CHAPTER XII

THE SPIRAL SHELLS OF THE FORAMINIFERA

We have already dealt in a few simple cases with the shells of the Foraminifera[538]; and we have seen that wherever the shell is but a single unit or single chamber, its form may be explained in general by the laws of surface tension: the assumption being that the little mass of protoplasm which makes the simple shell behaves as a _fluid drop_, the form of which is perpetuated when the protoplasm acquires its solid covering. Thus the spherical Orbulinae and the flask-shaped Lagenae represent drops in equilibrium, under various conditions of freedom or constraint; while the irregular, amoeboid body of Astrorhiza is a manifestation not of equilibrium, but of a varying and fluctuating distribution of surface energy. When the foraminiferal shell becomes multilocular, the same general principles continue to hold; the growing protoplasm increases drop by drop, and each successive drop has its particular phenomena of surface energy, manifested at its fluid surface, and tending to confer upon it a certain place in the system and a certain shape of its own.

It is characteristic and even diagnostic of this particular group of Protozoa (1) that development proceeds by a well-marked alternation of rest and of activity—of activity during which the protoplasm increases, and of rest during which the shell is formed; (2) that the shell is formed at the outer surface of the protoplasmic organism, and tends to constitute a continuous or all but continuous covering; and it follows (3) from these two factors taken together that each successive increment is added on outside of and distinct from its predecessors, that the successive parts or chambers of {588} the shell are of different and successive ages, that one part of the shell is always relatively new, and the rest old in various grades of seniority.

The forms which we set together in the sister-group of Radiolaria are very differently characterised. Here the cells or vesicles of which each little composite organism is made up are but little separated, and in no way walled off, from one another; the hard skeletal matter tends to be deposited in the form of isolated spicules or of little connected rods or plates, at the angles, the edges or the interfaces of the vesicles; the cells or vesicles form a coordinated and cotemporaneous rather than a successive series. In a word, the whole quasi-fluid protoplasmic body may be likened to a little mass of froth or foam: that is to say, to an aggregation of simultaneously formed drops or bubbles, whose physical properties and geometrical relations are very different from those of a system of drops or bubbles which are formed one after another, each solidifying before the next is formed.

With the actual origin or mode of development of the foraminiferal shell we are now but little concerned. The main factor is the adsorption, and subsequent precipitation at the surface of the organism, of calcium carbonate,—the shell so formed being interrupted by pores or by some larger interspace or “mouth” (Fig. 308), which interruptions we may doubtless interpret as being due to unequal distributions of surface energy. In many {589} cases the fluid protoplasm “picks up” sand-grains and other foreign particles, after a fashion which we have already described (p. 463); and it cements these together with more or less of calcareous material. The calcareous shell is a crystalline structure, and the micro-crystals of calcium carbonate are so set that their little prisms radiate outwards in each chamber through the thickness of the wall:—which symmetry is subject to corresponding modification when the spherical chambers are more or less symmetrically deformed[539].

In various ways the rounded, drop-like shells of the Foraminifera, both simple and compound, have been artificially imitated. Thus, if small globules of mercury be immersed in water in which a little chromic acid is allowed to dissolve, as the little beads of quicksilver become slowly covered with a crystalline coat of mercuric chromate they assume various forms reminiscent of the monothalamic Foraminifera. The mercuric chromate has a higher atomic volume than the mercury which it replaces, and therefore the fluid contents of the drop are under pressure, which increases with the thickness of the pellicle; hence at some weak spot in the latter the contents will presently burst forth, so forming a mouth to the little shell. Sometimes a long thread is formed, just as in _Rhabdammina linearis_; and sometimes unduloid swellings make their appearance on such a thread, just as in _R. discreta_. And again, by appropriate modifications of the experimental conditions, it is possible (as Rhumbler has shewn) to build up a chambered shell[540].

In a few forms, such as Globigerina and its close allies, the shell is beset during life with excessively long and delicate calcareous spines or needles. It is only in oceanic forms that these are present, because only when poised in water can such {590} delicate structures endure; in dead shells, such as we are much more familiar with, every trace of them is broken and rubbed away. The growth of these long needles is explained (as we have already briefly mentioned, on p. 440) by the phenomenon which Lehmann calls _orientirte Adsorption_—the tendency for a crystalline structure to grow by accretion, not necessarily in the outward form of a “crystal,” but continuing in any direction or orientation which has once been impressed upon it: in this case the spicular growth is simply in direct continuation of the radial symmetry of the micro-crystalline elements of the shell-wall. Over the surface of the shell the radiating spicules tend to occur in a hexagonal pattern, symmetrically grouped around the pores which perforate the shell. Rhumbler has suggested that this arrangement is due to diffusion-currents, forming little eddies about the base of the pseudopodia issuing from the pores: the idea being borrowed from Bénard, to whom is due the discovery of this type or order of vortices[541]. In one of Bénard’s experiments a thin layer of paraffin is strewn with particles of graphite, then warmed to melting, whereupon each little solid granule becomes the centre of a vortex; by the interaction of these vortices the particles tend to be repelled to equal distances from one another, and in the end they are found to be arranged in a hexagonal pattern[542]. The analogy is plain between this experiment and those diffusion experiments by which Leduc produces his beautiful hexagonal systems of artificial cells, with which we have dealt in a previous chapter (p. 320).

But let us come back to the shell itself, and consider particularly its spiral form. That the shell in the Foraminifera should tend towards a spiral form need not surprise us; for we have learned that one of the fundamental conditions of the production of a concrete spiral is just precisely what we have here, namely the gradual development of a structure by means of successive increments superadded to its exterior, which then form part, successively, of a permanent and rigid structure. This condition {591} is obviously forthcoming in the foraminiferal, but not at all in the radiolarian, shell. Our second fundamental condition of the production of a logarithmic spiral is that each successive increment shall be so posited and so conformed that its addition to the system leaves the form of the whole system unchanged. We have now to enquire into this latter condition; and to determine whether the successive increments, or successive chambers, of the foraminiferal shell actually constitute _gnomons_ to the entire structure.

It is obvious enough that the spiral shells of the Foraminifera closely resemble true logarithmic spirals. Indeed so precisely do the minute shells of many Foraminifera repeat or simulate the spiral shells of Nautilus and its allies that to the naturalists of the early nineteenth century they were known as the _Céphalopodes microscopiques_[543], until Dujardin shewed that their little bodies comprised no complex anatomy of organs, but consisted merely of that slime-like organic matter which he taught us to call “sarcode,” and which we learned afterwards from Schwann to speak of as “protoplasm.”

One striking difference, however, is apparent between the shell of Nautilus and the little nautiloid or rotaline shells of the Foraminifera: namely that the septa in these latter, and in all other {592} chambered Foraminifera, are convex outwards (Fig. 308), whereas they are concave outwards in Nautilus (Fig. 304) and in the rest of the chambered molluscan shells. The reason is perfectly simple. In both cases the curvature of the septum was determined before it became rigid, and at a time when it had the properties either of a fluid film or an elastic membrane. In both cases the actual curvature is determined by the tensions of the membrane and the pressures to which it was exposed. Now it is obvious that the extrinsic pressure which the tension of the membrane has to withstand is on opposite sides in the two cases. In Nautilus, the pressure to be resisted is that produced by the growing body of the animal, lying to the _outer side_ of the septum, in the outer, wider portion of the tubular shell. In the Foraminifer the septum at the time of its formation was no septum at all; it was but a portion of the convex surface of a drop-that portion namely which afterwards became overlapped and enclosed by the succeeding drop; and the curvature of the septum is concave towards the pressure to be resisted, which latter is _inside_ the septum, being simply the hydrostatic pressure of the fluid contents of the drop. The one septum is, speaking generally, the reverse of the other; the organism, so to speak, is outside the one and inside the other; and in both cases alike, the septum tends to assume the form of a surface of minimal area, as permitted, or as defined, by all the circumstances of the case.

The logarithmic spiral is easily recognisable in typical cases[544] (and especially where the spire makes more than one visible revolution about the pole), by its fundamental property of continued similarity: that is to say, by reason of the fact that the big many-chambered shell is of just the same shape as the smaller and younger shell—which phenomenon is apparent and even obvious in the nautiloid Foraminifera, as in Nautilus itself: but nevertheless the nature of the curve must be verified by careful measurement, just as Moseley determined or verified it in his {593} original study of nautilus (cf. p. 518). This has accordingly been done, by various writers: and in the first instance by Valerian von Möller, in an elaborate study of Fusulina—a palaeozoic genus whose little shells have built up vast tracts of carboniferous limestone over great part of European Russia[545].

In this genus a growing surface of protoplasm may be conceived as wrapping round and round a small initial chamber, in such a way as to produce a fusiform or ellipsoidal shell—a transverse section of which reveals the close-wound spiral coil. The following are examples of measurements of the successive whorls in a couple of species of this genus.

_F. cylindrica_, Fischer _F. Böcki_, v. Möller Breadth (in millimetres). Whorl Observed Calculated Observed Calculated I ·132 — ·079 — II ·195 ·198 ·120 ·119 III ·300 ·297 ·180 ·179 IV ·449 ·445 ·264 ·267 V — — ·396 ·401

In both cases the successive whorls are very nearly in the ratio of 1 : 1·5; and on this ratio the calculated values are based.

Here is another of von Möller’s series of measurements of _F. cylindrica_, the measurements being those of opposite whorls—that is to say of whorls 180° apart:

Breadth in mm. ·096 ·117 ·144 ·176 ·216 ·264 ·323 ·395 Log. of mm. ·982 ·068 ·158 ·246 ·334 ·422 ·509 ·597 Diff. of logs. — ·086 ·090 ·088 ·088 ·088 ·087 ·088

The mean logarithmic difference is here ·088, = log 1·225; or the mean difference of alternate logs (corresponding to a vector angle of 2π, i.e. to consecutive measurements along the _same_ radius) is ·176, = log 1·5, the same value as before. And this ratio of 1·5 between the breadths of successive whorls corresponds (as we see by our table on p. 534) to a constant angle of about {594} 86°, or just such a spiral as we commonly meet with in the Ammonites[546] (cf. p. 539).

In Fusulina, and in some few other Foraminifera (cf. Fig. 310, A), the spire seems to wind evenly on, with little or no external sign of the successive periods of growth, or successive chambers of the shell. The septa which mark off the chambers, and correspond to retardations or cessations in the periodicity of growth, are still to be found in sections of the shell of Fusulina; but they are somewhat irregular and comparatively inconspicuous; the measurements we have just spoken of are taken without reference to the segments or chambers, but only with reference to the whorls, or in other words with direct reference to the vectorial angle.

The linear dimensions of successive chambers have been {595} measured in a number of cases. Van Iterson[547] has done so in various Miliolinidae, with such results as the following:

_Triloculina rotunda_, d’Orb.

No. of chamber 1 2 3 4 5 6 7 8 9 10 Breadth of chamber in _µ_ — 34 45 61 84 114 142 182 246 319 Breadth of chamber in _µ_, calculated — 34 45 60 79 105 140 187 243 319

Here the mean ratio of breadth of consecutive chambers may be taken as 1·323 (that is to say, the eighth root of 319/34); and the calculated values, as given above, are based on this determination.

Again, Rhumbler has measured the linear dimensions of a number of rotaline forms, for instance _Pulvinulina menardi_ (Fig. 259): in which common species he finds the mean linear ratio of consecutive chambers to be about 1·187. In both cases, and especially in the latter, the ratio is not strictly constant from chamber to chamber, but is subject to a small secondary fluctuation[548].

When the linear dimensions of successive chambers are in continued proportion, then, in order that the whole shell may constitute a logarithmic spiral, it is necessary that the several chambers should subtend equal angles of revolution at the pole. In the case of the Miliolidae this is obviously the case (Fig. 311); for in this family the chambers lie in two rows (Biloculina), or three rows (Triloculina), or in some other small number of series: so that the angles subtended by them are large, simple fractions of the circular arc, such as 180° or 120°. In many of the nautiloid forms, such as Cyclammina (Fig. 312), the angles subtended, though of less magnitude, are still remarkably constant, as we {597} may see by Fig. 313; where the angle subtended by each chamber is made equal to 20°, and this diagrammatic figure is not perceptibly different from the other. In some cases the subtended angle is less constant; and in these it would be necessary to equate the several linear dimensions with the corresponding vector angles, according to our equation _r_ = _e_^{θ cot α}. It is probable that, by so taking account of variations of θ, such variations of _r_ as (according to Rhumbler’s measurements) Pulvinulina and other genera appear to shew, would be found to diminish or even to disappear.

The law of increase by which each chamber bears a constant ratio of magnitude to the next may be looked upon as a simple consequence of the structural uniformity or homogeneity of the organism; we have merely to suppose (as this uniformity would naturally lead us to do) that the rate of increase is at each instant proportional to the whole existing mass. For if _V__{0}, _V__{1} etc., be the volumes of the successive chambers, let _V__{1} bear a constant proportion to _V__{0}, so that _V__{1} = _q_ _V__{0}, and let _V__{2} bear the same proportion to the whole pre-existing volume: then

_V__{2} = _q_(_V__{0} + _V__{1}) = _q_(_V__{0} + _q_ _V__{0}) = _q_ _V__{0}(1 + _q_) and _V__{2}/_V__{1} = 1 + _q_.

{598}

This ratio of 1/(1 + _q_) is easily shewn to be the constant ratio running through the whole series, from chamber to chamber; and if this ratio of volumes be constant, so also are the ratios of corresponding surfaces, and of corresponding linear dimensions, provided always that the successive increments, or successive chambers, are similar in form.

We have still to discuss the similarity of form and the symmetry of position which characterise the successive chambers, and which, together with the law of continued proportionality of size, are the distinctive characters and the indispensable conditions of a series of “gnomons.”

The minute size of the foraminiferal shell or at least of each successive increment thereof, taken in connection with the fluid or semi-fluid nature of the protoplasmic substance, is enough to suggest that the molecular forces, and especially the force of surface-tension, must exercise a controlling influence over the form of the whole structure; and this suggestion, or belief, is already implied in our statement that each successive increment of growing protoplasm constitutes a separate _drop_. These “drops,” partially concealed by their successors, but still shewing in part their rounded outlines, are easily recognisable in the various foraminiferal shells which are illustrated in this chapter.

The accompanying figure represents, to begin with, the spherical shell characteristic of the common, floating, oceanic Orbulina. In the specimen illustrated, a second chamber, superadded to the {599} first, has arisen as a drop of protoplasm which exuded through the pores of the first chamber, accumulated on its surface, and spread over the latter till it came to rest in a position of equilibrium. We may take it that this position of equilibrium is determined, at least in the first instance, by the “law of the constant angle,” which holds, or tends to hold, in all cases where the free surface of a given liquid is in contact with a given solid, in presence of another liquid or a gas. The corresponding equations are precisely the same as those which we have used in discussing the form of a drop (on p. 294); though some slight modification must be made in our definitions, inasmuch as the consideration of surface-_tension_ is no longer appropriate at the solid surfaces, and the concept of surface-_energy_ must take its place. Be that as it may, it is enough for us to observe that, in such a case as ours, when a given fluid (namely protoplasm) is in surface contact with a solid (viz. a calcareous shell), in presence of another fluid (sea-water), then the angle of contact, or angle by which the common surface (or interface) of the two liquids abuts against the solid wall, tends to be constant: and that being so, the drop will have a certain definite form, depending (_inter alia_) on the form of the surface with which it is in contact. After a period of rest, during which the surface of our second drop becomes rigid by calcification, a new period of growth will recur and a new drop of protoplasm be accumulated. Circumstances remaining the same, this new drop will meet the solid surface of the shell at the same angle as did the former one; and, the other forces at work on the system remaining the same, the form of the whole drop, or chamber, will be the same as before.

According to Rhumbler, this “law of the constant angle” is the fundamental principle in the mechanical conformation of the foraminiferal shell, and provides for the symmetry of form as well as of position in each succeeding drop of protoplasm: which form and position, once acquired, become rigid and fixed with the onset of calcification. But Rhumbler’s explanation brings with it its own difficulties. It is by no means easy of verification, for on the very complicated curved surfaces of the shell it seems to me extraordinarily difficult to measure, or even to recognise, the actual angle of contact: of which angle of contact, by the way, {600} but little is known, save only in the particular case where one of the three bodies is air, as when a surface of water is exposed to air and in contact with glass. It is easy moreover to see that in many of our Foraminifera the angle of contact, though it may be constant in homologous positions from chamber to chamber, is by no means constant at all points along the boundary of each chamber. In Cristellaria, for instance (Fig. 315), it would seem to be (and Rhumbler asserts that it actually is) about 90° on the outer side and only about 50° on the inner side of each septal partition; in Pulvinulina (Fig. 259), according to Rhumbler, the angles adjacent to the mouth are of 90°, and the opposite angles are of 60°, in each chamber. For these and other similar discrepancies Rhumbler would account by simply invoking the heterogeneity of the protoplasmic drop: that is to say, by assuming that the protoplasm has a different composition and different properties (including a very different distribution of surface-energy), at points near to and remote from the mouth of the shell. Whether the differences in angle of contact be as great as Rhumbler takes them to be, whether marked heterogeneities of the protoplasm occur, and whether these be enough to account for the differences of angle, I cannot tell. But it seems to me that we had better rest content with a general statement, and that Rhumbler has taken too precise and narrow a view.

{601}

In the molecular growth of a crystal, although we must of necessity assume that each molecule settles down in a position of minimum potential energy, we find it very hard indeed to explain precisely, even in simple cases and after all the labours of modern crystallographers, why this or that position is actually a place of minimum potential. In the case of our little Foraminifer (just as in the case of the crystal), let us then be content to assert that each drop or bead of protoplasm takes up a position of minimum potential energy, in relation to all the circumstances of the case; and let us not attempt, in the present state of our knowledge, to define that position of minimum potential by reference to angle of contact or any other particular condition of equilibrium. In most cases the whole exposed surface, on some portion of which the drop must come to rest, is an extremely complicated one, and the forces involved constitute a system which, in its entirety, is more complicated still; but from the symmetry of the case and the continuity of the whole phenomenon, we are entitled to believe that the conditions are just the same, or very nearly the same, time after time, from one chamber to another: as the one chamber is conformed so will the next tend to be, and as the one is situated relatively to the system so will its successor tend to be situated in turn. The physical law of minimum potential (including also the law of minimal area) is all that we need in order to explain, _in general terms_, the continued similarity of one chamber to another; and the physiological law of growth, by which a continued proportionality of size tends to run through the series of successive chambers, impresses upon this series of similar increments the form of a logarithmic spiral.

In each particular case the nature of the logarithmic spiral, as defined by its constant angle, will be chiefly determined by the rate of growth; that is to say by the particular ratio in which each new chamber exceeds its predecessor in magnitude. But shells having the same constant angle (α) may still differ from one another in many ways—in the general form and relative position of the chambers, in their extent of overlap, and hence in the actual contour and appearance of the shell; and these variations must correspond to particular distributions of energy within the system, which is governed as a whole by the law of minimum potential. {602}

Our problem, then, becomes reduced to that of investigating the possible configurations which may be derived from the successive symmetrical apposition of similar bodies whose magnitudes are in continued proportion; and it is obvious, mathematically speaking, that the various possible arrangements all come under the head of the logarithmic spiral, together with the limiting cases which it includes. Since the difference between one such form and another depends upon the numerical value of certain coefficients of magnitude, it is plain that any one must tend to pass into any other by small and continuous gradations; in other words, that a _classification_ of these forms must (like any classification whatsoever of logarithmic spirals or of any other mathematical curves), be theoretic or “artificial.” But we may easily make such an artificial classification, and shall probably find it to agree, more or less, with the usual methods of classification recognised by biological students of the Foraminifera.

Firstly we have the typically spiral shells, which occur in great variety, and which (for our present purpose) we need hardly describe further. We may merely notice how in certain cases, for instance Globigerina, the individual chambers are little removed from spheres; in other words, the area of contact between the adjacent chambers is small. In such forms as Cyclammina and Pulvinulina, on the other hand, each chamber is greatly overlapped by its successor, and the spherical form of each is lost in a marked asymmetry. Furthermore, in Globigerina and some others we have a tendency to the development of a helicoid spiral in space, as in so many of our univalve molluscan shells. The mathematical problem of how a shell should grow, under the assumptions which we have made, would probably find its most general statement in such a case as that of Globigerina, where the whole organism lives and grows freely poised in a medium whose density is little different from its own.

The majority of spiral forms, on the other hand, are plane or discoid spirals, and we may take it that in these cases some force has exercised a controlling influence, so as to keep all the chambers in a plane. This is especially the case in forms like Rotalia or Discorbina (Fig. 316), where the organism lives attached to a rock or a frond of sea-weed; for here (just as in the case of {603} the coiled tubes which little worms such as Serpula and Spirorbis make, under similar conditions) the spiral disc is itself asymmetrical, its whorls being markedly flattened on their attached surfaces.

We may also conceive, among other conditions, the very curious case in which the protoplasm may entirely overspread the surface of the shell without reaching a position of equilibrium; in which case a new shell will be formed _enclosing_ the old one, {604} whether the old one be in the form of a single, solitary chamber, or have already attained to the form of a chambered or spiral shell. This is precisely what often happens in the case of Orbulina, when within the spherical shell we find a small, but perfectly formed, spiral “Globigerina[549].”

The various Miliolidae (Fig. 311), only differ from the typical spiral, or rotaline forms, in the large angle subtended by each chamber, and the consequent abruptness of their inclination to each other. In these cases the _outward_ appearance of a spiral tends to be lost; and it behoves us to recollect, all the more, that our spiral curve is not necessarily identical with the _outline_ of the shell, but is always a line drawn through corresponding points in the successive chambers of the latter.

We reach a limiting case of the logarithmic spiral when the chambers are arranged in a straight line; and the eye will tend to associate with this limiting case the much more numerous forms in which the spiral angle is small, and the shell only exhibits a gentle curve with no succession of enveloping whorls. This constitutes the Nodosarian type (Fig. 87, p. 262); and here again, we must postulate some force which has tended to keep the chambers in a rectilinear series: such for instance as gravity, acting on a system of “hanging drops.” {605}

In Textularia and its allies (Fig. 317), we have a precise parallel to the helicoid cyme of the botanists (cf. p. 502): that is to say we have a screw translation, perpendicular to the plane of the underlying logarithmic spiral. In other words, in tracing a genetic spiral through the whole succession of chambers, we do so by a continuous vector rotation, through successive angles of 180° (or 120° in some cases), while the pole moves along an axis perpendicular to the original plane of the spiral.

Another type is furnished by the “cyclic” shells of the Orbitolitidae, where small and numerous chambers tend to be added on round and round the system, so building up a circular flattened disc. This again we perceive to be, mathematically, a limiting case of the logarithmic spiral, where the spiral has become a circle and the constant angle is now an angle of 90°.

Lastly there are a certain number of Foraminifera in which, without more ado, we may simply say that the arrangement of the chambers is irregular, neither the law of constant ratio of magnitude nor that of constant form being obeyed. The chambers are heaped pell-mell upon one another, and such forms are known to naturalists as the Acervularidae.

While in these last we have an extreme lack of regularity, we must not exaggerate the regularity or constancy which the more ordinary forms display. We may think it hard to believe that the simple causes, or simple laws, which we have described should operate, and operate again and again, in millions of individuals to produce the same delicate and complex conformations. But we are taking a good deal for granted if we assert that they do so, and in particular we are assuming, with very little proof, the “constancy of species” in this group of animals. Just as Verworn has shewn that the typical _Amoeba proteus_, when a trace of alkali is added to the water in which it lives, tends, by alteration of surface tensions, to protrude the more delicate pseudopodia characteristic of _A. radiosa_,—and again when the water is rendered a little more alkaline, to turn apparently into the so-called _A. limax_,—so it is evident that a very slight modification in the surface-energies concerned, might tend to turn one so-called species into another among the Foraminifera. To what extent this process actually occurs, we do not know. {606}

But that this, or something of the kind, does actually occur we can scarcely doubt. For example in the genus Peneroplis, the first portion of the shell consists of a series of chambers arranged in a spiral or nautiloid series; but as age advances the spiral is apt to be modified in various ways[550]. Sometimes the successive chambers grow rapidly broader, the whole shell becoming fan-shaped. Sometimes the chambers become narrower, till they no longer enfold the earlier chambers but only come in contact each with its immediate predecessor: the result being that the shell straightens out, and (taking into account the earlier spiral portion) may be described as crozier-shaped. Between these extremes of shape, and in regard to other variations of thickness or thinness, roughness or smoothness, and so on, there are innumerable gradations passing one into another and intermixed without regard to geographical distribution:—“wherever Peneroplides abound this wide variation exists, and nothing can be more easy than to pick out a number of striking specimens and give to each a distinctive name, but _in no other way can they be divided into_ ‘_species._’[551]” Some writers have wondered at the peculiar variability of this particular shell[552]; but for all we know of the life-history of the Foraminifera, it may well be that a great number of the other forms which we distinguish as separate species and even genera are no more than temporary manifestations of the same variability[553]. {607}

_Conclusion._

If we can comprehend and interpret on some such lines as these the form and mode of growth of the foraminiferal shell, we may also begin to understand two striking features of the group, namely, on the one hand the large number of diverse types or families which exist and the large number of species and varieties within each, and on the other the persistence of forms which in many cases seem to have undergone little change or none at all from the Cretaceous or even from earlier periods to the present day. In few other groups, perhaps only among the Radiolaria, do we seem to possess so nearly complete a picture of all possible transitions between form and form, and of the whole branching system of the evolutionary tree: as though little or nothing of it had ever perished, and the whole web of life, past and present, were as complete as ever. It leads one to imagine that these shells have grown according to laws so simple, so much in harmony with their material, with their environment, and with all the forces internal and external to which they are exposed, that none is better than another and none fitter or less fit to survive. It invites one also to contemplate the possibility of the lines of possible variation being here so narrow and determinate that identical forms may have come independently into being again and again.

While we can trace in the most complete and beautiful manner the passage of one form into another among these little shells, and ascribe them all at last (if we please) to a series which starts with the simple sphere of Orbulina or with the amoeboid body of Astrorhiza, the question stares us in the face whether this be an “evolution” which we have any right to correlate with historic _time_. The mathematician can trace one conic section into another, and “evolve” for example, through innumerable graded ellipses, the circle from the straight line: which tracing of continuous steps is a true “evolution,” though time has no part therein. It was after this fashion that Hegel, and for that matter Aristotle himself, was an evolutionist—to whom evolution was {608} a mental concept, involving order and continuity in thought, but not an actual sequence of events in time. Such a conception of evolution is not easy for the modern biologist to grasp, and harder still to appreciate. And so it is that even those who, like Dreyer[554] and like Rhumbler, study the foraminiferal shell as a physical system, who recognise that its whole plan and mode of growth is closely akin to the phenomena exhibited by fluid drops under particular conditions, and who explain the conformation of the shell by help of the same physical principles and mathematical laws—yet all the while abate no jot or tittle of the ordinary postulates of modern biology, nor doubt the validity and universal applicability of the concepts of Darwinian evolution. For these writers the _biogenetisches Grundgesetz_ remains impregnable. The Foraminifera remain for them a great family tree, whose actual pedigree is traceable to the remotest ages; in which historical evolution has coincided with progressive change; and in which structural fitness for a particular function (or functions) has exercised its selective action and ensured “the survival of the fittest.” By successive stages of historic evolution we are supposed to pass from the irregular Astrorhiza to a Rhabdammina with its more concentrated disc; to the forms of the same genus which consist of but a single tube with central chamber; to those where this chamber is more and more distinctly segmented; so to the typical many-chambered Nodosariae; and from these, by another definite advance and later evolution to the spiral Trochamminae. After this fashion, throughout the whole varied series of the Foraminifera, Dreyer and Rhumbler (following Neumayr) recognise so many successions of related forms, one passing into another, and standing towards it in a definite relationship of ancestry or descent. Each evolution of form, from simpler to more complex, is deemed to have been attended by an advantage to the organism, an enhancement of its chances of survival or perpetuation; hence the historically older forms are, on the whole, structurally the simpler; or conversely the simpler forms, such as the simple sphere, were the first to come into being in primeval seas; and finally, the gradual development and increasing {609} complication of the individual within its own lifetime is held to be at least a partial recapitulation of the unknown history of its race and dynasty[555].

We encounter many difficulties when we try to extend such concepts as these to the Foraminifera. We are led for instance to assert, as Rhumbler does, that the increasing complexity of the shell, and of the manner in which one chamber is fitted on another, makes for advantage; and the particular advantage on which Rhumbler rests his argument is _strength_. Increase of strength, _die Festigkeitssteigerung_, is according to him the guiding principle in foraminiferal evolution, and marks the historic stages of their development in geologic time. But in days gone by I used to see the beach of a little Connemara bay bestrewn with millions upon millions of foraminiferal shells, simple Lagenae, less simple Nodosariae, more complex Rotaliae: all drifted by wave and gentle current from their sea-cradle to their sandy grave: all lying bleached and dead: one more delicate than another, but all (or vast multitudes of them) perfect and unbroken. And so I am not inclined to believe that niceties of form affect the case very much: nor in general that foraminiferal life involves a struggle for existence wherein breakage is a constant danger to be averted, and increased strength an advantage to be ensured[556].

In the course of the same argument Rhumbler remarks that Foraminifera are absent from the coarse sands and gravels[557], as Williamson indeed had observed many years ago: so averting, or {610} at least escaping, the dangers of concussion. But this is after all a very simple matter of mechanical analysis. The coarseness or fineness of the sediment on the sea-bottom is a measure of the current: where the current is strong the larger stones are washed clean, where there is perfect stillness the finest mud settles down; and the light, fragile shells of the Foraminifera find their appropriate place, like every other graded sediment, in this spontaneous order of lixiviation.

The theorem of Organic Evolution is one thing; the problem of deciphering the lines of evolution, the order of phylogeny, the degrees of relationship and consanguinity, is quite another. Among the higher organisms we arrive at conclusions regarding these things by weighing much circumstantial evidence, by dealing with the resultant of many variations, and by considering the probability or improbability of many coincidences of cause and effect; but even then our conclusions are at best uncertain, our judgments are continually open to revision and subject to appeal, and all the proof and confirmation we can ever have is that which comes from the direct, but fragmentary evidence of palaeontology[558].

But in so far as forms can be shewn to depend on the play of physical forces, and the variations of form to be directly due to simple quantitative variations in these, just so far are we thrown back on our guard before the biological conception of consanguinity, and compelled to revise the vague canons which connect classification with phylogeny.

The physicist explains in terms of the properties of matter, and classifies according to a mathematical analysis, all the drops and forms of drops and associations of drops, all the kinds of froth and foam, which he may discover among inanimate things; and his task ends there. But when such forms, such conformations and configurations, occur among _living_ things, then at once the biologist introduces his concepts of heredity, of historical evolution, of succession in time, of recapitulation of remote ancestry in individual growth, of common origin (unless contradicted by direct evidence) of similar forms remotely separated by geographic space or geologic time, of fitness for a function, of {611} adaptation to an environment, of higher and lower, of “better” and “worse.” This is the fundamental difference between the “explanations” of the physicist and those of the biologist.

In the order of physical and mathematical complexity there is no question of the sequence of historic time. The forces that bring about the sphere, the cylinder or the ellipsoid are the same yesterday and to-morrow. A snow-crystal is the same to-day as when the first snows fell. The physical forces which mould the forms of Orbulina, of Astrorhiza, of Lagena or of Nodosaria to-day were still the same, and for aught we have reason to believe the physical conditions under which they worked were not appreciably different, in that yesterday which we call the Cretaceous epoch; or, for aught we know, throughout all that duration of time which is marked, but not measured, by the geological record.

In a word, the minuteness of our organism brings its conformation as a whole within the range of the molecular forces; the laws of its growth and form appear to lie on simple lines; what Bergson calls[559] the “ideal kinship” is plain and certain, but the “material affiliation” is problematic and obscure; and, in the end and upshot, it seems to me by no means certain that the biologist’s usual mode of reasoning is appropriate to the case, or that the concept of continuous historical evolution must necessarily, or may safely and legitimately, be employed.

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