1910.| ina Mendelian Population Mating at Random. 47 
Member of first generation (AA), member of second generation (aa)— 
16 p°9?.8s.¢.48s+16p%¢°. 8s(¢. 484+ 2¢.28)+8p*9?.8s.t.8s 
+16 ptq*. 88 (¢.48+4+2¢.4s)+4p%9°. 8s. 27.85 
+16p°9%.4s(¢.4542¢.2s)+16pt¢*. 4s (¢.484+ 2¢.284+2¢.25447.s) 
+ 8ptgt.4s(¢.8s+4+2t.4s)+16p%9°. 48 (¢.4842¢. 2s+2t.45+47. 2s) 
+479 .48(2t.8s+4t.4s). 
This reduces to 512's*é 797 (p +9). 
The frequencies of the other pairs are (the member of the first generation 
in each case being placed first) 
(Aq@) with (AA)...... 512s*tp*9 (p+q)'(GAp+ 9), 
CAG: an, (AG) Aes 512s%t pq (p+q)* (p?+ 69+ 9°), 
CAG). SAG). se 512s7¢ pq? (p+q)* (p+ 349), 
(lO). 5. NAN occ 512s*¢ pq? (p+q)4, 
(COT eniog G2) eaenre 512s*t nq? (p+ ¢)' (p+ 39), 
(GG) CE eae 512s*t 9° (p+q)* (p+ 29). 
Subtracting from these expressions those found for the corresponding 
combinations in the case of parent and offspring of the second generation 
given above, we get the following frequencies for combinations of uncle and 
nephew :— 
Uncle (AA), nephew (AA)... 64st p? (p+ q)*[(16s— 1) p+(8s—1) gq], 
Pe COEA),. 5 (Aa)... 64st pg (p+q)t | (24s—1) p?+(8s—1) pq], 
mee AA) _,, (aa) ... 51287 p2q? (p+q). 
5) (GG) a (AA)... 64st pq (p+ 9) [(248—1)p? + (88—1) pq], 
Pe (Aa), ui (Aa)... 64st pq (p+q)' [(8s—1) p?+(48s—2) pg + 
| (8s—1) 
Pe eAa): if (aa) ... 64st pq? (p+q)' [(8s—1) p+(24s—1) 1 
» (a0), 5, (AA)... 51 28% pg? (pt git 
ee (ae), ‘ (Aa)... 64st pq? (p+q)' [(8s—1) p+ (248—1) g], 
» (ao), , (aa) ... 64st ¢° (p4+q)' [(8s—1) p4+(16s—1) g]. 
Correlation tables can now be formed from which to derive the gametic 
and the somatic relationships between uncle and nephew. Table V gives the 
gametic relationship; Table VI the somatic. In both of these tables the 
factor 64 st(»+q)*, which multiplies every cell, has been omitted. 
