MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 311 



In both cases, therefore, we may consider that the sign of K is heyond question, or 

 that the type selected is really a significant character of the frequency. 



With regard to the probable error made in estimating a criterion to be zero, and 

 using a curve of type 



we must remark that, the criterion being assumed zero is equivalent to assuming 

 that its probable error is zero. Accordingly the only satisfactory method of testing 

 whether a curve really falls under this type is to work out the probable error of its 

 criterion on the hypothesis that it belongs to one or other of the two types, with 

 positive or negative criterion as the case may be. If the probable error of the 

 criterion thus calculated is sensibly as large as the criterion itself, then we may 

 assume that the frequency distribution is of the type 



