Geographical Maps and Sailing Charts. 275 



ah, figure 20, crossing the central meridian at 90°, just midway 

 between N" and 8" . The line ab is the stereographic projec- 

 tion of the parallel 39° S., which in this case is a straight line 

 because P is at 39° S. ; compare the projection of the parallel 

 40° S., figure 16, page 269. Since angles are preserved in the 

 stereographic projection, the meridian must make equal angles 

 with one another (5°, figure 20) at N" and 8" ; hence N" and 

 8" may be considered as the poles of a projection on the plane 

 of a meridian having a diameter N"S n , and the construction 

 of the meridians is the same as described on page 256. In 

 drawing a map, such as that of the United States, on a large 

 scale, the location of the meridians and their curvature must be 

 determined by calculation, and one example will illustrate how 

 this may be done : On the diameter ew, passing through the 

 center of the map at right angles to the line N' 8", it is desired 

 to find the point x where that meridian intersects it, which is 35° 

 from the center of the large circle II. Knowing the radius 

 of the large circle II, the radius r, for describing the meridian 

 which intersects the diameter ab at 35° from the center, may 

 be found from a table described at the close of this article. A 

 right triangle Aux may then be constructed, in which the 

 hypothenuse r and the perpendicular p (equal to the distance 

 from c to the center of the map) are known; hence from sine 



A= — the value of A may be found. Construct the chord vx, 



and from its center m draw a line to A ; the line mA. bisects 

 the angle A. Also it follows from the construction that in the 

 triangle xvy the angle at v is equal to \A ; hence tangent 



\A — —j from which the value xy may be calculated. The 



distance cv being known, and equal to the distance from the 

 center of the map to y, the distance from the center of the 

 map to x is readily determined. 



A method like the foregoing was used in plotting the meri- 

 dians of a large stereographic map of the United States. In 

 addition to a construction line drawn through the center of the 

 map, corresponding to ew, figure 20, two other lines were 

 drawn parallel to ew at measured distances, one crossing near 

 the top, the other near the bottom of the map. The points of 

 intersection of the several meridians with the three construction 

 lines were then calculated, and each meridian was drawn 

 through the three points thus determined, making use of a 

 large circular arc ruler. The calculation was not especially 

 laborious, since only simple formulas were used, and the same 

 quantities were repeated several times, so that to a certain ex- 

 tent the work becomes almost mechanical. 



[To be continued.] 



