that of a meridian, the maps will be the east and west hemispheres; the other meridians will be ellipses, and the parallel circles will be right lines. Upon the plane of the equinoctial the meridians will be right lines crossing in the centre, which will represent the pole,-the parallels of latitude will be circles having that common centre,—and the maps will be the northern and southern hemispheres. The fault of this projection is, that, nearer the outside, the circles are too close to one another; and, therefore, equal' spaces on the earth are represented by very unequal spaces upon the map. The projection is seldom used.

2d method. Another way is to project the same hemispheres by the rules of stereographic projection; in which way all the parallels will be represented by circles, and the meridians by circles or right lines. In this projection the eye is supposed to be placed on the surface of the earth, and looking at the opposite hemisphere. And here the contrary fault happens; viz. the circles towards the outside are too far asunder; and those about the middle are too near together. Many of the maps of the world are drawn upon this projection.

3d method. As this method remedies the faults of the two former, it is now generally preferred; we shall, therefore, be more particular in the description of it.

Globular projection upon the plane of the meridian. From the centre C, fig. 1, with any radius, as CB, describe a circle; draw the diameter AB and NS at right angles, and divide them into nine equal parts; likewise divide each quadrant into nine equal parts, each of which contains 10°. If the scale admit of it, every one of these divisions may be subdivided into degrees.

Next, to draw the meridians, suppose the meridian 80 W. of Greenwich,-we have given the two poles, and the point 80 in the equator, or diameter, AB. Describe a circle to pass through these three points as follows:

With the radius SC, set one foot of the compasses on S, and describe the semicircle XX; with the centre N, and the same radius, describe the semicircle ZZ; then remove the compasses to the point 80 on the equator, and describe the arcs 1, 1, and 2, 2; where they intersect the semicircle, make the point as at 1 and 2, and draw the lines from the point 2 through point 1, till they intersect BA continued in D: then will D be the centre whence the meridian of 80° W. L. from London must be drawn: the same radius will draw the meridian expressing 1400 W. L. All the other meridians are drawn in like manner: suppose for 500 W. L. with the radius CB set one foot of the compasses in the point 50, and describe the arcs aa, bb; then draw the lines as before, and you will find the point E, the centre of 50° W. L.;-and so of all the rest.

For the parallels, suppose that of 60°; from the centre, O, with any radius describe the circle FGH; and from the points 60, 60, in the primitive circle, describe the arcs cc and dd, intersecting the circle FGH: through the points of intersection draw lines; and where these lines meet in NS continued, will be the centre of the 60th parallel. In the same manner are all the parallels drawn: only the circle FGH must always be drawn from that degree in the line NS through which the parallel you intend to draw must pass. Figure 2 is a projection of this sort completed.

When the map is very large, the centres of both meridians and parallels will be found more easily by the following method:

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Having divided the quadrants, and also the diameters, into 9 equal parts, as before, find, by making use of any scale of equal parts, the length of the half chord of each of the arcs, and also the versed sine of half the arc; then, to the square of the half chord, add the square of the versed sine of half the arc; and this sum, divided by the versed sine, will give the diameter, one-half of which is the radius of the circle. In this manner may be found the radii of all the parallels and meridians.

Globular projection upon the plane of the equator,

For the north or south hemisphere, draw the circle AQBE for the equator (fig. 3), dividing it into the four quadrants EA, AQ, QB, and BE, and each quadrant into 9 parts, representing each 10° of longitude; and then from the points of division draw lines to the centre P, for the circles of longitude.

Divide any circle of longitude, as in the first meridian EP, into 9 equal parts, and through these points describe circles from the centre P, for the parallels of latitude, numbering them as in the figure.

In the globular projection, equal spaces on the earth are represented by equal spaces on the map, as near as any projection will bear; for a spherical surface can no way be represented exactly upon a plane. Then the several countries of the world, islands, towns, &c. are to be entered in a map according to the latitudes and longitudes.

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In filling up the map, all places representing land are filled with such things as the countries contain; but the seas are left white, the shores being shaded. Rivers are marked by strong lines, or by double lines, drawn winding in form of the rivers they represent; and small rivers are