11 



quency of their occurrence, we get an ap- 

 proximation to the familiar curve of nor- 

 mal error. For the sake of simplicity, the 

 number of variable factors was made five 

 and the number of categories in which each 

 might occur was limited to two. If the 

 variables and the categories are made suffi- 

 ciently numerous, the curve of normal error 

 can be approximated within any desired 

 degree of exactitude. It is unnecessary to 

 point out the empirical fact that when the 

 sizes, weights, etc., of organisms or their 

 parts are divided into classes and the 

 classes are plotted against the number of 

 individuals in each class, the resulting 

 curve approaches the normal curve of error, 

 if a sufficiently large number of individ- 

 uals are used. Exceptional instances of 

 curves with more than one maximum, or 

 only parts of curves, are easily accounted 

 for and for convenience will be left out of 

 consideration. Since the empirical data 

 bear out the conclusions arrived at by the 

 above procedure, the explanation may be 

 considered valid. 



However, the explanation involves the 

 addition of the values of the various fac- 

 tors, which is in reality averaging them, 

 since' their value is measured in terms of 

 net gain or loss. Although this process of 

 averaging the various factors involved is 

 borne out by comparing the results with em- 

 pirical data, it is done, nevertheless, in con- 

 tradiction to the Law of the Minimum. Ac- 

 cording to this law n/S2 should be + 1 and 

 Zln/32 should be — 1, because all the fac- 

 tors are -f- 1 in only one permutation, and 

 — 1 occurs in all the others and would be 

 a limiting factor. The curve that would 

 result if the Law of Minimum held would 



