[34] The stem of the giant bamboo may attain a height of 60 metres, while not more than about 40 cm. in diameter near its base, which dimensions are not very far short of the theoretical limits (A. J. Ewart, Phil. Trans. vol. 198, p. 71, 1906).
[35] Trans. Zool. Soc. IV, 1850, p. 27.
[36] It would seem to be a common if not a general rule that marine organisms, zoophytes, molluscs, etc., tend to be larger than the corresponding and closely related forms living in fresh water. While the phenomenon may have various causes, it has been attributed (among others) to the simple fact that the forces of growth are less antagonised by gravity in the denser medium (cf. Houssay, La Forme et la Vie, 1900, p. 815). The effect of gravity on outward form is illustrated, for instance, by the contrast between the uniformly upward branching of a sea-weed and the drooping curves of a shrub or tree.
[37] The analogy is not a very strict one. We are not taking account, for instance, of a proportionate increase in thickness of the boiler-plates.
[38] Let L be the length, S the (wetted) surface, T the tonnage, D the displacement (or volume) of a ship; and let it cross the Atlantic at a speed V. Then, in comparing two ships, similarly constructed but of different magnitudes, we know that L = V2 , S = L2 = V4 , D = T = L3 = V6 ; also R (resistance) = S · V2 = V6 ; H (horse-power) = R · V = V7 ; and the coal (C) necessary for the voyage = H ⁄ V = V6 . That is to say, in ordinary engineering language, to increase the speed across the Atlantic by 1 per cent. the ship’s length must be increased 2 per cent., her tonnage or displacement 6 per cent., her coal-consumpt also 6 per cent., her horse-power, and therefore her boiler-capacity, 7 per cent. Her bunkers, accordingly, keep pace with the enlargement of the ship, but her boilers tend to increase out of proportion to the space available.
[39] This is the result arrived at by Helmholtz, Ueber ein Theorem geometrisch ähnliche Bewegungen flüssiger Körper betreffend, nebst Anwendung auf das Problem Luftballons zu lenken, Monatsber. Akad. Berlin, 1873, pp. 501–14. It was criticised and challenged (somewhat rashly) by K. Müllenhof, Die Grösse der Flugflächen, etc., Pflüger’s Archiv, XXXV, p. 407, XXXVI, p. 548, 1885.
[40] Cf. also Chabrier, Vol des Insectes, Mém. Mus. Hist. Nat. Paris, VI–VIII, 1820–22.
[41] Aerial Flight, vol. II (Aerodonetics), 1908, p. 150.
[42] By Lanchester, op. cit. p. 131.
[43] Cf. L’empire de l’air; ornithologie appliquée à l’aviation. 1881.