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MERIDIAN.

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LATITUDE AND LONGITUDE. LATITUDE (Lat. latitudo, breadth, from latus, OLat. stlatus, broad) AND LONGITUDE (Lat. longitudo, length, from longus, long; connected with Goth. laggs, OHG., Ger. lang, AS., Eng. long, Skt. dirgha, OPers. dränga, OChurch Slav. dlugu, Lith. ilgas, long). Geographical terms used in specifying the position of places on the earth's surface. Longitude is the angle at the pole between two great circles drawn on the earth's surface, passing through the poles, and touching respectively the place whose longitude is in question and the place selected as the origin of longitudes. Latitude is the angular distance of a place north or south of the equator. The geographic latitude is determined as follows: In the figure, let S be any assumed point on the surface of the earth; O P Q P is the section of the earth through the meridian of the place S; OQ is the plane of the equator; P P is the polar axis; and C is the centre of the earth. If T T is the tangent to the meridian at S and S C' is perpendicular to T T' at S, then the angle S CQ is the latitude of the place S. This differs from the true or geocentric latitude, which is the angle S C Q, and the difference is 11' 30" at the latitude of 45°. The geocentric latitude is used in navigation only in the correction of sights for lunar distances by the old methods. Latitude is reckoned from the equator to the poles, a place on the equator having latitude 0°, and the poles 90° N. and 90° S. respectively. Longitude is best measured along the equator from the prime meridian; but as nature has not, as in the case of latitude, supplied us with a fixed starting-point, each nation has chosen its own prime meridian; thus, in the United States, in Great Britain and her colonies, in Germany, Holland, and other States, longitude is reckoned from the meridian which passes through Greenwich; in France, from that through Paris, etc.; and in many old charts, as well as in German atlases down to a recent date, from Ferro (one of the Canary Isles), the meridian of which (17° 40′ W. from Greenwich) is the conventional dividing line between the Eastern and Western hemispheres, or from the Madeira Isles. It is reckoned east and west from 0° to 180°, though astronomers reckon from 0° west to 360° west, and never use east longitude. It will easily be seen that if the latitude and longitude of a place be given, its exact position is known, for the latitude confines its position to a circle called a parallel of latitude passing round the earth at a uniform fixed distance from the equator, and the longitude shows what point of this circle is intersected by the meridian of the place, the place being at the intersection.

The measurement both of latitude and longitude depends upon astronomical observation. The principle on which the more usual methods of finding the latitude depend will be understood from the following considerations: To an observer at the earth's equator. the celestial poles are in the horizon, and the highest point of the equator is in the zenith. If now he travel northward

LATITUDE AND LONGITUDE. over one degree of the meridian, the north celestial pole will appear one degree above the horizon, while the highest point of the equator will decline one degree southward; and so on, until, when he reached the terrestrial pole, the pole of the heavens would be in the zenith, and the equator in the horizon. The same thing is true with regard to the Southern Hemisphere. It thus appears that to determine the latitude of a place we have only to find the altitude of the pole, or the zenith distance of the highest point of the equator (which is the same thing as the complement of its altitude). The altitude of the pole is found most directly by observing the greatest and least altitudes of the polar star (see POLES), or of any circumpolar star (q.v.), and (correction being made for refraction) taking half the sum. The method most usual with navigators and travelers is to observe the meridian altitude of a star whose declination or distance from the equator is known; or of the sun, whose declination at the time may be found from the Nautical Almanac; the sum or difference (according to the direction of the declination) of the altitude and declination gives the meridian altitude of the equator, which is the co-latitude. Other methods of finding the latitude at sea require more or less trigonometrical calculation. For very precise latitude determinations astronomers and geodesists employ an instrument called a 'zenith telescope,' with which the difference of meridional zenith distance can be measured micrometrically for certain pairs of stars. From this difference the latitude can be computed, if the declinations of the stars are known. See NAVIGATION.

To understand the determination of longitude by observation, it is necessary to remember that differences of longitude correspond to differences of time. Thus, if a place be in longitude 15° west of Greenwich, its local time will be one hour slow of Greenwich time. Similarly 30° correspond to two hours, etc. (See INTERNATIONAL DATE-LINE.) To find the longitude in any place, it is thus only necessary to ascertain how much its local time is fast or slow of Greenwich. On shipboard the navigator uses a chronometer, the error of which in Greenwich mean time and its daily rate of gain or loss are ascertained before leaving port. Anywhere at sea he can find out his local time at any moment by observing the sun with a sextant, and thence determining the local time. This local time he compares with the Greenwich time shown at the same moment by the chronometer; and the difference in hours, multiplied by 15, is then the longitude in degrees. Longitudes on land are determined by astronomers and geodesists on the same principle, only here the comparison of local with Greenwich time can be made more accurately by direct telegraphic comparison of the standard Greenwich clock with the clock or chronometer at the observing station. If the latter station is very far from Greenwich, its time is usually compared telegraphically not with Greenwich itself, but with some nearer place whose longitude has already been determined. The above methods of determining longitude are so superior in precision to all others that they are practically the only ones now in use. See NAVIGATION.

When applied to a heavenly body, the terms latitude and longitude have the same relations

to the celestial equator and its poles, and to the point on the ecliptic called the equinox (q.v.), that terrestrial latitude and longitude have to the equator and a first meridian. The corresponding coördinates of a heavenly body relatively to the celestial equator are called its declination (q.v.) and right ascension (q.v.).

LATITUDE, VARIATION OF. For many years it has been suspected that terrestrial latitudes might be subject to small changes, and that these might possibly affect the results, of ordinary astronomical observations. But in spite of all efforts to detect with certainty the existence of such changes, it was not until the year 1888 that Küstner proved beyond a doubt that latitudes vary by observable amounts. His observations were made in Berlin, and he found that the latitude of that place was less by two-tenths of a second of arc in the spring of 1885 than it had been in the spring of 1884. His result has been abundantly confirmed by subsequent observers.

If we imagine two straight lines drawn from the centre of the earth, one to the pole, and the other to a given observatory, then the angle between these two lines is called the co-latitude of the observatory. The latitude, in the ordinary geographical or astronomical sense, is obtained simply by subtracting this co-latitude from 90°. It is evident that the co-latitude (and therefore also the latitude) will remain constant for any given observatory if the pole maintains an immovable position on the earth. Now, if we disregard, as we may, moderate irregularities in the earth's surface, we can take its figure to be a slightly flattened globe or sphere. The shortest possible line through the centre, and limited by the surface at each end, may be called the axis of figure of the earth. The points where this axis meets the surface are the poles of fig ure. But the earth has still another axis, viz. the axis of rotation. About this axis the planet revolves once in twenty-four hours, giving rise to all the diurnal phenomena of astronomy. Constancy of latitude would imply the relative fixity tinuously exactly the same position with respect to the other is the one necessary and sufficient condition for perfectly invariable terrestrial latitudes. If the axis of figure be subject to a slow revolution about the axis of rotation, there will be a corresponding variation of astronomically

of these two axes. That each shall maintain con

determined latitudes. The maximum amount of the variation will be the same as the small angle between the two axes, and its period will be equal to the time required for the rotation of the one axis about the other. At the end of every such period, the latitudes of all places on the earth should return to their original values.

Up to the publication of the work of Küstner, in 1888, fundamental astronomy had adopted invariability of latitude as a fact practically established. All the results of astronomical observations made prior to that date must therefore be subject to so much error as might be produced by assuming a constancy of latitudes in the discussion of the observations. Now, the aberration, constant (see ABERRATION OF LIGHT) is particularly liable to error from this source. It is evident, therefore, that a redetermination of this quantity was imperatively needed, and that the necessary observations must be arranged in such a manner as to take account of the effect of latitude variation. Careful study of the problem

brought out the fact that the two quantities involved are entangled in such a way that no available method of research could prove satisfactory, unless it had for its object the simultaneous determination of both aberration and variation of latitude. It seemed best to employ what is known as the 'zenith-telescope method,' and the best modification of this was suggested by Küstner himself. The observations, when made, must night and must be made on every clear night for be continued more or less through the entire a period of fourteen months, if it be desired to determine the aberration. For the latitude variation, the observations must of course be continued for a term of years-indeed, they must motion. It will be seen that the problem is one be kept up as long as we wish to trace the polar of great difficulty, testing to the utmost the pa

tience and endurance of the astronomer. More

over, as in the case of the solar parallax, the precision can be enhanced by making a simultaneous series of observations at more than one observatory. If the participating observatories are situated upon the same parallel of latitude, or very near it, the results obtained will enjoy a further increase of precision. This was first suggested by Fergola of Naples. The advantage consists in the possibility of observing just that the differences of latitude of the stations the same stars at all the observing stations, so are determined independently of any knowledge of the exact positions of the stars on the sky. stars are never known with absolute precision, This is most important, for the positions of the being themselves but the results of fallible human observation. Moreover, the polar motion can be deduced from the latitude differences of the observatories just as well as from the actual latitudes. If, for instance, the pole happens to be moving at a given time toward an American observatory, it will be moving away from observatories in Japan or the Philippine Islands. So that, if we can but measure, from time to time, the latitude differences of observatories properly situated, we can get an accurate and complete idea of the actual motions of the pole.

The International Geodetic Association, which includes all the civilized nations, has now underation. Four stations have been established upon taken the systematic observation of latitude varithe same parallel of latitude. Two are in the United States, one in Japan, and one in Sicily. Two private observatories participate volunabout the end of 1899. tarily. Systematic observations were begun

The accepted constant of aberration must also long as the latitude problem remains unsettled, be regarded as subject to slight correction, so especially as the most recent aberration results exhibit rather large discordances among them

selves. Consult Chandler's articles in the Astronomical Journal (Cambridge, Mass.), and Albrecht's articles published in the reports of the International Geodetic Association, and also, in abridged form, in the Astronomische Nachrichten (Kiel, Germany). See PARALLAX.

LATʼITU DINAʼRIANS. The name sometimes applied to a school of English writers in the seventeenth century who sought to reconcile the Church of England and the Puritan element upon the basis of subordinating differences in doctrine to the broad essentials of religion. See CAMBRIDGE PLATONISTS.

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