1904} SHULL—PLACE-CONSTANTS FOR ASTER 367 
Cases are well known in which the distribution does not appear 
to be normal under any ordinary conditions, the frequency curves 
being of the “half Galton” type, as for instance the petals of Caltha 
palustris, Potentilla anserina, Ranunculus bulbosus (DE VRIES 1894), _ 
Ranunculus repens (PLEDGE 1897), sepals and petals of Ranunculus 
anvensis (BURKILL 1902), leaflets of clover (DE VRIES 1899@), ascidia 
and other abnormalities of various species (DE VRIES 1899a, TAMMES 
1903), and other characters. Such cases may not be really so 
exceptional, however, as they at first appear. We have only to 
assume that the normal condition for these characters is one in which 
the value of o approaches zero to see that these are cases of “ pro- 
phetic” skewness due to the small proportion of abmodal variates; 
M other words, due to slight sensitiveness to conditions tending to 
produce a number of organs higher or lower than the normal mode. 
It may be found that any population or even any species is suffi- 
Gently uniform in its reactions to various degrees of environmental 
change to allow us to derive from the direction and amount of skew- 
tess the approximate value of the mean under average conditions 
. under conditions which would give a normal distribution of the 
ea Thus, the knowledge that this population of Aster prenan- 
& IS SO sensitive to change as to exhibit strong positive skewness 
when conditions are below average may be found to warrant the 
‘sumption that there will be a strong negative skewness under 
usually favorable conditions, and also that the skewness exhibited 
ae Collection from any new locality would give an indication by 
.. - fas whether that collection was below or above the 
ply ts condition for that place. But before on can 
Mean” . pple with any confidence in determining the “normal 
thy any particular population, it will be necessary to confirm 
"mptions (a) that the distribution for that population is normal 
Oia conditions, and (b) that the sensitiveness to Reon 
— 1S similar in intensity to the sensitiveness to 
Th - Conditions. = 
ble here presented of variability in individual sensitive- 
in ad of environment is likely to find a wide aimee 
termini, ‘lation of skew variation, and suggests the need 0 
8 Whether or not there is direct variation of the organ or 
