[620] Das mechanische Prinzip. im anatomischen Bau der Monocotylen, Leipzig, 1874.

[621] For further botanical illustrations, see (int. al.) Hegler, Einfluss der Zugkraften auf die Festigkeit und die Ausbildung mechanischer Gewebe in Pflanzen, SB. sächs. Ges. d. Wiss. p. 638, 1891; Kny, L., Einfluss von Zug und Druck auf die Richtung der Scheidewande in sich teilenden Pflanzenzellen, Ber. d. bot. Gesellsch. XIV, 1896; Sachs, Mechanomorphose und Phylogenie, Flora, LXXVIII, 1894; cf. also Pflüger, Einwirkung der Schwerkraft, etc., über die Richtung der Zelltheilung, Archiv, XXXIV, 1884.

[622] Among other works on the mechanical construction of bone see: Bourgery, Traité de l’anatomie (I. Ostéologie), 1832 (with admirable illustrations of trabecular structure); Fick, L., Die Ursachen der Knochenformen, Göttingen, 1857; Meyer, H., Die Architektur der Spongiosa, Archiv f. Anat. und Physiol. XLVII, pp. 615–628, 1867; Statik u. Mechanik des menschlichen Knochengerüstes, Leipzig, 1873; Wolff, J., Die innere Architektur der Knochen, Arch. f. Anat, und Phys. L, 1870; Das Gesetz der Transformation bei Knochen, 1892; von Ebner, V., Der feinere Bau der Knochensubstanz, Wiener Bericht, LXXII, 1875; Rauber, Anton, Elastizität und Festigkeit der Knochen, Leipzig, 1876; O. Meserer, Elast, u. Festigk. d. menschlichen Knochen, Stuttgart, 1880; MacAlister, Sir Donald, How a Bone is Built, English Illustr. Mag. pp. 640–649, 1884; Rasumowsky, Architektonik des Fussskelets, Int. Monatsschr. f. Anat. p. 197, 1889; Zschokke, Weitere Unters. über das Verhältniss der Knochenbildung zur Statik und Mechanik des Vertebratenskelets, Zürich, 1892; Roux, W., Ges. Abhandlungen über Entwicklungsmechanik der Organismen, Bd. I, Funktionelle Anpassung, Leipzig, 1895; Triepel, H., Die Stossfestigkeit der Knochen, Arch. f. Anat. u. Phys. 1900; Gebhardt, Funktionell wichtige Anordnungsweisen der feineren und gröberen Bauelemente des Wirbelthierknochens, etc., Arch. f. Entw. Mech. 1900–1910; Kirchner. A., Architektur der Metatarsalien, A. f. E. M. XXIV, 1907; Triepel, Herm., Die trajectorielle Structuren (in Einf. in die Physikalische Anatomie, 1908); Dixon, A. F., Architecture of the Cancellous Tissue forming the Upper End of the Femur, Journ. of Anat. and Phys. (3) XLIV, pp. 223–230, 1910.

[623] Sédillot, De l’influence des fonctions sur la structure et la forme des organes; C. R. LIX, p. 539, 1864; cf. LX, p. 97, 1865, LXVIII. p. 1444. 1869.

[624] E.g. (1) the head, nodding backwards and forwards on a fulcrum, represented by the atlas vertebra, lying between the weight and the power; (2) the foot, raising on tip-toe the weight of the body against the fulcrum of the ground, where the weight is between the fulcrum and the power, the latter being represented by the tendo Achillis; (3) the arm, lifting a weight in the hand, with the power (i.e. the biceps muscle) between the fulcrum and the weight. (The second case, by the way, has been much disputed; cf. Haycraft in Schäfer’s Textbook of Physiology, p. 251, 1900.)

[625] Our problem is analogous to Dr Thomas Young’s problem of the best disposition of the timbers in a wooden ship (Phil. Trans. 1814, p. 303). He was not long of finding that the forces which may act upon the fabric are very numerous and very variable, and that the best mode of resisting them, or best structural arrangement for ultimate strength, becomes an immensely complicated problem.

[626] In like manner, Clerk Maxwell could not help employing the term “skeleton” in defining the math­e­mat­i­cal conception of a “frame,” constituted by points and their interconnecting lines: in studying the equi­lib­rium of which, we consider its different points as mutually acting on each other with forces whose directions are those of the lines joining each pair of points. Hence (says Maxwell), “in order to exhibit the mechanical action of the frame in the most elementary manner, we may draw it as a skeleton, in which the different points are joined by straight lines, and we may indicate by numbers attached to these lines the tensions or compressions in the cor­re­spon­ding pieces of the frame” (Trans. R. S. E. XXVI, p. 1, 1870). It follows that the diagram so constructed represents a “diagram of forces,” in this limited sense that it is geometrical as regards the position and direction of the forces, but arithmetical as regards their magnitude. It is to just such a diagram that the animal’s skeleton tends to ap­prox­i­mate.

[627] When the jockey crouches over the neck of his race-horse, and when Tod Sloan introduced the “American seat,” the object in both cases is to relieve the hind-legs of weight, and so leave them free for the work of propulsion. Nevertheless, we must not exaggerate the share taken by the hind-limbs in this latter duty; cf. Stillman, The Horse in Motion, p. 69, 1882.

[628] This and the following diagrams are borrowed and adapted from Professor Fidler’s Bridge Construction.

[629] The method of constructing reciprocal diagrams, in which one should represent the outlines of a frame, and the other the system of forces necessary to keep it in equi­lib­rium, was first indicated in Culmann’s Graphische Statik; it was greatly developed soon afterwards by Macquorn Rankine (Phil. Mag. Feb. 1864, and Applied Mechanics, passim), to whom is mainly due the general application of the principle to engineering practice.