PROF. K. PEARSON ON THE MATHEMATICAL THEORY OP EVOLUTION. 77 
If h be any standard length, say 10 or 100 units, then the 7Mh moment is of the 
order h"a, if a be the area of ABC. It therefore equals /xVt"a, where is a purely 
numerical factor. We shall invariably represent it as the product of these three 
factors. 
(ii.) Given the first n moments about y'y', or the coefficients p-'j, ph, p'g, p'^ . . . p’„, 
to find the nth moment about yy or the coefficient p„. 
Let the distance between yy and y'y' be d = q/q then 
or 
p« 
— nqyf ,i_ I + 
n (M — 1) , 
^ _ 2 "“2 
11 (n 
1) (n — 2) 
+ , &C. 
In particular, since jj-'o = 1, 
H-i = H^i — 
P'3 = p'a “ 22 p'i + <f 
P3 = p's — 3 (?p'3 + 
Pi = P'i — 42 p' 3 + 6q2p'3 — 4gV'i + 
Po = P'o - S^p'i + lO^/p's - lOsVa + 5?V'i - 
(J). 
When the line y'y' passes through the centroid of the curve, and the curve is 
symmetrical about y'y' p\, p'g, p'g are all zero. Hence if in this case we take yy to 
the right of y'y', or d negative, 
