CHAPTER VI.

THE ROTATION OF THE EARTH-MOTION OF THE EARTH ABOUT THE SUN-GREAT DISTANCES OF THE FIXED STARS PRECESSION OF THE EQUINOXES.

77. HAVING acquired a knowledge of the vast distances of the sun and planets, and of their magnitudes, we are led to consider whether the diurnal motion we observe in these bodies be a real or only an apparent motion. Real and apparent motions are not at first readily distinguished from each other. The motions of a person in a ship, carriage, &c. daily afford instances that vision alone is not sufficient to distinguish between true and apparent motion. Either experience or judgment is necessary to distinguish between them.

Diurnal motion.-That the heavenly bodies really move, and, by so doing, cause the apparent diurnal motion, we can have no experience, nor can we readily perceive the motion of our earth, as we, in that respect, are in the same circumstances as a person in the cabin of a ship in motion. We could not easily understand whether the whole motion was in the ship, or in a bird, (the only visible external object), flying at a distance. But examining the reasons for each, we distinguish which motion is most probable, that of the earth round its axis or of all the celestial bodies in the space of 23h 56m. Either the celestial bodies revolve in the space of 23h 56m in great or small parallel circles, according to their apparent distance from the celestial poles, or the cause of that apparent diurnal motion is a real mo

tion of the earth about an axis in a direction from west to east. That the latter supposition will explain the diurnal phenomena is so evident, that it is hardly necessary to dwell upon it. By the rotation of the earth about an axis, the horizon of each spectator has a motion, and will revolve in the celestial sphere instead of the sphere with its circles, so that the parts of the celestial sphere will be successively uncovered and become visible, as they would do by a motion of the imaginary sphere itself, carrying the bodies situate in it.

78. The only argument against this motion is, that the spectator appears at rest and the celestial bodies appear to move. But as experience every day points out to us motions only apparent, nothing can be concluded from the apparent rest of the spectator. The arguments from analogy, in favour of the rotation of the earth are very strong. The Sun, Venus, Mars, Jupiter, and Saturn, all spherical bodies like the earth, (of which, three are vastly greater than the earth), revolve about their

axes.

79. Also against the diurnal motions of the celestial bodies about the earth, are the vast distances and magnitudes of the sun and planets. The immense motions to be given to each of these bodies at different and variable distances from the earth, and apparently unconnected with each other and with the earth, to produce their apparent diurnal motions, would require a very complicated celestial mechanism. To suppose the sun above a million times larger than the earth, to revolve about the earth in 24 hours, instead of the earth revolving about an axis in that time, is contrary to that rule of philosophy by which effects are deduced from the simplest causes.

80. Also we know that when a body moves in the circumference of a circle, there is requisite a force tending to the centre to keep it continually in that circle. Now we can assign no force acting upon the sun and planets, to make them describe

the diurnal circles. No bodies are situate in the different centres of those circles, by the continual attraction of which they might be continually impelled from the tangent to the circumference.a

81. We conclude, then, that the diurnal motions of the celestial bodies are only apparent, and that these appearances are produced by the motion of the earth about an axis parallel to the apparent celestial axis; although every appearance may be explained by supposing the eye in the centre of a revolving sphere, in the concave surface of which the heavenly bodies are situate.

tre.

Although the arguments for the rotation of the earth are so satisfactory, that no doubt whatever can remain; yet it is interesting to consider whether the matter cannot be subjected to a direct experiment. It will readily appear that a body let fall from a considerable height will, if the earth revolves from west to east, fall to the eastward of the vertical line. Let C (Fig. 11) be the centre of the earth, T the place from which the body is let fall, TB the vertical line in direction of the cenWhen the body reaches the earth let tb be the position of the vertical line, in consequence of the earth's motion. Take Bf= Tt and f will be the place of the body; because the body, leaving the top of the vertical with a motion equal to the motion of the top, is, at the end of its fall, as far from the first position of the vertieal as the top of the vertical itself is from its first position. But Bb is less than Tt and therefore than Bf, in the proportion of CB to CT, consequently f is to the eastward of b. This is on the supposition that the place is at the equator, and it may suffice for an illustration. An accurate investigation cannot conveniently be inserted here, but may be found in Simpson's Mathematical Dissertations, and Laplace's Mecanique celeste, tom. iv. On account of the small height BT at which we can make the experiment, bf must be very small, and the utmost nicety is required in this age, however, of accurate experiment, it has been attempted, and it is said with success. It has been tried at Bologna from the height of 257 English feet, also at Viviers and at Hamburgh; at Hamburgh the height was 250 feet, and the deviation found to be 0,35 inches to the east, and 0,13 inches to the south. Computation, not taking into the account the air's resistance, gives 0,34 inches to the east, and no perceptible deviation to the south.

Note by the Editor.-If h denote the height of the tower, and the latitude, the deviation to the east varies as h3 cos.λ; and the deviation to the south as h3. sin. 2λ.

82. The rotation of the earth has been established, beyond all controversy, since the time of Galileo, but the notion is a very old one; it is expressly mentioned by Cicero as the opinion of Hicetas, who lived about 400 years before the commencement of our æra. The words of Cicero are, "Hicetas Syracusius, ut "ait Theophrastus, cœlum, solem, lunam, stellas, supera deni66 que omnia stare censet; neque præter terram rem ullam in "mundo moveri : quæ cum circum axem se summâ celeritate "convertat et torqueat, eadem effici omnia, quasi stante terrâ "cœlum moveretur." Acad. Quæst. Lib. 2.a

83. Annual motion.-The apparent annual motion of the sun is explained, by supposing that either the sun moves round the earth or the earth round the sun, in a path or orbit nearly circular. For the sun, as has been stated, appears in the course of a year to describe, on the concave surface of the heavens, a great circle called the ecliptic. Observation shews that its apparent diameter does not vary much, its greatest being=32′ 34′′ and least 31 29", consequently the variation of distance, compared with the whole distance, is but small. Observations likewise shew that its apparent motion in the ecliptic or change of longitude is not equable, yet its difference from equable motion is not great. The motion for any given interval of time, if it moved equably, is found by dividing its whole motion in a year by the number of given intervals in a year. Thus it moves 360° in about 365 days, therefore in an hour the motion is 2' 28" nearly. This is called the mean motion in an hour. Its greatest hourly motion is 2' 33" and its least 2' 23".. Whence in a year the sun moves in an orbit nearly circular, and with a motion nearly equable, about the earth, or the earth moves in an orbit nearly circular,

a

Reperi apud Ciceronem primum Hicetam sensisse terram moveri. Inde igitur occasionem nactus, cœpi et ego de terræ mobilitate cogitare. Copernicus in suđ ræf. ad Paulum III. Ed.

with a motion nearly equable, about the sun.

That the latter

motion takes place is established by a variety of reasons.

84. It will be proved that the planets move about the sun in orbits nearly circular, in different periodic times and at different distances. Also that all the planets receive their light from the sun, a body vastly greater than them all in magnitude, some of which are of much greater magnitude than the earth. Again there is a certain relation between the periodic times of the planets and their distances from the sun, as will hereafter appear. Now considering the earth as a planet revolving round the sun, its distance and periodic time obey the law of the rest of the planets which circumstance affording such an harmony between the motions of all those bodies, receiving their light and apparently their heat, the source of animal and vegetable life, must at once persuade us to acknowledge the annual motion of the earth, rather than that of the sun: although all the principal phenomena of the planetary motions may be explained, by supposing them to revolve in orbits nearly circular round the sun, while the sun and planets are together carried with an annual motion round the earth.

85. But the most satisfactory proof is one that we cannot introduce with its full effect here, it requiring some preliminary principles of physical astronomy. This proof is from the knowledge of that universal attendant of matter, the principle of attraction or gravity. The sun, earth, and planets mutually attract each other, in proportion to their quantities of matter or their masses. It follows, from the laws of motion, that they must come together, or each of them revolve in an orbit round a fixed point, the common centre of gravity of all the bodies. Now we shall see hereafter that the mass of the sun, as well as its magnitude, is vastly greater than all the planets together, so much greater, that the common centre of gravity lies within the body of the sun; and the sun, in fact, will move about this point,