1904] SHULL—PLACE-CONSTANTS FOR ASTER 365 
as has been maintained by Lupwic (1899, r90r), as proof that 
variation in plants is fundamentally different from that in animals. 
When the phyllotactic series shall have been successfully analyzed, 
they may be found to result from the working out of more or less 
definite cell-lineages as supposed by Lupwic (1888), or they may be 
the result of purely mechanical relations, as believed by SCHWEN- 
DENER, followed by WeIssE (1897) and CHuRCH (1904), but either 
hypothesis, in explaining the occurrence of such series, must leave 
departures from the theoretical numbers to be accounted for as 
fluctuating variations. In addition to this variation about each num- 
ber of the series, there is the general variation which may have a 
suficiently wide range to allow the variates to coincide with two or 
hore numbers of the phyllotactic series, so that we have in the case 
of phyllotactic variants two series of variations, the one overlying and 
partially masking the other. There can be little doubt that these 
Taniations taken separately will be found to agree with all the laws of 
Yatlation determined for animals and the non-phyllotactic characters 
ot plants, 
ap DE VRIES (1899) was able by selection to establish 
faces of Chrysanthemum segetum having monomodal ray-curves, this 
aR he Né taken as supporting Lupwic’s (1gor) view that multi- 
el : to the establishment of a mixed population of petites 
sexual re ae the common occurrence of asexual and ee 
ria uction, for REINOEL (1903) was able to reduce the 
tion, by ale of Alsine media to monodal curves without selec- 
frent degrees of light and manuring. 
“ahha a ed that we shall soon have a method of treatment of 
. © Variants which will remove the Fibonacci mask an 
eae of the underlying individual variation with as 
Althouph € as is now attained with non-phyllotactic ~~ 
Curves to “ah S Impossible on account of the multimodality ) i 
and rays (ff i. the skewness, it is so marked in the case of the - : 
oy 9) wee be recognized at a glance. There ! i 
bavorite eari interpretations of skewness in different ae ’ 
by the li 8 Ws (DAVENPORT 1901) being that it results either 
smunation of one or other of the extremes through the 
of natural selection, or that heterogeneity is introduced by the 
