E. C. Snow 
457 
a small matter, but his failure to notice the emphasis placed on that word is, I think, the basis 
of the whole of the writer's attack on the method of measuring environment adopted in the 
memoir. He appears to think that by making those remaining deaths constant throughout the 
districts, I have also made the deaths of the particular cohorts I dealt with constant during 
their first five years of life. He asks, " Has Mr Snow found anything more than a somewhat 
obscured consequence of the obvious result that, in a group of districts with the same total 
mortality for the first five years of life, the districts with the higher mortality for the first three 
years will tend to have the lower mortality for the last two. It seems to us exceedingly doubtful 
whether the method of 'correction for environment' used has not led to a series of correlations 
which are largely fallacious and of no significance as regards selection." It is remarkable that 
the reviewer did not take the trouble to test the value of his suggestion, for I gave complete 
data in the table on p. 33 of the memoir for that to be done, and the time required was only 
a few moments at the outside. In fact an approximation sufficient for his purpose could be 
worked out mentally in the space of a few seconds. In the table referred to I gave values of 
03 o-i and m (T2 as well as of 03 r 12 for five sets of data (three from English figures and two from 
Prussian — the latter, however, dealing with the first ten years of life, ,i\ referring to the first two, 
and x 2 to the next eight years of life) distinguishing males from females. Thus there were ten 
distinct sets of values given, on any one of which he could have tested his suggestion. If we 
let x b denote x t + x 2 , the phrase "the same total mortality for the first five years of life" 
obviously requires the values of 03 o- 6 to be appreciably zero in each case. Values of this can 
be found from a well-known elementary formula 
03"" 5 2 = 03"" l 2 + 03C 2 2 + 2 03 r 12 • 03"" 1 • 03"" 2 ) 
a proof of which is given in Mr Yule's Introduction to the Theory of Statistics. The values of 
030-5 as found from this formula are given in the following table together with such of the other 
figures from the memoir as are necessary for an understanding of the matter in its present 
bearings. 
Data 
x 0 
-t'l 
x 2 
03*1 
03C2 
03 ''12 
03C5 
Males : 
(1870 
3227 
644 
51 
44-582 
10-634 
- -4483 
40-93 
English Rural 
h871 
3226 
602 
60 
42-247 
9-589 
- -3574 
39-84 
Districts 
(l872 
3291 
588 
62 
41 -220 
12-108 
- -2271 
40-24 
Prussian Rural 
J1881 
9407 
2270 
729 
198-042 
210-803 
- -9278 
78-68 
Districts 
(1882 
9297 
2424 
732 
148-377 
206-413 
- -6050 
166-02 
Females : 
(1870 
30.90 
531 
48 
34-340 
11-126 
- -4666 
30-77 
English Rural 
n87i 
3114 
491 
59 
28-468 
12-736 
- -2857 
27-67 
Districts 
(1872 
3150 
494 
61 
24-011 
11-175 
- -5089 
20-54 
Prussian Rural 
S1881 
8917 
1914 
711 
169-182 
183-986 
- -8483 
98-30 
Districts 
(1882 
8793 
2004 
729 
117-355 
178-700 
- -6078 
142-17 
The figures in the last column at once proclaim how groundless is the assertion that the 
negative values of 03 r 12 are due to the fact that the method I used for correcting for environment 
was equivalent to assuming all the districts had the same total mortality for the first five years 
of life. Taking the first case on the table — the cohort of English males born in rural districts 
in 1870 : — when correction is made for environment the mean total mortality in the first five years 
of life was 695, with a standard deviation of 41 ; the mean mortality in the first three years was 
644 with a standard deviation of 45; and in the next two the figures were 51 and 11 respectively, 
the partial correlation for a constant environment between the mortality in the first three years 
of life and the next two being — -45. With such a range of values as is indicated by a mean 
Biometrika vm 58 
