364 BOTANICAL GAZETTE [NOVEMBER 
however, whether the harmonic optimum for light-intensity is not 
likely to be above the normal, the shade habit of Aster prenanthoides, 
as well as of other green shade plants, being assumed on account of 
the protection afforded against excessive transpiration, and not against 
excessive lighting. If this be true, the conditions in 1900 were even 
more favorable than here assumed, since with the exception of July 
the light-intensity was higher in 1900 than in 1903, being generally 
above normal in the former year, while in 1903 it was generally much 
below normal, being strikingly below in April and June. 
These several advantages of 1900 over 1903 seem to be offset 
by the single factor of precipitation during May and June, the rain- 
fall being appreciably below normal during those two months of 
1900. As pointed out in the discussion of the habitat, it is probable 
that precipitation is of very slight importance in this case, leaving 
the low light-intensity and low temperature of the month of June, 
1903, as probably the most important factors in bringing about the 
great change in the number of parts in the heads, the factors of next 
importance being possibly the very high light-intensity coupled with 
slight precipitation in the month of July 1903. 
I wish to repeat that these conclusions are based on assumptions 
which need confirmation. It must not be forgotten that the after- 
effects of a preceding season or a rigorous winter may also be _— 
of importance, or even that there may be an internal periodicity 
which cannot be definitely referred to environmental fluctuations 
Two features of the frequency polygons for the bracts, Tay, - 
disk-florets (figs. 8-ro) are sufficiently striking to warrant considera- 
tion, their multimodality and their skewness. So much has ne 
written upon the multimodal character of the frequency curves' 0 
phyllotactic organs that it need only be pointed out here that this 
additional collection of material shows no tendency to eliminate the 
multimodality observed in 1900, and though the errors of —_ 
sampling, which are very great in material of such wide Tang® i 
be held to account for most, if not all, of the irregularities of 
; rmanent 
curves (PEARSON 1902), there are some evidences that Pe ee 
modes may be developed on the Fibonacci series and Lupw 
“Unterzihlen.” 
: figs however; 
The constant recurrence of this series is not to be taken, 
