In his “History of the Inductive Sciences,” Dr. Whewell says that the Greeks failed in physical philosophy because their “ideas were not distinct, and appropriate to the facts.” I do not quote this remark for its luminousness; since it would be equally proper to ascribe the indistinctness and inappropriateness of their ideas to the imperfection of their physical philosophy; but I quote it because it serves as good evidence of the indefiniteness of primitive science. The same work and its fellow on “The Philosophy of the Inductive Sciences,” supply other evidences equally good, because equally independent of any such hypothesis as is here to be established. Respecting mathematics we have the fact that geometrical theorems grew out of empirical methods; and that these theorems, at first isolated, did not acquire the clearness which complete demonstration gives, until they were arranged by Euclid into a series of dependent propositions. At a later period the same general truth was exemplified in the progress from the “method of exhaustions” and the “method of indivisibles” to the “method of limits;” which is the central idea of the infinitesimal calculus. In early mechanics, too, may be traced a dim perception that action and re-action are equal and opposite; though for ages after, this truth remained unformulated. And similarly, the property of inertia, though not distinctly comprehended until Kepler lived, was vaguely recognized long previously. “The conception of statical force,” “was never presented in a distinct form till the works of Archimedes appeared;” and “the conception of accelerating force was confused, in the mind of Kepler and his contemporaries, and did not become clear enough for purposes of sound scientific reasoning before the succeeding century.” To which specific assertions may be added the general remark, that “terms which originally, and before the laws of motion were fully known, were used in a very vague and fluctuating sense, were afterwards limited and rendered precise.” When we turn from abstract scientific conceptions to the concrete previsions of science, of which astronomy furnishes us with numerous examples, the like contrast is visible. The times at which celestial phenomena will occur, have been predicted with ever-increasing accuracy: errors once amounting to days, have been reduced down to seconds. The correspondence between the real and supposed forms of orbits, has been growing gradually more precise. Originally thought circular, then epicyclical, then elliptical, orbits are now ascertained to be curves which always deviate more or less from perfect ellipses, and which are ever undergoing change. But the general advance of Science in definiteness, is best shown by the contrast between its qualitative stage, and its quantitative stage. At first, the facts ascertained were, that between such and such phenomena some connexion existed—that the appearances _a_ and _b_ always occurred together or in