Any two sides of a spherical triangle are together greater than the third side; and the three sides of a spherical triangle are together less than the circumference of a great circle.

In a spherical triangle the greater side is opposite the greater angle, and the greater angle opposite the greater side.

THE FIGURE AND MAGNITUDE OF THE EARTH

The earth, consisting of land and water, is a body of a spherical or globular form, but not a perfect sphere, since it is flattened towards the poles. Hence it is a spheroid, or more properly an oblate spheroid.

The earth is certainly not flat, as may be proved by various facts and phenomena.

(1.) The most obvious of the several arguments which prove the sphericity of the earth, and what must particularly strike every mariner, are, that when approaching the shores of countries, the points of high rocks, lighthouses, steeples of churches, and other thin but lofty objects, come into view much sooner than houses or other buildings of greater magnitude, but less height; in like manner, when ships are approaching each other at sea, the masts and rigging are discerned some time before the hull and lower parts of the vessel, though much larger, come into view.

(2.) Seamen, it is well known, frequently discover distant lands from the tops of a ship's masts, long before they are visible to those who stand upon deck. These circumstances prove that the surface of the earth is convex ; and as the same appearances happen wherever the observer is situated, this convexity must be approximately uniform: hence we conclude that the earth is globular.

(3.) The sphericity of the earth is likewise demonstrated by navigators who have sailed quite round it, by constantly going westward and arriving home from the eastward, or going eastward and arriving home from westward, which could not be effected were the earth a plane.

(4.) During an eclipse of the moon the shadow of the earth is thrown by the sun on the moon's surface; the shadow thus projected is invariably found to be circular, and such as could only be given by a spherical body.

(5.) The actual measurements of an arc of a meridian in various parts of the world, together with a comparison of the results of pendulum experiments in high latitudes and at the equator, all tend to prove the same fact— that the earth is an oblate spheroid.

DIMENSIONS OF THE EARTH.-The Astronomer Bessel gave the following constants as admeasurements of the earth :

The approximate dimensions of the earth considered as a spheroid of revolution may be taken to be

Equatorial radius in feet, 20926202: in English miles, 3963.296

whence the equatorial diameter exceeds the polar diameter by 27 miles. Sir G. B. Airy makes it 26 miles, and the compression to nearly.

But from recent observations, and the result of actual surveying, the earth is not a spheroid of revolution; the determinations of its various dimensions are given in a work on Geodesy by Colonel A. R. Clarke, C.B., as follow:If it be supposed that the earth is an ellipsoid with three unequal axes (diameters), then

Equatorial radius...

Polar radius

(longest, in feet 20926629
shortest, in feet 20925105
20854477

and the longest equatorial diameter meets the surface in long. 8° 15′ W. of Greenwich; and the shortest in Ceylon. But it is necessary to guard against an impression that the figure of the equator is thus definitely fixed, for the available data are far too slender to warrant such a conclusion." Thus the equatorial circumference may be roughly estimated at 25,000 English miles, and the ellipticity or earth's compression at about

DEFINITIONS RELATING TO THE EARTH

To point out the relative situation of places on the surface of the globe, geographers imagine certain points, lines, and circles belonging thereto; of these it will be necessary here to explain such of them as appertain more immediately to Navigation.

AXIS. The axis of the earth is that diameter around which the earth daily revolves from west to east; the revolution is completed in 24 hours.

POLES. The poles are the two ends of the diameter (or axis) around which the earth's daily revolution is performed. The pole which is nearest to us, in Europe, is called the North Pole, and the other is the South Pole, and as the poles are the ends of a diameter they are 180° apart.

EQUATOR. The equator is a great circle on the earth equally distant from the two poles; it divides the earth into two equal parts, called hemispheres ; the part having the North Pole for its centre is the Northern Hemisphere; and the part having the South Pole for its centre is the Southern Hemisphere. Every point on the equator is 90° (of a great circle) from each pole.

MERIDIANS are great circles on the earth passing through both poles, and therefore perpendicular to the equator. Every place or point on the earth's surface has its meridian, and in this sense the meridian is a semi-circle extending from one pole to the other, and passes through the given place.

Most of the principal maritime nations have a national observatory; and some of these nations, for the purposes of Geography and Navigation, adopt a first meridian whence longitude is reckoned; thus the French adopt Paris

the Spaniards adopt San Fernando (Cadiz), and we (in the British Empire) select Greenwich, as the first meridian. Some such arrangement is necessary, for, while the starting point for latitude among all nations is the equatorthat well-defined great circle midway between the poles, and which divides the globe into two equal parts-there is no such well-defined great circle on the globe whence to reckon the longitude. A congress has recently been held at Washington for the purpose of adopting a universal prime meridian, to be used by all nations, and Greenwich has been selected for this purpose.

LATITUDE.—The distance of a place from the equator, measured (in degrees and parts of a degree) on the meridian of that place, is its latitude. As latitude begins at the equator, where it is o°; so it ends at the poles where it is greatest, or 90°. The latitude is N. when the place is situated in the Northern Hemisphere, and S. when it is situated in the Southern Hemisphere.

PARALLELS OF LATITUDE are small circles on the globe parallel to the equator; every place on the earth's surface has its parallel of latitude, and any two or more places or points on the circumference of any one of these small circles, being equally distant from the equator, have the same latitude.

The parallel of latitude 23° 28′ north of the equator is the Tropic of Cancer; and the parallel of latitude 23° 28′ south of the equator is the Tropic of Capricorn. These parallels mark the limits of the sun's N. and

S. declination.

Difference of Latitude (Diff. Lat.) is an arc of a meridian, or the least distance, between the parallels of latitude of two places, indicating how far one of them is to the northward, or southward, of the other. If two places have latitudes both north, or both south, their Diff. Lat. is found by subtracting the less latitude from the greater: but when one place is in north latitude, and the other in south latitude, the Diff. Lat. is found by taking the sum of the two latitudes. The Diff. Lat. can never exceed 180°.

LONGITUDE.-The longitude of any place on the earth's surface is expressed as an arc of the equator contained between the meridian passing through that place and the first meridian whence longitude is reckoned to begin. Longitude, like latitude, is estimated in degrees and parts of a degree, and may be Eastward or Westward of the first meridian, reckoned from o° (when a place is on that meridian) to 180°,—the meridian on the opposite side of the globe.

Longitude is also the measure of the angle at the pole between the first meridian and the meridian passing through a place.

Difference of Longitude (Diff. Long.) is the arc of the equator, or the angle at the pole included between the meridians passing through any two places. If two places have longitudes both east or both west, their Diff. Long. is found by subtracting the less longitude from the greater; but when one place is in east longitude and the other in west longitude, the Diff. Long. is found by taking the sum of the two longitudes; and in the latter case, since the Diff. Long. of two places can never exceed 180°, when that sum is greater than 180°, subtract it from 360°, and the remainder is the Diff, Long,

Note.-If we know the latitude of any place and not the longitude, or, on the other hand, the longitude and not the latitude, its position on the earth is not determined, because, if we say it is in lat. 42° N., it may be anywhere on the parallel of 42° N. in E. or W. long., in the Pacific or in the Atlantic Ocean; similarly, if we say a place is in long. 32° E., it may be in Europe, in Africa, in the Mediterranean, or in the seas south of the Cape of Good Hope. Hence both latitude and longitude are required to fix the position; and when we say that a ship is in lat. 46° 20′ N., long. 32° 40′ W., we have its PLACE AT SEA accurately noted-a spot in the Atlantic-and a course can be shaped therefrom towards the port of destination. It is part of the routine of a voyage to determine the ship's place day by day, approximately by dead reckoning, and more accurately by observation of the heavenly bodies.

The HORIZON of any place is that apparent circle which limits or bounds the view of a spectator on the sea, the eye being always supposed in the centre of the horizon. This circle is divided into parts similar to the divisions on the Mariner's Compass.

The ZONES.-The earth is considered to be divided by certain circles, parallel to the equator, into broad spaces, called ZONES; of these there are five, viz., one torrid, two frigid, and two temperate, in allusion to the general temperature which prevails in each of the regions.

The TORRID ZONE is that region of the earth over some part of which the sun is vertical at some time of the year. This zone is 47 degrees in breadth, extending to about 23° 28' on each side of the equator; the parallel of latitude bounding it in the northern hemisphere is called the Tropic of Cancer; and in the southern hemisphere the limiting parallel is called the Tropic of Capricorn.

The FRIGID ZONES are those regions of the earth around the Poles where the sun at certain times of the year does not rise or set for some days or weeks; they extend round the Poles to the distance of 23° 28'. The parallel which bounds this limit in our northern hemisphere is called the Arctic Circle, and that portion of the globe included within it is the North Frigid Zone or Arctic Regions. The parallel which is at the same distance from the South Pole, in the southern hemisphere, is called the Antarctic Circle, and the space included within it is the South Frigid Zone, or Antarctic Regions.

The TEMPERATE ZONES are those portions of the earth comprehended between the Torrid and the Frigid Zones; they are distinguished respectively as the North Temperate and South Temperate Zone.

I. To find the Difference of Latitude between two Places

RULE. When the latitudes are both of the same name, that is, both North or both South, subtract the less from the greater, and the remainder will be the difference of latitude. But when one is North, and the other South, their sum will be the difference of latitude.

II. With the Latitude left and the Difference of Latitude, to find the

Latitude in

RULE. When the latitude left and difference of latitude are of the same name, their sum gives the latitude in; but when they are of different names, their difference is the latitude in, of the same name with the greater.

EXAMPLE I. A ship from the West end of the Island of Madeira, in latitude 32° 48′ N., sails North 520 miles*: what latitude is she in? Latitude of Madeira .... 32° 48′ N. Diff. of latitude 520 m. = 8 40 N. Latitude in

.....

4I 28 N.

EXAMPLE II. A ship three days ago was in latitude 2° 48′ N., and has since then sailed South 426 miles required her present latitude. Latitude left 2° 48' N. Diff. of latitude 426 m. =

Latitude in

LAT. LEFT is the latitude from which the ship has departed.

DIFF. LAT. is the change of latitude in any interval.

LAT. IN is the latitude at which the ship arrives.

7 6 S.

4 18 S.

The method of obtaining the Lat. in, from the Lat. left and Diff. Lat., is shown in the following examples and explanations—

Understanding that latitude is reckoned from the equator towards the

pole:

(1) If you are in north latitude and sail north, Lat. left must be increased by Diff. Lat.

(2) If you are in north latitude and sail south, Lat. left must be decreased by Diff. Lat.

(3) If you are in north latitude and sail south, and the Diff. Lat. exceeds the Lat. left, take the less from the greater, and the remainder will be the Lat. in, south.

(4) If you are in south latitude and sail south, Lat. left must be increased by Diff. Lat.

When the difference of latitude or longitude is given in miles or minutes (') it is to be divided by 60, to reduce it to degrees and minutes.