46 Mr. E. C. Snow. Correlations between Collaterals [June 3, 
which can be obtained by taking any one in the first generation with any one 
of the same stock in the second generation (7.c. both sons and nephews). 
To economise space, the details of the terms are given in the case of three 
only of the nine pairs. The other six can be written out in the same 
manner, but the results alone are stated. The three pairs given in detail 
are :— 
~ Member of the first generation (AA), member of the second genera- 
tion (AA)— 
p®.16s.4¢.16s+4p%y.16s. (4¢.85+4+2¢. 8s) 
+489? 16s (40.454 22.85) +4+2p%9?. 16s. 2¢.16s 
+4p*°9?. 16s. 2¢.8s+4p'q.8s(4t.85+4+2¢. 8s) 
+ 16p%9?. 8s (4¢.4s4+2¢.454+2t.45+¢. 4s) 
+16p°q°. 8s (40. 28427. 45420. 28+. 4s) 
+ 8p°q?. 85(2¢.8s+7¢.8s)4+16p%q'. 8s(2¢.45+t. 4s) 
+499? .45(4¢.45+21.8s)4+16p%9?.45(4¢. 284+2¢.4542¢. 2547. 4s) 
+ 16ptq*. 4s (4¢.84+2¢.284+2¢.2s+7. 4s) 
+8p1q*.4s (2t.4s+¢.8s)+16p%9° . 4s (27. 2s+7t. 4s). 
When these terms are collected, and simplification performed, the whole 
expression reduces to the simple form 
912s*t p® (p+q) (2p +9). 
Member of first generation (AA), member of second generation (Aa)— 
4n'g.16s.2t.8s4+4p%q?. 165(2¢.88+4t.4s5)42p%?. 16s. 2¢.16s 
+4p°9?.16s (2t. 8544. 8s)+ptg*. 16s. 4¢.165 
+4'¢.8s8.2t. 85+ 16p%9?.8s(2¢.484 2¢.45+2¢. 4s) 
+ 16p°¢?.8s (2t.28s+2t.4s4+2¢.4s+4t.2s+2¢.2s) 
+8p°q?. 8s (2t.8s+42t.8s)4+ 16p19!. 85(2¢. 454 2¢.48+4t.4542t. 45) 
+4p%9° .88(4t.8s4+2¢.8s)+4p%o? .45(2¢.85+40. 4s) 
+ 16p°q?.4s(2¢.4s+4t.2s4+2¢.2542t.4542¢. 2s) 
+ 16ptg*.4s(2¢.2s4+4¢.5s4+2¢. 2542¢.454+2t.25+4+4t.542t. 2s) 
+ 8ptg*.4s(2¢.4s4+2t.8s4+2t. 4s) 
+ 16p%9°. 48 (2¢.284+2¢.4842¢.284+4t. 284 2¢.4s) 
+4798 .45(4¢.454+2t.8s). 
This, when simplified, becomes 
d12s*t p’¢ (p+q)*(8p+q). 
