MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 269 



Subtract the first column from the second, and add the double of it to the last, 

 we deduce 



A __ * 1, 0, 



P ^ " 0, (p 1) S, 



or, 



A = ., --' - . (xlvii.). 



The minors can now be written down at once. 



M_J t // | -L / Ifj O 

 M = ^/,-^iy ' 



whence 



, _ _ p_} ... 



or 



2,, = cr/^/n . (xlviii.). 



M., = '- , 

 p 1 



whence 



2;, = Mo., /A = p'/nB, 

 or 



V _L . / _ ^vllY ^ 



2, t , ^ A / Q ^AIIA.^. 



v n v o 



P (.P ^ ) 

 whence 



2; = M M /A = ~ ( 1 + , 

 tn \ ^o / 



or 



+ i) (i.). 



\ *"/ 



M = -^y , 



whence 



Wtt + S)} (") 



M 12 = 0, 

 whence 



B*, = (Hi.)- 



