when embarrassed by the earth's diurnal motion, we have learned to transfer, in imagination, our station of observation from its surface to its centre, by the application of the diurnal parallax; so, when we come to enquire into the movements of the planets, we shall find qurselves continually embarrassed by the orbitual motion of our point of view, unless, by the consideration of the annual or heliocentric parallax, as it may be termed, we consent to refer all our observations on them to the centre of the sun, or rather to the common centre of gravity of the sun, and the other bodies which are connected with it in our system. Hence arises the distinction between the geocentric and heliocentric place of an object. The former refers its situation in space to an imaginary sphere of infinite radius, having the centre of the earth for its centre - the latter to one concentric with the sun. Thus, when we speak of the heliocentric longitudes and latitudes of objects, we suppose the spectator situated in the sun, and referring them, by circles perpendicular to the plane of the ecliptic, to the great circle marked out in the heavens by the infinite prolongation of that plane. (317.) The point in the imaginary concave of an infinite heaven, to which a spectator in the sun refers the earth, must, of course, be diametrically opposite to that to which a spectator on the earth refers the sun's centre; consequently, the heliocentric latitude of the earth is always nothing, and its heliocentric longitude always equal to the sun's geocentric longitude + 180°. The heliocentric equinoxes and solstices are, therefore, the same as the geocentric; and to conceive them, we have only to imagine a plane passing through the sun's centre, parallel to the earth's equator, and prolonged infinitely on all sides. The line of intersection of this plane and the plane of the ecliptic is the line of equi. noxes, and the solstices are 90° distant from it. (318.) The position of the longer axis of the earth's orbit is a point of great importance. In the figure (art. 315.) let ECLI be the ecliptic, E the vernal MEAN AND TRUE LONGITUDE OF THE SUN. 201 equinox, L the autumnal (i. e. the points to which the earth is referred from the sun when its heliocentric longitudes are 0° and 180° respectively). Supposing the earth's motion to be performed in the direction ECLI, the angle ESA, or the longitude of the perihelion, in the year 1800 was 99° 30'5': we say in the year 1800, because, in point of fact, by the operation of causes hereafter to be explained, its position is subject to an extremely slow variation of about 12" per annum to the eastward, and which, in the progress of an immensely long period of no less than 20,984 years — carries the axis A S M of the orbit completely round the whole circumference of the ecliptic. But this motion must be disregarded for the present, as well as many other minute deviations, to be brought into view when they can be better understood. (319.) Were the earth's orbit a circle, described with a uniform velocity about the sun placed in its centre, nothing could be easier than to calculate its position at any time, with respect to the line of equinoxes, or its longitude, for we should only have to reduce to num. bers the proportion following ; viz. One year : the time elapsed :: 360° : the arc of longitude passed over. The longitude so calculated is called in astronomy the mean longitude of the earth. But since the earth's orbit is neither circular, nor uniformly described, this rule will not give us the true place in the orbit at any proposed moment. Nevertheless, as the excentricity and deviation from a circle are small, the true place will never deviate very far from that so determined (which, for distinction's sake, is called the mean place), and the former may at all times be calculated from the latter, by applying to it a correction or equation (as it is termed), whose amount is never very great, and whose computation is a question of pure geometry, depending on the equable description of areas by the earth about the sun. For since, in the elliptic motion, according to Kepler's law above stated, areas not angles are described uniformly, the proportion must now be stated thus ; One year : the time elapsed :: the whole area of the ellipse : the area of the sector swept over by the radius vector in that time. This area, therefore, becomes known, and it is then, as above observed, a problem of pure geometry to ascertain the angle about the sun (ASP, fig. art. 315.), which corresponds to any proposed fractional area of the whole ellipse supposed to be contained in the sector A PS. Suppose we set out from A the perihelion, then will the angle ASP at first increase more rapidly than the mean longitude, and will, therefore, during the whole semi-revolution from A to M, exceed it in amount; or, in other words, the true place will be in advance of the mean : at M, one half the year will have elapsed, and one half the orbit have been described, whether it be circular or elliptic. Here, then, the mean and true places coincide ; but in all the other half of the orbit, from M to A, the true place will fall short of the mean, since at M the angular motion is slowest, and the true place from this point begins to lag behind the mean — to make up with it, however, as it approaches A, where it once more overtakes it. (320.) The quantity by which the true longitude of the earth differs from the mean longitude is called the equation of the centre, and is additive during all the half-year in which the earth passes from A to M, beginning at 0° 0' 0", increasing to a maximum, and again diminishing to zero at M; after which it becomes subtractive, attains a maximum of subtractive magnitude between M and A, and again diminishes to O at A. Its maximum, both additive and subtractive, is 1° 55' 33.3. (321.) By applying, then, to the earth's mean longitude, the equation of the centre corresponding to any given time at which we would ascertain its place, the true longitude becomes known; and since the sun is always seen from the earth in 180° more longitude than the earth from the sun, in this way also the sun's true place in the ecliptic becomes known. The cal. CHAP. V. EQUATION OF THE CENTRE. 203 culation of the equation of the centre is performed by a table constructed for that purpose, to be found in all " Solar Tables.” (322.) The maximum value of the equation of the centre depends only on the ellipticity of the orbit, and may be expressed in terms of the excentricity. Vice versá, therefore, if the former quantity can be ascertained by observation, the latter may be derived from it; because, whenever the law, or numerical connection, between two quantities is known, the one can always be determined from the other. Now, by assiduous observation of the sun's transits over the meridian, we can ascertain, for every day, its exact right ascension, and thence conclude its longitude (art. 260.). After this, it is easy to assign the angle by which this observed longitude exceeds or falls short of the mean; and the greatest amount of this excess or defect which occurs in the whole year, is the maximum equation of the centre. This, as a means of ascertaining the excentricity of the orbit, is a far more easy and accurate me. thod than that of concluding its distance by measuring its apparent diameter. The results of the two methods coincide, however, perfectly. (323.) If the ecliptic coincided with the equinoctial, the effect of the equation of the centre, by disturbing the uniformity of the sun's apparent motion in longi. tude, would cause an inequality in its time of coming on the meridian on successive days. When the sun's centre comes to the meridian, it is apparent noon, and if its motion in longitude were uniform, and the ecliptic coincident with the equinoctial, this would always coincide with mean noon, or the stroke of 12 on a well-regulated solar clock. But, independent of the want of uniformity in its motion, the obliquity of the ecliptic gives rise to another inequality in this respect; in consequence of which, the sun, even supposing its motion in the ecliptic uniform, would yet alternately, in its time of attaining the meridian, anticipate and fall short of the mean noon as shown by the clock. For the right ascension of a celestial object, forming a side of a right-angled spherical triangle, of which its longitude is the hypothenuse, it is clear that the uniform increase of the latter must necessitate a deviation from uniformity in the increase of the former. (324.) These two causes, then, acting conjointly, produce, in fact, a very considerable fluctuation in the time as shown per clock, when the sun really attains the meridian. It amounts, in fact, to upwards of half an hour; apparent noon sometimes taking place as much as 164 min. before mean noon, and at others as much as 141 min. after. This difference between apparent and mean noon is called the equation of time, and is calculated and inserted in ephemerides for every day of the year, under that title; or else, which comes to the same thing, the moment, in mean time, of the sun's culmination for each day, is set down as an astronomical phenomenon to be observed. (325.) As the sun, in its apparent annual course, is carried along the ecliptic, its declination is continually varying between the extreme limits of 23° 28' 40" north, and as much south, which it attains at the solstices. It is consequently always vertical over some part or other of that zone or belt of the earth's surface which lies between the north and south parallels of 23° 28' 40”. These parallels are called in geography the tropics ; the northern one that of Cancer, and the southern of Capricorn; because the sun, at the respective solstices, is situated in the division, or signs of the ecliptic so denominated. Of these signs there are twelve, each occupying 30° of its circumference. They commence at the vernal equinox, and are named in order — Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. They are denoted also by the following symbols :-99, 8, II, O, 1, m, 1, m, t, u, H. The ecliptic itself is also divided into signs, degrees, and minutes, &c. thus, 58 27° 0' corresponds to 177° 0'; but this is beginning to be disused. |