i6o Journal of Agricultural Research voi. xvii, no. 4 



As determined from these figures, the coefHcient of correlation is o. 178 ± 

 0.017, indicating a positive correlation between the size of the inflores- 

 cence and the number of fruits it brings to maturity. The small value 

 of the coefficient, however, is worthy of note. It was previously men- 

 tioned that we should expect upon a priori grounds a definite relationship 

 between flowers and fruits, especially in the case of the smaller inflores- 

 cences. It will therefore be in order to inquire whether the larger 

 inflorescences are relatively as fruitful as the smaller. 



In order to secure a measure of the relative fruitfulness of the inflor- 

 escences, I have used a formula which Harris ^ published several years 

 ago. The correlation coefficient as here used is intended to measure the 

 correlation between the number of fruits produced per inflorescence and 

 the deviation of this number from its probable value, in case the number 

 of fruits per inflorescence is in the same proportion to the number of 

 buds per inflorescence as the total number of fruits to buds in the entire 

 population. It is computed from the formula, 



^xy * xl ^ V 



where x' = buds and >' = fruits per inflorescence, Vx and Vy are the coeffi- 

 cients of variability of the two characters, and z is to be read as "the 

 deviation of the number of fruits per inflorescence from its probable 

 value." 



The value of this correlation as computed for the lemon inflorescence 

 is Yxz = o. 1 83 ± o.oi 8. 



This negative value of r^z is interpreted to mean that there is a distinct 

 negative correlation between the size of the inflorescence and its power 

 to develop its buds into fruits. In other words, a bud on one of the 

 smaller inflorescences has a greater chance of becoming a mature fruit 

 than a bud on one of the larger inflorescences. The competition between 

 individual buds on larger inflorescences seems to be too severe to allow 

 all to survive. It is not, therefore, probable that the larger inflorescences 

 are able to mature proportionally larger numbers of buds. 



Heinicke ^ has recently reported that the reverse relationship exists in 

 the case of the apple trees he studied. His figures indicated that a higher 

 percentage of flowers develop into fruits on spurs producing six flowers 

 each than on spurs producing four or five flowers. Further data on this 

 question are to be desired. 



' Harris. J. Arthur. The correlation between a variable and the deviation of a dependent 

 VARLABLE from ITS PROBABLE v.\LUE. In Biomctrika, V. 6. pt. 4, p. 43S-443. 1909. 



Correlation in the inflorescence of Celastrus scandens. In Mo. Bot. Card. 20th Ann. 



Rpt. p. 116-122. 1909- 



2 Heinicke, Arthur J. Factors influencing the abscission of flowers and partlally developed 

 fruits of the apple (Pyrus malus L.). N. Y. Cornell Agr. Exp. Sta. Bui. 393. p. 41-114. iHus. 191 7. 

 Bibliography, p. 112-114. 



