No. 422.] QUANTITATIVE STUDY OF VARIATION. I5I 
While deprecating the selection of material on false bases, I 
take it that intelligent selection of material existing under 
known conditions is more certain to give valuable results than 
at-random selection, which, while sure to select, ignores the 
conditions under which the selection is made. 
Until we know the causes of variation and how great degree 
of variation may be produced by how slight causes, all general- 
izations based upon limited observations should be accepted 
with caution. Granting that observers have no preconceived 
notions as to what they ought to find, the conditions found by 
each investigator are true of the material upon which he worked, 
but how true his general conclusions are, further investigation 
alone can tell. 
If every valley and hillside is to have its own place-mode and 
every day and every season is to bring forth a changed condition 
in the variable characters of its living forms, only a universal 
collection of material covering a long period of years can give 
us true constants which may be verified by a repetition of the 
process. 
VI. SUMMARY. 
Quantitative studies were made upon the bracts, rays, and 
disk florets of four species of Aster growing at Yellow Springs, 
Ohio. i 
A close correlation was found between bracts and rays, and 
attributed to the fact that the rays are axillary to the bracts. 
The degree of imbrication of the bracts was observed to bear 
a relation to the number of empty bracts. 
Curves and “constants” were determined for the material 
of the four species studied. “Constants " determined for sev- 
eral individuals of A. puniceus L. growing in identical surround- 
ings indicated how great variations may exist in the variability 
“constants” of individuals. 
Studies upon successive collections from a single group of 
specimens of A. prenanthoides Muhl. showed that the number 
all decrease continuously from 
of bracts, rays, and disk florets 
the beginning to the end of the flowering season, and that the 
