405 Cf. p. 369.
520 It has been pointed out to me that it does not follow at once and obviously that, because the interspace AB is a mean proportional between the breadths of the adjacent whorls, therefore the whole distance OB is a mean proportional between OA and OC. This is a corollary which requires to be proved; but the proof is easy.
526 Macalister, Alex., Observations on the Mode of Growth of Discoid and Turbinated Shells, P. R. S. XVIII, pp. 529ã532, 1870.
573 Besides papers referred to below, and many others quoted in Sachãs Botany and elsewhere, the following are important: Braun, Alex., Vergl. Untersuchung û¥ber die Ordnung der Schuppen an den Tannenzapfen, etc., Verh. Car. Leop. Akad. XV, pp. 199ã401, 1831; Dr C. Schimperãs VortrûÊge û¥ber die MûÑglichkeit eines wissenschaftlichen VerstûÊndnisses der Blattstellung, etc., Flora, XVIII, pp. 145ã191, 737ã756, 1835; Schimper, C. F., Geometrische Anordnung der um eine Axe peripherische Blattgebilde, Verhandl. Schweiz. Ges., pp. 113ã117, 1836; Bravais, L. and A., Essai sur la disposition des feuilles curvisûˋriûˋes, Ann. Sci. Nat. (2), VII, pp. 42ã110, 1837; Sur la disposition symmûˋtrique des inflorescences, ibid., pp. 193ã221, 291ã348, VIII, pp. 11ã42, 1838; Sur la disposition gûˋnûˋrale des feuilles rectisûˋriûˋes, ibid. XII, pp. 5ã41, 65ã77, 1839; Zeising, NormalverhûÊltniss der chemischen und morphologischen Proportionen, Leipzig, 1856; Naumann, C. F., Ueber den Quincunx als Gesetz der Blattstellung bei Sigillaria, etc., Neues Jahrb. f. Miner. 1842, pp. 410ã417; Lestiboudois, T., Phyllotaxie anatomique, Paris, 1848; Henslow, G., Phyllotaxis, London, 1871; Wiesner, Bemerkungen û¥ber rationale und irrationale Divergenzen, Flora, LVIII, pp. 113ã115, 139ã143, 1875; Airy, H., On Leaf Arrangement, *Proc.
R. S. XXI, p. 176, 1873; Schwendener, S., Mechanische Theorie der Blattstellungen, Leipzig, 1878; Delpino, F., Causa meccanica della filotassi quincunciale, Genova, 1880; de Candolle, C., ûtude de Phyllotaxie*, Genû´ve, 1881.