1904] SHULL—PLACE-CONSTANTS FOR ASTER 357 
It was observed by BURKILL (1902) in Ranunculus arvensis L., but 
he did not “feel justified in suggesting a cause for it.” BURKILL 
(1895) showed in his earlier paper that in Caltha palustris, Ranwn- 
culus arvensis, and R. bulbosus the first flower of any individual has 
a higher number of stamens than any subsequent flower of that 
individual. HAACKE (1896) points out the same fact in regard to 
the number of rays in the heads of Tanacetum (Chrysanthemum) 
corymbosum. If this is also true in Aster prenanthoides (and I believe 
it is), how are we to account for the peculiarities of the curves in jig.7 ? 
The general fall in mean values from near the beginning to near the 
end of the flowering period can be best explained perhaps by the 
gradual waning of vegetative vigor during the time at which the © 
differentiation takes place which determines the number of parts 
inthe heads. This decreasing vigor was supposed by BURKILL (1895) 
to be largely due to changing temperature, but REINGHL (1903) has 
shown that temperature has little if any influence, while the important 
factor seems to him to be that of available food-supply. It is conceiv- 
able that there may be a decreasing lability of the protoplasm result- 
ing from lessened water-supply, or the accumulation of inert products 
of metabolism, or from other causes, which would bring about a 
Progressive fall in the number of parts in the heads, even though the 
food-supply remained unchanged. 
But if every individual produces the highest number of parts in the 
first head that blooms and the lowest number of parts in the last, how 
vc the mean number begin low—far below the maximum—and end 
with atise? This is to be explained by the fact that we are dealing 
with a population instead of an individual. The precocious flowering 
of starved or otherwise weakened individuals is a well-known phe- 
“omenon, and it is evident that the heads gathered at the first collection 
Here those produced by the very weakest individuals, and owe their 
low Values to that fact. Very soon, however, the mediocre plants, 
oe the great majority of the population, begin to bloom, 
they wanging the mean values at once to the maximum, oe eon 
ie ay fall until almost the end of the season. The ae 
Vigotousinar UL Undoubtedly be the last heads of hap: “4 
hae Sindividuals which did not begin to bloom till late in the seaso a 
ugh these heads have the lowest numbers of parts produc 
