He was at this time also deeply interested in a subject which originated as far back as 1610. It had occurred to him soon after the discovery of Jupiter’s moons, by a series of observations of them, to make astronomical calculations and tables which would enable him to predict every year their configurations, their relative positions and occasional eclipses with the utmost precision; this would furnish the means of ascertaining the longitude of the point of observation at any hour of the night, which appeared to be of special importance to navigation. For hitherto the eclipses of the sun and moon had had to be employed for the purpose, which, however, on account of their rarity and the want of precise calculation, were neither entirely to be relied on nor sufficient. Galileo had offered his discovery,—the practical value of which he overrated,—in 1612, to the Spanish Government, and in 1616 tedious negotiations were carried on about it, which however led to no result, were then postponed till 1620, and in 1630 entirely given up.[519] Now (August, 1636,) as he heard that the Dutch merchants had even offered a premium of thirty thousand scudi to any one who should invent a sure method of taking longitudes at sea, he ventured, without the knowledge of the Inquisition, to offer his invention to the Protestant States-General. Diodati at Paris was the mediator in these secret and ceremonious negotiations. On 11th November, Galileo’s offer was entertained in the most flattering manner in the Assembly of the States-General, and a commission was appointed, consisting of the four _savans_, Realius, Hortensius, Blavius, and Golius, to examine into the subject and report upon it.[520] While Galileo was impatiently waiting for the decision that was never come to, he made his last great telescopic discovery, although suffering much in his eyes, that of the libration and titubation of the moon, about which he wrote his remarkable letter to Alfonso Antonini, bearing the signal date: “Della mia carcere di Arcetri li 10 febbrajo 1637.”[521] The complaint in Galileo’s eyes grew rapidly worse. By the end of June the sight of the right eye was gone, and that of the other diminished with frightful rapidity from a constant discharge.[522] But in spite of this heavy calamity, combined with his other sufferings, his interest in science did not diminish for a moment. Even at this sad time we find him carrying on a brisk correspondence with the learned men of Germany, Holland, France, and Italy, continuing his negotiations with the States-General with great zest,[523] as well as occupying himself perpetually with astronomy and physics. He was indeed often obliged to employ the hand of another;[524] but his mind worked on with undiminished vigour, even though he was no longer able to commit to paper himself the ideas that continually occupied him.