II. The facts of humanity, with their complex and varied character, cannot be reduced like chemical facts to a few simple formulæ. Like the other sciences which deal with life, history needs descriptive formulæ in order to express the nature of the different phenomena. In order to be manageable, a formula must be short; in order to give an exact idea of the facts, it must be precise. Now, in the knowledge of human affairs, precision can only be obtained by attention to characteristic details, for these alone enable us to understand how one fact differed from others, and what there was in it peculiar to itself. There is thus a conflict between the need of brevity, which leads us to look for concrete formulæ, and the necessity of being precise, which requires us to adopt detailed formulæ. Formulæ which are too short make science vague and illusory, formulæ which are too long encumber it and make it useless. This dilemma can only be evaded by a perpetual compromise, the principle of which is to compress the facts by omitting all that is not necessary for the purpose of representing them to the mind, and to stop at the point where omission would suppress some characteristic feature. This operation, which is difficult in itself, is still further complicated by the state in which the facts which are to be condensed into formulæ present themselves. According to the nature of the documents from which they are derived, they come to us in all the different degrees of precision: from the detailed narrative which relates the smallest episodes (the battle of Waterloo) down to the barest mention in a couple of words (the victory of the Austrasians at Testry). On different facts of the same kind we possess an amount of details which is infinitely variable according as the documents give us a complete description or a mere mention. How are we to organise into a common whole, items of knowledge which differ so widely in point of precision? When facts are known to us from a vague word of general import, we cannot reduce them to a less degree of generality and a greater degree of precision; we do not know the details. If we add them conjecturally we shall produce an historical novel. This is what Augustin Thierry did in the case of his _Récits mérovingiens_. When facts are known in detail, it is always easy to reduce them to a greater degree of generality by suppressing characteristic details; this is what is done by the authors of abridgements. But the result of this procedure would be to reduce history to a mass of vague generalities, uniform for the whole of time except for the proper names and the dates. It would be a dangerous method of introducing symmetry, to bring all facts to a common degree of generality by levelling them all to the condition of those which are the most imperfectly known. In those cases, therefore, where the documents give details, our descriptive formulæ should always retain the characteristic features of the facts.