Map Projections.—The fundamental consideration in any map of a fairly large area is the projection, that is, the method by which a curved surface shall be represented as flat. The curved surface can not possibly be made flat, as is easily seen when one tries to flatten out an orange skin without breaking it into bits. This has led to many attempts to represent the earth's surface with its meridians and parallels as accurately as possible. These all fail in one or another of the following respects: (1) the shapes of the regions represented are wrong; (2) the areas are wrong; (3) the distances are wrong. Examples of three types of projection are given in Fig. 9. The first of these is the stereographic projection, which is sometimes used for hemispheres. The sheet on which the map is to be drawn touches the globe at a point on the equator. From a point directly opposite this and also on the equator straight lines are drawn through points in the hemisphere next to the map sheet and are prolonged to the sheet itself. As a matter of fact the parallels and meridians for this pro jection, or any other, are drawn by geometrical principles so that actual juxtaposition of the map sheet and the globe is not necessary.
The central part of a stereographic projection is in true proportion, but on the edges the distances are doubled.
In the Mercator projection a cylinder is supposed to be wrapped around the globe touching it everywhere at the equator. Lines are drawn from the center of the globe to the cylinder through the points which it is desired to locate. When such a cylinder is cut open the whole earth appears as a single map with no breaks between the hem ispheres. Both meridians and parallels are straight lines. Hence a given point of the compass is always in the same direction on all parts of the map, which is not true where the meridians or parallels are curved. Moreover, the parts of the map near the equator show the earth's features without distortion and with the correct relative areas. These advantages are offset by the fact that on a Mercator projection the poles cannot possibly be represented, and high lati tudes are so extremely exaggerated that they are usually omitted or arbitrarily reduced in size. Moreover, even in low latitudes the distances and areas become exaggerated as soon as one gets much away from the equator.
The conical projection is made by placing a conical map sheet so that it touches the earth on the circle of latitude passing through the center of the map. Lines are drawn from the center of the earth to the cone. When the cone is opened the meridians are found to be straight lines and the parallels are curves. The parts of such a map near the central parallel show no distortion or exaggeration. Maps of small areas are usually made on the conical projection, while for larger areas, such as countries or continents, it is common to employ a modified conical projection made by combining the conical pro jections for a series of parallels of latitude. Further information as
to map projections can be gained from exercise 9 at the end of this chapter and from Fig. 18.
The Effect of Tides.—Let us now turn from latitude, longitude, time and maps, and discuss still another geographical condition which depends largely on the earth's rotation.
During a visit to the seashore, the tides give rise to some of the most interesting experiences. At low tide in some places great stretches of oozy mudflats invite barefooted clam-diggers to wander over them with short-handled pitchforks. Elsewhere acres upon acres of sea grass lie flat on the ground, broad sandy beaches are strewn with stranded bits of seaweed, broken shells and jellyfish; while on more rugged coasts the rocks are carpeted with seaweed. In the coves many small boats lie on their sides where they have been left by the retreating water. A smell of decay burdens the air, not wholly unpleasant, yet suggesting that all is not quite as it should be.
Then the tide turns, and the water slowly rises. After three or four hours the mudflats, grassy places, and weed-strewn rocks are covered, fishermen with their nets embark in the boats which are now afloat, bathers appear on the sandy beaches, strong currents flow up the inlets where previously the water was flowing outward. The whole appearance of the shore suggests life and activity which reaches a maximum at high tide. Then the sea seems to be brimming full, all signs of death and decay are hidden, and a strong, life-giving odor pervades the air.
The Nature of Tides.—The tides are great waves with a length from crest to crest equal to half the earth's circumference. As the wave approaches the shore the water encroaches more and more on the land until the crest arrives, when it is high tide. In the same way the arrival of the trough of the tidal wave brings low tide. Ex actly the same thing can be seen in miniature and in an exceedingly brief time when a stone is thrown into a mud puddle. Notice how the margin of 'the water keeps changing its position, advancing with each wave and then retreating before the arrival of the next.
The height of the earth's tidal wave varies from 2 feet in the open ocean to 5 or 10 feet on ordinary shores and 20 or even 50 in funnel-shaped bays like the Bay of Fundy. This is partly because of the shape of the shore, and partly because as soon as the waves reach shallow water the velocity decreases; the crest rises and the trough sinks, making the height greater; and the front becomes so much steeper than the back that finally it may topple over. A good illustration is seen in the ordinary waves of any body of water where surf occurs. As a wave approaches the shore it can be seen to rise higher and higher, as appears in Fig. 10.