PRESIDENTIAL_ADDRfcSS. 401 



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 surfaces 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 multicellular 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 parti- 

 cularised) to set itself at right angles to the preceding 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 curvature 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 Trypansome, or of that around the tail of the 

 spermatozoon of a newt — every one of these, I declare, is a case where the 

 resultant form can be well explained by, 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 overriding, force. 



I believe, for my 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. 

 Suppqse 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 accord- 

 ance 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 {Globirierina), or, 

 with all intermediate degrees, may very nearly wholly enwrap the first. Take 

 any specific angle of contact, and presume the same conditions to be maintained, 

 and therefore the same angle to be repeated, as each successive chamber follows 

 on the one before; and you will thereby build up regular forms, spiral or 

 alternate, that correspond with marvellous accuracy to the actual forms of the 

 Foraminifera. And this case is all the more interesting because the allied and 

 successive forms so obtained differ only in degree, in the magnitude of a single 

 physical or mathematical factor; in other words, we get not only individual 

 phenomena, but lines of apparent orthogenesis, that seem explicable by physical 

 laws, and attributable to the continuity between successive states in the con- 

 tinuous or gradual variation of a physical condition. The resemblance between 

 allied and related forms, as Hartmann demonstrated and Giard admitted years 

 1911. D D 



