V] OF FIGURES OF EQUILIBRIUM 383 



This is a helicoid generated by a straight Hne perpendicular to an 

 axis, about which it turns at a uniform rate, while at the same time 

 it slides, also uniformly, along this same axis. At any point in this 

 surface, the curvatures are equal and of opposite sign, and the sum 

 of the curvatures is accordingly nil. Among what are called "ruled 

 surfaces," or surfaces capable of being defined by a system of 

 stretched strings*, the plane and the hehcoid are the only two whose 

 mean curvature is null, while the cyhnder is the only one whose 

 curvature is finite and constant. As this simplest of hehcoids 

 corresponds, in three dimensions, to what in two dimensions is 

 merely a plane (the latter being generated by the rotation of a 

 straight line about an axis without the superadded gliding motion 

 which generates the hehcoid), so there are other and much more 

 complicated helicoids which correspond to the sphere, the unduloid 

 and the rest of our figures of revolution, the generating planes of 

 these latter being supposed to wind spirally about an axis. In the 

 case of the cyhnder it is obvious that the resulting figure is indis- 

 tinguishable from the cyhnder itself. In the case of the unduloid 

 we obtain a grooved spiral, and we meet with something very like 

 it in nature (for instance in Spirochaetes, Bodo gracilis, etc.) ; but in 

 point of fact, the screw motion given to an unduloid or catenary 

 curve fails to give a minimal screw surface, as we might have 

 expected it to do. 



The foregoing considerations deal with a small part only of the 

 theory of surface-tension, or capillarity: with that part, namely, 

 which relates to the surfaces capable of subsisting in equilibrium 

 under the action of that force, either of itself or subject to certain 

 simple constraints. And as yet we have limited ourselves to the 

 case of a single surface, or of a single drop or bubble, leaving to 

 another occasion a discussion of the forms assumed when such drops 

 or vesicles meet and combine together. Ip short, what we have 

 said may help us to understand the form of a cell — considered, as 

 with certain hmitations we may legitimately consider it, as a Hquid 

 drop or liquid vesicle ; the conformation of a tissue or cell-aggregate 

 must be dealt with in the light of another series of theoretical con- 

 siderations. In both cases, we can do no more than touch on the 

 fringe of a large and difficult subject. There are many forms 



* Or rather, surfaces such that through every point there runs a straight line 

 which lies wholly in the surface. 



