CHAPTER IX
ON CONCRETIONS, SPICULES, AND SPICULAR SKELETONS
The deposition of inorganic material in the living body, usually in the form of calcium salts or of silica, is a very common and wide-spread phenomenon. It begins in simple ways, by the appearance of small isolated particles, crystalline or non-crystalline, whose form has little relation or sometimes none to the structure of the organism; it culminates in the complex skeletons of the vertebrate animals, in the massive skeletons of the corals, or in the polished, sculptured and mathematically regular molluscan shells. Even among many very simple organisms, such as the Diatoms, the Radiolarians, the Foraminifera, or the Sponges, the skeleton displays extraordinary variety and beauty, whether by reason of the intrinsic form of its elementary constituents or the geometric symmetry with which these are arranged and interconnected.
With regard to the form of these various structures (and this is all that immediately concerns us here), it is plain that we have to do with two distinct problems, which however, though theoretically distinct, may merge with one another. For the form of the spicule or other skeletal element may depend simply upon its chemical nature, as for instance, to take a simple but not the only case, when the form is purely crystalline; or the inorganic solid material may be laid down in conformity with the shapes assumed by the cells, tissues or organs, and so be, as it were, moulded to the shape of the living organism; and again, there may well be intermediate stages in which both phenomena may be simultaneously recognised, the molecular forces playing their part in conjunction with, and under the restraint of, the other forces inherent in the system. {412}
So far as the problem is a purely chemical one, we must deal with it very briefly indeed; and all the more because special investigations regarding it have as yet been few, and even the main facts of the case are very imperfectly known. This at least is evident, that the whole series of phenomena with which we are about to deal go deep into the subject of colloid chemistry, and especially with that branch of the science which deals with the properties of colloids in connection with capillary or surface phenomena. It is to the special student of colloid chemistry that we must ultimately and chiefly look for the elucidation of our problem[406].
In the first and simplest part of our subject, the essential problem is the problem of crystallisation in presence of colloids. In the cells of plants, true crystals are found in comparative abundance, and they consist, in the great majority of cases, of calcium oxalate. In the stem and root of the rhubarb, for instance, in the leaf-stalk of Begonia, and in countless other cases, sometimes within the cell, sometimes in the substance of the cell-wall, we find large and well-formed crystals of this salt; their varieties of form, which are extremely numerous, are simply the crystalline forms proper to the salt itself, and belong to the two systems, cubic and monoclinic, in one or other of which, according to the amount of water of crystallisation, this salt is known to crystallise. When calcium oxalate crystallises according to the latter system (as it does when its molecule is combined with two molecules of water of crystallisation), the microscopic crystals have the form of fine needles, or “raphides,” such as are very common in plants; and it has been found that these are artificially produced when the salt is crystallised out in presence of glucose or of dextrin[407].
Calcium carbonate, on the other hand, when it occurs in plant-cells (as it does abundantly, for instance in the “cystoliths” of the Urticaceae and Acanthaceae, and in great quantities in Melobesia {413} and the other calcareous or “stony” algae), appears in the form of fine rounded granules, whose inherent crystalline structure is not outwardly visible, but is only revealed (like that of a molluscan shell) under polarised light. Among animals, a skeleton of carbonate of lime occurs under a multitude of forms, of which we need only mention now a very few of the most conspicuous. The spicules of the calcareous sponges are triradiate, occasionally quadriradiate, bodies, with pointed rays, not crystalline in outward form but with a definitely crystalline internal structure. We shall return again to these, and find for them what would seem to be a satisfactory explanation of their form. Among the Alcyonarian zoophytes we have a great variety of spicules[408], which are sometimes straight and slender rods, sometimes flattened and more or less striated plates, and still more often rounded or branched concretions with rough or knobby surfaces (Figs. 194, 200). A third type, presented by several very different things, such as a pearl, or the ear-bone of a bony fish, consists of a more or less {414} rounded body, sometimes spherical, sometimes flattened, in which the calcareous matter is laid down in concentric zones, denser and clearer layers alternating with one another. In the development of the molluscan shell and in the calcification of a bird’s egg or the shell of a crab, for instance, spheroidal bodies with similar concentric striation make their appearance; but instead of remaining separate they become crowded together, and as they coalesce they combine to form a pattern of hexagons. In some cases, the carbonate of lime on being dissolved away by acid leaves behind it a certain small amount of organic residue; in most cases other salts, such as phosphates of lime, ammonia or magnesia are present in small quantities; and in most cases if not all the developing spicule or concretion is somehow or other so associated with living cells that we are apt to take it for granted that it owes its peculiarities of form to the constructive or plastic agency of these.
The appearance of direct association with living cells, however, is apt to be fallacious; for the actual _precipitation_ takes place, as a rule, not in actively living, but in dead or at least inactive tissue[409]: that is to say in the “formed material” or matrix which (as for instance in cartilage) accumulates round the living cells, in the interspaces between these latter, or at least, as often happens, in connection with the cell-wall or cell-membrane rather than within the substance of the protoplasm itself. We need not go the length of asserting that this is a rule without exception; but, so far as it goes, it is of great importance and to its consideration we shall presently return[410].
Cognate with this is the fact that it is known, at least in some cases, that the organism can go on living and multiplying with apparently unimpaired health, when stinted or even wholly deprived of the material of which it is wont to make its spicules {415} or its shell. Thus, Pouchet and Chabry[411] have shown that the eggs of sea-urchins reared in lime-free water develop in apparent health, into larvae entirely destitute of the usual skeleton of calcareous rods, and in which, accordingly, the long arms of the Pluteus larva, which the rods support and distend, are entirely suppressed. And again, when Foraminifera are kept for generations in water from which they gradually exhaust the lime, their shells grow hyaline and transparent, and seem to consist only of chitinous material. On the other hand, in the presence of excess of lime, the shells become much altered, strengthened with various “ornaments,” and assuming characters described as proper to other varieties and even species[412].
The crucial experiment, then, is to attempt the formation of similar structures or forms, apart from the living organism: but, however feasible the attempt may be in theory, we shall be prepared from the first to encounter difficulties, and to realise that, though the actions involved may be wholly within the range of chemistry and physics, yet the actual conditions of the case may be so complex, subtle and delicate, that only now and then, and in the simplest of cases, shall we find ourselves in a position to imitate them completely and successfully. Such an investigation is only part of that much wider field of enquiry through which Stephane Leduc and many other workers[413] have sought to produce, by synthetic means, forms similar to those of living things; but it is a well-defined and circumscribed part of that wider investigation. When by chemical or physical experiment we obtain configurations similar, for instance, to the phenomena of nuclear division, or conformations similar to a pattern of hexagonal cells, or a group of vesicles which resemble some particular tissue or cell-aggregate, we indeed prove what it is the main object of this book to illustrate, namely, that the physical forces are capable of producing particular organic forms. But it is by no means always that we can feel perfectly assured that the physical forces which we deal with in our experiment are identical with, and not merely analogous to, {416} the physical forces which, at work in nature, are bringing about the result which we have succeeded in imitating. In the present case, however, our enquiry is restricted and apparently simplified; we are seeking in the first instance to obtain by purely chemical means a purely chemical result, and there is little room for ambiguity in our interpretation of the experiment.
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When we find ourselves investigating the forms assumed by chemical compounds under the peculiar circumstances of association with a living body, and when we find these forms to be characteristic or recognisable, and somehow different from those which, under other circumstances, the same substance is wont to assume, an analogy presents itself to our minds, captivating though perhaps somewhat remote, between this subject of ours and certain synthetic problems of the organic chemist. There is doubtless an essential difference, as well as a difference of scale, between the visible form of a spicule or concretion and the hypothetical form of an individual molecule; but molecular form is a very important concept; and the chemist has not only succeeded, since the days of Wöhler, in synthesising many substances which are characteristically associated with living matter, but his task has included the attempt to account for the molecular _forms_ of certain “asymmetric” substances, glucose, malic acid and many more, as they occur in nature. These are bodies which, when artificially synthesised, have no optical activity, but which, as we actually find them in organisms, turn (when _in solution_) the plane of polarised light in one direction or the other; thus dextro-glucose and laevomalic acid are common products of plant metabolism; but dextromalic acid and laevo-glucose do not occur in nature at all. The optical activity of these bodies depends, as Pasteur shewed more than fifty years ago[414], upon the form, right-handed or left-handed, of their molecules, which molecular asymmetry further gives rise to a corresponding right or left-handedness (or enantiomorphism) in the crystalline aggregates. It is a distinct problem in organic or physiological chemistry, {417} and by no means without its interest for the morphologist, to discover how it is that nature, for each particular substance, habitually builds up, or at least selects, its molecules in a one-sided fashion, right-handed or left-handed as the case may be. It will serve us no better to assert that this phenomenon has its origin in “fortuity,” than to repeat the Abbé Galiani’s saying, “_les dés de la nature sont pipés._”
The problem is not so closely related to our immediate subject that we need discuss it at length; but at the same time it has its clear relation to the general question of _form_ in relation to vital phenomena, and moreover it has acquired interest as a theme of long-continued discussion and new importance from some comparatively recent discoveries.
According to Pasteur, there lay in the molecular asymmetry of the natural bodies and the symmetry of the artificial products, one of the most deep-seated differences between vital and non-vital phenomena: he went further, and declared that “this was perhaps the _only_ well-marked line of demarcation that can at present [1860] be drawn between the chemistry of dead and of living matter.” Nearly forty years afterwards the same theme was pursued and elaborated by Japp in a celebrated lecture[415], and the distinction still has its weight, I believe, in the minds of many if not most chemists.
“We arrive at the conclusion,” said Professor Japp, “that the production of single asymmetric compounds, or their isolation from the mixture of their enantiomorphs, is, as Pasteur firmly held, the prerogative of life. Only the living organism, or the living intelligence with its conception of asymmetry, can produce this result. Only asymmetry can beget asymmetry.” In these last words (which, so far as the chemist and the biologist are concerned, we may acknowledge to be perfectly true[416]) lies the {418} crux of the difficulty; for they at once bid us enquire whether in nature, external to and antecedent to life, there be not some asymmetry to which we may refer the further propagation or “begetting” of the new asymmetries: or whether in default thereof, we be rigorously confined to the conclusion, from which Japp “saw no escape,” that “at the moment when life first arose, a directive force came into play,—a force of precisely the same character as that which enables the intelligent operator, by the exercise of his will, to select one crystallised enantiomorph and reject its asymmetric opposite[417].”
Observe that it is only the first beginnings of chemical asymmetry that we need to discover; for when asymmetry is once manifested, it is not disputed that it will continue “to beget asymmetry.” A plausible suggestion is now at hand, which if it be confirmed and extended will supply or at least sufficiently illustrate the kind of explanation which is required[418].
We know in the first place that in cases where ordinary non-polarised light acts upon a chemical substance, the amount of chemical action is proportionate to the amount of light absorbed. We know in the second place[419], in certain cases, that light circularly polarised is absorbed in different amounts by the right-handed or left-handed varieties, as the case may be, of an asymmetric substance. And thirdly, we know that a portion of the light which comes to us from the sun is already plane-polarised light, which becomes in part circularly polarised, by reflection (according to Jamin) at the surface of the sea, and then rotated in a particular direction under the influence of terrestrial magnetism. We only require to be assured that the relation between absorption of light and chemical activity will continue to hold good in the case of circularly polarised light; that is to say {419} that the formation of some new substance or other, under the influence of light so polarised, will proceed asymmetrically in consonance with the asymmetry of the light itself; or conversely, that the asymmetrically polarised light will tend to more rapid decomposition of those molecules by which it is chiefly absorbed. This latter proof is now said to be furnished by Byk[420], who asserts that certain tartrates become unsymmetrical under the continued influence of the asymmetric rays. Here then we seem to have an example, of a particular kind and in a particular instance, an example limited but yet crucial (_if confirmed_), of an asymmetric force, non-vital in its origin, which might conceivably be the starting-point of that asymmetry which is characteristic of so many organic products.
The mysteries of organic chemistry are great, and the differences between its processes or reactions as they are carried out in the organism and in the laboratory are many[421]. The actions, catalytic and other, which go on in the living cell are of extraordinary complexity. But the contention that they are different in kind from what we term ordinary chemical operations, or that in the production of single asymmetric compounds there is actually to be witnessed, as Pasteur maintained, a “prerogative of life,” would seem to be no longer safely tenable. And furthermore, it behoves us to remember that, even though failure continued to attend all artificial attempts to originate the asymmetric or optically active compounds which organic nature produces in abundance, this would only prove that a certain _physical force_, or mode of _physical action_, is at work among living things though unknown elsewhere. It is a mode of action which we can easily imagine, though the actual mechanism we cannot set agoing when we please. And it follows that such a difference between living matter and dead would carry us but a little way, for it would still be confined strictly to the physical or mechanical plane.
Our historic interest in the whole question is increased by the {420} fact, or the great probability, that “the tenacity with which Pasteur fought against the doctrine of spontaneous generation was not unconnected with his belief that chemical compounds of one-sided symmetry could not arise save under the influence of life[422].” But the question whether spontaneous generation be a fact or not does not depend upon theoretical considerations; our negative response is based, and is so far soundly based, on repeated failures to demonstrate its occurrence. Many a great law of physical science, not excepting gravitation itself, has no higher claim on our acceptance.
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Let us return then, after this digression, to the general subject of the forms assumed by certain chemical bodies when deposited or precipitated within the organism, and to the question of how far these forms may be artificially imitated or theoretically explained.
Mr George Rainey, of St Bartholomew’s Hospital (to whom we have already referred), and Professor P. Harting, of Utrecht, were the first to deal with this specific problem. Mr Rainey published, between 1857 and 1861, a series of valuable and thoughtful papers to shew that shell and bone and certain other organic structures were formed “by a process of molecular coalescence, demonstrable in certain artificially-formed products[423].” Professor Harting, after thirty years of experimental work, published in 1872 a paper, which has become classical, entitled _Recherches de Morphologie Synthétique, sur la production artificielle de quelques formations calcaires organiques_; his aim was to pave the way for a “morphologie synthétique,” as Wöhler had laid the foundations of a “chimie synthétique,” by his classical discovery forty years before. {421}
Rainey and Harting used similar methods, and these were such as many other workers have continued to employ,—partly with the direct object of explaining the genesis of organic forms and partly as an integral part of what is now known as Colloid Chemistry. The whole gist of the method was to bring some soluble salt of lime, such as the chloride or nitrate, into solution within a colloid medium, such as gum, gelatine or albumin; and then to precipitate it out in the form of some insoluble compound, such as the carbonate or oxalate. Harting found that, when he added a little sodium or potassium carbonate to a concentrated solution of calcium chloride in albumin, he got at first a gelatinous mass, or “colloid precipitate”: which slowly transformed by the appearance of tiny microscopic particles, at first motionless, but afterwards as they grew larger shewing the typical Brownian movement. So far, very much the same phenomena were witnessed whether the solution were albuminous or not, and similar appearances indeed had been witnessed and recorded by Gustav Rose, so far back as 1837[424]; but in the later stages the presence of albuminoid matter made a great difference. Now, after a few days, the calcium carbonate was seen to be deposited in the form of large rounded concretions, with a more or less distinct central nucleus, and with a surrounding structure at once radiate and {422} concentric; the presence of concentric zones or lamellae, alternately dark and clear, was especially characteristic. These round “calcospherites” shewed a tendency to aggregate together in layers, and then to assume polyhedral, or often regularly hexagonal, outlines. In this latter condition they closely resemble the early stages of calcification in a molluscan (Fig. 198), or still more in a crustacean shell[425]; while in their isolated condition {423} they very closely resemble the little calcareous bodies in the tissues of a trematode or a cestode worm, or in the oesophageal glands of an earthworm[426].
When the albumin was somewhat scanty, or when it was mixed with gelatine, and especially when a little phosphate of lime was {424} added to the mixture, the spheroidal globules tended to become rough, by an outgrowth of spinous or digitiform projections; and in some cases, but not without the presence of the phosphate, the result was an irregularly shaped knobby spicule, precisely similar to those which are characteristic of the Alcyonaria[427].
The rough spicules of the Alcyonaria are extraordinarily variable in shape and size, as, looking at them from the chemist’s or the physicist’s point of view, we should expect them to be. Partly upon the form of these spicules, and partly on the general form or mode of branching of the entire colony of polypes, a vast number of separate “species” have been based by systematic zoologists. But it is now admitted that even in specimens of a single species, from one and the same locality, the spicules may vary immensely in shape and size: and Professor Hickson declares (in a paper published while these sheets are passing through the press) that after many years of laborious work in striving to determine species of these animal colonies, he feels “quite convinced that we have been engaged in a more or less fruitless task[428]”.
The formation of a tooth has very lately been shown to be a phenomenon of the same order. That is to say, “calcification in both dentine and enamel {425} is in great part a physical phenomenon; the actual deposit in both tissues occurs in the form of calcospherites, and the process in mammalian tissue is identical in every point with the same process occurring in lower organisms[429].” The ossification of bone, we may be sure, is in the same sense and to the same extent a physical phenomenon.
The typical structure of a calcospherite is no other than that of a pearl, nor does it differ essentially from that of the otolith of a mollusc or of a bony fish. (The otoliths, by the way, of the elasmobranch fishes, like those of reptiles and birds, are not developed after this fashion, but are true crystals of calc-spar.)
Throughout these phenomena, the effect of surface-tension is manifest. It is by surface-tension that ultra-microscopic particles are brought together in the first floccular precipitate or coagulum; by the same agency, the coarser particles are in turn agglutinated into visible lumps; and the form of the calcospherites, whether it be that of the solitary spheres or that assumed in various stages of aggregation (e.g. Fig. 202)[430], is likewise due to the same agency.
From the point of view of colloid chemistry the whole phenomenon is very important and significant; and not the least significant part is this tendency of the solidified deposits to assume the form of “spherulites,” and other rounded contours. In the phraseology of that science, we are dealing with a _two-phase_ system, which finally consists of solid particles in suspension in a liquid (the former being styled the _disperse phase_, the latter the {426} _dispersion medium_). In accordance with a rule first recognised by Ostwald[431], when a substance begins to separate out from a solution, so making its appearance as a _new phase_, it always makes its appearance first as a liquid[432]. Here is a case in point. The minute quantities of material, on their way from a state of solution to a state of “suspension,” pass through a liquid to a solid form; and their temporary sojourn in the former leaves its impress in the rounded contours which surface-tension brought about while the little aggregate was still labile or fluid: while coincidently with this surface-tension effect upon the surface, crystallisation tended to take place throughout the little liquid mass, or in such portion of it as had not yet consolidated and crystallised.
Where we have simple aggregates of two or three calcospherites, the resulting figure is precisely that of so many contiguous soap-bubbles. In other cases, composite forms result which are not so easily explained, but which, if we could only account for them, would be of very great interest to the biologist. For instance, when smaller calcospheres seem, as it were, to invade the substance of a larger one, we get curious conformations which in the closest possible way resemble the outlines of certain of the Diatoms (Fig. 203). Another very curious formation, which Harting calls a “conostat,” is of frequent occurrence, and in it we see at least a suggestion of analogy with the configuration which, in a protoplasmic structure, we have spoken of as a “collar-cell.” The {427} conostats, which are formed in the surface layer of the solution, consist of a portion of a spheroidal calcospherite, whose upper part is continued into a thin spheroidal collar, of somewhat larger radius than the solid sphere; but the precise manner in which the collar is formed, possibly around a bubble of gas, possibly about a vortex-like diffusion-current[433] is not obvious.
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Among these various phenomena, the concentric striation observed in the calcospherite has acquired a special interest and importance[434]. It is part of a phenomenon now widely known, and recognised as an important factor in colloid chemistry, under the name of “Liesegang’s Rings[435].”
If we dissolve, for instance, a little bichromate of potash in gelatine, pour it on to a glass plate, and after it is set place upon it a drop of silver nitrate solution, there appears in the course of a few hours the phenomenon of Liesegang’s rings. At first the silver forms a central patch of abundant reddish brown chromate precipitate; but around this, as the silver nitrate diffuses slowly through the gelatine, the precipitate no longer comes down in a continuous, uniform layer, but forms a series of zones, beautifully regular, which alternate with clear interspaces of jelly, and which stand farther and farther apart, in logarithmic ratio, as they recede from the centre. For a discussion of the _raison d’être_ of {428} this phenomenon, still somewhat problematic, the student must consult the text-books of physical and colloid chemistry[436].
But, speaking very generally, we may say the appearance of Liesegang’s rings is but a particular and striking case of a more general phenomenon, namely the influence on crystallisation of the presence of foreign bodies or “impurities,” represented in this case by the “gel” or colloid matrix[437]. Faraday shewed long ago that to the presence of slight impurities might be ascribed the banded structure of ice, of banded quartz or agate, onyx, etc.; and Quincke and Tomlinson have added to our scanty knowledge of the same phenomenon[438].
Besides the tendency to rhythmic action, as manifested in Liesegang’s rings, the association of colloid matter with a crystalloid in solution may lead to other well-marked effects. These, according to Professor J. H. Bowman[439], may be grouped somewhat as follows: (1) total prevention of crystallisation; (2) suppression of certain of the lines of crystalline growth; (3) extension of the crystal to abnormal proportions, with a tendency for it to become a compound crystal; (4) a curving or gyrating of the crystal or its parts. {429}
For instance, it would seem that, if the supply of material to the growing crystal be not forthcoming in sufficient quantity (as may well happen in a colloid medium, for lack of convection-currents), then growth will follow only the strongest lines of crystallising force, and will be suppressed or partially suppressed along other axes. The crystal will have a tendency to become filiform, or “fibrous”; and the raphides of our plant-cells are a case in point. Again, the long slender crystal so formed, pushing its way into new material, may initiate a new centre of crystallisation: we get the phenomenon known as a “relay,” along the principal lines of force, and sometimes along subordinate axes as well. This phenomenon is illustrated in the accompanying figure of crystallisation in a colloid medium of common salt; and it may possibly be that we have here an explanation, or part of an explanation, of the compound siliceous spicules of the Hexactinellid sponges. Lastly, when the crystallising force is nearly equalled by the resistance of the viscous medium, the crystal takes the line of least resistance, with very various results. One of these results would seem to be a gyratory course, giving to the crystal a curious wheel-like shape, as in Fig. 207; and other results are the feathery, fern-like {430} or arborescent shapes so frequently seen in microscopic crystallisation.
To return to Liesegang’s rings, the typical appearance of concentric rings upon a gelatinous plate may be modified in various experimental ways. For instance, our gelatinous medium may be placed in a capillary tube immersed in a solution of the precipitating salt, and in this case we shall obtain a vertical succession of bands or zones regularly interspaced: the result being very closely comparable to the banded pigmentation which we see in the hair of a rabbit or a rat. In the ordinary plate preparation, the free surface of the gelatine is under different conditions to the lower layers and especially to the lowest layer in contact with the glass; and therefore it often happens that we obtain a double series of rings, one deep and the other superficial, which by occasional blending or interlacing, may produce a netted pattern. In some cases, as when only the inner surface of our capillary tube is covered with a layer of gelatine, there is a tendency for the deposit to take place in a continuous spiral line, rather than in concentric and separate zones. By such means, according to Küster[440] various forms of annular, spiral and reticulated thickenings in the vascular tissue of plants may be closely imitated; and he and certain other writers have of late been inclined to carry the same chemico-physical phenomenon a very long way, in the explanation of various banded, striped, and other rhythmically successional types of structure or pigmentation. For example, the striped pigmentation of the leaves in many plants (such as _Eulalia japonica_), the striped or clouded colouring of many feathers or of a cat’s skin, the patterns of many fishes, such for instance as the brightly coloured tropical Chaetodonts and the like, are all regarded by him as so many instances of “diffusion-figures” closely related to the typical Liesegang phenomenon. Gebhardt has made a particular study of the same subject in the case of insects[441]. He declares, for instance, that the banded wings of _Papilio podalirius_ are precisely imitated in Liesegang’s experiments; that the finer markings on the wings of the Goatmoth (_Cossus ligniperda_) shew the double arrangement of larger and of {431} smaller intermediate rhythms, likewise manifested in certain cases of the same kind; that the alternate banding of the antennae (for instance in _Sesia spheciformis_), a pigmentation not concurrent with the segmented structure of the antenna, is explicable in the same way; and that the “ocelli,” for instance of the Emperor moth, are typical illustrations of the common concentric type. Darwin’s well-known disquisition[442] on the ocellar pattern of the feathers of the Argus Pheasant, as a result of sexual selection, will occur to the reader’s mind, in striking contrast to this or to any other direct physical explanation[443]. To turn from the distribution of pigment to more deeply seated structural characters, Leduc has shewn how, for instance, the laminar structure of the cornea or the lens is again, apparently, a similar phenomenon. In the lens of the fish’s eye, we have a very curious appearance, the consecutive lamellae being roughened or notched by close-set, interlocking sinuosities; and precisely the same appearance, save that it is not quite so regular, is presented in one of Küster’s figures as the effect of precipitating a little sodium phosphate in a gelatinous medium. Biedermann has studied, from the same point of view, the structure and development of the molluscan shell, the problem which Rainey had first attacked more than fifty years before[444]; and Liesegang himself has applied his results to the formation of pearls, and to the development of bone[445]. {432}
Among all the many cases where this phenomenon of Liesegang’s comes to the naturalist’s aid in explanation of rhythmic or zonary configurations in organic forms, it has a special interest where the presence of concentric zones or rings appears, at first sight, as a sure and certain sign of periodicity of growth, depending on the seasons, and capable therefore of serving as a mark and record of the creature’s age. This is the case, for instance, with the scales, bones and otoliths of fishes; and a kindred phenomena in starch-grains has given rise, in like manner, to the belief that they indicate a diurnal and nocturnal periodicity of activity and rest[446].
That this is actually the case in growing starch-grains is generally believed, on the authority of Meyer[447]; but while under certain circumstances a marked alternation of growing and resting periods may occur, and may leave its impress on the structure of the grain, there is now great reason to believe that, apart from such external influences, the internal phenomena of diffusion may, just as in the typical Liesegang experiment, produce the well-known concentric rings. The spherocrystals of inulin, in like manner, shew, like the “calcospherites” of Harting (Fig. 208), a concentric structure which in all likelihood has had no causative impulse save from within.
The striation, or concentric lamellation, of the scales and otoliths of fishes has been much employed of recent years as a trustworthy and unmistakeable mark of the fish’s age. There are difficulties in the way of accepting this hypothesis, not the least of which is the fact that the otolith-zones, for instance, are extremely well marked even in the case of some fishes which spend their lives in deep water, {433} where the temperature and other physical conditions shew little or no appreciable fluctuation with the seasons of the year. There are, on the other hand, phenomena which seem strongly confirmatory of the hypothesis: for instance the fact (if it be fully established) that in such a fish as the cod, zones of growth, _identical in number_, are found both on the scales and in the otoliths[448]. The subject has become a much debated one, and this is not the place for its discussion; but it is at least obvious, with the Liesegang phenomenon in view, that we have no right to _assume_ that an appearance of rhythm and periodicity in structure and growth is necessarily bound up with, and indubitably brought about by, a periodic recurrence of particular _external_ conditions.
But while in the Liesegang phenomenon we have rhythmic precipitation which depends only on forces intrinsic to the system, and is independent of any corresponding rhythmic changes in temperature or other external conditions, we have not far to seek for instances of chemico-physical phenomena where rhythmic alternations of appearance or structure are produced in close relation to periodic fluctuations of temperature. A well-known instance is that of the Stassfurt deposits, where the rock-salt alternates regularly with thin layers of “anhydrite,” or (in another series of beds) with “polyhalite[449]”: and where these zones are commonly regarded as marking years, and their alternate bands as having been formed in connection with the seasons. A discussion, however, of this remarkable and significant phenomenon, and of how the chemist explains it, by help of the “phase-rule,” in connection with temperature conditions, would lead us far beyond our scope[450].
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We now see that the methods by which we attempt to study the chemical or chemico-physical phenomena which accompany the development of an inorganic concretion or spicule within the {434} body of an organism soon introduce us to a multitude of kindred phenomena, of which our knowledge is still scanty, and which we must not attempt to discuss at greater length. As regards our main point, namely the formation of spicules and other elementary skeletal forms, we have seen that certain of them may be safely ascribed to simple precipitation or crystallisation of inorganic materials, in ways more or less modified by the presence of albuminous or other colloid substances. The effect of these latter is found to be much greater in the case of some crystallisable bodies than in others. For instance, Harting, and Rainey also, found as a rule that calcium oxalate was much less affected by a colloid medium than was calcium carbonate; it shewed in their hands no tendency to form rounded concretions or “calcospherites” in presence of a colloid, but continued to crystallise, either normally, or with a tendency to form needles or raphides. It is doubtless for this reason that, as we have seen, _crystals_ of calcium oxalate are so common in the tissues of plants, while those of other calcium salts are rare. But true calcospherites, or spherocrystals, of the oxalate are occasionally found, for instance in certain Cacti, and Bütschli[451] has succeeded in making them artificially in Harting’s usual way, that is to say by crystallisation in a colloid medium.
There link on to these latter observations, and to the statement already quoted that calcareous deposits are associated with the dead products rather than with the living cells of the organism, certain very interesting facts in regard to the _solubility_ of salts in colloid media, which have been made known to us of late, and which go far to account for the presence (apart from the form) of calcareous precipitates within the organism[452]. It has been shewn, in the first place, that the presence of albumin has a notable effect on the solubility in a watery solution of calcium salts, increasing the solubility of the phosphate in a marked degree, and that of the carbonate in still greater proportion; but the {435} sulphate is only very little more soluble in presence of albumin than in pure water, and the rarity of its occurrence within the organism is so far accounted for. On the other hand, the bodies derived from the breaking down of the albumins, their “catabolic” products, such as the peptones, etc., dissolve the calcium salts to a much less degree than albumin itself; and in the case of the phosphate, its solubility in them is scarcely greater than in water. The probability is, therefore, that the actual precipitation of the calcium salts is not due to the direct action of carbonic acid, etc. on a more soluble salt (as was at one time believed); but to catabolic changes in the proteids of the organism, which tend to throw down the salts already formed, which had remained hitherto in albuminous solution. The very slight solubility of calcium phosphate under such circumstances accounts for its predominance in, for instance, mammalian bone[453]; and wherever, in short, the supply of this salt has been available to the organism.
To sum up, we see that, whether from food or from sea-water, calcium sulphate will tend to pass but little into solution in the albuminoid substances of the body: calcium carbonate will enter more freely, but a considerable part of it will tend to remain in solution: while calcium phosphate will pass into solution in considerable amount, but will be almost wholly precipitated again, as the albumin becomes broken down in the normal process of metabolism.
We have still to wait for a similar and equally illuminating study of the solution and precipitation of _silica_, in presence of organic colloids.
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From the comparatively small group of inorganic formations which, arising within living organisms, owe their form solely to precipitation or to crystallisation, that is to say to chemical or other molecular forces, we shall presently pass to that other and larger group which appear to be conformed in direct relation to the forms and the arrangement of the cells or other protoplasmic elements[454]. {436} The two principles of conformation are both illustrated in the spicular skeletons of the Sponges.
In a considerable number, but withal a minority of cases, the form of the sponge-spicule may be deemed sufficiently explained on the lines of Harting’s and Rainey’s experiments, that is to say as the direct result of chemical or physical phenomena associated with the deposition of lime or of silica in presence of colloids[455]. This is the case, for instance, with various small spicules of a globular or spheroidal form, formed of amorphous silica, concentrically striated within, and often developing irregular knobs or tiny tubercles over their surfaces. In the aberrant sponge _Astrosclera_[456], we have, to begin with, rounded, striated discs or globules, which in like manner are nothing more or less than the {437} “calcospherites” of Harting’s experiments; and as these grow they become closely aggregated together (Fig. 210), and assume an angular, polyhedral form, once more in complete accordance with the results of experiment[457]. Again, in many Monaxonid sponges, we have irregularly shaped, or branched spicules, roughened or tuberculated by secondary superficial deposits, and reminding one of the spicules of some Alcyonaria. These also must be looked upon as the simple result of chemical deposition, the form of the deposit being somewhat modified in conformity with the surrounding tissues, just as in the simple experiment the form of the concretionary precipitate is affected by the heterogeneity, visible or invisible, of the matrix. Lastly, the simple needles of amorphous silica, which constitute one of the commonest types of spicule, call for little in the way of explanation; they are accretions or deposits about a linear axis, or fine thread of organic material, just as the ordinary rounded calcospherite is deposited about some minute point or centre of crystallisation, and as ordinary crystallisation is often started by a particle of atmospheric dust; in some cases they also, like the others, are apt to be roughened by more irregular secondary deposits, which probably, as in Harting’s experiments, appear in this irregular form when the supply of material has become relatively scanty.
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Our few foregoing examples, diverse as they are in look and kind and ranging from the spicules of Astrosclera or Alcyonium to the otoliths of a fish, seem all to have their free origin in some larger or smaller fluid-containing space, or cavity of the body: pretty much as Harting’s calcospheres made their appearance in the albuminous content of a dish. But we now come at last to a much larger class of spicular and skeletal structures, for whose regular and often complex forms some other explanation than the intrinsic forces of crystallisation or molecular adhesion is manifestly necessary. As we enter on this subject, which is certainly no small or easy one, it may conduce to simplicity, and to brevity, {438} if we try to make a rough classification, by way of forecast, of the chief conditions which we are likely to meet with.
Just as we look upon animals as constituted, some of a vast number of cells, and others of a single cell or of a very few, and just as the shape of the former has no longer a visible relation to the individual shapes of its constituent cells, while in the latter it is cell-form which dominates or is actually equivalent to the form of the organism, so shall we find it to be, with more or less exact analogy, in the case of the skeleton. For example, our own skeleton consists of bones, in the formation of each of which a vast number of minute living cellular elements are necessarily concerned; but the form and even the arrangement of these bone-forming cells or corpuscles are monotonously simple, and we cannot find in these a physical explanation of the outward and visible configuration of the bone. It is as part of a far larger field of force,—in which we must consider gravity, the action of various muscles, the compressions, tensions and bending moments due to variously distributed loads, the whole interaction of a very complex mechanical system,—that we must explain (if we are to explain at all) the configuration of a bone.
In contrast to these massive skeletons, or constituents of a skeleton, we have other skeletal elements whose whole magnitude, or whose magnitude in some dimension or another, is commensurate with the magnitude of a single living cell, or (as comes to very much the same thing) is comparable to the range of action of the molecular forces. Such is the case with the ordinary spicules of a sponge, with the delicate skeleton of a Radiolarian, or with the denser and robuster shells of the Foraminifera. The effect of _scale_, then, of which we had so much to say in our introductory chapter on Magnitude, is bound to be apparent in the study of skeletal fabrics, and to lead to essential differences between the big and the little, the massive and the minute, in regard to their controlling forces and their resultant forms. And if all this be so, and if the range of action of the molecular forces be in truth the important and fundamental thing, then we may somewhat extend our statement of the case, and include in it not only association with the living cellular elements of the body, but also association with any bubbles, drops, vacuoles or vesicles which {439} may be comprised within the bounds of the organism, and which are (as their names and characters connote) of the order of magnitude of which we are speaking.
Proceeding a little farther in our classification, we may conceive each little skeletal element to be associated, in one case, with a single cell or vesicle, and in another with a cluster or “system” of consociated cells. In either case there are various possibilities. For instance, the calcified or other skeletal material may tend to overspread the entire outer surface of the cell or cluster of cells, and so tend accordingly to assume some configuration comparable to that of a fluid drop or of an aggregation of drops; this, in brief, is the gist and essence of our story of the foraminiferal shell. Another common, but very different condition will arise if, in the case of the cell-aggregates, the skeletal material tends to accumulate in the interstices _between_ the cells, in the partition-walls which separate them, or in the still more restricted distribution indicated by the _lines_ of junction between these partition-walls. Conditions such as these will go a very long way to help us in our understanding of many sponge-spicules and of an immense variety of radiolarian skeletons. And lastly (for the present), there is a possible and very interesting case of a skeletal element associated with the surface of a cell, not so as to cover it like a shell, but only so as to pursue a course of its own within it, and subject to the restraints imposed by such confinement to a curved and limited surface. With this curious condition we shall deal immediately.
This preliminary and much simplified classification of skeletal forms (as is evident enough) does not pretend to completeness. It leaves out of account some kinds of conformation and configuration with which we shall attempt to deal, and others which we must perforce omit. But nevertheless it may help to clear or to mark our way towards the subjects which this chapter has to consider, and the conditions by which they are at least partially defined.
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Among the several possible, or conceivable, types of microscopic skeletons let us choose, to begin with, the case of a spicule, more or less simply linear as far as its _intrinsic_ powers of growth are {440} concerned, but which owes its now somewhat complicated form to a restraint imposed by the individual cell to which it is confined, and within whose bounds it is generated. The conception of a spicule developed under such conditions we owe to a distinguished physicist, the late Professor G. F. FitzGerald.
Many years ago, Sollas pointed out that if a spicule begin to grow in some particular way, presumably under the control or constraint imposed by the organism, it continues to grow by further chemical deposition in the same form or direction even after it has got beyond the boundaries of the organism or its cells. This phenomenon is what we see in, and this imperfect explanation goes so far to account for, the continued growth in straight lines of the long calcareous spines of Globigerina or Hastigerina, or the similarly radiating but siliceous spicules of many Radiolaria. In physical language, if our crystalline structure has once begun to be laid down in a definite orientation, further additions tend to accrue in a like regular fashion and in an identical direction; and this corresponds to the phenomenon of so-called “orientirte Adsorption,” as described by Lehmann.
In Globigerina or in Acanthocystis the long needles grow out freely into the surrounding medium, with nothing to impede their rectilinear growth and their approximately radiate distribution. But let us consider some simple cases to illustrate the forms which a spicule will tend to assume when, striving (as it were) to grow straight, it comes under the influence of some simple and constant restraint or compulsion.
If we take any two points on some curved surface, such as that of a sphere or an ellipsoid, and imagine a string stretched between them, we obtain what is known in mathematics as a “geodetic” curve. It is the shortest line which can be traced between the two points, upon the surface itself; and the most familiar of all cases, from which the name is derived, is that curve upon the earth’s surface which the navigator learns to follow in the practice of “great-circle sailing.” Where the surface is spherical, the geodetic is always literally a “great circle,” a circle, that is to say, whose centre is the centre of the sphere. If instead of a sphere we be dealing with an ellipsoid, the geodetic becomes a variable figure, according to the position of our two points. {441} For obviously, if they lie in a line perpendicular to the long axis of the ellipsoid, the geodetic which connects them is a circle, also perpendicular to that axis; and if they lie in a line parallel to the axis, their geodetic is a portion of that ellipse about which the whole figure is a solid of revolution. But if our two points lie, relatively to one another, in any other direction, then their geodetic is part of a spiral curve in space, winding over the surface of the ellipsoid.
To say, as we have done, that the geodetic is the shortest line between two points upon the surface, is as much as to say that it is a _projection_ of some particular straight line upon the surface in question; and it follows that, if any linear body be confined to that surface, while retaining a tendency to grow by successive increments always (save only for its confinement to that surface) in a straight line, the resultant form which it will assume will be that of a geodetic. In mathematical language, it is a property of a geodetic that the plane of any two consecutive elements is a plane perpendicular to that in which the geodetic lies; or, in simpler words, any two consecutive elements lie in a straight line _in the plane of the surface_, and only diverge from a straight line in space by the actual curvature of the surface to which they are restrained.
Let us now imagine a spicule, whose natural tendency is to grow into a straight linear element, either by reason of its own molecular anisotropy, or because it is deposited about a thread-like axis; and let us suppose that it is confined either within a cell-wall or in adhesion thereto; it at once follows that its line of growth will be simply a geodetic to the surface of the cell. And if the cell be an imperfect sphere, or a more or less regular ellipsoid, the spicule will tend to grow into one or other of three forms: either a plane curve of circular arc; or, more commonly, a plane curve which is a portion of an ellipse; or, most commonly of all, a curve which is a portion of a spiral in space. In the latter case, the number of turns of the spiral will depend, not only on the length of the spicule, but on the relative dimensions of the ellipsoidal cell, as well as upon the angle by which the spicule is inclined to the ellipsoid axes; but a very common case will probably be that in which the spicule looks at first sight to be {442} a plane C-shaped figure, but is discovered, on more careful inspection, to lie not in one plane but in a more complicated spiral twist. This investigation includes a series of forms which are abundantly represented among actual sponge-spicules, as illustrated in Figs. 211 and 212. If the spicule be not restricted to linear growth, but have a tendency to expand, or to branch out from a main axis, we shall obtain a series of more complex figures, all related to the geodetic system of curves. A very simple case will arise where the spicule occupies, in the first instance, the axis of the containing cell, and then, on reaching its boundary, tends to branch or spread outwards. We shall now get various figures, in some of which the spicule will appear as an axis expanding into a disc or wheel at either end; and in other cases, the terminal disc will be replaced, or represented, by a series of rays or spokes, with a reflex curvature, corresponding to the spherical or ellipsoid curvature of the surface of the cell. Such spicules as these are again exceedingly common among various sponges (Fig. 213).
Furthermore, if these mechanical methods of conformation, and others like to these, be the true cause of the shapes which the spicules assume, it is plain that the production of these spicular shapes is not a specific function of sponges or of any particular sponge, but that we should expect {443} the same or very similar phenomena to occur in other organisms, wherever the conditions of inorganic secretion within closed cells was very much the same. As a matter of fact, in the group of Holothuroidea, where the formation of intracellular spicules is a characteristic feature of the group, all the principal types of conformation which we have just described can be closely paralleled. Indeed in many cases, the forms of the Holothurian spicules are identical and indistinguishable from those of the sponges[458]. But the Holothurian spicules are composed of calcium carbonate while those which we have just described in the case of sponges are usually, if not always, siliceous: this being just another proof of the fact that in such cases the form of the spicule is not due to its chemical nature or molecular structure, but to the external forces to which, during its growth, the spicule is submitted.
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So much for that comparatively limited class of sponge-spicules whose forms seem capable of explanation on the hypothesis that they are developed within, or under the restraint imposed by, the surface of a cell or vesicle. Such spicules are usually of small size, as well as of comparatively simple form; and they are greatly outstripped in number, in size, and in supposed importance as guides to zoological classification, by another class of spicules. This new class includes such as we have supposed to be capable of explanation on the assumption that they develop in association (of some sort or another) with the _lines of junction_ of contiguous cells. They include the triradiate spicules of the calcareous sponges, the quadriradiate or “tetractinellid” spicules which occur in the same group, but more characteristically in certain siliceous sponges known as the Tetractinellidae, and lastly perhaps (though these last are admittedly somewhat harder to understand) the six-rayed spicules of the Hexactinellids.
The spicules of the calcareous sponges are commonly triradiate, and the three radii are usually inclined to one another at equal, or nearly equal angles; in certain cases, two of the three rays are nearly in a straight line, and at right angles to the {444} third[459]. They are seldom in a plane, but are usually inclined to one another in a solid, trihedral angle, not easy of precise measurement under the microscope. The three rays are very often supplemented by a fourth, which is set tetrahedrally, making, that is to say, coequal angles with the other three. The calcareous spicule consists mainly of carbonate of lime, in the form of calcite, with (according to von Ebner) some admixture of soda and magnesia, of sulphates and of water. According to the same writer (but the fact, though it would seem easy to test, is still disputed) there is no organic matter in the spicule, either in the form of an axial filament or otherwise, and the appearance of stratification, often simulating the presence of an axial fibre, is due to “mixed crystallisation” of the various constituents. The spicule is a true crystal, and therefore its existence and its form are _primarily_ due to the molecular forces of crystallisation; moreover it is a single crystal and not a group of crystals, as is at once seen by its behaviour in polarised light. But its axes are not crystalline axes, and its form neither agrees with, nor in any way resembles, any one of the many polymorphic forms in which calcite is capable of crystallising. It is as though it were carved out of a solid crystal; it is, in fact, a crystal under restraint, a crystal growing, as it were, in an artificial mould; and this mould is constituted by the surrounding cells, or structural vesicles of the sponge.
We have already studied in an elementary way, but amply for our present purpose, the manner in which three or more cells, or bubbles, tend to meet together under the influence of surface-tension, and also the outwardly similar phenomena which may be brought about by a uniform distribution of mechanical pressure. We have seen that when we confine ourselves to a plane assemblage of such bodies, we find them meeting one another in threes; that in a section or plane projection of such an assemblage we see the partition-walls meeting one another at equal angles of 120°; that when the bodies are uniform in size, the partitions are straight lines, which combine to form regular hexagons; and that when {445} the bodies are unequal in size, the partitions are curved, and combine to form other and less regular polygons. It is plain, accordingly, that in any flattened or stratified assemblage of such cells, a solidified skeletal deposit which originates or accumulates either between the cells or within the thickness of their mutual partitions, will tend to take the form of triradiate bodies, whose rays (in a typical case) will be set at equal angles of 120° (Fig. 214, _F_). And this latter condition of equality will be open to modification in various ways. It will be modified by any inequality in the specific tensions of adjacent cells; as a special case, it will be apt to be greatly modified at the surface of the system, where a spicule happens to be formed in a plane perpendicular to the cell-layer, so that one of its three rays lies between two adjacent cells and the other two are associated with the surface of contact between the cells and the surrounding medium; in such a case (as in the cases considered in connection with the forms of the cells themselves {446} on p. 314), we shall tend to obtain a spicule with two equal angles and one unequal (Fig. 214, _A_, _C_). In the last case, the two outer, or superficial rays, will tend to be markedly curved. Again, the equiangular condition will be departed from, and more or less curvature will be imparted to the rays, wherever the cells of the system cease to be uniform in size, and when the hexagonal symmetry of the system is lost accordingly. Lastly, although we speak of the rays as meeting at certain definite angles, this statement applies to their _axes_, rather than to the rays themselves. For, if the triradiate spicule be developed in the _interspace_ between three juxtaposed cells, it is obvious that its sides will tend to be concave, for the interspace between our three contiguous equal circles is an equilateral, curvilinear triangle; and even if our spicule be deposited, not in the space between our three cells, but in the thickness of the intervening wall, then we may recollect (from p. 297) that the several partitions never actually meet at sharp angles, but the angle of contact is always bridged over by a small accumulation of material (varying in amount according to its fluidity) whose boundary takes the form of a circular arc, and which constitutes the “bourrelet” of Plateau.
In any sample of the triradiate spicules of Grantia, or in any series of careful drawings, such as those of Haeckel among others, we shall find that all these various configurations are precisely and completely illustrated.
The tetrahedral, or rather tetractinellid, spicule needs no explanation in detail (Fig. 214, _D_, _E_). For just as a triradiate spicule corresponds to the case of three cells in mutual contact, so does the four-rayed spicule to that of a solid aggregate of four cells: these latter tending to meet one another in a tetrahedral system, shewing four edges, at each of which four surfaces meet, the edges being inclined to one another at equal angles of about 109°. And even in the case of a single layer, or superficial layer, of cells, if the skeleton originate in connection with all the edges of mutual contact, we shall, in complete and typical cases, have a four-rayed spicule, of which one straight limb will correspond to the line of junction between the three cells, and the other three limbs (which will then be curved limbs) will correspond to the edges where two cells meet one another on the surface of the system. {447}
But if such a physical explanation of the forms of our spicules is to be accepted, we must seek at once for some physical agency by which we may explain the presence of the solid material just at the junctions or interfaces of the cells, and for the forces by which it is confined to, and moulded to the form of, these intercellular or interfacial contacts. It is to Dreyer that we chiefly owe the physical or mechanical theory of spicular conformation which I have just described,—a theory which ultimately rests on the form assumed, under surface-tension, by an aggregation of cells or vesicles. But this fundamental point being granted, we have still several possible alternatives by which to explain the details of the phenomenon.
Dreyer, if I understand him aright, was content to assume that the solid material, secreted or excreted by the organism, accumulated in the interstices between the cells, and was there subjected to mechanical pressure or constraint as the cells got more and more crowded together by their own growth and that of the system generally. As far as the general form of the spicules goes, such explanation is not inadequate, though under it we may have to renounce some of our assumptions as to what takes place at the outer surface of the system.
But in all (or most) cases where, but a few years ago, the concepts of secretion or excretion seemed precise enough, we are now-a-days inclined to turn to the phenomenon of adsorption as a further stage towards the elucidation of our facts. Here we have a case in point. In the tissues of our sponge, wherever two cells meet, there we have a definite _surface_ of contact, and there accordingly we have a manifestation of surface-energy; and the concentration of surface-energy will tend to be a maximum at the _lines_ or edges whereby the three, or four, such surfaces are conjoined. Of the micro-chemistry of the sponge-cells our ignorance is great; but (without venturing on any hypothesis involving the chemical details of the process) we may safely assert that there is an inherent probability that certain substances will tend to be concentrated and ultimately deposited just in these lines of intercellular contact and conjunction. In other words, adsorptive concentration, under osmotic pressure, at and in the surface-film which constitutes the mutual boundary between contiguous {448} cells, emerges as an alternative (and, as it seems to me, a highly preferable alternative) to Dreyer’s conception of an accumulation under mechanical pressure in the vacant spaces left between one cell and another.
But a purely chemical, or purely molecular adsorption, is not the only form of the hypothesis on which we may rely. For from the purely physical point of view, angles and edges of contact between adjacent cells will be _loci_ in the field of distribution of surface-energy, and any material particles whatsoever will tend to undergo a diminution of freedom on entering one of those boundary regions. In a very simple case, let us imagine a couple of soap bubbles in contact with one another. Over the surface of each bubble there glide in every direction, as usual, a multitude of tiny bubbles and droplets; but as soon as these find their way into the groove or re-entrant angle between the two bubbles, there their freedom of movement is so far restrained, and out of that groove they have little or no tendency to emerge. A cognate phenomenon is to be witnessed in microscopic sections of steel or other metals. Here, amid the “crystalline” structure of the metal (where in cooling its imperfectly homogeneous material has developed a cellular structure, shewing (in section) hexagonal or polygonal contours), we can easily observe, as Professor Peddie has shewn me, that the little particles of graphite and other foreign bodies common in the matrix, have tended to aggregate themselves in the walls and at the angles of the polygonal cells—this being a direct result of the diminished freedom which the particles undergo on entering one of these boundary regions[460].
It is by a combination of these two principles, chemical adsorption on the one hand, and physical quasi-adsorption or concentration of grosser particles on the other, that I conceive the substance of the sponge-spicule to be concentrated and aggregated at the cell boundaries; and the forms of the triradiate and tetractinellid spicules are in precise conformity with this hypothesis. A few general matters, and a few particular cases, remain to be considered.
It matters little or not at all, for the phenomenon in question, {449} what is the histological nature or “grade” of the vesicular structures on which it depends. In some cases (apart from sponges), they may be no more than the little alveoli of the intracellular protoplasmic network, and this would seem to be the case at least in one known case, that of the protozoan _Entosolenia aspera_, in which, within the vesicular protoplasm of the single cell, Möbius has described tiny spicules in the shape of little tetrahedra with concave sides. It is probably also the case in the small beginnings of the Echinoderm spicules, which are likewise intracellular, and are of similar shape. In the case of our sponges we have many varying conditions, which we need not attempt to examine in detail. In some cases there is evidence for believing that the spicule is formed at the boundaries of true cells or histological units. But in the case of the larger triradiate or tetractinellid spicules of the sponge-body, they far surpass in size the actual “cells”; we find them lying, regularly and symmetrically arranged, between the “pore-canals” or “ciliated chambers,” and it is in conformity with the shape and arrangement of these rounded or spheroidal structures that their shape is assumed.
Again, it is not necessarily at variance with our hypothesis to find that, in the adult sponge, the larger spicules may greatly outgrow the bounds not only of actual cells but also of the ciliated chambers, and may even appear to project freely from the surface of the sponge. For we have already seen that the spicule is capable of growing, without marked change of form, by further deposition, or crystallisation, of layer upon layer of calcareous molecules, even in an artificial solution; and we are entitled to believe that the same process may be carried on in the tissues of the sponge, without greatly altering the symmetry of the spicule, long after it has established its characteristic form of a system of slender trihedral or tetrahedral rays.
Neither is it of great importance to our hypothesis whether the rayed spicule necessarily arises as a single structure, or does so from separate minute centres of aggregation. Minchin has shewn that, in some cases at least, the latter is the case; the spicule begins, he tells us, as three tiny rods, separate from one another, each developed in the interspace between two sister-cells, which are themselves the results of the division of one of a {450} little trio of cells; and the little rods meet and fuse together while still very minute, when the whole spicule is only about 1/200 of a millimetre long. At this stage, it is interesting to learn that the spicule is non-crystalline; but the new accretions of calcareous matter are soon deposited in crystalline form.
This observation threw considerable difficulties in the way of former mechanical theories of the conformation of the spicule, and was quite at variance with Dreyer’s theory, according to which the spicule was bound to begin from a central nucleus coinciding with the meeting-place of the three contiguous cells, or rather the interspace between them. But the difficulty is removed when we import the concept of adsorption; for by this agency it is natural enough, or conceivable enough, that the process of deposition should go on at separate parts of a common system of surfaces; and if the cells tend to meet one another by their interfaces before these interfaces extend to the angles and so complete the polygonal cell, it is again conceivable and natural that the spicule should first arise in the form of separate and detached limbs or rays.
Among the tetractinellid sponges, whose spicules are composed of amorphous silica or opal, all or most of the above-described main types of spicule occur, and, as the name of the group implies, the four-rayed, tetrahedral spicules are especially represented. A somewhat frequent type of spicule is one in which one of the four rays is greatly developed, and the other three constitute small prongs diverging at equal angles from the main or axial ray. In all probability, as Dreyer suggests, we have here had to do with a group of four vesicles, of which three were large and co-equal, while a fourth and very much smaller one lay above and between the other three. In certain cases where we have likewise one large and three much smaller {451} rays, the latter are recurved, as in Fig. 215. This type, save for the constancy of the number of rays, and the limitation of the terminal ones to three, and save also for the more important difference that they occur only at one and not at both ends of the long axis, is similar to the type of spicule illustrated in Fig. 213, which we have explained as being probably developed within an oval cell, by whose walls its branches have been conformed to geodetic curves. But it is much more probable that we have here to do with a spicule developed in the midst of a group of three coequal and more or less elongated or cylindrical cells or vesicles, the long axial ray corresponding to their common line of contact, and the three short rays having each lain in the surface furrow between two out of the three adjacent cells.
Just as in the case of the little curved or S-shaped spicules, formed apparently within the bounds of a single cell, so also in the case of the larger tetractinellid and analogous types do we find among the Holothuroidea the same configurations reproduced as we have dealt with in the sponges. The holothurian spicules are a little less neatly formed, a little rougher, than the sponge-spicules; and certain forms occur among the former group which do not present themselves among the latter; but for the most part a community of type is obvious and striking (Fig. 216).
A curious and, physically speaking, strictly analogous formation to the tetrahedral spicules of the sponges is found in the {452} spores of a certain little group of parasitic protozoa, the Actinomyxidia. These spores are formed from clusters of six cells, of which three come to constitute the capsule of the spore; and this capsule, always triradiate in its symmetry, is in some species drawn out into long rays, of which one constitutes a straight central axis, while the others, coming off from it at equal angles, are recurved in wide circular arcs. The account given of the development of this structure by its discoverers[461] is somewhat obscure to me, but I think that, on physical grounds, there can be no doubt whatever that the quadriradiate capsule has been somehow modelled upon a group of three surrounding cells, its axis lying between the three, and its three radial arcs occupying the furrows between adjacent pairs.
The typically six-rayed siliceous spicules of the hexactinellid sponges, while they are perhaps the most regular and beautifully formed spicules to be found within the entire group, have been found very difficult to explain, and Dreyer has confessed his complete inability to account for their conformation. But, though it is doubtless only throwing the difficulty a little further back, we may so far account for them by considering that the cells or vesicles by which they are conformed are not arranged in {453} what is known as “closest packing,” but in linear series; so that in their arrangement, and by their mutual compression, we tend to get a pattern, not of hexagons, but of squares: or, looking to the solid, not of dodecahedra but of cubes or parallelopipeda. This indeed appears to be the case, not with the individual cells (in the histological sense), but with the larger units or vesicles which make up the body of the hexactinellid. And this being so, the spicules formed between the linear, or cubical series of vesicles, will have the same tendency towards a “hexactinellid” shape, corresponding to the angles and adjacent edges of a system of cubes, as in our former case they had to a triradiate or a tetractinellid form, when developed in connection with the angles and edges of a system of hexagons, or a system of dodecahedra.
Histologically, the case is illustrated by a well-known phenomenon in embryology. In the segmenting ovum, there is a tendency for the cells to be budded off in linear series; and so they often remain, in rows side by side, at least for a considerable time and during the course of several consecutive cell divisions. Such an arrangement constitutes what the embryologists call the “radial type” of segmentation[462]. But in what is described as the “spiral type” of segmentation, it is stated that, as soon as the first horizontal furrow has divided the cells into an upper and a lower layer, those of “the upper layer are shifted in respect to the lower layer, by means of a rotation about the vertical axis[463].” It is, of course, evident that the whole process is merely that which is familiar to physicists as “close packing.” It is a very simple case of what Lord Kelvin used to call “a problem in tactics.” It is a mere question of the rigidity of the system, of the freedom of movement on the part of its constituent cells, whether or at what stage this tendency to slip into the closest propinquity, or position of minimum potential, will be found to manifest itself.
However the hexactinellid spicules be arranged (and this is {454} not at all easy to determine) in relation to the tissues and chambers of the sponge, it is at least clear that, whether they be separate or be fused together (as often happens) in a composite skeleton, they effect a symmetrical partitioning of space according to the cubical system, in contrast to that closer packing which is represented and effected by the tetrahedral system[464].
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This question of the origin and causation of the forms of sponge-spicules, with which we have now briefly dealt, is all the more important and all the more interesting because it has been discussed time and again, from points of view which are characteristic of very different schools of thought in biology. Haeckel found in the form of the sponge-spicule a typical illustration of his theory of “bio-crystallisation”; he considered that these “biocrystals” represented “something midway—_ein Mittelding_—between an inorganic crystal and an organic secretion”; that there was a “compromise between the crystallising efforts of the calcium carbonate and the formative activity of the fused cells of the syncytium”; and that the semi-crystalline secretions of calcium carbonate “were utilised by natural selection as ‘spicules’ for building up a skeleton, and afterwards, by the interaction of adaptation and heredity, became modified in form and differentiated in a vast variety of ways in the struggle for existence[465].” What Haeckel precisely signified by these words is not clear to me.
F. E. Schultze, perceiving that identical forms of spicule were developed whether the material were crystalline or non-crystalline, abandoned all theories based upon crystallisation; he simply saw in the form and arrangement of the spicules something which was “best fitted” for its purpose, that is to say for the support and strengthening of the porous walls of the sponge, and found clear evidence of “utility” in the specific structure of these skeletal elements. {455}
Sollas and Dreyer, as we have seen, introduced in various ways the conception of physical causation,—as indeed Haeckel himself had done in regard to one particular, when he supposed the _position_ of the spicules to be due to the constant passage of the water-currents. Though even here, by the way, if I understand Haeckel aright, he was thinking not merely of a direct or immediate physical causation, but of one manifesting itself through the agency of natural selection[466]. Sollas laid stress upon the “path of least resistance” as determining the direction of growth; while Dreyer dealt in greater detail with the various tensions and pressures to which the growing spicule was exposed, amid the alveolar or vesicular structure which was represented alike by the chambers of the sponge, by the reticulum of constituent cells, or by the minute structure of the intracellular protoplasm. But neither of these writers, so far as I can discover, was inclined to doubt for a moment the received canon of biology, which sees in such structures as these the characteristics of true organic species, and the indications of an hereditary affinity by which blood-relationship and the succession of evolutionary descent throughout geologic time can be ultimately deduced.
Lastly, Minchin, in a well-known paper[467], took sides with Schultze, and gave reasons for dissenting from such mechanical theories as those of Sollas and of Dreyer. For example, after pointing out that all protoplasm contains a number of “granules” or microsomes, contained in the alveolar framework and lodged at the nodes of the reticulum, he argued that these also ought to acquire a form such as the spicules possess, if it were the case that these latter owed their form to their very similar or identical position. “If vesicular tension cannot in any other instance cause the granules at the nodes to assume a tetraxon form, why should it do so for the sclerites?” In all probability the answer to this question is not far to seek. If the force which the “mechanical” hypothesis has in view were simply that of mechanical _pressure_, {456} as between solid bodies, then indeed we should expect that any substances whatsoever, lying between the impinging spheres, would tend (unless they were infinitely hard) to assume the quadriradiate or “tetraxon” form; but this conclusion does not follow at all, in so far as it is to _surface-energy_ that we ascribe the phenomenon. Here the specific nature of the substances involved makes all the difference. We cannot argue from one substance to another; adsorptive attraction shews its effect on one and not on another; and we have not the least reason to be surprised if we find that the little granules of protoplasmic material, which as they lie bathed in the more fluid protoplasm have (presumably, and as their shape indicates) a strong surface-tension of their own, behave towards the adjacent vesicles in a very different fashion to the incipient aggregations of calcareous or siliceous matter in a colloid medium. “The ontogeny of the spicules,” says Professor Minchin, “points clearly to their regular form being a _phylogenetic adaptation, which has become fixed and handed on by heredity, appearing in the ontogeny as a prophetic adaptation_.” And again, “The forms of the spicules are the result of adaptation to the requirements of the sponge as a whole, produced by _the action of natural selection upon variation in every direction_.” It would scarcely be possible to illustrate more briefly and more cogently than by these few words (or the similar words of Haeckel quoted on p. 454), the fundamental difference between the Darwinian conception of the causation and determination of Form, and that which is characteristic of the physical sciences.
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If I have dealt comparatively briefly with the inorganic skeleton of sponges, in spite of the obvious importance of this part of our subject from the physical or mechanical point of view, it has been owing to several reasons. In the first place, though the general trend of the phenomena is clear, it must be at once admitted that many points are obscure, and could only be discussed at the cost of a long argument. In the second place, the physical theory is (as I have shewn) in manifest conflict with the accounts given by various embryologists of the development of the spicules, and of the current biological theories which their descriptions embody; it is beyond our scope to deal with such descriptions {457} in detail. Lastly, we find ourselves able to illustrate the same physical principles with greater clearness and greater certitude in another group of animals, namely the Radiolaria. In our description of the skeletons occurring within this group we shall by no means abandon the preliminary classification of microscopic skeletons which we have laid down; but we shall have occasion to blend with it the consideration of certain other more or less correlated phenomena.
The group of microscopic organisms known as the Radiolaria is extraordinarily rich in diverse forms, or “species.” I do not know how many of such species have been described and defined by naturalists, but some thirty years ago the number was said to be over four thousand, arranged in more than seven hundred genera[468]. Of late years there has been a tendency to reduce the number, it being found that some of the earlier species and even genera are but growth-stages of one and the same form, sometimes mere fragments or “fission-products” common to several species, or sometimes forms so similar and so interconnected by intermediate forms that the naturalist denominates them not “species” but “varieties.” It has to be admitted, in short, that the conception of species among the Radiolaria has not hitherto been, and is not yet, on the same footing as that among most other groups of animals. But apart from the extraordinary multiplicity of forms among the Radiolaria, there are certain other features in this multiplicity which arrest our attention. For instance, the distribution of species in space is curious and vague; many species are found all over the world, or at least every here and there, with no evidence of specific limitations of geographical habitat; others occur in the neighbourhood of the two poles; some are confined to warm and others to cold currents of the ocean. In time also their distribution is not less vague: so much so that it has been asserted of them that “from the Cambrian age downwards, the families and even genera appear identical with those now living.” Lastly, except perhaps in the case of a few large “colonial forms,” we seldom if ever find, as is usual {458} in most animals, a local predominance of one particular species. On the contrary, in a little pinch of deep-sea mud or of some fossil “Radiolarian earth,” we shall probably find scores, and it may be even hundreds, of different forms. Moreover, the radiolarian skeletons are of quite extraordinary delicacy and complexity, in spite of their minuteness and the comparative simplicity of the “unicellular” organisms within which they grow; and these complex conformations have a wonderful and unusual appearance of geometric regularity. All these _general_ considerations seem such as to prepare us for the special need of some physical hypothesis of causation. The little skeletal fabrics remind us of such objects as snow-crystals (themselves almost endless in their diversity), rather than of a collection of distinct animals, constructed in apparent accordance with functional needs, and distributed in accordance with their fitness for particular situations. Nevertheless great efforts have been made of recent years to attach “a biological meaning” to these elaborate structures; and “to justify the hope that in time the utilitarian character [of the skeleton] will be more completely recognised[469].”
In the majority of cases, the skeleton of the Radiolaria is composed, like that of so many sponges, of silica; in one large family, the Acantharia (and perhaps in some others), it is composed, in great part at least, of a very unusual constituent, namely strontium sulphate[470]. There is no fundamental or important morphological character in which the shells formed of these two constituents differ from one another; and in no case can the chemical properties of these inorganic materials be said to influence the form of the complex skeleton or shell, save only in this general way that, by their rigidity and toughness, they may give rise to a fabric far more delicate and slender than we find developed among calcareous organisms.
A slight exception to this rule is found in the presence of true crystals, which occur within the central capsules of certain {459} Radiolaria, for instance the genus Collosphaera[471]. Johannes Müller (whose knowledge and insight never fail to astonish us) remarked that these were identical in form with crystals of celestine, a sulphate of strontium and barium; and Bütschli’s discovery of sulphates of strontium and of barium in kindred forms render it all but certain that they are actually true crystals of celestine[472].
In its typical form, the Radiolarian body consists of a spherical mass of protoplasm, around which, and separated from it by some sort of porous “capsule,” lies a frothy mass, composed of protoplasm honeycombed into a multitude of alveoli or vacuoles, filled with a fluid which can scarcely differ much from sea-water[473]. According to their surface-tension conditions, these vacuoles may appear more or less isolated and spherical, or joining together in a “froth” of polygonal cells; and in the latter, which is the commoner condition, the cells tend to be of equal size, and the resulting polygonal meshwork beautifully regular. In many cases, a large number of such simple individual organisms are associated together, forming a floating colony, and it is highly probable that many other forms, with whose scattered skeletons we are alone acquainted, had in life formed part likewise of a colonial organism.
In contradistinction to the sponges, in which the skeleton always begins as a loose mass of isolated spicules, which only in a few exceptional cases (such as Euplectella and Farrea) fuse into a continuous network, the characteristic feature of the Radiolarians lies in the possession of a continuous skeleton, in the form of a netted mesh or perforated lacework, sometimes however replaced by and often associated with minute independent spicules. Before we proceed to treat of the more complex skeletons, we may begin, then, by dealing with these comparatively simple cases where either the entire skeleton or a considerable part of it is represented, not by a continuous fabric, but by a quantity of loose, separate spicules, or aciculae, which seem, like the spicules of Alcyonium, {460} to be developed as free and isolated formations or deposits, precipitated in the colloid matrix, with no relation of form to the cellular or vesicular boundaries. These simple acicular spicules occupy a definite position in the organism. Sometimes, as for instance among the fresh-water Heliozoa (e.g. Raphidiophrys), they lie on the outer surface of the organism, and not infrequently (when the spicules are few in number) they tend to collect round the bases of the pseudopodia, or around the large radiating spicules, or axial rays, in the cases where these latter are present. When the spicules are thus localised around some prominent centre, they tend to take up a position of symmetry in regard to it; instead of forming a tangled or felted layer, they come to lie side by side, in a radiating cluster round the focus. In other cases (as for instance in the well-known Radiolarian _Aulacantha scolymantha_) the felted layer of aciculae lies at some depth below the surface, forming a sphere concentric with the entire spherical organism. In either case, whether the layer of spicules be deep or be superficial, it tends to mark a “surface of discontinuity,” a meeting place between two distinct layers of protoplasm or between the protoplasm and the water around; and it is obvious that, in either case, there are manifestations of surface-energy at the boundary, which cause the spicules to be retained there, and to take up their position in its plane. The case is somewhat, though not directly, analogous to that of a cirrus cloud, which marks the place of a surface of discontinuity in a stratified atmosphere.
We have, then, to enquire what are the conditions which shall, apart from gravity, confine an extraneous body to a surface-film; and we may do this very simply, by considering the surface-energy of the entire system. In Fig. 218 we have two fluids in contact with one another (let us call them water and protoplasm), and a body (_b_) which may be immersed in either, or may be restricted to the boundary {461} between. We have here three possible “interfacial contacts” each with its own specific surface-energy, per unit of surface area: namely, that between our particle and the water (let us call it α), that between the particle and the protoplasm (β), and that between water and protoplasm (γ). When the body lies in the boundary of the two fluids, let us say half in one and half in the other, the surface-energies concerned are equivalent to (_S_/2)α + (_S_/2)β; but we must also remember that, by the presence of the particle, a small portion (equal to its sectional area _s_) of the original contact-surface between water and protoplasm has been obliterated, and with it a proportionate quantity of energy, equivalent to _s_γ, has been set free. When, on the other hand, the body lies entirely within one or other fluid, the surface-energies of the system (so far as we are concerned) are equivalent to _S_α + _s_γ, or _S_β + _s_γ, as the case may be. According as α be less or greater than β, the particle will have a tendency to remain immersed in the water or in the protoplasm; but if (_S_/2)(α + β) − _s_γ be less than either _S_α or _S_β, then the condition of minimal potential will be found when the particle lies, as we have said, in the boundary zone, half in one fluid and half in the other; and, if we were to attempt a more general solution of the problem, we should evidently have to deal with possible conditions of equilibrium under which the necessary balance of energies would be attained by the particle rising or sinking in the boundary zone, so as to adjust the relative magnitudes of the surface-areas concerned. It is obvious that this principle may, in certain cases, help us to explain the position even of a _radial_ spicule, which is just a case where the surface of the solid spicule is distributed between the fluids with a minimal disturbance, or minimal replacement, of the original surface of contact between the one fluid and the other.
In like manner we may provide for the case (a common and an important one) where the protoplasm “creeps up” the spicule, covering it with a delicate film. In Acanthocystis we have yet another special case, where the radial spicules plunge only a certain distance into the protoplasm of the cell, being arrested at a boundary-surface between an inner and an outer layer of cytoplasm; here we have only to assume that there is a tension {462} at this surface, between the two layers of protoplasm, sufficient to balance the tensions which act directly on the spicule[474].
In various Acanthometridae, besides such typical characters as the radial symmetry, the concentric layers of protoplasm, and the capillary surfaces in which the outer, vacuolated protoplasm is festooned upon the projecting radii, we have another curious feature. On the surface of the protoplasm where it creeps up the sides of the long radial spicules, we find a number of elongated bodies, forming in each case one or several little groups, and lying neatly arranged in parallel bundles. A Russian naturalist, Schewiakoff, whose views have been accepted in the text-books, tells us that these are muscular structures, serving to raise or lower the conical masses of protoplasm about the radial spicules, which latter serve as so many “tent-poles” or masts, on which the protoplasmic membranes are hoisted up; and the little elongated bodies are dignified with various names, such as “myonemes” or “myophriscs,” in allusion to their supposed muscular nature[475]. This explanation is by no means convincing. To begin with, we have precisely similar festoons of protoplasm in a multitude of other cases where the “myonemes” are lacking; from their minute size (·006–·012 mm.) and the amount of contraction they are said to be capable of, the myonemes can hardly be very efficient instruments of traction; and further, for them to act (as is alleged) for a specific purpose, namely the “hydrostatic regulation” of the organism giving it power to sink or to swim, would seem to imply a mechanism of action and of coordination which is difficult to conceive in these minute and simple organisms. The fact is (as it seems to me), that the whole method of explanation is unnecessary. Just as the supposed “hauling up” of the protoplasmic festoons is at once explained by capillary phenomena, so also, in all probability, is the position and arrangement of the little elongated bodies. Whatever the actual nature of these bodies may be, whether they are truly portions of differentiated protoplasm, or whether they are foreign bodies or spicular structures (as bodies occupying a similar position in other cases undoubtedly are), we can explain their situation on the surface {463} of the protoplasm, and their arrangement around the radial spicules, all on the principles of surface-tension[476].
This last case is not of the simplest; and I do not forget that my explanation of it, which is wholly theoretical, implies a doubt of Schewiakoff’s statements, which are founded on direct personal observation. This I am none too willing to do; but whether it be justly done in this case or not, I hold that it is in principle justifiable to look with great suspicion upon a number of kindred statements where it is obvious that the observer has left out of account the purely physical aspect of the phenomenon, and all the opportunities of simple explanation which the consideration of that aspect might afford.
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Whether it be wholly applicable to this particular and complex case or no, our general theorem of the localisation and arrestment of solid particles in a surface-film is of very great biological importance; for on it depends the power displayed by many little naked protoplasmic organisms of covering themselves with an “agglutinated” shell. Sometimes, as in _Difflugia_, _Astrorhiza_ (Fig. 219) and others, this covering consists of sand-grains picked up from the surrounding medium, and sometimes, on the other hand, as in _Quadrula_, it consists of solid particles which are said to arise, as inorganic deposits or concretions, within the protoplasm itself, and which find their way outwards to a position of equilibrium in the surface-layer; and in both cases, the mutual capillary attractions between the particles, confined to the boundary-layer but enjoying a certain measure of freedom therein, tends to the orderly arrangement of the particles one with another, and even to the appearance of a regular “pattern” as the result of this arrangement.
The “picking up” by the protoplasmic organism of a solid particle with which “to build its house” (for it is hard to avoid this customary use of anthropomorphic figures of speech, misleading though they be), is a physical phenomenon kindred to that by which an Amoeba “swallows” a particle of food. This latter process has been reproduced or imitated in various pretty experimental {465} ways. For instance, Rhumbler has shewn that if a thread of glass be covered with shellac and brought near a drop of chloroform suspended in water, the drop takes in the spicule, robs it of its shellac covering, and then passes it out again[477]. It is all a question of relative surface-energies, leading to different degrees of “adhesion” between the chloroform and the glass or its covering. Thus it is that the Amoeba takes in the diatom, dissolves off its proteid covering, and casts out the shell.
Furthermore, as the whole phenomenon depends on a distribution of surface-energy, the amount of which is specific to certain particular substances in contact with one another, we have no difficulty in understanding the _selective action_, which is very often a conspicuous feature in the phenomenon[478]. Just as some caddis-worms make their houses of twigs, and others of shells and again others of stones, so some Rhizopods construct their agglutinated “test” out of stray sponge-spicules, or frustules of diatoms, or again of tiny mud particles or of larger grains of sand. In all these cases, we have apparently to deal with differences in specific {466} surface-energies, and also doubtless with differences in the total available amount of surface-energy in relation to gravity or other extraneous forces. In my early student days, Wyville Thomson used to tell us that certain deep-sea “Difflugias,” after constructing a shell out of particles of the black volcanic sand common in parts of the North Atlantic, finished it off with “a clean white collar” of little grains of quartz. Even this phenomenon may be accounted for on surface-tension principles, if we assume that the surface-energy ratios have tended to change, either with the growth of the protoplasm or by reason of external variation of temperature or the like; and we are by no means obliged to attribute the phenomenon to a manifestation of volition, or taste, or aesthetic skill, on the part of the microscopic organism. Nor, when certain Radiolaria tend more than others to attract into their own substance diatoms and such-like foreign bodies, is it scientifically correct to speak, as some text-books do, of species “in which diatom selection has become _a regular habit_.” To do so is an exaggerated misuse of anthropomorphic phraseology.
The formation of an “agglutinated” shell is thus seen to be a purely physical phenomenon, and indeed a special case of a more general physical phenomenon which has many other important consequences in biology. For the shell to assume the solid and permanent character which it acquires, for instance, in Difflugia, we have only to make the additional assumption that some small quantities of a cementing substance are secreted by the animal, and that this substance flows or creeps by capillary attraction between all the interstices of the little quartz grains, and ends by binding them all firmly together. Rhumbler[479] has shewn us how these agglutinated tests, of spicules or of sand-grains, can be precisely imitated, and how they are formed with greater or less ease, and greater or less rapidity, according to the nature of the materials employed, that is to say, according to the specific surface-tensions which are involved. For instance if we mix up a little powdered glass with chloroform, and set a drop of the mixture in water, the glass particles gather neatly round the surface of the drop so quickly that the eye cannot follow the {467} operation. If we perform the same experiment with oil and fine sand, dropped into 70 per cent. alcohol, a still more beautiful artificial Rhizopod shell is formed, but it takes some three hours to do.
It is curious that, just at the very time when Rhumbler was thus demonstrating the purely physical nature of the Difflugian shell, Verworn was studying the same and kindred organisms from the older standpoint of an incipient psychology[480]. But, as Rhumbler himself admits, Verworn was very careful not to overestimate the apparent signs of volition, or selective choice, in the little organism’s use of the material of its dwelling.
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This long parenthesis has led us away, for the time being, from the subject of the Radiolarian skeleton, and to that subject we must now return. Leaving aside, then, the loose and scattered spicules, which we have sufficiently discussed, the more perfect Radiolarian skeletons consist of a continuous and regular structure; and the siliceous (or other inorganic) material of which this framework is composed tends to be deposited in one or other of two ways or in both combined: (1) in the form of long spicular axes, usually conjoined at, or emanating from, the centre of the protoplasmic body, and forming a symmetric radial system; (2) in the form of a crust, developed in various ways, either on the outer surface of the organism or in relation to the various internal surfaces which separate its concentric layers or its component vesicles. Not unfrequently, this superficial skeleton comes to constitute a spherical shell, or a system of concentric or otherwise associated spheres.
We have already learned that a great part of the body of the Radiolarian, and especially that outer portion to which Haeckel has given the name of the “calymma,” is built up of a great mass of “vesicles,” forming a sort of stiff froth, and equivalent in the physical sense (though not necessarily in the biological sense) to “cells,” inasmuch as the little vesicles have their own well-defined boundaries, and their own surface phenomena. In short, all that we have said of cell-surfaces, and cell conformations, in our discussion of cells and of tissues, will apply in like manner, and under appropriate conditions, to these. In certain cases, even in {468} so common and simple a one as the vacuolated substance of an Actinosphaerium, we may see a very close resemblance, or formal analogy, to an ordinary cellular or “parenchymatous” tissue, in the close-packed arrangement and consequent configuration of these vesicles, and even at times in a slight membranous hardening of their walls. Leidy has figured[481] some curious little bodies, like small masses of consolidated froth, which seem to be nothing else than the dead and empty husks, or filmy skeletons, of Actinosphaerium. And Carnoy[482] has demonstrated in certain cell-nuclei an all but precisely similar framework, of extreme delicacy and minuteness, as the result of partial solidification of interstitial matter in a close-packed system of alveoli (Fig. 220).
Let us now suppose that, in our Radiolarian, the outer surface of the animal is covered by a layer of froth-like vesicles, uniform or nearly so in size. We know that their tensions will tend to conform them into a “honeycomb,” or regular meshwork of hexagons, and that the free end of each hexagonal prism will be a little spherical cap. Suppose now that it be at the outer surface of the protoplasm (that namely which is in contact with the surrounding sea-water), that the siliceous particles have a tendency to be secreted or adsorbed; it will at once follow that they will show a tendency to aggregate in the grooves which separate the vesicles, and the result will be the development of a most delicate sphere composed of tiny rods arranged in a regular hexagonal network (e.g. _Aulonia_). Such a conformation is {469} extremely common, and among its many variants may be found cases in which (e.g. _Actinomma_), the vesicles have been less regular in size, and some in which the hexagonal meshwork has been developed not only on one outer surface, but at successive {470} surfaces, producing a system of concentric spheres. If the siliceous material be not limited to the linear junctions of the cells, but spread over a portion of the outer spherical surfaces or caps, then we shall have the condition represented in Fig. 223 (_Ethmosphaera_), where the shell appears perforated by circular instead of hexagonal apertures, and the circular pores are set on slight spheroidal eminences; and, interconnected with such types as this, we have others in which the accumulating pellicles of skeletal matter have extended from the edges into the substance of the boundary walls and have so produced a system of films, normal to the surface of the sphere, constituting a very perfect honeycomb, as in _Cenosphaera favosa_ and _vesparia_[483].
In one or two very simple forms, such as the fresh-water _Clathrulina_, just such a spherical perforated shell is produced out of some organic, acanthin-like substance; and in some examples of _Clathrulina_ the chitinous lattice-work of the shell is just as {471} regular and delicate, with the meshes just as beautifully hexagonal, as in the siliceous shells of the oceanic Radiolaria. This is only another proof (if proof be needed) that the peculiar conformation of these little skeletons is not due to the material of which they are composed, but to the moulding of that material upon an underlying vesicular structure.
Let us next suppose that, upon some such lattice-work as has just been described, another and external layer of cells or vesicles is developed, and that instead of (or perhaps only in addition to) a second hexagonal lattice-work, which might develop concentrically to the first in the boundary-furrows of this new layer of cells, the siliceous matter now tends to be deposited radially, or normally to the surface of the sphere, just in the lines where the external layer of vesicles meet one another, three by three. The result will be that, when the vesicles themselves are removed, a series of radiating spicules will be revealed, directed outwards from each of the angles of the original hexagon; as is seen in Fig. 225. And it may further happen that these radiating skeletal rods are continued at their distal ends into divergent rays, forming a triple fork, and corresponding (after a fashion {472} which we have already described as occurring in certain sponge-spicules) to the three superficial furrows between the adjacent cells. This last is, as it were, an intermediate stage between the simple rods and the complete formation of another concentric sphere of latticed hexagons. Another possible case is when the large and uniform vesicles of the outer protoplasm are mixed with, or replaced by, much smaller vesicles, piled on one another in more or less concentric layers; in this case the radiating rods will no longer be straight, but will be bent into a zig-zag pattern, with angles in three vertical planes, corresponding to the successive contacts of the groups of cells around the axis (Fig. 226).
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Among a certain group called the Nassellaria, we find geometrical forms of peculiar simplicity and beauty,—such for instance as that which I have represented in Fig. 227. It is obvious at a glance that this is such a skeleton as may have been formed {473} (I think we may go so far as to say _must_ have been formed) at the interfaces of a little tetrahedral group of cells, the four equal cells of the tetrahedron being in this particular case supplemented by a little one in the centre of the system. We see, precisely as in the internal boundary-system of an artificial group of four soap-bubbles, the plane surfaces of contact, six in number; the relation to one another of each triple set of interfacial planes, meeting one another at equal angles of 120°; and finally the relation of the four lines or edges of triple contact, which tend (but for the little central vesicle) to meet at co-equal solid angles in the centre of the system, all as we have described on p. 318. In short, each triple-walled re-entrant angle of the little shell has essentially the configuration (or a part thereof) of what we have called a “Maraldi pyramid” in our account of the architecture of the honeycomb, on p. 329[484].
There are still two or three remarkable or peculiar features in this all but mathematically perfect shell, and they are in part easy and in part they seem more difficult of interpretation.
We notice that the amount of solid matter deposited in the plane interfacial boundaries is greatly increased at the outer margin of each boundary wall, where it merges or coincides with the superficial furrow which separates the free, spherical surfaces of the bubbles from one another; and we may sometimes find that, along these edges, the skeleton remains complete and strong, while it shows signs of imperfect development or of breaking away over great part of the rest of the interfacial surfaces. In this there is nothing anomalous, for we have already recognised that it is at the edges or margins of the interfacial partition-walls that the manifestation of surface-energy will tend to reach its maximum. And just as we have seen that, in certain of our “multicellular” spherical Radiolarians, it is at the superficial {474} edges or borders of the partitions, and here only, that skeletal formation occurs (giving rise to the netted shell with its hexagonal meshes of Fig. 221), so also at times, in the case of such little aggregates of cells or vesicles as the four-celled system of Callimitra, it may happen that about the external boundary-_lines_, and not in the interior boundary-_planes_, the whole of the skeletal matter is aggregated. In Fig. 228 we see a curious little skeletal structure or complex spicule, whose conformation is easily accounted for after this fashion. Little spicules such as this form isolated portions of the skeleton in the genus _Dictyocha_, and occur scattered over the spherical surface of the organism (Fig. 229). The more or less basket-shaped spicule has evidently been developed about a little cluster of four cells or vesicles, lying in or on the plane of the surface of the organism, and therefore arranged, not in the tetrahedral form of Callimitra, but in the manner in which four contiguous cells lying side by side normally set themselves, like the four cells of a segmenting egg: that is to say with an intervening “polar furrow,” whose ends mark the meeting place, at equal angles, of the cells in groups of three.
The little projecting spokes, or spikes, which are set normally to the main basket-work, seem to be incompleted portions of a larger basket, or in other words imperfectly formed elements corresponding to the interfacial contacts in the surrounding parts {475} of the system. Similar but more complex formations, all explicable as basket-like frameworks developed around a cluster of cells, are known in great variety.
In our Nassellarian itself, and in many other cases where the plane interfacial boundary-walls are skeletonised, we see that the siliceous matter is not deposited in an even and continuous layer, like the waxen walls of a bee’s cell, but constitutes a meshwork of fine curvilinear threads; and the curves seem to run, on the whole, isogonally, and to form three main series, one approximately parallel to, or concentric with, the outer or free edge of the partition, and the other two related severally to its two edges of attachment. Sometimes (as may also be seen in our figure), the system is still further complicated by a fourth series of linear elements, which tend to run radially from the centre of the system to the free edge of each partition. As regards the former, their arrangement is such as would result if deposition or solidification had proceeded in waves, starting independently from each of the three boundaries of the little partition-wall; and something of this kind is doubtless what has happened. We are reminded at once of the wave-like periodicity of the Liesegang phenomenon. But apart from this we might conceive of other explanations. For instance, the liquid film which originally constitutes the partition must easily be thrown into _vibrations_, and (like the dust upon a Chladni’s plate) minute particles of matter in contact with the film would tend to take up their position in a symmetrical arrangement, in direct relation to the nodal points or lines of the vibrating surface[485]. Some such explanation as this (to my thinking) must be invoked to account for the minute and varied and very beautiful patterns upon many diatoms, the resemblance of which patterns (in certain of their simpler cases) to the Chladni figures is sometimes striking and obvious. But the many special problems which the diatom skeleton suggests I have not attempted to consider.
The last peculiarity of our Nassellarian lies in an apparent departure from what we should at first expect in the way of its {476} external symmetry. Were the system actually composed of four spherical vesicles in mutual contact, the outer margin of each of the six interfacial planes would obviously be a circular arc; and accordingly, at each angle of the tetrahedron, we should expect to have a depressed, or re-entrant angle, instead of a prominent cusp. This is all doubtless due to some simple balance of tensions, whose precise nature and distribution is meanwhile a matter of conjecture. But it seems as though an extremely simple explanation would go a long way, and possibly the whole way, to meet this particular case. In our ordinary plane diagram of three cells, or soap-bubbles, in contact, we know (and we have just said) that the tensions of the three partitions draw inwards the outer walls of the system, till at each point of triple contact (_P_) we tend to get a triradiate, equiangular junction. But if we introduce another bubble into the centre of the system (Fig. 230), then, as Plateau shewed, the tensions of its walls and those of the three partitions by which it is now suspended, again balance one another, and the central bubble appears (in plane projection) as a curvilinear, equilateral triangle. We have only got to convert this plane diagram into that of a tetrahedral solid to obtain _almost_ precisely the configuration which we are seeking to explain. Now we observe that, so far as our figure of Callimitra informs us, this is just the shape of the little bubble which occupies the centre of the tetrahedral system in that Radiolarian skeleton. And I conceive, accordingly, that the entire organism was not limited to the four cells or vesicles (together with the little central {477} fifth) which we have hitherto been imagining, but there must have been an outer tetrahedral system, enclosing the cells which fabricated the skeleton, just as these latter enclosed, and deformed, the little bubble in the centre of all. We have only to suppose that this hypothetical tetrahedral series, forming the outer layer or surface of the whole system, was for some chemico-physical reason incapable of secreting at its interfacial contacts a skeletal fabric[486].
In this hypothetical case, the edges of the skeletal system would be circular arcs, meeting one another at an angle of 120°, or, in the solid pyramid, of 109°: and this latter is _very nearly_ the condition which our little skeleton actually displays. But we observe in Fig. 227 that, in the immediate neighbourhood of the tetrahedral angle, the circular arcs are slightly drawn out into projecting cusps (cf. Fig. 230, _B_). There is no S-shaped curvature of the tetrahedral edges as a whole, but a very slight one, a very slight change of curvature; close to the apex. This, I conceive, is nothing more than what, in a material system, we are bound to have, to represent a “surface of continuity.” It is a phenomenon precisely analogous to Plateau’s “bourrelet,” which we have already seen to be a constant feature of all cellular systems, rounding off the sharp angular contacts by which (in our more elementary treatment) we expect one film to make its junction with another[487].
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In the foregoing examples of Radiolaria, the symmetry which the organism displays would seem to be identical with that symmetry of forces which is due to the assemblage of surface-tensions in the whole system; this symmetry being displayed, in one class of cases, in a complex spherical mass of froth, and in {478} another class in a simpler aggregate of a few, otherwise isolated, vesicles. But among the vast number of other known Radiolaria, there are certain forms (especially among the Phaeodaria and Acantharia) which display a still more remarkable symmetry, the origin of which is by no means clear, though surface-tension doubtless plays a part in its causation. These are cases in which (as in some of those already described) the skeleton consists (1) of radiating spicular rods, definite in number and position, and (2) of interconnecting rods or plates, tangential to the more or less spherical body of the organism, whose form becomes, accordingly, that of a geometric, polyhedral solid. It may be that there is no mathematical difference, save one of degree, between such a hexagonal polyhedron as we have seen in _Aulacantha_, and those which we are about to describe; but the greater regularity, the numerical symmetry, and the apparent simplicity of these latter, makes of them a class apart, and suggests problems which have not been solved nor even investigated.
The matter is sufficiently illustrated by the accompanying figures, all drawn from Haeckel’s Monograph of the Challenger Radiolaria[488]. In one of these we see a regular octahedron, in another a regular, or pentagonal dodecahedron, in a third a regular icosahedron. In all cases the figure appears to be perfectly symmetrical, though neither the triangular facets of the octahedron and icosahedron, nor the pentagonal facets of the dodecahedron, are necessarily plane surfaces. In all of these cases, the radial spicules correspond to the solid angles of the figure; and they are, accordingly, six in number in the octahedron, twenty in the dodecahedron, and twelve in the icosahedron. If we add to these three figures the regular tetrahedron, which we have had frequent occasion to study, and the cube (which is represented, at least in outline, in the skeleton of the hexactinellid sponges), we have completed the series of the five regular polyhedra known to geometers, the _Platonic bodies_[489] of the older mathematicians. It is at first sight all the more remarkable that we should here meet {480} with the whole five regular polyhedra, when we remember that, among the vast variety of crystalline forms known among minerals, the regular dodecahedron and icosahedron, simple as they are from the mathematical point of view, never occur. Not only do these latter never occur in Crystallography, but (as is explained in text-books of that science) it has been shewn that they cannot occur, owing to the fact that their indices (or numbers expressing the relation of the faces to the three primary axes) involve an irrational quantity: whereas it is a fundamental law of crystallography, involved in the whole theory of space-partitioning, that “the indices of any and every face of a crystal are small whole numbers[490].” At the same time, an imperfect pentagonal dodecahedron, whose pentagonal sides are non-equilateral, is common among crystals. If we may safely judge from Haeckel’s figures, the pentagonal dodecahedron of the Radiolarian is perfectly regular, and we must presume, accordingly, that it is not brought about by principles of space-partitioning similar to those which manifest themselves in the phenomenon of crystallisation. It will be observed that in all these radiolarian polyhedral shells, the surface of each external facet is formed of a minute hexagonal network, whose probable origin, in relation to a vesicular structure, is such as we have already discussed.
In certain allied Radiolaria (Fig. 232), which, like the dodecahedral form figured in Fig. 231, 5, have twenty radial spines, these latter are commonly described as being arranged in a certain very singular way. It is stated that their arrangement may be referred {481} to a series of five parallel circles on the sphere, corresponding to the equator (_c_), the tropics (_b_, _d_) and the polar circles (_a_, _e_); and that beginning with four equidistant spines in the equator, we have alternating whorls of four, radiating outwards from the sphere in each of the other parallel zones. This rule was laid down by the celebrated Johannes Müller, and has ever since been used and quoted as Müller’s law. The chief point in this alleged arrangement which strikes us at first sight as very curious, is that there is said to be no spine at either pole; and when we come to examine carefully the figure of the organism, we find that the received description does not do justice to the facts. We see, in the first place, from such figures as Figs. 232, 234, that here, unlike our former cases, the radial spines issue through the facets (and through _all_ the facets) of the polyhedron, instead of through its solid angles; and accordingly, that our twenty spines correspond (not, as before, to a dodecahedron) but to some sort of an icosahedron. We see in the next place, that this icosahedron is composed of faces, or plates, of two different kinds, some hexagonal and some pentagonal; and when we look closer, we discover that the whole figure is that of a hexagonal prism, whose twelve solid angles are replaced by pentagonal facets. Both hexagons and pentagons {482} appear to be perfectly equilateral, but if we try to construct a plane-sided polyhedron of this kind, we soon find that it is impossible; for into the angles between the six equatorial hexagons those of the six united pentagons will not fit. The figure however can be easily constructed if we replace the straight edges (or some of them) by curves, and the plane facets by corresponding, slightly curved, surfaces. The true symmetry of this figure, then, is hexagonal, with a polar axis, produced into two polar spicules; with six equatorial spicules, or rays; and with two sets of six spicular rays, interposed between the polar axis and the equatorial rays, and alternating in position with the latter.
Müller’s description was emended by Brandt, and what is now known as “Brandt’s law,” viz. that the symmetry consists of two polar rays, and three whorls of six each, coincides with the above description so far as the spicular axes go: save only that Brandt specifically states that the intermediate whorls stand equidistant between the equator and the poles, i.e. in latitude 45°. While not far from the truth, this statement is not exact; for according to the geometry of the figure, the intermediate cycles obviously stand in a slightly higher latitude, but this latitude I have not attempted to determine; for the calculation seems to be a little troublesome owing to the curvature of the sides of the figure, and the enquiring mathematician will perform it more easily than I. Brandt, if I understand him rightly, did not propose his “law” as a substitute for Müller’s law, but as a second law applicable to a few particular cases. I on the other hand can find no case to which Müller’s law properly applies.
If we construct such a polyhedron, and set it in the position of Fig. 232, _B_, we shall easily see that it is capable of explanation (though improperly) in accordance with Müller’s law; for the four equatorial rays of Müller (_c_) now correspond to the two polar and to two opposite equatorial facets of our polyhedron: the four “polar” rays of Müller (_a_ or _e_) correspond to two adjacent hexagons and two intermediate pentagons of the figure: and Müller’s “tropical” rays (_b_ or _d_) are those which emanate from the remaining four pentagonal facets, in each half of the figure. In some cases, such as Haeckel’s _Phatnaspis cristata_ (Fig. 233), we have an ellipsoidal body, from which the spines emerge in the order described, but which is not obviously divided by facets. In Fig. 234 I have indicated the facets corresponding to the rays, and dividing the surface in the usual symmetrical way. {483}
{484}
Within any polyhedron we may always inscribe another polyhedron, whose corners correspond in number to the sides or facets of the original figure, or (in alternative cases) to a certain number of these sides; and a similar result is obtained by bevelling off the corners of the original polyhedron. We may obtain a precisely similar symmetrical result if (in such a case as these Radiolarians which we are describing), we imagine the radial spines to be interconnected by tangential rods, instead of by the complete facets which we have just been dealing with. In our complicated polyhedron with its twenty radial spines arranged in the manner described there are various symmetrical ways in which we may imagine these interconnecting bars to be arranged. The most symmetrical of these is one in which the whole surface is divided into eighteen rhomboidal areas, obtained by systematically connecting each group of four adjacent radii. This figure has eighteen faces (_F_), twenty corners (_C_), and therefore thirty-six edges (_E_), in conformity with Euler’s theorem, _F_ + _C_ = _E_ + 2.
Another symmetrical arrangement will divide the surface into fourteen rhombs and eight triangles. This latter arrangement is obtained by linking up the radial rods as follows: _aaaa_, _aba_, _abcb_, _bcdc_, etc. Here we have again twenty corners, but we have twenty-two faces; the number of edges, or tangential spicular bars, will be found, therefore, by the above formula, to be forty. In Haeckel’s figure of _Phractaspis prototypus_ we have a spicular skeleton which appears to be constructed precisely upon this plan, and to be derivable from the faceted polyhedron precisely after this manner.
In all these latter cases it is the arrangement of the axial rods, or in other words the “polar symmetry” of the entire organism, which lies at the root of the matter, and which, if only {485} we could account for it, would make it comparatively easy to explain the superficial configuration. But there are no obvious mechanical forces by which we can so explain this peculiar polarity. This at least is evident, that it arises in the central mass of protoplasm, which is the essential living portion of the organism as distinguished from that frothy peripheral mass whose structure has helped us to explain so many phenomena of the superficial or external skeleton. To say that the arrangement depends upon a specific polarisation of the cell is merely to refer the problem to other terms, and to set it aside for future solution. But it is possible that we may learn something about the lines in which _to seek for_ such a solution by considering the case of Lehmann’s “fluid crystals,” and the light which they throw upon the phenomena of molecular aggregation.
The phenomenon of “fluid crystallisation” is found in a number of chemical bodies; it is exhibited at a specific temperature for each substance; and it would seem to be limited to bodies in which there is a more or less elongated, or “chain-like” arrangement of the atoms in the molecule. Such bodies, at the appropriate temperature, tend to aggregate themselves into masses, which are sometimes spherical drops or globules (the so-called “spherulites”), and sometimes have the definite form of needle-like or prismatic crystals. In either case they remain liquid, and are also doubly refractive, polarising light in brilliant colours. Together with them are formed ordinary solid crystals, also with characteristic polarisation, and into such solid crystals all the fluid material ultimately turns. It is evident that in these liquid crystals, though the molecules are freely mobile, just as are those of water, they are yet subject to, or endowed with, a “directive force,” a force which confers upon them a definite configuration or “polarity,” the _Gestaltungskraft_ of Lehmann.
Such an hypothesis as this had been gradually extruded from the theories of mathematical crystallography[491]; and it had come to be believed that the symmetrical conformation of a homogeneous crystalline structure was sufficiently explained by the mere mechanical fitting together of appropriate structural units along the easiest and simplest lines of “close packing”: just as {486} a pile of oranges becomes definite, both in outward form and inward structural arrangement, without the play of any _specific_ directive force. But while our conceptions of the tactical arrangement of crystalline molecules remain the same as before, and our hypotheses of “modes of packing” or of “space-lattices” remain as useful as ever for the definition and explanation of the molecular arrangements, an entirely new theoretical conception is introduced when we find such space-lattices maintained in what has hitherto been considered the molecular freedom of a liquid field; and we are constrained, accordingly, to postulate a specific molecular force, or “Gestaltungskraft” (not unlike Kepler’s “facultas formatrix”), to account for the phenomenon.
Now just as some sort of specific “Gestaltungskraft” had been of old the _deus ex machina_ accounting for all crystalline phenomena (_gnara totius geometriæ, et in ea exercita_, as Kepler said), and as such an hypothesis, after being dethroned and repudiated, has now fought its way back and has made good its right to be heard, so it may be also in biology. We begin by an easy and general assumption of _specific properties_, by which each organism assumes its own specific form; we learn later (as it is the purpose of this book to shew) that throughout the whole range of organic morphology there are innumerable phenomena of form which are not peculiar to living things, but which are more or less simple manifestations of ordinary physical law. But every now and then we come to certain deep-seated signs of protoplasmic symmetry or polarisation, which seem to lie beyond the reach of the ordinary physical forces. It by no means follows that the forces in question are not essentially physical forces, more obscure and less familiar to us than the rest; and this would seem to be the crucial lesson for us to draw from Lehmann’s surprising and most beautiful discovery. For Lehmann seems actually to have demonstrated, in non-living, chemical bodies, the existence of just such a determinant, just such a “Gestaltungskraft,” as would be of infinite help to us if we might postulate it for the explanation (for instance) of our Radiolarian’s axial symmetry. But further than this we cannot go; for such analogy as we seem to see in the Lehmann phenomenon soon evades us, and refuses to be pressed home. Not only is it the case, as we have already {487} seen, that certain of the geometric forms assumed by the symmetrical Radiolarian shells are just such as the “space-lattice” theory would seem to be inapplicable to, but it is in other ways obvious that symmetry of _crystallisation_, whether liquid or solid, has no close parallel, but only a series of analogies, in the protoplasmic symmetry of the living cell.
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