_C. integra_; (B) _C. groenlandica_; (C) _C. bispinosa_; (D) _C.
raridentata_.]
Another phenomenon displayed in the same experiments is the formation
of a rope-like or cord-like thickening of the edge of the annulus.
This is due to the more or less sudden checking at the rim of the flow
of liquid rising from below: and a similar peripheral thickening is
frequently seen, not only in some of our hydroid cups, but in many
Vorticellas (cf. Fig. 75), and other organic cup-like conformations. A
perusal of Mr Worthington’s book will soon suggest that these are not
the only manifestations of surface-tension in connection with splashes
which present curious resemblances and analogies to phenomena of
organic form.
The phenomena of an ordinary liquid splash are so swiftly {238}
transitory that their study is only rendered possible by
“instantaneous” photography: but this excessive rapidity is not
an essential part of the phenomenon. For instance, we can repeat
and demonstrate many of the simpler phenomena, in a permanent or
quasi-permanent form, by splashing water on to a surface of dry sand,
or by firing a bullet into a soft metal target. There is nothing,
then, to prevent a slow and lasting manifestation, in a viscous
medium such as a protoplasmic organism, of phenomena which appear
and disappear with prodigious rapidity in a more mobile liquid. Nor
is there anything peculiar in the “splash” itself; it is simply a
convenient method of setting up certain motions or currents, and
producing certain surface-forms, in a liquid medium,—or even in such
an extremely imperfect fluid as is represented (in another series of
experiments) by a bed of sand. Accordingly, we have a large range
of possible conditions under which the organism might conceivably
display configurations analogous to, or identical with, those which Mr
Worthington has shewn us how to exhibit by one particular experimental
method.
To one who has watched the potter at his wheel, it is plain that the
potter’s thumb, like the glass-blower’s blast of air, depends for
its efficacy upon the physical properties of the medium on which it
operates, which for the time being is essentially a fluid. The cup
and the saucer, like the tube and the bulb, display (in their simple
and primitive forms) beautiful surfaces of equilibrium as manifested
under certain limiting conditions. They are neither more nor less than
glorified “splashes,” formed slowly, under conditions of restraint
which enhance or reveal their mathematical symmetry. We have seen, and
we shall see again before we are done, that the art of the glass-blower
is full of lessons for the naturalist as also for the physicist:
illustrating as it does the development of a host of mathematical
configurations and organic conformations which depend essentially on
the establishment of a constant and uniform pressure within a _closed_
elastic shell or fluid envelope. In like manner the potter’s art
illustrates the somewhat obscurer and more complex problems (scarcely
less frequent in biology) of a figure of equilibrium which is an
_open_ surface, or solid, of revolution. It is clear, at the same
time, that the two series of problems are closely akin; for the {239}
glass-blower can make most things that the potter makes, by cutting
off _portions_ of his hollow ware. And besides, when this fails, and
the glass-blower, ceasing to blow, begins to use his rod to trim
the sides or turn the edges of wineglass or of beaker, he is merely
borrowing a trick from the craft of the potter.
It would be venturesome indeed to extend our comparison with these
liquid surface-tension phenomena from the cup or calycle of the
hydrozoon to the little hydroid polype within: and yet I feel convinced
that there is something to be learned by such a comparison, though
not without much detailed consideration and mathematical study of
the surfaces concerned. The cylindrical body of the tiny polype, the
jet-like row of tentacles, the beaded annulations which these tentacles
exhibit, the web-like film which sometimes (when they stand a little
way apart) conjoins their bases, the thin annular film of tissue which
surrounds the little organism’s mouth, and the manner in which this
annular “peristome” contracts[295], like a shrinking soap-bubble, to
close the aperture, are every one of them features to which we may find
a singular and striking parallel in the surface-tension phenomena which
Mr Worthington has illustrated and demonstrated in the case of the
splash.
Here however, we may freely confess that we are for the present on the
uncertain ground of suggestion and conjecture; and so must we remain,
in regard to many other simple and symmetrical organic forms, until
their form and dynamical stability shall have been investigated by the
mathematician: in other words, until the mathematicians shall have
become persuaded that there is an immense unworked field wherein they
may labour, in the detailed study of organic form.
――――――――――
According to Plateau, the viscidity of the liquid, while it helps to
retard the breaking up of the cylinder and so increases the length of
the segments beyond that which theory demands, has nevertheless less
influence in this direction than we might have expected. On the other
hand, any external support or adhesion, such as contact with a solid
body, will be equivalent to a reduction of surface-tension and so will
very greatly increase the {240} stability of our cylinder. It is for
this reason that the mercury in our thermometer tubes does not as a
rule separate into drops, though it occasionally does so, much to our
inconvenience. And again it is for this reason that the protoplasm in
a long and growing tubular or cylindrical cell does not necessarily
divide into separate cells and internodes, until the length of these
far exceeds the theoretic limits. Of course however and whenever it
does so, we must, without ever excluding the agency of surface tension,
remember that there may be other forces affecting the latter, and
accelerating or retarding that manifestation of surface tension by
which the cell is actually rounded off and divided.
In most liquids, Plateau asserts that, on the average, the influence
of viscosity is such as to cause the cylinder to segment when its
length is about four times, or at most from four to six times that
of its diameter: instead of a fraction over three times as, in a
perfect fluid, theory would demand. If we take it at four times, it
may then be shewn that the resulting spheres would have a diameter
of about 1·8 times, and their distance apart would be equal to about
2·2 times the diameter of the original cylinder. The calculation is
not difficult which would shew how these numbers are altered in the
case of a cylinder formed around a solid core, as in the case of
the spider’s web. Plateau has also made the interesting observation
that the _time_ taken in the process of division of the cylinder is
directly proportional to the diameter of the cylinder, while varying
considerably with the nature of the liquid. This question, of the time
occupied in the division of a cell or filament, in relation to the
dimensions of the latter, has not so far as I know been enquired into
by biologists.
――――――――――
From the simple fact that the sphere is of all surfaces that whose
surface-area for a given volume is an absolute minimum, we have already
seen it to be plain that it is the one and only figure of equilibrium
which will be assumed under surface-tension by a drop or vesicle, when
no other disturbing factors are present. One of the most important of
these disturbing factors will be introduced, in the form of complicated
tensions and pressures, when one drop is in contact with another drop
and when a system of intermediate films or partition walls is developed
between them. {241} This subject we shall discuss later, in connection
with cell-aggregates or tissues, and we shall find that further
theoretical considerations are needed as a preliminary to any such
enquiry. Meanwhile let us consider a few cases of the forms of cells,
either solitary, or in such simple aggregates that their individual
form is little disturbed thereby.
Let us clearly understand that the cases we are about to consider
are those cases where the perfect symmetry of the sphere is replaced
by another symmetry, less complete, such as that of an ellipsoidal
or cylindrical cell. The cases of asymmetrical deformation or
displacement, such as is illustrated in the production of a bud or
the development of a lateral branch, are much simpler. For here we
need only assume a slight and localised variation of surface-tension,
such as may be brought about in various ways through the heterogeneous
chemistry of the cell; to this point we shall return in our chapter on
Adsorption. But the diffused and graded asymmetry of the system, which
brings about for instance the ellipsoidal shape of a yeast-cell, is
another matter.
If the sphere be the one surface of complete symmetry and therefore
of independent equilibrium, it follows that in every cell which is
otherwise conformed there must be some definite force to cause its
departure from sphericity; and if this cause be the very simple and
obvious one of the resistance offered by a solidified envelope, such as
an egg-shell or firm cell-wall, we must still seek for the deforming
force which was in action to bring about the given shape, prior to the
assumption of rigidity. Such a cause may be either external to, or may
lie within, the cell itself. On the one hand it may be due to external
pressure or to some form of mechanical restraint: as it is in all our
experiments in which we submit our bubble to the partial restraint of
discs or rings or more complicated cages of wire; and on the other
hand it may be due to intrinsic causes, which must come under the head
either of differences of internal pressure, or of lack of homogeneity
or isotropy in the surface itself[296]. {242}
Our full formula of equilibrium, or equation to an elastic surface,
is _P_ = _p_{e}_ + (_T_/_R_ + _T′_/_R′_), where _P_ is the internal
pressure, _p_{e}_ any extraneous pressure normal to the surface,
_R_, _R′_ the radii of curvature at a point, and _T_, _T′_, the
corresponding tensions, normal to one another, of the envelope.
Now in any given form which we are seeking to account for, _R_, _R′_
are known quantities; but all the other factors of the equation are
unknown and subject to enquiry. And somehow or other, by this formula,
we must account for the form of any solitary cell whatsoever (provided
always that it be not formed by successive stages of solidification),
the cylindrical cell of Spirogyra, the ellipsoidal yeast-cell, or (as
we shall see in another chapter) the shape of the egg of any bird. In
using this formula hitherto, we have taken it in a simplified form,
that is to say we have made several limiting assumptions. We have
assumed that _P_ was simply the uniform hydrostatic pressure, equal in
all directions, of a body of liquid; we have assumed that the tension
_T_ was simply due to surface-tension in a homogeneous liquid film,
and was therefore equal in all directions, so that _T_ = _T′_; and we
have only dealt with surfaces, or parts of a surface, where extraneous
pressure, _p_{n}_, was non-existent. Now in the case of a bird’s egg,
the external pressure _p_{n}_, that is to say the pressure exercised by
the walls of the oviduct, will be found to be a very important factor;
but in the case of the yeast-cell or the Spirogyra, wholly immersed in
water, no such external pressure comes into play. We are accordingly
left, in such cases as these last, with two hypotheses, namely that
the departure from a spherical form is due to inequalities in the
internal pressure _P_, or else to inequalities in the tension _T_,
that is to say to a difference between _T_ and _T′_. In other words,
it is theoretically possible that the oval form of a yeast-cell is due
to a greater internal pressure, a greater “tendency to grow,” in the
direction of the longer axis of the ellipse, or alternatively, that
with equal and symmetrical tendencies to growth there is associated
a difference of external resistance in {243} respect of the tension
of the cell-wall. Now the former hypothesis is not impossible; the
protoplasm is far from being a perfect fluid; it is the seat of various
internal forces, sometimes manifestly polar; and accordingly it is
quite possible that the internal forces, osmotic and other, which
lead to an increase of the content of the cell and are manifested in
pressure outwardly directed upon its wall may be unsymmetrical, and
such as to lead to a deformation of what would otherwise be a simple
sphere. But while this hypothesis is not impossible, it is not very
easy of acceptance. The protoplasm, though not a perfect fluid, has
yet on the whole the properties of a fluid; within the small compass
of the cell there is little room for the development of unsymmetrical
pressures; and, in such a case as Spirogyra, where a large part of the
cavity is filled by a fluid and watery cell-sap, the conditions are
still more obviously those under which a uniform hydrostatic pressure
is to be expected. But in variations of _T_, that is to say of the
specific surface-tension per unit area, we have an ample field for
all the various deformations with which we shall have to deal. Our
condition now is, that (_T_/_R_ + _T′_/_R′_) = a constant; but it
no longer follows, though it may still often be the case, that this
will represent a surface of absolute minimal area. As soon as _T_ and
_T′_ become unequal, it is obvious that we are no longer dealing with
a perfectly liquid surface film; but its departure from a perfect
fluidity may be of all degrees, from that of a slight non-isotropic
viscosity to the state of a firm elastic membrane[297]. And it matters
little whether this viscosity or semi-rigidity be manifested in the
self-same layer which is still a part of the protoplasm of the cell,
or in a layer which is completely differentiated into a distinct and
separate membrane. As soon as, by secretion or “adsorption,” the
molecular constitution of the surface layer is altered, it is clearly
conceivable that the alteration, or the secondary chemical changes
which follow it, may be such as to produce an anisotropy, and to render
the molecular forces less capable in one direction than another of
exerting that contractile force by which they are striving to reduce
to an absolute minimum the {244} surface area of the cell. A slight
inequality in two opposite directions will produce the ellipsoid cell,
and a very great inequality will give rise to the cylindrical cell[298].
I take it therefore, that the cylindrical cell of Spirogyra, or any
other cylindrical cell which grows in freedom from any manifest
external restraint, has assumed that particular form simply by reason
of the molecular constitution of its developing surface-membrane; and
that this molecular constitution was anisotropous, in such a way as to
render extension easier in one direction than another.
Such a lack of homogeneity or of isotropy, in the cell-wall is often
rendered visible, especially in plant-cells, in various ways, in the
form of concentric lamellae, annular and spiral striations, and the
like.
But this phenomenon, while it brings about a certain departure from
complete symmetry, is still compatible with, and coexistent with,
many of the phenomena which we have seen to be associated with
surface-tension. The symmetry of tensions still leaves the cell a solid
of revolution, and its surface is still a surface of equilibrium. The
fluid pressure within the cylinder still causes the film or membrane
which caps its ends to be of a spherical form. And in the young cell,
where the surface pellicle is absent or but little differentiated, as
for instance in the oögonium of Achlya, or in the young zygospore of
Spirogyra, we always see the tendency of the entire structure towards
a spherical form reasserting itself: unless, as in the latter case, it
be overcome by direct compression within the cylindrical mother-cell.
Moreover, in those cases where the adult filament consists of
cylindrical cells, we see that the young, germinating spore, at first
spherical, very soon assumes with growth an elliptical or ovoid form:
the direct result of an incipient anisotropy of its envelope, which
when more developed will convert the ovoid into a cylinder. We may also
notice that a truly cylindrical cell is comparatively rare; for in most
cases, what we call a cylindrical cell shews a distinct bulging of
its sides; it is not truly a cylinder, but a portion of a spheroid or
ellipsoid. {245}
Unicellular organisms in general, including the protozoa, the
unicellular cryptogams, the various bacteria, and the free, isolated
cells, spores, ova, etc. of higher organisms, are referable for the
most part to a very small number of typical forms; but besides a
certain number of others which may be so referable, though obscurely,
there are obviously many others in which either no symmetry is to be
recognized, or in which the form is clearly not one of equilibrium.
Among these latter we have Amoeba itself, and all manner of amoeboid
organisms, and also many curiously shaped cells, such as the
Trypanosomes and various other aberrant Infusoria. We shall return to
the consideration of these; but in the meanwhile it will suffice to
say that, as their surfaces are not equilibrium-surfaces, so neither
are the living cells themselves in any stable equilibrium. On the
contrary, they are in continual flux and movement, each portion of
the surface constantly changing its form, and passing from one phase
to another of an equilibrium which is never stable for more than a
moment. The former class, which rest in stable equilibrium, must fall
(as we have seen) into two classes,—those whose equilibrium arises
from liquid surface-tension alone, and those in whose conformation
some other pressure or restraint has been superimposed upon ordinary
surface-tension.
To the fact that these little organisms belong to an order of magnitude
in which form is mainly, if not wholly, conditioned and controlled
by molecular forces, is due the limited range of forms which they
actually exhibit. These forms vary according to varying physical
conditions. Sometimes they do so in so regular and orderly a way that
we instinctively explain them merely as “phases of a life-history,” and
leave physical properties and physical causation alone: but many of
their variations of form we treat as exceptional, abnormal, decadent
or morbid, and are apt to pass these over in neglect, while we give
our attention to what we suppose to be the typical or “characteristic”
form or attitude. In the case of the smallest organisms, the bacteria,
micrococci, and so forth, the range of form is especially limited,
owing to their minuteness, the powerful pressure which their highly
curved surfaces exert, and the comparatively homogeneous nature of
their substance. But within their narrow range of possible diversity
{246} these minute organisms are protean in their changes of form.
A certain species will not only change its shape from stage to stage
of its little “cycle” of life; but it will be remarkably different
in outward form according to the circumstances under which we find
it, or the histological treatment to which we submit it. Hence the
pathological student, commencing the study of bacteriology, is early
warned to pay little heed to differences of _form_, for purposes of
recognition or specific identification. Whatever grounds we may have
for attributing to these organisms a permanent or stable specific
identity (after the fashion of the higher plants and animals), we can
seldom safely do so on the ground of definite and always recognisable
_form_: we may often be inclined, in short, to ascribe to them a
physiological (sometimes a “pathogenic”), rather than a morphological
specificity.
[Illustration: Fig. 73. A flagellate “monad,” _Distigma proteus_, Ehr.
(After Saville Kent.)]
[Illustration: Fig. 74. _Noctiluca miliaris._]
――――――――――
Among the Infusoria, we have a small number of forms whose symmetry is
distinctly spherical, for instance among the small flagellate monads;
but even these are seldom actually spherical except when we see them
in a non-flagellate and more or less encysted or “resting” stage. In
this condition, it need hardly be remarked that the spherical form is
common and general among a great variety of unicellular organisms.
When our little monad developes a flagellum, that is in itself an
indication of “polarity” or symmetrical non-homogeneity of the cell;
and accordingly, we {247} usually see signs of an unequal tension of
the membrane in the neighbourhood of the base of the flagellum. Here
the tension is usually less than elsewhere, and the radius of curvature
is accordingly less: in other words that end of the cell is drawn out
to a tapering point (Fig. 73). But sometimes it is the other way, as in
Noctiluca, where the large flagellum springs from a depression in the
otherwise uniformly rounded cell. In this case the explanation seems
to lie in the many strands of radiating protoplasm which converge upon
this point, and may be supposed to keep it relatively fixed by their
viscosity, while the rest of the cell-surface is free to expand (Fig.
74).
[Illustration: Fig. 75. Various species of Vorticella. (Mostly after
Saville Kent.)]
A very large number of Infusoria represent unduloids, or portions of
unduloids, and this type of surface appears and reappears in a great
variety of forms. The cups of the various species of Vorticella (Fig.
75) are nothing in the world but a beautiful series of unduloids, or
partial unduloids, in every gradation from a form that is all but
cylindrical to one that is all but a perfect sphere. These unduloids
are not completely symmetrical, but they are such unduloids as develop
themselves when we suspend an oil-globule between two unequal rings,
or blow a soap-bubble between two unequal pipes; for, just as in these
cases, the surface of our Vorticella bell finds its terminal supports,
on the one hand in its attachment to its narrow stalk, and on the other
in the thickened ring from which spring its circumoral cilia. And here
let me say, that a point or zone from which cilia arise would seem
always to have a peculiar relation to the surrounding tensions. It
usually forms a sharp salient, a prominent point or ridge, as in our
little monads of Fig. 73; shewing that, in its formation, the surface
tension had here locally diminished. But if such a ridge or fillet
consolidate in the least degree, it becomes a source of strength, and
a _point d’appui_ for the adjacent film. We shall deal with this point
again in the next chapter. {248}
[Illustration: Fig. 76. Various species of _Salpingoeca_.]
[Illustration: Fig. 77. Various species of _Tintinnus_, _Dinobryon_ and
_Codonella_. (After Saville Kent and others.)]
[Illustration: Fig. 78. _Vaginicola._]
[Illustration: Fig. 79. _Folliculina._]
[Illustration: Fig. 80. _Trachelophyllum._ (After Wreszniowski.)]
Precisely the same series of unduloid forms may be traced in even
greater variety among various other families or genera of the
Infusoria. Sometimes, as in Vorticella itself, the unduloid is seen
merely in the contour of the soft semifluid body of the living
animal. At other times, as in Salpingoeca, Tintinnus, and many other
genera, we have a distinct membranous cup, separate from the animal,
but originally secreted by, and moulded upon, its semifluid living
surface. Here we have an excellent illustration of the contrast
between the different ways in which such a structure may be regarded
and interpreted. The teleological explanation is that it is developed
for the sake of protection, as a domicile and shelter for the little
organism within. The mechanical explanation of the physicist (seeking
only after the “efficient,” and not the “final” cause), is that it is
{249} present, and has its actual conformation, by reason of certain
chemico-physical conditions: that it was inevitable, under the given
conditions, that certain constituent substances actually present in
the protoplasm should be aggregated by molecular forces in its surface
layer; that under this adsorptive process, the conditions continuing
favourable, the particles should accumulate and concentrate till
they formed (with the help of the surrounding medium) a pellicle or
membrane, thicker or thinner as the case might be; that this surface
pellicle or membrane was inevitably bound, by molecular forces, to
become a surface of the least possible area which the circumstances
permitted; that in the present case, the symmetry and “freedom” of
the system permitted, and _ipso facto_ caused, this surface to be a
surface of revolution; and that of the few surfaces of revolution
which, as being also surfaces _minimae areae_, were available, the
unduloid was manifestly the one permitted, and _ipso facto_ caused, by
the dimensions of the organisms and other circumstances of the case.
And just as the thickness or thinness of the pellicle was obviously
a subordinate matter, a mere matter of degree, so we also see that
the actual outline of this or that particular unduloid is also a very
subordinate matter, such as physico-chemical variants of a minute kind
would suffice to bring about; for between the various unduloids which
the various species of Vorticella represent, there is no more real
difference than that difference of ratio or degree which exists between
two circles of different diameter, or two lines of unequal length.
{250}
In very many cases (of which Fig. 80 is an example), we have an
unduloid form exhibited, not by a surrounding pellicle or shell,
but by the soft, protoplasmic body of a ciliated organism. In such
cases the form is mobile, and continually changes from one to another
unduloid contour, according to the movements of the animal. We have
here, apparently, to deal with an unstable equilibrium, and also
sometimes with the more complicated problem of “stream-lines,” as in
the difficult problems suggested by the form of a fish. But this whole
class of cases, and of problems, we can merely take note of in passing,
for their treatment is too hard for us.
――――――――――
In considering such series of forms as the various unduloids which
we have just been regarding, we are brought sharply up (as in the
case of our Bacteria or Micrococci) against the biological concept of
organic _species_. In the intense classificatory activity of the last
hundred years, it has come about that every form which is apparently
characteristic, that is to say which is capable of being described or
portrayed, and capable of being recognised when met with again, has
been recorded as a species,—for we need not concern ourselves with the
occasional discussions, or individual opinions, as to whether such
and such a form deserve “specific rank,” or be “only a variety.” And
this secular labour is pursued in direct obedience to the precept of
the _Systema Naturae_,—“_ut sic in summa confusione rerum apparenti,
summus conspiciatur Naturae ordo_.” In like manner the physicist
records, and is entitled to record, his many hundred “species” of
snow-crystals[299], or of crystals of calcium carbonate. But regarding
these latter species, the physicist makes no assumptions: he records
them _simpliciter_, as specific “forms”; he notes, as best he can, the
circumstances (such as temperature or humidity) under which they occur,
in the hope of elucidating the conditions determining their formation;
but above all, he does not introduce {251} the element of time, and of
succession, or discuss their origin and affiliation as an _historical_
sequence of events. But in biology, the term species carries with it
many large, though often vague assumptions. Though the doctrine or
concept of the “permanence of species” is dead and gone, yet a certain
definite value, or sort of quasi-permanency, is still connoted by the
term. Thus if a tiny foraminiferal shell, a Lagena for instance, be
found living to-day, and a shell indistinguishable from it to the eye
be found fossil in the Chalk or some other remote geological formation,
the assumption is deemed legitimate that that species has “survived,”
and has handed down its minute specific character or characters,
from generation to generation, unchanged for untold myriads of
years[300]. Or if the ancient forms be like to, rather than identical
with the recent, we still assume an unbroken descent, accompanied
by the hereditary transmission of common characters and progressive
variations. And if two identical forms be discovered at the ends of
the earth, still (with occasional slight reservations on the score of
possible “homoplasy”), we build hypotheses on this fact of identity,
taking it for granted that the two appertain to a common stock, whose
dispersal in space must somehow be accounted for, its route traced,
its epoch determined, and its causes discussed or discovered. In
short, the naturalist admits no exception to the rule that a “natural
classification” can only be a _genealogical_ one, nor ever doubts that
“_The fact that we are able to classify organisms at all in accordance
with the structural characteristics which they present, is due to
the fact of their being related by descent_[301].” But this great
generalisation is apt in my opinion, to carry us too far. It may be
safe and sure and helpful and illuminating when we apply it to such
complex entities,—such thousand-fold resultants of the combination
and permutation of many variable characters,—as a horse, a lion or an
eagle; but (to my mind) it has a very different look, and a far less
firm foundation, when we attempt to extend it to minute organisms
whose specific characters are few and simple, whose simplicity {252}
becomes much more manifest when we regard it from the point of view of
physical and mathematical description and analysis, and whose form is
referable, or (to say the least of it) is very largely referable, to
the direct and immediate action of a particular physical force. When we
come to deal with the minute skeletons of the Radiolaria we shall again
find ourselves dealing with endless modifications of form, in which
it becomes still more difficult to discern, or to apply, the guiding
principle of affiliation or _genealogy_.
[Illustration: Fig. 81.]
Among the more aberrant forms of Infusoria is a little species known
as _Trichodina pedicidus_, a parasite on the Hydra, or fresh-water
polype (Fig. 81.) This Trichodina has the form of a more or less
flattened circular disc, with a ring of cilia around both its upper
and lower margins. The salient ridge from which these cilia spring may
be taken, as we have already said, to play the part of a strengthening
“fillet.” The circular base of the animal is flattened, in contact
with the flattened surface of the Hydra over which it creeps, and the
opposite, upper surface may be flattened nearly to a plane, or may at
other times appear slightly convex or slightly concave. The sides of
the little organism are contracted, forming a symmetrical equatorial
groove between the upper and lower discs; and, on account of the minute
size of the animal and its constant movements, we cannot submit the
curvature of this concavity to measurement, nor recognise by the eye
its exact contour. But it is evident that the conditions are precisely
similar to those described on p. 223, where we were considering the
conditions of stability of the catenoid. And it is further evident
that, when the upper disc is actually plane, the equatorial groove is
strictly a catenoid surface of revolution; and when on the other hand
it is depressed, then the equatorial groove will tend to assume the
form of a nodoidal surface.
Another curious type is the flattened spiral of _Dinenympha_[302]
{253} which reminds us of the cylindrical spiral of a Spirillum among
the bacteria. In Dinenympha we have a symmetrical figure, whose two
opposite surfaces each constitute a surface of constant mean curvature;
it is evidently a figure of equilibrium under certain special
conditions of restraint. The cylindrical coil of the Spirillum, on the
other hand, is a surface of constant mean curvature, and therefore of
equilibrium, as truly, and in the same sense, as the cylinder itself.
[Illustration: Fig. 82. _Dinenympha gracilis_, Leidy.]
[Illustration: Fig. 83.]
A very curious conformation is that of the vibratile “collar,” found
in Codosiga and the other “Choanoflagellates,” and which we also
meet with in the “collar-cells” which line the interior cavities of
a sponge. Such collar-cells are always very minute, and the collar
is constituted of a very delicate film, which shews an undulatory or
rippling motion. It is a surface of revolution, and as it maintains
itself in equilibrium (though a somewhat unstable and fluctuating
one), it must be, under the restricted circumstances of its case,
a surface of minimal area. But it is not so easy to see what these
special circumstances are; and it is obvious that the collar, if left
to itself, must at once {254} contract downwards towards its base,
and become confluent with the general surface of the cell; for it has
no longitudinal supports and no strengthening ring at its periphery.
But in all these collar-cells, there stands within the annulus of the
collar a large and powerful cilium or flagellum, in constant movement;
and by the action of this flagellum, and doubtless in part also by the
intrinsic vibrations of the collar itself, there is set up a constant
steady current in the surrounding water, whose direction would seem to
be such that it passes up the outside of the collar, down its inner
side, and out in the middle in the direction of the flagellum; and
there is a distinct eddy, in which foreign particles tend to be caught,
around the peripheral margin of the collar. When the cell dies, that
is to say when motion ceases, the collar immediately shrivels away and
disappears. It is notable, by the way, that the edge of this little
mobile cup is always smooth, never notched or lobed as in the cases we
have discussed on p. 236: this latter condition being the outcome of
a definite instability, marking the close of a period of equilibrium;
while in the vibratile collar of Codosiga the equilibrium, such as
it is, is being constantly renewed and perpetuated like that of a
juggler’s pole, by the motions of the system. I take it that, somehow,
its existence (in a state of partial equilibrium) is due to the current
motions, and to the traction exerted upon it through the friction of
the stream which is constantly passing by. I think, in short, that it
is formed very much in the same way as the cup-like ring of streaming
ribbons, which we see fluttering and vibrating in the air-current of a
ventilating fan.
It is likely enough, however, that a different and much better
explanation may yet be found; and if we turn once more to Mr
Worthington’s _Study of Splashes_, we may find a curious suggestion
of analogy in the beautiful craters encircling a central jet (as the
collar of Codosiga encircles the flagellum), which we see produced in
the later stages of the splash of a pebble[303]. {255}
Among the Foraminifera we have an immense variety of forms, which,
in the light of surface tension and of the principle of minimal
area, are capable of explanation and of reduction to a small number
of characteristic types. Many of the Foraminifera are composite
structures, formed by the successive imposition of cell upon cell, and
these we shall deal with later on; let us glance here at the simpler
conformations exhibited by the single chambered or “monothalamic”
genera, and perhaps one or two of the simplest composites.
We begin with forms, like Astrorhiza (Fig. 219, p. 464), which are in
a high degree irregular, and end with others which manifest a perfect
and mathematical regularity. The broad difference between these two
types is that the former are characterised, like Amoeba, by a variable
surface tension, and consequently by unstable equilibrium; but the
strong contrast between these and the regular forms is bridged over by
various transition-stages, or differences of degree. Indeed, as in all
other Rhizopods, the very fact of the emission of pseudopodia, which
reach their highest development in this group of animals, is a sign
of unstable surface-equilibrium; and we must therefore consider that
those forms which indicate symmetry and equilibrium in their shells
have secreted these during periods when rest and uniformity of surface
conditions alternated with the phases of pseudopodial activity. The
irregular forms are in almost all cases arenaceous, that is to say
they have no solid shells formed by steady adsorptive secretion, but
only a looser covering of sand grains with which the protoplasmic body
has come in contact and cohered. Sometimes, as in Ramulina, we have a
calcareous shell combined with irregularity of form; but here we can
easily see a partial and as it were a broken regularity, the regular
forms of sphere and cylinder being repeated in various parts of the
ramified mass. When we look more closely at the arenaceous forms, we
find that the same thing is true of them; they represent, either in
whole or part, approximations to the form of surfaces of equilibrium,
spheres, cylinders and so forth. In Aschemonella we have a precise
replica of the calcareous Ramulina; and in Astrorhiza itself, in
the forms distinguished by naturalists as _A. crassatina_, what is
described as the “subsegmented interior[304]” {256} seems to shew the
natural, physical tendency of the long semifluid cylinder of protoplasm
to contract, at its limit of stability, into unduloid constrictions, as
a step towards the breaking up into separate spheres: the completion of
which process is restrained or prevented by the rigidity and friction
of the arenaceous covering.
[Illustration: Fig. 84. Various species of _Lagena_. (After Brady.)]
Passing to the typical, calcareous-shelled Foraminifera, we have
the most symmetrical of all possible types in the perfect sphere of
Orbulina; this is a pelagic organism, whose floating habitat places it
in a position of perfect symmetry towards all external forces. Save for
one or two other forms which are also spherical, or approximately so,
like Thurammina, the rest of the monothalamic calcareous Foraminifera
are all comprised by naturalists within the genus Lagena. This large
and varied genus consists of “flask-shaped” shells, whose surface is
simply that of an unduloid, or more frequently, like that of a flask
itself, an unduloid combined with a portion of a sphere. We do not know
the circumstances {257} under which the shell of Lagena is formed, nor
the nature of the force by which, during its formation, the surface is
stretched out into the unduloid form; but we may be pretty sure that
it is suspended vertically in the sea, that is to say in a position of
symmetry as regards its vertical axis, about which the unduloid surface
of revolution is symmetrically formed. At the same time we have other
types of the same shell in which the form is more or less flattened;
and these are doubtless the cases in which such symmetry of position
was not present, or was replaced by a broader, lateral contact with the
surface pellicle[305].
[Illustration: Fig. 85. (After Darling.)]
While Orbulina is a simple spherical drop, Lagena suggests to our
minds a “hanging drop,” drawn out to a long and slender neck by
its own weight, aided by the viscosity of the material. Indeed the
various hanging drops, such as Mr C. R. Darling shews us, are the
most beautiful and perfect unduloids, with spherical ends, that it is
possible to conceive. A suitable liquid, a little denser than water
and incapable of mixing with it (such as ethyl benzoate), is poured on
a surface of water. It spreads {258} over the surface and gradually
forms a hanging drop, approximately hemispherical; but as more liquid
is added the drop sinks or rather grows downwards, still adhering
to the surface film; and the balance of forces between gravity and
surface tension results in the unduloid contour, as the increasing
weight of the drop tends to stretch it out and finally break it in
two. At the moment of rupture, by the way, a tiny droplet is formed in
the attenuated neck, such as we described in the normal division of a
cylindrical thread (p. 233).
To pass to a much more highly organised class of animals, we find the
unduloid beautifully exemplified in the little flask-shaped shells
of certain Pteropod mollusca, e.g. Cuvierina[306]. Here again the
symmetry of the figure would at once lead us to suspect that the
creature lived in a position of symmetry to the surrounding forces, as
for instance if it floated in the ocean in an erect position, that is
to say with its long axis coincident with the direction of gravity;
and this we know to be actually the mode of life of the little
Pteropod.
Many species of Lagena are complicated and beautified by a pattern, and
some by the superaddition to the shell of plane extensions or “wings.”
These latter give a secondary, bilateral symmetry to the little shell,
and are strongly suggestive of a phase or period of growth in which it
lay horizontally on the surface, instead of hanging vertically from
the surface-film: in which, that is to say, it was a floating and not
a hanging drop. The pattern is of two kinds. Sometimes it consists of
a sort of fine reticulation, with rounded or more or less hexagonal
interspaces: in other cases it is produced by a symmetrical series of
ridges or folds, usually longitudinal, on the body of the flask-shaped
cell, but occasionally transversely arranged upon the narrow neck. The
reticulated and folded patterns we may consider separately. The netted
pattern is very similar to the wrinkled surface of a dried pea, or
to the more regular wrinkled patterns upon many other seeds and even
pollen-grains. If a spherical body after developing a “skin” begin
to shrink a little, and if the skin have so far lost its elasticity
as to be unable to keep pace with the shrinkage of the inner mass,
it will tend to fold or wrinkle; and if the shrinkage be uniform,
and the elasticity and flexibility of the skin be also uniform, then
the amount of {259} folding will be uniformly distributed over the
surface. Little concave depressions will appear, regularly interspaced,
and separated by convex folds. The little concavities being of equal
size (unless the system be otherwise perturbed) each one will tend
to be surrounded by six others; and when the process has reached its
limit, the intermediate boundary-walls, or raised folds, will be found
converted into a regular pattern of hexagons.
But the analogy of the mechanical wrinkling of the coat of a seed
is but a rough and distant one; for we are evidently dealing with
molecular rather than with mechanical forces. In one of Darling’s
experiments, a little heavy tar-oil is dropped onto a saucer of water,
over which it spreads in a thin film showing beautiful interference
colours after the fashion of those of a soap-bubble. Presently tiny
holes appear in the film, which gradually increase in size till they
form a cellular pattern or honeycomb, the oil gathering together in the
meshes or walls of the cellular net. Some action of this sort is in
all probability at work in a surface-film of protoplasm covering the
shell. As a physical phenomenon the actions involved are by no means
fully understood, but surface-tension, diffusion and cohesion doubtless
play their respective parts therein[307]. The very perfect cellular
patterns obtained by Leduc (to which we shall have occasion to refer in
a subsequent chapter) are diffusion patterns on a larger scale, but not
essentially different.
[Illustration: Fig. 86.]
The folded or pleated pattern is doubtless to be explained, in a
general way, by the shrinkage of a surface-film under certain {260}
conditions of viscous or frictional restraint. A case which (as it
seems to me) is closely analogous to that of our foraminiferal shells
is described by Quincke[308], who let a film of albumin or of resin set
and harden upon a surface of quicksilver, and found that the little
solid pellicle had been thrown into a pattern of symmetrical folds.
If the surface thus thrown into folds be that of a cylinder, or any
other figure with one principal axis of symmetry, such as an ellipsoid
or unduloid, the direction of the folds will tend to be related to
the axis of symmetry, and we might expect accordingly to find regular
longitudinal, or regular transverse wrinkling. Now as a matter of fact
we almost invariably find in the Lagena the former condition: that is
to say, in our ellipsoid or unduloid cell, the puckering takes the form
of the vertical fluting on a column, rather than that of the transverse
pleating of an accordion. And further, there is often a tendency for
such longitudinal flutings to be more or less localised at the end of
the ellipsoid, or in the region where the unduloid merges into its
spherical base. In this latter region we often meet with a regular
series of short longitudinal folds, as we do in the forms of Lagena
denominated _L. semistriata_. All these various forms of surface can
be imitated, or rather can be precisely reproduced, by the art of the
glass-blower[309].
Furthermore, they remind one, in a striking way, of the regular ribs or
flutings in the film or sheath which splashes up to envelop a smooth
ball which has been dropped into a liquid, as Mr Worthington has so
beautifully shewn[310]. {261}
In Mr Worthington’s experiment, there appears to be something of the
nature of a viscous drag in the surface-pellicle; but whatever be the
actual cause of variation of tension, it is not difficult to see that
there must be in general a tendency towards _longitudinal_ puckering
or “fluting” in the case of a thin-walled cylindrical or other
elongated body, rather than a tendency towards transverse puckering, or
“pleating.” For let us suppose that some change takes place involving
an increase of surface-tension in some small area of the curved wall,
and leading therefore to an increase of pressure: that is to say let
_T_ become _T_ + _t_, and _P_ become _P_ + _p_. Our new equation of
equilibrium, then, in place of _P_ = _T_/_r_ + _T_/_r′_ becomes
_P_ + _p_ = (_T_ + _t_)/_r_ + (_T_ + _t_)/_r′_,
and by subtraction,
_p_ = _t_/_r_ + _t_/_r′_.
Now if _r_ < _r′_, _t_/_r_ > _t_/_r′_.
Therefore, in order to produce the small increment of pressure _p_,
it is easier to do so by increasing _t_/_r_ than _t_/_r′_; that is
to say, the easier way is to alter, or diminish _r_. And the same
will hold good if the tension and pressure be diminished instead of
increased.
This is as much as to say that, when corrugation or “rippling” of
the walls takes place owing to small changes of surface-tension, and
consequently of pressure, such corrugation is more likely to take
place in the plane of _r_,—that is to say, _in the plane of greatest
curvature_. And it follows that in such a figure as an ellipsoid,
wrinkling will be most likely to take place not only in a longitudinal
direction but near the extremities of the figure, that is to say again
in the region of greatest curvature.
[Illustration: Fig. 87. _Nodosaria scalaris_, Batsch.]
[Illustration: Fig. 88. Gonangia of Campanularians. (_a_) _C.
gracilis_; (_b_) _C. grandis_. (After Allman.)]
The longitudinal wrinkling of the flask-shaped bodies of our Lagenae,
and of the more or less cylindrical cells of many other Foraminifera
(Fig. 87), is in complete accord with the above theoretical
considerations; but nevertheless, we soon find that our result is not
a general one, but is defined by certain limiting conditions, and is
accordingly subject to what are, at first sight, important exceptions.
For instance, when we turn to the narrow neck of the Lagena we see at
once that our theory no longer holds; for {262} the wrinkling which
was invariably longitudinal in the body of the cell is as invariably
transverse in the narrow neck. The reason for the difference is not
far to seek. The conditions in the neck are very different from
those in the expanded portion of the cell: the main difference being
that the thickness of the wall is no longer insignificant, but is of
considerable magnitude as compared with the diameter, or circumference,
of the neck. We must accordingly take it into account in considering
the _bending moments_ at any point in this region of the shell-wall.
And it is at once obvious that, in any portion of the narrow neck,
_flexure_ of a wall in a transverse direction will be very difficult,
while flexure in a longitudinal direction will be comparatively easy;
just as, in the case of a long narrow strip of iron, we may easily
bend it into folds running transversely to its long axis, but not the
other way. The manner in which our little Lagena-shell tends to fold
or wrinkle, longitudinally in its wider part, and transversely or
annularly in its narrow neck, is thus completely and easily explained.
An identical phenomenon is apt to occur in the little flask-shaped
gonangia, or reproductive capsules, of some of the hydroid zoophytes.
In the annexed drawings of these gonangia in two species of
Campanularia, we see that in one case the little vesicle {263} has
the flask-shaped or unduloid configuration of a Lagena; and here the
walls of the flask are longitudinally fluted, just after the manner we
have witnessed in the latter genus. But in the other Campanularian the
vesicles are long, narrow and tubular, and here a transverse folding
or pleating takes the place of the longitudinally fluted pattern. And
the very form of the folds or pleats is enough to suggest that we are
not dealing here with a simple phenomenon of surface-tension, but with
a condition in which surface-tension and _stiffness_ are both present,
and play their parts in the resultant form.
[Illustration: Fig. 89. Various Foraminifera (after Brady), _a_,
_Nodosaria simplex_; _b_, _N. pygmaea_; _c_, _N. costulata_; _e_, _N.
hispida_; _f_, _N. elata_; _d_, _Rheophax_ (_Lituola_) _distans_; _g_,
_Sagrina virgata_.]
Passing from the solitary flask-shaped cell of Lagena, we have, in
another series of forms, a constricted cylinder, or succession of
unduloids; such as are represented in Fig. 89, illustrating certain
species of Nodosaria, Rheophax and Sagrina. In some of these cases,
and certainly in that of the arenaceous genus Rheophax, we have to do
with the ordinary phenomenon of a segmenting or partially segmenting
cylinder. But in others, the structure is not developed out of a
continuous protoplasmic cylinder, but as we can see by examining
the interior of the shell, it has been formed in successive stages,
beginning with a simple unduloid “Lagena,” about whose neck, after its
solidification, another drop of protoplasm accumulated, and in turn
assumed the unduloid, or lagenoid, form. The chains of interconnected
bubbles which {264} Morey and Draper made many years ago of melted
resin are a very similar if not identical phenomenon[311].
――――――――――
There now remain for our consideration, among the Protozoa, the
great oceanic group of the Radiolaria, and the little group of their
freshwater allies, the Heliozoa. In nearly all these forms we have this
specific chemical difference from the Foraminifera, that when they
secrete, as they generally do secrete, a hard skeleton, it is composed
of silica instead of lime. These organisms and the various beautiful
and highly complicated skeletal fabrics which they develop give us
many interesting illustrations of physical phenomena, among which the
manifestations of surface-tension are very prominent. But the chief
phenomena connected with their skeletons we shall deal with in another
place, under the head of spicular concretions.
In a simple and typical Heliozoan, such as the Sun-animalcule,
_Actinophrys sol_, we have a “drop” of protoplasm, contracted by
its surface tension into a spherical form. Within the heterogeneous
protoplasmic mass are more fluid portions, and at the surface which
separates these from the surrounding protoplasm a similar surface
tension causes them also to assume the form of spherical “vacuoles,”
which in reality are little clear drops within the big one; unless
indeed they become numerous and closely packed, in which case, instead
of isolated spheres or droplets they will constitute a “froth,” their
mutual pressures and tensions giving rise to regular configurations
such as we shall study in the next chapter. One or more of such clear
spaces may be what is called a “contractile vacuole”: that is to say,
a droplet whose surface tension is in unstable equilibrium and is apt
to vanish altogether, so that the definite outline of the vacuole
suddenly disappears[312]. Again, within the protoplasm are one or
more nuclei, whose own surface tension (at the surface between the
nucleus and the surrounding protoplasm), has drawn them in turn into
the shape {265} of spheres. Outwards through the protoplasm, and
stretching far beyond the spherical surface of the cell, there run
stiff linear threads of modified or differentiated protoplasm, replaced
or reinforced in some cases by delicate siliceous needles. In either
case we know little or nothing about the forces which lead to their
production, and we do not hide our ignorance when we ascribe their
development to a “radial polarisation” of the cell. In the case of the
protoplasmic filament, we may (if we seek for a hypothesis), suppose
that it is somehow comparable to a viscid stream, or “liquid vein,”
thrust or squirted out from the body of the cell. But when it is once
formed, this long and comparatively rigid filament is separated by a
distinct surface from the neighbouring protoplasm, that is to say from
the more fluid surface-protoplasm of the cell; and the latter begins
to creep up the filament, just as water would creep up the interior of
a glass tube, or the sides of a glass rod immersed in the liquid. It
is the simple case of a balance between three separate tensions: (1)
that between the filament and the adjacent protoplasm, (2) that between
the filament and the adjacent water, and (3) that between the water
and the protoplasm. Calling these tensions respectively _T__{_fp_},
_T__{_fw_}, and _T__{_wp_}, equilibrium will be attained when the angle
of contact between the fluid protoplasm and the filament is such that
cos α = (_T__{_fw_} − _T__{_wp_})/_T__{_fp_}. It is evident in this
case that the angle is a very small one. The precise form of the curve
is somewhat different from that which, under ordinary circumstances,
is assumed by a liquid which creeps up a solid surface, as water in
contact with air creeps up a surface of glass; the difference being due
to the fact that here, owing to the density of the protoplasm being
practically identical with that of the surrounding medium, the whole
system is practically immune from gravity. Under normal circumstances
the curve is part of the “elastic curve” by which that surface of
revolution is generated which we have called, after Plateau, the
nodoid; but in the present case it is apparently a catenary. Whatever
curve it be, it obviously forms a surface of revolution around the
filament.
Since the attraction exercised by this surface tension is symmetrical
around the filament, the latter will be pulled equally {266} in all
directions; in other words it will tend to be set normally to the
surface of the sphere, that is to say radiating directly outwards
from the centre. If the distance between two adjacent filaments be
considerable, the curve will simply meet the filament at the angle α
already referred to; but if they be sufficiently near together, we
shall have a continuous catenary curve forming a hanging loop between
one filament and the other. And when this is so, and the radial
filaments are more or less symmetrically interspaced, we may have a
beautiful system of honeycomb-like depressions over the surface of
the organism, each cell of the honeycomb having a strictly defined
geometric configuration.
[Illustration: Fig. 90. A, _Trypanosoma tineae_ (after Minchin); B,
_Spirochaeta anodontae_ (after Fantham).]
In the simpler Radiolaria, the spherical form of the entire organism is
equally well-marked; and here, as also in the more complicated Heliozoa
(such as Actinosphaerium), the organism is differentiated into several
distinct layers, each boundary surface tending to be spherical, and
so constituting sphere within sphere. One of these layers at least
is close packed with vacuoles, forming an “alveolar meshwork,” with
the configurations of which we shall attempt in another chapter to
correlate the characteristic structure of certain complex types of
skeleton.
――――――――――
An exceptional form of cell, but a beautiful manifestation of
surface-tension (or so I take it to be), occurs in Trypanosomes, those
tiny parasites of the blood that are associated with sleeping-sickness
and many other grave or dire maladies. These tiny organisms consist of
elongated solitary cells down one side of which runs a very delicate
frill, or “undulating membrane,” the free edge of which is seen
to be slightly thickened, and the whole of {267} which undergoes
rhythmical and beautiful wavy movements. When certain Trypanosomes are
artificially cultivated (for instance _T. rotatorium_, from the blood
of the frog), phases of growth are witnessed in which the organism has
no undulating membrane, but possesses a long cilium or “flagellum,”
springing from near the front end, and exceeding the whole body in
length[313]. Again, in _T. lewisii_, when it reproduces by “multiple
fission,” the products of this division are likewise devoid of an
undulating membrane, but are provided with a long free flagellum[314].
It is a plausible assumption to suppose that, as the flagellum waves
about, it comes to lie near and parallel to the body of the cell, and
that the frill or undulating membrane is formed by the clear, fluid
protoplasm of the surface layer springing up in a film to run up and
along the flagellum, just as a soap-film would be formed in similar
circumstances.
[Illustration: Fig. 91. A, _Trichomonas muris_, Hartmann; B,
_Trichomastix serpentis_, Dobell; C, _Trichomonas angusta_, Alexeieff.
(After Kofoid.)]
This mode of formation of the undulating membrane or frill appears to
be confirmed by the appearances shewn in Fig. 91. {268} Here we have
three little organisms closely allied to the ordinary Trypanosomes, of
which one, Trichomastix (_B_), possesses four flagella, and the other
two, Trichomonas, apparently three only: the two latter possess the
frill, which is lacking in the first[315]. But it is impossible to
doubt that when the frill is present (as in _A_ and _C_), its outer
edge is constituted by the apparently missing flagellum (_a_), which
has become _attached_ to the body of the creature at the point _c_,
near its posterior end; and all along its course, the superficial
protoplasm has been drawn out into a film, between the flagellum (_a_)
and the adjacent surface or edge of the body (_b_).
[Illustration: Fig. 92. Herpetomonas assuming the undulatory membrane
of a Trypanosome. (After D. L. Mackinnon.)]
Moreover, this mode of formation has been actually witnessed and
described, though in a somewhat exceptional case. The little flagellate
monad Herpetomonas is normally destitute of an undulating membrane,
but possesses a single long terminal flagellum. According to Dr D. L.
Mackinnon, the cytoplasm in a certain stage of growth becomes somewhat
“sticky,” a phrase which we may in all probability interpret to mean
that its surface tension is being reduced. For this stickiness is shewn
in two ways. In the first place, the long body, in the course of its
various bending movements, is apt to adhere head to tail (so to speak),
giving a rounded or sometimes annular form to the organism, such as
has also been described in certain species or stages of Trypanosomes.
But again, the long flagellum, if it get bent backwards upon the body,
tends to adhere to its surface. “Where the flagellum was pretty long
and active, its efforts to continue movement under these abnormal
conditions resulted in the gradual lifting up from the cytoplasm of the
body of a sort of _pseudo_-undulating membrane (Fig. 92). The movements
of this structure were so exactly those of a true undulating membrane
that it was {269} difficult to believe one was not dealing with a
small, blunt trypanosome[316].” This in short is a precise description
of the mode of development which, from theoretical considerations
alone, we should conceive to be the natural if not the only possible
way in which the undulating membrane could come into existence.
There is a genus closely allied to Trypanosoma, viz. Trypanoplasma,
which possesses one free flagellum, together with an undulating
membrane; and it resembles the neighbouring genus Bodo, save that the
latter has two flagella and no undulating membrane. In like manner,
Trypanosoma so closely resembles Herpetomonas that, when individuals
ascribed to the former genus exhibit a free flagellum only, they are
said to be in the “Herpetomonas stage.” In short all through the
order, we have pairs of genera, which are presumed to be separate
and distinct, viz. Trypanosoma-Herpetomonas, Trypanoplasma-Bodo,
Trichomastix-Trichomonas, in which one differs from the other mainly if
not solely in the fact that a free flagellum in the one is replaced by
an undulating membrane in the other. We can scarcely doubt that the two
structures are essentially one and the same.
The undulating membrane of a Trypanosome, then, according to our
interpretation of it, is a liquid film and must obey the law of
constant mean curvature. It is under curious limitations of freedom:
for by one border it is attached to the comparatively motionless body,
while its free border is constituted by a flagellum which retains its
activity and is being constantly thrown, like the lash of a whip,
into wavy curves. It follows that the membrane, for every alteration
of its longitudinal curvature, must at the same instant become curved
in a direction perpendicular thereto; it bends, not as a tape bends,
but with the accompaniment of beautiful but tiny waves of double
curvature, all tending towards the establishment of an “equipotential
surface”; and its characteristic undulations are not originated by an
active mobility of the membrane but are due to the molecular tensions
which produce the very same result in a soap-film under similar
circumstances.
In certain Spirochaetes, _S. anodontae_ (Fig. 90) and _S. balbiani_
{270} (which we find in oysters), a very similar undulating membrane
exists, but it is coiled in a regular spiral round the body of the
cell. It forms a “screw-surface,” or helicoid, and, though we might
think that nothing could well be more curved, yet its mathematical
properties are such that it constitutes a “ruled surface” whose “mean
curvature” is everywhere _nil_; and this property (as we have seen)
it shares with the plane, and with the plane alone. Precisely such a
surface, and of exquisite beauty, may be produced by bending a wire
upon itself so that part forms an axial rod and part a spiral wrapping
round the axis, and then dipping the whole into a soapy solution.
These undulating and helicoid surfaces are exactly reproduced among
certain forms of spermatozoa. The tail of a spermatozoon consists
normally of an axis surrounded by clearer and more fluid protoplasm,
and the axis sometimes splits up into two or more slender filaments. To
surface tension operating between these and the surface of the fluid
protoplasm (just as in the case of the flagellum of the Trypanosome),
I ascribe the formation of the undulating membrane which we find, for
instance, in the spermatozoa of the newt or salamander; and of the
helicoid membrane, wrapped in a far closer and more beautiful spiral
than that which we saw in Spirochaeta, which is characteristic of the
spermatozoa of many birds.
――――――――――
Before we pass from the subject of the conformation of the solitary
cell we must take some account of certain other exceptional forms,
less easy of explanation, and still less perfectly understood. Such is
the case, for instance, with the red blood-corpuscles of man and other
vertebrates; and among the sperm-cells of the decapod crustacea we find
forms still more aberrant and not less perplexing. These are among the
comparatively few cells or cell-like structures whose form _seems_ to
be incapable of explanation by theories of surface-tension.
In all the mammalia (save a very few) the red blood-corpuscles are
flattened circular discs, dimpled in upon their two opposite sides.
This configuration closely resembles that of an india-rubber ball when
we pinch it tightly between finger and thumb; and we may also compare
it with that experiment of Plateau’s {271} (described on p. 223),
where a flat cylindrical oil-drop, of certain relative dimensions,
can, by sucking away a little of the contained oil, be made to assume
the form of a biconcave disc, whose periphery is part of a nodoidal
surface. From the relation of the nodoid to the “elastic curve,” we
perceive that these two examples are closely akin one to the other.
[Illustration: Fig. 93.]
The form of the corpuscle is symmetrical, and its surface is a surface
of revolution; but it is obviously not a surface of constant mean
curvature, nor of constant pressure. For we see at once that, in the
sectional diagram (Fig. 93), the pressure inwards due to surface
tension is positive at _A_, and negative at _C_; at _B_ there is no
curvature in the plane of the paper, while perpendicular to it the
curvature is negative, and the pressure therefore is also negative.
Accordingly, from the point of view of surface tension alone, the
blood-corpuscle is not a surface of equilibrium; or in other words,
it is not a fluid drop suspended in another liquid. It is obvious
therefore that some other force or forces must be at work, and the
simple effect of mechanical pressure is here excluded, because the
blood-corpuscle exhibits its characteristic shape while floating freely
in the blood. In the lower vertebrates the blood-corpuscles have the
form of a flattened oval disc, with rather sharp edges and ellipsoidal
surfaces, and this again is manifestly not a surface of equilibrium.
Two facts are especially noteworthy in connection with the form of the
blood-corpuscle. In the first place, its form is only maintained, that
is to say it is only in equilibrium, in relation to certain properties
of the medium in which it floats. If we add a little water to the
blood, the corpuscle quickly loses its characteristic shape and becomes
a spherical drop, that is to say a true surface of minimal area and of
stable equilibrium. If on the other hand we add a strong solution of
salt, or a little glycerine, the corpuscle contracts, and its surface
becomes puckered and uneven. In these phenomena it is so far obeying
the laws of diffusion and of surface tension. {272}
In the second place, it can be exactly imitated artificially by means
of other colloid substances. Many years ago Norris made the very
interesting observation that in an emulsion of glue the drops assumed
a biconcave form resembling that of the mammalian corpuscles[317]. The
glue was impure, and doubtless contained lecithin; and it is possible
(as Professor Waymouth Reid tells me) to make a similar emulsion with
cerebrosides and cholesterin oleate, in which the same conformation
of the drops or particles is beautifully shewn. Now such cholesterin
bodies have an important place among those in which Lehmann and others
have shewn and studied the formation of fluid crystals, that is to
say of bodies in which the forces of crystallisation and the forces
of surface tension are battling with one another[318]; and, for want
of a better explanation, we may in the meanwhile suggest that some
such cause is at the bottom of the conformation the explanation of
which presents so many difficulties. But we must not, perhaps, pass
from this subject without adding that the case is a difficult and
complex one from the physiological point of view. For the surface of a
blood-corpuscle consists of a “semi-permeable membrane,” through which
certain substances pass freely and not others (for the most part anions
and not cations), and it may be, accordingly, that we have in life a
continual state of osmotic inequilibrium, of negative osmotic tension
within, to which comparatively simple cause the imperfect distension
of the corpuscle may be also due[319]. The whole phenomenon would
be comparatively easy to understand if we might postulate a stiffer
peripheral region to the corpuscle, in the form for instance of a
peripheral elastic ring. Such an annular thickening or stiffening, like
the “collapse-rings” which an engineer inserts in a boiler, has been
actually asserted to exist, but its presence is not authenticated.
But it is not at all improbable that we have still much to learn about
the phenomena of osmosis itself, as manifested in the case of minute
bodies such as a blood-corpuscle; and (as Professor Peddie suggests to
me) it is by no means impossible that _curvature_ {273} of the surface
may itself modify the osmotic or perhaps the adsorptive action. If it
should be found that osmotic action tended to stop, or to reverse,
on change of curvature, it would follow that this phenomenon would
give rise to internal currents; and the change of pressure consequent
on these would tend to intensify the change of curvature when once
started[320].
[Illustration: Fig. 94. Sperm-cells of Decapod Crustacea (after
Koltzoff). _a_, _Inachus scorpio_; _b_, _Galathea squamifera_; _c_,
_do._ after maceration, to shew spiral fibrillae.]
The sperm-cells of the Decapod crustacea exhibit various singular
shapes. In the Crayfish they are flattened cells with stiff curved
processes radiating outwards like a St Catherine’s wheel; in Inachus
there are two such circles of stiff processes; in Galathea we have a
still more complex form, with long and slightly twisted processes.
In all these cases, just as in the case of the blood-corpuscle, the
structure alters, and finally loses, its characteristic form when the
nature or constitution (or as we may assume in particular—the density)
of the surrounding medium is changed.
Here again, as in the blood-corpuscle, we have to do with a very
important force, which we had not hitherto considered in this
connection,—the force of osmosis, manifested under conditions similar
to those of Pfeffer’s classical experiments on the plant-cell. The
surface of the cell acts as a “semi-permeable membrane,” {274}
permitting the passage of certain dissolved substances (or their
“ions”) and including or excluding others; and thus rendering manifest
and measurable the existence of a definite “osmotic pressure.” In the
case of the sperm-cells of Inachus, certain quantitative experiments
have been performed[321]. The sperm-cell exhibits its characteristic
conformation while lying in the serous fluid of the animal’s body, in
ordinary sea-water, or in a 5 per cent. solution of potassium nitrate;
these three fluids being all “isotonic” with one another. As we alter
the concentration of potassium nitrate, the cell assumes certain
definite forms corresponding to definite concentrations of the salt;
and, as a further and final proof that the phenomenon is entirely
physical, it is found that other salts produce an identical effect
when their concentration is proportionate to their molecular weight,
and whatever identical effect is produced by various salts in their
respective concentrations, a similarly identical effect is produced
when these concentrations are doubled or otherwise proportionately
changed[322].
[Illustration: Fig. 95. Sperm-cells of _Inachus_, as they appear in
saline solutions of varying density. (After Koltzoff.)]
Thus the following table shews the percentage concentrations of certain
salts necessary to bring the cell into the forms _a_ and _c_ of Fig.
95; in each case the quantities are proportional to the molecular
weights, and in each case twice the quantity is necessary to produce
the effect of Fig. 95_c_ compared with that which gives rise to the all
but spherical form of Fig. 95_a_. {275}
% concentration of salts
in which the sperm-cell
of Inachus assumes the form of
─────────────────────
fig. _a_ fig. _c_
Sodium chloride 0·6 1·2
Sodium nitrate 0·85 1·7
Potassium nitrate 1·0 2·0
Acetic acid 2·2 4·5
Cane sugar 5·0 10·0
[Illustration: Fig. 96. Sperm-cell of _Dromia_. (After Koltzoff.)]
If we look then, upon the spherical form of the cell as its true
condition of symmetry and of equilibrium, we see that what we call
its normal appearance is just one of many intermediate phases of
shrinkage, brought about by the abstraction of fluid from its interior
as the result of an osmotic pressure greater outside than inside the
cell, and where the shrinkage of _volume_ is not kept pace with by a
contraction of the _surface-area_. In the case of the blood-corpuscle,
the shrinkage is of no great amount, and the resulting deformation is
symmetrical; such structural inequality as may be necessary to account
for it need be but small. But in the case of the sperm-cells, we must
have, and we actually do find, a somewhat complicated arrangement of
more or less rigid or elastic structures in the wall of the cell, which
like the wire framework in Plateau’s experiments, restrain and modify
the forces acting on the drop. In one form of Plateau’s experiments,
instead of supporting his drop on rings or frames of wire, he laid
upon its surface one or more elastic coils; and then, on withdrawing
oil from the centre of his globule, he saw its uniform shrinkage
counteracted by the spiral springs, with the result that the centre
of each elastic coil seemed to shoot out into a prominence. Just such
spiral coils are figured (after Koltzoff) in Fig. 96; and they may
be regarded as precisely akin to those local thickenings, spiral and
other, to which we have already ascribed the cylindrical form of the
Spirogyra cell. In all probability we must in like manner attribute the
peculiar spiral and other forms, for instance of many Infusoria, to
the {276} presence, among the multitudinous other differentiations of
their protoplasmic substance, of such more or less elastic fibrillae,
which play as it were the part of a microscopic skeleton[323].
――――――――――
But these cases which we have just dealt with, lead us to another
consideration. In a semi-permeable membrane, through which water
passes freely in and out, the conditions of a liquid surface are
greatly modified; and, in the ideal or ultimate case, there is neither
surface nor surface tension at all. And this would lead us somewhat
to reconsider our position, and to enquire whether the true surface
tension of a liquid film is actually responsible for _all_ that we
have ascribed to it, or whether certain of the phenomena which we have
assigned to that cause may not in part be due to the contractility of
definite and elastic membranes. But to investigate this question, in
particular cases, is rather for the physiologist: and the morphologist
may go on his way, paying little heed to what is no doubt a difficulty.
In surface tension we have the production of a film with the properties
of an elastic membrane, and with the special peculiarity that
contraction continues with the same energy however far the process
may have already gone; while the ordinary elastic membrane contracts
to a certain extent, and contracts no more. But within wide limits
the essential phenomena are the same in both cases. Our fundamental
equations apply to both cases alike. And accordingly, so long as our
purpose is _morphological_, so long as what we seek to explain is
regularity and definiteness of form, it matters little if we should
happen, here or there, to confuse surface tension with elasticity, the
contractile forces manifested at a liquid surface with those which come
into play at the complex internal surfaces of an elastic solid.
{277}