400 TRANSACTIONS OF SECTION D. 



6i form that are apparent in its movements and in its growth, may in ail 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 the 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 

 gas), 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 substance that we must interpret in terms of 

 Force (according 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 Amoeba or a Spirogyra, we see a something 

 which exhibits certain active movements, 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 mathematical 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 pre- 

 liminary 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 wath which the pursuit of this, sub- 

 ject 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. I propose only to take one or 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 sur- 

 face to a minimal area. Thirdly, when three substances are in contact (and sub- 

 ject 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 curva- 

 ture is everywhere 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 beyond 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 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 

 net the effect of physiological or vital contractility, but is a simple consequence of 



