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.
[Illustration: Fig. 308. _Hastigerina_ sp.; to shew the “mouth.”]
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.”
[Illustration: Fig. 309. _Nummulina antiquior_, R. and V. (After V. von
Möller.)]
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.
[Illustration: Fig. 310. A, _Cornuspira foliacea_, Phil.; B,
_Operculina complanata_, Defr.]
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].
[Illustration: Fig. 311. 1, 2, _Miliolina pulchella_, d’Orb.; 3–5, _M.
linnaeana_, d’Orb. (After Brady.)]
[Illustration: Fig. 312. _Cyclammina cancellata_, Brady.]
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.
[Illustration: Fig. 313. _Cyclammina_ sp. (Diagrammatic.)]
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.
[Illustration: Fig. 314. _Orbulina universa_, d’Orb.]
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.
[Illustration: Fig. 315. _Cristellaria reniformis_, d’Orb.]
{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.
[Illustration: Fig. 316. _Discorbina bertheloti_, d’Orb.]
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.
[Illustration: Fig. 317. A, _Tertularia trochus_, d’Orb. B, _T.
concava_, Karrer.]
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.
{612}