Geographical Maps and Sailing Charts. 373 



considerable thought to the subject, asks the privilege of 

 making a few suggestions to those who may be interested in 

 teaching geography. Models, such as shown in figures 1 

 and 16, pages 247 and 269, ought to be most useful for demon- 

 strating how stereographic maps are made. Maps of the hemi- 

 spheres one foot in diameter, executed with much care and 

 accompanied by accurately engraved protractors, would serve a 

 most useful purpose. The adoption of some of the methods 

 indicated in this paper into schools would introduce new 

 features of mathematical geography, which have the advantage 

 of being simple, accurate, and useful. As far as measure- 

 ments are concerned, the practical manipulation of stereo- 

 graphic protractors is so simple that any one could soon learn 

 to use them. Naturally, the mathematical principles of the 

 projection would not need to be introduced ; all that beginners 

 would need might be comprehended from studying models 

 such as shown in figures 1 and 16. For advanced work, 

 maps of the hemispheres two feet in diameter, with accom- 

 panying protractors, could be used to advantage, and it is prob- 

 able that a stereographic map of the world, such as shown 

 in figure 14, page 265, would be found most useful, especially 

 as giving a ready means of solving many problems in Physical 

 and Commercial Geography. Maps of the several continents 

 and oceans, all drawn to one scale and accompanied by a pro- 

 tractor, would serve to give correct ideas of their size and 

 shape. They should be of sufficient size to admit of. all nec- 

 essary detail, and accurate measurements could be made on 

 them. Figures 41 to 46, all drawn on a small but uniform 

 scale, serve to give an idea of this method of presentation. 

 For a map of a single country, such, for example, as the 

 United States, the stereographic projection is unquestionably 

 the best that could be employed. For presenting the princi- 

 ples of navigation, and it is believed also for practical use, the 

 stereographic projection has no equal. 



It would doubtless be best to have the maps printed on card- 

 board, in order that the accompanying protractors could be 

 used freely in connection with them, and they could be issued 

 with the protractors in portfolios. It would not be necessary 

 to have many maps; a few accurately engraved ones would 

 answer all purposes. 



Expansion and Contraction. — During the past year some 

 attention has been paid to the behavior of paper, cardboard 

 and celluloid under different atmospheric conditions. During 

 the summer period, when the humidity is high, they all swell 

 somewhat, and they contract during the winter, when sub- 

 jected to the unusually dry atmosphere of a steam-heated 

 room. The large map of the United States, page 348, the 



