1874] Dr. H. Airy on Leaf -Arrangement. 305 



Supposing, then, that, by strokes of variation, forms have been pro- 

 duced with (2) 3, 4, 5, 6, &c. vertical leaf-ranks, it is next to be con- 

 sidered how the arrangement of the leaves in each form would be affected 

 by the demands of economy of space and mutual accommodation of ranks, 

 supposing the ranks to be similar in point of size and number of leaves. 



Two vertical ranks would gain lateral accommodation by taking 



alternate order -. Under vertical condensation, with twist in either 



direction, they would give rise to the successive orders of series A. (Two 

 ranks are found in uneconomical opposite order in the genus Mesembry- 

 anthemum. This arrangement would be prone to fall into crucial order 

 under vertical compression.) 



Three vertical ranks would, with least surrender of lateral accommo- 

 dation, assume alternate order = (illustrated by diagram). A slight twist 



in one direction (No. 3 towards No. 1) would allow perfect lateral 

 accommodation. In three-ranked plants (e. g. Carex and Alnus) such 

 twist is usually found. Vertical condensation operating on three ranks 

 possessing this obliquity would produce subsequent orders of series A. If 

 the obliquity were in the opposite direction (No. 3 towards No. 2), con- 

 densation would produce successive orders of series B. 



Four vertical ranks would economically fall into crucial order, the 

 members of each rank fitting into the intervals between those of its 

 neighbours. Opposite members therefore would stand at the same 

 height, and would occupy one and the same node ; they would also 

 divide the circumference equally, and would stand over the intervals of 

 the next lower pair. This crucial order under vertical condensation 

 would produce series a. In rare cases four ranks might assume an 



alternate order -. Vertical condensation of this order -, with twist 

 4 4 



(No. 4 towards No. 1) would produce series B ; with opposite twist 

 (No. 4 towards No. 3) it would produce series C. 



Five vertical ranks would, with least surrender of lateral accommoda- 

 tion, assume alternate order - . A slight obliquity (No. 5 towards No. 2), 



o 



such as is usually found in nature, would allow perfect lateral accom- 

 modation. Condensation would then produce further orders of series 

 A. With opposite- obliquity (No. 5 towards No. 3) a new series 



/-, -, ^, , &c.\ would be produced. Five ranks might also take 

 alternate order ? , which, condensed, would give with one twist series C, 

 with the other a new series -, ^, , ^-, &c. 



O D 11 17 



Six vertical ranks would economically fall into whorls of three, the 

 members of each whorl dividing the circumference equally, and standing 

 over the intervals of the next lower whorl. Condensation would give 



