MATHEMATICS AND ENGINEERING IN NATURE 451 





•30^* X. vsf -*L 



cross-sections are subject to con- 

 stant specific stresses, are geometric- 

 ally defined by cubic parabolas. This 

 form results from the law of stresses 

 under the given conditions, and may 

 be seen in the contour of heavily 

 supporting bridge piers, the Eiffel 

 tower in Paris and numerous other 

 structures. Precisely the same prob- 

 lem nature has solved in building 

 the trunks of tall trees. The famous 

 coniferous trees of California (Fig. 

 1) offer the best illustration for 

 this principle. The reason for this 

 lies in the fact that the maximum 

 strength of the material used in one 

 and the same engineering structure, 

 or in a tree, being a known con- 

 stant, it is evidently of the great- 

 est economic advantage to make the 

 specific stresses throughout as uni- 

 form as possible. 



To resist great lateral bending 

 forces, or moments caused by strong 

 and irregular winds, the large trees 

 of the forest are equipped with 

 powerful wind-struts near the base 

 and extending to the anchoring roots 

 (Pigs. 2 and 3). The same thing 

 the architect does when he provides 

 for buttresses in Gothic buildings, 

 or when he reinforces the base of a 

 column to secure lateral stability. 

 The more the trees are exposed to 

 the winds, the larger the crown, the 

 more the principle of buttresses 



and pillars assumes its functions. Wherever winds from a certain 

 direction prevail, one notices plainly that in such a region the wind- 

 struts of the trees on the side opposite to the attack of the wind are 

 most strongly developed. In mountainous regions where on account of 

 the rough character of the surface, the winds are very turbulent and are 

 making their attacks in violent gusts from all directions, one may 

 observe wonderful and grotesque shapes of root-stocks. In a seemingly 

 almost impossible manner the roots crawl over each other, over rocks 



Fig. 1. 



