206 
Peccavlnius ! 
In Table II on p. 39, the third column is unaltered, the second column becomes 
(the coefficients of </> being apjDroximated) 
u 
^1 
2 
8 (x' - 
n X 
3 
0 
4 
102 (x'- 0-1080)2 
n X 
5 
0 
6 
1099 (x'-0'040</))- 
11 X 
The corrected form of Table III (p. 40 of paper cited) is now as follows : 
Table III. Apjm>ajw)ate values of ff^, fi.. for samples q/'lOOO out of 
a population o/ 1,000,000. 
Pi 
ft 
2 
0-001 
3-012 
3 
0-000 
3-090 
4 
0-081 
3-204 
Thus the effect of the correction is to change the values of /3i for u = 2 and 
M = 4 from the values O'OOS and 0-102 to O'OOl and O'OSl respectively, but it 
remains true that the frequency of the fourth moment-coefficient differs appreciably 
from the normal distribution. 
(III) ] )r Isserlis also wishes to make the following emendations in his paper 
in the last number of Biometrika, Vol. xil, p. 134. On p. 138 near the foot + ABC 
has been dropped from the bracket {^FGH + 2AF- + 2BG" + ^GH"). Also in 1. 6 
of the same page for " on Q " read " and Q." 
(IV) The point indicated by Professor Tchouproff, namely: that fourth-order 
mean products are of the same order finally in as third-order mean products and 
cannot be neglected therefore in compai'ison with third-order mean products, is of 
great importance in investigations into the probable errors of frequency constants 
in the case of small samples. In expanding functions of the deviations from mean 
values of subfrequencies such as Su,, we cannot neglect products of the fourth 
order in the Sn^'s compared with products of the third order. In obtaining results 
true to products of an odd order in the " statistical differentials " we must proceed 
to products of the next highest even order to reach correctness. 
