W. L. Tower 
311 
The Modal condition of the rays at Yellow Sjjrings, 0. 
To obtain the modes about which the number of rays tend to gather in this locality, the two 
lots of variates must be combined, since neither lot 1 nor 2 represents the whole condition as 
regards variation in the rays for the generation from which the lots were taken. When the 
two lots are combined into one polygon of distribution, there are represented in it variates from 
the early, middle and late parts of the generation, and it shows fairly well the entire generation 
for 1901. In this polygon (Fig. 3) 452 variates, with a range from 1.3 to 39, are found grouped 
about three modes 13, 21, 33, with the mode on 21 strongest, 33 next, and 13 last. This 
corresponds closely with Ludwig's results, difiering only in that the highest mode in my counts 
falls upon 33 instead of 34 rays. The reason for this ajiparent shifting of the mode 34 I have 
called attention to in the account of Lot No. 1. The mean for the generation is 24'62.5. 
In studying the variations of the rays, florets and bracts of Asters, ShuU (1902) found that 
those heads which blossomed first had a prevailingly larger number of parts than those which 
appeared later in the season. The polygons of distribution for the heads were found t(5 be 
multimodal in every species studied, and these modes were correlated with the time in the 
season when the heads appeared. Material taken early in the season gave modes on high 
numbers with almost no variates in the lower part of the range; material taken in the middle 
of the season gave modes on the mid-range numbers with variates over the entire range ; and 
material taken at the end of the season gave modes upon the lower numbers with a range 
limited to the lower and middle numbers. Material taken at only one time would not in this 
case have given data of any value. In C. leucantheimnn L. the heads which blossom first have a 
prevailingly larger number of parts than those which follow later in the season. The observa- 
tions of Shull (1902) upon specific plants of Asters and my own upon C. leucanthenium, where 
every flower that appeared during the growing season upon marked plants was studied, show 
that in individual plants there is no tendency to ha\'e even a majority of the heads in one 
modal group, but in every plant the heads are distributed over the entire range of variation 
observed for the species. It has been pointed out by Shull that probably the heads which 
blossom first are the buds which are formed first and have a maximum amount of nourishment 
and space for growth, while the later formed buds have progressively less space and nourishment 
and this causes a decrease in the number of parts in the heads of comjiosite plants. 
These observations will, I believe, sufficiently explain the difference between my two lots of 
material. In the first lot there are rejjresented the first blossomed heads with a prevailingly 
larger number of parts, and in the second lot the high numbers have disappeared and the lower 
modes have appeared. Neither of the two lots alone can give data of much value as regards 
variation, but the two (or more) combined lots represent, as I have pointed out, the condition 
for the season, which is the thing sought. 
As regards the observations of Lucas's (1898), I believe that the deviation of the modes of his 
counts from those of Ludwig can be fully explained by the above observations, and the fact that 
Lucas evidently took his material at one time or very nearly so. His determinations are for 
momentary states in the season and are comparable roughly with my lots 1 and 2. In the 
material from Yarmouth and Grand Pic, Nova Scotia, Lucas found modes on 22 and 29, and in 
that from Cambridge and Milton, Mass., the modes were on 21 and 29. The Nova Scotia lot 
has the mode on 29 well developed and separated by a deep sinus from the lower mode on 22. 
The group about the mode on 29 is strongly skewed towards the higher numbers, which may 
indicate a tendency in this group to move away from the lower mode. In the lot from 
Massachusetts the higher mode has almost disappeared, as in my Lot No. 2, and there is a 
strong modal grouji about 21. 
The difference between Lucas's two lots is explained by the ftict that the season is .some weeks 
earlier in Massachusetts than in Nova Scotia, and, although the lots were taken at near dates, 
