orbit is very far from uniform; but it is so far regnlar, that, with the exception of some small inequa lities caused by the action of the moon and planets, the radius vec tor, or line joining the centres of the earth and sun, describes equal areas or sectors of the ellipse, in equal times. gularities in the direction of gravity, particularly those occasioned by the attraction of mountains. "There are," says he, "no doubt, situations in which the measurement of a small arch might, from this cause, give the radius of curvature of the meridian infinite, or even negative." Another kind of local irregularity is that arising from the unequal density of the materials under the surface of the earth, and not far from it: errors thus produced might amount to 10" or 12. And this cause of error is the more formidable, not only because it may go to a great extent, but because there is not any visible mark by which its existence can be distinguished. He also justly observes, that in order to avoid any material error in determining the figure of the earth, the arches measured should be large, consisting each of several degrees, as an error would then be render-ences of astronomy and geograed inconsiderable, by being spread over a greater interval. Motion of the Earth-There are three principal motions of the earth. 1. A motion of rotation on its own axis; 2. A motion in an orbit round the sun; 3. A motion of its axis about the poles of the ecliptic. The rotation of the earth on its axis, called its diurnal motion, is the most uniform we are acquaint ed with. It is performed in 23h 56/4/1, of mean solar time, or one sidereal day. The earth, or more strictly speaking, the common centre of gravity of the earth and moon, describe an orbit round the sun, which orbit is of an elliptic forni of small eccentricity; the sun being placed in one of its foci. If we suppose the plane of this orbit extended to the fixed stars, it will trace in the heavens a circle called the ecliptic. The plane of the earth's equator, which remains very nearly parallel to itself dur ing the whole of this revolution, is inclined to the ecliptic at an angle of 23° 28. The points in the earth's orbit, which are intersected by this plane, are called the equinoc tial points. The motion of the earth in its The third motion of the earth, is that which produces the pre cession of the equinoxes. The motion of rotation having produced a protuberant form in the equatorial regions of the earth, the continual action of the sun and moon on this surrounding mass or annulus, produces a rotary motion in the axis of the earth round the axis of the ecliptic; the inclination of these axis remaining the same. This revolution is accomplished in 25,063 years. The principal elements of the earth, as connected with the sci 7908 phy, according to the determina- Solidity } 24869 09.08 196862256 sq. mls. 259726936416 cubic [miles. Density of the earth is 3 9326 times greater than the density of the sun, and about five times that of common water. Mass of the earth is 33786 of the sun. The weight of a body at the equator, is to the weight of the same body at the poles, as 1:1-00569. The length of a second's pendu. lum at the equator is 39 027 inches, and at the poles 39.197 inches. The centrifugal force at the equator is about of gravity. If the rotatory motion of the earth was seventeen times greater than it is, the centrifugal force would be equal to that of gravity; and therefore bodies at the equator would then have no weight. The mean distance of the earth from the sun is 23,578 times its own semi-diameter, or about 93,321,724 | is observed to decrease at the rate English miles. of 52 1 in a century; but this va Its aphelion distance is 94,889,528 riation of the angle is confined miles. within certain limits, and cannot exceed 2° 42'. Its perihelion distance is 91,753,920 miles. We are, therefore, more than three million miles nearer the sun at the winter, thàn at the summer solstice. The eccentricity of its orbit is 0168, the semi-axis major being considered as unity. The earth performs one complete sidereal revolution in 365d 6h 9' 11-5; but the tropical year is only 365d 5h 48′ 516; being less than in the time of Hipparchus by 11/1.2. The nutation of the axis is 19.3. The annual intersection of the equator with the ecliptic is not always in the same point, but is retrograde, or contrary to the order of the signs. Consequently, the equinoctial points appear to move forward on the ecliptic: and whence this phenomenon is called the precession of the equinoxes. The quantity of this annual change is 501; or 1° 23' 30" in a century. A complete revolution is performed in 25,868 years. The mean velocity of the earth, The sidereal day, or the time in its orbit is 59' 107 each day. employed by the earth in revolv When in its perihelion this velo-ing on its axis, is always the same. city is 1° 1' 99 per day; and in If the mean astronomical or civil its aphelion 57' 10"-7. day be taken equal to 24 hours, the duration of the sidereal day will be 23 56′ 41. The mean longitude of the earth, at the commencement of the present century, was 3° 10° 9' 13". The mean longitude of its perihelion, at the same period, was 33 9° 301 51. But the line of the apsides has a direct sidereal motion of 19 40 8 in a century; which being referred to the ecliptic will give it a motion, according to the order of the signs, of 1' 19 in a year, or 1° 43′ 108 in a century. The astronomical or civil day is constantly changing. This variation arises from two causes: 1. The unequal motion of the earth in its orbit; 2. The obliquity of that orbit to the plane of the equator. The mean and apparent solar days are never equal, except when the sun's daily motion in right ascen sion is 59' 8". This is the case A complete revolution about the about April 16, June 16, September line of the apsides is called the 1, and December 25: on these days anomalistic year; and is performed the difference vanishes, or nearly in 365d 6 14 2. The perihelion so. It is at its greatest about Nocoincided with the vernal equinox vember 1, when it is 16' 16". about the year 4089 before the The astronomical year is divided Christian æra; it coincided with into four parts, determined by the the summer solstice about the year two equinoxes and the two sol1250 after Christ; and will coin-stices. The interval between the cide with the autumnal equinox about the year 6483. vernal and autumnal equinoxes is (on account of the eccentricity of the earth's orbit, and its unequal velocity therein) near eight days longer than the interval between the autumnal and vernal equi noxes. These intervals are, at pre sent, nearly as follow: dh m From the spring equinox to the 92 21 45 A complete tropical revolution of the apsides is performed in 20,931 years. The axis of the earth is inclined to the plane of the ecliptic in an angle of 23° 27' 57"; which angle summer solstice From the autumnal equinox to the From the winter solstice to the 155 93 13 35 89 16 47 d. h. m. 185 35 20 ECCENTRICITY in the Orbit of contrary direction, and striking a Planet, is the distance between the centre and focus of the ellipse in which it revolves. The eccentricity of the orbit is computed from the greatest equation of the centre by the following proportion: As 57° 17' 44'8 (the arc = rad.) Is to half the greatest equation, So is radius = 1 To the eccentricity. Another formula for computing the eccentricity is given by Lambert in the Ephem. of Berlin. Eccentricities of the Planets, at the commencement of the present Century; the greater Semi-axis being expressed by unity. Mercury Venus Earth Mars. • ...... •20551494 ⚫00685298 01685318 09313400 The eccentricity of a planet being added to the mean distance, gives the greatest distance; or, taken from the mean distance, leaves the least distance from the sun. ECHO, a reflected sound, from a solid body, returned or repeated to the ear. The formation of echoes has generally been ascribed to the reflection of sound, similar to that experienced by light when it falls on a polished body. Sound, it is known, is propagated in every direction by the vibration of the particles of the air; but if any column of air rests against some obstacle that prevents the direct movement of the elastic globules, which serve as the vehicle of sound, it must rebound in a the ear, if it meets with one in the line of repercussion, convey to it a repetition of the same sound, pro. vided the original sound does not affect that organ at the same instant. But we are taught by exIperience that the ear does not distinguish the succession of two sounds, unless there be between them the interval of at least onetwelfth of a second; for during the most rapid movement of instrumental music, each measure of which cannot be estimated at less than a second, twelve notes are the utmost that can be compresuccession of the sounds distinhended in a measure, to render the guishable; consequently, the obstacle, which reflects the sound, must be at such a distance, that the reverberated sound shall not succeed the direct sound till after one-twelfth of a second; and as sound moves at the rate of about 1142 feet in a second, and consequently about 95 feet in the twelfth of a second, it thence follows that, to render the reverberated sound distinguishable from the direct sound, the obstacles must be at a distance of not less than about 48 feet. There are single and compound echoes. In the former, only one repetition of the sound is heard; in the latter, there are 2, 3, 4, 5, &c. repetitions. We are even told of echoes that can repeat the same word 40 or 50 times. ECHо, in Architecture, a name given to such kinds of vaults and arches as are erected for the purpose of producing artificial echoes. These are generally chosen of a parabolic or elliptic form. Of this kind is the whispering gallery in St. Paul's Cathedral, and in some other large buildings. ECLIPSE, in Astronomy, a privation of light of one of the lumi naries by the interposition of some opaque body, either between it and the observer, or between it and the sun. To the first class belong solar eclipses, and occultations of the fixed stars by the moon or planets, and to the second lunar eclipses, and of the other satellites, particularly those of Jupiter. 1 lunar eclipses are universal, or visible in all parts of the earth which have the moon above their horizon, and are everywhere of the same magnitude and duration. ECLIPSES are divided with respect to the objects eclipsed into solar and lunar eclipses, and those of Jupiter's satellites. And with respect to circumstances, into total, partial, annular, and central eclip-2. In all lunar eclipses, the eastern ses. Every planet and satellite in the solar system, is illuminated by the sun; and casts a shadow towards that point of the heavens which is opposite to the illuminating body; which shadow is nothing more than a privation of light in the space hid from the sun by the opaque body that intercepts his rays. When the sun's light is so intercepted by the moon, that to any place of the earth it appears partly or wholly covered, he is said to undergo an eclipse; though, properly speaking, it is only an eclipse of that part of the earth where the moon's shadow or penumbra falls. When the earth comes between the sun and moon, the moon falls into the earth's shadow; and having no light of her own, she suffers a real eclipse from the interception of the sun's rays. When the sun is eclipsed to us, the inhabitants of the moon on the side next the earth, see her shadow like a dark spot travelling over the earth, about twice as fast as its equatorial parts move, and in the same direction. When the moon is eclipsed, the sun appears eclipsed to her, total to all those parts on which the earth's shadow falls, and of as long continuance as they are in the shadow. Lunar ECLIPSES happen only at the time of full moon; because it is only then that the earth is be tween the sun and moon: nor do they happen every full moon, because of the obliquity of the moon's path with respect to the earth's, but only in such full moons as happen either at the intersection of those two paths, called the moon's nodes, or very near them; viz. when the moon's latitude, or distance between the centres of the earth and moon, is less than the sum of the apparent semi-dia. meters of the moon and the earth's shadow. The principal circumstances in lunar eclipses are as follow: 1. All side (or the left-hand side, as we look towards her from the north) is that which first immerges into the shadow, and emerges again; for the proper motion of the moon being swifter than that of the earth's shadow, the moon approaches it from the west, overtakes and passes through it with the moon's east side foremost, leaving the shadow behind, or to the westward. 3. Although total eclipses of the longest duration happen in the node, yet there may be total eclipses within a small distance of the nodes, namely, within that distance where the moon's latitude is equal to the apparent semi-diameter of the earth's shadow, minus the semidiameter of the moon's disc, but in these situations the duration of total darkness will be short; whereas in central eclipses it will continue nearly two hours. 4. If the earth had no atmosphere, the moon, when she was totally eclipsed, would be invisible; but as the earth has an atmosphere, some of the light from the sun will be refracted thereby, and transmitted to the moon, on which ac count she will be visible at that time, and appear of a dull red colour. Lastly, she grows sensibly paler and dimmer, before entering into the real shadow; owing to a penumbra which surrounds that shadow to a certain distance. Solar ECLIPSES, happen only when the moon is in conjunction with the sun, that is at the new moon, and also in the nodes, or near them, the limit being about 1 on each side a node; such eclipses only happening when the latitude of the moon, viewed from the earth, is less than the sum of the apparent semi-diameters of the sun and moon. In the nodes, when the moon has no visible latitude, the occultation is total; with some continuance when the disc of the moon in perigee appears greater than that of the sun in apogee, and its shadow is extended beyond the surface of the earth; and without continuance, when the point of the moon's shadow barely covers the earth. Lastly, out of the nodes, but within the limits, the eclipses are partial. which case he will pass by the 2 An eclipse of the sun does not appear the same in all parts of the earth where it is seen, but is in which will occupy some total or annular, while in nearly 173 days. And if either others it is partial. A solar eclipse node be within 17° of the sun at does not happen at the same time the time of new moon, the sun in all places where it is seen, but will be eclipsed; and at the subseappears earlier in the western quent opposition, the moon will be parts than in those to the eastward, eclipsed in the other node, and because the motion of the moon come round to the next conjuncbeyond the sun, and consequently tion before the former node be 17°› of her shadow, is from west to east. beyond the sun, and eclipse him An eclipse of the sun begins on again. When three eclipses hap the western side, and ends on the eastern. No eclipse happens to all pen about either node, the like the places where the sun is visi- the opposite one; as the sun comes number commonly happens about ble, for the penumbra at no time to it in 173 days afterwards, and 6 covers an entire hemisphere of the lunations contain only 4 days more. earth. The portion of the cusp of Thus there may be two eclipses of the horns of the unobscured part the sun, and one of the moon, of the sun's disc, may be easily about each of the nodes. Speaking found in the middle of the eclipse, generally, there will be more solar for the line which joins them is than lunar eclipses, as they will parallel to the moon's apparent nearly bear the proportion of their way. The middle of a solar eclipse limits, viz. about 4 to 3. But more will not be at the same time in all lunar than solar eclipses are seen places on the same meridian; for the parallax of longitude will be lunar eclipse is visible on a whole at any given place; because a different in different longitudes. terrestrial hemisphere at once, The excess of the apparent semi-whereas a solar eclipse is visible diameter of the moon above that only in a small portion of it. of the sun in a total eclipse is so small, that total darkness seldom constitutes more than four minutes in the latitude of London. In most solar eclipses the moon's disc is covered with a faint light, which is attributed to the reflection of the light from the illuminated part of the earth. In total eclipses of the sun the darkness is so great as to render the stars and planets perfectly visible; these however are very rare occurrences in any particular place. The moon's nodes move back wards 191° every year, therefore they would shift through all the points of the ecliptic in eighteen be the regular period of the return years and 225 days; and this would of eclipses, if any complete num ber of lunations were performed in it, without a fraction; which is however not the case. But in 223 mean lunations, after the sun, moon, and nodes, have been once in a line of conjunction, they return so nearly to the same state The Number of Eclipses of both again, that the same node which luminaries cannot be fewer than was in conjunction with the sun two, nor more than seven, in one and moon at the beginning of these year; the most usual number is lunations will be within 28 12" of four, and it is rare to have more the line of conjunction, when the than six. The reason is obvious; last of these lunations is completed; for the sun passes by both the and in this period there will be a nodes of the moon's orbit but once regular return of eclipses, till it in a year, unless he pass by one of be repeated about forty times, or them in the beginning of it, inin about 720 years, when the line |