On Growth and Form

+ As a matter of fact, the phenomena associated with the development of an “ocellus” are or may be of great complexity, inasmuch as they involve not only a graded distribution of pigment, but also, in “optical” coloration, a symmetrical distribution of structure or form. The subject therefore deserves very careful discussion, such as Bateson gives to it (Variation, chap. xii). This, by the way, is one of the very rare cases in which Bateson appears inclined to suggest a purely physical explanation of an organic phenomenon: “The suggestion is strong that the whole series of rings (in Morpho) may have been formed by some one central disturbance, somewhat as a series of concentric waves may be formed by the splash of a stone thrown into a pool, etc.”

t Cf. also Sir D. Brewster, On optical properties of Mother of Pearl, Phil. Tans. 1814, p. 397. § Biedermann, W., Ueber die Bedeutung von Kristallisationsprozessen der Skelette wirbelloser Thiere, namentlich der Molluskenschalen, Z. f. allg. Physiol. I, p. 154, 1902; Ueber Bau und Entstehung der Molluskenschale, Jen. Zeitschr. Xxxvi, pp. 1-164, 1902. Cf. also Stemmann, Ueber Schale und Kalksteinbildungen, 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 ike manner, to the belief that they indicate a diurnal and nocturnal periodicity of activity and rest*.

That this is actually the case in growing starch-grains is generally believed, on the authority of Meyer}; 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 hke 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, Fig. 209. Otoliths of Plaice, showing are extremely well marked even four zones or “age-rings.”” (After jn the case of some fishes which Wallace.)

* Cf. Biitschli, Ueber die Herstellung kiinstlicher Stirkek6rner oder von Spharokrystallen der Stiirke, Verh. nat. med. Ver. Heidelberg, v, pp. 457-472, 1896. + Untersuchungen iiber die Stdrkekérner, Jena, 1905. 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*. 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 asswme 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+’: 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 f.

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 .+ The anhydrite is sulphate of lime (CaSO,); the polyhalite is a triple sulphate of lime, magnesia and potash (2CaSO,. MgSO,. K,SO,+ 2H,0). t Cf. van’t Hoff, Physical Chemistry in the Service of the Sciences, p. 99 seq, Chicago, 1903. 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 Biitschli* 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 organismy. 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

+ Pauli, W. u. Samec, M., Ueber Loslichkeitsbeeinfliissung von Elektrolyten durch Eiweisskérper, Biochem. Zeitschr. xvu, p. 235, 1910. Some of these results 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 catabole 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*; 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 whcelly 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 szlica, in presence of organic colloids. 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 7.

* Which, in 1000 parts of ash, contains about 840 parts of phosphate and 76 parts of calcium carbonate. + Cf. Dreyer, Fr., Die Principien der Geriistbildung bei Rhizopoden, Spongien und Echinodermen, Jen. Zeitschr. xxvi, pp. 204-468, 1892. 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 1s to say as the direct result of chemical or physical phenomena associated with the deposition of lime or of silica in presence of colloids*. This is the case, for instance, with various small spicules of a globular or spheroidal form, formed of amorphous silica, con-

Fig. 210. Close-packed calcospherites, or so-called “spicules,” of Astrosclera. (After Lister.) centrically striated within, and often developing irregular knobs or tiny tubercles over their surfaces. In the aberrant sponge Astrosclerat, we have, to begin with, rounded, striated discs or globules, which in like manner are nothing more or less than the * In an anomalous and very remarkable Australian sponge, just described by Professor Dendy (Nature, May 18, 1916, p. 253) under the name of Collosclerophora, the spicules are “gelatinous,” consisting of a gel of colloid silica with a high percentage of water. It is not stated whether an organic colloid is present together with the silica. These gelatinous spicules arise as exudations on the outer surface of cells, and come to lie in intercellular spaces or vesicles.

“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*. 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 crystalhsation 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 im this irregular form when the supply of material has become relatively scanty.

Our few foregoing examples, diverse as they are in look and kind and ranging from the spicules of Astrosclera or Aleyonium 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,

* The peculiar spicules of Astrosclera are now said to consist of spherules, or calcospherites, of aragonite, spores of a certain red seaweed forming the nuclei, or starting-points, of the concretions (R. Kirkpatrick, Proc. R. S. Lxxxtv (B), p. 579, 1911. 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.

Tn contrast to these massi¥e 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

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. .

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 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 ine 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.

For obviously, 1f they le 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 le 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 he, 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 le 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 threadlike axis; and let us suppose that it is confined either within a cell-wall or in adhesion thereto: it at once follows that its lne 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

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 VO. ito, dimear 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 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 dise 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 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*. 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.

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.