197 



same kind as those of Lilium Martagon. In thèse whorls there are 

 clearly three left-hand parastichies to be seen; the numbers of leaves 

 in them are too small to show the five right-hand parastichies, and 

 the two right-hand are neither very clear. 



But it is not be denied that even in those whorls a Fibonacci 

 phyllotaxis with left-hand spiral is incorporated. 



At the end of the stem, there was a terminal compound umbel, 

 with 22 little umbels. Thèse could ail be numbered very regularly 

 according to the same normal spiral. Only 13 of them, 35 — 47, 

 arose from the axils of small bracts; the innermost 9 had no bracts 

 at ail. By the smalness of the top of the main axis it was not possible 

 to render this part of the shoot in the figure at the same scale as the 

 rest; the internode under the termmal umbel, which had a peri- 

 phery of only about 6 mm was represented m the origmal figure 

 with the same periphery of 14 mm as the lower parts; the position 

 of the small umbels was partly plotted by construction. The 

 bracts of the umbels are only indicated by small vertical lines. 



This shoot shows us, that the whorls of bracts of Ferida thyrsù 

 flora may arise in the same way as those of Lilium Martagon as 

 growth whorls. The existence of a true normal Fibonacci spiral 

 is clearly established by the regular arrangement of the umbels 

 in the terminal compound umbel; the whorls themselves show 

 three left-hand parastichies, so that there can be no doubt in that 

 respect. 



The four other shoots of the same plant I examined, showed generally similar 

 conditions. Two of them had quite regular terminal compound umbels, as the one 

 described, the position of the leaves and the bracts on the shoot was much of the 

 same order as in the previous spécimen, only still more regular in so far that they 

 did not exhibit any , .négative" internode of the stem. The fourth and the fifth shoot 

 were somewhat less regularly built. 



The terminal compound umbel of the fourth was composed of 17 rays, which 

 were not quite regular in position and development. They might be numbered as 

 34—52 but the numbers 50 and 51 were absent; another anomaly was that 41 was 

 only developed as a single flower, not as an umbel, while 49 which was placed be- 

 hind 41 was an umbel again. The leaves and bracts on the shoot showed also more 

 déviations from the regular position, as they had several , .négative" internodes, 

 one of them of 65 mm length. The fifth spécimen was the most irregular; the „nega- 



