314 Variation in Chrysanthemum leucanthemum 
Summary. 
1. The ray-flowers in the heads of Chrysanthemum leucanthemum L. at Yellow Springs, 
Greene Co., 0., were found to vary from 12 to 39 in number, and were grouped about the series of 
Fibonacci, 13, 21, 33 (34), as modes, with 21 as the primary, and 33 (34) and 13 as secondary 
modes. The species in this locality shows for this generation no change from that of Europe. 
2. A " place-mode" is the average prevailing state of one or more characters of a homogeneous 
lot of individuals [i.e. of the same pleomorphic condition and stage of development] characteristic 
of a particular place and season, as determined by observations carried on long enough to 
eliminate the effects of secular climatic fluctuations. 
3. A " secular-mode " is the prevailing state of one or more characters of a homogeneous lot 
of individuals, of the same pleomorphic condition and stage of development, for a particular 
place and year. 
BIBLIOGRAPHY. 
Davenport, C. B., 1899. The Importance of Establishing Specific Place-Modes. Science, 
N. S. Vol. IX, No. 220, pp. 415—416. 
Lucas, F. C, 1898. Variation in the Number of Ray-Flowers in the White Daisy. American 
Naturalist, Vol. xxxii. No. 379, pp. 509—511. 
LuDWiG, F., 1895. Ueber Variationskurven und Variationsfliichen der Pflanzen. Bot. Centralb. 
LXiv, 1—8, 2 taf. 
LuDWiG, F., 1896 a. Weiteres iibor Fibonacci-Kurven und die numerische Variation der 
gesammten Bliithenstando der Kompositen. Bot. Centralb. Lxviii, 1 et folg. 1 taf. 
LuDwiG, F., 1896 b. Eine fiinfgipfelige Variations- Kurve. Ber. Deutsch. Bot. Ges. xiv, 
204—207. 
LuDWiG, F., 1898 a. Die pflauzlichen Variations-Kurven und die Gauss'sche Wahrscheinlich- 
keitskurven. Bot. Centralb. lxxiii, 241 — 250, 1 taf. 
Lddwig, F., 1898 b. Ueber Variationskurven. Bot. Centralb. lxxv, 97 — 107; 178 — 183, 1 taf. 
Shull, Geo. H., 1902. A Quantitative Study of Variation in the Bracts, Rays and Disc florets 
of AstL'7- shortii Hook., A. Novae-Anyleae L., A. puniams L., and A. prenanthoides 
Muhl., from Yellow Springs, Ohio. American Nat., Vol. xxxvi. No. 422. 
EXPLANATION OF PLATE. 
The polygons of distribution are all from counts of the ray-tiowers in the heads of Chrysanthemum 
leucanthemum L. from Yellow Springs, Greene Co., 0. TLie mean for the season is represented by the 
heavy line ntj 7Hj jnj about which the polygons are centered to facilitate comparison. 
Fig. 1. Polygon of distribution of Lot No. 1, collected July 5, 1901. Modes on 22 — 25 and 33 rays. 
Mean (m^ m^) 27-87. n = 284. 
Fig. 2. Polygon of distribution of Lot No. 2, collected July 30, 1901. Modes on 13 and 21. Mean 
(m^ Wj) 21-30. »i=168. 
Fig. 3. Polygon of distribution for the "character-mode" for the generation of 1901. Mode 21, 
secondary modes 33 (34) and 13. Mean (m^ 7Hj) 24-62. m = 452. 
