Kepler had previously published a treatise on Optics (Frankfort, 1604). He now extended it to the consideration of the theory of the telescope, and explained the principle of Galileo’s telescope; he also showed another combination of lenses which would produce a similar effect. This was the principle of the common astronomical telescope, often called, from this circumstance, Kepler’s telescope, though he did not construct it. The account of Galileo’s later astronomical discoveries of Saturn’s ring and the phases of Venus is taken from the preface of this work.—(Kepler’s _Dioptrics_; Augsburg, 1611.) In 1612 Galileo published a series of observations of solar spots, and in 1618 some observations of three comets. There exist also long series of minute observations of Jupiter and his satellites, continued to November 1619.—(Galileo’s _Works_; Florence, 1845.) Further astronomical researches may have been hindered by failing sight. One more astronomical discovery, however, that of the moon’s librations, was made as late as 1637, and the announcement of it is dated “dalla mia carcere di Arcetri.” Galileo died January 8, 1642. The following editions have been used for the translation:— Galileo’s _Works_. 1. Florence, 1718. 2. Padua, 1744. 3. Florence, 1842-56. _Sidereus Nuncius._ 1. Venice, 1610. 2. London, 1653. Kepler’s _Works_, ed. C. Frisch. Frankfurt a. M., 1858-71. Prodromus dissertationum mathematicarum continens Mysterium Cosmographicum de admirabili proportione orbium cœlestium. Tübingen, 1596. Astronomia nova αἰτιολογητός (Commentaria de motibus stellæ Martis). [Prague,] 1609. THE SIDEREAL MESSENGER OF GALILEO GALILEI THE SIDEREAL MESSENGER _UNFOLDING GREAT AND MARVELLOUS SIGHTS, AND PROPOSING THEM TO THE ATTENTION OF EVERY ONE, BUT ESPECIALLY PHILOSOPHERS AND ASTRONOMERS_, BEING SUCH AS HAVE BEEN OBSERVED BY GALILEO GALILEI A GENTLEMAN OF FLORENCE, PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF PADUA, WITH THE AID OF A TELESCOPE _lately invented by him_, _Respecting the Moon’s Surface, an innumerable number of Fixed Stars, the Milky Way, and Nebulous Stars, but especially respecting Four Planets which revolve round the Planet Jupiter at different distances and in different periodic times, with amazing velocity, and which, after remaining unknown to every one up to this day, the Author recently discovered, and determined to name the_ MEDICEAN STARS. Venice 1610. TO THE MOST SERENE COSMO DE’ MEDICI, THE SECOND, _FOURTH GRAND-DUKE OF TUSCANY_.