1910.] ina Mendelian Population Mating at Random. 51 
First grandchild (Aq), second grandchild (av)— 
51297? pq? (p+q)* (Bp +129). 
First grandchild (aa), second grandchild (aa)— 
32st g? (p+ ¢q)* [(4st —1) p? + (62st —2) pg + (64st —1) ¢’]. 
To obtain the frequencies of the various pairs of cousins, we have to 
subtract from the above six expressions the corresponding expressions for 
pairs of brothers. We then get the following frequencies :— 
Both cousins (AA)—32 st? p?(p + 9) [64s—4) p? + (382s—4) pg + (4s—1)¢°]. 
One cousin (AA), other (Aq)... 128s¢? p?¢ (p+ ¢) [(48s—2) p+(12s—1) ¢]. 
f (AA), , (aa)... 64st? p?q?(p+q)* (86s—1). 
Both cousins (Aa)— 
128st? pg (p + 9)* |(8s—1) p? + (528—3) pg + (88—1) ¢"}- 
One cousin (Aq), other (aa)— 
128 st? pq? (p+ 9) [(12s—1) p + (48s—2) q]. 
Both cousins (aa)— 
32st? ¢? (p+) [(4s—1) p? + (828s—4) pg + (64s—4) ¢']. 
The correlations tables for cousins can now be formed. Table VII gives 
the arrangement for the gametic relationship, Table VIII for the somatic. In 
both cases the factor 64 st?(y+q)* has been omitted. The tables must, of 
course, be made symmetrical. 
Table VII.—Gametic Correlation between Cousins. 
(Factor 64 st? (p+q)* omitted.) 
First cousin. 
Second 
a i ae Totals. 
(AA). (Aa). (aa). 
(AA) | (64s—4) pt + (82s—4) p%q |(96s—4) p3q + (248—2) pq? (36s—1) p?¢? 4 (16s—1) p? (p+q)? 
+ (4s—1) pq? 
(Aa) |(96s—4)p%q + (24s—2) p?q? (32s—4) pig (24.s—2) pq* + (96s—4) pq’, 8 (16s—1) pq (p+)? 
+ (208s—12) pq? 
+ (82s—4) pq? 
(aa) | (36s—1) p’¢? (24s—2) p*q? + (96s—4) pq? 
(4s—1) pq? + (82s—4) pg?| 4 (16s—1) 4? (p+q)? 
+ (645—4) q' 
Totals 4(16s—1) p> (p+q)? 8 (16s—1) pg (p+q)? | 4(16s—1) g?(p+q) 4 (16s—1) (p+q)* 
