FOUNDATIONS OF THEORETICAL STATISTICS 
339 
Now 
hence 
The quantity, 
j r i-r r /c-i 
xl-d+f*)* f_ *’ 
,/r _ i. 
0 - ~2 
and 
5L _ J 
2 n 
a 2a 
2a 
n 
■>n~' 
which is the factor by which n is multiplied in calculating the weight of the estimate 
made from n measurements, maybe called the intrinsic accuracy of an error curve. In 
the above example we see that errors distributed so that 
7 r « dx 
dj — —2-g 
7 T a ~\~ oc 
have the same intrinsic accuracy as errors distributed according to the normal curve 
1 
df 
provided 
(T V 7 2x 
' 2oa dx, 
— 2a“ 
Fig. 1 illustrates two such curves of equal intrinsic accuracy. 
Keturning now to the general problem in which 
we have 
and 
L = C —n log a + S (</>), 
Ay = I s-(*'+&") = A s (#") 
on ca a a~ 
id = - a s(2ft/+fV') +-Is(fV'-1). 
da a a 2 a 2 
The latter expression will directly give the accuracy with which a is determined only if 
02 I 
0 Li 
= 0. 
cm ca 
and we can always arrange that this shall be so by subtracting from y the quantity 
y¥ r 
77> 
0 
Thus in a Type ITT. curve where, referred to the end of the range, 
1 
ir = -h 0 — 
P-1 
