MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 293 



ml (m, 1) 



s (w, 



o, 



m., I, 

 (TO, + TO.,), 



TO, + TOo/3, 



m&, 



m, 



4. m ., t 



A 24 = 



?l 3 (7?l, 



l s m t mr, (m 1 1)(? 2 1) 



- i, o, 



t,m.,e 3 , in, 2io -4- 1 



0, 2(m,+ TOO + 1) 



1 \ / 1 \ 



1, 

 0. 



TOO 2m, + 1, ('i + m -2 2) 



TOO (TO, 1) 



W,, TO,TO 2 C ; , 



(TO, + in., 2), w, 2j,, + 1) 



w, + TOO, (TO, 1), 



1, 



0. 



In our particular case we found 



e, = -232,4012, ., = "067,9945, e :! = '051,3099, 



m,a = -164,4934, m 2 ^8 = '607,8513. 



With the aid of the values for TO, and ni. 2 given above, the determinantal parts of 

 the A's were then calculated. If these be 8, ,,, , :i ,, a, 4 , a, 2 , a, :! , 14 , a.,.,, a., 4 , a ;J4 , 

 we have 



8 = '153,7969, 

 = '348,3713, 

 22 = 13-018,7332, 

 33 = 47-671,9443, 

 44 = 13-357,1309, 



,., =r '274,9969, 

 a, 3 = -111,8280, 

 a, 4 = '211,9650, 

 a., 3 = 22706,5156, 

 a., 4 = 11-507,0153, 

 OL^= 25-088,6121. 



From these the standard deviations and correlations of errors in the algebraical 

 constants are at once found. We have 



S 7l = -2325, 

 2 ffll = 7784, 

 t at = 5-5908, 

 2,, = 3-7602, 



R imi = -9387, 



R, jM2 = -7548, 

 R u = 7143, 



R Mi ,, = -8726, 

 ='9942, 



