X.—CORRELATION : ILLUSTRATIONS AND METHODS. 195 
engaged in agriculture, but the statistics of occupations are not 
given in the census for individual unions. Finally, it was decided 
to use a classification by density of population, the grouping used 
being—Rural, 0-3 person per acre or less: Mixed, more than 
0°3 but not more than 1 person peracre: Urban, more than 1 person 
per acre. The metropolitan unions were also treated by them- 
selves. The limit 03 for rural unions was suggested by the 
density of those agricultural unions the conditions in which 
were investigated by the Labour Commission (the unions of 
Table VII, Chap. IX.): the average density of these was 0-25, 
and 34 of the 38 were under 0:3. The lower limit of density for 
urban unions—1 per acre—was suggested by a grouping of Mr 
Booth’s (group xiv.) : of course 1 person per acre is not a density 
associated with an urban district in the ordinary sense of the 
term, but a country district cannot reach this density unless it 
include a small town or portion of a town, ze. unless a large 
proportion of its inhabitants live under urban conditions. 
The method by which the relations between four variables are 
discussed is fully described in Chapter XII. : at the present stage 
it can only be stated that the discussion is based on the correlations 
between all the possible (6) pairs that can be formed from the four 
variables. 
9. lustration ii, —The subject of investigation is the inheritance 
of fertility in man. (Cf. Pearson and others, ref. 3.) One table, 
from the memoir cited, was given as an example in the last chapter 
(Table IV.). 
Fertility in man (i.e. the number of children born to a given pair) 
is very largely influenced by the age of husband and wife at 
marriage (especially the latter), and by the duration of marriage. 
It is desired to find whether it is also influenced by the heritable 
constitution of the parents, 7.e. whether, allowance being made for 
the effect of such disturbing causes as age and duration of marriage, 
fertility is itself a heritable character. 
The effect of duration of marriage may be largely eliminated 
by excluding all marriages which have not lasted, say, 15 years 
at least. This will rather heavily reduce the number of records 
available, but will leave a sufficient number for discussion. It 
would be desirable to eliminate the effect of late marriages in 
the same way by excluding all cases in which, say, husband was 
over 30 years of age or wife over 25 (or even less) at the time 
of marriage. But, unfortunately, this is impossible ; the age of 
the wife—the most important factor—is only exceptionally given 
in peerages, family histories, and similar works, from which the 
data must be compiled. All marriages must therefore be 
included, whatever the age of the parents at marriage, and the