E. C. Snow 
65 
English Rural Districts 
for 1870 
Prussian Rural Districts tor 
1882 
Five Years 
Ten 
Male 
Female 
Male 
Female 
Male 
r e llltll V 
■184 
•156 
•241 
•209 
•241 
•209 
•037 
•036 
•069 
•069 
■100 
•103 
h 
•187 
•214 
•264 
■292 
■290 
■315 
°"0 
•0201 
•0184 
•0541 
•0508 
•0541 
■0508 
0"! 
•0079 
•0092 
•0263 
•0241 
•0291 
•0253 
°"2 
•0232 
•0219 
■0611 
■0653 
•0595 
•0647 
»*01 
•271543 
•463227 
•634918 
■633825 
■596721 
■576631 
»02 
•854400 
■877328 
■951975 
•975109 
•937904 
•967319 
ru 
■528884 
•567130 
■817686 
•755164 
•811763 
■723951 
2 r 01 
- 409 
- -087 
-•814 
- 705 
- 813 
- -707 
2""0 
•0104 
•0088 
•0166 
•0113 
•0188 
•0129 
2°"1 
■0067 
•0076 
•0151 
•0158 
•0170 
■0174 
2^10 
-•262 
- 075 
- -744 
- -990 
- -734 
- -958 
If the values of 2 r 01 here are compared with the values of M r 12 in the earlier 
tables for the corresponding cases we find very little difference. Thus : 
Correlations obtained without using Rates, 
-•415 -158 — 917 -'768 -'920 --789 
Corresponding Correlations by use of Rates, 
-•409 --087 - -814 - -705 - -813 — *707 
If we reduce the figures in the first of these by the values of 04 e 12 we have the 
sequence 
-•347 -'105 --809 -710 -781 -'701 
The agreement between the last two lines of figures is surprising and remarkable. 
In all cases we get approximately the same numbers as before, a quite unexpected 
result, 
Lest these results should hastily be pointed to as evidence against the possi- 
x z 
bility of spurious correlation arising when such variables as - and are 
•> r ° y & — y 
correlated, it should be pointed out that the deviations from the mean values of 
the variables are in some cases considerable, and that the third and fourth powers 
of those deviations cannot be neglected in comparison with the corresponding 
powers of the means. Thus the formula which is usually exhibited to show the 
possibility of spurious correlation does not apply to this case. Whatever the 
magnitude of the 'spurious' element, if any, involved in the correlations just found, 
they can only be construed as supporting those previously found and as evidence of 
the existence of selective mortality in the populations dealt with. 
Professor Pearson, also, has pointed out to me another possible mode of 
attacking the problem. This is to render constant x 0 — x t instead of x 0 , and in 
Biometrika ix 9 
