242 MEMOIRS OF THE NEW YORK BOTANICAL GARDEN 



breadth, and form of base and apex are extremely variable. Gen- 

 erally the leaves were moderately plane, but in some instances 

 they were highly irregular, with revolute margins. 



In some, but not numerous, instances filiform filaments occupy 

 the positions of primordial leaves, and have been counted as such. 



Alonophyllous obliquely infundibuliform ascidia are abundant. 

 In the less mature series 2.42 per cent of the leaves and in the 

 more mature series 2.38 per cent of the leaves are thus modified. 

 This i& extremely abundant as compared with any other strain of 

 Pliaseolus vulgaris with which I have had experience. 



The various combinations of cotyledons and primordial leaves 

 per seedling are shown by the double entry tables II and III. 

 the totals of which have already served in the discussions of coty- 

 ledon and leaf number. Here the entries in the body of the 

 table show the frequency of occurrence of plants with the number 

 of cotyledons indicated at the left and the number of primordial 

 leaves designated in the upper margin. 



From these tables the degree of correlation between the number 

 of cotyledons and the number of primordial leaves can be at once 

 determined. The results are: 



For less mature series, r = .117 ± .032 

 For more mature series, r = .157 db .024 

 For both series combined, r = .139 ± .019 



Since perfect correlation is numerically represented by a coef- 

 ficient of unity, it is clear that the degree of interdependence 

 between cotyledon number and primordial leaf number is very 

 slight. This result may come as something of a surprise to genet- 

 icists who have stated that the correlation between the two is 

 l')erfect. 



The actual relationship between the two variates can be clearly 

 brought out by calculating equations to smooth the mean number 

 of cotyledons associated with different numbers of primordial 

 leaves and the mean number of primordial leaves associated with 

 dilTerent numbers of cotyledons. They are: 



I'or less mature series — 



/ = 3.792 + .325 c 

 c = 3-475 + -04^ / 



