No. 629] FLOWER NUMBER IN VERNONIA 533 



experience with the phuits, the writer is led to the ten- 

 tative idea that two sets of factors, which may be en- 

 vironmental, or hereditary, or both, act on the plants 

 independently, one determining the nmnber of heads pro- 

 duced and the other the average number of flowers in 

 each, so that there may result plants with many large 

 heads (as no. 1), many small heads (no. 10), few large 

 heads (no. 15), or few small heads (nos. 5, 18). 



Table 4 shows the distribution of flower-numbers for 

 all the heads of five plants. In each case the curves show 

 a close relation to the main or secondary numbers of the 

 Fibonacci series, 55, 29, 29, 34 and 34 respectively, al- 

 though in only two cases do the modes fall precisely on 

 these figures. Plant 1 shows a rather close grouping of 

 heads just short of 55, plant 9 has over half of the heads 

 grouped at 28-30, and plant 11 has almost half grouped 

 at 33-35. It is scarcely to be expected that the series will 

 be followed closely with such large numbers of flowers ; 

 in fact, Stout has demonstrated that there is no relation 

 whatever to the Fibonacci series in the heads of CicJior- 

 ium Intyhus. Since the numbers were determined in 

 every case by counting the mature achenes, the numbers 

 should fall somewhat below the Fibonacci series, rather 

 than above them, because of the possibility of some 

 flowers not setting seed. 



The plants used for these five tabulations were selected 

 merely because of their large number of heads, which 

 offer Itrttcr (lata for developing a representative curve. 

 Phiiits 2i> 22. with large numbers of heads also, agree 

 closely with plant 19. A moment's inspection of the 

 averages for the other plants, as sho^\^l in Table III, 

 shows that in many cases, such as plants 2 and 3, thoy 

 could not agree closely with the Fibonacci series, or that 

 an apparent a.u'reement miglit l)o fictitious if based on 

 plants with a few heads milx . a> numbers 12 and 13. 



