158 PRESENT-DAY RATIONALISM 



Dr. Vernon quotes several instances of the mathematical 

 statistics of the parts of flowers giving maxima and minima. 

 But they are just what a botanist would anticipate. In fact, 

 I did so before studying the tables, because, knowing the 

 origin of the normal number of parts in floral whorls, the 

 maxima only mark off phyllotactical "cycles". Dr. Vernon 

 makes no mention of phyllotaxis ; I can only conclude, there- 

 fore, that he is not aware of the peculiarities of leaf-arrange- 

 ments. 



Thus, we are informed that Ludwig counted the number of 

 pedicels or "rays" of the umbel of Torilis Anthriscus and 

 de Vries the ray florets of Chrysanthemmn segetiim. In the 

 former the maxima were 5, 8, 10 (= 2 x 5). In the latter, 13, 

 21, 26 (= 2 X 13), 34. In the case of the stigmatic rays of 

 poppies, 13 is the maximum. 



Now, these numbers do nothing more than indicate the 

 prevailing phyllotactical cycles corresponding to the " angular 

 divergencies " of the series : — 



1 1 2 .J 6 8 c^^r- 

 •2.1 3^' ¥' F' T¥' ^T' ^'^^* 



If the object of these investigations be a search for the 

 Origin of Varieties, they will not afford much help, and 

 generally none at all.^ 



Since the above paragraph was written, a friend in Australia 

 has communicated to me an interesting fact, which bears out 

 the origin of variations by adaptation. He found the phyllo- 

 tactical cycles of the Mediterranean species of marigold 

 {Calendula) to be localised according to the nature of the 

 environment. He has observed that the large orange Calendula 

 has normally twenty-one ray florets ; but near the sea it is pre- 

 paring to develop a thirty-four-rayed form, many individuals 

 having reached twenty-six {i.e., 2 x 13). He adds that the point 

 he wishes to bring out is that the number of ray-florets in 

 different composites varies with their habitats. " Thus, the ox- 

 eye daisy has generally twenty-one ray-florets at the level of Lake 



' The reader is referred to Biometrika for other examples. 



