A NOTE ON ADSORPTION
A very important corollary to, or amplification of the theory of
surface tension is to be found in the modern chemico-physical doctrine
of Adsorption[324]. In its full statement this subject soon becomes
complicated, and involves physical conceptions and mathematical
treatment which go beyond our range. But it is necessary for us to take
account of the phenomenon, though it be in the most elementary way.
In the brief account of the theory of surface tension with which our
last chapter began, it was pointed out that, in a drop of liquid,
the potential energy of the system could be diminished, and work
manifested accordingly, in two ways. In the first place we saw that,
at our liquid surface, surface tension tends to set up an equilibrium
of form, in which the surface is reduced or contracted either to the
absolute minimum of a sphere, or at any rate to the least possible
area which is permitted by the various circumstances and conditions;
and if the two bodies which comprise our system, namely the drop of
liquid and its surrounding medium, be simple substances, and the
system be uncomplicated by other distributions of force, then the
energy of the system will have done its work when this equilibrium of
form, this minimal area of surface, is once attained. This phenomenon
of the production of a minimal surface-area we have now seen to be
of fundamental importance in the external morphology of the cell,
and especially (so far as we have yet gone) of the solitary cell or
unicellular organism. {278}
But we also saw, according to Gauss’s equation, that the potential
energy of the system will be diminished (and its diminution will
accordingly be manifested in work) if from any cause the specific
surface energy be diminished, that is to say if it be brought more
nearly to an equality with the specific energy of the molecules in
the interior of the liquid mass. This latter is a phenomenon of great
moment in modern physiology, and, while we need not attempt to deal
with it in detail, it has a bearing on cell-form and cell-structure
which we cannot afford to overlook.
In various ways a diminution of the surface energy may be brought
about. For instance, it is known that every isolated drop of fluid
has, under normal circumstances, a surface-charge of electricity: in
such a way that a positive or negative charge (as the case may be) is
inherent in the surface of the drop, while a corresponding charge,
of contrary sign, is inherent in the immediately adjacent molecular
layer of the surrounding medium. Now the effect of this distribution,
by which all the surface molecules of our drop are similarly charged,
is that by virtue of this charge they tend to repel one another, and
possibly also to draw other molecules, of opposite charge, from the
interior of the mass; the result being in either case to antagonise or
cancel, more or less, that normal tendency of the surface molecules to
attract one another which is manifested in surface tension. In other
words, an increased electrical charge concentrating at the surface of a
drop tends, whether it be positive or negative, to _lower_ the surface
tension.
But a still more important case has next to be considered. Let
us suppose that our drop consists no longer of a single chemical
substance, but contains other substances either in suspension or in
solution. Suppose (as a very simple case) that it be a watery fluid,
exposed to air, and containing droplets of oil: we know that the
specific surface tension of oil in contact with air is much less than
that of water, and it follows that, if the watery surface of our drop
be replaced by an oily surface the specific surface energy of the
system will be notably diminished. Now under these circumstances it is
found that (quite apart from gravity, by which the oil might _float_
to the surface) the oil has a tendency to be _drawn_ to the surface;
and this phenomenon of molecular attraction {279} or “adsorption”
represents the work done, equivalent to the diminished potential energy
of the system[325]. In more general terms, if a liquid (or one or other
of two adjacent liquids) be a chemical mixture, some one constituent
in which, if it entered into or increased in amount in the surface
layer, would have the effect of diminishing its surface tension, then
that constituent will have a tendency to accumulate or concentrate
at the surface: the surface tension may be said, as it were, to
exercise an attraction on this constituent substance, drawing it into
the surface layer, and this tendency will proceed until at a certain
“surface concentration” equilibrium is reached, its opponent being that
osmotic force which tends to keep the substance in uniform solution or
diffusion.
In the complex mixtures which constitute the protoplasm of the living
cell, this phenomenon of “adsorption” has abundant play: for many of
these constituents, such as oils, soaps, albumens, etc. possess the
required property of diminishing surface tension.
Moreover, the more a substance has the power of lowering the surface
tension of the liquid in which it happens to be dissolved, the more
will it tend to displace another and less effective substance from
the surface layer. Thus we know that protoplasm always contains fats
or oils, not only in visible drops, but also in the finest suspension
or “colloidal solution.” If under any impulse, such for instance as
might arise from the Brownian movement, a droplet of oil be brought
close to the surface, it is at once drawn into that surface, and tends
to spread itself in a thin layer over the whole surface of the cell.
But a soapy surface (for instance) would have in contact with the
surrounding water a surface tension even less than that of the film
of oil: and consequently, if soap be present in the water it will in
turn be adsorbed, and will tend to displace the oil from the surface
pellicle[326]. And this is all as {280} much as to say that the
molecules of the dissolved or suspended substance or substances will
so distribute themselves throughout the drop as to lead towards an
equilibrium, for each small unit of volume, between the superficial and
internal energy; or so, in other words, as to lead towards a reduction
to a minimum of the potential energy of the system. This tendency
to concentration at the surface of any substance within the cell by
which the surface tension tends to be diminished, or _vice versa_,
constitutes, then, the phenomenon of _Adsorption_; and the general
statement by which it is defined is known as the Willard-Gibbs, or
Gibbs-Thomson law[327].
Among the many important physical features or concomitants of this
phenomenon, let us take note at present that we need not conceive of a
strictly superficial distribution of the adsorbed substance, that is
to say of its direct association with the surface layer of molecules
such as we imagined in the case of the electrical charge; but rather of
a progressive tendency to concentrate, more and more, as the surface
is nearly approached. Indeed we may conceive the colloid or gelatinous
precipitate in which, in the case of our protoplasmic cell, the
dissolved substance tends often to be thrown down, to constitute one
boundary layer after another, the general effect being intensified and
multiplied by the repeated addition of these new surfaces.
Moreover, it is not less important to observe that the process of
adsorption, in the neighbourhood of the surface of a heterogeneous
liquid mass, is a process which _takes time_; the tendency to surface
concentration is a gradual and progressive one, and will fluctuate with
every minute change in the composition of our substance and with every
change in the area of its surface. In other words, it involves (in
every heterogeneous substance) a continual instability of equilibrium:
and a constant manifestation {281} of motion, sometimes in the mere
invisible transfer of molecules but often in the production of visible
currents of fluid or manifest alterations in the form or outline of the
system.
――――――――――
The physiologist, as we have already remarked, takes account of
the general phenomenon of adsorption in many ways: particularly in
connection with various results and consequences of osmosis, inasmuch
as this process is dependent on the presence of a membrane, or
membranes, such as the phenomenon of adsorption brings into existence.
For instance it plays a leading part in all modern theories of muscular
contraction, in which phenomenon a connection with surface tension
was first indicated by FitzGerald and d’Arsonval nearly forty years
ago[328]. And, as W. Ostwald was the first to shew, it gives us an
entirely new conception of the relation of gases (that is to say, of
oxygen and carbon dioxide) to the red corpuscles of the blood[329].
But restricting ourselves, as much as may be, to our morphological
aspect of the case, there are several ways in which adsorption begins
at once to throw light upon our subject.
In the first place, our preliminary account, such as it is, is
already tantamount to a description of the process of development
of a cell-membrane, or cell-wall. The so-called “secretion” of this
cell-wall is nothing more than a sort of exudation, or striving towards
the surface, of certain constituent molecules or particles within the
cell; and the Gibbs-Thomson law formulates, in part at least, the
conditions under which they do so. The adsorbed material may range
from the almost unrecognisable pellicle of a blood-corpuscle to the
distinctly differentiated “ectosarc” of a protozoan, and again to the
development of a fully formed cell-wall, as in the cellulose partitions
of a vegetable tissue. In such cases, the dissolved and adsorbable
material has not only the property of lowering the surface tension,
and hence {282} of itself accumulating at the surface, but has also
the property of increasing the viscosity and mechanical rigidity
of the material in which it is dissolved or suspended, and so of
constituting a visible and tangible “membrane[330].” The “zoogloea”
around a group of bacteria is probably a phenomenon of the same order.
In the superficial deposition of inorganic materials we see the same
process abundantly exemplified. Not only do we have the simple case of
the building of a shell or “test” upon the outward surface of a living
cell, as for instance in a Foraminifer, but in a subsequent chapter,
when we come to deal with various spicules and spicular skeletons such
as those of the sponges and of the Radiolaria, we shall see that it is
highly characteristic of the whole process of spicule-formation for the
deposits to be laid down just in the “interfacial” boundaries between
cells or vacuoles, and that the form of the spicular structures tends
in many cases to be regulated and determined by the arrangement of
these boundaries.
In physical chemistry, an important distinction is drawn between
adsorption and _pseudo-adsorption_[331], the former being a
_reversible_, the latter an irreversible or permanent phenomenon.
That is to say, adsorption, strictly speaking, implies the
surface-concentration of a dissolved substance, under circumstances
which, if they be altered or reversed, will cause the concentration to
diminish or disappear. But pseudo-adsorption includes cases, doubtless
originating in adsorption proper, where subsequent changes leave the
concentrated substance incapable of re-entering the liquid system. It
is obvious that many (though not all) of our biological illustrations,
for instance the formation of spicules or of permanent cell-membranes,
belong to the class of so-called pseudo-adsorption phenomena. But the
apparent contrast between the two is in the main a secondary one, and
however important to the chemist is of little consequence to us. {283}
While this brief sketch of the theory of membrane-formation is cursory
and inadequate, it is enough to shew that the physical theory of
adsorption tends in part to overturn, in part to simplify enormously,
the older histological descriptions. We can no longer be content
with such statements as that of Strasbürger, that membrane-formation
in general is associated with the “activity of the kinoplasm,” or
that of Harper that a certain spore-membrane arises directly from
the astral rays[332]. In short, we have easily reached the general
conclusion that, the formation of a cell-wall or cell-membrane is a
chemico-physical phenomenon, which the purely objective methods of the
biological microscopist do not suffice to interpret.
――――――――――
If the process of adsorption, on which the formation of a membrane
depends, be itself dependent on the power of the adsorbed substance to
lower the surface tension, it is obvious that adsorption can only take
place when the surface tension already present is greater than zero.
It is for this reason that films or threads of creeping protoplasm
shew little tendency, or none, to cover themselves with an encysting
membrane; and that it is only when, in an altered phase, the protoplasm
has developed a positive surface tension, and has accordingly gathered
itself up into a more or less spherical body, that the tendency to
form a membrane is manifested, and the organism develops its “cyst” or
cell-wall.
It is found that a rise of temperature greatly reduces the
adsorbability of a substance, and this doubtless comes, either in part
or whole, from the fact that a rise of temperature is itself a cause
of the lowering of surface tension. We may in all probability ascribe
to this fact and to its converse, or at least associate with it, such
phenomena as the encystment of unicellular organisms at the approach
of winter, or the frequent formation of strong shells or membranous
capsules in “winter-eggs.”
Again, since a film or a froth (which is a system of films) can only
be maintained by virtue of a certain viscosity or rigidity of {284}
the liquid, it may be quickly caused to disappear by the presence in
its neighbourhood of some substance capable of reducing the surface
tension; for this substance, being adsorbed, may displace from the
adsorptive layer a material to which was due the rigidity of the film.
In this way a “bathytonic” substance such as ether causes most foams
to subside, and the pouring oil on troubled waters not only stills the
waves but still more quickly dissipates the foam of the breakers. The
process of breaking up an alveolar network, such as occurs at a certain
stage in the nuclear division of the cell, may perhaps be ascribed in
part to such a cause, as well as to the direct lowering of surface
tension by electrical agency.
Our last illustration has led us back to the subject of a previous
chapter, namely to the visible configuration of the interior of the
cell; and in connection with this wide subject there are many phenomena
on which light is apparently thrown by our knowledge of adsorption, and
of which we took little or no account in our former discussion. One of
these phenomena is that visible or concrete “polarity,” which we have
already seen to be in some way associated with a dynamical polarity of
the cell.
This morphological polarity may be of a very simple kind, as when,
in an epithelial cell, it is manifested by the outward shape of
the elongated or columnar cell itself, by the essential difference
between its free surface and its attached base, or by the presence in
the neighbourhood of the former of mucous or other products of the
cell’s activity. But in a great many cases, this “polarised” symmetry
is supplemented by the presence of various fibrillae, or of linear
arrangements of particles, which in the elongated or “monopolar” cell
run parallel with its axis, and which tend to a radial arrangement in
the more or less rounded or spherical cell. Of late years especially,
an immense importance has been attached to these various linear or
fibrillar arrangements, as they occur (_after staining_) in the
cell-substance of intestinal epithelium, of spermatocytes, of ganglion
cells, and most abundantly and most frequently of all in gland cells.
Various functions, which seem somewhat arbitrarily chosen, have been
assigned, and many hard names given to them; for these structures now
include your mitochondria and your chondriokonts (both of these being
varieties {285} of chondriosomes), your Altmann’s granules, your
microsomes, pseudo-chromosomes, epidermal fibrils and basal filaments,
your archeoplasm and ergastoplasm, and probably your idiozomes,
plasmosomes, and many other histological minutiae[333].
[Illustration: Fig. 97. _A_, _B_, Chondriosomes in kidney-cells, prior
to and during secretory activity (after Barratt); _C_, do. in pancreas
of frog (after Mathews).]
The position of these bodies with regard to the other cell-structures
is carefully described. Sometimes they lie in the neighbourhood of
the nucleus itself, that is to say in proximity to the fluid boundary
surface which separates the nucleus from the cytoplasm; and in this
position they often form a somewhat cloudy sphere which constitutes the
_Nebenkern_. In the majority of cases, as in the epithelial cells, they
form filamentous structures, and rows of granules, whose main direction
is parallel to the axis of the cell, and which may, in some cases,
and in some forms, be conspicuous at the one end, and in some cases
at the other end of the cell. But I do not find that the histologists
attempt to explain, or to correlate with other phenomena, the tendency
of these bodies to lie parallel with the axis, and perpendicular to
the extremities of the cell; it is merely noted as a peculiarity, or
a specific character, of these particular structures. Extraordinarily
complicated and diverse functions have been ascribed to them.
Engelmann’s “Fibrillenkonus,” which was almost certainly another aspect
of the same phenomenon, was held by him and by cytologists like Breda
and Heidenhain, to be an apparatus connected in some {286} unexplained
way with the mechanism of ciliary movement. Meves looked upon the
chondriosomes as the actual carriers or transmitters of heredity[334].
Altmann invented a new aphorism, _Omne granulum e granulo_, as a
refinement of Virchow’s _omnis cellula e cellula_; and many other
histologists, more or less in accord, accepted the chondriosomes as
important entities, _sui generis_, intermediate in grade between
the cell itself and its ultimate molecular components. The extreme
cytologists of the Munich school, Popoff, Goldschmidt and others,
following Richard Hertwig, declaring these structures to be identical
with “chromidia” (under which name Hertwig ranked all extra-nuclear
chromatin), would assign them complex functions in maintaining the
balance between nuclear and cytoplasmic material; and the “chromidial
hypothesis,” as every reader of recent cytological literature knows,
has become a very abstruse and complicated thing[335]. With the help of
the “binuclearity hypothesis” of Schaudinn and his school, it has given
us the chromidial net, the chromidial apparatus, the trophochromidia,
idiochromidia, gametochromidia, the protogonoplasm, and many other
novel and original conceptions. The names are apt to vary somewhat in
significance from one writer to another.
The outstanding fact, as it seems to me, is that physiological science
has been heavily burdened in this matter, with a jargon of names and a
thick cloud of hypotheses; while, from the physical point of view we
are tempted to see but little mystery in the whole phenomenon, and to
ascribe it, in all probability and in general terms, to the gathering
or “clumping” together, under surface tension, of various constituents
of the heterogeneous cell-content, and to the drawing out of these
little clumps along the axis of the cell towards one or other of its
extremities, in relation to osmotic currents, as these in turn are set
up in direct relation {287} to the phenomena of surface energy and of
adsorption[336]. And all this implies that the study of these minute
structures, if it teach us nothing else, at least surely and certainly
reveals to us the presence of a definite “field of force,” and a
dynamical polarity within the cell.
――――――――――
Our next and last illustration of the effects of adsorption, which
we owe to the investigations of Professor Macallum, is of great
importance; for it introduces us to a series of phenomena in regard
to which we seem now to stand on firmer ground than in some of the
foregoing cases, though we cannot yet consider that the whole story
has been told. In our last chapter we were restricted mainly, though
not entirely, to a consideration of figures of equilibrium, such as
the sphere, the cylinder or the unduloid; and we began at once to
find ourselves in difficulties when we were confronted by departures
from symmetry, as for instance in the simple case of the ellipsoidal
yeast-cell and the production of its bud. We found the cylindrical cell
of Spirogyra, with its plane or spherical ends, a comparatively simple
matter to understand; but when this uniform cylinder puts out a lateral
outgrowth, in the act of conjugation, we have a new and very different
system of forces to explain. The analogy of the soap-bubble, or of the
simple liquid drop, was apt to lead us to suppose that the surface
tension was, on the whole, uniform over the surface of our cell; and
that its departures from symmetry of form were therefore likely to be
due to variations in external resistance. But if we have been inclined
to make such an assumption we must now {288} reconsider it, and be
prepared to deal with important localised variations in the surface
tension of the cell. For, as a matter of fact, the simple case of a
perfectly symmetrical drop, with uniform surface, at which adsorption
takes place with similar uniformity, is probably rare in physics, and
rarer still (if it exist at all) in the fluid or fluid-containing
system which we call in biology a cell. We have mostly to do with
cells whose general heterogeneity of substance leads to qualitative
differences of surface, and hence to varying distributions of surface
tension. We must accordingly investigate the case of a cell which
displays some definite and regular heterogeneity of its liquid surface,
just as Amoeba displays a heterogeneity which is complex, irregular and
continually fluctuating in amount and distribution. Such heterogeneity
as we are speaking of must be essentially chemical, and the preliminary
problem is to devise methods of “microchemical” analysis, which shall
reveal _localised_ accumulations of particular substances within the
narrow limits of a cell, in the hope that, their normal effect on
surface tension being ascertained, we may then correlate with their
presence and distribution the actual indications of varying surface
tension which the form or movement of the cell displays. In theory the
method is all that we could wish, but in practice we must be content
with a very limited application of it; for the substances which may
have such action as we are looking for, and which are also actual or
possible constituents of the cell, are very numerous, while the means
are very seldom at hand to demonstrate their precise distribution
and localisation. But in one or two cases we have such means, and
the most notable is in connection with the element potassium. As
Professor Macallum has shewn, this element can be revealed, in very
minute quantities, by means of a certain salt, a nitrite of cobalt
and sodium[337]. This salt penetrates readily into the tissues and
into the interior of the cell; it combines with potassium to form a
sparingly soluble nitrite of cobalt, sodium and potassium; and this,
on subsequent treatment with ammonium sulphide, is converted into a
characteristic black precipitate of cobaltic sulphide[338]. {289}
By this means Macallum demonstrated some years ago the unexpected
presence of accumulations of potassium (i.e. of chloride or other
salts of potassium) localised in particular parts of various cells,
both solitary cells and tissue cells; and he arrived at the conclusion
that the localised accumulations in question were simply evidences
of _concentration_ of the dissolved potassium salts, formed and
localised in accordance with the Gibbs-Thomson law. In other words,
these accumulations, occurring as they actually do in connection with
various boundary surfaces, are evidence, when they appear irregularly
distributed over such a surface, of inequalities in its surface
tension[339]; and we may safely take it that our potassium salts, like
inorganic substances in general, tend to _raise_ the surface tension,
and will therefore be found concentrating at a portion of the surface
whose tension is weak[340].
In Professor Macallum’s figure (Fig. 98, 1) of the little green alga
Pleurocarpus, we see that one side of the cell is beginning to bulge
out in a wide convexity. This bulge is, in the first place, a sign of
weakened surface tension on one side of the cell, which as a whole had
hitherto been a symmetrical cylinder; in the second place, we see that
the bulging area corresponds to the position of a great concentration
of the potassic salt; while in the third place, from the physiological
point of view, we call the phenomenon the first stage in the process of
conjugation. In Fig. 98, 2, of Mesocarpus (a close ally of Spirogyra),
we see the same phenomenon admirably exemplified in a later stage.
From the adjacent cells distinct outgrowths are being emitted, where
the surface tension has been weakened: just as the glass-blower warms
and softens a small part of his tube to blow out the softened area
into a bubble or diverticulum; and in our Mesocarpus cells (besides a
certain amount of potassium rendered visible over the boundary which
{290} separates the green protoplasm from the cell-sap), there is a
very large accumulation precisely at the point where the tension of the
originally cylindrical cell is weakening to produce the bulge. But in a
still later stage, when the boundary between the two conjugating cells
is lost and the cytoplasm of the two cells becomes fused together,
then the signs of potassic concentration quickly disappear, the salt
becoming generally diffused through the now symmetrical and spherical
“zygospore.”
[Illustration: Fig. 98. Adsorptive concentration of potassium salts in
(1) cell of _Pleurocarpus_ about to conjugate; (2) conjugating cells of
_Mesocarpus_; (3) sprouting spores of _Equisetum_. (After Macallum.)]
In a spore of Equisetum (Fig. 98, 3), while it is still a single cell,
no localised concentration of potassium is to be discerned; but as
soon as the spore has divided, by an internal partition, into two
cells, the potassium salt is found to be concentrated in the smaller
one, and especially towards its outer wall, which is marked by a
pronounced convexity. And as this convexity (which corresponds to one
pole of the now asymmetrical, or quasi-ellipsoidal spore) grows out
into the root-hair, the potassium salt accompanies its growth, and is
concentrated under its wall. The concentration is, {291} accordingly,
a concomitant of the diminished surface tension which is manifested in
the altered configuration of the system.
In the case of ciliate or flagellate cells, there is to be found a
characteristic accumulation of potassium at and near the base of the
cilia. The relation of ciliary movement to surface tension lies beyond
our range, but the fact which we have just mentioned throws light
upon the frequent or general presence of a little protuberance of the
cell-surface just where a flagellum is given off (cf. p. 247), and of
a little projecting ridge or fillet at the base of an isolated row of
cilia, such as we find in Vorticella.
Yet another of Professor Macallum’s demonstrations, though its interest
is mainly physiological, will help us somewhat further to comprehend
what is implied in our phenomenon. In a normal cell of Spirogyra, a
concentration of potassium is revealed along the whole surface of the
spiral coil of chlorophyll-bearing, or “chromatophoral,” protoplasm,
the rest of the cell being wholly destitute of the former substance:
the indication being that, at this particular boundary, between
chromatophore and cell-sap, the surface tension is small in comparison
with any other interfacial surface within the system.
Now as Macallum points out, the presence of potassium is known to be
a factor, in connection with the chlorophyll-bearing protoplasm, in
the synthetic production of starch from CO_{2} under the influence of
sunlight. But we are left in some doubt as to the consecutive order
of the phenomena. For the lowered surface tension, indicated by the
presence of the potassium, may be itself a cause of the carbohydrate
synthesis; while on the other hand, this synthesis may be attended
by the production of substances (e.g. formaldehyde) which lower the
surface tension, and so conduce to the concentration of potassium. All
we know for certain is that the several phenomena are associated with
one another, as apparently inseparable parts or inevitable concomitants
of a certain complex action.
――――――――――
And now to return, for a moment, to the question of cell-form. When
we assert that the form of a cell (in the absence of mechanical
pressure) is essentially dependent on surface tension, and even when
we make the preliminary assumption that protoplasm is essentially
{292} a fluid, we are resting our belief on a general consensus of
evidence, rather than on compliance with any one crucial definition.
The simple fact is that the agreement of cell-forms with the forms
which physical experiment and mathematical theory assign to liquids
under the influence of surface tension, is so frequently and often
so typically manifested, that we are led, or driven, to accept the
surface tension hypothesis as generally applicable and as equivalent
to a universal law. The occasional difficulties or apparent exceptions
are such as call for further enquiry, but fall short of throwing doubt
upon our hypothesis. Macallum’s researches introduce a new element
of certainty, a “nail in a sure place,” when they demonstrate that,
in certain movements or changes of form which we should naturally
attribute to weakened surface tension, a chemical concentration which
would naturally accompany such weakening actually takes place. They
further teach us that in the cell a chemical heterogeneity may exist
of a very marked kind, certain substances being accumulated here and
absent there, within the narrow bounds of the system.
Such localised accumulations can as yet only be demonstrated in the
case of a very few substances, and of a single one in particular;
and these are substances whose presence does not produce, but whose
concentration tends to follow, a weakening of surface tension. The
physical cause of the localised inequalities of surface tension remains
unknown. We may assume, if we please, that it is due to the prior
accumulation, or local production, of chemical bodies which would
have this direct effect; though we are by no means limited to this
hypothesis.
But in spite of some remaining difficulties and uncertainties, we have
arrived at the conclusion, as regards unicellular organisms, that
not only their general configuration but also _their departures from
symmetry_ may be correlated with the molecular forces manifested in
their fluid or semi-fluid surfaces.
{293}