Galileo and His Judges

by F. R. Wegg-Prosser

One remark, arising from the questions connected with stellar parallax, is most striking, as showing how far Galileo was advanced in his knowledge of pure mathematics as well as of mechanics and astronomy. Salviati is made to say that the circumference of an infinite circle is identical with a straight line: “sono l’istessa cosa.” This idea, familiar though it be to modern mathematicians, is one that we should not have expected to find enunciated in the early part of the seventeenth century; even the intelligent Sagredo cannot understand or believe it, and it is not further discussed; but the fact of its being here stated is especially noteworthy.[11]

Another (less felicitous) guess is hazarded by the same interlocutor Salviati, who, as I have already remarked, appears to be the one that most nearly represents the author’s own mind,—to account for the Earth keeping her axis pointed (approximately, that is to say) in the same direction during each annual revolution round the Sun. Salviati suggests that it may be due to some magnetic influence, and that the interior of the Earth may be a vast loadstone. This is strange, because it is evident from what immediately preceded, that the author was aware of the true reason, which in fact he illustrates by the well-known experiment of a light ball floating in a bucket of water, to which a revolving motion is imparted. It seems, however, that a work by William Gilbert on the subject of magnetism had had some influence on the scientific thought of the period, and that Galileo had considered it worthy of his attention. The writer had maintained the probability of this theory, of the Earth’s interior being an enormous loadstone—not an unnatural idea in the then-existing state of science—and Galileo was evidently somewhat fascinated by the hypothesis. Magnetism was attracting the notice of the philosophers of that day, and the property of the needle, which is termed the dip, had been recently discovered.

There is not much else worthy of special mention in the third day’s dialogue; which in fact, as a whole, is not equal to that of the second day.

The fourth day is mainly devoted to the argument drawn from the tides. It was in handling this branch of the subject that Galileo’s great sagacity and power of discernment seem to have deserted him. It is a curious thing that the inhabitant of a Mediterranean country, who, for all that one knows, never saw a really great tide in his life, should have seized upon this topic, and so utterly misused and perverted it.

If, instead of living in Italy, he had resided at an English seaport, he would probably have never fallen into the mistakes he thus made. In the Mediterranean there are currents, arising from other causes, which he, however, attributed to tidal action; but for the most part there is little, if any, appreciable ebb and flow of the tides, scarcely any perceptible rise and fall of the sea, a fact which he particularly notices. But in some few places, and notably at Venice, there is a sensible tide, so it is said, causing a difference of a few feet between high and low water.

Now Galileo was under the impression that the ebb and flow took each about six hours, following the ordinary solar day; whereas, if he had observed the phenomenon on the shores of any sea, where the tidal wave of the ocean made its full force to be felt, or again, at the mouth of a great tidal river, he never could have failed to perceive that the rise and fall of the water follow approximately the lunar, and not the solar day, the former being fifty minutes longer than the latter. It must of course be understood that the theory of the tides was first investigated fully and scientifically by the same great genius to whom we owe the theory of universal gravitation; and Galileo, who lived half a century earlier, may well be excused for not having grasped it. But it had long been known that the Sun and Moon had an influence upon the tides, and as I have just stated, any one who watched the movements of the sea from day to day, and from week to week, at a place where there is a great rise and fall—as for instance, in the Bristol Channel—could not fail to perceive that the Moon had the principal share in the work, however unable he might be to comprehend the theory. Besides which, the theory, however obvious to us (at least in its main outlines), was not by any means so intelligible to the men of Galileo’s age. They might just guess that the Sun exercised some attractive influence over the Earth, and the Earth again over the Moon, but they did not know that the Moon attracted the Earth exactly in the same way, though with far inferior potency, owing to her much smaller mass; and consequently they were not aware of the Moon’s power to raise the great tidal wave in the ocean, to which are due the remarkable phenomena so familiar to the inhabitants of the English coasts.

Galileo would have been wise if he had not touched on a point which he neither understood in theory, nor had properly acquainted himself with by practical observation. Good causes are often damaged by bad arguments, and such was the case on this occasion.[12] There was, however, something ingenious in his argument. If you take a basin of water, and move it along quite smoothly and evenly, no great commotion in the water takes place; but suppose some stoppage or jerk to occur, the result will be, as we know, very different. Now the Earth has two motions, one round its axis in twenty-four hours, and the other round the Sun in one year; every point, then, on the Earth’s surface moves through space more rapidly while on that side of the globe which is turned away from the Sun, than on that side which by the diurnal revolution is turned round in the contrary direction. Here, then, with the sea lying in its vast basin, and revolving with other things on the surface of the Earth from west to east every day, and thus accelerated in its motion through space during twelve hours and retarded during the other twelve hours, you have on a large scale the same result that a basin, half full of water, held in your hands and checked by some retarding obstacle, gives you on a very small and minute scale. Strange indeed it is that a man who was acquainted with the laws of motion sufficiently to know that anything thrown or dropped in a vessel or a vehicle, partook of the motion of the latter and followed its course (so long as it remained within the vehicle) just as if the whole were at rest—that he should have failed to perceive that the ocean, lying in its bed in that mighty vehicle the Earth, would be carried round in the daily rotation with an uniform velocity, unless interfered with by the attraction of other bodies. Simplicio, who for once is right, puts the difficulty, that if the sea behaved in the way supposed, the air would do so in the same way: the reply to which is that the air being thin and light is less adherent to the Earth than the water which is heavier, and does not accommodate itself to the Earth’s movements as water does; further, that where the air is not hemmed in, as it were, by mountains and other inequalities on the Earth’s surface, it really is partially left behind by the diurnal rotation, and in the neighbourhood of the tropics, where the effect is chiefly felt, a constant wind blows accordingly from east to west. Our philosopher had evidently heard of the trade winds, though he had not acquired an accurate knowledge of their course or of their origin. It is undoubtedly true that they do help strongly to prove the revolution of the Earth, because they arise from cold currents of air flowing in from the north and from the south respectively towards the tropics, to supply the place of the atmosphere rarefied by the sun’s heat, and consequently ascending, as is the case in those regions. Then these cold currents, coming from latitudes where there is a less velocity of rotation, tend to preserve that velocity and lag behind the Earth as it revolves, so that they have the effect of north-easterly winds in the northern hemisphere, and south-easterly in the southern hemisphere. Galileo’s imperfect information prevented him from using this important argument.

However, to return to the tides. He had to account for other phenomena, besides the daily rise and fall, namely, for the much greater rise and fall which take place soon after new and full moon, and which are known as the spring-tides. Unable to deny that these were in some way due to lunar influence, he took refuge in the supposition that the Moon, when at the full, retarded the motion of the Earth in its orbit, since as the two travel together round the Sun at those particular times, they form, as it were, a lengthened pendulum, longer than at other times by the semi-diameter of the lunar orbit; and therefore (like any other pendulum) must vibrate more slowly. I should say that he does not appear to have been aware of the existence of two spring-tides in each lunation, and therefore only tries to account for one; and it is obvious that this method of explaining them is not only utterly inadequate, but even absurd. The Moon truly enough exercises a certain disturbing influence on the orbital motion of the Earth, but that has nothing to do with the spring-tides.

There remained the necessity of accounting for the annual, or, more properly, semi-annual increase of the ebb and flow of the sea. Galileo suggests that this arises from the angle made by the plane of the equator with the ecliptic at the equinoxes, owing to which there would not be the same counteraction exercised by the Earth’s motion in its orbit on the waters of the ocean at those periods as there would at the solstices. But it seems that this would rather tend to diminish the tides than to increase them, as, indeed, would be the case as regards the last-mentioned explanation with respect to the ordinary spring-tides. What really does happen at the equinoxes is, that the Sun and the full or new Moon being at those times vertical to the equator (or nearly so), they have a greater attractive force than at other spring-tides over the vast expanse of the ocean, and the tides are consequently greater. There is also another increase which sometimes occurs when the Moon happens to be at its least distance from the Earth at the time of spring-tides, but that was unknown to Galileo. He touches, however, and very properly so, on the great modifications in the tides caused by various gulfs, by the forms of the great continents, and the shapes of different seas—modifications, in fact, which are well known to be almost innumerable, and have been learnt only by careful observation and experience.

One of the worst features of this Dialogue is the contempt which the author shows for those opinions on the subject which differ from his own; and it is difficult to suppress a feeling of disgust when he alludes in this way to Kepler, who had partly guessed the true cause of the tides, and of whom he otherwise speaks in terms of respect.[13]