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At the end of the four years, the dialogues being now completed except for introduction and index and a final revision, Galileo determined to go once more to Rome to arrange for the printing. Castelli, now the Pope's mathematician, highly approved this decision, as also did Riccardi, the chief censor, and others, who retailed remarks made by the Pope, disclaiming any responsibility for the action taken in 1616 against the Copernican doctrines. But when it came to the point the Pope insisted that the title originally chosen, "Dialogues on the Flux and Reflux of the Tides," did not indicate the real purpose of the work, which was a discussion of the relative merits of the systems of Copernicus and Ptolemy. Besides requiring that this be made more clear, and that the subject be treated as merely a hypothesis. Urban laid it down that his own favourite argument, which has already been mentioned, must be inserted at the end. Galileo accepted the conditions, and the manuscript was passed by Riccardi as censor after a few alteration's had been made by his assistant.

Thus in the summer of 1630 we find Galileo back in Florence with the coveted Imprimatur granted on the understanding that a preface and conclusion as demanded by the Pope should be added. The plague was then raging in Florence, and it spread to the suburb of Bellosguardo where Galileo lived. One of his employees, a glass-blower, was attacked by it and died, and Vincenzio fled with his wife, a sister of one of Maria Celeste's intimates at the convent, leaving his infant baby out at nurse and his invalid father almost alone. Vincenzio, however, was too idle to stay away long from his father's house when the panic was over, and the next year we find him back again helping to choose a villa nearer the convent. Such a one was found at Arcetri, and is still known as Villa Galileo, and contains a room arranged as a Galileo museum.

The plague was not the only cause of delay. Prince Cesi, of the Academy, to whom Galileo intended entrusting the work for superintendence during the printing, died a few weeks after Galileo's return from Rome, and Galileo, being unable on account of the plague to send the MS. away, determined to have it printed at Florence instead of Rome. On hearing this the censor Riccardi desired to look at the book again, but it seemed risky to send the whole work while communications were still interrupted on account of the plague, and Galileo therefore suggested a compromise, under which he was to send to Rome only the additions, the preface and conclusion, not before seen at Rome, while the body of the work should be submitted to a deputy censor at Florence appointed for the purpose. The one chosen, Stefani, Counsellor of the Inquisition in Florence, was so pleased with the work and the tone of humility in which it was written that he not only made none but the slightest verbal alterations, but declared that so far from putting obstacles in the way they ought to have urged Galileo to publish it. But it was otherwise in regard to the preface, which was kept at Rome an unconscionable time and only returned in July, 1631, after the Tuscan Ambassador Niccolini had made formal protest: Stefani was ordered to revise the whole work once more, and then the licence was at length granted for printing the book in Florence.

The plan of the work, as indicated by the word dialogue, is that of an argument between supporters of the two systems. There are, however, three interlocutors instead of two, as it seemed expedient to provide a third party to weigh the merits of the controversy provided by the two champions, and to represent what is now commonly called "The man in the street". Galileo gave the name of Simplicio, a noted commentator on Aristotle, to the personage who has to produce all the arguments against the new system, however foolish they may be. To the other characters he gave the names of two former friends of his own, Salviati of Florence, who speaks really for Galileo himself, and Sagredo of Venice, who is responsible for common-sense objections, and for the introduction of a lighter vein from time to time, but who, as is only natural, is very ready to be convinced by Salviati's arguments. The exigencies of the censorship prevented any of the most powerful arguments being pushed right home, as it was necessary at every critical point to emphasise the formality that the Copernican system was not to be regarded as true but only as a not impossible hypothesis. Some such display might be made by a skilled fencer against a hopelessly inferior opponent, who wears, however, a coat of adamant guaranteed to shatter the blade that touches it, so that no victory is to be allowed, every stroke being obliged to recoil.

Of the four days over which the dialogue is spread, the first combats the Aristotelian doctrine of perfect and unchangeable heavens by means of the evidence of new stars and sun-spots, and emphasises the similarity between the earth, moon, and planets, pointing to Jupiter with his attendant moons as a model of the solar system with its attendant planets. The chief point on the second day is the principle of the difference between common and relative motion. The objection to the earth's rotation, that if true a stone dropped from a tower would not fall at its foot, is met by the fact that in a moving vessel a stone dropped from the top of a mast does fall at its foot, although the Aristotelians, not having tried the experiment, maintained that it would fall towards the stern. On the score of simplicity, therefore, a daily rotation of the earth, once admitted as possible, is obviously far more probable than a daily rotation of the whole universe about the earth. The precession of the equinoxes is brought in finally to show how much more complicated and improbable, are the motions necessary to reconcile the facts with the Ptolemaic theory. On the third day the revolution of the earth about the sun is considered, of course as a mere hypothesis. The great difficulty contemplated by Copernicus was that, if the earth really went round the sun, in an orbit nearly two hundred million miles in diameter, the stars ought to show a displacement corresponding to the great change in view-point through the year. The modern reply is that they do, but this could not be proved until nearly two centuries later, though Galileo, speaking as Salviati, grasped the position very clearly. He pointed out that on the one hand the stars must be so far off that the relative displacement of nearer ones is too small to be detected by his instruments, while on the other hand their apparent size, which would on the hypothesis of enormous distance lead to inconceivable dimensions, is an optical illusion; this is shown by their remaining as points when viewed through a telescope, unlike the comparatively near planets which show discs under sufficient magnifying power. Reference to Gilbert's work on the magnet indicates that Galileo had some inkling of the idea that crystallised later in Newton's theory of universal gravitation. The fourth day elaborates Galileo's erroneous theory of the tides, to which previous reference has been made.

If we wish to form a clear idea of Galileo's services to science, we must not only take account of his great inventions and discoveries, but also of his elegant style, his comprehensive sagacity and fertility of argument, whether on behalf of truth or in the exposure of error. This was insisted upon in the Supplement to the 7th Edition of the "Encyclopædia Britannica" by Professor Playfair, who wrote: "The 'Dialogues on the Two Systems' are written with such singular felicity that one reads them at the present day, when the truths contained in them are known and admitted, with all the delight of novelty, and feels one's self carried back to the period when the telescope was first directed to the heavens, and when the earth's motion with its train of consequences was proved for the first time. Of all the writers who have lived in an age which was only emerging from ignorance and barbarism, Galileo has most entirely the tone of true philosophy, and is most free from the contamination of the time in taste, sentiment, and opinion."