OF HORATIU CHUTE

SCHOOL SCIENCE AND MATHEMATICS

VOL. XI. No. 6 CHICAGO, JUNE, 1911 WHOLE No. 89

SOME SUGGESTIONS TO MAP PUBLISHERS.

BY RULIFF S. HOLWAY,

University of California.

A good map of the surface of the earth gives more knowledge. of that surface in less space than any other known device and also presents the total of that knowledge more clearly than is possible by any verbal description. Nevertheless it remains an incontestabic fact that few people are able to get clearly from maps the full and definite information which they contain. The latter statement is borne out by the fact that most people read all maps in the same way without any regard to the properties of the particular projection upon which the map before them is constructed. In general the reading public scarcely realizes that there are various projections upon which the world's surface may be mapped-each projection having certain advantages and also invariably being accompanied by certain disadvantages.

As the reading public is on the average just as intelligent as the smaller number who have had more or less training in the properties of map projections it would seem that something is wrong in our common school education, or in our methods of map printing, or in both. In general the mother tongue is so well taught that all who have had the advantages of the common schools are equally able to read any ordinary book-the appreciation of the contents varying of course with the previous experience and with the native ability of each individual. Everyone should be able to read maps with a facility equal to that with which he reads his native language.

This result it seems to the writer could be obtained by map publishers making some additions to the data on maps of large areas and by schools recognizing more clearly the few simple principles of map projections which should be thoroughly taught. The suggested changes in map printing are limited to maps of large areas because the errors in flat maps, while theoretically always present, are too minute to be noticed when small areas

are represented. The error grows rapidly with the extent of surface covered and in many projections becomes very great for a hemisphere or even a continent. The recent study of the relations of the Panama Canal to the rest of the world has led many people to extremely erroneous conclusions because they did. not know the kind and amount of distortion incidental to the projection upon which their particular map of the world was based.

The simplicity of the changes to be suggested may be best appreciated by briefly noticing the very few ideas that need be taught in the public schools to enable anyone to fully understand the meaning and the limitations of common map projections. In fact the new style maps would be far more intelligible to the untrained man than those in use at present. He would really need nothing more than to lose his simple faith in the absolute accuracy of a flat map as a reproduction in miniature of the shapes and sizes of the countries of the earth's surface. But to give fullest appreciation of the properties of maps, the schools should teach thoroughly a few things that involve the general principles of map projections.

First will come in the primary school the fundamental conception of a map as a representation of the surface of the home locality and then of larger areas. Study of the surface of the earth as pictured on a globe should lead to the realization of the impossibility of the entirely correct representation of that surface on a flat map. Location of position on the globe by latitude and longitude should be followed by the presentation of two maps of the world with different schemes for drawing the parallels and the meridians and the statement that each map records true location by latitude and by longitude but cannot show correctly all other relations such as shapes, sizes, compass direction and shortest distance or true direction. Projections can now be presented on which some one thing is shown with entire accuracy at the expense of distortion of other things. An ideal series would be the Mercator projection for compass direction, the great circle map for shortest distance or true direction and an equal area projection for showing correctly the relative size of countries. Comparison with the globe in each case as well as with the other projections should be made to emphasize the general idea that accuracy in one detail means distortion in others. The course can now be completed by studying some of the general projections that try to minimize the distortion in everything

by sacrificing absolute accuracy in any one thing excepting the record of position by latitude and longitude, which all maps may give correctly. The names of only a few well-known projections need be taught.

Practically the brief summary above covers the essentials that are needed for the work of the elementary schools. The wealth of detail necessary and the number of years of school life through which this work should be distributed are minor problems for the schools and should not be confused with the main point of this paper, namely the suggestion of additional explanatory data to be printed on maps of large areas.

The additional data would serve to keep fresh in the minds of pupils the ideas of map projections obtained from the above course and should also be so definite as to be self-explanatory to any intelligent adult reader who uses the new maps.

The essential idea in the new data desired is that there should be index diagrams printed on every map showing the kind and amount of distortion incidental to the projection used. If a square of large size could be accurately laid off on the round earth it would be an ideal index figure, as distortion would be so casily noticed. The nearest approach to a square on the surface of a sphere is a regular quadrangle bounded by arcs of great circles. Such a figure bounded, we will say, by arcs of twenty degrees on each side would be identical in size and shape no matter upon what part of the earth's surface it were constructed, but reproduced in different parts of a map, it would vary in shape and size with the projection.

In figure I we have index diagrams (twenty degrees on a side) reproduced in different parts of a map of the world on the muchused Mercator projection. These widely differing figures, A, B, and C, represent areas of exactly the same size and shape on the earth.

We have been so accustomed to the gross exaggeration of the Mercator projection that I venture to assert that very few readers of this journal will see in the North America and Greenland of figure I the same distortion which strikes them so forcibly as they compare diagram C with diagram A and remember that each represents the same size and shape on the earth.

Pupils with a Mercator map of the world before them with index diagrams added as shown above would be interested in the method of construction of the projection. The following expianation is sufficient for common school purposes. The meridi

ans which on the earth meet at the poles are drawn as parallel

lines. As this makes them too far apart north or south of the equator the parallels of latitude are also drawn too far apartthe distance being constantly increased as the poles are approached so as to make at any point the distortion from N to S equal to the distortion from E to W. The result is that this