342 
MR. R. A. FISHER ON THE MATHEMATICAL 
the intrinsic accuracy of scaling is therefore independent of v . Now for these curves 
ft 2 = 
3 r— 1 
r — 2 r—3 
8> ’ 2 
r + 6- - —2 / , 
v + v 
so that 
and 
&-I _ r A r- 2 + C (V-+ 10r-12) 
■ 3 (r 2 +1' 2 ) 
n 
2 r 3 r — 2 +v 2 (r 2 +10r—12) 
2r-2r-3 (r 2 + /) 
The efficiency of the method of moments for scaling is thus 
■ — 2 ?• — 3 r + 4 (r 2 + v 2 ) 
r+I {r 3 r —2 + v 2 (r 2 + 10r-12)} 
when v = 0, we have for curves of Type VII. an efficiency of scaling 
12 
1- 
r r +1 
( 4 ) 
The efficiency of the method of moments in scaling these curves vanishes at r — 3, 
where j3 2 becomes infinite ; for r = 7, the efficiency of scaling is 
55 49 + p 2 
2 ' 1715 + 10 lv 2 ' 
varying in value from 78*57 per cent, for the symmetrical Type VII. curve, to 25*70 
per cent, when v oo and the curve to Type V. 
10. The Efficiency of the Method of Moments in fitting the Pearsonian 
Curves. 
The Pearsonian group of skew curves are obtained as solutions of the equation 
1 dy _ —(x—m) _ 
y dx a + bx + cx 2 ’ 
algebraically these fall into two main classes, 
and 
df cc (l + — ) ( 1 — — ) d x 
\m 
aj 
x 
\ 
aj 
dfcc 
r + 2 
2 —v tan 
e 
l£ 
a dx, 
( 5 ) 
according as the roots of the quadratic expression in (5) are real or imaginary. 
