20 ON MAGNITUDE [ch. 



some assumptions, — for instance, with regard to the trunk, that 

 it tapers uniformly, and with regard to the branches that their 

 sectional area varies according to some definite law, or (as Ruskin 

 assumed*) tends to be constant in any horizontal plane; and the 

 mathematical treatment is apt to be somewhat difficult. But 

 Greenhill has shewn that (on such assumptions as the above), 

 a certain British Columbian pine-tree, which yielded the Kew flag- 

 staff measuring 22f ft. in height with a diameter at the base of 



21 inches, could not possibly, by theory, have grown to more 

 than about 300 ft. It is very curious that Galileo suggested 

 precisely the same height {dugento braccia alta) as the utmost 

 limit of the growth of a tree. In general, as Greenhill shews, the 

 diameter of a homogeneous body must increase as the power 3/2 

 of the height, which accounts for the slender proportions of young 

 trees, compared with the stunted appearance of old and large 

 ones|. In short, as Goethe says in Wahrheit und Dichtung, "Es 

 ist dafiir gesorgt dass die Baume nicht in den Himmel wachsen." 

 But Eiffel's great tree of steel (1000 feet high) is built to a 

 very differeiit plan; for here the profile of the tower follows the 

 logarithmic curve, giving equal strength throughout, according 

 to a principle which we shall have occasion to discuss when we 

 come to treat of "form and mechanical efficiency" in connection 

 with the skeletons of animals. 



Among animals, we may see in a general way, without the help 

 of mathematics or of physics, that exaggerated bulk brings with 

 it a certain clumsiness, a certain inefiiciency, a new element of 

 risk and hazard, a vague preponderance of disadvantage. The 

 case was well put by Owen, in a passage which has an interest 

 of its own as a premonition (somewhat like De Candolle's) of the 

 "struggle for existence." Owen wrote as follows $: "In pro- 

 portion to the bulk of a species is the difficulty of the contest 

 which, as a living organised whole, the individual of such species 



equilibrium is possible in a vertical position. The kitten's tail, on the other hand, 

 stands up spiky and straight. 



* Modern Painters. 



t 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). 



X Trans. Zool. Soc. iv, 1850, p. 27. 



