2G0 
Peccmnmm ! 
We may now turn to the numerical illustrations. It will be sufficient to show 
the correct values of cr^a in the table on p. 224. 
First and secontl terms 
of (xiv) 
All terms of (xiv) 
Old Values 
Corrected Value.s 
•02709 
•02725 
•02729 
•02744 
For practical purposes, these would all bo taken as •027, and accordingly the 
.errors, although sufficiently distressing, do not modify the conclusions, that for 
a sample over 1000 the first and second terms of (xiv) are adequate. In the second 
example, p. 227, more serious changes are made, chiefly owing to the error in the 
sign of the second-order term (2 — 40-)r, whicli becomes of greater importance now 
that N is reduced from 1801 in the first illustration to the 21 (S of the second 
illustration. We have for o-aj : 
First and second terms 
of (.xiv) 
All terms of (xiv) 
Old Values 
Corrected Values 
•0798 
•0693 
•0823 
•0719 
Thus for pi'actical purposes the •0(jO of the first and second-order terms is only 
raised to '072, if we include the third-order term. We may therefore conclude that 
250 cases marks something like the limit at which we need to consider the third- 
order term as well as the tiist- and the second-order terms. 
We now turn to the test for zero-contingency. Equation (xvii) of the original 
paper is correct, but the wrong value of 'x_;-. was inserted to obtain (xviii); it should 
of course be 1 — 2/i\''. This leads to 
1 (c c(c-2)-2(c'^-l) , .... 
-V = ^ + ^ + 2 (c - 1) (xvni), 
or pei'haps as it is better expressed : 
N 
.(xviii) his. 
The formulae summarised on p. 229 must be altered to accord with the results 
given above. (C) must be (xiv) of the present paper. (D) must have —2c and 
not -f- 2c for its last term. (C) must be (xviii) above. 
(II) The object of our next note is to make some additions and con-ections provided 
by Dr Isserlis himself to his paper: " On the Conditions under which the ' Probable 
Errors ' of Frequency Distributions have a real significance " {R. S. Proc. Vol. 92, A, 
