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PRACTICAL CONSTRUCTION OF MAPS.
Definitions. Prob. 1. To construct a Map of the World, on the plane of a 'meridian, according to the globular projection of the sphere.- (See fg. 1 and 2, plate 1)
1. The globular projection of the sphere, is that in which equal spaces on the surface of the globe are represented by equal spaces of the projected map, as nearly as a spherical surface can be represented on a plane.
2. The plane of a meridian is the plane of one of the great circles of the sphere passing through both poles, and crossing the equator at right angles.
3. A hemispherical map of the world, is a representation of the en. tire surface of the globe of Earth, projected on the plane of one of its great circles.
1. To draw the meridians, or circles of longitude,
2 From C as a centre, with any radius, CA or CB, according to the size of your paper, describe the circle ANBS.
3. This circle is then the plane of your projection.
4. Divide the four radii, CA, CN, CB, CS, each into nine equal parts.
5. Now, to draw the meridian 80° west of Greenwich, we have the two poles 90goo, and the point so° in the equator, or diameter AB.
6. From N as a centre, and with NC as a radius, describe the arc ZCZ; also from S, with the same radius, describe the arc XCX.
7. Then remove compasses to the point 80 on the equator, and describe the arcs 1,1, and 2,2.
8. Through the intersections, as at 1 and 2, draw lines from 2,2, through the points 1,1, till they intersect the diameter BA produced in D.
9. Then will D be the centre from which, with the radius D 80°, OF DN, or DS, the meridian of 80° west longitude from Greenwich must be described.
Nute. The same radius will draw the meridiau expressing 140° W. L.; and, in the other bemisphere, the corresponding meridians of east longitude.
• A B represents the equator, and N S the aris meridian.
10. The meridian of 50° is drawn in the same manner as that of 80°, except that the point 50 on the equator (AB) is the centre from which, with the radius CB, the intersections are made at a,a, and b,l, on the arcs decribed from N and S. The point E, where the lines la, la, meet on the equator, is the centre for the meridian of 50° W. long. The same radius serves for the other three meridians 30° within the circle of projection.
Note.-In this manner are all the other meridians for both hemispheres to be drawn; as may be seen in fig. 7th, Plate II.
II. To draw the parallels of latitude.— Fig. 2, plate I.
1. The same construction remaining, and the radii CN, CS, divided each into nine equal parts.
2. Divide the circumference ANBS into thirty-six equal parts ; so shall each quadrant AN, BN ; AS, BS, be divided into nine equal parts, which, being again subdivided into ten equal parts each, will give us 360 equal parts or degrees.
3. To draw, now, the parallel of 30° north latitude, set one foot of the compasses in the point 30 on the axis meridian NS, and with any radius describe the circle KTL.
4. Set, again, one foot of the compasses in the points 30, 30, in the circumference, and intersect the circle KTL in the points s, s, n, n.
5. Through nn and ss draw the straight lines nn, ss, meeting each other in the point R of the axis SN, produced to R.
6. with R as a centre, and R30 as a radius, describe now the parallel of 30° north laticude.
Note.-The same radius is, of course, used for 30 south latitude.
7. After the same process the parallel of 60° north latitude is drawn, as may be easily conceived by inspecting the figure.
Note.–And in this way proceed with all the other parallels in both hemispheres; as is evident from fig. 7th, Piate II.
8. This is the rationale of construction. That which respects the minutiæ of filling up the map requires only the attention of the delineator, in strictly observing the proper situations of objects or lines, as far as they respectively bear on the practice of map-making.
Prob. 2. To project a map of the world on the plane of a meridian, according to the stereographic projection of the sphere.-(fig. 3, plate I.)
I. To draw the circles of latitude.
1. Describe, from any centre C, the circle ENQS, which will represent one half of the earth's surface.
2. Draw the diameters EQ and NS, intersecting each other at right angles.
3. EQ will be the equator, and NS the axis meridian.
4. Divide the circumference into 360 equal parts; numbered 10, 20, 30, &c. as on the figure.
3. From E to 140 draw the line E 140 ; bisect the portion a 140