a uniformly accelerated motion toward a fixed point, Newton's wonderful mastery of geometrical reasoning enabled him to show that, if these dynamical assumptions be granted, Kepler's phenomenal "laws," being a necessary consequence of them, must be universally true. And while that demonstration would have been alone sufficient to give him an imperishable renown, it was his still greater glory to divine that the fall of the moon toward the earth—that is, the deflection of her path from a tangential line to an ellipse—is a phenomenon of the same order as the fall of a stone to the ground; and thus to show the applicability to the entire universe of those simple dynamical conceptions which constitute the basis of the geometry of the "Principia."
Thus, then, while no "law" which is simply a generalization of phenomena can be considered as having any coercive action, we may assign that value to laws which express the universal conditions of the action of a force, the existence of which we learn from the testimony of our own consciousness. The assurance we feel, that the attraction of gravitation must act under all circumstances according to its one simple law, is of a very different order from that which we have in regard (for example) to the laws of chemical attraction, which are as yet only generalizations of phenomena. And yet, even in that strong assurance, we are required, by our examination of the basis on which it rests, to admit a reserve of the possibility of something different—a reserve which we may well believe that Newton himself must have entertained.
A most valuable lesson as to the allowance we ought to make for the unknown "possibilities of Nature" is taught us by an exceptional phenomenon so familiar that it does not attract the notice it has a right to claim. Next to the law of the universal attraction of masses of matter, there is none that has a wider range than that of the expansion of bodies by heat. Excluding water and one or two other substances, the fact of such expansion might be said to be invariable, and, as regards bodies whose gaseous condition is known, the law of expansion can be stated in a form no less simple and definite than the law of gravitation. Supposing those exceptions then to be unknown, the law would be universal in its range. But it comes to be discovered that water, while conforming to it in its expansion from 39 upward to its boiling-point, as also, when it passes into steam, to the special law of expansion of vapors, is exceptional in its expansion also from 39½° downward to its freezing-point; and of this failure in the universality of the law no rationale can be given. Still more strange is it that by dissolving a little salt in water we should remove this exceptional peculiarity, for sea-water continues to contract from 39 downward to its freezing-point 12° or 14° lower, just as it does with reduction of temperature at higher ranges.
Thus, from our study of the mode in which we arrive at those conceptions of the orderly sequence observable in the phenomena of Na-
