ORGANS AND SYSTEMS OF GROANS. 175 



O. THE MECHANICAL THEORY OF PHYLLOTAXY AND THE IDEALISTIC 

 CONCEPTION OF NATURE. 



Because of the important bearing of this subject upon the true 

 idealistic and the so-called mechanical conception of nature I can- 

 not refrain from commenting upon SCHWENDENER'S theory of phyl- 

 lotaxy. By idealistic I do not mean anything fantastic and 

 dreamy, but rather that clear and definite conception of the laws of 

 nature as given by the Creator, and of matter as created by him ; 

 furthermore, that causality does not cease where causal-mechanics 

 fail ; that, moreover, the usual tendency of natural history or science 

 to indicate this or that as something "given " points to the imma- 

 terial Giver as the highest Being and the CREATOR of all. It would 

 be wrong to suppose that SCHWENDENER'S mechanical theory of 

 phyllotaxy had, so to speak, destroyed the very foundation of the 

 idealistic conception of phyllotaxy. Schwendener's mechanical 

 principle of causality is far from satisfactory. The thoughtful in- 

 vestigator would naturally expect that the mechanical theory would 

 trace complicated phenomena to simpler causes w r hich must then be 

 considered as granted or given. 



The question why certain divergences occur most frequently was 

 considered of great importance by the opponents of Schwendener's 

 new theory. This question was proposed by C. DE CANDOLLE in 

 the year 1881. The divergence fractions ^, J, -|, f, y 5 , etc., ex- 

 pressed in degrees approach the limiting value 137 28' 30", 

 which is the ratio of the golden section (sectio aurea) to the circum- 

 ference of a circle. This is only true of the normal series; other 

 series have different limiting values. The principal reason why the 

 earlier advocates of the idealistic theory (C. SCHIMPER and A. BRAUN) 

 failed to substantiate their doctrine was because these authors treated 

 the organs under consideration as mathematical points, and not as 

 bodies in actual contact. To them the fractions of divergence con- 

 stituted the part " given," while to us they are simply the necessary 

 mechanical results of certain given relations. Although we reject 

 the spiral theory of Schimper and Braun, we must not allow " num- 

 ber mysteries" to carry us too far, as they evidently did Schwen- 

 dener, at least in his leading work (1878). In 1883 * this author 

 undertook the consideration of the question proposed by de Candolle. 



Sitzungsbericbte der Berl. Akademie. 



