[343] A similar “bourrelet” is admirably seen at the line of junction between a floating bubble and the liquid on which it floats; in which case it constitutes a “masse annulaire,” whose math­e­mat­i­cal properties and relation to the form of the nearly hemispherical bubble, have been investigated by van der Mensbrugghe (cf. Plateau, op. cit., p. 386). The form of the superficial vacuoles in Actinophrys or Actinosphaerium involves an identical problem.

[344] In an actual calculation we must of course always take account of the tensions on both sides of each film or membrane.

[345] Hofmeister, Pringsheim’s Jahrb. III, p. 272, 1863; Hdb. d. physiol. Bot. I, 1867, p. 129.

[346] Sachs, Ueber die Anordnung der Zellen in jüngsten Pflanzentheilen, Verh. phys. med. Ges. Würzburg, XI, pp. 219–242, 1877; Ueber Zellenanordnung und Wachsthum, ibid. XII, 1878; Ueber die durch Wachsthum bedingte Verschiebung kleinster Theilchen in trajectorischen Curven, Monatsber. k. Akad. Wiss. Berlin, 1880; Physiology of Plants, chap. xxvii, pp. 431–459, Oxford, 1887.

[347] Schwendener, Ueber den Bau und das Wachsthum des Flechtenthallus, Naturf. Ges. Zürich, Febr. 1860, pp. 272–296.

[348] Reinke, Lehrbuch der Botanik, 1880, p. 519.

[349] Cf. Leitgeb, Unters. über die Lebermoose, II, p. 4, Graz, 1881.

[350] Rauber, Neue Grundlegungen zur Kenntniss der Zelle, Morph. Jahrb. VIII, pp. 279, 334, 1882.

[351] C. R. Acad. Sc. XXXIII, p. 247, 1851; Ann. de chimie et de phys. (3), XXXIII, p. 170, 1851; Bull. R. Acad. Belg. XXIV, p. 531, 1857.

[352] Klebs, Biolog. Centralbl. VII, pp. 193–201, 1887.