RELATIVES ON THE SUPPOSITION OF MEN DELIAN INHERITANCE. 407 
types of mating down to the second generation. The three Mendelian phases will 
yield six types of mating, and ordinary cousinships are therefore connected by one of 
six types of sibship. The especially interesting case of double cousins, in which two 
members of one sibship mate with two members of another, can occur in twenty-one 
distinct ways, since any pair of the' six types of sibship may be taken. The pro- 
portionate numbers of the three Mendelian phases in the children produced by the 
random matings of such pairs of sibships is given in the accompanying table : — 
Type of sibship . 
1 . 
0. 
0 
1 
. 1 . 
0 1 
0. 
1 . 
0 
1 . 
2 . 
1 
0 
. 1 . 
1 
0 . 
. 0. 
1 
Frequency . . 
P 4 
4 p 3 q 
1 
2 P 2 q 
2 
4 P\ 
4 pq 3 
qi 
P 4 . 
1 
.0. 
0 
3 
. 1. 
0 
1 . 
1 . 
0 
1 . 
. 1 . 
,0 
1 
. 3. 
0 
0. 
. 1 . 
0 
4 p 3 q 
3 
. 1 . 
.0 
9 
. 6. 
1 
3. 
,4. 
1 
3, 
. 4 . 
1 
3 
. 10. 
3 
0, 
. 3 . 
1 
2j? 2 2 2 
1 
. 1 . 
. 0 
3 
. 4. 
1 
1 . 
, 2 . 
1 
1 , 
. 2 . 
1 
1 
. 4. 
3 
0 
. 1 . 
1 
4 p 2 q 2 
1 
. 1 
.0 
3 
. 4. 
1 
1 1 
.2. 
1 
1 
2 
. 1 
1 
. 4. 
3 
0 
. 1 . 
1 
ipq 3 
1 
.3, 
. 0 
3 
. 10. 
1 
1. 
.4. 
3 
1 
. 4 . 
, 3 
1 
. 6. 
9 
0 
. 1 . 
3 
q i 
0 

. 1 
. 0 
0 
. 3. 
1 
0 
. 1 . 
1 
0 
. 1 . 
. i 
0 
. 1 . 
3 
0 
. 0. 
1 
V 
.0 
3 P 
P + 3g q 
P 
1 
<1 
P 
1 
2 
p 
3 p + 1 
q 3 q 
0 
. a 
\ F 
' 
4 
4 
4 
\ 2 • 
2 
' 2 
2 * 
”2 
* 2 
4 ■ 
4 
' 4 
• Jr 
• 'i 
The lowest line gives the proportions of the phases in the whole cousinship whose 
connecting sibship is of each of the six types. 
If we pick out all possible pairs of uncle (or aunt) and nephew (or niece) we obtain 
the table 
p 3 (p + k) 
*P 2 <Z(3 p + q) 
ipY 
| p 2 q(3p + q ) 
%pq(p*+6pq + q 2 ) 
\P<?{P + 3?) 
w 
\vq\p + 3 q) 
<?(hP+q) 
the quadratic from which reduces exactly to 5/d 2 , showing that when mating is at 
random the avuncular correlation is exactly one half of the paternal. 
From the twenty-one types of double cousinship pairs may be picked, the pro- 
portions of which are shown in the table : — 
p 2 {p + iq) 2 
1 p\(p + h) 
tVpV 
I p\(p + h) 
ipq{p 2 + 1 i-pq + q 2 ) 
I p<iWp + 2 ) 
t\pV 
| pq 2 (ip + q) 
q\\p + qf 
which agrees with the table given by Snow for ordinary first cousins. I cannot 
explain this divergence, unless it be that Snow is in error, my values for ordinary 
first cousins leading to less than half this value for the correlation. Simplifying the 
quadratic in i,j, k, which is most easily done in this case by comparison with the 
avuncular table, we find for the correlation of double cousins 
showing that double cousins, like brothers, show some similarity in the distribution 
TRANS. ROY. SOC. EDIN., VOL. LII, PART II (NO. 15). 63 
