242 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



more in accord with a mathematical conception of what the 

 relations of lateral members to one another should be. 



As previously noted, the orthogonal quality of the system, and 

 the possibility of representing primordia as either circles or the 

 homologues of circles, the two points assumed by Schwendener, 

 before postulating the disturbing agency, are just the two factors 

 for which a more rigid proof has been sought. It will thus be 

 seen that Schwendener's Dachstuhl theory can only apply to the 

 displacement of members after they have been formed, and such 

 apparent displacements are, no doubt, very general ; they may be 

 due to secondary bilateralify of the members, inequalities in the 

 rates of growth of different parts of the members, as well as to 

 different growth-relations between primordia and the axis. But 

 all these features are secondary, and require to be carefully 

 separated from the mode of initiation of the new impulses which 

 produce the growth-centres of new members before these become 

 visible. 



Such secondary relations of displacement, so far as they may 

 be due to contact-pressures, may be briefly considered from the 

 standpoints of : — 



I. The pressure of older members on younger ones as they are 



formed. 

 II. The reciprocal pressures of growing primordia against all 

 with which they come into contact. 



III. The effect of a rigid boundary on a growing system. 



So many entirely diverse phenomena have been included under 

 the heading Phyllotaxis, that some consideration of these secondary 

 relations of phyllotaxis systems is required in order to clear the 

 ground before the primary and essential features can be treated 

 without prejudice. To repeat the present standpoint, — Phyllotaxis 

 has to deal with the processes which determine the rhythmic 

 origin and regular arrangement of the primary lateral members 

 (appendages) of a plant-shoot in the first Zone of Growth; the 

 arrangement of primary members and secondary derivatives 

 (lateral axes) on the adult stem being merely the relic of such a 

 formation, which may have no obvious relation to the primary 

 system. The fact that secondary axillary shoots, or formations of 



