MATHEMATICS AND ENGINEERING IN NATURE 453 



necessary in the construction of a high tower. The base of the whole 

 structure is subject to the pressure of the entire load above, and must 

 be able to resist it by compressive strength. Horizontally inserted 

 beams, carrying loads, must have strength to resist bending. There 

 are, furthermore, forces of gravity and all kinds of strains, caused by 

 shearing and torsional forces, which must be accounted for. Consider- 

 ing the fact that in the growth of a rye-plant nature provides completely 

 for the resistance against this complicated system of stresses, and com- 



Fig. 3. 



paring this kind of engineering with corresponding human efforts, then 

 even the famous and much admired Eiffel tower appears as a relatively 

 large and clumsy structure. 



According to France,* a rye stalk has an average height of 1,500 

 millimeters and a diameter of 3 mm. at the base. This, transformed to 

 the proportions of architecture, means that nature has here established 

 a structure which in comparison is 33 times the height of one of the 

 towers of the Cathedral of Cologne. Imagine now that at the top of 

 such a colossal tower a proportionally large and heavy ear of rye be 

 pendling, and we get an idea of the amount of compressive, tensile and 

 bending strength a plant-stalk may acquire. We become aware that the 

 plant, with extreme perfection, applies the same principles with which 

 the engineer is working. One discovers relations which the engineer 

 finds in studying moments of inertia, bending moments, etc., in beams, 

 girders, columns, and all kinds of trusses. Thus the plant produces 

 extremely complex structural phenomena, which, from the standpoint 

 of the engineer, reveal a masterful knowledge of the laws of mechanics 

 and the consequent economy of materials. The same statement applies 

 to the physiological problems of zoology. 



4 " Illustrierte Zeitung," 1909. 



