I. Repeating time, not only has mechanical skill introduced great accu- BOOK racy in the construction of instruments, but the ingenious invention of the repeating circle of Mayer, which was brought to perfection by Magellan and Borda,* enables circle. observers, by taking the multiple of the observed angle, to increase at pleasure the rigour with which its magnitude is determined, and to diminish the possible error almost to a second. The two methods of finding the latitude, which we have already pointed out, are not sufficient for the purpose of navigators, who, in order to calculate their longitude by lunar distances, require to know at the same instant under what latitude they are placed. This inconvenience bas been in part remedied by solar tables, calculated before hand, and which give for every day of the year the place of the sun. The principle upon which the construction of these tables is founded, consists in presenting first the mean values of all the principal elements calculated for the beginning of the year, and then to give the means of deducing for any other instant, either the true or the mean values of these elements. In all these calculations, the first thing to be known, is the mean longitude of the sun, and of his perigee, or of his apogee, for the instant which is assumed. for the commencement of the tables. These initial values are called the epoch of the astronomical tables. By help of these tables then, we can find the position of the sun in his orbit at any instant, and may obtain the latitude of a Calculaplace, on any day, by subtracting from the altitude of the tion of the sun, his distance from the equator, if he is above that cir- the altitude cle, or by adding it, if he is below, and then taking the of the sun. complement of the result to 90°. But, in order to multiply the means of determining the latitude, astronomers, having first fixed the position of their observatory, have calculated the distance of the principal stars from the equator, and the time which elapses between their respective passages Bossut, Histoire des Mathématiques, ii. 489. latitude by BOOK I. over a given meridian, and that of the point of the ecliptic which corresponds to the spring equinox. The results of these calculations have been arranged in tables, by the aid of which the stars may be substituted for the sun in determining latitude. These observations require that the position of the meridian be previously known. The pole-star indicates it nearly in the northern hemisphere of the earth; but the most universal and accurate method of finding it is afforded by the motion of the sun. Let us suppose the sun to be in one of the solstitial points; in which point it remains for some time apparently at the same distance from the equator, and appears to describe a circle parallel to the equator, whereof the part def, Fig 1. which lies above the horizon, is divided by the meridian into two equal portions. The altitude of the sun is therefore precisely the same when observed before and after its passage over the meridian at equal intervals of time: on the other hand, if we take in the morning the altitude of the sun, and watch the moment in the afternoon when it returns to this same altitude, the hour of its passage over the meridian must necessarily lie in the middle between these two instants. The length of shadows furnish the most simple method of determining the altitude of the sun. It is easy to see that this length depends not only upon the height of the objects by which the shadows are projected, but also upon that of the sun, relatively to the plane upon which the objects stand. If upon this horizontal plane we raise the vertical line AD, Fig. 12. the solar ray being directed along SD, the shadow will fall upon AC, and its length will depend upon the angle SCA, which evidently corresponds to the height of the sun above the horizon. When the sun, after having passed the meridian, returns therefore to the same altitude on the other side, and in the direction S'D, the shadow AB and the vertical line AD will be again of the same length with the shadow AC; and if we take the middle position of the shadow between the direction of the It was by such means that I. one and of the other, by dividing the angle BAC into two BOOK equal parts, by the straight line AN, we shall find the meridian. If the length of the staff AC is now measured, and that of its shadow, we shall be able to find the altitude of the sun, by the resolution of the rectilineal triangle CAD, which is rectangular at A, and in which the sides AD and AC are known, so that we may calculate the angle ACD, which is the altitude sought. The meridian altitude will be obtained, if we measure the length of the shadow when it falls in the direction of AN. the first astronomers determined the altitudes of the heavenly bodies. This rude instrument is called a Gnomon; but Gnomon, it has been abandoned since the instruments which measure angles immediately by arcs of the circle, have been brought to perfection. These last are employed even in determining the meridian, by combining them with pendulum clocks, of which the motion is very regular. Having observed in the morning an altitude of the sun, we mark at the same time the hour, then we watch the instant in the afternoon when the sun is at the same altitude, and taking half the interval, we find the time which has elapsed between the passage of the sun over the meridian, and either of the observations. If, for example, the clock indicate for the same altitude, in the morning 8h 45' 30", and in the afternoon Sh 23' 12"; the interval between these two instants is 6h 37' 42", of which the half is 3h 18' 51", and this added to the time of the first observation, namely 8h 45' 30", gives 12h 4' 21", for the hour which the clock must have indicated at the instant when the sun passed the meridian. The observation of these corresponding altitudes, many times repeated, serves to regulate the clock, and to ascertain exactly the moment of the sun's passage over the meridian, whence the direction of the meridian line may be immediately determined. The observation of equal altitudes may be employed at every other season of the year, as well as at the solstice, by applying to the result a small correction for the change which the sun's declination undergoes in the interval be BOOK I. Horary angle. Azimuth. Amplitude. tween the two altitudes, and which causes the length of that interval to vary. A great many circumstances influence this kind of observations, and renders them more or less subject to error, particularly when made on shipboard. The details must be sought for in works which treat professedly of these subjects.* The position of the heavenly bodies relatively to the meridian, and their bearings from the north and south, and east and west points of the horizon, inasmuch as the former serves to ascertain the true hour, and the latter to fix the true north and south points, contribute to facilitate or to verify, the operations by which we determine the position of places upon the earth. The horary angle of a heavenly body, is the angle which is formed at the pole, at the instant of observation, between the meridian of the place of the observer, and the circle of declination or hour circle, passing through the body. This last circle is nothing else than the meridian of the body. The horary angle is measured by the arc of the equator which has passed, or will pass, under the meridian of the observer, between the instant of observation, and the moment when the heavenly body is upon this same meridian. The azimuth of a body, is the arc of the horizon intercepted between the south point, and that in which a vertical circle passing through the zenith and the body, cuts the horizon. Amplitude is the arc of the horizon intercepted between the point where the body rises or sets, and the true east or west point. The former is called eastern amplitude, the latter western amplitude. The horary angle, the azimuth, and the amplitude, contribute in several ways to the determination of longitudes and latitudes; the first serves to ascertain the true hour, by only one observation of the altitude of the sun, and so gives the means of regulating the chronometer; the other two indicate to the navigator how *Levéque, Guide du Navigateur. Dubourguet, Traité de Navigation. I. much the magnetic needle deviates from the true north and BOOK south line; they teach also the method of placing a geographical map due east and west.* Upon these relations of the heavenly bodies to the meridian and horizon, are likewise founded various subsidiary methods for calculating by approximation the latitude of a ship at sea;† but as these methods, though ingenious, are very subject to error, and are seldom used in geography, we shall not stop to describe them. nals made To all these methods which the observation and calcula- Use of sig tion of the celestial motions furnish, for determining geo- by gungraphical positions, is now added the use of signals made powder. by gun-powder. In a very elevated place, during a serene night, a quantity of powder is from time to time inflamed in the open air; two observers, each provided with a clock, and stationed at the places of which the difference of longitude is required, mark with care the appearance of these flashes, an appearance which, notwithstanding the distances, is instantaneous at the two places, in consequence of the prodigious velocity of light. The difference of the times indicated by the two clocks, will give the difference of longitude sought.t Let us conclude this sketch, which is necessarily dry, of the methods by which longitudes and latitudes are determined, with observing to those of our readers who have no taste for such matters, that the exact knowledge of positions is the ground-work of all geography; and that without this knowledge, the most splendid description would only possess a merit altogether illusory. Puissant, Traité de Géodésie, p. 200. sqq. + Mendoza, Connaiss. des Temps, 1793, p. 289, 302. Dubourguet, Traité de Navigation, b. iii, chap. 3, 4. Puissant, Géodesie, p. 299. Zach. Astron. Corresp. M. Schumacher, Professor of Astronomy at Copenhagen, has lately brought this method to singular perfection. In the measurement of the arc of the meridian, and of the perpendicular to that arc, which is committed to his superintendance by the King of Denmark, he has made use only of a luminous signal. |