2 On the Probable Errors of Frequency Constants 
Further if n s = S(n gs >) for all values of s', 
n s n ts' / -\ 
Wn.rn,,. = 7W ( 1 - % ) (vii). 
~ J T 
See Biometrika, Vol. v. pp. 191 — 2. 
(2) We have, if 8 denote a variation in any frequency constant due to random 
sampling, 
Mp, h 9 > - S(Sn ss .x s Vi/ s u') (vii) bis, 
and if m be number of random samples : 
= 8 K W #,V') + 2£ («r /w tr„ M ,r, v;i<t , x x^iy/y^) 
= Sn s , (l - .'•,-','/,•'' " 2S (^^Bfxfyjy^ 
Thus -V, = fe F^ 
Again N8p UjU , - 8 (Sn^w g u y/^) t 
= N ('Pq+ Ut q'+ U > Pq,q'Pu,u')> 
thus <r p ,a p _ = P9*«.*+<-P*.&+« ( ix) . 
(viii) and (ix) refer only to the higher moment coefficients about a fixed origin. 
About the mean we have 
N Pa* = 8 { ]} ss' («i - ®) q (y* - y) q '\, 
n ^Pq,i' = s {& n ss' - «) 2 (y* - y) q '\ - q8xp q - hq ' - q'Sypq,?-! (?). 
Now it is clear that before going further we want to know the correlation 
between variations in n ss > and x or y. Now 
m = S(n t x t ), 
N8x = S (8n t x t ), 
Nhxhn ss i = S (8n SS '8n t Xt), 
= n SS '(x s — x), using (vi) and (vii), 
