TO THE THEORY OF EVOLUTION. 
23 
same character in brethren, and even in this case the statistics ought to be collected 
ad hoc, i.e., we ought to make a very full quantitative order, and then notice for each 
individual case the number above and below the type. For example, suppose we had 
a diagram of some twenty-five to thirty eye tints in order (e.g ., like Bertrand’s), 
then we take any individual, note his tint, and observe how many relatives of a 
particular class—brethren or cousins, say—have lighter and how many darker 
eyes ; the difference of the two would be the excess for this individual. The same 
plan would be possible with horses’ coat-colour and other characters. After trying the 
plan of the excesses on the data at my disposal for horses’ coat-colour and human eye- 
colour (which were not collected ad hoc), I abandoned it for the earlier method of 
this Memoir ; for, the classification being in large groups, the proportioning of the 
excess (as well as the differences in the means) introduced too great errors for such 
investigations. 
§ 7. On a Generalisation of the Fundamental Theorem of the Present Memoir. 
If we measure deviations in units of standard deviations, we may take for the 
(lxx.), 
equation to the 
correlation 
surface for 
n variables 
N 
j 
— e 2 
+ 2 S 2 ( E - 
rv. 
(27 rf‘^/R 
where 
R = 
1 
A2 
? ’l 3 • 
• • Ail 
Ai 
1 
^*23 • 
■ • A;, 
An 
r 32 
1 . 
• A» 
Ai-1 
, 1 Ai- 
-1,2 
^ n— 1, 
3 • • • 
1 
^ 71 — 1 , n 
Ai, 1 
V n, 
0 
Ai, 3 
.... 
Ai—1, n 
1 
and ~R pq is the minor obtained by striking out the jpth row and yth column. r pq is, of 
course, the correlation between the _pth and qth variables, and equals r qp . denotes 
a summation for s from 1 to n, and S 2 a summation of every possible pair out of the 
n quantities 1 to n. 
Now take the logarithmic differential of z with regard to r pr We find 
1 dz 
z dr, 
n 
1 dR 
r M 
2P. dr.„ ^‘{*>,( 1 ; ' :C ' 2 
V + MTp - * 
J pq j q I -t-^ps ^qs ^ 2 \ | g / - li 2 W J - t qs' T ^ps' J - t ’qs 
Er/5/ "I" Efij' -Rtf 
R 2 
OCoOCc 
For 
dK/dr pq — 2 Ft 
J M 
