58. I am the more led to speak of Mr. Mill as not having given due importance to this process of successive generalization, by the way in which he speaks in another place (ii. 525) of this doctrine of Bacon. He conceives Bacon "to have been radically wrong when he enunciates, as a universal rule, that induction should proceed from the lowest to the middle principles, and from those to the highest, never reversing that order, and consequently, leaving no room for the discovery of new principles by way of deduction[285] at all." 59. I conceive that the Inductive Table of Astronomy, to which I have already referred, shows that in that science,--the most complete which has yet existed,--the history of the science has gone on, as to its general movement, in accordance with the view which Bacon's sagacity enjoined. The successive generalizations, _so far as they were true_, were made by successive generations. I conceive also that the Inductive Table of Optics shows the same thing; and this, without taking for granted the truth of the Undulatory Theory; for with regard to all the steps of the progress of the science, lower than that highest one, there is, I conceive, no controversy. 60. Also, the Science of Mechanics, although Mr. Mill more especially refers to it, as a case in which the highest generalizations (for example the Laws of Motion) were those earliest ascertained with any scientific exactness, will, I think, on a more careful examination of its history, be found remarkably to confirm Bacon's view. For, in that science, we have, in the first place, very conspicuous examples of the vice of the method pursued by the ancients in flying to the highest generalizations first; as when they made their false distinctions of the laws of _natural_ and _violent_ motions, and of _terrestrial_ and _celestial_ motions. Many erroneous laws of motion were asserted through neglect of facts or want of experiments. And when Galileo and his school had in some measure succeeded in discovering some of the true laws of the motions of terrestrial bodies, they did not at once assert them as general: for they did not at all apply those laws to the celestial motions. As I have remarked, all Kepler's speculations respecting the causes of the motions of the planets, went upon the supposition that the First Law of terrestrial Motion did not apply to celestial bodies; but that, on the contrary, some continual force was requisite to keep up, as well as to originate, the planetary motions. Nor did Descartes, though he enunciated the Laws of Motion with more generality than his predecessors, (but not with exactness,) venture to trust the planets to those laws; on the contrary, he invented his machinery of Vortices in order to keep up the motions of the heavenly bodies. Newton was the first who extended the laws of terrestrial motion to the celestial spaces; and in doing so, he used all the laws of the celestial motions which had previously been discovered by