IOWA ACADEMY OF SCIENCES. 
57 
The mean magnitude, the index of variability, and coef- 
ficient of variability, with probable error, has been worked 
out very carefully for each species and each locality with 
the exception of Erigeron, for which these would have 
been of little value. 
The following formulae have been used in working out 
the mean, the index of variability, the coefficient of vari- 
ability, and the probable error. 
E (V f) 
A = — — — where A = the mean; 
n 
V == the frequency of a class, and n = the total number of 
variates. 
E(x^ f) ^ where 0 —the index of variability 
n 
(standard deviation), x=the deviation of a class magni- 
tude from the mean, and (C= the difference between the 
upper and lower limits of a class, which is unity in this 
case. 
C — — ^ — where C== the coefficient of variability. 
Ea —.6745 and Eo— 6745 ^ where Ea and Eo 
y n V 2n 
denote the probable error of mean and probable error in- 
dex of variability respectively. 
The subject of the variation of ray flowers in the 
Compositae has been studied by a number of investigators 
in recent years. G. H. Shull (1902) studied the variation 
in the bracts, rays and disk florets of a number of species 
of Asters. W. S. Tower (1902) studied the variation of 
ray flowers of Chrysanthemum leucanthemum. Shull in the 
