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129. The Dialogue extends over four successive days, and is carried on by three speakers, of whom Salviati is a Coppernican and Simplicio an Aristotelian philosopher, while Sagredo is avowedly neutral, but on almost every occasion either agrees with Salviati at once or is easily convinced by him, and frequently joins in casting ridicule upon the arguments of the unfortunate Simplicio. Though many of the arguments have now lost their immediate interest, and the book is unduly long, it is still very readable, and the specimens of scholastic reasoning put into the mouth of Simplicio and the refutation of them by the other speakers strike the modern reader as excellent fooling.
Many of the arguments used had been published by Galilei in earlier books, but gain impressiveness and cogency by being collected and systematically arranged. The Aristotelian dogma of the immutability of the celestial bodies is once more belaboured, and shewn to be not only inconsistent with observations of the moon, the sun, comets, and new stars, but to be in reality incapable of being stated in a form free from obscurity and self-contradiction. The evidence in favour of the earth’s motion derived from the existence of Jupiter’s satellites and from the undoubted phases of Venus, from the suspected phases of Mercury and from the variations in the apparent size of Mars, are once more insisted on. The greater simplicity of the Coppernican explanation of the daily motion of the celestial sphere and of the motion of the planets is forcibly urged and illustrated in detail. It is pointed out that on the Coppernican hypothesis all motions of revolution or rotation take place in the same direction (from west to east), whereas the Ptolemaic hypothesis requires some to be in one direction, some in another. Moreover the apparent daily motion of the stars, which appears simple enough if the stars are regarded as rigidly attached to a material sphere, is shewn in a quite different aspect if, as even Simplicio admits, no such sphere exists, and each star moves in some sense independently. A star near the pole must then be supposed to move far more slowly than one near the equator, since it describes a much smaller circle in the same time; and further—an argument very characteristic of Galilei’s ingenuity in drawing conclusions from known facts—owing to the precession of the equinoxes (chapter II., § 42, and IV., § 84) and the consequent change of the position of the pole among the stars, some of those stars which in Ptolemy’s time were describing very small circles, and therefore moving slowly, must now be describing large ones at a greater speed, and vice versa. An extremely complicated adjustment of motions becomes therefore necessary to account for observations which Coppernicus explained adequately by the rotation of the earth and a simple displacement of its axis of rotation.
Salviati deals also with the standing difficulty that the annual motion of the earth ought to cause a corresponding apparent motion of the stars, and that if the stars be assumed so far off that this motion is imperceptible, then some of the stars themselves must be at least as large as the earth’s orbit round the sun. Salviati points out that the apparent or angular magnitudes of the fixed stars, avowedly difficult to determine, are in reality almost entirely illusory, being due in great part to an optical effect known as irradiation, in virtue of which a bright object always tends to appear enlarged;75 and that there is in consequence no reason to suppose the stars nearly as large as they might otherwise be thought to be. It is suggested also that the most promising way of detecting the annual motion of stars resulting from the motion of the earth would be by observing the relative displacement of two stars close together in the sky (and therefore nearly in the same direction), of which one might be presumed from its greater brightness to be nearer than the other. It is, for example, evident that if, in the figure, E, E′ represent two positions of the earth in its path round the sun, and A, B two stars at different distances, but nearly in the same direction, then to the observer at E the star A appears to the left of B, whereas six months afterwards, when the observer is at E′, A appears to the right of B. Such a motion of one star with respect to another close to it would be much more easily observed than an alteration of the same amount in the distance of the star from some standard point such as the pole. Salviati points out that accurate observations of this kind had not been made, and that the telescope might be of assistance for the purpose. This method, known as the double-star or differential method of parallax, was in fact the first to lead—two centuries later—to a successful detection of the motion in question (chapter XIII., § 278).
130. Entirely new ground is broken in the Dialogue when Galilei’s discoveries of the laws of motion of bodies are applied to the problem of the earth’s motion. His great discovery, which threw an entirely new light on the mechanics of the solar system, was substantially the law afterwards given by Newton as the first of his three laws of motion, in the form: Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force applied to it to change that state. Putting aside for the present any discussion of force, a conception first made really definite by Newton, and only imperfectly grasped by Galilei, we may interpret this law as meaning that a body has no more inherent tendency to diminish its motion or to stop than it has to increase its motion or to start, and that any alteration in either the speed or the direction of a body’s motion is to be explained by the action on it of some other body, or at any rate by some other assignable cause. Thus a stone thrown along a road comes to rest on account of the friction between it and the ground, a ball thrown up into the air ascends more and more slowly and then falls to the ground on account of that attraction of the earth on it which we call its weight. As it is impossible to entirely isolate a body from all others, we cannot experimentally realise the state of things in which a body goes on moving indefinitely in the same direction and at the same rate; it may, however, be shewn that the more we remove a body from the influence of others, the less alteration is there in its motion. The law is therefore, like most scientific laws, an abstraction referring to a state of things to which we may approximate in nature. Galilei introduces the idea in the Dialogue by means of a ball on a smooth inclined plane. If the ball is projected upwards, its motion is gradually retarded; if downwards, it is continually accelerated. This is true if the plane is fairly smooth—like a well-planed plank—and the inclination of the plane not very small. If we imagine the experiment performed on an ideal plane, which is supposed perfectly smooth, we should expect the same results to follow, however small the inclination of the plane. Consequently, if the plane were quite level, so that there is no distinction between up and down, we should expect the motion to be neither retarded nor accelerated, but to continue without alteration. Other more familiar examples are also given of the tendency of a body, when once in motion, to continue in motion, as in the case of a rider whose horse suddenly stops, or of bodies in the cabin of a moving ship which have no tendency to lose the motion imparted to them by the ship, so that, e.g., a body falls down to all appearances exactly as if the rest of the cabin were at rest, and therefore, in reality, while falling retains the forward motion which it shares with the ship and its contents. Salviati states also that—contrary to general belief—a stone dropped from the masthead of a ship in motion falls at the foot of the mast, not behind it, but there is no reference to the experiment having been actually performed.
This mechanical principle being once established, it becomes easy to deal with several common objections to the supposed motion of the earth. The case of a stone dropped from the top of a tower, which if the earth be in reality moving rapidly from west to east might be expected to fall to the west in its descent, is easily shewn to be exactly parallel to the case of a stone dropped from the masthead of a ship in motion. The motion towards the east, which the stone when resting on the tower shares with the tower and the earth, is not destroyed in its descent, and it is therefore entirely in accordance with the Coppernican theory that the stone should fall as it does at the foot of the tower.76 Similarly, the fact that the clouds, the atmosphere in general, birds flying in it, and loose objects on the surface of the earth, shew no tendency to be left behind as the earth moves rapidly eastward, but are apparently unaffected by the motion of the earth, is shewn to be exactly parallel to the fact that the flies in a ship’s cabin and the loose objects there are in no way affected by the uniform onward motion of the ship (though the irregular motions of pitching and rolling do affect them). The stock objection that a cannon-ball shot westward should, on the Coppernican hypothesis, carry farther than one shot eastward under like conditions, is met in the same way; but it is further pointed out that, owing to the imperfection of gunnery practice, the experiment could not really be tried accurately enough to yield any decisive result.
The most unsatisfactory part of the Dialogue is the fourth day’s discussion, on the tides, of which Galilei suggests with great confidence an explanation based merely on the motion of the earth, while rejecting with scorn the suggestion of Kepler and others—correct as far as it went—that they were caused by some influence emanating from the moon. It is hardly to be wondered at that the rudimentary mechanical and mathematical knowledge at Galilei’s command should not have enabled him to deal correctly with a problem of which the vastly more powerful resources of modern science can only give an imperfect solution (cf. chapter XI., § 248, and chapter XIII.,
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