CORRELATION, INFLORESCENCE OF CELASTRUS SCANDENS. 119 



For present purposes the constant of most significance is 

 not that for the relationship between the number of flowers 

 formed and the actual number of fruits developing per in- 

 florescence, but between the number of flowers formed per 

 inflorescence and the deviation of the number of fruits de- 

 veloping per inflorescence from the number which would 

 have developed had the number of fruits per inflorescence 

 been merely proportional to the number of flowers formed in 

 a ratio determined by the total number of flowers and fruits 

 in the population as a whole. This constant shows us at 

 once whether there is on the whole any difference in the 

 capacity of the inflorescences for developing their ovaries 

 into fruits depending upon the number of flowers of which 

 they are composed. When I pointed out the desirability of 

 such a constant as this to Professor Pearson while working 

 in his laboratory he kindly worked out the mathematical 

 formulae necessary. 



The constant* is calculated from the formula 



_ ^ ^xy ^xl^ y 



' xz ^_ 



y^ i-r^' + ix^-yjyy) 



where a: = flowers and ?/ = fruits per inflorescence, V^ and V^ 

 are the coefficients of variation of the two characters, and 

 z is to be read as "the deviation of the number of fruits per 

 inflorescence from its probable value." 



Substituting constants in the above formula we find 



r^^ = .024±.034 



This constant, differing from by less than its probable er- 

 ror, shows at once that there is no sensible difference in the 

 capacity of inflorescences with different numbers of flowers 

 to mature their fruits. The results are not at all in accord 

 with those for the only other inflorescence so far investigated 

 with regard to this point, the Staphylea series above referred 

 to. There we found a considerable positive correlation be- 

 tween the actual number of flowers formed and fruits ma- 

 turing, but a marked negative correlation of about — .65 be- 

 tween the number of flowers per inflorescence and the devia- 



* Harris, J. A. Biometrika. 6 : 439. 1909. 



