APPLICABILITY OF A COEFFICIENT OF CORRELATION 331 

 EARLIER APPLICATIONS 



The method has been most extensively applied to problems of fertility 

 and fecundity. Thus the relationship between the number of ovaries 

 formed and the number of ovaries developing into fruits has been investi 

 gated in the inflorescence of Staphylea (HARRIS 1909), Celastrus (HAR 

 RIS 1909 b) and Crinum (HARRIS 1912). In Staphylea and Crinum 

 inflorescences which produce larger numbers of flowers mature relatively 

 fewer fruits. In Celastrus there is apparently no relationship between 

 the number of flowers formed and the capacity of the inflorescence for 

 maturing the ovaries into fruits. 



In the fruit, the relationship between the total number of ovules 

 laid down and the deviation of the number of seeds matured from their 

 probable number has been investigated in Sanguinaria (HARRIS 1910 a). 



For Phase ohts rulgaris a first study (HARRIS 1913) of 53 series 

 comprising 166,130 pods and a supplemental investigation of 16 series 

 comprising- 56,698 pods (HARRIS 1917 a) leave no doubt that the 

 pods with the larger number of ovules mature relatively fewer of their 

 ovules into seeds. The same relationship holds in the arborescent legume, 

 Ccrcis canadcnsis, as is shown by studies based on massed data (HARRIS 

 1914 a) and on series from individual trees (HARRIS 1914 b). 



The relationship found in Cercis and Phaseolus is not universal for the 

 Leguminosae. In a series of 1427 pods of Robinia (HARRIS 1909 a), 

 the pods with larger numbers of ovules mature a relatively higher propor 

 tion of their ovules into seeds. The correlation between the actual num 

 ber of ovules formed and the actual number of seeds developing is 

 r og == .693 .009, while that between the number of ovules formed and 

 the deviation of the number of seeds matured from their probable value 

 is r oz = .365 .015. 



That this result represents a real biological relationship is indicated 

 by the correlations, hitherto unpublished, for the individual trees. Only 

 three of the twelve constants in table i are negative in sign. No one of 

 these can be regarded as statistically significant when the probable error 

 is taken into consideration, while seven of the nine positive coefficients 

 must be looked upon as statistically trustworthy. 



The formula has also been advantageously applied to the problem of 

 the interrelationship of the number of male and female flowers in the 

 inflorescence of the aroid Arisarum (HARRIS 1916 a) and that of the 

 interdependence of numbers of stamens and pistils in the ranuncula- 

 ceous genus, Ficaria (HARRIS 1918). In Arisarum the relative number 



GENETICS 3: Tl 1918 



