On Growth and Form

matter by saying that, if you have caryokinetic figures developing inside the cell, that of itself indicates that the dynamic system and the localised forces arising from it are in continual alteration ; and, consequently, changes in the outward configuration of the system are bound to take place. As regards the phenomena of fertilisation,—of the union of the spermatozoon with the “pronucleus” of the egg,—we might study these also in illustration, up to a certain point, of the polarised forces which are manifestly at work. But we shall merely take, as a single illustration, the paths of the male and female pronuclei, as they travel to their ultimate meeting place.

The spermatozoon, when within a very short distance of the egg-cell, is attracted by it. Of the nature of this attractive force we have no certain knowledge, though we would seem to have a pregnant hint in Loeb’s discovery that, in the neighbourhood of other substances, such even as a fragment, or bead, of glass, the spermatozoon undergoes a similar attraction. But, whatever the force may be, it is one acting normally to the surface of the ovum, and accordingly, after entry, the sperm-nucleus points straight towards the centre of the egg; from the fact that other spermatozoa, subsequent to the first, fail to effect an entry, we may safely conclude that an immediate consequence of the entry of the spermatozoon is an increase in the surface-tension of the ege*. Somewhere or other, near or far away, within the egg, lies its own nuclear body, the so-called female pronucleus, and we find after a while that this has fused with the head of the spermatozoon (or male pronucleus), and that the body resulting from their fusion has come to occupy the centre of the egg. This musi be due (as Whitman pointed out long ago) to a force of attraction acting between the two bodies, and another force acting upon one or other or both in the direction of the centre of the cell. Did we know the magnitude of these several forces, it would be a very easy task to calculate the precise path which the two pronuclei would follow, leading to conjugation and the central

* But under artificial conditions, “‘polyspermy” may take place, e.g. under the action of dilute poisons, or of an abnormally high temperature, these being all, doubtless, conditions under which the surface-tension is diminished. position. As we do not know the magnitude, but only the direction, of these forces we can only make a general statement: (1) the paths of both moving bodies will lie wholly within a plane triangle drawn between the two bodies and the centre of the cell; (2) unless the two bodies happen to lie, to begin with, precisely on a diameter of the cell, their paths until they meet one another will be curved paths, the convexity of the curve being towards the straight line joining the two bodies; (3) the two bodies will meet a little before they reach the centre; and, having met and fused, will travel on to reach the centre in a straight line. The actual study and observation of the path followed is not very easy, owing to the fact that what we usually see is not the path itself, but only a projection of the path upon the plane of the microscope; but the curved path is particularly well seen in the frog’s egg, where the path of the spermatozoon is marked by a little streak of brown pigment, and the fact of the meeting of the pronuclei before reaching the centre has been repeatedly seen by many observers.

The problem is nothing else than a particular case of the famous problem of three bodies, which has so occupied the astronomers; and it is obvious that the foregoing brief description is very far from including all possible cases. Many of these are particularly described in the works of Fol, Roux, Whitman and others *. The intracellular phenomena of which we have now spoken have assumed immense importance in biological literature and discussion during the last forty years; but it is open to us to doubt — whether they will be found in the end to possess more than a remote and secondary biological significance. Most, if not all of them, would seem to follow immediately and inevitably from very simple assumptions as to the physical constitution of the cell, and from an extremely simple distribution of polarised forces within it. We have already seen that how a thing grows, and what it grows into, is a dynamic and not a merely material problem; so far as the material substance is concerned, it is so only by reason

of the chemical, electrical or other forces which are associated with it. But there is another consideration which would lead us to suspect that many features in the structure and configuration of the cell are of very secondary biological importance; and that is, the great variation to which these phenomena are subject in similar or closely related organisms, and the apparent impossibility of correlating them with the peculiarities of the organism as a whole. ‘Comparative study has shewn that almost every detail of the processes (of mitosis) described above is subject to variation in different forms of cells*.” A multitude of cells divide to the accompaniment of caryokinetic phenomena; but others do so without any visible caryokinesis at all. Sometimes the polarised field of force is within, sometimes it is adjacent to, and at other times it lies remote from the nucleus. The distribution of potential is very often symmetrical and bipolar, as in the case described ; but a less symmetrical distribution often occurs, with the result that we have, for a time at least, numerous centres of force, instead of the two main correlated poles: this is the simple explanation of the numerous stellate figures, or “ Strahlungen,” which have been described in certain eggs, such as those of Chaetopterus. In one and the same species of worm (Ascaris megalocephala), one group or two groups of chromosomes may be present. And remarkably constant, in general, as the number of chromosomes in any one species undoubtedly is, yet we must not forget that, in plants and animals alike, the whole range of observed numbers is but a small one; for (as regards the germ-nuclei) few organisms have less than six chromosomes, and fewer still have more than sixteen}.

In closely related animals, such as various species of Copepods, and even in the same species of worm or insect, the form of the chromosomes, and their arrangement in relation to the nuclear spindle, have been found to differ in the various ways alluded to above. In short, there seem to be strong grounds for believing that these and many similar phenomena are in no way specifically related to the particular organism in which they have + Eight and twelve are by much the commonest numbers, six and sixteen coming next in order. If we may judge by the list given by E. B. Wilson (The Cell, p. 206), over 80 % of the observed cases lie between 6 and 16, and nearly 60 % between 8 and 12.

been observed, and are not even specially and indisputably connected with the organism as such. They include such manifestations of the physical forces, in their various permutations and combinations, as may also be witnessed, under appropriate conditions, in non-living things. When we attempt to separate our purely morphological or “purely embryological” studies from physiological and physical investigations, we tend zpso facto to regard each particular structure and configuration as an attribute, or a particular “character,” of this or that particular organism. From this assumption we are apt to go on to the drawing of new conclusions or the framing of new theories as to the ancestral history, the classificatory position, the natural affinities of the several organisms: in fact, to apply our embryological knowledge mainly, and at times exclusively, to the study of phylogeny. When we find, as we are not long of finding, that our phylogenetic hypotheses, as drawn from embryology, become complex and unwieldy, we are nevertheless reluctant to admit that the whole method, with its fundamental postulates, is at fault. And yet nothing short of this would seem to be the case, in regard to the earlier phases at least of embryonic development. All the evidence at hand goes, as it seems to me, to shew that embryological data, prior to and even long after the epoch of segmentation, are essentially a subject for physiological and physical investigation and have but the very slightest link with the problems of systematic or zoological classification. Comparative embryology has its own facts to classify, and its own methods and principles of classification. Thus we may classify eggs according to the presence or absence, the paucity or abundance, of their associated food-yolk, the chromosomes according to their form and their number, the segmentation according to its various “types,” radial, bilateral, spiral, and so forth.

But we have little night to expect, and in point of fact we shall very seldom and (as it were) only accidentally find, that these embryological categories coincide with the lines of ‘‘natural’’ or “phylogenetic” classification which have been arrived at by the systematic zoologist. The cell, which Goodsir spoke of as a “centre of force,” is in reality a “sphere of action” of certain more or less localised forces; and of these, surface-tension is the particular force which is especially responsible for giving to the cell its outline and its morphological individuality. The partially segmented differs from the totally segmented egg, the unicellular Infusorian from the minute multicellular Turbellarian, in the intensity and the range of those surface-tensions which in the one case succeed and in the other fail to form a visible separation between the “cells.” Adam Sedgwick used to call attention to the fact that very often, even in eggs that appear to be totally segmented, it is yet impossible to discover an actual separation or cleavage, through and through between the cells which on the surface of the egg are so clearly delimited; so far and no farther have the physical forces effectuated a visible “cleavage.” The vacuolation of the protoplasm in Actinophrys or Actinosphaerium is due to localised surface-tensions, quite irrespective of the multinuclear nature of the latter organism. In short, the boundary walls due to surface-tension may be present or may be absent with or without the delimination of the other specific fields of force which are usually correlated with these boundaries and with the independent individuality of the cells. What we may safely admit, however, is that one effect of these circumscribed fields of force is usually such a separation or segregation of the protoplasmic constituents, the more fluid from the less fluid and so forth, as to give a field where surface-tension may do its work and bring a visible boundary into being.

When the formation of a “surface” is once effected, its physical condition, or phase, will be bound to differ notably from that of the interior of the cell, and under appropriate chemical conditions the formation of an actual cell-wall, cellulose or other, is easily intelligible. To this subject we shall return again, in another chapter. From the moment that we enter on a dynamical conception of the cell, we perceive that the old debates were in vain as to what visible portions of the cell were active or passive, living or non-living. For the manifestations of force can only be due to the interaction of the various parts, to the transference of energy from one to another. Certain properties may be manifested, certain functions may be carried on, by the protoplasm apart

from the nucleus; but the interaction of the two is necessary, that other and more important properties or functions may be manifested. We know, for instance, that portions of an Infusorian are incapable of regenerating lost parts in the absence of a nucleus, while nucleated pieces soon regain the specific form of the organism : and we are told that reproduction by fission cannot be initiated, though apparently all its later steps can be carried on, independently of nuclear action. Nor, as Verworn pointed out, can the nucleus possibly be regarded as the “sole vehicle of inheritance,” since only in the conjunction of cell and nucleus do we find the essentials of cell-life. “Kern und Protoplasma sind nur vereint lebensfihig,” as Nussbaum said. Indeed we may, with EH. B. Wilson, go further, and say that “the terms ‘nucleus’ and ‘cellbody’ should probably be regarded as only topographical expressions denoting two differentiated areas in a common structural basis.”

Endless discussion has taken place regarding the centrosome, some holding that it is a specific and essential structure, a permanent corpuscle derived from a similar pre-existing corpuscle, a “‘fertilising element” in the spermatozoon, a special “organ of cell-division,”” a material “dynamic centre” of the cell (as Van Beneden and Boveri call it); while on the other hand, it is pointed out that many cells live and multiply without any visible centrosomes, that a centrosome may disappear and be created anew, and even that under artificial conditions abnormal chemical stimuli may lead to the formation of new centrosomes... We may safely take it that the centrosome, or the “attraction sphere,’ is essentially a “centre of force,” and that this dynamic centre may or may not be constituted by (but will be very apt to produce) a concrete and visible concentration of matter.

It is far from correct to say, as is often done, that the cell-wall, or cell-membrane, belongs “to the passive products of protoplasm rather than to the living cell itself’; or to say that in the animal cell, the cell-wall, because it is “‘shghtly developed,” is relatively unimportant compared with the important role which it assumes in plants. On the contrary, it is quite certain that, whether visibly differentiated into a semi-permeable membrane, or merely constituted by a liquid film, the surface of the cell is the seat of

important forces, capillary and electrical, which play an essential part in the dynamics of the cell. Even in the thickened, largely solidified cellulose wall of the plant-cell, apart from the mechanical resistances which it affords, the osmotic forces developed in connection with it are of essential importance. But if the cell acts, after this fashion, as a whole, each part interacting of necessity with the rest, the same is certainly true of the entire multicellular organism: as Schwann said of old, in very precise and adequate words, “the whole organism subsists only by means of the reciprocal action of the single elementary parts*.”’

As Wilson says again, “the physiological autonomy of the individual cell falls into the background...and the apparently composite character which the multicellular organism may exhibit is owing to a secondary distribution of its energies among local centres of actiony.” It is here that the homology breaks down which is so often drawn, and overdrawn, between the unicellular organism and the individual cell of the metazoont. Whitman, Adam Sedgwick§, and others have lost no opportunity of warning us against a too literal acceptation of the cell-theory, against the view that the multicellular organism is a colony (or, as Haeckel called it (in the case of the plant), a “republic”) of independent units of life||. As Goethe said long ago, “Das lebendige ist zwar in Elemente

{ E.g. Briicke. Hlementarorganismen, p. 387: ‘Wir miissen in der Zelle einen kleinen Thierleib sehen, und diirfen die Analogien, welche zwischen ihr und den kleinsten Thierformen existiren, niemals aus den Augen lassen.” || Cf. Hertwig, O., Die Zelle und die Gewebe, 1893, p. 1; “Die Zellen, in welche der Anatom die pflanzlichen und thierischen Organismen zerlegt, sind die Trager der Lebensfunktionen; sie sind, wie Virchow sich ausgedriickt hat, die ‘Lebenseinheiten.’ Von diesem Gesichtspunkt aus betrachtet, erscheint der Gesammtlebensprocess eines zusammengesetzten Organismus nichts Anderes zu sein als das héchst

verwickelte Resultat der einzelnen Lebensprocesse seiner zahlreichen, verschieden functionirenden Zellen.”’ zerlegt, aber man kann es aus diesen nicht wieder zusammenstellen und beleben;” the dictum of the Cellularpathologie being just the opposite, “Jedes Thier erscheint als eine Summe vitaler Kinheiten, von denen jede den vollen Charakter des Lebens an sich tragt.” Hofmeister and Sachs have taught us that in the plant the srowth of the mass, the growth of the organ, is the primary fact, that “cell formation is a phenomenon very general in organic. life, but still only of secondary significance.” ‘Comparative embryology” says Whitman, “reminds us at every turn that the organism dominates cell-formation, using for the same purpose one, several, or many cells, massing its material and directing its movements and shaping its organs, as if cells did not exist*.”’ So Rauber declared that, in the whole world of organisms, “das Ganze liefert die Theile, nicht die Theile das Ganze: letzteres setzt die Theile zusammen, nicht diese jenesy.’”’ And on the botanical side De Bary has summed up the matter in an aphorism, ‘‘Die Pflanze bildet Zellen, nicht die Zelle bildet Pflanzen.”

Discussed almost wholly from the concrete, or morphological point of view, the question has for the most part been made to turn on whether actual protoplasmic continuity can be demonstrated between one cell and another, whether the organism be an actual reticulum, or syncytium. But from the dynamical point of view the question is much simpler. We then deal not with material continuity, not with little bridges of connecting protoplasm, but with a continuity of forces, a comprehensive field of force, which runs through and through the entire organism and is by no means restricted in its passage to a protoplasmic continuum. And such a continuous field of force, somehow shaping the whole organism, independently of the number, magnitude and form of the individual cells, which enter, like a froth, into its fabric, seems to me certainly and obviously to exist. As Whitman says, “the fact that physiological unity is not broken by cell-boundaries is confirmed in so many ways that it must be accepted as one of the fundamental truths of biolcgyt.”

y+ Neue Grundlegungen zur Kenntniss der Zelle, Morph. Jahrb. vim, pp. 272, Protoplasm, as.we have already said, is a fluid or rather a semifluid substance, and we need not pause here to attempt to describe the particular properties of the semifluid, colloid, or jelly-like substances to which it is allied; we should find it no easy matter. Nor need we appeal to precise theoretical definitions of fluidity, lest we come into a debateable land. It is in the most general sense that protoplasm is “fluid.” As Graham said (of colloid matter in general), “its softness partakes of fluidity, and enables the colloid to become a vehicle for liquid diffusion, like water itself*.”” When we can deal with protoplasm in sufficient quantity we see it flow; particles move freely through it, airbubbles and liquid droplets shew round or spherical within it; and we shall have much to say about other phenomena manifested by its own surface, which are those especially characteristic of hquids. It may encompass and contain solid bodies, and it may “secrete”? within or around itself solid substances; and very often in the complex living organism these solid substances formed by the living protoplasm, like shell or nail or horn or feather, may remain when the protoplasm which formed them is dead and gone; but the protoplasm itself is fluid or semifluid, and accordingly permits of free (though not necessarily rapid) diffusion and easy convection of particles within itself. This simple fact is of elementary importance in connection with form, and with what appear at first sight to be common characteristics or peculiarities of the forms of living things.

The older naturalists, in discussing the differences between inorganic and organic bodies, laid stress upon the fact or statement that the former grow by “agglutination,” and the latter by what they termed “intussusception.”” The contrast is true, rather, of solid as compared with jelly-like bodies of all kinds, living or dead, the great majority of which as it so happens, but by no means all, are of organic origin. A crystal “grows” by deposition of new molecules, one by one and layer by layer, superimposed or aggregated upon the solid substratum already formed. Each particle would seem to be influenced, practically speaking, only by the particles in its immediate neighbourhood, and to be in a state of freedom and independence from the influence, either direct or indirect, of its remoter neighbours. As Lord Kelvin and others have explained the formation and the resulting forms of crystals, so we believe that each added particle takes up its position in relation to its immediate neighbours already arranged, generally in the holes and corners that their arrangement leaves, and in closest contact with the greatest number*. And hence we may repeat or imitate this process of arrangement, with great or apparently even with precise accuracy (in the case of the simpler crystalline systems), by piling up spherical pills or grains of shot. In so doing, we must have regard to the fact that each particle must drop into the place where it can go most easily, or where no easier place offers. In more technical language, each particle is free to take up, and does take up, its position of least potential energy relative to those already deposited; in other words, for each particle motion is induced until the energy of the system is so distributed that no tendency or resultant force remains to move it more. The application of this principle has been shewn to lead to the production of planes} (in all cases where by the limitation of material, surfaces must occur); and where we have planes, straight edges and solid angles must obviously also occur; and, if equilibrium is

* Cf. Kelvin, On the Molecular Tactics of a Crystal, The Boyle Lecture, Oxford, 1893, Baltimore Lectures, 1904, pp. 612-642. Here Kelvin was mainly following Bravais’s (4nd Frankenheim’s) theory of “space-lattices,”’ but he had been largely anticipated by the crystallographers. For an account of the development of the subject in modern crystallography, by Sohncke, von Fedorow, Schénfliess, Barlow and others, see Tutton’s Crystallography, chap. ix, pp. 118-134, 1911.

+ In a homogeneous crystalline arrangement, symmetry compels a locus of one property to be a plane or set of planes; the locus in this case being that of least surface potential energy. to follow, must occur symmetrically. Our piling up of shot, or manufacture of mimic crystals, gives us visible demonstration that the result is actually to obtain, as in the natural crystal, plane surfaces and sharp angles, symmetrically disposed. But the living cell grows in a totally different way, very much as a piece of glue swells up in water, by “imbibition,” or by interpenetration into and throughout its entire substance. The semifluid colloid mass takes up water, partly to combine chemically with its individual molecules*, partly by physical diffusion into the interstices between these molecules, and partly, as it would seem, in other ways; so that the entire phenomenon is a very complex and even an obscure one. But, so far as we are concerned, the net result is a very simple one. For the equilibrium or tendency to equilibrium of fluid pressure in all parts of its interior while the process of imbibition is going on, the constant rearrangement of its fluid mass, the contrast in short with the crystalline method of growth where each particle comes to rest to move (relatively to the whole) no more, lead the mass of jelly to swell up, very much as a bladder into which we blow air, and so, by a graded and harmonious distribution of forces, to assume everywhere a rounded and more or less bubble-like external formf. So, when the same school of older naturalists called attention to a new distinction or contrast of form between the organic and inorganic objects, in that the contours of the former tended to roundness and curvature, and those of the latter to be bounded by straight lines, planes and sharp angles, we see that this contrast was not a new and different one, but only another aspect of their former statement, and an immediate consequence of the difference between the processes of agglutination and intussusception.

This common and general contrast between the form of the erystal on the one hand, and of the colloid or of the organism on the other, must by no means be pressed too far. For Lehmann, * This is what Graham called the water of gelatination, on the analogy of water of crystallisation; Chem. and Phys. Researches, p. 597. + Here, in a non-crystalline or random arrangement of particles, symmetry ensures that the potential energy shall be the same per unit area of all surfaces; and it follows from geometrical considerations that the total surface energy will be least if the surface be spherical.

in his great work on so-called Fluid Crystals*, to which we shall afterwards return, has shewn how, under certain circumstances, surface-tension phenomena may coexist with crystallisation, and produce a form of minimal potential which is a resultant of both: the fact being that the bonds maintaining the crystalline arrangement are now so much looser than in the solid condition that the tendency to least total surface-area is capable of being satisfied. Thus the phenomenon of “liquid crystallisation” does not destroy the distinction between crystalline and colloidal forms, but gives added unity and continuity to the whole series of phenomena f. Lehmann has also demonstrated phenomena within the crystal, known for instance as transcrystallisation, which shew us that we must not speak unguardedly of the growth of crystals as limited to deposition upon a surface, and Biitschli has already pointed out the possible great importance to the biologist of the various phenomena which Lehmann has describedt. So far then, as growth goes on, unaffected by pressure or other external force, the fluidity of protoplasm, its mobility internal and external, and the manner in which particles move with comparative freedom from place to place within, all manifestly tend to the production of swelling, rounded surfaces, and to their great predominance over plane surfaces in the contour of the organism. These rounded contours will tend to be preserved, for a while, in the case of naked protoplasm by its viscosity, and in . the presence of a cell-wall by its very lack of fluidity.

In a general way, the presence of curved boundary surfaces will be especially obvious in the unicellular organisms, and still more generally in the external forms of all organisms; and wherever mutual pressure between adjacent cells, or other adjacent parts, has not come into play to flatten the rounded surfaces into planes. But the rounded contours that are assumed and exhibited by * Lehmann, O., Fliissige Krystalle, sowie Plasticitat von Krystallen im allgemeinen, etc., 264 pp. 39 pll., Leipsig, 1904. For a semi-popular, illustrated account, see Tutton’s Crystals (Int. Sci. Series), 1911.

+ As Graham said of an allied phenomenon (the so-called blood-crystals of Funke), it “illustrates the maxim that in nature there are no abrupt transitions, and that distinctions of class are never absolute.” t Cf. Przibram, H., Kristall-analogien zur Entwickelungsmechanik der Organ- a piece of hard glue, when we throw it into water and see it expand as it sucks the water up, are not nearly so regular or so beautiful as are those which appear when we blow a bubble, or form a drop, or pour water into a more or less elastic bag. For these curving contours depend upon the properties of the bag itself, of the film or membrane that contains the mobile gas, or that contains or bounds the mobile liquid mass. And hereby, in the case of the fluid or semifluid mass, we are introduced to the subject of surface tension: of which indeed we have spoken in the preceding chapter, but which we must now examine with greater care.

Among the forces which determine the forms of cells, whether they be solitary or arranged in contact with one another, this force of surface-tension is certainly of great, and is probably of paramount importance. But while we shall try to separate out the phenomena which are directly due to it, we must not forget that, in each particular case, the actual conformation which we study may be, and usually is, the more or less complex resultant of surface tension acting together with gravity, mechanical pressure, osmosis, or other physical forces.

Surface tension is that force by which we explain the form of a drop or of a bubble, of the surfaces external and internal of a “froth” or collocation of bubbles, and of many other things of like nature and in like circumstances*. It is a property of liquids (in the sense at least with which our subject is concerned), and it is manifested at or very near the surface, where the liquid comes into contact with another liquid, a solid or a gas. We note here that the term swrface is to be interpreted in a wide sense; for wherever we have solid particles imbedded in a fluid, wherever we have a non-homogeneous fluid or semi-fluid such as a particle * The idea of a “surface-tension”’ in liquids was first enunciated by Segner, De figuris superficierum fluidarum, in Comment. Soc. Roy. Gottingen, 1751, p. 301. Hooke, in the Micrographia (1665, Obs. vim, etc.), had called attention to the globular or spherical form of the little morsels of steel struck off by a flint, and had shewn how to make a powder of such spherical grains, by heating fine filings to melting point. “This Phaenomenon” he said “proceeds from a propriety which belongs to all kinds of fluid Bodies more or less, and is caused by the Incongruity

of the Ambient and included Fluid, which so.acts and modulates each other, that they acquire, as neer as is possible, a spherical or globular form....”’ of protoplasm, wherever we have the presence of “impurities,” as - in a mass of molten metal, there we have always to bear in mind the existence of “surfaces” and of surface tensions, not only on the exterior of the mass but also throughout its interstices, wherever like meets unlike. Surface tension is due to molecular force, to force that is to say arising from the action of one molecule upon another, and it is accordingly exerted throughout a small thickness of material, comparable to the range of the molecular forces. We imagine that within the interior of the liquid mass such molecular interactions negative one another: but that at and near the free surface, within a layer or film approximately equal to the range of the molecular force, there must be a lack of such equilibrium and consequently a manifestation of force.

The action of the molecular forces has been variously explained. But one simple explanation (or mode of statement) is that the molecules of the surface layer (whose thickness is definite and constant) are being constantly attracted into the interior by those which are more deeply situated, and that consequently, as molecules keep quitting the surface for the interior, the bulk of the latter increases while the surface diminishes; and the process continues till the surface itself has become a minimum, the swrfaceshrinkage exhibiting itself as a surface-tension. This is a sufficient description of the phenomenon in cases where a portion of liquid is subject to no other than its own molecular forces, and (since the sphere has, of all solids, the smallest surface for a given volume) it accounts for the spherical form of the raindrop, of the grain of shot, or of the living cellin many simple organisms. It accounts also, as we shall presently see, for a great number of much more complicated forms, manifested under less simple conditions.

Let us here briefly note that surface tension is, in itself, a comparatively small force, and easily measurable: for instance that of water is equivalent to but a few grains per linear inch, or a few grammes per metre. But this small tension, when it exists in a curved surface of very great curvature, gives rise to a very great pressure directed towards the centre of curvature. We can easily calculate this pressure, and so satisfy ourselves that, when the radius of curvature is of molecular dimensions, the