8 J. ARTHUR HARRIS. 



proportion of the two types of spore bearing organs is correlated 

 with the total number of sporophylls, which in lieu of any better 

 character may serve as a measure of the total influence of in- 

 trinsic and extrinsic factors influencing degree of development. 



Several years ago Professor Pearson and I (Harris, '09) showed 

 that problems of this kind can be approached by determining the 

 correlation between the total organs laid down and the deviation 

 of the number of a particular kind from the probable number on 

 the assumption that the proportion of the particular kind is 

 independent of the total number. 



The statistical method may of course be applied to experi- 

 mental data or to series of determinations made on organisms 

 developing under natural conditions. As yet experimental 

 series are not available. 



In a former paper ('16) I showed that in the inflorescences of 

 both Arisarum vulgare and A. proboscidium there is a significant 

 negative correlation between the total number of flowers and 

 the deviation of the number of staminate flowers from their 

 probable number on the theory of proportional distribution. 

 Thus the male flowers while absolutely more numerous in the 

 inflorescences with larger total numbers of flowers are relatively 

 less numerous than in the inflorescences with smaller total num- 

 bers of flowers. Or, conversely, the larger inflorescences tend 

 to produce a larger proportion of pistillate flowers. 



In this paper the same analytical methods will be applied to 

 the problem of the relationship of the number of stamens and 

 the number of pistils to the total number of stamens and pistils 

 produced by the flower. 



II. MATERIALS. 



The materials upon which the coefficients discussed in this 

 paper are based have been tabled and the chief biometric con- 

 stants deduced by competent statisticians. The special methods 

 upon which the conclusions of this paper are based were not, 

 however, available at the time their calculations were made. 

 The results are, therefore, quite new. 



The series employed are the following: 



1-2. A series of 283 countings of number of stamens and 



