334 
ME, B, A. FTSHEE ON THE MATHEMATICAL 
of which the mean value is 
n (p +1 
2 
a 
The variance of a, determined from this pair of simultaneous equations, is found by 
8 2 L 
dividing 
by the determinant 
which reduces to 
whence 
n 
, 2 
cm" a 2 (p — 1) 
n 
a 2 (p- 1) 
_ n 
a 2 
n 
9 
a 
n(p + 1) 
9 
a “ 
2 _ n 2 
_p — 1 « 4 
a a 
(Tii = — 
•? 
'An 
and the efficiency of scaling by the method of moments is 
P f 1 _ 1 _ 
p I- 4 p + 4 
Efficiency of over 80 per cent, for scaling are, therefore, obtained when p exceeds 11. 
The efficiency of scaling does not, however, vanish for any possible value of p, though 
it tends to zero, as p approaches its limiting value, —1. 
Lastly, p is found by the method of moments by putting 
Now 
4 
P + 1 
= /Si- 
°7». 
_ A 
(4 A — 24 / 32+36 + 9 A A — 1 2 A + 3 5 A ), 
and for curves of Type III, 
hence 
A = 3 + § A, 
Ai — 2/3 jA+ 4A = A (3A + 1.o), 
A — 2 (A-s+2 A) = ^2 (3ydi* +13A + 3), 
°>, 2 — “ 1_ (9A + 4) (A + 4), 
n 
A 2 _ 6 (p + 2) (p + 6) 
n p +1 
