CONSTANT PHYLLOTAXIS. 93 



In the same way, the third member falls into the largest gap 

 between members 1 and 2, but asymmetrically, being on the side 

 of the gap farthest from the last formed member. Hofmeister's 

 law, which is clearly a simple way of expressing what is observed 

 in such a series of diagrams, may be thus enlarged by adding the 

 point that the new member falls asymmetrically into the next 

 largest gap. 



The fourth member establishes lateral contact with No. 1, and 

 thus initiates the first contact-parastichy — the long curve of the 

 system, while the sixth member similarly commences the first 

 short curve parastichy, the system being (3 + 5); the parastichies 

 thus appear as subjective spirals joining the centres of members 

 in orthogonal contact (fig. 37, 9). 



The subjective spiral joining the centre of successive members 

 becomes the ontogenetic spiral (fig. 37, 7) ; but the growth move- 

 ment is equally clearly defined as an oscillation across the apex of 

 the stem at an approximately constant angle (fig. 37, 8). 



The ninth member falling -on a new log. spiral line passing 

 through No. 1, gives the so-called " orthostichy " line of Schimper. 



Of these spirals, then, the genetic spiral is of interest solely that 

 it marks the ontogenetic path of construction ; the contact- 

 parastichy spirals are, however, structural and map out the system, 

 in that they may be regarded as representing lines of equal and 

 asymmetric distribution of growth-energy in the protoplasm of the 

 apex. These are not necessarily the cause of the appearances, hut 

 rather both phenomena are equally expressions of the fact that growth 

 is asymmetrical, and therefore represented by the geometrical con- 

 struction of a spiral-vortex. 



Uniform and Vaeying-geowth Phenomena. 



It would so far appear that the inherent property of protoplasm, 

 which determines the phyllotaxis of lateral members, thus reduces 

 to the fact that in every shoot the bulk-ratio of the lateral 

 primordia, or rather the ratio of the distance between two initial 

 points to the diameter of the axis, may be a constant, and definite 

 for each shoot, though less definite as a specific constant. Of such 



