217.Determination of Latitude. -In Fig. 121 consider the sun as vertically above the point where our meridian crosses the equator and the lines AB and ED as representing rays from the sun. The line FI tangent at the point A will representa level surface at that point. Draw the line CH through the point A . It will be at right angles to the tangent line FI . The latitude of the point A is mea- sured by the angle ECA , as this angle measures the number of degrees oflatitude between the point E , which is
on the equator, and the point A .
Fig. 121.
It can be proved by geometry that the angle HAB is equal to the angle HCE , since if the sun is vertical, the line CED is a straight line. The angle HAB is equal to a right angle, or 90° minus the angle BAI . As the angle BAI can be easily found by measuring the elevation of the sun above a horizontal plane, it is not a difficult thing to find the latitude of a place when the sun is vertical at the equator.
As the sun is vertical at the equator but twice in a year, on March 21 and September 23, this method can be used without modification only on those days; but since the angle of the sun above or below the plane of the equator is given in the Nautical Almanac for every day in the year, by adding this angle to the angle BAI when the sun is above the equator, and subtracting it when the sun is below the equator, the latitude of a place can be found for any day.
On board ship, every fair day, the officers will be seen just before noon coming on deck with their sextants to take the elevation of thesun. They find the elevation several times until they are sure that the sun has reached its highest point, and at this moment they call for the time to be taken on the chronometer; for when the sun reaches its highest point, it is noon for that place. Thus by making use of this one observation they are enabled, with the help of the chronometer, to find both their latitude and their longitude, or their exact position on the earth.
218.Topographical Maps. -Maps which attempt to show thesurface features of the earth are called topographical maps. There are several ways in which we may try to show on a map the irregularities of the surface. One of these is shading, that is, making the hills and ridges light, while the valleys are shaded dark. A somewhat similar way is to draw short broken lines in the direction of the slopes. This gives a more accurate representation of the steepness of the descents, since the lines are made short and heavy when the slope is steep and longer and lighter when it is gradual. Such maps are called hachure maps.
The commonest way in this country is to draw lines connectingplaces of equal elevation. These lines wander in and out of the valleys and around the hills, but always pass through places which are of the same altitude. The distances apart of the lines vary continually, but the elevations never. From these maps the height of any place can be determined with great accuracy, for its height will be indicated by the line passing through it or near it. These maps are called contour maps.
219.Contour Maps. -Although it is easy to find the elevations ofplaces on a contour map, it is hard to get a clear idea of what a contour map really expresses. The best way to gain an appreciation of a contour map is to get a map of the region in which you live, take it into the field, and study map and region together. Another excellent way is to make a contour map of a model. When once you have made a map of this kind, you will readily understand all other similar maps.
We must remember that a contour is the projection on a flat surface of a line which passes through places of equal elevation. It shows where the margin of water would come if the place in question weresubmerged to a given depth. No two contours can possibly cross each other, as no place can have two elevations. No contours can ever end except at the edge of the map, for a sheet of water must have a continuous boundary and only where the map terminates can the line representing the edge of the water appear to end.
Experiment 133. -Provide each pupil with a contour map representing the home locality if possible; if not, use the contour map in section 160. Let the teacher or different pupils pick out places and ask some one to give their elevations. In this way you will get an idea of how elevations can be determined by use of a contour map. Notice the different topographical symbols used on the map.
220.Maps of Curved Surfaces. Projections. -The accurate mapping of small areas offers no great difficulty because these are practically flat, but when an attempt is made to represent a curved surface upon a flat surface, difficulties present themselves which are insurmountable. If the rind of an orange is taken off, it cannot be made to lie flat, and if crushed into this shape, it will break into pieces and only partly cover the surface over which it spreads. The same is true of any curved surface. Thus the continents of the earth, if they were flat- tened out, would of necessity be broken into fragments. If they could not themselves be made to occupy a flat surface, then no accurate map of them can be made on such a surface.
Although there are several ways of representing a curved surface upon a flat surface, yet no method has been found which is perfectly satisfactory. If the areas are in the right proportions, the outlines are not; and when the outlines are right, the areas are not. These different ways of mapping the surface of the earth are called projections. As a large part of our knowledge of the earth"s surface is obtained from maps, it is very essential to have some idea of how these maps are made and wherein the essential error of each consists. Two very important kinds of projection are the cylindrical and the stereographic.