39 



tern presently brings into play a new alignment of thirty-four 

 vertical ranks, forming a pattern familiar to Californians in the 

 cones of Pinits Sahiniana and P. Jcffrcyi (cf. Chart, Zone V). 

 For a long time no further change was discovered beyond this 

 point. 



3. The appearance of fruit at this stage marks the attainment of 

 maturity, and since during this portion of the study no indication 

 of further change appeared, it was tentatively assumed that the 

 34-ranked pattern was final. Not until after the study was sup- 

 posedly complete and the paper was actually in the Editor's 

 hands, did the writer discover that in a few older trees the bend- 

 ing to one side of the thirteen ranks is carried beyond the point 

 at which the 34-ranked alignment becomes vertical, being con- 

 tinued in some instances until the 55-ranked scheme is passed, 

 and the 21-ranked scheme is reached. Whether this is or is not 

 the final scheme, cannot yet be afftrmed. Meantime it has not 

 been thought necessary to reconstruct the Chart or to discuss the 

 matter further here. 



II 



Thus in the phyllotaxy of this tree there are seen to be at least 

 five distinct phases, namely: three of well-known "regular" pat- 

 terns, while two different groupings of leaves showing none of 

 the recognized alignments occupy the intervals between them. 

 Leaf -development, however, is perfectly continuous throughout 

 the whole series ; nowhere is there node or break of any sort. 

 Each of the undescribed arrangements grows directly out of the 

 pattern below it, and grows directly into the pattern above it. 

 Obviously these are organic transformations. What is the essen- 

 tial factor in the process, and how does it work out these changes ? 



I. In all these patterns, regular and irregular alike, four ele- 

 ments are absolutely constant, namely: (a) The primary spiral 

 of growth; (b) its direction, left or right; (c) the axis about 

 which it coils; and (d) its division into equal parts by applying 

 to it a constant unit of measurement, namely, the circumferential 

 arc of 360 degrees, or one turn about the axis. The only other 



