might have an important bearing on biological mechanics, but I know no evidence from which the point can be determined with certainty. In order to decide this question it would be necessary to have cases in which the paired repetition affected a limb markedly differentiated on the two sides of the body, and of course the development of the extra parts in order to be decisive must be fairly complete. One example only is known to me which at all satisfies these requirements, that of the lobster's chela figured (after Van Beneden) inMaterials for the Study of Variation, p. 531, Fig. 184, III.
Here the drawing distinctly suggests that one of the extra dactylopodites, namely that lettered R, is differentiated as a left and not merely a reversed right. For the teeth on this dactylopodite are those of a cutting claw, not of a crushing claw, whereas the dactylopodites R' and L' bear crushing teeth. The figure makes it fairly certain also that the limb affected was acrushing claw. Accepting this interpretation, we reach the remarkable conclusion that the bud of new growth consisted of halves differentiated into cutter and crusher as the normal claws are, and that the extra crusher is geometrically a left but physiologically a right. Though shaped as a left in respect of the direction in which it points, the extra crusher is really an optically reversed right, while the dactylopodite R, which is placed pointing like a right, is really a reversed left (Fig. 12).