194 THEORY OF STATISTICS.
at the census of 1891, and are not available for earlier years.
Some trial was made of rateable value per head, but with not
very satisfactory results. For any given year, and for a group of
unions of somewhat similar character, e.g. rural, the rateable value
per head appears to be highly (negatively) correlated with the
pauperism, but changes in the two are not very highly correlated :
probably the movements of assessments are sluggish and irregular,
especially in the case of falling assessments in rural unions, and
do not correspond at all accurately with the real changes in the
value of agricultural land. After some consideration, it was
decided to use a very simple index to the changing fortunes of a
district, viz. the movement of the population itself. If the
population of a district is increasing at a rate above the average,
this is primd facie evidence that its industries are prospering ; if
the population is decreasing, or not increasing as fast as the
average, this strongly suggests that the industries are suffering
from a temporary lack of prosperity or permanent decay. The
population of every union was therefore tabulated for the censuses
of 1871, 1881, 1891.
7. Age Distribution.—As already stated, the figures that are
known clearly indicate a very rapid rise of the percentage relieved
after 65 years of age. The percentage of the population over 65
years of age was therefore worked out for every union and tabu-
lated from the same three censuses. This is not, of course,
at all a complete index to the composition of the population as
affecting the rate of pauperism, which is sensibly dependent on
the proportion of the two sexes, and the numbers of children as
well. As the percentage in receipt of relief was, however, 20 per
cent. for those over 65, and only 1-2 per cent. for those under that
age, it is evidently a most important index. (A more complete
method might have been used by correcting the observed rate of
pauperism to the basis of a standard population with given num-
bers of each age and sex. (Cf. below, Chap. XI. pp. 223-25.)
8. The changes in each of the four quantities that had been
tabulated for every union were then measured by working out the
ratios for the intercensal decades 1871-81 and 1881-91, taking
the value in the earlier year as 100 in each case. The percentage
ratios so obtained were taken as the four variables. Further, as
the conditions are and were very different for rural and for urban
unions, it seemed very desirable to separate the unions into groups
according to their character. But this cannot be done with any
exactness: the majority of unions are of a mixed character, con-
sisting, say, of a small town with a considerable extent of the
surrounding country. It might seem best to base the classification
on returns of occupations, e.g. the proportions of the population
