jiNF. im.i KOrJBA.— VAPJATT'jy IN TEE RAY-FLOWEES. HI 



season."" What, then, is the cause for this fewer number of 

 rays in the earliest flowers here ? The eai'lier buds are sub- 

 jected to the lower temperature, and it must affect undoubted- 

 h' the developement of the flowers. In the multicipital com- 

 positae the first-formed buds undergo a very vigorous deve- 

 lopement on account of the better supply of nourishment com- 

 pared with the later buds, and thus cancels the unfavourable 

 climatic influence of the earlier season, while Avith this single- 

 headed Arnica the condition is quite different, where the larger 

 amount of nourishment stored in the perennial root of the 

 longer vegetating stock does not cancel the unfavourable 

 climatic influence. There are two opposed external causes which 

 influence the formation of ra\'S of Arnica, the thawing of snow 

 and the climatic change, the combined action of which causes 

 the highest number of rays to appear at the end of the first 

 on:-tliird period of the season, though the highest extremity in 

 my material appeared in the third collection. 



Secondh', as to the change of mode, though the poh'gon 

 changes continuoush^, the class 16 constituted alwav^s a distinct 

 mode, except the last lot, in which however, there was a well- 

 marked difference with 17, so that we ma3' saj' 16 rays as 

 the type of this Arnica. The mode on 13 was not very con- 

 stant, 12 and 14? were equalh" probable, so that we may 

 assume a thick, accessory mode on 12 to 11. There appeared 

 usually a deep sinus on 15, except the lots Nos. 3 and 7, in 

 which, however, 16 or 14- was more probable (Fig. 3 and 7). 

 As to the other series of Fibonacci, sometimes there appeared 

 slight indications of them, but sometimes no such sign was 

 seen, being rather indeterminable in such a small number of 

 specimens. 



If we compare these results with those of the allied species 

 A. montana, which was counted by Ludwig and others/' the 

 highest mode on 16, the sinus on 15, and the indistinctness of 



1) Tower, Variation in the Kay-tiowers . of Clirysantliemim leucanthemuui L. 

 Biometrika, Vol. 1. 1901-2. P. 311. SauLL, ]. c. p. 148. 



2) LuDVViG, Variationsstatistisclie Problem und Materialien. Biometrika, Vol. 

 1. P. 26. 



