ON VARIATION OF THE ROSTRUM IN PALÆ- 
MONETES VULGARIS HERBST. 
GEORG DUNCKER. 
Lasr summer, at the Cold Spring Harbor Biological Labo- 
ratory of the Brooklyn Institute, I investigated the number of 
rostral spines in 1050 shrimps, in order to test the relation 
between the average value of a varying character and its 
variability. 
As is well known, Verschaeffelt (94) first assumed the ratio 
between the probable deviation of a character and its median 
to be an absolute measure of its variability. Such ratios as 
probable deviation or median average deviation, or root of 
average square deviation to mean have been called “ coeff- 
cients of variation " and have been frequently used, not only 
in merely arithmetical processes, but also in dealing with 
morphological questions ; for instance, in applying them, 
Brewster (97) and Field (98) meant to show the variability of 
systematically important characters to be higher than that of 
other ones. Both Davenport (see Brewster ['97]) and Pearson 
(97) believe the higher variability of homologous characters to 
be connected with the higher average value. Dr. Davenport, 
to whom I am much indebted for his kind interest and for 
numerous suggestions during my stay at Cold Spring Harbor, 
assumes the relation between the index of variability of a char- 
acter and its average value to be similar to that between the 
errors of measurement and the length of a course measured 
by the chain used in surveying. 
Now, in my opinion (99), there is no relation whatever 
between the average and the variability of a character. 
While the average value is determined by such conditions as 
equally affect all the individuals of a form unit, external con- 
ditions (environment, climate, food, quality of soil or water), 
as well as constitutional conditions (specific nature, sex, stage 
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