the action), working under such and such material conditions (locality, instrument), performed such and such actions, which had for their result such and such a modification. For the determination of the motives of the actions, the only method is to compare the actions, firstly, with the declarations of those who performed them; secondly, with the interpretation of those who witnessed their performance. There is often a doubt remaining: this is the field of party polemics; every one attributes noble motives to the actions of his own party and discreditable motives to those of the opposite party. But actions described without any indication of motive would be unintelligible.
(2) The extension of the event will be indicated both in space (the place where it happened, and the region in which its immediate effects were felt) and in time, the moment when its realisation began, and the moment when the result was brought about.
V. Descriptive formulæ relating to characters, being merely qualitative, only give an abstract idea of the facts; in order to realise the place they occupied in reality, quantity is necessary. It is not a matter of indifference whether a given usage was practised by a hundred men or by millions.
For the purpose of introducing quantity into formulæ 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