
No. 422.] QUANTITATIVE STUDY OF VARIATION. 149 
question whether the difference may not have been in part 
due to the difference in the time at which the collections 
were made.! 
Although the material of A. prenanthoides Muhl., upon which 
this study of successive collections is based, is even less than 
that used by Lucas, the constancy of the fall in numbers of all 
the parts can leave little doubt as to the essential correctness 
of my results. As a few days makes a marked difference in 
the condition of these variable characters, different seasons 
may likewise be found to give different results upon material 
collected from the same individuals. 
As the capitula which terminate the axes in the Asters are 
the first to bloom, my observations on the decline in the 
number of parts in the heads of A. prenanthoides Muhl. bear a 
close relation to those of Burkill (95) on Caltha palustris L., 
Ranunculus arvensis L., R. bulbosus L., R. Ficaria, and Tha- 
lictrum flavum, where he arrives at the conclusion that the 
“ position of the flower on the axis affects the sexual organs, if 
they vary." ? 
Ludwig (00) remarks concerning this, that “weil die Zahl 
der Carpelle, ebenso wie die der anderen Blütentheile und der 
Blütenzahlen in der Inflorescenz von der Stellung an der Axe 
abhángig ist, wird man Mischcurven erhalten, wenn man die 
Zahlungen auf sámmtliche Organe der einzelnen Pflanze, nicht 
auf einzelne gleichwerthige Organe der verschiedenen Pflanzen 
1 Since this was written, W. L. Tower has investigated Chrysanthemum leu- 
canthemum L. with reference to this point, and found that there is a continuous 
decrease in the values of mean and modes from the beginning to pa end of the 
flowering season. His results will appear in pment vol. I, n 
? In his studies on the plants named, and others in which Pn uL of sta- 
mens and carpels vary, he finds that *the earlier formed flowers on the plant 
carry more stamens or more -— or perhaps more of both organs, than those 
formed later in the season,” and that “flowers holding any position of advantage 
on an inflorescence, 7.e., terminal on a cyme, or at the base of a raceme, even if 
not maturing earliest, carry more stamens or carpels or more of both, than in the 
other flowers of the same inflorescence.” 
Finally, he finds that in forms such as Ste//aria media, and fe 
which have a long flowering season, there is a kg decrease pares 
of stamens and carpels during the flowering season, re of a 
on the inflorescence, — a result which is closely "pudiicied by my work on 
prenanthoides Muhl. 
