NUMEEICAL ILLUSTEATIONS OF THE YAKIATE 
DIFFERENCE CORRELATION METHOD. 
By BEATRICE M. CAVE and KARL PEARSON, F.RS. 
In 1904 Miss F. E. Cave in a memoir on the correlation of barometric heights, 
published in the R. S. Froc. Vol. LXXIV. pp. 407 et seq., endeavoured to get rid of 
seasonal change hy correlating first differences of daily readings at two stations. 
A similar method was used by Mr R. H. Hooker in a paper published some time 
later in the Journal of the Royal Statistical Society, Vol. LXVlll. pp. 396 et seq., 
1905. This method was generalised by "Student" in the last number of 
Biometrika (Vol. x. pp. 179, 180). He showed that if there were two variates 
X and y, such that 
x = (l>{t) + X, 
y=f{t)+ y, 
where X and Y .are the parts of x and y independent of the time t, then the 
spurious correlation arising from x and // being both functions of the time could 
be got rid of by correlating the differences of x and y, and that ultimately, when 
m is sufficiently large : 
SO that the correlation of x and y, free from the spurious time (or it might be 
position) correlation, i e. ?-yi., could be found by correlating the successive differ- 
ences of X and y. When the correlations of the differences remain steady for 
several successive values, then we may reasonably suppose that we have reached 
the correlation Txy*- 
This method is still fui'ther developed by Dr Anderson of Petrograd, who in 
a valuable memoir published in this Journal has provided the probable errors of 
the successive difl'erence correlations of a system of variables : 
X\, X2, Xn, 
y y y 
* Having been in communication with " Student," while he was writing his paper, I know that the 
interpretation put by Dr Anderson (Biometrika, Vol. x. p. 279) on "Student's" words {Ibid. p. 180) is 
incorrect. "Student" had in mind, if he did not clearly express it, the ultimate steadiness of 
»m for a succession of values of m. K. P. 
