CHAPTER XI 



STUDIES ON PHYLLOTAXIS 



Perhaps no subject has fascinated BEIJERINCK more than the 

 problem of phyllotaxis, which was first attacked in the treatise of 

 1886 on root buds and adventitious roots. The publications of 

 BRAUN !), and of L. and A. BRAVAIS 2 ), and of SCHWENDENER 3 ) 

 on that subject were studied again and again during the years 1890 

 to 1900, and they led him to make various constructions and calcula- 

 tions. BEIJERINCK was no mathematician, and he was not able to 

 treat the problem along purely mathematical lines. It is remarkable, 

 however, that mathematics had a strong attraction for him. In 

 his library there was a series of mathematical works, which one 

 would never have expected of a biologist at that time. However, 

 he treated geometrical and even algebraical problems usually along 

 empirical lines, and attempted to find solutions by trial and measure- 

 ment. Naturally this led very often to serious errors, but with such 

 a man as BEIJERINCK even this method sometimes brought remarkable 

 results. 



BEIJERINCK'S interest in the problem of phyllotaxis was re- 

 awakened by the appearance of the wonderfully illustrated work of 

 A. H. CHURCH, containing many new ideas, entitled "On the Relation 

 of Phyllotaxis to Mechanical Laws" 4 ). Herein - - in contradistinction 

 to most of the earlier literature - - stress was laid on the arrangement 

 of the organs at the growing-point, and less significance was attached 

 to the mature state. BEIJERINCK also considered the mode of develop- 

 ment of the leaf-primordial pattern to be of the greatest importance 

 for the solution of the problem. 



CHURCH'S work led BEIJERINCK to put before his assistant VAN 

 ITERSON the case of three circles, whose diameters decrease in a con- 

 stant ratio, tangent to each other by pairs, with the problem of 

 discovering the conditions that a fourth circle could be constructed in 

 the space between those given, tangent to all three, and at the same 

 time smaller again than the third by the same ratio. BEIJERINCK ex- 



') A. BRAUX, Vcrgleichende Untersuchung iiber die Ordnung der Schuppen an 

 den Tannenzapfen als Einleitung zur Untersuchung der Blattstellung iiberhaupt, 

 I'.'-rliner Akademie der Wissensch. 16 Juli, 1830. 



2 ) L. et A. BRAVAIS, Essai sur la disposition des fcuilles curviseriees, Ann. scien- 

 ces nat. Bot., 2e ser. 7, 42-1 10, 1837. 



3 ) S. SCHWENDENER, Mechanische Theorie der Blattstellungen, Leipzig 1878. 



4 ) London 1904. 



