Editorial 
7 
Illustrations, (a) To find the correlation between a deviation due to random 
sampling in a mean and one in the standard deviation of the same variate. 
Take q — l,q—0, .'. p q ^ = x; u = 2, u' = 0, .'. p u ,u' = fa- 
But p 10 = 0, *- = aJ>jN, 
Hence = = -T (xxvi). 
This is perfectly general ; we see that variations in the mean are independent of 
variations in the variability for all symmetrical systems including the Gaussian. 
(/3) To find the correlation between a deviation due to random sampling in 
the mean of one variate and one in the standard deviation of a correlated variate. 
Take q = 1, q' = 0, .'. p q ,q> = %; u = 0, a =2, .'. p xt)U - =p^ = /* 2 ' = <r y \ 
But p w = p 01 = 0, * s = *j*JN, ^^'V&'-l/V^ 
It remains to consider 
Vn = fl- S !>**' 0* - x) (y s > - yf\ 
where av = mean of array of flj's corresponding to the of y. Hence if the 
regression be linear 
pi = r xy <7 x o;/ v'/3/. 
Thus we have r J(r = = Vft'/V^a' — 1 (xxvii). 
Similarly r 5 = V/^/V/S,,— 1 (xxviii). 
Clearly = »W • > r . =^-^ 
an d, r j/a-.,. = r a;.'/ • '"iov = r .rj/ ■ '"Soy 
by (xv), which show us that these correlations are second order correlations, and 
proves that the correlation of the mean of one variate with the variability of 
a second is zero, for constant mean value of the second, since 
y xa v Vl - r 2 — Vl - r 2 - 
