214 
Miscellanea 
Below 
1-10 
1-10 
1 '22 
1-34 
1-34 
l-kii 
1-58 
1-58 
1-70 
1-70 
1-82 
1-82 
1-94 
1- 94 
2- 06 
2-06 
2-18 
2-18 
2-30 
2-30 
2-42 
2-42 
2-54 
2-54 
2-66 
0 
2-66 
2-78 
Above 
2-78 
Actual ... 
4 
8 
14 
12 
12 
5 
7 
6-90 
5 
2 
1 
2 
1 
Calculated 
No Corre- 
lation 
1-01 
1-85 
2-42 
.5-28 
8-86 
11-69 
13-07 
12-18 
9-97 
4-27 
2-36 
1-18 
•92 
Corre- 
lation "01 
3-27 
6-02 
8-92 
11-01 
11-71 
10-84 
8-95 
6-64 
4-52 
2-82 
1-64 
•90 
•85 
These give P=-46 and P=-86 respectively, the first being a good deal helj^ed by the conven- 
tion that the tail should not be carried beyond the point at which a single unit may be expected, 
and the second much less so. 
As the empirical curve fitted from the actual moments has a P of -92, the second curve may be 
considered fairly good depending as it does on a guess following on calculation. On the other 
hand a P of -46 with so few cases as 80 is not particularly good, and as Prof. Pearson has pointed 
out to mo the graph distinctly gives an idea of greater skewness than is represented by the 
no correlation curve. I do not however wish to contend that the circumstances attending the 
production of the sample actually conformed to the arbitrary conditions which I found it 
necessary to assume in order to simplify the analysis. But seeing that the fit is good and that 
with such a small sample even the divergent Bi is not altogether impossible, I think it likely 
that there was some sort of correlation, though probably not that particular kind which has been 
assumed in this note. 
Co7iclusions: 
(1) That the approach to normality of the distribution of means of samples drawn from a 
non-Gaussian population is delayed by the existence of correlation between the individuals com- 
posing the samples. 
(2) That on certain arbiti'ary assumptions the constants of the new distribution can be 
found given the constants of the old one and r according to formulae given above. 
(3) That using the above formulae and choosing a likely looking value of r, a curve can be 
drawn to represent the sample in Drs Greenwood and White's paper with fair likelihood. 
II. A Short Method of Calculating the Coefficient of Correlation in 
the Case of Integral Variates. 
By J. ARTHUR HARRIS, Ph.D., Cold Spring Harbor, Long Island, U.S.A. 
For symmetrical correlation tables in which both variates have the same mean and standard 
deviation, Professor Pearson has suggested* that his difierence method "may possibly be of 
good service," but warns the reader : — 
" At the same time too much reliance must not be placed upon the difierence method, not 
only because it assumes normality of distribution but because it involves a somewhat rough 
method of approximation in the case of the diagonal cell." 
* Drapers' Company Research Memoirs, Biometric Series, iv. pp. 4 — 9, 1907. 
