

MATHEMATICAL CONTRIBUTIONS TO THE THEORY OP EVOLUTION. 257 



' /r r \ 



\ ? !.'> nji 



trjcrfffpl 5 



R+RU, -, 2 R,..., 



r, 2 R ia> R+R 22 , 



r T? i- T? 



' 13*->'13> '28-"28l 



0, R, 3 , 



o, 



o, ^~ 



2E 1 ., ! lt, 

 E 



0, 



E 



2E| 

 E 



Add the first three rows together, multiply by R, 2 /R and subtract from the fourth, 

 and by R..,.,/R and subtract from the fifth, we find 



M (r,,, r,,) = 



R + R u , 



R + Roo, 



R 12 , 



o, 



0, 



TV,,, 



R M , 



Multiply the fourth column by ?', 3 , and the fifth by r., 3 , and subtract from the third 

 column 



M (r 12) r ia ) = - 



+ RH. ^3i2, 



,.R ls , R + R, 2 , 



0, 



0, 



Rl3 



o 

 R 



-2R., 3 , -R, 3 , 0, 



Multiply the third row by r ]2 , and the fourth by 1 r; 2 or R 33 , and subtract the 

 latter ; the determinant now reduces to one of the fourth order, and we find : 

 VOL. cxci. A, 2 L 



