/S. L. Penfield — Stereographic Projection. 129 



ones which would be correct within certain limits, depending 

 upon the size of the projection and the skill with which the 

 drawing and plotting were done. Map-drawing is generally 

 a feature of grammar-school education, and by making use 

 of printed charts, showing stereographically projected meridians 

 and parallels, it would be no more difficult to construct an 

 accurate map than a mere sketch, and probably it would be 

 easier. It would be at least more profitable and instructive. 



Having demonstrated on a globe that the shortest distance 

 between two points is along the arc of a great circle, the use of 

 protractor No. IV, figure 14, could be explained, and by turn- 

 ing the protractor, the great circle passing through any two 

 points could be easily and quickly found. It is probable that 

 by making use of a suitable wire model, the principles under- 

 lying the construction of protractors II and III could be made 

 clear. In any event, an intelligent person would soon learn to 

 turn protractors II and III to the right position, and determine 

 in degrees the distance between two stereographically projected 

 points. 



Students come to the universities with altogether too little 

 knowledge of how to do things accurately, and the lack of 

 proper training in this respect is a serious defect in their edu- 

 cation. By applying to geography the mathematically correct 

 principles of the stereographic projection, it would be possible 

 to inculcate into pupils of high-school, possibly also of gram- 

 mar-school, age, methods of absolute accuracy as pertaining to 

 map construction. The essential features of the projection are 

 so simple, that, if properly presented with the aid of a few 

 models and diagrams, it should be possible to teach compara- 

 tively young pupils how to construct maps intelligently and 

 to make geodetic measurements accurately. It seems to the 

 writer that training of such a nature would be most beneficial, 

 not alone because it is important to know how maps are con- 

 structed and geodetic measurements are made, but, in a broader 

 sense, because of the advantages derived from that kind of 

 training which teaches pupils how to do things and to do them 

 correctly. 



This opportunity will be taken to present a brief demon- 

 stration showing the advantages of the stereographic over the 

 ordinary methods of map construction. In maps comprising 

 small areas, it is possible to measure the distance between two 

 points, in a straight line across the map, with considerable 

 accuracy. Not so, however, for long, transcontinental dis- 

 tances, as such must be measured with reference to the curva- 

 ture of the earth along arcs of great circles. Most persons 

 have no means of determining the distance between distant 

 points other than the very crude, and necessarily incorrect 



Am. Jour. Sci.— Fourth Series, Yol. XI, No. 62.— February, 1901. 

 9 



