40 



element in the whole system is the leaf-interval, or rather the 

 interf oliar arc ; for it is not a linear dimension measurable on the 

 surface, but an arc measured by the angle at the center. This arc 

 thus becomes a second unit of measurement applied to the pri- 

 mary spiral along with the other. When these two arcs are com- 

 mensurable, by virtue of their coincidence at regular intervals, 

 they gradually build up those systems of vertical ranks by which 

 we recognize the "regular" patterns. Each of these has its 

 own dimensions of arc. and only so long as the dimension remains 

 constant is the pattern identifiable. 



2. Our transition zones then are areas in which gradual change 

 in the interfoliar arc operates to rearrange one of the regular pat- 

 terns, building up out of it the transitional formation, and out of 

 that again the next regular pattern of the series. What at first 

 seemed to be mere disorder and confusion, turns out to be a 

 marvel of order and symmetry when once its method and struc- 

 ture are understood. 



3. Let us assume that the primary spiral is a right-hand one 

 like that in the chart. Any increase of the leaf-interval will set 

 each successive leaf a little beyond — i.e., to the right of — the 

 place where it would otherwise have been. If the increase con- 

 tinues, it will presently cause the vertical ranks of the pattern 

 to swerve visibly to the right — toward the direction of the pri- 

 mary spiral. On the other hand, any diminution of the interval 

 will set each successive leaf a little behind — to the left — of what 

 would otherwise have been its place ; and the vertical ranks will 

 then swerve to the left, or away from the primary spiral. In 

 either case all the other alignments of the pattern will be simi- 

 larly affected, though in less degree the further they are removed 

 from verticality. The whole pattern thus undergoes a sort of 

 rotation to right or to left as the case may be; and this, if con- 

 tinued, will gradually swing into verticality some one or other of 

 the ranks which were secondary spirals of the original pattern. 

 Whenever the predestined secondary rank thus becomes vertical, 

 further change in the leaf-interval is brought to an end as we 

 have seen, and the transformation is complete. The whole proc- 



