May 1908.] 



KORFBA.— VARIATION IN THE RAY-FLOWERS. 



89 



bloom in the crater, but in the valley and slope, they were just 

 beginning to flower, and the collection was made only in the 

 first place. Among the specimens collected, I have counted only 

 the healthy, fully blossomed heads, and those which have been 

 injured mechanicallj^ or by insects w^ere rejected. Results 

 obtained are as follows -^ 



First collection. July 29. Lot No. 1 (Crater). 



Further details are given in Table I. The rays in 265 heads 

 were counted, and were found to vary in number from 10 to 24, 

 but the larger number of variates fell on classes 12 to 16 (PI. Y 

 Fig. 1), with equally developed modes on 13 and 16, either of 

 which being a member of the Fibonacci-series."' The number of 

 variates on class 12 was a little less than that on 13, and that 

 on 15 formed a sinus. 



A w^eek later, on my second visit, sufficient specimens were 

 obtained both in the crater and vallc}', but on the slope only a 

 few heads were in bloom amongst the scanty bamboo-bushes in 

 the upper part, and no material was collected here. From those 

 two lots the follow^ing results were obtained : 



1) The notations and calculations of the statistical data are based on Daven- 

 port's "Statistical Methods with special Eeference to Biological Variation." 2. Ed. 

 New York, 1904. where 



n= number of variates, 

 .4=average or mean, 

 (7=standard deviation, and 



(7=coefficient of variability (-j-XlOO^j. 



2) After LuDWJG tlie number of pnrts of multiple organs has a tendency to fall 

 on either of the series 3, 5, 8, 13, 16, (=2x8), 18 (=5+13), 21, 24 (=3x8), 26 

 ( = 2x13), 29 ( = 8 + 21), 34, etc. See LuDWiCi, ULer Variationskurven. Bot. Centralbl. 

 Bd. 75. p. 97-107, 178-183, 1898. 



