1908] CURRENT LITERATURE 65 
paper read before the third Flemish Natural History Congress at Antwerp in 
1899, MacLrop" shows that in Centaurea Cyanus the mean numbers of rays 
and disk-florets are highest in heads which bloom earliest and that they fall 
continually as the flowering season progresses, the change in disk-florets being 
the greater. When individuals are considered, the terminal heads have the 
highest numbers, and each successive bud-generation has a less number than the 
preceding. Three series of cultures under different conditions of soil led to the 
conclusion that the first heads of each plant behave like the terminal heads of 
well-nourished plants; and that the last heads of each plant and of the season 
resemble the terminal heads of poorly nourished plants. There is no indication 
in this species that the Fibonacci numbers tend to predominate. This paper is 
not listed in DAVENPoRT’s rather comprehensive bibliography, and was unfortu- 
nately unknown to me when I was investigating the seasonal variability in Aster 
prenanthoides. The conclusions reached for Centaurea are the same as those 
reached by me about a year later in Aster. 
More recently MacLeop and BurvenicH'S have made an experimental 
study of the variability in the number of rays of Chrysanthemum carinatum and 
find essentially the same condition as in Centaurea, except that, unlike that species, 
Chrysanthemum carinatum shows the modes on the Fibonacci numbers, and as 
the mean number changes with the change of nutrition, the prominence of one 
mode is lessened as the neighboring one increases. The variation goes by steps 
or leaps from one favored value to the next. In discussing these “‘variation- 
steps” (Varietietrappen), three types of behavior are recognized: first, that in 
Ww ich the modes, whether one or several, agree with the terms of the relevant 
series, €. g., Chrysanthemum carinatum, 13 and 21; second, that in which the 
number of parts is constant or but very slightly variable and the values are those 
of the terms of the series, e. g., Senecio Jacobaea, 13, S. nemorensis, 5, S. nemorensis 
octoglossus, 8, etc.; third, the condition found in Centaurea Cyanus and in Aster 
in Which the mode may fall upon any of the values lying between the terms of the 
series and in which as the mean values rise or fall the mode passes gradually 
through all the successive values. Seven variation-scales or series are recog- 
nized as fully demonstrated for one or more plant-characters; viz., (1) the Fibo-— 
nace series, 3, 5, 8, 13, 21, 34; (2) 5, 10, 15, 20 (carpels of Geranium); (3) 3, 
®, 7 (leaflets of Trifolium); (4) 3, 6, 9 (flowers of Lonicera); (5) 2, 5, 8, 11 
(flowers of Cardamine pratense); (6) 4, 8, 12, 16 (flowers of Cornus mas); (7) 4, 8, 
> 32, 64 (peristome of mosses). The author gives a lucid explanation of the 
Cause for the existence of such series by referring them back to the period in 
a 
wines MacLrop, J., Over de veranderlijkeid van het aantal randbloemen en het 
‘tal schijfbloemen bij de korenbloem (Centaurea Cyanus) en over correlatiever- 
Schijnselen. Bo 
tanisch Jaarboek 12: 40-74. 1900 
1 
op 5 MacLeon, J., and BuRVENICcH, J. V., Over den invloed der levensvoorwaarden 
Cree achat bij Chrysanthemum carinatum en over de trappen der 
tlijkheid. Botanisch Jaarboek 12:77-170. 1907. — 
