MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 241 



will produce changes in all other organic characters, which, if small, are still sensible 

 and capable of quantitative expression.* 



(6) Returning now to the algebra of our investigation, \ve have to discuss the 

 second part of (xi.) by aid of the formulae given in (viii.), p. 237. 



We require, in the first place; to evaluate the determinant A. 



Now 



A = 



Divide the first row by - ~T\> ^ ne second row by 

 j- , the first column by cr,, and the second by a-.,. Hence 



, the third row by 



Subtract the second column from the first, and then add the first row to the 

 second ; we have 



A = 



2 



r , 



1 + >*, 



The minors are now easily found to be 



2n- 



A u = 



4n 



2*'. 



Ao, = 



Aoj 



* Take (xvii.) below, for example; it expresses for the first time quantitatively the important 

 biological principle that, if a group be selected at random from the general population, and it has more 

 variability in one character, it will be more variable than the general population in all other characters. 

 VOL. CXCI. A. 2 I 



