310 Variation in Chrysanthemum leucanthemum 
Of the two localities, one is a field of about five acres' area, lying upon a hillside which 
sloi^es southward towards the Little Miami River. This place, — one mile south of the Yellow 
Springs, and one hundred and fifty yards east of the Little Miami R.R., — is uniformly 
but not thickly covered by the plants. The second locality is one half mile west of Antioch 
College, where a few j^lants grow in some glacial gravels. 
My material all came fi'om the first locality, there being too few heads of flowers at the 
second to be of use. In collecting the specimens, lots were obtained on July 5 and July 30, and 
only fresh, fully blossomed heads were counted. All that were injured, wilted, or had begun to 
go to seed were rejected, since many, if not all such individuals, had lost a greater or less 
number of rays. In gathering the material I walked at random across the field, picking the 
heads in the most mechanical manner possible, and then rejecting those that were too old or 
that had been injured. The two lots collected gave quite different results as regards the 
number of ray flowers in the heads, and had one lot only been taken it would have been almost 
certain to have forced the conclusion that the species had changed in this locality from the 
ancestral condition of Europe. 
Lot No. 1. Collected July 5, 1901. 
The rays in 284 heads were coiuited and were found to vary in number from 16 to 39. The 
polygon of distribution (Fig. 1) shows two strongly developed modes, on 22 — 25, and on 33, each 
surrounded by a considerable body of variates and with a deep sinus between the two modes. 
The mean of the lot was 27'87 rays, or 3-25 above the mean for lots one and two combined, 
which is the mean for the season. The modes of this lot do not fall upon those numbers which 
were found by Ludwig to be the modes of this species in Germany. The modes of my lot 
22 — 25, and 33, have no relation to the series of Fibonacci, 8, 13, 21, 34, which are the modes 
in Europe. The difference between my results and Ludwig's as well as the discrepancy of 
Lucas's (1898) results do not indicate a change of modal condition in America but are due to an 
entirely diflerent cause. This cause I shall briefly discuss in the latter part of this paper. 
At the time this first lot was collected a considerable number of the heads had already passed 
their prime and begun to lose their ray flowers. These were rejected from the material used. 
Counts of some of this rejected material showed that all of the heads had a large number of rays 
and that they would have fallen in the group about the mode on 33. It is quite possible that 
had I made a collection of material a few days earlier, the specimens I was forced to reject, 
being then in their prime, would have fallen about 34 as a mode, thus conforming with Ludwig's 
results. 
In the variates which are grouped about the lower mode 22 — 25, there is an evident skewness 
toward a lower number of rays, and there is no clearly defined modal number. This condition 
is associated with the time in the blossoming period when the material was taken. 
Lot No. 2. Collected July 30, 1901. 
The second lot of material, although from the same field as the first, and taken both in the 
same mechanical way and with the same precautions, showed, when the rays were counted, a 
condition that was decidedly different from that of the earlier material. In 168 heads the rays 
varied in number from 12 to 34, with modes on 13 and 21 (Polygon, Fig. 2). The mode on 33 
(34) rays found in the first lot (Fig. 1) disappeared in the second ; the lower mode on 22 — 25 
was replaced by a strong one on 21 and a new mode on 13 appeared. The mean of this second 
lot was 21 '38 or 3'26 below the mean for the generation. 
