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Galileo's health was bad for some time after his return to Florence, and though he wrote and circulated long private letters he was unable to do much in the way of observation even of the bright comet of 1618. He must have made some observations, however, for he came to the conclusion that comets were atmospheric phenomena, but his views, published ostensibly by one of his pupils, gave offence to the Jesuit College at Rome, and called forth from Father Grassi, whose opinions were attacked in the pamphlet, a violent reply full of abuse of Galileo. He was urged to take up the cudgels himself, but waited for three years partly on account of ill-health, and partly from caution. The Papal Imprimatur was granted in 1623 after various impolitic passages had been altered by members of the Academy, to whom it was first submitted, and the essay published under the title of "II Saggiatore" (Assayer). Pope Paul V. had died shortly before this, and his successor Gregory XV. died while the work was being printed, so that a new Pope was at the Vatican when the book appeared, and this new Pope, Urban VIII., was none other than Cardinal M. Barberini, who had frequently shown sympathy with Galileo. To him the "Saggiatore" was consequently dedicated, and Galileo must have hoped confidently to meet with less opposition in the future. The success of the book was immediate and well justified the delay in publication, but it gave great offence to the Jesuits, whose champion found his arguments turned into ridicule with great dialectic skill and in the choicest Italian. The Pope was much pleased and had the book read aloud at table, while the general of the Jesuits forbade its mere mention among members of the order.

We may note that Cardinal Bellarmine, who had taken a prominent part in the opposition to Copernican views, had died about the same time as Pope Paul V., so that for this reason also Galileo thought that another visit to Rome would now be expedient. Ill-health and other matters, however, delayed the project, about which Galileo's elder daughter was most enthusiastic. Both daughters were by this time nuns, having taken the veil under the names of Maria Celeste and Arcangela. Galileo had broken up his establishments on leaving Padua, and brought the girls to Florence, the boy Vincenzio, then only four years old, remaining for two years longer with his mother, who, soon after he was removed from her care, married in her own station of life, with Galileo's approval and financial assistance. The convent appeared to be the only resource for the daughters, as their father's means were not enough to make them independent, and the stigma of their birth was a bar to them in other directions, besides furnishing a frequent cause of complaint to Galileo's mother. In course of time Vincenzio was legitimised by the Grand Duke, but it was Maria Celeste who proved of the greatest comfort to her father, Vincenzio being idle, selfish, and extravagant, not unlike his uncle Michelangelo, while Arcangela was frequently ailing and discontented. Many of Maria Celeste's letters are extant and show her constant solicitude for her father; and her anxiety to help him in every possible way, writing out letters for him, mending or laundering his linen, making little delicacies to tempt his appetite, and so on, as she found occasion.

In 1624 Galileo went to Rome once more and had several audiences with the new Pope, who received him in a most friendly manner, but absolutely refused to remove the embargo from Copernican doctrines. We may conclude from the evidence of the sympathy he displayed that this was a matter more of policy than conviction. Ecclesiastical authority was being assailed in many directions, and it was felt that its strongest bulwark must be the Bible. To admit the possibility of error in the Bible itself was unthinkable, and as to the translation and interpretation of it, any suggestion of even uncertainty would appear to weaken the authority of the Church dignitaries who took the responsibility for the accepted language and interpretation. The Pope's argument, as given to Galileo, was that if anything stated in Scripture appeared to present insuperable difficulty, it must not be called impossible, or else there would be an implicit limitation of Omnipotence. The acceptance of this argument would at once demolish all Galileo's plausible hypotheses, and he returned to Florence disappointed of his main object, though bearing many evidences of the Pope's personal favour, in the form of valuable gifts, and the promise of a pension for his son. This pension was subsequently transferred to Galileo himself, as Vincenzio refused to undertake the religious exercises which were a condition of acceptance. Moreover, Galileo's friend and patron Cosmo dei Medici having died in 1624, the Pope warmly commended Galileo to the new Grand Duke Ferdinand, now a boy of thirteen, eulogising not only the philosopher's services to science but also his religious sentiments.

It was during this visit to Rome that Galileo was shown a microscope. He speedily grasped the principle and proceeded to make better ones, with image not inverted, just as he had in the case of the telescope without seeing the early inverting pattern. His microscopes were soon as much in demand as his telescopes, as they were much more powerful and gave better definition than those previously made.

There is no doubt that he was all the time pining for a favourable opportunity of openly defending the Copernican system. An attack made on it by Ingoli in 1616, addressed to Galileo, had remained unanswered at the time, owing to the hostile attitude of the Inquisition. Kepler answered it in 1618 in his "Epitome of the Copernican Astronomy," but Galileo felt that he might now venture to reply more fully, taking special precautions to emphasise the point that he was merely treating the system as a working hypothesis. He professed to have two objects in view, one personal, to clear himself from the suspicion of having propounded an absurd and irreligious theory, by showing that he had supported it before it was under theological ban, and that from every other point of view it was quite reasonable and probable; the other, from a sense of loyalty to Church and country, to give the Protestant Copernicans of Germany the true explanation of the apparent rejection of their system in Italy. On the advice of friends he only circulated his reply in manuscript, and was told that the Pope approved of it after hearing passages read, saying that the Church had not condemned the Copernican doctrine as heretical, but as rash.

It is not at all surprising that this and other similar encouraging reports should have convinced Galileo that the time was getting ripe for the complete victory of the new system, provided that it advanced cautiously at first. So for the next four years, 1626 to 1629, he did little else, in the intervals between frequent attacks of illness and domestic troubles, but concentrate his energies on the production of his most imposing astronomical work, the "Dialogues on the Two Principal Systems of the World". The domestic troubles included not only illness of his daughters and annoyance at unsatisfactory reports of his son, but also difficulties in connection with his selfish brother, who, having now a family of seven, came to the conclusion that it would be an excellent thing for him to send them to Florence to live on Galileo. The latter, on the question being raised, offered temporary quarters until his brother should obtain work in Florence. The whole family except the eldest daughter took advantage of the offer. Galileo sent the eldest boy Vincenzio to Rome to study music in charge of his friend Castelli, and there, but for his bad conduct, he would have had the pension refused by his cousin, which in consequence, as we have seen, was transferred to Galileo. The nephew soon had to leave Rome, and before the end of the year (1628) Michelangelo had them all back again at Munich, though Galileo was willing to keep them. During the same year the other Vincenzio, Galileo's son, completed his Law course at the University of Pisa and took his Doctor's degree. He was nevertheless disinclined to seek a post in the Civil Service, for which he was now qualified, but preferred to idle away his time at home.

About this time an unsuccessful attempt was made to deprive Galileo of his practical sinecure at Pisa, some of his enemies questioning the power of the Grand Duke to assign a university salary to a man who neither lectured nor lived at Pisa; but it was decided that Ferdinand had power to do this, and to avoid the possibility of the question being raised again, the young Grand Duke appointed Galileo to a permanent post of equal value in the magistracy of the University, so that his income and leisure were if possible more secure than before.