[383] It is highly probable, and we may reasonably assume, that the two little triangles do not actually meet at an apical point, but merge into one another by a twist, or minute surface of complex curvature, so as not to contravene the normal conditions of equilibrium.
[384] Professor Peddie has given me this interesting and important result, but the mathematical reasoning is too lengthy to be set forth here.
[385] Cf. Rhumbler, Arch. f. Entw. Mech. XIV, p. 401, 1902; Assheton, ibid. XXXI, pp. 46–78, 1910.
[386] M. Robert (l. c. p. 305) has compiled a long list of cases among the molluscs and the worms, where the initial segmentation of the egg proceeds by equal or unequal division. The two cases are about equally numerous. But like many other writers, he would ascribe this equality or inequality rather to a provision for the future than to a direct effect of immediate physical causation: “Il semble assez probable, comme on l’a dit souvent, que la plus grande taille d’un blastomère est liée à l’importance et au développement précoce des parties du corps qui doivent en naître: il y aurait là une sorte de reflet des stades postérieures du développement sur les premières phénomènes, ce que M. Ray Lankester appelle precocious segregation. Il faut avouer pourtant qu’on est parfois assez embarrassé pour assigner une cause à pareilles différences.”
[387] The principle is well illustrated in an experiment of Sir David Brewster’s (Trans. R.S.E. XXV, p. 111, 1869). A soap-film is drawn over the rim of a wine-glass, and then covered by a watch-glass. The film is inclined or shaken till it becomes attached to the glass covering, and it then immediately changes place, leaving its transverse position to take up that of a spherical segment extending from one side of the wine-glass to its cover, and so enclosing the same volume of air as formerly but with a great economy of surface, precisely as in the case of our spherical partition cutting off one corner of a cube.
[388] Cf. Wildeman, Attache des Cloisons, etc., pls. 1, 2.
[389] Nova Acta K. Leop. Akad. XI, 1, pl. IV.
[390] Cf. Protoplasmamechanik, p. 229: “Insofern liegen also die Verhältnisse hier wesentlich anders als bei der Zertheilung hohler Körperformen durch flüssige Lamellen. Wenn die Membran bei der Zelltheilung die von dem Prinzip der kleinsten Flächen geforderte Lage und Krümmung annimmt, so werden wir den Grund dafür in andrer Weise abzuleiten haben.”
[391] There is, I think, some ambiguity or disagreement among botanists as to the use of this latter term: the sense in which I am using it, viz. for any partition which meets the outer or peripheral wall at right angles (the strictly radial partition being for the present excluded), is, however, clear.
[392] Cit. Plateau, Statique des Liquides, i, p. 358.