Castelli informed Galileo in a letter of 12th July[507] of all this, and advised him to write a letter of thanks to Cardinal Antonio for his kind intercession, which he at once did.[508] Noailles placed all his hopes on a farewell audience with the Pope, in which he meant to ask for Galileo’s pardon. On 8th August he drove for the last time to the Vatican. Urban was very gracious, and when Galileo’s affairs were introduced he even promised at last to bring the subject before the Holy Congregation.[509] Noailles told Cardinal Antonio of this most favourable result with joyful emotion, who said at once: “Good! good! and I will speak to all the cardinals of the Holy Congregation.”[510] They were apparently justified in entertaining the most sanguine hopes, but the future taught them that all this was nothing but fair speeches with which Urban had taken leave of the French ambassador. For there can be no doubt that if the Pope, with his absolute power, had been in earnest about Galileo’s liberation, the Congregation would not have been slow to comply with his wishes. Galileo, however, remained as before, a prisoner in his villa at Arcetri, which he had meanwhile bought, and the papal favour, of which a promise had been held out, was limited to allowing him, at the end of September, to accept an invitation from the Grand Duke to visit him at his Villa Mezzomonte, three miles from Florence,[511] and on 16th October to leave his place of exile for one day to greet the Count de Noailles, at Poggibonsi, in passing through it on his way to France.[512] This was the extent of the papal clemency for the present, and it was not till the old man was quite blind and hopelessly ill, with one foot in the grave, that any humane feeling was awakened for him at the Vatican. CHAPTER II. _FAILING HEALTH AND LOSS OF SIGHT._ Galileo’s Labours at Arcetri.—Completion of the “Dialoghi delle Nuove Scienze.”—Sends it to the Elzevirs at Leyden.—Method of taking Longitudes at Sea.—Declined by Spain and offered to Holland.—Discovery of the Libration and Titubation of the Moon.—Visit from Milton.—Becomes Blind.—Letter to Diodati.—On a hint from Castelli petitions for his Liberty.—The Inquisitor to visit him and report to Rome.—Permitted to live at Florence under Restrictions.—The States-General appoint a Delegate to see him on the Longitude Question.—The Inquisitor sends word of it to Rome.—Galileo not to receive a Heretic.—Presents from the States-General refused from fear of Rome.—Letter to Diodati.—Galileo supposed to be near his End.—Request that Castelli might come to him.—Permitted under Restrictions.—The new “Dialoghi” appear at Leyden, 1638.—They founded Mechanical Physics.—Attract much Notice.—Improvement of Health.—In 1639 goes to Arcetri again, probably not voluntarily.