January 3, 1902 ] 



SCIENCE. 



variability of tlie individual cells that con- 

 stitute an organism must always be greater 

 than the variability of the whole organism. 



It may be well to illustrate the effects of 

 correlation by assuming simplified condi- 

 tions of correlation. 



Assiuning first, that the elements may be 

 classed in a limited number of groups, each 

 consisting of interdependent ' elements, so 

 that the enlargement of one element of each 

 group would necessitate a definite amount 

 of enlargement of all the others. Further- 

 more be it assumed that the chances of a 

 small number of these groups being en- 

 larged are subject to accidental causes. 

 Then the probability that one, two, three, 

 or more of these groups are affected can be 

 calculated according to the binomial law. 

 Each group would contribute a definite, in- 

 variable amount to the total variability and 

 the general variability would, therefore, 

 also conform to the binomial law. 



We will next assume a case which is 

 somewhat nearer natural conditions. When 

 we count and measure the total number of 

 elements in all the individuals of a vari- 

 able series, we obtain certain definite num- 

 bers of elements of various sizes and we 

 can express numerically the frequency or 

 probability of each size. In order to sim- 

 plify matters, we will speak only of ele- 

 ments of decreased size and of enlarged 

 size. The proportion of these two classes is 

 definite in the total number of elements be- 

 longing to the different organisms of the 

 series. If inside of each organism there 

 were no correlation, then the proportion of 

 large and small elements in each organism 

 would, on account of the great number of 

 elements, correspond to their proportions 

 in the whole mass of elements. On account 

 of the existence of correlations in each 

 organism the occurrence of each enlarged 

 element will have the effect, that an addi- 

 tional number of enlarged elements may be 

 expected in the same organism, and the 



occurrence of an element of decreased size 

 will add to the probability of elements of 

 this character in the organism in which it 

 occurs. The arrangement of these elements 

 becomes, therefore, similar to that in a 

 mechanical mixture of elements of two 

 sizes, which are not uniformly distributed, 

 but in which large and small parts cluster 

 together. It is qi^ite clear that the varia- 

 bility of distribution in such a mixture 

 must be quite different from that found in 

 cases of even mixtnre. It will depend en- 

 tirely upon the distribution of large and 

 small elements, and the number of ele- 

 ments of both classes that are found in a 

 unit of space, how their proportion in each 

 unit of space will vary. 



We may obtain an insight into such 

 variabilities by a consideration of the re- 

 sults obtained by taking a certain number 

 of contiguous balls out of a row containing 

 large and small balls that are not thor- 

 oughly mixed. The two arrangements 

 given under 1 and 2 may serve as examples : 

 !■•••••••••• 



2. ••• ••••••• 



If four contiguous balls are taken out of 

 each of these rows, we find that in the 

 dra-\vings made from tlie two series large 

 balls occur as follows: 



4 large balls 



3 " 



2 " 



1 " ball 



Evidently, the distribution in cases of 

 this kind cannot be foretold. This result 

 may be expressed in a more general form 

 as follows: If only one series of elements 

 of an organism are interdependent, and all 

 the others independent, the variability of 

 form of all the individuals will depend 

 primarily upon the distribution of disturb- 

 ances in the interdependent elements in the 

 whole series of indi^'iduals. Therefore the 

 distribution of variations cannot be fore- 



