No. 572] SHORTER ARTICLES AND DISCUSSION 493 



III. Let us see how this formula works out in a concrete case. 

 Assume the same conditions of fertility as in the former paper, 

 that is, put 2s = 32, or 5 = 16. Start with a single AA + 2Aa 

 + aa family. 



Then 0,^ = 0, 



Then in the next generation we shall have 

 16(0 + 1/4(0) +1/16(1) } = 1AA family 



+ 16(1/2(0) + 1/4(1) }=MAA-\-Aa) families 



+ 16 ( 1/8 ( 1 ) } = 2 Aa families 



+ 16(1/2(0) + + 1/4(1)} = 4(AA +2.4o + aa) families 

 + 4(J.a + aa) families 

 + laa family. 

 This is the fact. 



In the next generation we shall have 

 16(1 + 1 + 1/16(4)} =36AA families 



+ 16(1/2(4) + 1/4(4) } =48(AA + Aa) families 



+ 16(1/8(4) } = 8Aa families 



+ 16(1/2(4) + 2 + 1/4(4)} = 80(AA + 2Aa + aa) families 

 + 48 (ifl + oa) families 

 + 36(aa) families. 

 This is the fact. 



In the next generation we shall have 



16(36+ 1/4(48) +1/16(80)} =16 X 53 = 848AA f amilies 

 + 16(1/2(48) + 1/4(80)} =16 X 44 = 704(^A + Aa) 

 families 



+ 16(1/8(80)} = 160.4a families 



+ 16(1/2 (48) + 8 + 1/4(80) } = 16 X 52 = 832 (AA + 2Aa 



+ aa) families 

 + 704(,ia + aa) families 

 + 848aa families. 

 Succeeding generations follow the same law and need not be 

 worked out in detail. 



IV. So far the discussion has confined itself to families, as this 

 must be the basic unit in the theory of any form of inbreeding. 

 Turning to individuals we have the following simple relations to 

 pass to individuals. 



In the nth. generation the number of 



