8o BOTANICAL GAZETTE [July 



season, which attributes it to a change of nutrition, an interpretation which was 

 given independently by MacLeod and the reviewer about ten years ago. The 

 polymorphism shown by the multimodal curves is interpreted by De Bruyker 

 as due to differences in nutrition acting in conjunction with a discontinuous 

 mode of development, through which the new organs tend to be added in 

 groups instead of singly. The same explanation or one essentially similar is 

 applicable to other multimodal variation curves, the series of modes being 

 determined by the manner in w T hich each succeeding group of organs added is 

 related to the preceding group or groups. 



De Bruyker recognizes nine series of modes for multimodal variation 

 curves. These are as follows: (a) the powers of 2 (2, 4, 8, 16, etc.), as in the 

 peristome teeth of mosses; (b) multiples of 3 (3, 6, 9, 12, etc.), as number of 

 flowers in Lonicera caprifolium; (c) multiples of 4 (4, 8, 12, 16, etc.), as in the 

 number of flowers per umbel in Cornus Mas; (d) multiples of 5 (5, 10, 15, 20, 

 etc.), as in the number of stamens in Pyrus communis; (e) the Fibonacci- 

 Ludwig series (1, 2, 3, 5, 8, [10], 13, [16], etc.), as in many Compositae, Umbel- 

 liferae, etc.; (J) the Trientalis series (1, 3, 4, 7, 11, 18, etc.), as in Trientalis, 

 secondary umbels of Astrantia major, lateral heads of Arnica, etc.; (g) Car- 

 damine series (2, 5, 8, 11, 13, 16, 19, 22), as found by Vogler for the number 

 of flowers in Cardamine pratensis; (h) the odd series (1, 3, 5, 7, 9, etc.), as in 

 number of leaflets in imparipinnate leaves, etc.; (i) the even series (2, 4, 6, 8, 

 etc.), as in paripinnate leaves, rows of grains on ears of maize, etc. 



By selecting for higher number of rays in Calliopsis bicolor, under conditions 

 of high nourishment, De Bruyker was able to secure a strain of this species, 

 by far the largest number of whose heads had 13 rays, though the material with 

 which he began selecting gave a very high percentage with only 8 rays. This 

 result corresponds with that of DeVries with Chrysanthemum segetum. The 

 sensitive period for the influence of nourishment on the number of ray flowers 

 was investigated in Chrysanthemum carinatum, and this period was observed to 

 close four or five weeks before the opening of the heads. De Bruyker's work 

 closes with a succinct statement of the principal results of the author's investi- 

 gations on Primula elatior, Chrysanthemum carinatum, C. segetum, Calliopsis 

 bicolor, Scabiosa atropurpurea percapita, rye, barley, and wheat. The bibliog- 

 raphy contains references to a few more than 100 papers dealing with the subject 

 of variation and its statistical study, and a full index is added. 



Nieuwenhuis 17 has studied the changes in the variations and in the mean 

 values of the number of ray flowers in nine species of Compositae from the 

 beginning to the end of the flowering season. He finds in seven of these species 

 an essential agreement with the behavior found by the reviewer 18 in Aster 



v Nieuwenhuis, M., Die Periodicitat in der Ausbildung der Strahibluten bei den 

 Kompositen. Recueil Trav. Bot. Neerl. 8: 1 08-181. figs. 23. 191 1. 



18 Shull, G. H., Place-constants for Aster prenanthoides. Box. Gaz. 38: 333~375 • 



1904 



