In order to construct a formula, we should know beforehand what elements ought to enter into it. We must here make a distinction between general facts (habits and evolutions) and unique facts (events).
III. General facts consist in actions which are often repeated, and are common to a number of men. We have to determine their character, extent, and duration.
In order to formulate their character, we combine all the features which constitute a fact (habit, institution) and distinguish it from all others. We unite under the same formula all the individual cases which greatly resemble each other, by neglecting the individual differences.
This concentration is performed without effort in the case of habits which have to do with forms (language, handwriting), and in the case of all intellectual habits; those who practised these habits have already given them expression in formulæ, which we have only to collect. The same holds of these institutions which are sanctioned by expressly formulated rules (regulations, laws, private statutes). Accordingly the special branches of history were the first to yield methodical formulæ. On the other hand, these special branches do not go beyond superficial and conventional facts, they do not reach the real actions and thoughts of men: in language they deal with written words, not the real pronunciation; in religion with official dogmas and rites, not with the real beliefs of the mass of the people; in morals with avowed precepts, not with the effective ideals; in institutions with official rules, not with the real practice. On all these subjects the knowledge of conventional forms must some day be supplemented by a parallel study of the real habits.
It is much more difficult to embrace in a single formula a habit which is composed of real actions, as is the case with economic phenomena, private life, politics; for we have to find in the different actions those common characteristics which constitute the habit; or, if this work has already been done in the documents, and condensed into a formula (the most common case), we must criticise this formula in order to make sure that it really represents a homogeneous habit.
The same difficulty occurs in constructing the formula for a group; we have to describe the characteristic common to all the members of the group and to find a collective name which shall exactly designate it. In documents there is no lack of names of groups; but, as they have their origin in usage, many of them correspond but ill to the real groups; we have to criticise these names to fix their precise meaning, sometimes to correct their application.
This first operation should yield formulæ expressive of the conventional and real characteristics of all the habits of the different groups.
In order to fix the precise extent of a habit we shall seek the most distant points where it appears (this will give the area of distribution), and the region where it is most common (the centre). Sometimes the operation takes the form of a map (for example the map of the tumuli and the dolmens of France). It will also be necessary to indicate the groups of men who practised each habit, and the sub-groups in which it was most pronounced.
The formula should also indicate the duration of the habit. We shall look for the extreme cases, the first and the last appearance of the form, the doctrine, the usage, the institution, the group. But it will not be enough to note the two isolated cases, the earliest and the most recent; we must ascertain the period in which it was really active.
The formula of an evolution ought to indicate the successive variations in the habit, giving in each case precise limits of extent and duration. Then, by comparing all the variations, it will be possible to determine the general course of the evolution. The general formula will indicate when and where the evolution began and ended, and the nature of the change which it effected. All evolutions present common features which enable them to be divided into stages. Every habit (usage or institution) begins by being the spontaneous act of several individuals; when others imitate them it becomes a usage. Similarly social functions are in the first instance performed by persons who undertake them spontaneously, when these persons are recognised by others they acquire an official status. This is the first stage; individual initiative followed by general imitation and recognition. The usage becomes traditional and is transformed into an obligatory custom or rule; the persons acquire a permanent status and are invested with powers of material or moral constraint. This is the stage of tradition and authority; very often it is the last stage, and continues till the society is destroyed. The usage is relaxed, the rules are violated, the persons in authority cease to be obeyed; this is the stage of revolt and decomposition. Finally, in certain civilised societies, the rule is criticised, the persons in authority are censured, by the action of a part of the subjects a rational change is effected in the composition of the governing body, which is subjected to supervision; this is the stage of reform and of checks.