practised by a hundred men or by
millions.

For the purpose of introducing quantity into formulae we have at our
disposal several methods, of various degrees of imperfection, which help
us to attain the end in view with various degrees of precision. Arranged
in descending order of precision they are as follows:--

(1) _Measurement_ is a perfectly scientific procedure, for equal numbers
represent absolutely identical values. But a common unit is necessary,
and that can only be had for time and for physical phenomena (lengths,
surfaces, weights). Figures relating to production and sums of money are
the essential elements in the statement of economic and financial facts.
But facts of the psychological order remain inaccessible to measurement.

(2) _Enumeration_, which is the process employed in statistics,[204] is
applicable to all the facts which have in common a definite
characteristic which can be made use of for counting them. The facts
which are thus comprehended under a single number do not all belong to
the same species, they may have in common but a single characteristic,
abstract (crime, lawsuit) or conventional (workman, lodging); the
figures merely indicate the number of cases in which a given
characteristic is met with; they do not represent a homogeneous whole. A
natural tendency is to confuse number with measurement, and to suppose
that facts are known with scientific precision because it has been
possible to apply number to them; this is an illusion to be guarded
against, we must not take the figures which give the number of a
population or an army for the measure of its importance.[205] Still,
enumeration yields results which are necessary for the construction of
formulae relating to groups. But the operation is restricted to those
cases in which it is possible to know all the units of a given species
lying within given limits, for it is performed by first ticking off,
then adding. Before undertaking a retrospective enumeration, therefore,
it will be well to make sure that the documents are complete enough to
exhibit all the units which are to be enumerated. As to figures given in
documents, they are to be distrusted.

(3) _Valuation_ is a kind of incomplete enumeration applying to a
portion of the field, and made on the supposition that the same
proportions hold good through the whole of the field. It is an expedient
to which, in history, it is often necessary to have recourse when
documents are unequa