18 ON MAGNITUDE [ch. 



This effect of scale is simply due to the fact that, of the physical 

 forces, some act either directly at the surface of a body, or other- 

 wise in proportion to the area of surface; and others, such as 

 gravity, act on all particles, internal and external ahke, and exert 

 a force which is proportional to the mass, and so usually to the 

 volume, of the body. 



The strength of an iron girder obviously varies with the 

 cross-section of its members, and each cross-section varies as the 

 square of a linear dimension ; but the weight of the whole structure 

 varies as the cube of its linear dimensions. And it follows at once 

 that, if we build two bridges geometrically similar, the larger is 

 the weaker of the two *. It was elementary engineering experience 

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

 simihtude to biology. 



The same principle had been admirably applied, in a few clear 

 instances, by LesageJ, a celebrated eighteenth century physician 

 of Geneva, in an unfinished and unpublished work§. Lesage 

 argued, for mstance, that the larger ratio of surface to mass would 

 lead in a small animal to excessive transpiration, were the skin 

 as "porous" as our own; and that we may hence account for 

 the hardened or thickened skins of insects and other small terrestrial 

 animals. Again, since the weight of a fruit increases as the cube 

 of its dimensions, while the strength of the stalk increases as the 

 square, it follows that the stalk should grow out of apparent due 

 proportion to the fruit; or alternatively, that tall trees should 

 not bear large fruit on slender branches, and that melons and 

 pumpkins must lie upon the ground. And again, that in quad- 

 rupeds a large head must be supported on a neck which is either 



* The subject is treated from an engineering j^oint of view by Prof. James 

 Thomson, Comparisons of Similar Structures as to Elasticity, Strength, and 

 StabUity, Trans. Inst. Engineers, Scotland, 1876 {Collected Papers, 1912, pp. 361- 

 372), and by Prof. A. Barr, ibid. 1899; see also Rayleigh, Nattire, April 22, 1915. 



t Cf. Spencer, The Form of the Earth, etc., Phil. Mag. xxx, pp. 194-6, 

 1847; also Principles of Biology, pt. n, ch. i, 1864 (p. 123, etc.). 



% George Louis Lesage (1724-1803), well known as the author of one of the few 

 attempts to explam gravitation. (Cf. Leray, Constitution de la Matiere, 1869; 

 Kelvin, Proc. R. S. E. vn, p. 577, 1872, etc. ; Clerk Maxwell, Phil. Trans, vol. 157, 

 p. 50, 1867; art. "Atom," Emycl. Brit. 1875, p. 46.) 



§ Cf. Pierre Prevost, Noticts de la vie et des ecrits de Lesage, 1805; quoted by 

 Janet, Causes Finales, app. in. 



