MATHEMATICAL GEOGRAPHY.
The form of the earth is spherical, with a slight flattening at the poles. Its equatorial diameter is 7926 and its polar diameter 7900 miles, the differ ence between them, 26 miles, measuring the eccen tricity. This flattening of the earth at the poles is a necessary consequence of the earth's rotation about its axis. See EARTH.
The chief method employed in the determina tion of the size and form of the earth may be ex plained in general terms, without going into de tails. The latitudes and longitudes of two points, widely separated, are determined by astronomical means, and the direct distance between them is measured by geodetic methods. A comparison of the two methods gives the length of a degree or series of degrees of latitude and of longitude. Such arcs have been measured in various parts of the earth, from Northern Africa northward across Europe, in India, in the Andes of South America, across the United States from east to west, and southwest from New England to the Gulf coast.
Latitude is distance north or south of the equa tor expressed in terms of the angle subtended at the earth's centre. It is determined by measuring the angle of elevation of the sun or of any star whose position is known, when crossing the me ridian of the place of observation ; or most accu rately, by measuring the difference between the zenith distances of two stars, whose position is known, such measurement being made by zenith telescope. See LATITUDE AND LONGITUDE; DE GREF OF LATITUDE.
Longitude is distance east or west of a selected meridian, expressed in terms of the angle sub tended at the earth's axis. The meridian of the observatory at Greenwich, England, has been al most universally adopted as the initial point for the statement of longitudes. Difference of longi tude is difference of time. Since the earth re volves on its axis, i.e. turns 360°, once in 24 hours, an hour corresponds to 15° of longitude. Hence, in order to determine the difference of longitude between two places it is only necessary to determine and compare the local sidereal times of those two places. The determination of time
is made by observing, with a transit instrument and chronometer, the passage of stars, whose position is known, across the meridian. The ob served sidereal times of their passage, or transit, compared with their right ascensions, gives the error of the chronometer, and hence the true sidereal time. Local sidereal time of the two places is compared by the use of the telegraph. See LATITUDE AND LONGITUDE; DEGREE OF LONGI TUDE.
Measurements of distance on the earth's surface are commonly made by triangulation. A base line, two to five miles long, is first measured directly, using steel wire, or tape, or bars. Angles are measured at each end of the base, between the other end and certain signals erected to the right and left, and from these signals the third angle of each triangle is measured. Then with the angles and one side known in each triangle the other sides may be computed, and these in turn become the bases for other triangles, as the work is extended. See ASTRONOMY; GEODESY.
The plane of the earth's orbit about the sun, known as the ecliptic, is inclined to the earth's equator at an angle of 23° 28'. Hence, in the course of the year the sun apparently moves north and south through an angle of 46° 56', the equator being in the middle. The sun reaches its most northern position, which is known as the Tropic of Cancer, about June 21st, and its most southern point, the Tropic of Capricorn, about December 21st, passing the equator about March 21st and September 21st. This apparent move ment of the sun causes the change of seasons.
There is an area about each of the poles of the earth where, in midwinter, the sun fails to rise above the horizon, even at midday, and where in midsummer it does not sinkbelow the horizon, even at midnight. The circles bounding these areas are the polar circles, and the areas are the polar zones, distinguished as the Arctic and Antarctic. The areas lying between the polar circles and the tropics are the temperate zones, and that lying within the tropics the torrid zone.