(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 formulæ 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 unequally abundant for the different divisions of the subject. The result is open to doubt, unless we are sure that the portion to which enumeration was applied was exactly similar to the remainder.