SCIENCE. 



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



stituted in which the total number of cells 

 is the same, we find that they cannot pos- 

 sess any variability, because the variations 

 of the constituent cells would compensate 

 each other. This can be proven as follows : 

 If we determine the form of an organism 

 by a number of measurements taken in 

 various directions, then each measurement 

 may be considered as made up of many con- 

 stituent elements. On the average, the 

 variability of the combined elements will 

 be proportionate to the square root of the 

 number of elements, while the value of the 

 total length of the combined elements will 

 be proportionate to their number. If, 

 therefore, the number of elements is very 

 great— and there is nothing to hinder us 

 in assuming each element as very small and 

 their number as very great — the variability 

 of the whole measurement must be very 

 small, according to the small value of the 

 proportion between the square root of the 

 number of elements, and the number of 

 elements. Since this contradicts the fact 

 that all organisms are variable, it follows 

 that the elements cannot be constant in 

 number and mutually independent. This 

 conclusion is obvious from a morphological 

 point of view, but it seemed desirable to 

 point out that the independence and con- 

 stant number of elements would entail lack 

 of variability in the whole organism. 



If the elements were independent of each 

 other but varied in number, we might as- 

 sume in accordance with morphological ob- 

 servation that each group of elements had 

 a certain limited period of multiplication 

 which proceeds at a definite average rate. 

 Then it may be said that this period under- 

 goes certain changes that are due to chance. 

 If this were the case, the size of the organ 

 would increase approximately in geometric- 

 al progression when the period increases 

 in arithmetical progression. 



It is probable that, on the whole, the 

 periods of development of various organisms 



vary around the typical period accordingto 

 the laws of chance. Then the frequencies of 

 periods belonging to different individuals 

 would be arranged symmetrically around the 

 typical period, while the measurements cor- 

 responding to each period and belonging to 

 different individuals would be arranged 

 asymmetrically around the type, in accord- 

 ance with the relations between size and 

 period. It is quite evident that the ob- 

 served distributions of variations around a 

 type do not generally conform with a law 

 of this character, and therefore this theory 

 must also be rejected as insufficient, al- 

 though we recognize that it may explain a 

 part of the general phenomena of varia- 

 bility. 



It is, therefore, necessary to assume the 

 elements of organisms to be correlated. 

 This is entirely in accord with the evidence 

 of morphology and of pathology. If the 

 number of elements is assumed as constant, 

 it is easy to determine what the results of 

 such correlation must be. ' Correlation ' 

 means that the change in form and size of 

 one element influences more or less the 

 forms and sizes of other elements. Such 

 correlated elements may either be con- 

 tiguous, or they may be related in some 

 other way. The degree of their relation 

 may be expressed by an index of correla- 

 tion. 



If the correlation of all the elements were 

 perfect, that is to say, if a change in one 

 would necessitate a corresponding change 

 of a certain definite amount in all the 

 others, the variability of the whole organ- 

 ism would be proportioned to the average 

 variability and number of the homologous 

 elements. This condition is as unlikely as 

 that of complete independence of the ele- 

 ments. We must draw the conclusion that 

 the variability of the organism as a whole 

 will always be less, in proportion to its size, 

 than the variability of its constituent ele- 

 ments; or, as we might perhaps say, the 



