176 COMPENDIUM OF GENERAL BOTANY. 



His explanation of the phenomenon shall soon claim our attention. 

 We, from our point of view, deduce from it that the finding of 

 mechanical-causal relations does not imply that all idealistic con- 

 ceptions of nature are thereby destroyed, but rather that it assists in 

 exposing and making clear the great simple ideas. Schwendener 

 has rightly named his theory of phyllotaxy the accessory theory 

 ( i; Anschlusstheorie"). It is always necessary to assume a basis, 

 or, so to speak, a frame, upon which or within which the arrange- 

 ment of contiguous and variously superimposed organs, such as leaves 

 and branches, must take place. This assumed basis for monocotyle- 

 dons is the two-ranked arrangement of the single cotyledon and the 

 succeeding leaves. See the copy of Scbwendener's figure (Fig. 104). 



In dicotyledons this "given " basis is the crossed position of the 

 opposite leaf-pairs, an arrangement initiated by the two cotyledons. 

 While the normal spiral of monocotyledons may be produced by 

 other means than the acropetal decrease in size of the foliar begin- 

 nings, that is, by slow displacement due to longitudinal pressure, it 

 is evident that such pressure, producing displacement of equally 

 large organs in dicotyledons, would only convert the opposite whorl 

 into a twisted whorl. But if one member of the leaf-pair is smaller, 

 or if other irregularities appear in the crossing of the pairs, the 

 above normal series 1, 2, 3, 5, 8, etc., will of necessity be devel- 

 oped provided there is a gradual decrease in the size of the organs 

 in an acropetal direction. 



According to Schwendener's explanation, it is again the given 

 basis of the system, as well as the deviations from absolute regu- 

 larity which necessarily work together to produce the spiral ar- 

 rangement of organs in the dicotyledons. 



Schwendener also studied coniferous seedlings which begin with 

 a whorl of 3-8 cotyledons, and established the remarkable fact that, 

 in spite of the unequal initial position of organs and irregular addi- 

 tions of subsequent organs, the final result is nearly always a normal 

 spiral. These small deviations mentioned above, which are of 

 normal occurrence, are the essential mechanical factors in the ar- 

 rangement of lateral organs. TEITZ, a pupil of Sch wendener, carried 

 on a series of experiments which seemed to prove that longitudinal 

 tensions proceeding from the vascular system of leaves and ex- 

 tending along the connected bundles of the stem determine the 

 position of lateral organs. The causes leading to the position of 

 leaves mav therefore be stated as follows : The given 'basis of the 



