376 THE FORMS OF CELLS [ch. 



whole result of our calculations, and materialise our whole ap- 

 paratus of curves. Such a case is what Bacon calls a "collective 

 instance," bearing witness to the fact that one common law is 

 obeyed by every point or particle of the system. Where the under- 

 lying equations are unknown to us, as happens in so many natural 

 configurations, we may still rest assured that kindred mathematical 

 laws are being automatically followed, and rigorously obeyed, and 

 sometimes half-revealed. 



Of all the surfaces which we have been describing, the sphere is 

 the only one which can enclose space of itself; the others can only 

 help to do so, in combination with one another or with the sphere. 

 Moreover, the sphere is also, of all possible figures, that which 

 encloses the greatest volume with the least area of surface * ; it is 

 strictly and absolutely the surface of minimal area, and it is, ipso 

 facto, the form which will be assumed by a unicellular organism 

 (just as by a raindrop), if it be practically homogeneous and if, Hke 

 Orhulina floating in the ocean, its surroundings be likewise homo- 

 geneous and its field of force symmetrical f. It is only relatively 

 speaking that the rest of these configurations are surfaces minimae 

 areae', for they are so under conditions which involve various 

 pressures or restraints. Such restraints are imposed by the pipe or 

 annulus which supports and confines our oil-globule or soap-bubble ; 

 and in the case of the organic cell, similar restraints are supplied 

 by solidifications partial or complete, or other modifications local 

 or general, of the cell-surface or cell-wall. 



One thing we must not fail to bear in mind. In the case of the 

 soap-bubble we look for stabihty or instability, equihbrium or non- 

 equilibrium, in its several configurations. But the living cell is 

 seldom in equihbrium. It is continually using or expending energy; 

 and this ceaseless flow of energy gives rise to a "steady state," 

 taking the place of and simulating equilibrium. In like manner the 



* On the circle and sphere as giving the smallest boundary for a given content, 

 see (e.g.) Jacob Steiner, Einfache Beweisen der isoperimetrischen Hauptsatze, 

 Berlin. Abhandlungen, 1836, pp. 123-132. 



t The essential conditions of homogeneity and symmetry are none too common, 

 and a spherical organism is only to be looked for among simple things. The 

 floating (or pelagic) eggs of fishes, the spores of red seaweeds, the oospheres of 

 Fucus or Oedogonium, the plasma-masses escaping from the cells of Vaucheriaf 

 are among the instances which come to mind. 



