Andreav W. Young and Karl Pearson 
225 
but there is a considerable difference between the values given according as the 
second terra is used or not and it seems that in some cases it would be advisable 
to calculate this term or at least the most important terms in it, viz. 

Using this approximation in the above case, we obtain ct^j = •02730, a result 
which — by a mere chance, of course — is almost exactly that given by the full 
expression in (xiv). 
II. Contingency between the Hair-colours of Pairs of Female Cousins. 
In the example just given the total number N in the sample was fairly large, 
viz. 1801, and it might be expected that in smaller samples the corrective terms 
would be of increased importance. With a view to testing this a contingency- 
table given by Miss Elderton in her Memoir on " The Measure of the Resemblance 
of First Cousins"* was selected. There are 36 cells in this table and the total 
number in the sample is only 218, there being several cells with zero or very small 
content. 
The Table is given in full on p. 226 along with the quantities required for the 
calculation of and a^2 ; it is there evident from the figures how large a proportion 
of the variability depends on the cells of small content. This is of course to be 
expected but the importance of having large numbers in all the cells is not always 
appreciated. In this particular case physiological reasons would prevent us 
from clubbing together the "Fairs" and "Reds" and with the fewness of the 
observations at our disposal we must use the table simply as it stands. 
The scheme followed in each cell of the table is shown in the last column, 
and in the marginal totals are given the values of all the summations required 
for (xiv). These are 
.(4)^-1.8481, S{(,f|^ 19-162, 
5(1)^5170.9, S(i£,).. 08277. 
When these are substituted in equation (xiv), we have, preserving the algebraic 
order as before, 
aV= [-08277 + -14895 ~ -02218] 
+ 7-orox9 [114-9714 - 13-6837 - -9932 + 50-5515 - 22 - 8-3411 - -2219] 
(218)' 
+ ^oA^3 [- 2336-8 + 5170-9 + 3-4 - 38-3 + 125-7 + 1224], 
and the whole work is again summarised in Table III (p. 227) : 
* Evgenics Laboratori/ Mtm.oirs, iv. Cambridge University Press 1907. 
Biometrika xi 15 
