April 1. 1920 A Teosinte-Maize Hybrid 33 



This character might be expected to be closely related to number of 

 nodes on third, since in a mathematical sense it is a function of that 

 character. However, the correlation between length of internode on the 

 third branch and nodes on third is —0.05. 



Length of internode on third shows a larger number of significant 

 correlations than does any other character. 



A high expression of the character might be expected to be associated 

 with increased general vigor, but many of the correlations are in the 

 opposite direction. There is distinctly more evidence of disherence than 

 of coherence. In fact, three of the four significant coherences may be 

 physiological, while most of the disherences are not to be explained in 

 this way. 



Especially significant are the pronounced negative correlations with 

 height and total leaves. Only slightly less striking are the negative corre- 

 lations with two of the tassel characters. 



DISCUSSION OF CORRELATIONS 



It would be very difficult, if not impossible, to determine with accuracy 

 the number of independent correlations. The interrelation of the charac- 

 ters is of a most intricate nature; and even if the data warranted the 

 calculation of the partial correlations of each pair with all other characters 

 constant, the facts would still be very inadequately represented. Cor- 

 relations take no account of causation or the sequence in which characters 

 are determined. 



It is clear that the values of some characters are directly influenced 

 by others, the relation being causal in nature. Thus the number of total 

 leaves acts as a limiting factor to the number of branches ending in male 

 flowers, and the correlation of any character with number of branches 

 ending in male flowers may to some extent follow as a secondary relation 

 to the correlation between the character in question and total leaves. 

 On the other hand, it is obviously absurd to reason that branches ending 

 in male flowers may influence the total leaves; and to correct the cor- 

 relation with total leaves by making branches ending in male flowers 

 constant might represent a mathematical relation, but the determination 

 would have no biological significance. 



An attempt was made to determine whether the more striking disherent 

 correlations might result from the correlations of other interrelated char- 

 acters. Thus height and the index of nodes silking on the third branch, 

 which showed a disherent correlation of —0.46, were found to be mu- 

 tually correlated with four other characters to an extent that would 

 materially influence the correlation in question. The partial correlation 

 of height and index of nodes silking on the third branch with all of the 

 164175°— 20 3 



