With regard to Tycho's discoveries respecting the moon, it is to be recollected that besides the first inequality of the moon's motion, (the _equation of the centre_, arising from the elliptical form of her orbit,) Ptolemy had discovered a second inequality, the _evection_, which, as we have observed in the History of this subject[164], might have naturally suggested the suspicion that there were still other inequalities. In the middle ages, however, such suggestions, implying a constant progress in science, were little attended to; and, we have seen, that when an Arabian astronomer[165] had really discovered another inequality of the moon, it was soon forgotten, because it had no place in the established systems. Tycho not only rediscovered the lunar inequality, (the _variation_,) thus once before won and lost, but also two other inequalities; namely[166], the _change of inclination_ of the moon's orbit as the line of nodes moves round, and an inequality in the motion of the line of nodes. Thus, as I have elsewhere said, it appeared that the discovery of a rule is a step to the discovery of deviations from that rule, which require to be expressed in other rules. It became manifest to astronomers, and through them to all philosophers, that in the application of theory to observation, we find, not only the stated phenomena, for which the theory does account, but also _residual phenomena_, which are unaccounted for, and remain over and above the calculation. And it was seen further, that these residual phenomena might be, altogether or in part, exhausted by new theories. These were valuable lessons; and the more valuable inasmuch as men were now trying to lay down maxims and methods for the conduct of science. A revolution was not only at hand, but had really taken place, in the great body of real cultivators of science. The occasion now required that this revolution should be formally recognized;--that the new intellectual power should be clothed with the forms of government;--that the new philosophical republic should be acknowledged as a sister state by the ancient dynasties of Aristotle and Plato. There was needed some great Theoretical Reformer, to speak in the name of the Experimental Philosophy; to lay before the world a declaration of its rights and a scheme of its laws. And thus our eyes are turned to Francis Bacon, and others who like him attempted this great office. We quit those august and venerable names of discoverers, whose appearance was the prelude and announcement of the new state of things then opening; and in doing so, we may apply to them the language which Bacon applies to himself[167]:-- Χαίρετε Κήρυκες Διὸ ς ἄγγελοι ἠδὲ καὶ ἀνδρῶν. Hail, Heralds, Messengers of Gods and Men! FOOTNOTES: [Footnote 128: His works have never been published, and exist in manuscript in the library of the Institute at Paris. Some extracts were published by Venturi, _Essai sur les Ouvrages de Leonard da Vinci_. Paris, 1797.]