144 THE CAUSES OF SPECIFIC SHAPE 



meristematic in a plaster-cast, but the tissue-differentiation progresses closer to the 

 apex, and with it the appearance of secondary roots 1 . 



The production of a locality for their development forms one of the conditions 

 for the formation of lateral appendages, which, however, only appear when the 

 required tendency to such formation exists. These determinants normally succes- 

 sively reappear as the growing apex elongates, but this is not always the case, as 

 is shown by the absence of lateral roots from some main roots, and by the non- 

 formation of leaves on stem-tendrils. The plant is able to automatically regulate 

 the frequency with which the conditions for the development of a lateral appendage 

 are repeated, and thus determines whether they shall appear close together as in 

 the case of leaves, or far apart as in roots. 



The mode of development of the cotyledons shows that leaves occupying 

 definite positions may be formed without being preceded by special primordia. 

 Hence when leaf-primordia are close together we have only to consider how far their 

 natural tendency to occupy particular positions may be modified by their immediate 

 relationship to one another, and by their interactions during the subsequent course 

 of development. The problems of phyllotaxis fall, however, more within the province 

 of morphology, and the various works based upon Schwendener's theory of phyllo- 

 taxis are at variance on the essential point as to whether the primordia are in 

 contact at the moment of their formation or not 2 . Schwendener's theory is in 

 fact really based upon the consideration of the adult structure, and the embryonic 

 phyllotaxis is considered as representing the adult one so long as no secondary 

 modifications are produced by torsion and displacement during development, or 

 by the diminution in size of the successive lateral axes. Such discussions can, 

 of course, never reveal the inherent causes which determine the embryonic phyllo- 

 taxis, or the laws which regulate the latter. 



Young primordia are easily deformed by pressure 3 , and in addition differences 

 of pressure may exercise pronounced stimulatory effects, as is shown by the effect 

 of trifling differences of pressure in determining at which end of a segment of 

 a branch callus shall develop. On the other hand a primordium may be formed 

 against considerable external pressure, and Hofmeister 3 long ago concluded that 

 the productive activity of the apex of the stem could be but little influenced 

 by the pressure existing in the bud. 



1 Pfeffer, Druck- u. Arbeitsleistungen, 1893, p. 335. 



2 S. Schwendener, Mechan. Theorie d. Blattstellungen, 1878; Sitzungsb. d. Berlin. Akad., 

 1894, p. 979; 1895, p. 465; 1899, p. 50 ; 1900, p. 1042 ; Vochting, Jahrb. f. wiss. Bot., 1898, Bd. 

 XXXI, p. 454; A. Weisse, Jahrb. f. wiss. Bot., 1897, Bd. XXXI, p. 456 and in Goebel, Organography, 

 1900, I, p. 77; K. Schumann, Morphol. Studien, 1899, p. 311; L. Jost, Bot. Ztg., 1899, P- J 93 > 

 W. Arnold!, Flora, 1900, p. 440; Winkler, Jahrb. f. wiss. Bot., 1901, Bd. xxxvi, p. i. [Church 

 (The Relation of Phyllotaxis to Mechanical Laws, Pts. l-iv, 1901-2) has pointed out that in 

 many cases the supposed necessity for torsion, pressure, and displacement to explain phyllotaxis 

 arrangement simply arises from a miscomprehension of the mathematics of the subject, which is, 

 however, hardly yet ripe for purely mathematical treatment. The primordial papillae of the 

 leaves on fern rhizomes and of other plants also are certainly not in contact, and the statement 

 that the actual boundaries of the primordia may extend beyond the visible papilla is simply an 

 improbable assumption made to bolster up a doubtful fact.] 



3 Hofmeister, Allgem. Morphol., 1868, p. 639. 





