Miscellanea 
201 
the value of thi.s, if we remember that <^;,^ = + "t^'da the a column, is given by 
= * (1 +V,) (1 - V) <^62 ^-^2 + 1 (1+^^) ^,^,2/,,^ (vii). 
(iii) (^') = 1(1 + ,S' (^) =1(1+ nf o,,^ ( viii), 
-•=!(^) <'^)- 
(iv) |<Sg ' '^^^''^ since the summation is for only two rows is given by 
or l'S',(^*) = |(l+''6^)<^6V«6 (X). 
Writing (vi), (vii), (viii) and (x) in (iv) we find : 
Xb'<^\ = W{^ - vb'Hn' <t>b'lH] {1 +i (1 +.6) M -i {(1 + V) ^'+(1 + ..)'^ j . 
But by the line above equation (iii) X6^ = (l +''6) Hence : 
- {(1 - ^. + -.^) '^(-H(l +.,,) ''^'} (xi). 
This involves a knowledge of ^5^^ aiid co;/. Tlie first will have been found in determining 
the contingency coefficient of the entire table ; the second in determining its probable error, and 
the third only has to be specially calculated. 
Finally we have* 
cre, = {l-C6f <r,^ (Xii). 
Or the 
Probable Error of C;, = -67449 (1 - C^^f a^^. 
(3) I propose to illustrate this numerically on a table already largely worked out in the 
paper referred to above. It has been shown that handwriting is contingent in a certain 
degree on grade of intelligence. I propose to investigate which group of hand writers has a 
distribution of intelligence most markedly diflerent from that of the general population, i.e. 
which is intellectually most heterogeneous. This is not in itself a problem of any importance 
but it will serve to illustrate the application of the above formula3, and the numerical work 
needful for their evaluation. Turning to the table, p. 197, I extracted the results given in 
Table III. The only new quantities to be calculated are the values of 
Now N(^\^ is the fourth number in each constituent of the table on p. 197. The squares of 
these from Barlow's Tables are the first number in each constituent of Table IV. ; is given 
under the total at the foot and immediately above 71^, its reciprocal. These reciprocals 
placed successively on the calculator and multiplied by the first number in each column 
* Joe. cit. p. 194. 
Biometrika v 26 
