KmsTiNE Smith 
17 
With the accuracy here employed, which exchides the determination of terms 
containing the higher power of - , we have 
Pi' = pp = ■ 1=^— = • 
From (35) we find by squaring and taking the mean value for a great number 
of samples 
0-- = r. 
iiii ,,ct2 Tin /.o'i . , rio 
which by introducing the values from (3), (12), (22), (28), (29), (31), (32), (33) and 
(34) and neglecting the term containing the higher power of - leads to 
-^{l + (7-l)r;-^'''^' + '^, 
or a"-^^^ = |] + (ry - 1) r - '| [,y + 3 + (ry - 1) r (1 - r)] + qr^ 
which may be written 
-V='^-«-^(l-'-)il-V^^--1 (36). 
P" n nq ^ '{ ^2 
The first term is the usual expression obtained for q = 1. From this, for q >1, 
one must subtract a term which for given values of ?• and fj, increases with q. 
(/ ) The Standard Deviattuii of the Slopes of the Regression Curves. 
We shall finally add the formulae of the s.D. of the slope of the regression curves 
for the calculation of which we have all the material ready. The regression 
coefficients are determined by 
Ho:*/ 1 
«p = —V anci o« = —ir ■ 
a ' a- 
By differentiation, squaring and taking mean value, we find 
1^ - 2 
i(n,,)^ {o-f an],, 
and a corresponding equation for o-^^. 
From these we find by introducing the S.D. and product moments 
'^'"f " »?7^ {1 + »• (7 - 1) - * 
/■J 
and a\ = ^^[l+r {q - 1) - fyr/ + 2 (ry - 1 ) r/ (1 - ry}. 
* Vide K. Smith, I.e., pp. 6, 7, where the same formiUa is deduced in a different form, containing 
(Tq instead of r. The two expressions are easily seen to be identical when the term is neglected. 
Biometrika xiv 2 
