VARIATION AND CORRELATION-IN RAYS AND DISK 
FLORETS OF ASTER FASTIGIATUS: 
H. Nakano 
(WITH FOUR FIGURES) 
Through various researches on the variation of Compositae, 
Umbelliferae, etc., Lupwic (1, 2, 3, 5, 6, 7, 10) came to the con- 
clusion that multimodal curves prevail in plants, and that the mode 
always falls on some member of the Fibonacci series, or often on 
some member of ScHimPEeR-BRAUN’S accessory series, that is, on the 
so-called ‘“Nebenzahlen.”” When a mode comes on a number other 
than that in the principal and accessory series, he considers this as a 
Scheingipjel, in which two curves with modes on two adjacent classes 
are combined. 
On the other hand, in the variation of the rays of Chrysanthemum 
Leucanthemum, Lucas (8) obtained the principal mode on 22, a 
result which is an exception to Lupwic’s rule, but which seemed to 
find confirmation later in the researches of SHULL (12) and TOWER 
(13). The curves of these two authors, however, were altogether 
multimodal and obtained from comparatively scanty material. For 
example, SHULL doubled the classes on account of the sparseness of 
his material, so that the apparent multimodal curves changed to 
monomodal ones. It may not be useless, therefore, to examine the 
applicability of Lupwic’s rule in the variation of the rays and disk 
florets of Aster jastigiatus Fisch. and Mey., using a tolerably large 
number of variates, 
The true significance of two different results in Lucas’s calcula- 
tion was not clearly known until ToweEr’s discussion (13) appeared. 
According to him, the number of rays of Chrysanthemum Leucanthe- 
mum decreases continuously during the flowering season (27.87- 
21.38 between July 5 and July 30), and Lucas’s curve and his own 
Were not influenced by the difference of the place-modes. 
A little before the publication of Tower’s work, SHULL’s admirable 
Paper (12) on the variation and correlation in the bracts, rays, and 
« Preliminary note. 
371] [Botanical Gazette, vol. 49 
