Ethel M. Eldbrton and Karl Pearson 
489 
the time factor has been eliminated. It is the deviations from the continuous 
curves of secular change which may turn out on careful analysis to be truly 
indicative of causal relationship between the variates under consideration. 
The first attempt to get rid of secular change by a method of differences was 
made by Miss F. E. Cave in 1904 in a paper on barometric correlations*, and 
shortly afterwards Mr R. H. Hooker published a paper dealing with the same 
pointf. Both these authors used only first differences and gave no general theory 
of the method. Quite recently " Student " has published a paper J giving the 
fundamental formulae, and indicating how by taking successive differences of two 
variates and correlating them, we free ourselves from the time or locality influence, 
and approach the true and probably causal relationship between them. When the 
correlation of the differences becomes steady, then we have reached the actual 
correlation of the variates corrected for the time factor, provided an assumption is 
made which we shall discuss at greater length below : see footnote, p. 495. Mean- 
while Dr Anderson of Petrograd has been working on the subject, and in a 
most valuable memoir§ he has added to " Student's " results a number of new 
theorems; for example, the probable errors of the successive difference corre- 
lations when they become steady, and the relations which should be fulfilled 
between the squares of the standard deviations of successive differences, when 
the series has become steady. We have thus a double means of ascertaining 
whether the desired object — the elimination of the time-factor — has been approxi- 
mately achieved. A third additional test will be indicated in this paper. 
This new statistical process has been termed the Variate Difference Correlation 
Method'^, and there is small doubt that it is the most important conti'ibution to 
the apparatus of statistical research which has been made for a number of years 
past. Its field of application to physical problems alone seems inexhaustible. We 
are no longer limited to the method of partial correlation, nor compelled to seek 
for factors which rendered constant will remove the changing influence of environ- 
ment. In the present case, that of the influence of infantile mortality on child 
mortality, Pearson endeavoured to eliminate the influence of continual environ- 
mental improvement by making the expectation of life at six years constantlF. 
Snow achieved the same object by correlating the deathrates of one sex for a 
constant deathrate of the other**. In both these cases substantial evidence of 
Natural Selection was obtained from the mortality tables. The object of the 
present paper is to demonstrate by the still more complete elimination of the 
* R. S. Proc. Vol. Lxxiv. pp. 407 et seq. 
t Ruijal Statistical Society Journal, Vol. lxviii. pp. 396 ct seq. 1905. 
X Biometrika, Vol. x. pp. 179, 180. 
§ Ibid. pp. 269—279. 
II Pearson and Cave: "Numerical Illustrations of the Variate Difference Correlation Method." 
Biometrika, Vol. x. pp. 340 — 355. 
U R. S. Proc. B. Vol. 85, p, 472. 
** " The Intensity of Natural Selection in Man." Drapers' Company Research Memoirs, Dulau & Co., 
1911. 
