VARIABILITY OF SUCCESSIVELY FORMED WHORLS. 



97 



with the means. The matter is one of such considerable importance 

 that it will be considered in some detail. 



Table 50. — Variability of successively formed secondary-branch whorls. 



Confining- our attention at first to the primary branches, I think it 

 reasonably clear that, disregarding minor fluctuations due to the relative 

 smallness of the numbers of observations, there is a tendency for the 

 variability of whorls in leaf-number [to decrease, the farther out on the 

 branch we go. The minor fluctuations are, however, rather disturbing, 

 and in order to get clear results we must resort to graphical representa- 

 tion and graduation. In that way we can get an idea of the general trend 

 of the variability, apart from its accidental fluctuations. In order that 

 the diagrams might not be too extended, and that at the same time we 

 might get a sort of "first smooth" of the observations, I have combined 



the whorls into pairs and taken the weighted means of the ratio -^ for 



a-y 



each pair. Thus, whorls 1 and 2 have been combined and a weighted 

 mean taken; whorls 3 and 4 combined together, and so on for the whole 

 length of the branch. In taking the means, each single observation 



was weighted with the frequency in the array from which— ^ was calcu- 



a-y 



lated. Proceeding in this way, we have for Series I, II, and III combined 

 the series of values given in table 51. 



