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STOUT & Boas: STATISTICAL STUDIES IN CICHORIUM 343 
stellung der Blätter.” He is evidently led to this view chiefly 
by his observation that partial variability is strongly in evidence. 
Also in summarizing the statistical work done in the Compositae, 
he (711) finds that only about 85 per cent. of the species exhibit 
maxima that fall on main and duplica numbers of the Fibonacci 
series. 
Vogler's (708, 700, то, 711) original studies оп Umbelliferae 
and Compositae bear directly on the question of maxima and 
their occurrence according to the law of Fibonacci. His study of 
the umbellifer Astrantia major L. (708) is of special interest, for 
here he finds the maxima for the number of bracts, perfect flowers, 
and male flowers to be lower for lateral umbels than for those on 
the main stem. In all cases the variability was less for the parts 
of the lateral umbels than for the main umbels. His conclusion 
is that the maxima for the parts of the umbels of the main stem 
follow in general the series of Fibonacci, while those of the lateral 
stems follow another and quite different series, the Trientalis. 
Vogler also reports data on the number of ray-flowers in 31,000 
heads of Senecio alpinus ('o9, 710) collected at different localities 
and at different times of the year. For these the number ranges 
from то to 28 with a maximum at I9, which, as he points out, is 
not one of the primary or secondary numbers of the Fibonacci 
series, 
In the case of two plants of Boltonia latisquama, Vogler ( "00, 
710) studied the production of flowers in successive years. For 
three successive years 500 flower heads were counted on each. 
Although the weather conditions were different in the three years 
each plant was quite constant in respect to ray-flower number 
during the three years of observation. 
Furthermore, Vogler (’10) undertook in Arnica montana and 
Eupatorium album to determine various facts of partial variability, 
especially the relation of position of heads to variation in the 
number of ray-flowers. In counts made on ray-flowers of Arnica 
montana іп 1909 and тото, he separated data for terminals and 
laterals. In both years the terminals gave a higher average ray- 
flower number than the laterals. In 1909, 266 terminals averaged 
14.7, while 153 laterals averaged only 11.6. In 1910 (counts were 
made in a different locality from that of 1909), 314 terminals 
