7 8 RELATIONSHIPS OF SYMMETRY 



are the morphological ground-work upon which Schwendener has built up his 

 limitation-theory. 



It has been already stated that this contact is observed in the parastichies 

 but not as a rule in the orthostichies ; the three-ribbed species of Cacteae amongst 

 the Spermaphyta are however an exception to this 1 . In them the three ortho- 

 stichies are contact-lines whilst a lateral contact cannot be established even in 

 the very youngest primordia of the leaves. The formation of the ribs must in this 

 case have a definite influence upon the procedure at the apex, although they only 

 begin beneath the uppermost leaf-primordia. The absence of lateral contact has 

 only been certainly established for the three-ribbed forms; in the four-ribbed, 

 and still more in the five-ribbed, shoots of Cacteae the young primordia touch 

 each other in the lateral direction. Variations in the number of the ribs are 

 found not infrequently as is well known in the same shoot; a four-ribbed portion, 

 for example, may suddenly appear between three-ribbed ones, or a rib may cease 

 with a definite leaf-cushion. Changes of the leaf-position are of course associated 

 with such transitions, but the changes are not in these cases brought about by 

 mechanical causes they are relations of a morphological kind. From Vochting's 

 interesting investigations 2 we learn that the form of the shoots of the Cacteae is 

 in a very striking manner dependent upon the intensity of the illumination. 



Whilst in Spermaphyta, apart from the exceptions mentioned above, every 

 point of the apex has a like capacity to become the centre of a new group of 

 formations, we find in certain cryptogamous plants a definite relationship between the 

 position of the lateral shoots and the process of segmentation which takes place at 

 the apex. In the mosses, for example, it is well known that a leaf proceeds from 

 each segment that is cut off from the apical cell, but in the Pteridophyta on the 

 other hand a dependence upon cell-division of the apex is no longer visible. It is 

 easy to convince oneself that the spiral in which the segments in the apical cell of 

 the stem of a fern follow one another is by no means always directed in the same 

 way as the leaf-spiral; homodromy and heterodromy are about equally common. 

 Struthiopteris germanica furnishes an instructive example, for in it the apical cell is 

 two-sided whilst the leaves have a spiral arrangement with the divergence of the 

 chief series 3 . 



We have previously seen what displacements organs are subjected to in the 

 course of their development when the relationship of their size to the circumference 

 of the mother-organ is changed by its unequal growth in length and thickness, and 

 quite analogous changes of position must result if the relative size of the lateral 

 organs be changed from any other cause. If, for example, the lateral organs 

 gradually become smaller at a definite period of the development, say, at the 



1 Schwendener, Znr Kenntnis der Blattstellungen in gewundenen Zeilen, in Sitzungsber. d. Berliner 

 Akademie d. Wissensch., 1894, p. 974. 



3 Herm. Vochting, Uber die Bedeutung des Lichtes fiir die Gestaltung blattformiger Kakteen. 

 Zur Theorie der Blattstellungen, in Pringsh. Jahrb. xxvi (1894), p. 438. 



3 Schwendener, Uber Scheitelwnchstum und Blattstellung, in Sitzungsber. d. Berliner Akademie 

 d. Wissensch., 1885, p. 927. 



