8. The degrees of longitude, as on the equator EAQ, or of latitude, as on the meridian 140°, may now be inserted; or upon the parallel lines OM, WL, and OW, ML.

Note. The outline of the Asiatic continent, as in the figure on the plate, will materially assist the student; but his great reliance must be in a Table of Latitude and Longitude. The eye is never to be depended on where the process of operation proceeds on such data as such a Table affords.

Prob. 11. To project a map of a particular portion of the earth's surface, as of Italy, containing 6° of latitude (viz. from the 39th to the 45th degree), and 9° of longitude (viz. from the 7th to the 16th of east longitude).—(Fig. 14, plate IV.)

1. Draw the line EF, and in the middle of this line raise the perpendicular DC, which divide into six equal parts, or degrees of latitude, and through C draw the line IK parallel to EF.

Obs. The projection will, of course, be regulated, as to size, by the size of the paper.

2. Divide a degree into 10 equal parts, or, if large enough, into 60; and find the number of miles which a degree of longitude contains in the latitude of 39°, viz.-46 62, and, from any scale of equal parts, set off one half of the same, viz.-23.31, on each side of D.

3. Find the number of miles contained in a degree of longitude, in the latitude of 45°, viz.-42:43; and from the same scale of equal parts, from which the former measure was taken, set off 21.215 on each side of C. Draw straight lines from I to E, and from R to F; divide them into the same number of parts as the line CD contains, and through the points draw parallel lines. Thus, IKFE is a projection for one degree of longitude, including six degrees of latitude.

Since the degrees must be so drawn, that the two diagonal lines in each must be equal to each other, they are to be projected in the following manner :

First,-Take the distance from E to K, or from F to I, and, setting one foot of the compasses first in E, and then in F, describe the arcs L and M. Then set one foot, first in I, and afterwards in K; and, with the same extent, draw the arcs N and O.

Secondly,-Take the distance between E and F, and set it off on the arcs described from E to N, and from F to O; then take the distance between I and K, and set it off from I to L, and from K to M.

Thirdly,-Draw the lines between L and N, and M and O; divide them into degrees, and draw parallels from those points to the corresponding ones in the meridians IE and KF. The same method must be pursued in drawing all the other meridians and parallels, which the conditions of the map require.

Note.-If the map may be very large, so much so that the compasses will not extend to the furthest degree, or from F to I, then draw one or more diagonals at once, and afterwards proceed with the rest. Thus, when the parallelogram PGEN and HQOF are described, LIGP and KMQH may be done.

4. Number the degrees of latitude up both sides the degrees of longitude on the top and bottom.

of the map, and Then make the

proper divisions and subdivisions of the country; and, from a Table of Latitudes and Longitudes, it will be easy to set down in the map the principal places which should be found in it; for any town must be placed in the intersection of the lines which would indicate its latitude and longitude.

5. Thus Florence must be placed at A, where the circles of 43° 46′ 30" N. lat. and of 11° 3' 30" E. long. cut each other. And Naples must be placed at B, on the sea-shore, at 40' 45' 15" N. lat. and 14° 17' 30" E. long.

6. In like manner, the mouth of a river, as the Tiber, for instance, must be set down; but, to describe its whole course, every turning must be laid down according to its latitude and longitude, and the towns and bridges also by which it passes.

Obs. In the projection now described, the diagonals being all equal, the number of meridians causes no defect in the representation, because equal spaces on the globe are represented by equal spaces on the map; conse quently, places lying in the most remote degrees of longitude are as truly represented as those towards the middle of projection, and their distances will agree with a common measure; so that a pair of compasses, extended be tween any two places, and applied to the scale, will give the distance without further trouble.

2. When the extent of country is not great, of which a map is to be made, as of a province or country, for example, the meridians, as to senes are paral lel to each other, and may be represented by straight lines. The whole, indeed, will differ so very little from a plane, that it will be sufficient to mea sure the distances of places in miles, aud to lay them down in a plane rightlined map, of which the successive spaces, formed by the meridians and parallels, would be right-angled parallelograms, or, more properly, squares. Prob. 12. To project a map of Europe.

1. Having drawn a line for the central meridian of the map, numbered in the plate 20, 20, assume any convenient distance for 5°, and set it off on this meridian seven times from 35° to 70°; or, to obtain at once the common centre for all the parallels of latitude, set it off 11 times from 35, because 90-35=55, and 55+5=11 equal the number of spaces of 5° between 35 and 90.

2. The eleventh, or extreme division, is the pole; and 6 degrees more, beyond it, will be the common centre from which the successive and concentric parallels of latitude are to be drawn.

3. To draw the meridians, take from a Table of decreasing Latitude, the number of miles in 35° latitude, and set this off as often as is necessary on each side of the central meridian (20'), on the parallel, or circle, of latitude 35°.

4. From these points of division draw right lines to the common centre, and they will represent the meridians. But, because the meridians in this map are portions of circles, they are curved after the following manner :-Take the number of miles in 40', and set this off on the parallel of 40'; take from the Table the number of miles in 45o, and set this off on the parallel of 45°; take for 50°, 60°, 65°, 70°, in like manner; and, having set off these measures on the concentric parallels as often as necessary, the points, when joined to indicate the meri

of

GLOBULAR PROJECTION

AMAP OF

Fig. 13.

20

10

ASIA.

Plate 4.p.586.

dias, will form as many segments of circles as there are meridians : and hence the construction is obvious.

Note. For the purpose of drawing maps geometrically correct, it is necessary that schools, or preceptors, or students for themselves, provide a bow-rule and also beam-compasses. The former is purchased at any mathematical instrument maker's for half-a-guinea; and the latter seldom exceeds twentyfive or thirty shillings. In drawing large maps, it will be found most convenient to fasten down the edges of the paper on an even board, which is covered with a smooth oil-cloth.

Prob. 13. To construct a map, which shall contain the degrees of longitude and latitude of Great Britain.

1. This island lies between 50° and 60o N. latitude, and between 10° east and 6 west longitude. Having, therefore, chosen any unit of measure for a degree of latitude, the degrees of longitude must be proportioned to it.

2. The length of a degree of longitude in latitude 5o is to one of latitude as 38:57 is to 60; that is to say, a degree of longitude is something more than half the length of a degree of latitude.

3. The exact proportion may, however, be had by a diagonal line, which is divided thus:-Draw an indefinite line, of perhaps three inches; at each extremity raise two perpendiculars, which make equal to the assumed degree of latitude; complete the parallelogram by drawing its fourth side parallel to the first or base line: reduce the figure to two right-angled triangles by a diagonal. Divide this diagonal into 60 equal parts, and through the points of division draw lines parallel to the sides of the parallelogram, which are of equal length with the degree of latitude.

4. The length of a degree of longitude in latitude 60°, is 3000. Of course, on the diagonal scale, we take off this quantity where the number 30 is found. Then, on each side of the perpendicular, on which we set off the degrees of latitude, this measure 30 is set off three times to the east, and seven times to the west, to answer the conditions of the map.

5. For the corresponding measures at 50° of latitude, take off at 38.57 on the diagonal scale, the proper quantity, and set it off thrice to the east, and seven times to the west, of the perpendicular, or first meridian.

6. Through the corresponding points, at 50° and 60° of latitude, draw now the meridians; and, through the equal divisions on the first meridian, draw the parallels of latitude.

7. Then, from 3° east and from 7° west longitude, raise perpendiculars, which will complete the parallelogram that must contain the map.

8. Having next divided into minutes and seconds the degrees of longitude and latitude, towns, cities, or rivers, or mountains, may be accurately laid down; since, by intersectional lines through the correspondent points of latitude and longitude, whatever is to be represented on the map may be readily depicted.

Note. A mariner's compass, on any such map, will show the bearing of one place from another.