We may exemplify this progress in the history of the science of Mechanics. Thus the property of the lever, the inverse proportion of the weights and arms, was known as a fact before the time of Aristotle, and known as no more; for he gives many fantastical and inapplicable reasons for the fact. But in the writings of Archimedes we find this fact brought within the domain of necessary truth. It was there transferred from the empirical to the ideal side of the Fundamental Antithesis; and thus a progressive step was made in science. In like manner, it was at first taken by Galileo as a mere fact of experience, that in a falling body, the velocity increases in proportion to the time; but his followers have seen in this the necessary effect of the uniform force of gravity. In like manner, Kepler's empirical Laws were shown by Newton to be necessary results of a central force attracting inversely as the square of the distance. And if it be still, even at present, doubtful whether this is the _necessary_ law of a central force, as some philosophers have maintained that it is, we cannot doubt that if now or hereafter, those philosophers could establish their doctrine as certain, they would make an important step in science, in addition to those already made. And thus, such steps in science are made, whenever empirical facts are discerned to be necessary laws; or, if I may be allowed to use a briefer expression, whenever _facts are idealized_. 4. In order to show how widely this statement is applicable, I will exemplify it in some of the other sciences. In Chemistry, not to speak of earlier steps in the science, which might be presented as instances of the same general process, we may remark that the analyses of various compounds into their elements, according to the quantity of the elements, form a vast multitude of facts, which were previously empirical only, but which are reduced to a law, and therefore to a certain kind of ideal necessity, by the discovery of their being compounded according to definite and multiple proportions. And again, this very law of definite proportions, which may at first be taken as a law given by experience only, it has been attempted to make into a necessary truth, by asserting that bodies must necessarily consist of atoms, and atoms must necessarily combine in definite small numbers. And however doubtful this Atomic Theory may at present be, it will not be questioned that any chemical philosopher who could establish it, or any other Theory which would produce an equivalent change in the aspect of the science, would make a great scientific advance. And thus, in this Science also, the Progress of Science consists in the transfer of facts from the empirical to the necessary side of the antithesis; or, as it was before expressed, in the idealization of facts.