Beatrice M. Cave and Karl Pearson 
355 
affairs* on the steadiness of the series and on the approach to the standard- 
deviation formulae. But apart from these lesser points, our present numerical 
investigation has convinced us of the very great value of the new method of 
Variate Difference Correlations. 
* For example if we measure X from its mean, 
since is by hypothesis zero, = Scr^ + {(rS;^^ - A (Xj^ + AV) ! - (AA')^. The first term 
— 1 «-i 1 
2<r^j^^ gives Dr Anderson's value of (7^^^. Now AA' equals ^ 1 .5 (A', - A',4,j) = — ^(A'j-A'J. Thus the 
remainder is — ^ j^cr^ ^ - i jxj^ + A'„2 _). _!_ - A'J-| J . Now the average value on many trials of 
2 
^(Xi^ + X^^) will be 0-2 and of (A'l - X^J^, so that the full value may be jy^ — —-, 0-2^, and small 
for n large ; but for n small as above such a relation as a^^^ = 2ir'^ and the similar but more complex 
relations of the standard deviation formulae for the higlier differences need not hold for any individual 
case, and thus the steadiness of the difference correlation series, and the approach to the Andersonian 
formulae are very far from attained. 
