50 Mr. E. C. Snow. Correlations between Collaterals [June 8, 
First grandchild (AA), second grandchild (AA)— 
pr.s. 64k (644—1)+4p'¢. 3.484 (48k—1)4+ 4p'9? . 4. 32k (82k—1) 
+2p%¢?.4 32h (82h—1)+4p°¢?. 4. 16k 16k—1)+4p%q.4. 48% (48k—1) 
+16p%?.3$.362(3864—1)+16p%9?.4. 244(244—1)+ 8p'q?. 4. 24k(24h—1) 
+16pt¢*.4.12k 12k—1)4+4p%9?.4.32k (82h—1)4+ 16 p%¢?.$. 24h (24k—1) 
+16pt¢!. 4.164 (164—1)+8p4yt. 4.164 (16k—1)4+16p39°. 4. 8k(8k—1) 
+ 2p%9?.4.382h(82k—1)+8p¢?. 3. 24h (24h—1)4+ 8ptq* .$. 164 (16k—1) 
4-4p%9*.$.164 (164—1)4+ 8p%9?.4.84 (8k—1)+4p°¢?. 4.164 (164-1) 
+16pt9*. 5.124 12k—1)+16p%9?. 4. 8k (8k—1)4+8p%9°.§. 8k (8k—1) 
4 .4h(4h—1). 
This reduces to 
32st p? (p+q)* [(64st —1) p? + (82st —2) pq +(4st—1) g?]. 
First grandchild (AA), second grandchild (Aa)— 
Ang .48k.16k +4 p89? . 32k. 382kh+4+ 2%? . 32k. 32k 
+4°9?.16k.48k+4p%¢.48k.16h4+16p%o?. 36k. 24k 
416 p93. 24h. 32k+8p%q?. 24h. 32k+ 16ptgt. 12h. 40k 
+4897. 32k. 32k+16p%9?. 24k. 32k+16ptg*. 16h. 32k 
+ 8ptgt.16k.32k+16p%q°. 8k. 32h 2 pq? . 32k. 32k 
+8p°q?. 24k.32k+8ptq*.16k.32k+4ptq* . 16k. 382k 
+8p%¢°. 8k. 32k+4p%°q?. 16k .48k+ 16pt¢ 12k. 40% 
+16p%9°.8k .32k+8p%9q°. 8k .32k+4+16p?¢° 4k. 24k. 
This becomes 512s*t? y?¢ (p+q)* 12p4+ 39). 
First grandchild (AA), second grandchild (aa)— 
16p%@? . 36k .4h416 p°¢?. 24k. 8k+8p%9q?. 24h. 8k 
+ 16ptg* .12h.12k+416p*9?. 244.8% 
+16p%q* 16% .1644 8p4gq*. 16% .16k+16p%9°. 8k. 24k 
+ 8pq?. 24k .8k+8ptq*.16k.16h+4pt¢* 164.164 
+8p%9>. 8k. 24k4+16ptqt.12k.12k+4+16p%9°. 8h. 24k 
+8p%¢°.8k.24k+416p7¢°. 4h. 364. 
This becomes 2304: s?t? pq? (p+ q)t. 
The other combinations reduce to :— 
‘First grandchild (Aa), second grandchild (Aa)— 
64st pq (p+q)* [(16st—1) p?+(104st —2) pg + (16st-—1) 9]. 
L 
2 
ae 
2 
+1679. 
