The great changes which thus take place in the history of science, the revolutions of the intellectual world, have, as a usual and leading character, this, that they are steps of generalization; — transitions from particular truths to others of a wider extent, in which the former are included. This progress of knowledge, from individual facts to universal laws, — from particular propositions to general ones, — and from these to others still more general, with reference to which the former generalizations are particular,— is so far familiar to men’s minds, that without here entering into further explanation, its nature will be understood sufficiently to prepare the reader to recognise the exemplifications of such a process, which he will find at every step of our advance.

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Since the advance of science consists in collecting by induction general laws from particular facts, and in combining several laws into one higher generalization, in which they still retain their former truth, we might form a Chart, or Table, of the progress of each science, by setting down the particulars which thus flow together, so as to form general truths, and marking the junction of these general truths into others more comprehensive. The table of the progress of any science would thus resemble the map of a river, in which the waters from separate sources unite and make rivulets, which again meet with rivulets from other fountains, and thus go on forming by their junction trunks of a higher and higher order. The representation of the state of a science in this form, would necessarily exhibit all the principal doctrines of the science; for each general truth contains the particular truths from which it was derived, and may be followed backwards till we have these before us in their separate state.