76 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



The correlation tables showing the relation between number of leaves 

 in the whorl and position on the branch for this division of the plant 

 are given in table 37. 



The correlation coefficients (r) and correlation ratios (v) deduced from 

 the preceding table are given in table 38. From this table the following 

 points are to be noted: 



(a) As in the case of the primary branches there is a high correlation 

 between the number of leaves in the whorl and position on the branch. 

 Comparing the values of the correlation constants for secondary branches 

 with those for primary branches given in table 33 above, we see that 



Table 39. — Mean number of leaves in successive whorls on secondary branches. 



they are without exception higher in the case of the secondaries. The 

 reason for this is found in part in the fact that the secondaries are 

 shorter than the primary branches. Consequently they do not have at the 

 distal ends of the long branches the long string of whorls with, as has been 

 shown above (p. 62) , a very nearly constant number of leaves. These 

 distal whorls, from about 15 on, operate in the case of the primaries to 

 lower the correlations. To get a fair test of the relative degree of the 

 positional correlations in the two orders of branches we must compare 

 branches of roughly the same length. From table 37 we see that the 

 secondary branches of Series I, II, and III run up to 13 whorls, while 

 in Series IV they go to 18 whorls. If, now, we calculate the coeffi- 

 cient of correlation between leaf -number and position, for the first 13 



