September 7, 191 1] 



NATURE 



127 



deal with it. But on the whole it seems to me that the 

 subject has attracted too little attention, and that it is 

 well worth our while to think of it to-day. 



1 lii first point, then, that I wish to make in this con- 

 on is that the Form of any portion of matter, whether 

 it be living or dead, its form and the changes of form 

 that are apparent in its movements and in its growth, may 

 in all cases alike be described as due to the action of 

 Force. In short, the form of an object is a '* diagram of 

 forces " — in this sense, at least, that from it we can judge 

 of or deduce the forces that are acting or have acted upon 

 it ; in this strict and particular sense it is a diagram ; in 

 I he case of a solid, of the forces that have been impressed 

 upon it when its conformation was produced, together 

 with those that enable it to retain its conformation ; in the 

 case of a liquid (or of a gasi, of the forces that are for 

 the moment acting on it to restrain or balance its own 

 inherent mobility. In an organism, great or small, it is 

 not merely the nature of the motions of the living sub- 

 stance that we must interpret in terms of Force (accord- 

 ing to Kinetics), but also the conformation of the organism 

 itself, whose permanence or equilibrium is explained by the 

 interaction or balance of forces, as described in Statics. 



If we look at the living cell of an Amceba or a Spirogyra 

 we see a something which exhibits certain active move- 

 ments, and a certain fluctuating, or more or less lasting, 

 form : and its form at a given moment, just like its 

 motions, is to be investigated by the help of physical 

 methods, and explained by the invocation of the mathe- 

 matical conception of force. 



Now the state, including the shape or form, of a portion 

 of matter is the resultant of a number of forces, which 

 represent or symbolise the manifestations of various kinds 

 of Energy ; and it is obvious, accordingly, that a great 

 part of physical science must be understood or taken for 

 granted as the necessary preliminary to the discussion on 

 which we are engaged. 



I am not going to attempt to deal with, or even to 

 enumerate, all the physical forces or the properties of 

 matter with which the pursuit of this subject would oblige 

 us to deal — with gravity, pressure, cohesion, friction, 

 viscosity, elasticity, diffusion, and all the rest of the 

 physical factors that have a bearing on our problem. 1 

 propose only to take one ur two illustrations from the 

 subject of surface-tension, which subject has already so 

 largely engaged the attention of the physiologists. Nor 

 will I even attempt to sketch the general nature of this 

 phenomenon, but will only state (as I fear for my purpose 

 I must) a few of its physical manifestations or laws. Of 

 these, the most essential facts for us are as follows : — 

 Surface-tension is manifested only in fluid or semi-fluid 

 bodies, and only at the surface of these : though we may 

 have to interpret surface in a liberal sense in cases where 

 the interior of the mass is other than homogeneous. 

 Secondly, a fluid may. according to the nature of the 

 substance with which it is in contact, or (more strictly 

 speaking) according to the distribution of energy in the 

 system to which it belongs, tend either to spread itself out 

 in a film, or, conversely, to contract into a drop, striving 

 in the latter case to reduce its surface to a minimal area. 

 Thirdly, when three substances are in contact (and subject 

 to surface-tension), as when water surrounds a drop of 

 protoplasm in contact with a solid, then at any and every 

 point of contact certain definite angles of equilibrium are 

 set up and maintained between the three bodies, which 

 angles are proportionate to the magnitudes of the surface- 

 tensions existing between the three. Fourthly, a fluid film 

 can only remain in equilibrium when its curvature is every- 

 where constant. Fifthly, the only surfaces of revolution 

 which meet this condition are six in number, of which the 

 plane, the sphere, the cylinder, and the so-called unduloid 

 and catenoid are the most important. Sixthly, the cylinder 

 cannot remain in free equilibrium if prolonged bevond a 

 length equal to its own circumference, but, passing through 

 the unduloid, tends to break up into spheres : though this 

 limitation may be counteracted or relaxed, for instance, 

 by viscosity. Finally, we have the curious fact that, in a 

 complex system of films, such as a homogeneous froth of 

 bubbles, three partition-walls and no more always meet at 



NO. 2184, VOL. 87] 



a crest, at equal angles, as, for instance, in the very 

 simple case of a layer of uniform hexagonal cells ; and (in 

 a solid system) the crests, which may be straight or curved, 

 always meet, also at equal angles, four by four, in a 

 common point. From these physical facts, or laws, the 

 morphologist, as well as the physiologist, may draw- 

 important consequences. 



It was Hofmeister who first showed, more than forty 

 years ago, that when any drop of protoplasm, either over 

 all its surface or at some free end (as at the tip of the 

 pseudopodium of an Amoeba), is seen to " round itself off," 

 that is not the effect of physiological or vital contractility, 

 but is a simple consequence of surface-tension — of the law 

 of the minimal surface ; and in the physiological side, 

 Engelmann, Biitschli, and others have gone far in their 

 development of the idea. 



It was Plateau, I think, who first showed that the 

 myriad sticky drops or beads upon the weft of a spider's 

 web, their form, their size, their distance apart, and the 

 presence of the tiny intermediate drops between, were in 

 every detail explicable as the result of surface-tension, 

 through the law of minimal surface and through the 

 corollary to it which defines the limits of stability of the 

 cylinder ; and, accordingly, that with their production, the 

 will or effort or intelligence of the spider had nothing to 

 do. The beaded form of a long, thin pseudopodium, for 

 instance, of a Heliozoan, is an identical phenomenon. 



It was Errera who first conceived the idea that not only 

 the naked surface of the cell, but the contiguous surface's 

 of two naked cells, or the delicate incipient cell-membrane 

 or cell-wall between, might be regarded as a weightless 

 film, whose position and form were assumed in obedience 

 to surface-tension. And it was he who first showed that 

 the symmetrical forms of the unicellular and simple multi- 

 cellular organisms, up to the point where the development 

 of a skeleton complicates the case, were one and all 

 identical with the plane, sphere, cylinder, unduloid and 

 catenoid, or with combinations of these. 



It was Berthold and Errera who, almost simultaneously, 

 showed (the former in far the greater detail) that in a 

 plant each new cell-partition follows the law of minimal 

 surface, and tends (according to another law which I have 

 not particularised) to set itself at right angles to the pre- 

 ceding solidified wall, so giving a simple and adequate 

 physical explanation of what Sachs had stated as an 

 empirical morphological rule. And Berthold further showed 

 how, when the cell-partition was curved, its precise curva- 

 ture, as well as its position, was in accordance with 

 physical law. 



There are a vast number of other things that we can 

 satisfactorily explain on the same principle and by the 

 same laws. The beautiful catenary curve of the edge of 

 the pseudopodium, as it creeps up its axial rod in a 

 Heliozoan or a Radiolarian, the hexagonal mesh of bubbles, 

 or vacuoles, on the surface of the same creatures, the 

 form of the little groove that runs round the waist of a 

 Peridinian, even (as I believe) the existence, form, and 

 undulatory movements of the undulatory membrane of a 

 Trypanosome, or of that around the tail of the spermato- 

 zoon of a newt — every one of these, I declare, is a case 

 where the resultant form can be well explained bv, and 

 cannot possibly be understood without, the phenomena of 

 surface-tension ; indeed, in many of the simpler cases the 

 facts are so well explained by surface-tension that it is 

 difficult to find place for a conflicting, much less an over- 

 riding, force. 



I _ believe, for ray own part, that even the beautiful and 

 varied forms of the Foraminifera may be ascribed to the 

 same cause ; but here the problem is just a little more 

 complex, by reason of the successive consolidations of the 

 shell. Suppose the first cell or chamber to be formed, 

 assuming its globular shape in obedience to our law, and 

 then to secrete its calcareous envelope. The new growing 

 bud of protoplasm, accumulating outside the shell, "will, in 

 strict accordance with the surface-tensions concerned, either 

 fail to " wet " or to adhere to the first-formed shell, and 

 will so detach itself as a unicellular individual (Orbulina), 

 or else it will flow over a less or greater part of the 

 original shell until its free surface meets it at the required 

 angle of equilibrium. Then, according to this angle, the 

 second chamber may happen to be all but detached 



