II] THE PRINCIPLE OF SIMILITUDE 19 



excessively thick and strong, like a bull's, or very short like the 

 neck of an elephant. 



But it was Galileo who, wellnigh 300 years ago, had first laid 

 down this general principle which we now know by the name of the 

 principle of siniihtude ; and he did so with the utmost possible 

 clearness, and with a great wealth of illustration, drawn from 

 structures hving and dead*. He showed that neither can man 

 build a house nor can nature construct an animal beyond a certain 

 size, while retaining the same proportions and employing the 

 same materials as sufiiced in the case of a smaller structure f. 

 The thing will fall to pieces of its own weight unless we either 

 change its relative proportions, which will at length cause it to 

 become clumsy, monstrous and inefficient, or else we must find 

 a new material, harder and stronger than was used before. Both 

 processes are famihar to us in nature and in art, and practical 

 appUcations, undreamed of by Gahleo, meet us at every turn in 

 this modern age of steel. 



Again, as Gahleo was also careful to explain, besides the 

 questions of pure stress and strain, of the strength of muscles to 

 lift an increasing weight or of bones to resist its crushing stress, 

 we have the very important question of bending moments. This 

 question enters, more or less, into our whole range of problems ; 

 it afiects, as we shall afterwards see, or even determines the whole 

 form of the skeleton, and is very important in such a case as that 

 of a tall tree J. 



Here we have to determine the point at which the tree will 

 curve under its own weight, if it be ever so little displaced from 

 the perpendicular §. In such an investigation we have to make 



* Discorsi e Dimostrazioni majematiche, intorno a due nuove scienze. 

 attenenti alia Mecanica, ed ai Movimenti Local! : appresso gli Elzevirii, mdcxxxviii. 

 Opere, ed. Favaro, vni, p. 169 seq. Transl. by Henry Crew and A. de Salvio, 

 1914, p. 130, etc. See Nature, June 17, 191.5. 



t So Werner remarked that Michael Angelo and Bramanti could not have built 

 of gypsum at Paris on the scale they built of travertin in Rome. 



X Sir G. Greenhill, Determination of the greatest height to which a Tree of 

 given proportions can grow, Cambr. Phil. Soc. Pr. iv, p. 65, 1881, and Chree, 

 ibid. VII, 1892. Cf. Pojoiting and Thomson's Properties of Matter, 1907, p 99. 



§ In like manner the wheat-straw bends over under the weight of the loaded 

 ear, and the tip of the cat's tail bends over when held upright,— not because they 

 "possess flexibility," but because they outstrip the dimensions withm which stable 



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