Will be twenty hours the 19th of May at Greenwich, astronomical account, and also 8 A. M. on the 20th, civil account. Mean time at Greenwich, Time shown by chronometer, Chronometer two hours too slow of Greenwich time, 6 2 Which is to be applied as a constant quantity to the time by chronometer. Explanation of the difference between Mean and Apparent Time, to shew how one may be derived from the other. APPARENT time is that which is derived immediately from the sun, either from observing its transit over the meridian, at the instant of apparent noon, or by observing its altitude at a distance from the meridian. Mean time is that which is shewn by good clocks or watches properly regulated to go twenty-four hours. As the earth revolves uniformly on its axis, if it had no annual motion in its orbit, or if that motion was uniform, and in a plane, parallel to the plane of the equinoctial, the natural days would be always of the same length, and the apparent and mean time would be the same. But this is not the case; and thus the time which elapses between the sun's being on the meridian of any place, and its return to it, is considerably longer at some times than it is at others. The annual motion of the earth, is not perceived by us who are upon it, but it is the cause of an apparent motion in the sun, the same way, namely, eastward, and of the same quantity; consequently, when the earth, by its diurnal rotation on its axis, has brought any place on its surface, opposite to the point where the sun was the preceding noon, the inhabitants of that place will not find the sun there, but will have to follow it still further eastward, by a quantity equal to the sun's apparent diurnal motion in its orbit, before the place they inhabit will come opposite to it: and, as it has been observed, this motion is not only un On the difference between Mean and Apparent Time. 33 equal in itself, but is rendered apparently more so, by the obliquity of its direction. It is obvious that the earth will have to follow the sun sometimes a longer, and sometimes a shorter space, before the same points on its surface will come opposite to it, and of course the length of the natural days will be sometimes longer, and sometimes shorter. But as all good clocks and watches go uniformly, the mean day of twenty-four hours, which is shown by them, must necessarily be always the same length; it therefore follows, that when the sun's apparent motion in its orbit is slow, and the earth in consequence has a less space to follow, before any given place on its surface comes opposite to the sun; the sun at such time will be on the meridian of that place before the end of the twenty-four mean hours: and when the sun's apparent motion in his orbit is quickest, and when of course any given place on the earth's surface has a greater space to follow the sun, before it comes opposite to it; the sun will not be on the meridian of that place, till some time after the expiration of the twenty-four mean hours. This inequality in the length of the natural days, is called the equation of time. This equation of time is inserted in page 2, of every month in the Nautical Almanac for the noon of each day at Greenwich, and is marked subtractive when the sun comes to the meridian sooner, and additive when it comes to the meridian later than mean noon, and the meaning is, that the quantity of time expressed by the equation is to be subtracted, in the former case, from the apparent time, or that which is immediately observed from the sun, to obtain the mean time shown by clocks and watches, and added to it in the latter. As every meridian, therefore, passes in the same time, through similar ones in the celestial equator, and all circles parallel to the equator [and such are the tropics at the solstices] every arc of the ecliptic passed through by the meridian, in a given time, will be to the arc of the equator passed through in the same time, as fifty-five is to sixty. Mr. Ferguson explains this subject by a very easy problem; upon a common globe, if small patches of paper, (or any other mark) be put upon every tenth or fifteenth degree, both of the equator and the ecliptic, as described on the globe, beginning at Aries, and turn the globe gently round, westward, we shall find all the patches, or marks on the ecliptic, from Aries to Cancer, come to the brazen meridian sooner than the corresponding marks on the equator. Those from Cancer to Libra will come later to the meridian than the marks on the equator, those from Libra to Capricorn sooner, and lastly, those from Capricorn to Aries later again. The marks at the beginning of Aries, Cancer, Libra and Capricorn, will come to the meridian at the same time with the equator. If a circle be supposed to circumscribe the globe, exactly in the middle between the two poles, that circle is called the equator. The circle which corresponds to it in the heavens is called the equinoctial. The ecliptic is that great circle in the heavens which the sun. appears to describe in a year, or, it is the real path of the earth round the sun, and cuts the equinoctial in an angle of 23° 28'. The points of intersection are as follows. The ecliptic and the equator, (and these, being great circles, must bisect each other) and their intersection, is called the ob liquity of the ecliptic. The method used by astronomers to obtain the obliquity of the ecliptic is taking half the difference of the greatest and least meridian altitude of the sun in winter and in summer. The sun's right ascension is an arc of the equator, intercepted between the first point of Aries, and a declination circle passing through the sun, measured according to the order of the signs. The sun's place in the ecliptic is called his longitude, and is reckoned in signs, degrees and minutes, each sign being thirty degrees. The declination of the sun, a star, or a planet, is its distance from the equinoctial northward or southward. When the sun is in the equinoctial, he has no declination, but enlightens the globe from pole to pole. As he increases in north declination, he gradually shines farther over the north pole, and leaves the south pole in darkness. In a similar manner, when he has south declination he shines over the south pole, and leaves the north pole in darkness. The greatest declination the sun can have is 23° 28'. The greatest declination a star can have is 90°, and that of a planet 30° 28', north or south. It is necessary to remark the equinoctial, which is a circle on the celestial globe, and is represented by the figure in the following page; beginning at the first point of Aries, and extending in a straight line. Consequently we must consider the two extremities as joining each other, that is, where one leaves. off, the other begins. At the distance of twenty-three degrees and twenty-eight miles of declination north and south, two lines are drawn parallel to the equinoctial, which touch the ecliptic at the beginning of the signs, Cancer and Capricorn. See the following figure. These lines are called tropics; the one on the north side, the tropic of Cancer; and that on the south side, the tropic of Capricorn. In the following figure, the perpendicular line represents the sun's declination on the 20th July, 1820. Fig. 16. Tropic of Cancer represented by this line. North. ရာ ရာ South. Line representing the tropic of Capricorn. The curve line in the above figure represents the ecliptic, or apparent annual path of the sun among the stars, through which he advances eastward, nearly a degree every day. It is divided into twelve signs, from right to left, beginning at Y, Aries, and the names and characters of them are as follows: each sign thirty degrees, making three hundred and sixty degrees. from Y to Y. m Oct. 23. Nov. 22. Dec. 21. Jan. 20. * Feb. 18. 8. Scorpio, the Scorpion, 9. Sagittarius, the Hunter, The time given in the foregoing statement is according to the civil account, from the 20th of March, 1820, to the 18th of February, 1821. The Nautical Almanac gives the times at which the sun enters the different signs of the zodiac, according to astronomical account. The Precession of the Equinoxes. THE sun returning to the equinoxes every year, before it returns to the same point in the heavens, shows that the equinoc tial points have a retrograde motion; and this arises from the motion of the equator, which is caused by the attraction of the sun and moon upon the earth, in consequence of its spheroidal figure. The effect of this is, that the longitude of the stars must constantly increase; and by comparing the longitude of the same stars, at different times, the motion of the equinoctial points or precession of the equinoxes may be found. The equinoctial points, according to Mr. Ferguson, retreat along the ecliptic, contrary to the order of the signs, at the rate of fifty seconds and three-tenths in the year; so that they will perform a whole revolution in the heavens in twenty-six thousand years. Since the longitude of the stars, therefore, is reckoned from the vernal equinoctial point, and since this point recedes on the ecliptic, the longitudes of the stars must increase fifty seconds and three-tenths every year. For reasons mentioned under the head of Reformation of the Calendar, page 38, the sun's declination became too much advanced. And as this is not allowed for in some of the old editions of the epitomes of navigation, say before the year 1800, a number of masters of vessels have taken out the declination one day wrong. I should have been led into this error myself, had I not been aware of it; and, not long since, having met with some erroneous epitomes in use, I think it best to mention it here as a caution, and to recommend the use of the Nautical Almanac, the declination therein being corrected every year. This error is very great in March and September, nearly twenty-four miles in one day. In the year 1800, about the middle of March, being bound to the Havanna, I made use of one of Hamilton Moore's epitomes, printed before 1800. Knowing this error, I took the declination for one day earlier. Had I not been aware of it, I should have used the declination for the day as given in the epitome, and should have been about twenty-three miles out in the latitude. Although the foregoing figure has been explained already, I must refer to it again, to show the mode of finding the sun's declination, his right ascension, and longitude, by spherical trigonometry. Thus, then, as before, the equinoctial, which is a circle on the celestial globe, is represented as beginning at the first point of Aries, and ending in a straight line, which, from the circular form of the earth, must surround it, and, of course, return to the point whence it set out. Then, as before, the sun's place in the ecliptic being his longitude, and his right ascension, are reckoned on the equinoctial, the angle made by the intersection of the ecliptic and equinoctial |