378 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
Adding and dividing out by 7 — 2, we have 
yen 6 (By = Bi ae) 
28, — 3B, — 6’ 
hence 
m=4(r + 2) 
is known. Further 
ye 
a 
“~— 5 
qa A (r — 2) 
16 r—1 
is known, whence 
p= /(z—7") 
Ponte a/ e v= 5) 
act 
is given.* Finally 
and 
4) See one 
a| sin’ 6 ce” dé 
0 
completely determine the problem. 
Remarks. The solution is clearly unique. 
(i.) To determine the skewness we must find the position of the ordinate for which 
dy/dx = 0; this is y= va/(2m) —— va/(r+2). 
But 
AS gyi DE, MMe Nee L OM 
d=—p,+u= pr oP +2. r(r+2) 
Hence 
skewness = d/,/ py 
2p y—1- r—2 Bn & 
= an, G J: +H = 4,/ By Panes (cf. Pp: 370). 



Hence, since 48, is always > 3, (see p. 369), it follows, since > 1, that we must 
have 
or 
2p» (Bya” — py) + 3pg” < 0. 
* Whether we give v the — or + sign will depend upon the sign of u, in the actual statistics. 
