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cluster Præsepe (in the Crab), for example, he counted 40 stars.

121. By far the most striking discovery announced in the Sidereal Messenger was that of the bodies now known as the moons or satellites of Jupiter. On January 7th, 1610, Galilei turned his telescope on to Jupiter, and noticed three faint stars which caught his attention on account of their closeness to the planet and their arrangement nearly in a straight line with it. He looked again next night, and noticed that they had changed their positions relatively to Jupiter, but that the change did not seem to be such as could result from Jupiter’s own motion, if the new bodies were fixed stars. Two nights later he was able to confirm this conclusion, and to infer that the new bodies were not fixed stars, but moving bodies which accompanied Jupiter in his movements. A fourth body was noticed on January 13th, and the motions of all four were soon recognised by Galilei as being motions of revolution round Jupiter as a centre. With characteristic thoroughness he watched the motions of the new bodies night after night, and by the date of the publication of his book had already estimated with very fair accuracy their periods of revolution round Jupiter, which ranged between about 42 hours and 17 days; and he continued to watch their motions for years.

Fig. 54.—Jupiter and its satellites as seen on Jan. 7, 1610. From the Sidereus Nuncius.

The new bodies were at first called by their discoverer Medicean planets, in honour of his patron Cosmo de Medici, the Grand Duke of Tuscany; but it was evident that bodies revolving round a planet, as the planets themselves revolved round the sun, formed a new class of bodies distinct from the known planets, and the name of satellite, suggested by Kepler as applicable to the new bodies as well as to the moon, has been generally accepted.

The discovery of Jupiter’s satellites shewed the falsity of the old doctrine that the earth was the only centre of motion; it tended, moreover, seriously to discredit the infallibility of Aristotle and Ptolemy, who had clearly no knowledge of the existence of such bodies; and again those who had difficulty in believing that Venus and Mercury could revolve round an apparently moving body, the sun, could not but have their doubts shaken when shewn the new satellites evidently performing a motion of just this character; and—most important consequence of all—the very real mechanical difficulty involved in the Coppernican conception of the moon revolving round the moving earth and not dropping behind was at any rate shewn not to be insuperable, as Jupiter’s satellites succeeded in performing a precisely similar feat.

The same reasons which rendered Galilei’s telescopic discoveries of scientific importance made them also objectionable to the supporters of the old views, and they were accordingly attacked in a number of pamphlets, some of which are still extant and possess a certain amount of interest. One Martin Horky, for example, a young German who had studied under Kepler, published a pamphlet in which, after proving to his own satisfaction that the satellites of Jupiter did not exist, he discussed at some length what they were, what they were like, and why they existed. Another writer gravely argued that because the human body had seven openings in it—the eyes, ears, nostrils, and mouth—therefore by analogy there must be seven planets (the sun and moon being included) and no more. However, confirmation by other observers was soon obtained and the pendulum even began to swing in the opposite direction, a number of new satellites of Jupiter being announced by various observers. None of these, however, turned out to be genuine, and Galilei’s four remained the only known satellites of Jupiter till a few years ago (chapter XIII., § 295).

122. The reputation acquired by Galilei by the publication of the Messenger enabled him to bring to a satisfactory issue negotiations which he had for some time been carrying on with the Tuscan court. Though he had been well treated by the Venetians, he had begun to feel the burden of regular teaching somewhat irksome, and was anxious to devote more time to research and to writing. A republic could hardly be expected to provide him with such a sinecure as he wanted, and he accordingly accepted in the summer of 1610 an appointment as professor at Pisa, and also as “First Philosopher and Mathematician” to the Grand Duke of Tuscany, with a handsome salary and no definite duties attached to either office.

123. Shortly before leaving Padua he turned his telescope on to Saturn, and observed that the planet appeared to consist of three parts, as shewn in the first drawing of fig. 67 (chapter VIII., § 154). On subsequent occasions, however, he failed to see more than the central body, and the appearances of Saturn continued to present perplexing variations, till the mystery was solved by Huygens in 1655 (chapter VIII., § 154).

The first discovery made at Florence (October 1610) was that Venus, which to the naked eye appears to vary very much in brilliancy but not in shape, was in reality at times crescent-shaped like the new moon and passed through phases similar to some of those of the moon. This shewed that Venus was, like the moon, a dark body in itself, deriving its light from the sun; so that its similarity to the earth was thereby made more evident.

Fig. 55.—Sun-spots. From Galilei’s Macchie Solari.

[To face p. 154.

124. The discovery of dark spots on the sun completed this series of telescopic discoveries. According to his own statement Galilei first saw them towards the end of 1610,69 but apparently paid no particular attention to them at the time; and, although he shewed them as a matter of curiosity to various friends, he made no formal announcement of the discovery till May 1612, by which time the same discovery had been made independently by Harriot (§ 118) in England, by John Fabricius (1587-? 1615) in Holland, and by the Jesuit Christopher Scheiner (1575-1650) in Germany, and had been published by Fabricius (June 1611). As a matter of fact dark spots had been seen with the naked eye long before, but had been generally supposed to be caused by the passage of Mercury in front of the sun. The presence on the sun of such blemishes as black spots, the “mutability” involved in their changes in form and position, and their formation and subsequent disappearance, were all distasteful to the supporters of the old views, according to which celestial bodies were perfect and unchangeable. The fact, noticed by all the early observers, that the spots appeared to move across the face of the sun from the eastern to the western side (i.e. roughly from left to right, as seen at midday by an observer in our latitudes), gave at first sight countenance to the view, championed by Scheiner among others, that the spots might really be small planets revolving round the sun, and appearing as dark objects whenever they passed between the sun and the observer. In three letters to his friend Welser, a merchant prince of Augsburg, written in 1612 and published in the following year,70 Galilei, while giving a full account of his observations, gave a crushing refutation of this view; proved that the spots must be on or close to the surface of the sun, and that the motions observed were exactly such as would result if the spots were attached to the sun, and it revolved on an axis in a period of about a month; and further, while disclaiming any wish to speak confidently, called attention to several of their points of resemblance to clouds.

One of his arguments against Scheiner’s views is so simple and at the same time so convincing, that it may be worth while to reproduce it as an illustration of Galilei’s method, though the controversy itself is quite dead.

Galilei noticed, namely, that while a spot took about fourteen days to cross from one side of the sun to the other, and this time was the same whether the spot passed through the centre of the sun’s disc, or along a shorter path at some distance from it, its rate of motion was by no means uniform, but that the spot’s motion always appeared much slower when near the edge of the sun than when near the centre. This he recognised as an effect of foreshortening, which would result if, and only if, the spot were near the sun.

If, for example, in the figure, the circle represent a section of the sun by a plane through the observer at O, and A, B, C, D, E be points taken at equal distances along the surface of the sun, so as to represent the positions of an object on the sun at equal intervals of time, on the assumption that the sun revolves uniformly, then the apparent motion from A to B, as seen by the observer at O, is measured by the angle A O B, and is obviously much less than that from D to E, measured by the angle D O E, and consequently an object attached to the sun must appear to move more slowly from A to B, i.e. near the sun’s edge, than from D to E, near the centre. On the other hand, if the spot be a body revolving round the sun at some distance from it, e.g. along the dotted circle c d e, then if c, d, e be taken at equal distances from one another, the apparent motion from c to d, measured again by the angle c O d, is only very slightly less than that from d to e, measured by the angle d O e. Moreover, it required only a simple calculation, performed by Galilei in several cases, to express these results in a numerical shape, and so to infer from the actual observations that the spots could not be more than a very moderate distance from the sun. The only escape from this conclusion was by the assumption that the spots, if they were bodies revolving round the sun, moved irregularly, in such a way as always to be moving fastest when they happened to be between the centre of the sun and the earth, whatever the earth’s position might be at the time, a procedure for which, on the one hand, no sort of reason could be given, and which, on the other, was entirely out of harmony with the uniformity to which mediæval astronomy clung so firmly.

Fig. 56.—Galilei’s proof that sun-spots are not planets.

The rotation of the sun about an axis, thus established, might evidently have been used as an argument in support of the view that the earth also had such a motion, but, as far as I am aware, neither Galilei nor any contemporary noticed the analogy. Among other facts relating to the spots observed by Galilei were the greater darkness of the central parts, some of his drawings (see fig. 55) shewing, like most modern drawings, a fairly well-marked line of division between the central part (or umbra) and the less dark fringe (or penumbra) surrounding it; he noticed also that spots frequently appeared in groups, that the members of a group changed their positions relatively to one another, that individual spots changed their size and shape considerably during

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