142 
Vai'iation and Inheritance in Aphis 
is different from that to which the parents were subjected, then the correlation of 
organ B between parent and offspring would not necessarily be changed. 
We saw above that the con-elation between frontal breadth and length of 
antenna in the individual was 8028, and now we wish to know the correlation 
between the frontal breadth of the mother and the length of" antenna of the 
offspring. The correlation table is given in Table XIII. ; the coefficient of corre- 
lation is -3004 + -0320. 
TABLE XIII. 
Frontal Breadth of Parents and Length of Antenna of Offspring. 
Offspring: Length of Antenna. Unit = 2 divisions of Ocular Micrometer = •0442 mm. 
S( 
1 
O 
?>( 
1 
9) 
Ci 
<?( 
1 
Oi 
>-s 
eo 
1 
9> 
5^ 
s 
1 
C5 
lb 
=■0 
1 
C5 
CO 
'i 
9^ 
1 
00 
1 
03 
T 
05 
1 
Cl 
C2 
■<^ 
1 
o 
Ad 
lO 
1 
o 
Weighted 
Mothers 
Number 
of 
Families 
14-0—14-9 
2 
3 
1 
6 
1 
15-0— 15-9 
2 
4 
7 
6 
8 
6 
8 
8 
2 
3 
5 
1 
1 
61 
9 
16-0— 16-9 
1 
0 
5 
9 
13 
15 
28 
27 
20 
9 
7 
2 
2 
138 
25 
17-0— 17-9 
1 
9 
I 
8 
8 
9 
9 
8 
8 
1 
68 
11 
18-0— 18-9 
3 
11 
13 
11 
13 
10 
5 
2 
1 
75 
11 
19-0— 19-9 
1 
1 
2 
3 
3 
10 
2 
20-0— 20-9 
2 
5 
2 
1 
10 
1 
Totals 
1 
2 
12 
31 
33 
42 
55 
56 
51 
33 
31 
15 
5 
I 
368 
60 
Also we saw that the correlation between the frontal breadth {AB) and the 
CD 
ratio -rj\ of the individual was + '3200. In Table XIV. is shown the correlation 
AB 
distribution for the frontal breadth of mother and the ratio of offspring; the 
coefficient of correlation is '1688 + '0342. 
Now let us calculate the values of the cross-correlations by aid of Professor 
Pearson's theorem* that: 
Cross-inheritance = mean of direct inheritances x organic correlation. 
We find in the first case: 
Cross-correlation = | (-3354 -f- -4273) x -8023 = -3059, 
and in the second case : 
Cross-correlation = \ (-3354 -|- -4392) x -3200 = -1239. 
The first result is in good agreement and the second as close as could be 
anticipated from the large probable errors of our I'esults. 
* R. S. Proc. Vol. 62, p. 411. 
