SELECTION ON THE VARIABILITY AND CORRELATION OF ORGANS. 
7 
where 
S = 
•^15 '^’l30'lCr3, 
i'-ZlO'iO'z, cr-^, '>'•13^2^3^ 
ni^iO-3, r.^(To(T^, a■3^ 
^ i«cr|Cr,; 
0'2 cr /, 
^ 3>t ^3^n 
^ ^ ^ ii3^3 ^hi 
and S^y is the minor corresponding to the constituent rp,^(Tp(Tq 
But S = (Ticr.f cr^ . . . cr,dB, 
a ^ 2 
^pq — ^ 
where R is the determinant, 
1) ^‘l2i 
(T„ 
^q • 
r. 
• 21 ) 
1, 
^ 31 ) '^'oZi 
F 
cr/R 
'^'vi 
rzu 
r.„ 
(xvi.), 
and Ry,y is the minor corresponding to the constituent Thus we have 
or, generallv. 
Thus 3 may he written'’ 
^'ii “ A 2 I’Ll/ 
_ 1 
a:r ll ’ 
ly 
^pq 
L^/ 'p 
1l a 
v / 
= ^ ] 
CTiCTy 
Vjy/R . . . 
. . (xvil.) 
: --- R^y/R .... 
O-pCTq 
(xviii.), 
) + 2Sj 
/ R'<7 ''Y'V \ 1 
\ h aj,a,J\ 
It remains to determine in from the fact that the volume of the surface = N. 
Or, 
r+r. - + X r + x 
N = i|j I I • • • expt. (— jQ) dxi d'x. 2 . . . dx„ 
• —DC* — X * — X 
px ,-+K 
r+ 37 
• — X • — X 
&c. 
■ J-X 
R 
R,: 
dx\ dx'o ■ ■ ■ dx'n. 
ISIow, integrate first with regard to x\ writing first 
(xx.). 
* ‘Phil. Trans.,’ A, vol. 187, p. 302. 
