TO THE THEORY OF EVOLUTION. 
33 
A numerical illustration of these formulae will be given in the latter part of this 
Memoir. It will, however, be clear that what we want are tables of log including 
lo g (jJ or log j for a series of values of h. Such tables would render the compu¬ 
tation of ^ fairly direct and rapid; they could be fairly easily calculated from 
existing tables for the ordinate and area of the normal curve, and I hope later to 
find some one willing to undertake them. 
Meanwhile let us look at special cases. In the first place, suppose, in the case of 
three variables, that the division of the groups is taken at the mean, i.e., h x — h» = 
h 3 = 0. Then we have 
0 , = & = & = JV»*&= v / p 
v = — v{" — 0 
v 2 = v 2 " = v 2 "' = —1 
% = V 3 = V 3 = 0 
v 4 = = v 4 = 3. 
Hence we have 
Q = I [ f o 2 <b\ dx s = Qo 11 + ~ (r n + r Y . + r M )| 
+ j? {Av + V + ns 3 )} + 4 j|-9 O-ss 5 + ni 5 + n/)} + ■ • • 
r 2 1 
— Qo j 1 + ~ (sin -1 r 12 + sin -1 r L3 -f sin" 1 r . 23 ) j.(lxxxv.). 
Let r 12 = cos D 12 , r l3 — cos D 13 , r 23 = cos D,, 2 , and let E be the spherical excess of 
the spherical triangle whose angles are the divergences D 12 , D 1S , D 23 . Then 
we have 
h* — Qo T. _ fiT T) "n T'i _ 7r tt 
o — o ~ ~~ ^ 13 ~ ^ 23 — 9 ” L. 
Qo 
Or 
sm 
Q — Q 0 7T 
Qo 2 
7 T = cos E 
(lxxxvi.). 
Now take the case of four variables. Here we have 
0, = ft = 0, = 0 t = 
V, — V , — V, — V, lv — 
Vi = 
= <" = V” = 3, 
and all the odd v’s zero. 
VOL. CXCV.—A. 
Hence 
