Editorial 
2(31 
pp. 23 — 41, 1915). In that paper he gave the vahies of the fre(]uency constants 
B,' and B.^ (fornudae (19) and (23), pp. 30 and 31) of the distribution of the 
moment-coefficient of any order a about a fixed origin for a sample of size n dr;i\vn 
from a })opu]ation of size N. These formulae are exact and no alterations are pro- 
posed here in them nor in any conclusions drawn from them. In the latter part of 
the paper Dr Isserlis deals with the value of the ^-constants for moment-coefficients 
referred to the mean of the sample. These latter values were approximate and 
intended to be correct to terms in - . We are indebted to Professor Tchouprott" 
n 
for pointing out that there is an error in the approximation, for one of the neglected 
terms rises. When the correction is nuide, however, the statement (p. 24) remains 
true that "for coefficients of high order the sample has to be an inconveniently 
large fraction of the population itself if /3i and (3., are t(j approach even approximately 
their Gaussian values " (i.e. 0 and 3). The results in the pajjer cited are exact and 
correct* until section 5 (p. 35) is reached. In that section, formulae (38), (39) and 
(41) are approximations and for the purposes of the paper should be given correct 
1 . . 1 . 
to terms in - for (38) and to terms in for (41). The use of the incomplete value 
n )i- ' 
dfiu = j^^ (f^"s AV ) - « M,,-, dx 
in equation (37) has introduced an ei-ror in the value of il/3 given by equation (39). 
We proceed to amend this error. 
We have u„, = ~S\ n, (*•, - xY'] = - 8 ( n,X/), dX, = -dx; 
. dfiu = S {dn, X/' - uih Xs"'-' dx] 
+ \ S |- udnJJiX--^ + "L^^L^ n,X--^dxj + ... 
= A + B + terms of third and higher orders in rf??,, dx. 
Now it is well known that the mean value of fifth and higher powers ui'dn,,, 
dx, . . . contains no terms of lower degree than the third in 1 jn. 
In the formulae (38), (39) and (41) the values of M., M,, were obtained as 
the mean values of A'\ J.^ and respectively. The inclusion of the neglected 
terms does not attect .'1/. which is given correct to - nor M^, for the only term of the 
fourth order in f/«,,, dx. in {A + B + ... f is A^. 
But {diJbuf = A'' -1- f^A'B + fifth-order terms in dii^, dx. 
* There are some obvious printers' errors overlooked in proof, of which the omission of the factor 
(/"'m)'' - 2ai'2u (/^'it)^ + (A''-2w)'^ ii the first line of equation (21) is most likely to mislead. It may also be 
noted that the factor fx-fi is missing in the first term of (20) and the factor 3 in the first term of (41). 
