only form of the hypothesis on which we may rely. For from the purely
physical point of view, angles and edges of contact between adjacent
cells will be _loci_ in the field of distribution of surface-energy,
and any material particles whatsoever will tend to undergo a diminution
of freedom on entering one of those boundary regions. In a very
simple case, let us imagine a couple of soap bubbles in contact with
one another. Over the surface of each bubble there glide in every
direction, as usual, a multitude of tiny bubbles and droplets; but
as soon as these find their way into the groove or re-entrant angle
between the two bubbles, there their freedom of movement is so far
restrained, and out of that groove they have little or no tendency to
emerge. A cognate phenomenon is to be witnessed in microscopic sections
of steel or other metals. Here, amid the “crystalline” structure of
the metal (where in cooling its imperfectly homogeneous material has
developed a cellular structure, shewing (in section) hexagonal or
polygonal contours), we can easily observe, as Professor Peddie has
shewn me, that the little particles of graphite and other foreign
bodies common in the matrix, have tended to aggregate themselves
in the walls and at the angles of the polygonal cells—this being a
direct result of the diminished freedom which the particles undergo on
entering one of these boundary regions[460].
It is by a combination of these two principles, chemical adsorption
on the one hand, and physical quasi-adsorption or concentration of
grosser particles on the other, that I conceive the substance of
the sponge-spicule to be concentrated and aggregated at the cell
boundaries; and the forms of the triradiate and tetractinellid spicules
are in precise conformity with this hypothesis. A few general matters,
and a few particular cases, remain to be considered.
It matters little or not at all, for the phenomenon in question, {449}
what is the histological nature or “grade” of the vesicular structures
on which it depends. In some cases (apart from sponges), they may be no
more than the little alveoli of the intracellular protoplasmic network,
and this would seem to be the case at least in one known case, that
of the protozoan _Entosolenia aspera_, in which, within the vesicular
protoplasm of the single cell, Möbius has described tiny spicules in
the shape of little tetrahedra with concave sides. It is probably
also the case in the small beginnings of the Echinoderm spicules,
which are likewise intracellular, and are of similar shape. In the
case of our sponges we have many varying conditions, which we need
not attempt to examine in detail. In some cases there is evidence for
believing that the spicule is formed at the boundaries of true cells
or histological units. But in the case of the larger triradiate or
tetractinellid spicules of the sponge-body, they far surpass in size
the actual “cells”; we find them lying, regularly and symmetrically
arranged, between the “pore-canals” or “ciliated chambers,” and it
is in conformity with the shape and arrangement of these rounded or
spheroidal structures that their shape is assumed.
Again, it is not necessarily at variance with our hypothesis to find
that, in the adult sponge, the larger spicules may greatly outgrow the
bounds not only of actual cells but also of the ciliated chambers, and
may even appear to project freely from the surface of the sponge. For
we have already seen that the spicule is capable of growing, without
marked change of form, by further deposition, or crystallisation,
of layer upon layer of calcareous molecules, even in an artificial
solution; and we are entitled to believe that the same process may
be carried on in the tissues of the sponge, without greatly altering
the symmetry of the spicule, long after it has established its
characteristic form of a system of slender trihedral or tetrahedral
rays.
Neither is it of great importance to our hypothesis whether the rayed
spicule necessarily arises as a single structure, or does so from
separate minute centres of aggregation. Minchin has shewn that, in
some cases at least, the latter is the case; the spicule begins, he
tells us, as three tiny rods, separate from one another, each developed
in the interspace between two sister-cells, which are themselves the
results of the division of one of a {450} little trio of cells; and
the little rods meet and fuse together while still very minute, when
the whole spicule is only about 1/200 of a millimetre long. At this
stage, it is interesting to learn that the spicule is non-crystalline;
but the new accretions of calcareous matter are soon deposited in
crystalline form.
This observation threw considerable difficulties in the way of former
mechanical theories of the conformation of the spicule, and was quite
at variance with Dreyer’s theory, according to which the spicule was
bound to begin from a central nucleus coinciding with the meeting-place
of the three contiguous cells, or rather the interspace between them.
But the difficulty is removed when we import the concept of adsorption;
for by this agency it is natural enough, or conceivable enough, that
the process of deposition should go on at separate parts of a common
system of surfaces; and if the cells tend to meet one another by their
interfaces before these interfaces extend to the angles and so complete
the polygonal cell, it is again conceivable and natural that the
spicule should first arise in the form of separate and detached limbs
or rays.
[Illustration: Fig. 215. Spicules of tetractinellid sponges (after
Sollas). _a_–_e_, anatriaenes; _d_–_f_, protriaenes.]
Among the tetractinellid sponges, whose spicules are composed of
amorphous silica or opal, all or most of the above-described main
types of spicule occur, and, as the name of the group implies, the
four-rayed, tetrahedral spicules are especially represented. A
somewhat frequent type of spicule is one in which one of the four
rays is greatly developed, and the other three constitute small
prongs diverging at equal angles from the main or axial ray. In all
probability, as Dreyer suggests, we have here had to do with a group of
four vesicles, of which three were large and co-equal, while a fourth
and very much smaller one lay above and between the other three. In
certain cases where we have likewise one large and three much smaller
{451} rays, the latter are recurved, as in Fig. 215. This type, save
for the constancy of the number of rays, and the limitation of the
terminal ones to three, and save also for the more important difference
that they occur only at one and not at both ends of the long axis, is
similar to the type of spicule illustrated in Fig. 213, which we have
explained as being probably developed within an oval cell, by whose
walls its branches have been conformed to geodetic curves. But it is
much more probable that we have here to do with a spicule developed
in the midst of a group of three coequal and more or less elongated
or cylindrical cells or vesicles, the long axial ray corresponding to
their common line of contact, and the three short rays having each lain
in the surface furrow between two out of the three adjacent cells.
[Illustration: Fig. 216. Various holothurian spicules. (After Théel.)]
Just as in the case of the little curved or S-shaped spicules, formed
apparently within the bounds of a single cell, so also in the case of
the larger tetractinellid and analogous types do we find among the
Holothuroidea the same configurations reproduced as we have dealt with
in the sponges. The holothurian spicules are a little less neatly
formed, a little rougher, than the sponge-spicules; and certain forms
occur among the former group which do not present themselves among
the latter; but for the most part a community of type is obvious and
striking (Fig. 216).
A curious and, physically speaking, strictly analogous formation to
the tetrahedral spicules of the sponges is found in the {452} spores
of a certain little group of parasitic protozoa, the Actinomyxidia.
These spores are formed from clusters of six cells, of which three
come to constitute the capsule of the spore; and this capsule, always
triradiate in its symmetry, is in some species drawn out into long
rays, of which one constitutes a straight central axis, while the
others, coming off from it at equal angles, are recurved in wide
circular arcs. The account given of the development of this structure
by its discoverers[461] is somewhat obscure to me, but I think that, on
physical grounds, there can be no doubt whatever that the quadriradiate
capsule has been somehow modelled upon a group of three surrounding
cells, its axis lying between the three, and its three radial arcs
occupying the furrows between adjacent pairs.
[Illustration: Fig. 217. Spicules of hexactinellid sponges. (After F.
E. Schultze.)]
The typically six-rayed siliceous spicules of the hexactinellid
sponges, while they are perhaps the most regular and beautifully formed
spicules to be found within the entire group, have been found very
difficult to explain, and Dreyer has confessed his complete inability
to account for their conformation. But, though it is doubtless only
throwing the difficulty a little further back, we may so far account
for them by considering that the cells or vesicles by which they
are conformed are not arranged in {453} what is known as “closest
packing,” but in linear series; so that in their arrangement, and by
their mutual compression, we tend to get a pattern, not of hexagons,
but of squares: or, looking to the solid, not of dodecahedra but of
cubes or parallelopipeda. This indeed appears to be the case, not with
the individual cells (in the histological sense), but with the larger
units or vesicles which make up the body of the hexactinellid. And this
being so, the spicules formed between the linear, or cubical series of
vesicles, will have the same tendency towards a “hexactinellid” shape,
corresponding to the angles and adjacent edges of a system of cubes, as
in our former case they had to a triradiate or a tetractinellid form,
when developed in connection with the angles and edges of a system of
hexagons, or a system of dodecahedra.
Histologically, the case is illustrated by a well-known phenomenon in
embryology. In the segmenting ovum, there is a tendency for the cells
to be budded off in linear series; and so they often remain, in rows
side by side, at least for a considerable time and during the course
of several consecutive cell divisions. Such an arrangement constitutes
what the embryologists call the “radial type” of segmentation[462]. But
in what is described as the “spiral type” of segmentation, it is stated
that, as soon as the first horizontal furrow has divided the cells into
an upper and a lower layer, those of “the upper layer are shifted in
respect to the lower layer, by means of a rotation about the vertical
axis[463].” It is, of course, evident that the whole process is merely
that which is familiar to physicists as “close packing.” It is a very
simple case of what Lord Kelvin used to call “a problem in tactics.”
It is a mere question of the rigidity of the system, of the freedom of
movement on the part of its constituent cells, whether or at what stage
this tendency to slip into the closest propinquity, or position of
minimum potential, will be found to manifest itself.
However the hexactinellid spicules be arranged (and this is {454} not
at all easy to determine) in relation to the tissues and chambers of
the sponge, it is at least clear that, whether they be separate or be
fused together (as often happens) in a composite skeleton, they effect
a symmetrical partitioning of space according to the cubical system, in
contrast to that closer packing which is represented and effected by
the tetrahedral system[464].
――――――――――
This question of the origin and causation of the forms of
sponge-spicules, with which we have now briefly dealt, is all the
more important and all the more interesting because it has been
discussed time and again, from points of view which are characteristic
of very different schools of thought in biology. Haeckel found in
the form of the sponge-spicule a typical illustration of his theory
of “bio-crystallisation”; he considered that these “biocrystals”
represented “something midway—_ein Mittelding_—between an inorganic
crystal and an organic secretion”; that there was a “compromise
between the crystallising efforts of the calcium carbonate and the
formative activity of the fused cells of the syncytium”; and that
the semi-crystalline secretions of calcium carbonate “were utilised
by natural selection as ‘spicules’ for building up a skeleton, and
afterwards, by the interaction of adaptation and heredity, became
modified in form and differentiated in a vast variety of ways in the
struggle for existence[465].” What Haeckel precisely signified by these
words is not clear to me.
F. E. Schultze, perceiving that identical forms of spicule were
developed whether the material were crystalline or non-crystalline,
abandoned all theories based upon crystallisation; he simply saw in the
form and arrangement of the spicules something which was “best fitted”
for its purpose, that is to say for the support and strengthening of
the porous walls of the sponge, and found clear evidence of “utility”
in the specific structure of these skeletal elements. {455}
Sollas and Dreyer, as we have seen, introduced in various ways the
conception of physical causation,—as indeed Haeckel himself had done
in regard to one particular, when he supposed the _position_ of the
spicules to be due to the constant passage of the water-currents.
Though even here, by the way, if I understand Haeckel aright, he was
thinking not merely of a direct or immediate physical causation, but of
one manifesting itself through the agency of natural selection[466].
Sollas laid stress upon the “path of least resistance” as determining
the direction of growth; while Dreyer dealt in greater detail with
the various tensions and pressures to which the growing spicule was
exposed, amid the alveolar or vesicular structure which was represented
alike by the chambers of the sponge, by the reticulum of constituent
cells, or by the minute structure of the intracellular protoplasm. But
neither of these writers, so far as I can discover, was inclined to
doubt for a moment the received canon of biology, which sees in such
structures as these the characteristics of true organic species, and
the indications of an hereditary affinity by which blood-relationship
and the succession of evolutionary descent throughout geologic time can
be ultimately deduced.
Lastly, Minchin, in a well-known paper[467], took sides with Schultze,
and gave reasons for dissenting from such mechanical theories as those
of Sollas and of Dreyer. For example, after pointing out that all
protoplasm contains a number of “granules” or microsomes, contained in
the alveolar framework and lodged at the nodes of the reticulum, he
argued that these also ought to acquire a form such as the spicules
possess, if it were the case that these latter owed their form to their
very similar or identical position. “If vesicular tension cannot in any
other instance cause the granules at the nodes to assume a tetraxon
form, why should it do so for the sclerites?” In all probability the
answer to this question is not far to seek. If the force which the
“mechanical” hypothesis has in view were simply that of mechanical
_pressure_, {456} as between solid bodies, then indeed we should
expect that any substances whatsoever, lying between the impinging
spheres, would tend (unless they were infinitely hard) to assume the
quadriradiate or “tetraxon” form; but this conclusion does not follow
at all, in so far as it is to _surface-energy_ that we ascribe the
phenomenon. Here the specific nature of the substances involved makes
all the difference. We cannot argue from one substance to another;
adsorptive attraction shews its effect on one and not on another; and
we have not the least reason to be surprised if we find that the little
granules of protoplasmic material, which as they lie bathed in the
more fluid protoplasm have (presumably, and as their shape indicates)
a strong surface-tension of their own, behave towards the adjacent
vesicles in a very different fashion to the incipient aggregations
of calcareous or siliceous matter in a colloid medium. “The ontogeny
of the spicules,” says Professor Minchin, “points clearly to their
regular form being a _phylogenetic adaptation, which has become fixed
and handed on by heredity, appearing in the ontogeny as a prophetic
adaptation_.” And again, “The forms of the spicules are the result of
adaptation to the requirements of the sponge as a whole, produced by
_the action of natural selection upon variation in every direction_.”
It would scarcely be possible to illustrate more briefly and more
cogently than by these few words (or the similar words of Haeckel
quoted on p. 454), the fundamental difference between the Darwinian
conception of the causation and determination of Form, and that which
is characteristic of the physical sciences.
――――――――――
If I have dealt comparatively briefly with the inorganic skeleton of
sponges, in spite of the obvious importance of this part of our subject
from the physical or mechanical point of view, it has been owing to
several reasons. In the first place, though the general trend of the
phenomena is clear, it must be at once admitted that many points are
obscure, and could only be discussed at the cost of a long argument.
In the second place, the physical theory is (as I have shewn) in
manifest conflict with the accounts given by various embryologists of
the development of the spicules, and of the current biological theories
which their descriptions embody; it is beyond our scope to deal with
such descriptions {457} in detail. Lastly, we find ourselves able to
illustrate the same physical principles with greater clearness and
greater certitude in another group of animals, namely the Radiolaria.
In our description of the skeletons occurring within this group we
shall by no means abandon the preliminary classification of microscopic
skeletons which we have laid down; but we shall have occasion to blend
with it the consideration of certain other more or less correlated
phenomena.
The group of microscopic organisms known as the Radiolaria is
extraordinarily rich in diverse forms, or “species.” I do not know how
many of such species have been described and defined by naturalists,
but some thirty years ago the number was said to be over four thousand,
arranged in more than seven hundred genera[468]. Of late years there
has been a tendency to reduce the number, it being found that some
of the earlier species and even genera are but growth-stages of one
and the same form, sometimes mere fragments or “fission-products”
common to several species, or sometimes forms so similar and so
interconnected by intermediate forms that the naturalist denominates
them not “species” but “varieties.” It has to be admitted, in short,
that the conception of species among the Radiolaria has not hitherto
been, and is not yet, on the same footing as that among most other
groups of animals. But apart from the extraordinary multiplicity of
forms among the Radiolaria, there are certain other features in this
multiplicity which arrest our attention. For instance, the distribution
of species in space is curious and vague; many species are found all
over the world, or at least every here and there, with no evidence
of specific limitations of geographical habitat; others occur in the
neighbourhood of the two poles; some are confined to warm and others
to cold currents of the ocean. In time also their distribution is
not less vague: so much so that it has been asserted of them that
“from the Cambrian age downwards, the families and even genera appear
identical with those now living.” Lastly, except perhaps in the case
of a few large “colonial forms,” we seldom if ever find, as is usual
{458} in most animals, a local predominance of one particular species.
On the contrary, in a little pinch of deep-sea mud or of some fossil
“Radiolarian earth,” we shall probably find scores, and it may be even
hundreds, of different forms. Moreover, the radiolarian skeletons
are of quite extraordinary delicacy and complexity, in spite of
their minuteness and the comparative simplicity of the “unicellular”
organisms within which they grow; and these complex conformations have
a wonderful and unusual appearance of geometric regularity. All these
_general_ considerations seem such as to prepare us for the special
need of some physical hypothesis of causation. The little skeletal
fabrics remind us of such objects as snow-crystals (themselves almost
endless in their diversity), rather than of a collection of distinct
animals, constructed in apparent accordance with functional needs, and
distributed in accordance with their fitness for particular situations.
Nevertheless great efforts have been made of recent years to attach “a
biological meaning” to these elaborate structures; and “to justify the
hope that in time the utilitarian character [of the skeleton] will be
more completely recognised[469].”
In the majority of cases, the skeleton of the Radiolaria is composed,
like that of so many sponges, of silica; in one large family, the
Acantharia (and perhaps in some others), it is composed, in great
part at least, of a very unusual constituent, namely strontium
sulphate[470]. There is no fundamental or important morphological
character in which the shells formed of these two constituents
differ from one another; and in no case can the chemical properties
of these inorganic materials be said to influence the form of the
complex skeleton or shell, save only in this general way that, by
their rigidity and toughness, they may give rise to a fabric far more
delicate and slender than we find developed among calcareous organisms.
A slight exception to this rule is found in the presence of true
crystals, which occur within the central capsules of certain {459}
Radiolaria, for instance the genus Collosphaera[471]. Johannes Müller
(whose knowledge and insight never fail to astonish us) remarked that
these were identical in form with crystals of celestine, a sulphate
of strontium and barium; and Bütschli’s discovery of sulphates of
strontium and of barium in kindred forms render it all but certain that
they are actually true crystals of celestine[472].
In its typical form, the Radiolarian body consists of a spherical
mass of protoplasm, around which, and separated from it by some sort
of porous “capsule,” lies a frothy mass, composed of protoplasm
honeycombed into a multitude of alveoli or vacuoles, filled with a
fluid which can scarcely differ much from sea-water[473]. According
to their surface-tension conditions, these vacuoles may appear more
or less isolated and spherical, or joining together in a “froth” of
polygonal cells; and in the latter, which is the commoner condition,
the cells tend to be of equal size, and the resulting polygonal
meshwork beautifully regular. In many cases, a large number of such
simple individual organisms are associated together, forming a floating
colony, and it is highly probable that many other forms, with whose
scattered skeletons we are alone acquainted, had in life formed part
likewise of a colonial organism.
In contradistinction to the sponges, in which the skeleton always
begins as a loose mass of isolated spicules, which only in a few
exceptional cases (such as Euplectella and Farrea) fuse into a
continuous network, the characteristic feature of the Radiolarians lies
in the possession of a continuous skeleton, in the form of a netted
mesh or perforated lacework, sometimes however replaced by and often
associated with minute independent spicules. Before we proceed to treat
of the more complex skeletons, we may begin, then, by dealing with
these comparatively simple cases where either the entire skeleton or
a considerable part of it is represented, not by a continuous fabric,
but by a quantity of loose, separate spicules, or aciculae, which seem,
like the spicules of Alcyonium, {460} to be developed as free and
isolated formations or deposits, precipitated in the colloid matrix,
with no relation of form to the cellular or vesicular boundaries.
These simple acicular spicules occupy a definite position in the
organism. Sometimes, as for instance among the fresh-water Heliozoa
(e.g. Raphidiophrys), they lie on the outer surface of the organism,
and not infrequently (when the spicules are few in number) they tend
to collect round the bases of the pseudopodia, or around the large
radiating spicules, or axial rays, in the cases where these latter are
present. When the spicules are thus localised around some prominent
centre, they tend to take up a position of symmetry in regard to it;
instead of forming a tangled or felted layer, they come to lie side by
side, in a radiating cluster round the focus. In other cases (as for
instance in the well-known Radiolarian _Aulacantha scolymantha_) the
felted layer of aciculae lies at some depth below the surface, forming
a sphere concentric with the entire spherical organism. In either case,
whether the layer of spicules be deep or be superficial, it tends to
mark a “surface of discontinuity,” a meeting place between two distinct
layers of protoplasm or between the protoplasm and the water around;
and it is obvious that, in either case, there are manifestations
of surface-energy at the boundary, which cause the spicules to be
retained there, and to take up their position in its plane. The case
is somewhat, though not directly, analogous to that of a cirrus cloud,
which marks the place of a surface of discontinuity in a stratified
atmosphere.
[Illustration: Fig. 218.]
We have, then, to enquire what are the conditions which shall, apart
from gravity, confine an extraneous body to a surface-film; and we may
do this very simply, by considering the surface-energy of the entire
system. In Fig. 218 we have two fluids in contact with one another
(let us call them water and protoplasm), and a body (_b_) which may
be immersed in either, or may be restricted to the boundary {461}
between. We have here three possible “interfacial contacts” each with
its own specific surface-energy, per unit of surface area: namely, that
between our particle and the water (let us call it α), that between the
particle and the protoplasm (β), and that between water and protoplasm
(γ). When the body lies in the boundary of the two fluids, let us say
half in one and half in the other, the surface-energies concerned are
equivalent to (_S_/2)α + (_S_/2)β; but we must also remember that, by
the presence of the particle, a small portion (equal to its sectional
area _s_) of the original contact-surface between water and protoplasm
has been obliterated, and with it a proportionate quantity of energy,
equivalent to _s_γ, has been set free. When, on the other hand, the
body lies entirely within one or other fluid, the surface-energies of
the system (so far as we are concerned) are equivalent to _S_α + _s_γ,
or _S_β + _s_γ, as the case may be. According as α be less or greater
than β, the particle will have a tendency to remain immersed in the
water or in the protoplasm; but if (_S_/2)(α + β) − _s_γ be less than
either _S_α or _S_β, then the condition of minimal potential will be
found when the particle lies, as we have said, in the boundary zone,
half in one fluid and half in the other; and, if we were to attempt
a more general solution of the problem, we should evidently have to
deal with possible conditions of equilibrium under which the necessary
balance of energies would be attained by the particle rising or sinking
in the boundary zone, so as to adjust the relative magnitudes of the
surface-areas concerned. It is obvious that this principle may, in
certain cases, help us to explain the position even of a _radial_
spicule, which is just a case where the surface of the solid spicule is
distributed between the fluids with a minimal disturbance, or minimal
replacement, of the original surface of contact between the one fluid
and the other.
In like manner we may provide for the case (a common and an important
one) where the protoplasm “creeps up” the spicule, covering it with
a delicate film. In Acanthocystis we have yet another special case,
where the radial spicules plunge only a certain distance into the
protoplasm of the cell, being arrested at a boundary-surface between
an inner and an outer layer of cytoplasm; here we have only to assume
that there is a tension {462} at this surface, between the two layers
of protoplasm, sufficient to balance the tensions which act directly on
the spicule[474].
In various Acanthometridae, besides such typical characters as the
radial symmetry, the concentric layers of protoplasm, and the capillary
surfaces in which the outer, vacuolated protoplasm is festooned
upon the projecting radii, we have another curious feature. On the
surface of the protoplasm where it creeps up the sides of the long
radial spicules, we find a number of elongated bodies, forming in
each case one or several little groups, and lying neatly arranged in
parallel bundles. A Russian naturalist, Schewiakoff, whose views have
been accepted in the text-books, tells us that these are muscular
structures, serving to raise or lower the conical masses of protoplasm
about the radial spicules, which latter serve as so many “tent-poles”
or masts, on which the protoplasmic membranes are hoisted up; and the
little elongated bodies are dignified with various names, such as
“myonemes” or “myophriscs,” in allusion to their supposed muscular
nature[475]. This explanation is by no means convincing. To begin
with, we have precisely similar festoons of protoplasm in a multitude
of other cases where the “myonemes” are lacking; from their minute
size (·006–·012 mm.) and the amount of contraction they are said to be
capable of, the myonemes can hardly be very efficient instruments of
traction; and further, for them to act (as is alleged) for a specific
purpose, namely the “hydrostatic regulation” of the organism giving it
power to sink or to swim, would seem to imply a mechanism of action
and of coordination which is difficult to conceive in these minute
and simple organisms. The fact is (as it seems to me), that the whole
method of explanation is unnecessary. Just as the supposed “hauling
up” of the protoplasmic festoons is at once explained by capillary
phenomena, so also, in all probability, is the position and arrangement
of the little elongated bodies. Whatever the actual nature of these
bodies may be, whether they are truly portions of differentiated
protoplasm, or whether they are foreign bodies or spicular structures
(as bodies occupying a similar position in other cases undoubtedly
are), we can explain their situation on the surface {463} of the
protoplasm, and their arrangement around the radial spicules, all on
the principles of surface-tension[476].
This last case is not of the simplest; and I do not forget that my
explanation of it, which is wholly theoretical, implies a doubt
of Schewiakoff’s statements, which are founded on direct personal
observation. This I am none too willing to do; but whether it be justly
done in this case or not, I hold that it is in principle justifiable
to look with great suspicion upon a number of kindred statements where
it is obvious that the observer has left out of account the purely
physical aspect of the phenomenon, and all the opportunities of simple
explanation which the consideration of that aspect might afford.
――――――――――
Whether it be wholly applicable to this particular and complex case or
no, our general theorem of the localisation and arrestment of solid
particles in a surface-film is of very great biological importance; for
on it depends the power displayed by many little naked protoplasmic
organisms of covering themselves with an “agglutinated” shell.
Sometimes, as in _Difflugia_, _Astrorhiza_ (Fig. 219) and others,
this covering consists of sand-grains picked up from the surrounding
medium, and sometimes, on the other hand, as in _Quadrula_, it consists
of solid particles which are said to arise, as inorganic deposits or
concretions, within the protoplasm itself, and which find their way
outwards to a position of equilibrium in the surface-layer; and in
both cases, the mutual capillary attractions between the particles,
confined to the boundary-layer but enjoying a certain measure of
freedom therein, tends to the orderly arrangement of the particles one
with another, and even to the appearance of a regular “pattern” as the
result of this arrangement.
[Illustration: Fig. 219. Arenaceous Foraminifera; _Astrorhiza limicola_
and _arenaria_. (From Brady’s _Challenger Monograph_.)]
The “picking up” by the protoplasmic organism of a solid particle with
which “to build its house” (for it is hard to avoid this customary use
of anthropomorphic figures of speech, misleading though they be), is
a physical phenomenon kindred to that by which an Amoeba “swallows” a
particle of food. This latter process has been reproduced or imitated
in various pretty experimental {465} ways. For instance, Rhumbler has
shewn that if a thread of glass be covered with shellac and brought
near a drop of chloroform suspended in water, the drop takes in the
spicule, robs it of its shellac covering, and then passes it out
again[477]. It is all a question of relative surface-energies, leading
to different degrees of “adhesion” between the chloroform and the
glass or its covering. Thus it is that the Amoeba takes in the diatom,
dissolves off its proteid covering, and casts out the shell.
Furthermore, as the whole phenomenon depends on a distribution of
surface-energy, the amount of which is specific to certain particular
substances in contact with one another, we have no difficulty
in understanding the _selective action_, which is very often a
conspicuous feature in the phenomenon[478]. Just as some caddis-worms
make their houses of twigs, and others of shells and again others
of stones, so some Rhizopods construct their agglutinated “test”
out of stray sponge-spicules, or frustules of diatoms, or again
of tiny mud particles or of larger grains of sand. In all these
cases, we have apparently to deal with differences in specific {466}
surface-energies, and also doubtless with differences in the total
available amount of surface-energy in relation to gravity or other
extraneous forces. In my early student days, Wyville Thomson used
to tell us that certain deep-sea “Difflugias,” after constructing a
shell out of particles of the black volcanic sand common in parts of
the North Atlantic, finished it off with “a clean white collar” of
little grains of quartz. Even this phenomenon may be accounted for on
surface-tension principles, if we assume that the surface-energy ratios
have tended to change, either with the growth of the protoplasm or by
reason of external variation of temperature or the like; and we are
by no means obliged to attribute the phenomenon to a manifestation of
volition, or taste, or aesthetic skill, on the part of the microscopic
organism. Nor, when certain Radiolaria tend more than others to attract
into their own substance diatoms and such-like foreign bodies, is it
scientifically correct to speak, as some text-books do, of species “in
which diatom selection has become _a regular habit_.” To do so is an
exaggerated misuse of anthropomorphic phraseology.
The formation of an “agglutinated” shell is thus seen to be a purely
physical phenomenon, and indeed a special case of a more general
physical phenomenon which has many other important consequences in
biology. For the shell to assume the solid and permanent character
which it acquires, for instance, in Difflugia, we have only to make
the additional assumption that some small quantities of a cementing
substance are secreted by the animal, and that this substance flows
or creeps by capillary attraction between all the interstices of the
little quartz grains, and ends by binding them all firmly together.
Rhumbler[479] has shewn us how these agglutinated tests, of spicules
or of sand-grains, can be precisely imitated, and how they are formed
with greater or less ease, and greater or less rapidity, according to
the nature of the materials employed, that is to say, according to the
specific surface-tensions which are involved. For instance if we mix up
a little powdered glass with chloroform, and set a drop of the mixture
in water, the glass particles gather neatly round the surface of the
drop so quickly that the eye cannot follow the {467} operation. If we
perform the same experiment with oil and fine sand, dropped into 70
per cent. alcohol, a still more beautiful artificial Rhizopod shell is
formed, but it takes some three hours to do.
It is curious that, just at the very time when Rhumbler was thus
demonstrating the purely physical nature of the Difflugian shell,
Verworn was studying the same and kindred organisms from the older
standpoint of an incipient psychology[480]. But, as Rhumbler himself
admits, Verworn was very careful not to overestimate the apparent signs
of volition, or selective choice, in the little organism’s use of the
material of its dwelling.
――――――――――
This long parenthesis has led us away, for the time being, from the
subject of the Radiolarian skeleton, and to that subject we must now
return. Leaving aside, then, the loose and scattered spicules, which
we have sufficiently discussed, the more perfect Radiolarian skeletons
consist of a continuous and regular structure; and the siliceous (or
other inorganic) material of which this framework is composed tends
to be deposited in one or other of two ways or in both combined: (1)
in the form of long spicular axes, usually conjoined at, or emanating
from, the centre of the protoplasmic body, and forming a symmetric
radial system; (2) in the form of a crust, developed in various ways,
either on the outer surface of the organism or in relation to the
various internal surfaces which separate its concentric layers or its
component vesicles. Not unfrequently, this superficial skeleton comes
to constitute a spherical shell, or a system of concentric or otherwise
associated spheres.
[Illustration: Fig. 220. “Reticulum plasmatique.” (After Carnoy.)]
We have already learned that a great part of the body of the
Radiolarian, and especially that outer portion to which Haeckel has
given the name of the “calymma,” is built up of a great mass of
“vesicles,” forming a sort of stiff froth, and equivalent in the
physical sense (though not necessarily in the biological sense) to
“cells,” inasmuch as the little vesicles have their own well-defined
boundaries, and their own surface phenomena. In short, all that we have
said of cell-surfaces, and cell conformations, in our discussion of
cells and of tissues, will apply in like manner, and under appropriate
conditions, to these. In certain cases, even in {468} so common and
simple a one as the vacuolated substance of an Actinosphaerium, we
may see a very close resemblance, or formal analogy, to an ordinary
cellular or “parenchymatous” tissue, in the close-packed arrangement
and consequent configuration of these vesicles, and even at times in
a slight membranous hardening of their walls. Leidy has figured[481]
some curious little bodies, like small masses of consolidated froth,
which seem to be nothing else than the dead and empty husks, or filmy
skeletons, of Actinosphaerium. And Carnoy[482] has demonstrated in
certain cell-nuclei an all but precisely similar framework, of extreme
delicacy and minuteness, as the result of partial solidification of
interstitial matter in a close-packed system of alveoli (Fig. 220).
[Illustration: Fig. 221. _Aulonia hexagona_, Hkl.]
[Illustration: Fig. 222. _Actinomma arcadophorum_, Hkl.]
Let us now suppose that, in our Radiolarian, the outer surface of the
animal is covered by a layer of froth-like vesicles, uniform or nearly
so in size. We know that their tensions will tend to conform them into
a “honeycomb,” or regular meshwork of hexagons, and that the free end
of each hexagonal prism will be a little spherical cap. Suppose now
that it be at the outer surface of the protoplasm (that namely which
is in contact with the surrounding sea-water), that the siliceous
particles have a tendency to be secreted or adsorbed; it will at once
follow that they will show a tendency to aggregate in the grooves which
separate the vesicles, and the result will be the development of a most
delicate sphere composed of tiny rods arranged in a regular hexagonal
network (e.g. _Aulonia_). Such a conformation is {469} extremely
common, and among its many variants may be found cases in which (e.g.
_Actinomma_), the vesicles have been less regular in size, and some
in which the hexagonal meshwork has been developed not only on one
outer surface, but at successive {470} surfaces, producing a system
of concentric spheres. If the siliceous material be not limited to
the linear junctions of the cells, but spread over a portion of the
outer spherical surfaces or caps, then we shall have the condition
represented in Fig. 223 (_Ethmosphaera_), where the shell appears
perforated by circular instead of hexagonal apertures, and the circular
pores are set on slight spheroidal eminences; and, interconnected with
such types as this, we have others in which the accumulating pellicles
of skeletal matter have extended from the edges into the substance of
the boundary walls and have so produced a system of films, normal to
the surface of the sphere, constituting a very perfect honeycomb, as in
_Cenosphaera favosa_ and _vesparia_[483].
[Illustration: Fig. 223. _Ethmosphaera conosiphonia_, Hkl.]
[Illustration: Fig. 224. Portions of shells of two “species” of
_Cenosphaera_: upper figure, _C. favosa_, lower, _C. vesparia_, Hkl.]
In one or two very simple forms, such as the fresh-water _Clathrulina_,
just such a spherical perforated shell is produced out of some organic,
acanthin-like substance; and in some examples of _Clathrulina_ the
chitinous lattice-work of the shell is just as {471} regular and
delicate, with the meshes just as beautifully hexagonal, as in the
siliceous shells of the oceanic Radiolaria. This is only another proof
(if proof be needed) that the peculiar conformation of these little
skeletons is not due to the material of which they are composed, but to
the moulding of that material upon an underlying vesicular structure.
[Illustration: Fig. 225. _Aulastrum triceros_, Hkl.]
Let us next suppose that, upon some such lattice-work as has just
been described, another and external layer of cells or vesicles is
developed, and that instead of (or perhaps only in addition to) a
second hexagonal lattice-work, which might develop concentrically to
the first in the boundary-furrows of this new layer of cells, the
siliceous matter now tends to be deposited radially, or normally to
the surface of the sphere, just in the lines where the external layer
of vesicles meet one another, three by three. The result will be
that, when the vesicles themselves are removed, a series of radiating
spicules will be revealed, directed outwards from each of the angles of
the original hexagon; as is seen in Fig. 225. And it may further happen
that these radiating skeletal rods are continued at their distal ends
into divergent rays, forming a triple fork, and corresponding (after a
fashion {472} which we have already described as occurring in certain
sponge-spicules) to the three superficial furrows between the adjacent
cells. This last is, as it were, an intermediate stage between the
simple rods and the complete formation of another concentric sphere of
latticed hexagons. Another possible case is when the large and uniform
vesicles of the outer protoplasm are mixed with, or replaced by, much
smaller vesicles, piled on one another in more or less concentric
layers; in this case the radiating rods will no longer be straight,
but will be bent into a zig-zag pattern, with angles in three vertical
planes, corresponding to the successive contacts of the groups of cells
around the axis (Fig. 226).
[Illustration: Fig. 226.]
[Illustration: Fig. 227. A Nassellarian skeleton, _Callimitra
carolotae_, Hkl.]
――――――――――
Among a certain group called the Nassellaria, we find geometrical
forms of peculiar simplicity and beauty,—such for instance as that
which I have represented in Fig. 227. It is obvious at a glance that
this is such a skeleton as may have been formed {473} (I think we
may go so far as to say _must_ have been formed) at the interfaces
of a little tetrahedral group of cells, the four equal cells of the
tetrahedron being in this particular case supplemented by a little
one in the centre of the system. We see, precisely as in the internal
boundary-system of an artificial group of four soap-bubbles, the plane
surfaces of contact, six in number; the relation to one another of
each triple set of interfacial planes, meeting one another at equal
angles of 120°; and finally the relation of the four lines or edges
of triple contact, which tend (but for the little central vesicle)
to meet at co-equal solid angles in the centre of the system, all as
we have described on p. 318. In short, each triple-walled re-entrant
angle of the little shell has essentially the configuration (or a part
thereof) of what we have called a “Maraldi pyramid” in our account of
the architecture of the honeycomb, on p. 329[484].
There are still two or three remarkable or peculiar features in this
all but mathematically perfect shell, and they are in part easy and in
part they seem more difficult of interpretation.
[Illustration: Fig. 228. An isolated portion of the skeleton of
_Dictyocha_.]
[Illustration: Fig. 229. _Dictyocha stapedia_, Hkl.]
We notice that the amount of solid matter deposited in the plane
interfacial boundaries is greatly increased at the outer margin of
each boundary wall, where it merges or coincides with the superficial
furrow which separates the free, spherical surfaces of the bubbles
from one another; and we may sometimes find that, along these edges,
the skeleton remains complete and strong, while it shows signs of
imperfect development or of breaking away over great part of the rest
of the interfacial surfaces. In this there is nothing anomalous, for
we have already recognised that it is at the edges or margins of the
interfacial partition-walls that the manifestation of surface-energy
will tend to reach its maximum. And just as we have seen that, in
certain of our “multicellular” spherical Radiolarians, it is at the
superficial {474} edges or borders of the partitions, and here only,
that skeletal formation occurs (giving rise to the netted shell with
its hexagonal meshes of Fig. 221), so also at times, in the case of
such little aggregates of cells or vesicles as the four-celled system
of Callimitra, it may happen that about the external boundary-_lines_,
and not in the interior boundary-_planes_, the whole of the skeletal
matter is aggregated. In Fig. 228 we see a curious little skeletal
structure or complex spicule, whose conformation is easily accounted
for after this fashion. Little spicules such as this form isolated
portions of the skeleton in the genus _Dictyocha_, and occur scattered
over the spherical surface of the organism (Fig. 229). The more or
less basket-shaped spicule has evidently been developed about a little
cluster of four cells or vesicles, lying in or on the plane of the
surface of the organism, and therefore arranged, not in the tetrahedral
form of Callimitra, but in the manner in which four contiguous cells
lying side by side normally set themselves, like the four cells of a
segmenting egg: that is to say with an intervening “polar furrow,”
whose ends mark the meeting place, at equal angles, of the cells in
groups of three.
The little projecting spokes, or spikes, which are set normally to the
main basket-work, seem to be incompleted portions of a larger basket,
or in other words imperfectly formed elements corresponding to the
interfacial contacts in the surrounding parts {475} of the system.
Similar but more complex formations, all explicable as basket-like
frameworks developed around a cluster of cells, are known in great
variety.
In our Nassellarian itself, and in many other cases where the plane
interfacial boundary-walls are skeletonised, we see that the siliceous
matter is not deposited in an even and continuous layer, like the waxen
walls of a bee’s cell, but constitutes a meshwork of fine curvilinear
threads; and the curves seem to run, on the whole, isogonally, and to
form three main series, one approximately parallel to, or concentric
with, the outer or free edge of the partition, and the other two
related severally to its two edges of attachment. Sometimes (as may
also be seen in our figure), the system is still further complicated
by a fourth series of linear elements, which tend to run radially from
the centre of the system to the free edge of each partition. As regards
the former, their arrangement is such as would result if deposition or
solidification had proceeded in waves, starting independently from each
of the three boundaries of the little partition-wall; and something
of this kind is doubtless what has happened. We are reminded at once
of the wave-like periodicity of the Liesegang phenomenon. But apart
from this we might conceive of other explanations. For instance, the
liquid film which originally constitutes the partition must easily be
thrown into _vibrations_, and (like the dust upon a Chladni’s plate)
minute particles of matter in contact with the film would tend to take
up their position in a symmetrical arrangement, in direct relation to
the nodal points or lines of the vibrating surface[485]. Some such
explanation as this (to my thinking) must be invoked to account for
the minute and varied and very beautiful patterns upon many diatoms,
the resemblance of which patterns (in certain of their simpler cases)
to the Chladni figures is sometimes striking and obvious. But the
many special problems which the diatom skeleton suggests I have not
attempted to consider.
[Illustration: Fig. 230.]
The last peculiarity of our Nassellarian lies in an apparent departure
from what we should at first expect in the way of its {476} external
symmetry. Were the system actually composed of four spherical vesicles
in mutual contact, the outer margin of each of the six interfacial
planes would obviously be a circular arc; and accordingly, at each
angle of the tetrahedron, we should expect to have a depressed, or
re-entrant angle, instead of a prominent cusp. This is all doubtless
due to some simple balance of tensions, whose precise nature and
distribution is meanwhile a matter of conjecture. But it seems as
though an extremely simple explanation would go a long way, and
possibly the whole way, to meet this particular case. In our ordinary
plane diagram of three cells, or soap-bubbles, in contact, we know
(and we have just said) that the tensions of the three partitions draw
inwards the outer walls of the system, till at each point of triple
contact (_P_) we tend to get a triradiate, equiangular junction. But
if we introduce another bubble into the centre of the system (Fig.
230), then, as Plateau shewed, the tensions of its walls and those of
the three partitions by which it is now suspended, again balance one
another, and the central bubble appears (in plane projection) as a
curvilinear, equilateral triangle. We have only got to convert this
plane diagram into that of a tetrahedral solid to obtain _almost_
precisely the configuration which we are seeking to explain. Now we
observe that, so far as our figure of Callimitra informs us, this
is just the shape of the little bubble which occupies the centre of
the tetrahedral system in that Radiolarian skeleton. And I conceive,
accordingly, that the entire organism was not limited to the four cells
or vesicles (together with the little central {477} fifth) which
we have hitherto been imagining, but there must have been an outer
tetrahedral system, enclosing the cells which fabricated the skeleton,
just as these latter enclosed, and deformed, the little bubble in
the centre of all. We have only to suppose that this hypothetical
tetrahedral series, forming the outer layer or surface of the whole
system, was for some chemico-physical reason incapable of secreting at
its interfacial contacts a skeletal fabric[486].
In this hypothetical case, the edges of the skeletal system would be
circular arcs, meeting one another at an angle of 120°, or, in the
solid pyramid, of 109°: and this latter is _very nearly_ the condition
which our little skeleton actually displays. But we observe in Fig.
227 that, in the immediate neighbourhood of the tetrahedral angle, the
circular arcs are slightly drawn out into projecting cusps (cf. Fig.
230, _B_). There is no S-shaped curvature of the tetrahedral edges as a
whole, but a very slight one, a very slight change of curvature; close
to the apex. This, I conceive, is nothing more than what, in a material
system, we are bound to have, to represent a “surface of continuity.”
It is a phenomenon precisely analogous to Plateau’s “bourrelet,”
which we have already seen to be a constant feature of all cellular
systems, rounding off the sharp angular contacts by which (in our more
elementary treatment) we expect one film to make its junction with
another[487].
――――――――――
In the foregoing examples of Radiolaria, the symmetry which the
organism displays would seem to be identical with that symmetry of
forces which is due to the assemblage of surface-tensions in the
whole system; this symmetry being displayed, in one class of cases,
in a complex spherical mass of froth, and in {478} another class
in a simpler aggregate of a few, otherwise isolated, vesicles. But
among the vast number of other known Radiolaria, there are certain
forms (especially among the Phaeodaria and Acantharia) which display
a still more remarkable symmetry, the origin of which is by no means
clear, though surface-tension doubtless plays a part in its causation.
These are cases in which (as in some of those already described) the
skeleton consists (1) of radiating spicular rods, definite in number
and position, and (2) of interconnecting rods or plates, tangential to
the more or less spherical body of the organism, whose form becomes,
accordingly, that of a geometric, polyhedral solid. It may be that
there is no mathematical difference, save one of degree, between such a
hexagonal polyhedron as we have seen in _Aulacantha_, and those which
we are about to describe; but the greater regularity, the numerical
symmetry, and the apparent simplicity of these latter, makes of them a
class apart, and suggests problems which have not been solved nor even
investigated.
[Illustration: Fig. 231. Skeletons of various Radiolarians, after
Haeckel. 1. _Circoporus sexfurcus_; 2. _C. octahedrus_; 3. _Circogonia
icosahedra_; 4. _Circospathis novena_; 5. _Circorrhegma dodecahedra_.]
The matter is sufficiently illustrated by the accompanying figures,
all drawn from Haeckel’s Monograph of the Challenger Radiolaria[488].
In one of these we see a regular octahedron, in another a regular,
or pentagonal dodecahedron, in a third a regular icosahedron. In all
cases the figure appears to be perfectly symmetrical, though neither
the triangular facets of the octahedron and icosahedron, nor the
pentagonal facets of the dodecahedron, are necessarily plane surfaces.
In all of these cases, the radial spicules correspond to the solid
angles of the figure; and they are, accordingly, six in number in the
octahedron, twenty in the dodecahedron, and twelve in the icosahedron.
If we add to these three figures the regular tetrahedron, which we have
had frequent occasion to study, and the cube (which is represented,
at least in outline, in the skeleton of the hexactinellid sponges),
we have completed the series of the five regular polyhedra known to
geometers, the _Platonic bodies_[489] of the older mathematicians. It
is at first sight all the more remarkable that we should here meet
{480} with the whole five regular polyhedra, when we remember that,
among the vast variety of crystalline forms known among minerals, the
regular dodecahedron and icosahedron, simple as they are from the
mathematical point of view, never occur. Not only do these latter never
occur in Crystallography, but (as is explained in text-books of that
science) it has been shewn that they cannot occur, owing to the fact
that their indices (or numbers expressing the relation of the faces
to the three primary axes) involve an irrational quantity: whereas it
is a fundamental law of crystallography, involved in the whole theory
of space-partitioning, that “the indices of any and every face of a
crystal are small whole numbers[490].” At the same time, an imperfect
pentagonal dodecahedron, whose pentagonal sides are non-equilateral, is
common among crystals. If we may safely judge from Haeckel’s figures,
the pentagonal dodecahedron of the Radiolarian is perfectly regular,
and we must presume, accordingly, that it is not brought about by
principles of space-partitioning similar to those which manifest
themselves in the phenomenon of crystallisation. It will be observed
that in all these radiolarian polyhedral shells, the surface of each
external facet is formed of a minute hexagonal network, whose probable
origin, in relation to a vesicular structure, is such as we have
already discussed.
[Illustration: Fig. 232. _Dorataspis_ sp.; diagrammatic.]
In certain allied Radiolaria (Fig. 232), which, like the dodecahedral
form figured in Fig. 231, 5, have twenty radial spines, these latter
are commonly described as being arranged in a certain very singular
way. It is stated that their arrangement may be referred {481} to a
series of five parallel circles on the sphere, corresponding to the
equator (_c_), the tropics (_b_, _d_) and the polar circles (_a_, _e_);
and that beginning with four equidistant spines in the equator, we
have alternating whorls of four, radiating outwards from the sphere
in each of the other parallel zones. This rule was laid down by the
celebrated Johannes Müller, and has ever since been used and quoted
as Müller’s law. The chief point in this alleged arrangement which
strikes us at first sight as very curious, is that there is said to
be no spine at either pole; and when we come to examine carefully the
figure of the organism, we find that the received description does not
do justice to the facts. We see, in the first place, from such figures
as Figs. 232, 234, that here, unlike our former cases, the radial
spines issue through the facets (and through _all_ the facets) of the
polyhedron, instead of through its solid angles; and accordingly,
that our twenty spines correspond (not, as before, to a dodecahedron)
but to some sort of an icosahedron. We see in the next place, that
this icosahedron is composed of faces, or plates, of two different
kinds, some hexagonal and some pentagonal; and when we look closer,
we discover that the whole figure is that of a hexagonal prism, whose
twelve solid angles are replaced by pentagonal facets. Both hexagons
and pentagons {482} appear to be perfectly equilateral, but if we
try to construct a plane-sided polyhedron of this kind, we soon find
that it is impossible; for into the angles between the six equatorial
hexagons those of the six united pentagons will not fit. The figure
however can be easily constructed if we replace the straight edges
(or some of them) by curves, and the plane facets by corresponding,
slightly curved, surfaces. The true symmetry of this figure, then, is
hexagonal, with a polar axis, produced into two polar spicules; with
six equatorial spicules, or rays; and with two sets of six spicular
rays, interposed between the polar axis and the equatorial rays, and
alternating in position with the latter.
Müller’s description was emended by Brandt, and what is now known as
“Brandt’s law,” viz. that the symmetry consists of two polar rays, and
three whorls of six each, coincides with the above description so far
as the spicular axes go: save only that Brandt specifically states
that the intermediate whorls stand equidistant between the equator
and the poles, i.e. in latitude 45°. While not far from the truth,
this statement is not exact; for according to the geometry of the
figure, the intermediate cycles obviously stand in a slightly higher
latitude, but this latitude I have not attempted to determine; for the
calculation seems to be a little troublesome owing to the curvature of
the sides of the figure, and the enquiring mathematician will perform
it more easily than I. Brandt, if I understand him rightly, did not
propose his “law” as a substitute for Müller’s law, but as a second
law applicable to a few particular cases. I on the other hand can find
no case to which Müller’s law properly applies.
If we construct such a polyhedron, and set it in the position of
Fig. 232, _B_, we shall easily see that it is capable of explanation
(though improperly) in accordance with Müller’s law; for the four
equatorial rays of Müller (_c_) now correspond to the two polar and
to two opposite equatorial facets of our polyhedron: the four “polar”
rays of Müller (_a_ or _e_) correspond to two adjacent hexagons and
two intermediate pentagons of the figure: and Müller’s “tropical”
rays (_b_ or _d_) are those which emanate from the remaining four
pentagonal facets, in each half of the figure. In some cases, such as
Haeckel’s _Phatnaspis cristata_ (Fig. 233), we have an ellipsoidal
body, from which the spines emerge in the order described, but which
is not obviously divided by facets. In Fig. 234 I have indicated the
facets corresponding to the rays, and dividing the surface in the usual
symmetrical way. {483}
[Illustration: Fig. 233. _Phatnaspis cristata_, Hkl.]
[Illustration: Fig. 234. The same, diagrammatic.]
{484}
Within any polyhedron we may always inscribe another polyhedron,
whose corners correspond in number to the sides or facets of the
original figure, or (in alternative cases) to a certain number of
these sides; and a similar result is obtained by bevelling off the
corners of the original polyhedron. We may obtain a precisely similar
symmetrical result if (in such a case as these Radiolarians which we
are describing), we imagine the radial spines to be interconnected by
tangential rods, instead of by the complete facets which we have just
been dealing with. In our complicated polyhedron with its twenty radial
spines arranged in the manner described there are various symmetrical
ways in which we may imagine these interconnecting bars to be arranged.
The most symmetrical of these is one in which the whole surface is
divided into eighteen rhomboidal areas, obtained by systematically
connecting each group of four adjacent radii. This figure has eighteen
faces (_F_), twenty corners (_C_), and therefore thirty-six edges
(_E_), in conformity with Euler’s theorem, _F_ + _C_ = _E_ + 2.
[Illustration: Fig. 235. _Phractaspis prototypus_, Hkl.]
Another symmetrical arrangement will divide the surface into fourteen
rhombs and eight triangles. This latter arrangement is obtained by
linking up the radial rods as follows: _aaaa_, _aba_, _abcb_, _bcdc_,
etc. Here we have again twenty corners, but we have twenty-two faces;
the number of edges, or tangential spicular bars, will be found,
therefore, by the above formula, to be forty. In Haeckel’s figure of
_Phractaspis prototypus_ we have a spicular skeleton which appears to
be constructed precisely upon this plan, and to be derivable from the
faceted polyhedron precisely after this manner.
In all these latter cases it is the arrangement of the axial rods, or
in other words the “polar symmetry” of the entire organism, which lies
at the root of the matter, and which, if only {485} we could account
for it, would make it comparatively easy to explain the superficial
configuration. But there are no obvious mechanical forces by which we
can so explain this peculiar polarity. This at least is evident, that
it arises in the central mass of protoplasm, which is the essential
living portion of the organism as distinguished from that frothy
peripheral mass whose structure has helped us to explain so many
phenomena of the superficial or external skeleton. To say that the
arrangement depends upon a specific polarisation of the cell is merely
to refer the problem to other terms, and to set it aside for future
solution. But it is possible that we may learn something about the
lines in which _to seek for_ such a solution by considering the case
of Lehmann’s “fluid crystals,” and the light which they throw upon the
phenomena of molecular aggregation.
The phenomenon of “fluid crystallisation” is found in a number of
chemical bodies; it is exhibited at a specific temperature for each
substance; and it would seem to be limited to bodies in which there
is a more or less elongated, or “chain-like” arrangement of the atoms
in the molecule. Such bodies, at the appropriate temperature, tend
to aggregate themselves into masses, which are sometimes spherical
drops or globules (the so-called “spherulites”), and sometimes have
the definite form of needle-like or prismatic crystals. In either case
they remain liquid, and are also doubly refractive, polarising light
in brilliant colours. Together with them are formed ordinary solid
crystals, also with characteristic polarisation, and into such solid
crystals all the fluid material ultimately turns. It is evident that
in these liquid crystals, though the molecules are freely mobile,
just as are those of water, they are yet subject to, or endowed with,
a “directive force,” a force which confers upon them a definite
configuration or “polarity,” the _Gestaltungskraft_ of Lehmann.
Such an hypothesis as this had been gradually extruded from the
theories of mathematical crystallography[491]; and it had come to be
believed that the symmetrical conformation of a homogeneous crystalline
structure was sufficiently explained by the mere mechanical fitting
together of appropriate structural units along the easiest and simplest
lines of “close packing”: just as {486} a pile of oranges becomes
definite, both in outward form and inward structural arrangement,
without the play of any _specific_ directive force. But while our
conceptions of the tactical arrangement of crystalline molecules
remain the same as before, and our hypotheses of “modes of packing” or
of “space-lattices” remain as useful as ever for the definition and
explanation of the molecular arrangements, an entirely new theoretical
conception is introduced when we find such space-lattices maintained
in what has hitherto been considered the molecular freedom of a liquid
field; and we are constrained, accordingly, to postulate a specific
molecular force, or “Gestaltungskraft” (not unlike Kepler’s “facultas
formatrix”), to account for the phenomenon.
Now just as some sort of specific “Gestaltungskraft” had been of old
the _deus ex machina_ accounting for all crystalline phenomena (_gnara
totius geometriæ, et in ea exercita_, as Kepler said), and as such an
hypothesis, after being dethroned and repudiated, has now fought its
way back and has made good its right to be heard, so it may be also
in biology. We begin by an easy and general assumption of _specific
properties_, by which each organism assumes its own specific form; we
learn later (as it is the purpose of this book to shew) that throughout
the whole range of organic morphology there are innumerable phenomena
of form which are not peculiar to living things, but which are more
or less simple manifestations of ordinary physical law. But every now
and then we come to certain deep-seated signs of protoplasmic symmetry
or polarisation, which seem to lie beyond the reach of the ordinary
physical forces. It by no means follows that the forces in question
are not essentially physical forces, more obscure and less familiar
to us than the rest; and this would seem to be the crucial lesson for
us to draw from Lehmann’s surprising and most beautiful discovery.
For Lehmann seems actually to have demonstrated, in non-living,
chemical bodies, the existence of just such a determinant, just such
a “Gestaltungskraft,” as would be of infinite help to us if we might
postulate it for the explanation (for instance) of our Radiolarian’s
axial symmetry. But further than this we cannot go; for such analogy as
we seem to see in the Lehmann phenomenon soon evades us, and refuses
to be pressed home. Not only is it the case, as we have already {487}
seen, that certain of the geometric forms assumed by the symmetrical
Radiolarian shells are just such as the “space-lattice” theory would
seem to be inapplicable to, but it is in other ways obvious that
symmetry of _crystallisation_, whether liquid or solid, has no close
parallel, but only a series of analogies, in the protoplasmic symmetry
of the living cell.
{488}