1910.] ina Mendelian Population Mating at Random. 41 
Table I. 
: oie SR 
First parent. 
Second a 
parent. 
pr(AA). 2pq (Aa). | ¢? (aa). 
p’ (AA) p* [16s (AA) } 2 p*q [8s (AA) +85 (Aa) ] pg? (16s (Az) ] 
7 29 (Aa) | 2p?g [8s (AA) +8s(Aa)] | 4p297[4s (AA) + 85 (Aa) + 45(aa)] | 2p9q3[8s (Aa) +85 (aa) | 
(a2) | pq’ [16s (Aq) ] 2pq° [8s (Aa) +85 (aa) ] | q* [16s (aa) ] 
(A.) Correlation between Brothers. | 
(7) From Table I we can pick out all the pairs of brothers and arrange 
them according to the gametic character exhibited by each member of the 
pair. The cases which can arise, and the number of pairs of brothers in each 
case are :-— 
Both brothers (AA)— 
pt. 4 .16s(16s—1)4+2p%q.4. sp Sais 
+2n%¢.4.8s8(8s—1)+4p7q?.4.4s(4s—1). 
Both brothers (Aa)— 
2p*q.4. es, 4. pen Ane i. 8s(8s—1) 
+479? .4.8s(8s—1)+2pq?.4. 85(8s 1p? g’.4.16s(16s—1) 
+ 2pq9°?.4.88(8s—1). 
Both brothers (aa)— | 
Ap*q?. 5.48 (4s—1)+2pq*.$.8s5(88s—1)4+ 2p9*.4.8s (8s—1) 
+g*.4.16s(16s—1). 
One brother (AA), other brother (Aa)— | 
2p°¢.8s.88+2p%¢.8s.88+4p?¢?.4s.8s. 
One brother (AA), other brother (aa)— 
Ag: 45 48. 
One brother (Aa), other brother (aa)— 
4n*q?.8s.48+2pq?.8s.8s+2pq?.8s.85. 
From the above expressions a symmetrical table can be constructed, from 
which to obtain the gametic correlation between brothers. This is given in 
Table II. By arranging the above expressions under the headings “ A” and 
“not A” another table can be formed to give the somatic correlation. This is 
given in Table III. In both tables the factor 16s, which ea ae every 
term occurring, has, for brevity, been omitted. 
