The result has been the development of an endless variety of projections, each of which tries to show on a plane surface that portion of the globe which it aims to represent, with a minimum of distortion for one particular purpose, or with a compromise which has some errors everywhere, but a minimum all told. Projections can be made which show all areas proportional to their size, but the shapes look very queer indeed. On the other hand Mercator's well-known projection has reasonable shapes, but because the longitudes are drawn parallel to one another, instead of converging at the poles, Greenland comes out looking as large as the whole of North America, and all the other polar regions are similarly enlarged.
The really proper way of showing the Earth is on a globe, the only source of sound geographical ideas. Whenever a globe and a map disagree, the award for accuracy must go to the globe every time. Unfortunately, like all things, globes suffer from tradition. Their purpose is to show the form and arrangement of the Earth, to serve as an index to maps of the continents, which in turn serve as indexes to maps of countries. The amount of information put on a globe should be limited to what can be read and followed easily, else they defeat their own purposes. All else should be eliminated.
Above all there is no place on a terrestrial globe for astronomical features. The signs of the zodiac, often put on the stands, are meaningless. The ecliptic is hopelessly out of place. It is no more in the north of India, where custom has it, than in Mexico, and the same might be said of the figure-8-shaped "analemma" which represents the "Equation of Time." If the barren wastes of the Pacific Ocean offend the aesthetic souls of the globe makers, they might just as well put in the lost continents of Atlantis or Mu. Vague as these districts are, they have a great deal more meaning than has the lost continent of Analemma plumped down in the middle of the Pacific. One of these days some poor sea-struck lad will run away to find it, and no one but the globe makers will be to blame.
A plane map may have many shapes and the form that it takes depends usually upon the subject matter chosen, and the area to be covered; upon them depends the projection to be used. Topographic maps, which show elevations, are usually of such small areas that the type of projection is not important, except where a number of them have to be arranged so that they can be mounted on a single sheet. Even that would not be difficult were it not for the general requirement that outlines must be rectangular.
A map is a representation of a portion of a sphere on a plane surface. A so-called grid is usually laid out first. It may be set by "projection," hence its name, or it may be laid out according to any preconceived idea of the map maker that this particular projection will illustrate his point better than any other.
Sometimes the projection is so complicated from the requirement that even the outlines of the continents cannot be shown on it. One of these was produced a few years ago by the Royal Geographical Society. It was called a "Reverse Azimuth" Map, and its purpose was to enable anyone with a directional radio to turn his aerial until it pointed to the Rugby broadcasting station in England. The distortion was so terrific that nothing on the map looked like anything. It might just as well have been a portrait of the other side of the Moon, as a map of the Earth. However it was not hard to use. Knowledge of the latitude and longitude of one's own radio was required; from these we could determine the direction to which the aerial should be pointed. I worked it out but, having a certain distrust of this villainous appearing map, I took the trouble to write my finding to the Secretary of the Royal Geographical Society, who informed me by return mail that the bearing was correct!
Certain projections have marked advantages. An old favorite commonly used on astrolabes was the stereographic in which all circles on the sphere appear as circles on the projection. It was made by taking a point on the surface of the opposite hemisphere as the point of projection.
The gnomonic projection has the advantage that all great circles (that is circles which bisect the sphere, like the equator or meridians) are shown as straight lines. These maps give directly the shortest distances between two ports, and that is the line which steamers follow, unless forced out by intervening land or danger from icebergs. It is just because the great circle is the shortest route between any two ports on a sphere, that steamers run the hazards they do, from northern weather and icebergs. Washington and Pekin are on almost the same latitude, but the shortest path between them lies not along the fortieth parallel as it would look from Mercator's projection but along the great circle which the Lindberghs took when they flew via the Arctic in search of the Orient. In the Southern Hemisphere ships must start out by heading to the south, and in the Northern Hemisphere they must head to the north if they wish the shortest routes. All this is shown clearly on the gnomonic projection. The constant compass direction is circuitous, and would tend all the time to form a spiral going around one of the poles unless the course be due north or south or east or west.
Mercator's projection has its fame, because it was one of the earliest devices used, and it still has merit for navigation. The course between two near-by points can be taken off readily with a parallel ruler, so most harbor maps are made with Mercator's projection. It can also show the whole world unbroken into hemispheres, and parts of the world can be repeated at each end. With this arrangement, journeys across both the Atlantic and Pacific can be planned on the same map. Of course there is rank favoritism at the poles, but a trained eye can put the arctic zones back to the small area where they belong, and the "conventional signs," which the snark hunters so scorned, might have been of some use even to them, for like most men who set out with a blank, their griefs came later:
This was charming, no doubt: but they shortly found out
That the Captain they trusted so well
Had only one notion for crossing the ocean,
And that was to tingle his bell.
But the principal failing occurred in the sailing,
And the Bellman, perplexed and distressed,
Said he had hoped, at least, when the wind blew due east,
That the ship would not travel due west!
A few of the "merely conventional signs" are not out of place for snark hunters or for anyone else.