SCIENCE. 



[N. S. Vol. XV. No. 366. 



told. The same is true if the number of 

 groups of interdependent elements is small. 



When, however, the number of these 

 groups of interdependent elements is some- 

 what greater and each group of correlations 

 is independent of the other, then the con- 

 ditions approach again those described be- 

 fore, when we assumed a nvimber of groups 

 in which the size of one element of a group 

 determines the sizes of all the other ele- 

 ments of the same group. We may then 

 expect to find a distribution the type of 

 which is determined by the binomial law, 

 because the combinations of groups that 

 occur in each individual are determined by 

 this law, while the law must be modified by 

 the variability of the size of each correlated 

 group, taken as a total. It is quite e\'ident 

 that the resultant curve must be similar in 

 its general character to the series of bi- 

 nomial points, but continuous on account of 

 the variability of each group. This phe- 

 nomenon is still further complicated by the 

 variation in the number of elements, the 

 effect of which was discussed before. 



We may reach the same result by assum- 

 ing that the form of the whole organism is 

 afl'ected by a limited number of causes 

 variable in intensity, each of which in- 

 fluences to a measurable degree the form of 

 the organism. The combination of such 

 groups of independent causes, limited in 

 number and each having measurable results 

 will bring about a distribution of varia- 

 tions of the same character as the one de- 

 scribed before. The phenomenon, ex- 

 pressed in this manner, does not differ from 

 the expression found before, because it does 

 not seem probable that each cause would 

 affect all the elements comprising the or- 

 ganism in the same manner. It seems much 

 more likely that certain groups of elements 

 will be affected more by one cause than by 

 another. At the same time, it is possible 

 that the same element may be subject to 

 several causes and thus belong to various 



groups of coi-related elements. Karl Pear- 

 son 's discussions have shown that many dis- 

 tributions can be explained satisfactorily 

 by assuming that they correspond to a con- 

 tinuous function determined by the points 

 binomial. 



It will be noted that, on the whole, the 

 greater a variable measurement, the more 

 nearly will the distribution of variations be 

 symmetrical and in conformity with the 

 exponential law. This may be expected, 

 because the greater the measurement, the 

 greater will probably be the number of in- 

 dependent, correlated groups. The in- 

 crease of their number necessitates an ap- 

 proach to the exponential law. On the 

 other hand, the smaller the measurement, 

 the more probable that a great part of its 

 constituent elements are subject to the 

 same causes, so that the conditions are 

 favorable to the combination of a small 

 number of independent causes, each of 

 which brings about considerable variation, 

 so that we may expect as a resultant skew 

 distributions of variations. 



It would seem, therefore, that the whole 

 range of phenomena of variability can be 

 understood on the basis of our conception 

 of the relations between the variability of 

 the small constituent elements of an organ- 

 ism and the variability of the organism 

 itself. We are justified in drawing the fol- 

 lowing conclusions: 



1. The elements of organisms are more 

 variable than the organisms themselves. 



2. The elements of organisms vary in 

 correlated groups. 



3. The characteristics of the variability 

 of an organism dej^end upon the correla- 

 tions of its constituent elements, so that a 

 knowledge of these correlations will enable 

 us to determine the characteristics of the 

 variability of the organism. 



It follows from this that the problem of 

 variability may be treated by a study of 

 the variabilitv and of the correlations of 



