336 -BOTANICAL GAZETTE [NovEMBER 
resulting from the loss of rays due to age or other causes—and it saves 
the necessity of discarding any material on this ground, since the 
remains of the ray-flowers are always distinguishable from the disk- 
flowers when they are separated. 
It ought not to be necessary in work of this kind to give assurance 
that no material has been arbitrarily discarded, either in collection 
or in seriation, but the importance of this matter seems to be too 
little appreciated. If one student arbitrarily discards material, 
who else in working over the same material will arbitrarily discard 
on the same basis? And if an investigation cannot be repeated 
by another investigator with at least approximately identical results, 
of what value is it? Tower (1902) assumed that his failure to get 
a mode at 34 in Chrysanthemum Leucanthemum might be due to the 
fact that he discarded a number of heads on account of age. He 
states that counts of some of this rejected material showed that all 
of the heads had a large number of rays. What would have been 
the result had he counted all the heads he rejected ? Miss SMALL- 
WOOD (1903) “arbitrarily threw out the small” specimens of beach-flea 
and then presented statistics as to the size and variability of the 
remainder, as if these data could have either interest or scientific 
value.? If anomalies appear when all the data are setiated, yd 
should be explained if possible, but explained or unexplained : 
data should be given, because these have value whether the explana 
tion has or not. ules 
In calculating the various constants I have again used the wing 
tabulated in DavENPoRT’s (1899) Statistical methods, except 
instead of DUNCKER’s method of calculating the coeflicient of en 
lation I have used the neat method adopted by YULE (1897)> ¥ 
may be expressed by the formula 
Sfx'x’” I 
p=( 2 —v,! vy" af 
nN 5) wed 
. , as i ] assume 
in which x’ and x” are the deviations from an a kecocsey 
mean of subject and relative classes respectively, / a 3 a iat 
f : : Vv 
of occurrence of each combination of subject and relat — 
. : r deals ¢ < i 
2 In justice to Miss SmaLtwoop it should be said that = nie soe 
With the ethological relations of the beach-flea, and that she er 
the unsatisfactory character of her quantitative results. 
