26 ON MAGNITUDE [ch. 



sions. It follows at once that, if we build two bridges geometrically 

 similar, the larger is the weaker of the two*, and is so in the ratio 

 of their linear dimensions. It was elementary engineering experience 

 such as this that led Herbert Spencer to apply the principle of 

 simihtude to biologyf. 



But here, before w^e go further, let us take careful note that 

 increased weakness is no necessary concomitant of increasing size. 

 There are exceptions to the rule, in those exceptional cases where we 

 have to deal only with forces which vary merely with the area on 

 which they impinge. - If in a big and a httle ship two similar masts 

 carry two similar sails, the two sails will be similarly strained, and 

 equally stressed at homologous places, and alike suitable for resisting 

 the force of the same wind. Two similar umbrellas, however 

 differing in size, will serve ahke in the same weather; and the 

 expanse (though not the leverage) of a bird's wing may be enlarged 

 with little alteration. 



The principle of similitude had been admirably apphed in a few 

 clear instances by Lesage J, a celebrated eighteenth-century physician, 

 in an unfinished and unpublished work. Lesage argued, for example, 

 that the larger ratio of surface to mass in a small animal would lead 

 to excessive transpiration, were the skin as "porous" as our own; 

 and that we may thus account for the hardened or thickened skins 

 of insects and many other small terrestrial animals. Again, since 

 the weight of a fruit increases as the cube of its linear dimensions, 

 while the strength of the stalk increases as the square, it follows 

 that the stalk must needs grow out of apparent due proportion to 

 the fruit: or, alternatively, that tall trees should not bear large 



* The subject is treated from the engineer's point of view by Prof. James 

 Thomson, Comparison of similar structures as to elasticity, strength and stability, 

 Coll. Papers, 1912, pp. 361-372, and Trans. Inst. Engineers, Scotland, 1876; also 

 by Prof. A. Barr, ibid. 1899. See also Rayleigh, Nature, April 22, 1915; Sir G. 

 Greenhill, On mechanical similitude, Math. Gaz. March 1916, Coll. Works, vi, 

 p. 300. For a mathematical account, sec (e.g.) P. VV. Bridgeman, Dimensional 

 Analysis (2nd ed.), 1931, or F. W. Lanchester, The Theory of Dimensions, 1936. 



t Herbert Spencer, The form of the earth, etc., Phil. Mag. xxx, pp. 194-6, 

 1847; also Principles of Biology, pt. ii, p. 123 seq., 1864. 



I See Pierre Prevost, Notices de la vie et des ecrits de Lesage, 1805. George 

 Louis Lesage, born at Geneva in 1724, devoted sixty-three years of a life of eighty 

 to a mechanical theory of gravitation; see W. Thomson (Lord Kelvin), On the 

 ultramundane corpuscles of Lesage, Proc. E.S.E. vii, pp. 577-589, 1872; Phil. Mag. 

 XLV, pp. 321-345, 1873; and Clerk Maxwell, art. "Atom," Encyd. Brit. (9), p.' 46. 



