148 THE AMERICAN NATURALIST. [Vov. XXXVI. 
possess but single variates of the kind used in determining 
those constants. 
The above-stated results in J. puniceus L. make obvious the 
same truth in regard to species such as those of Composite, in 
which the individual may have a sufficient number of variates 
to give a good frequency polygon and constants with small 
“ probable errors.” The wide differences between the three indi- 
viduals of A. puniceus L. show that the variability * constants " 
for individuals are only in a measure less variable than the 
characters upon which they depend. 
The study of the successive collections shows another phase 
of the subject of variability which would materially affect the 
value of statistical methods in taxonomic questions relative to 
the Composite. In these successive collections there was a 
continuous decline in the numbers of bracts, rays, and disk 
florets, and a continuous change in the position of means and 
modes. These results could have been in no way dependent 
upon unnatural conditions induced by the clipping of the heads, 
since even the last to bloom were well-developed buds at the 
time the first collection was made; and had there been a change 
brought about in this way, it must have been in the opposite 
direction, since it is a well-known fact that the removal of the 
earlier flowers gives increased vigor to later ones. 
This continuous change of means and modes during the 
blooming season is suggested as a possible explanation of 
Lucas's (98) results upon Chrysanthemum leucanthemum Asi, 
other than that of difference of locality. He found that there 
was a marked difference between the results obtained from 
material collected at Yarmouth and Grand Pic, Nova Scotia, 
and that collected later at Milton and Cambridge, Mass. The 
earlier material from Nova Scotia showed the mean on 24.389 
and the principal mode on 22, while the later collection from 
Massachusetts had the mean on 21.61 and the mode on 21. 
Ludwig (00), in commenting on these results, attributes 
their deviation from his own Observations to the scantiness of 
Lucas's material, while Lucas implies, though he does not say 
it definitely, that the difference is a local one. In the light of 
my observations on 4. prenanthoides Muhl. it seems a fair 
