46 JOURNAL OF THE ROYAL HORTICULTURAL SOCIETY. 



Black Briony, and Asparagus are both provided with it. Several grasses 

 appear to have such a rudiment.* 



Changes from the tricussate arrangement, i.e. decussating whorls of 

 threes, into the f divergence of the secondary series were frequent. It 

 takes place in the following manner : The first step is to cause the 

 three leaves of the different whorls to separate slightly by a development 

 of their internodes. Then, if any two consecutive whorls be examined, 

 the order of succession of the six leaves (No. 1 being the lowest) is 

 thus : — 



6 



3 2 

 7 9 

 4 8 5 

 1 



Fig. 4. 



In which it will be noticed that the fourth leaf, instead of being over 

 the interval between the first and second, is over that between the third 

 and first, so that the angle between the first and second leaf, or between 

 the second and third, is double that between the third anfl fourth. These 

 latter, it will be remembered, are separated by a long internode. The 

 same order obtains with the succeeding whorls ; the nodes, however, are 

 now much more widely separated, while a true spiral arrangement, with 

 the same angular distance between all its leaves, is ultimately secured, 

 and is henceforth continued uninterruptedly into the terminal bud, and 

 represented by the fraction f. 



The method by which this is secured is much the same as for the 4f 

 from opposite and decussate leaves, for in order to reduce the angle between 

 1 and 2 from 120° to 103° (nearly), and to enlarge the angle between 

 3 and 4 from 60° to 103°, Nos. 1 and 3 approach No. 2, Nos. 4 and 6 

 approach No. 5, and Nos. 7 and 9 approach No. 8. By this means the 

 larger angles are reduced and the smaller, i.e. between Nos. 3 and 4, 6 and 

 7, 8, and 9, are increased till they all reach 103°. 



From very many observations on stems of the Jerusalem Artichoke, it 

 appears that to resolve opposite and decussate leaves into spirals of the 

 primary series and tricussate verticils into those of the secondary series 

 is more easily accomplished than any other kinds of transition. To reverse 

 the process, or to bring back spirals into verticils, seems quite contrary 

 to all nature's tendencies to change, except in flowers. Stems of the 

 Jerusalem Artichoke occasionally had their leaves arranged spirally below, 

 and verticillate above ; but then the change was abrupt. The spiral 

 suddenly terminated, and the last leaf was succeeded by three in a whorl. 

 The extra third leaf is often " thrown out," as it were, as a supernumerary 

 member. 



Leaf arrangements are usually pretty constant to any species ; but 

 this is not absolutely so ; because plants have the power to change it if it 

 be desirable to secure light in different ways. Thus the common laurel, 



* For further particulars the reader is referred to my paper on " A Theoretical 

 Origin of Fndogens from Exogens through Self- Adaptation to an Aquatic Habit " 

 (Journ. Linn. Soc. vol. xxix. p. 485). 



