Karl Pearson and David Heron 
185 
Or, again, between 6 and 7 vertically and 8 and 4 horizontally 
Q =-60002, 
576-60 
42-40 
619 
294-40 
86-60 
381 
871 
129 
1000 
which sufficiently illustrate the feasibility of the construction of the surface. 
But at once the fictitious character of Mr Yule's idea of association comes to 
light. He tells us that it is "natural" to put a table in the equivalent symmetrical 
form — one for example in which we have 50 °/ 0 deaths and 50 °j 0 recoveries, 
50 °/ 0 vaccinated and 50 % un vaccinated. And this is possible because his Q does 
not change by such a process. But surely if it is "natural" to have equal 
numbers of deaths and recoveries, it is also "natural" to have equal numbers of 
fathers, and for the matter of that equal numbers of sons, in each eye-class. 
Equal light blue eyes, and equal dark blue eyes, equal light brown eyes, equal 
dark browns and blacks. But the instant we study a table of this kind some 
TABLE I. 
Table of Variates in Father and Son Eye-Classes for Constant Association 
Coefficient 0"6. 
1 
2 | , 
4 
5 + 6 
V 
8 
Totals 
1 
4-08 
19-04 
6-25 
2-60 
0-78 
1-00 
0-25 
34 
19-54 
148-89 
75-33 
32-54 
9-68 
12-05 
2-97 
301 
3 
7-41 
90-46 
90-17 
52-97 
16-86 
21-03 
5-10 
284 
2-19 
28-54 
39-43 
33-19 
12-53 
16-89 
4-23 
137 
5 + 6 
1-35 
17-12 
25-63 
26-40 
11-82 
17-83 
4-85 
105 
i 
1-03 
13-15 
19-94 
23-33 
12-18 
21-60 
6-77 
98 
8 
0-40 
4-80 
7-25 
8-97 
5-15 
10-60 
383 
41 
Totals 
36 
322 
264 
180 
69 
101 
28 
1000 
remarkable points arise, (i) The selection which is advocated by Mr Yule and which 
keeps his coefficient constant is a perfectly arbitrary one, and (ii) it must be stopped 
at a perfectly artificial limit, namely that at which the arbitrary division has been 
made. Mr Yule does not equalise each sub-group, but if, for example, he divides into 
light and dark eyes between 3 and 4, he multiplies his light blue eyes, his dark 
blue eyes and his greys, not by different factors which would equalise these groups 
with each other, but by the same common factor, so that the sub-groups really 
remain in the same proportions as before the equalising. Surely if it is ' natural" 
to equalise light and dark eye totals, it is equally " natural " to equalise the totals 
of light blue aud dark blue eyes. If it is " natural " to equalise the vaccinated 
and unvaccinated totals, it is surely for the same reason " natural " to equalise the 
several groups of individuals who have one, two, three vaccination scars, for the 
number of their scars " is dependent to a large degree on a purely arbitrary 
circumstance, the activity of the authorities" in making 1, 2, or 3 punctures. 
It is equally "natural" to equalise the numbers who have lived 5, 10, 20, 30 
Biometrika ix 24 
