FAMILIAR ASTRONOMY. No. III. THE APPARENT DIURNAL AND ANNUAL MOTIONS OF THE HEAVENLY BODIES, AND THE PRECESSION OF THE EQUINOXES, ARISE FROM THE REAL MOTIONS OF THE EARTH. "What if The planet Earth, so stedfast though she seem, Paradise Lost, Book VIII. 128. HERE is scarcely any operation of the mind more difficult than that of entirely withdrawing the attention. from the impressions made by the senses. Those senses are, in fact, the main inlets of knowledge; and the reflex act of the understanding, by which the information communicated by the senses is corrected, and sometimes shewn to be illusory, is a slow and deliberate process, often leaving some degree of vagueness and uncertainty, even when the judgment is fully convinced. This effect is very frequently found with reference to the simplest facts of physical astronomy. No one has now any doubt, that the earth is of a form nearly spherical. If Virgil had written at the present day, he would not have represented it simply as one guess out of many, that at the antipodes, the vicissitudes of day and night are exactly reversed, with reference to those which we experience: "There, as they say, perpetual night is found In silence brooding o'er the unhappy ground: She lights the downward heaven, and rises there, And when on us she breathes the living light, Red Vesper kindles there the tapers of the night." Georgic I. 338.-Dryden's Translation.* * It would be doing injustice to this noble passage, not to subjoin it in the original. Illic, ut perhibent, ant intempesta silet nox NO. III.-VOL. I. W Georgic I. 247. Yet how difficult it is to feel fully satisfied in our minds, as an indisputable fact, that as we watch the sun descending below the western horizon, he is, at the very same instant, awakening the inhabitants of another hemisphere, and just beginning to illuminate and warm their eastern skies. A similar remark may be made respecting the diurnal motion of the earth. It is no longer a question "Whether the sun, predominant in heaven, Or she from the west her silent course advance, On her soft axle, while she paces even, And bears thee soft with the smooth air along." Paradise Lost, VIII. 160. Yet long thought and much patient enquiry are necessary to enable the mind fully to acquiesce in the existence, and rightly to estimate all the consequences, of a movement at once so gentle, and so rapid, so perfectly imperceptible in its action, yet so important in its effects. The same slowness to distrust the evidence apparently afforded by the senses was the principal cause which, for many ages, prevented the discovery of the annual motion of the earth, and occasioned the existence of that motion to be long disbelieved, after it was discovered. In order to render more easily intelligible this transition from the apparent motions of the heavens, to the real motions of the earth, our present object will be to point out some circumstances which lead to a knowledge of the form, magnitude, and motions of the earth. I. The first fact to be established is, that the earth is nearly a sphere, or globe, the diameter of which is, in round numbers, about 4000 miles. The globular figure of the earth is usually illustrated by referring to the manner in which a ship disappears, as it sails away from a port: the lower parts being first intercepted from the sight, and the higher parts, the sails and rigging, successively disappearing below the horizon. In order to perceive the full force of this illustration, it is necessary to bear in mind, that there are two causes which may occasion an object to become lost to sight. The first is, the apparent diminution in magnitude, occasioned by increased distance, combined with the loss of light, arising both from the distance of the object, and from the greater proportion of light intercepted by the increased thickness of the plate of air, through which the light passes. The second of these causes is, that the light, by which any object is visible, passes in straight lines from the object to the eye, (refraction not being here considered), so that if any thing is interposed between the object and the eye, it cuts off a portion or the whole of the object from sight. The first mode of disappearance may be observed extremely well, as a balloon rises in the air, and is gradually carried away by the currents of the atmosphere. At first the whole balloon with its net-work, flags, and aeronauts, is distinctly visible. Then, the fainter parts begin first to disappear. The flags are scarcely seen, except by their motion, The broad stripes upon the silk, and the indentations on its pear-like surface, rendered perceptible by the oblique falling of the sun's rays upon it, are soon the principle marks: until the whole becomes bathed in light, dwindles into a flickering point, and is at last absorbed in the liquid expanse of the sky. Now if the surface of the sea were a plane, the disappearance of a ship would be similar to that of a balloon. The cordage and higher masts, which are the smallest and finest portion of the whole mass, would first be lost to sight, and the hull and large lower sails would continue to be seen the longest; just as we do perceive this to be the case in hazy weather, when the imperfect transparency of the atmosphere renders objects invisible at a comparatively small distance. And since increase of distance alone would not account for the manner in which a ship generally disappears from view, the observed facts evidently are owing to the earth not being a plane, but a sphere. The globular form of the earth may be rendered sensible in another manner. Suppose a person standing near an extensive piece of still water, such as a lake, a tide river, or a calm arm of the sea. Let him place his eye at about two feet distance from the surface of the water, and observe the line of junction between the water and some object, as a boat, floating upon it, at the distance of about half a mile, or less. Now let him gradually bring his eye as nearly as possible to the level of the water, and he will distinctly perceive, that the surface of the water, which before appeared to be a horizontal plane, is, in reality, a curved surface, which bulges out, so as to intercept his view, and prevent him from seeing the former water line. This experiment is best made, when a person is bathing; and any one, who has not noticed the fact, will be surprised to find how pal pably curved the surface of smooth water is; so much, indeed, as to become perceptible on elevating the eye only a few inches from the level of the water. Another obvious fact, showing that the figure of the earth does not differ much from a sphere, is the form of the shadow of the earth, in a lunar eclipse. The shape of that shadow does not sensibly differ from a circle: and since this shadow may be cast by any portion of the earth, at different times, it follows that the solid figure of the earth must be such as would in all directions present a circular shadow upon a plane perpendicular to the line joining the centres of the earth and sun: and that figure can be no other than a sphere. If the earth, indeed, manifestly differed from the spherical form,for instance, if it were like a very elongated egg, or a very flat orange -the boundary of the horizon, upon the open ocean, would not be every where circular. In some parts of the world, a ship would go out of sight at a less distance, in some directions, than in others; a result which is contrary to universal experience. Taking it, then, as an established fact, that the earth is nearly a sphere, we are now to enquire in what manner its magnitude can be found. The most obvious way of discovering the magnitude of a sphere is to measure its diameter. Thus, to determine the size of a cannon ball, callipers, a kind of compasses, are employed, which can be opened exactly to such an extent as to enclose the ball, that extent being afterwards measured upon a scale. Common globes are measured, in the same way, by ascertaining the number of inches in their diameter. Thus we speak of a globe of six inches, eighteen inches, three feet; and the like. But we may ascertain the magnitude of a globe in a different manner. For example, we may pass a string round the globe, and measure its length: and knowing the proportion of the circumference of a circle to its diameter, namely, 355 to 113; or about 22 to 7, or a little more than 3 to 1, we can compute the diameter of the globe. Thus, if a globe were 22 inches in circumference, its diameter would be about 7 inches. Any of these methods would become inconvenient, or impracticable, if the globe in question were very large. But the magnitude of such a globe might still be ascertained, if we could measure a certain portion of its circumference accurately, and could also know what proportion the part measured bears to the whole circumference. For instance, suppose the hemispherical dome of a cathedral to be divided into a hundred equal gores, one of which at its widest part is measured, and found to be 9 feet in width: the whole circumference of the hemisphere would be known to be 900 feet; and the diameter somewhat less than 300 feet, There is still another less obvious method of ascertaining the magnitude of a sphere, by a gauge which measures its curvature. Suppose a plane, or flat surface, to be laid upon a sphere. It would touch the sphere only at one point. Every other point of the sphere, not very distant from the point of contact, will be at a certain determinate small distance from the plane. And what is called the curvature of the sphere, or its deviation from the plane at a small fixed distance from the point of contact, is greater in the same proportion as the diameter is less. For instance, if the diameter of the sphere be 5 feet, a point taken in a plane, at the distance of one inch from the point of contact, will be at the distance of about one-sixtieth of an inch, or 0.0166in. from the surface of the sphere. Whereas, if the diameter of the sphere be twice as great, or 10 feet, the same point in the plane will be at half the former distance, that is about the one hundred and twentieth of an inch, or 0-0083in. from the surface of the sphere. It is easy to show this, by drawing several circles, which shall all have their centres in the same straight line, and shall all touch another line at right angles to that in which their centres lie. It will be then evident to the eye, that the smaller circles are more deflected from the straight line which touches all the circles, than the larger circles are. Hence it follows, that if we can mea sure the deflection of a circle, or of a sphere from a line or plane which touches it, we have the means of calculating the diameter of the circle or sphere, and consequently of ascertaining its magnitude. A gauge might thus be formed, which, when applied to any globe would measure its curvature, and thence show what its diameter is. We are now to show how any of these methods may be applied to measure the magnitude of the earth. Now it is plainly impracticable to measure directly either the diame ter or the circumference of the earth. Consequently, we must be |