have come, is the result of a succession of perceptions of the same identity presented under different aspects. Supposing the conceptions, through which it has been necessary to pass, to be A, B, C, D, E, M, the law of their scientific connection may be thus expressed: A = B, B = C, C = D, D = E, E = M; therefore A = M. 271. What we have just explained cannot be well understood unless we recall some characteristics of our intellect, in which is found the reason of so great anomalies. Our intellect is so weak as to perceive things only successively: only after much study does it see what is contained in the clearest ideas. Hence a necessity, to which corresponds with admirable harmony a faculty that satisfies it: the necessity is of conceiving under various, and different, as well as distinct, forms, even the simplest things: the faculty is that of decomposing the conception into many parts, and multiplying in the order of ideas what in that of reality is only one. This faculty of decomposition would be useless were not the intellect, in passing through the succession of conceptions, to find means of connecting and retaining them: otherwise it would continually lose the fruit of its labors; it would slip from its hands as fast as it grasped it. Happily it has this means in signs either written, spoken, or thought; those mysterious expressions which at times not only designate an idea, but also are the compendium of the labors of a whole life, and perhaps of a long series of ages. When the sign is presented to us, we do not see certainly and with full clearness all that it expresses, nor why the expression is legitimate; but we know confusedly the meaning therein contained; we know that in case of necessity, it is enough for us to follow the thread of the perceptions through which we have passed, thus going back even to the simplest elements of science. In making calculations, the most eminent mathematician does not clearly see the meaning of the expressions he uses, except as they relate to the object before him; but he is certain that they do not deceive him, that the rules by which he is guided are sure; because he knows that at another time he established them by incontestible demonstrations. The progress of a science may be compared to a series of posts on which the distances of a road are marked: he who marked the numbers on the posts uses them without necessity of recalling the operations which led him to mark the quantity before him; he is satisfied with knowing that the operations were well made, and that he wrote the result correctly.