__ The different methods of projecting the sphere, ari- 
sing from the different distances of the pr point, 
, are generally reckoned four, the gnomonic or central, 
‘the orthographic, the stereographic, and the globular. 
In the gnomonic projection, the eye is supposed to be 
laced in the centre, and the plane of projection is tan- 
to the pole aS y hemisp chert is ea oe In 
the orthographic, the eye is sup to be at an in- 
finite distance from Gia rahek®, so that the rays of light 
coming frem every point of the hemisphere, may be 
eonsidered - as 1 to one another. n Linge 
graphic projection, the eye is situated on the surface o 
Saauplacre,: in the pole of the circle of projection. And 
in the globular, its distance from’ the sphere is equal 
to the sine of 45°, In each of these methods of projec- 
ng from tion as applied'to the globe, there may be three dif- 
i- ferent 
cases, according to the position of the sphere, with 
of the ard to the projecting point. These are called the 
y , and: horizontal projections. © In the 
first, the plane of projection or primitive circle, coin- 
’  Gides with the equator, and one of the poles “is in the 
centre'of the map. In the second, the primitive is a 
meridian, and a point of the equator is in the centre ; 
tizontal, and in the last, the horizon is e primitive, of which 
__ the given place occupies the centre. We shall now 
_. proceed to the mechanical construction of aplanisphere 
map of the world, according to these different me- 
thods, referring to the article OJECTION, for the in- 
vestigation of the principles of each. 
L. By Gnomonic Projection. 
~ This methed, as its name 
foundation of dialling, but is very seldom used in the 
construction of maps. The disadvan with which it 
is attended in its application to the latter, arethe distorted 
appearance which it gives to countries at a distance from 
i centre of projection, andthe difficulty of describ- 
an ee latitude, which in the equatorial and 
izontal projections are ‘parabolas, ellipses, or hyper- 
bolas. In the po/ar projection, however, where the pri- 
ve i el to the equator, this difficulty is re- 
seiee, the parallels of latitude being projected into 
concentric circles, while the meridians, which in eve: 
case of this method are pi pee by straight lines, 
one another in the centre of the projection, 
1 forming at that point, the same angles that they do on 
[= the ce of the sphere. By this method, ther ore, we 
; obtain a very simple and expeditious petty of the 
northérn or sou ern parts of the globe, and at the 
same time a tolerably accurate representation, at least of 
é the polar regions. This projection is shewn in’ Fig. 10. 
which is constructed thus. 
~ From the centre P, with 60 from the line of: chords, 
describe the circle WLEM for the primitive, and draw 
the diameter LM to represent the first meridian. From M 
- set off successively towards E and W the chordof 5,10, or 
pies sg according to the number of meridians wanted ; 
and igh these points, draw diameters for the meri. 
| dians required. To find the parallels of latitude, take 
. the tangents of their respective co-latitudes, or distances 
! from the pole, and with these radii, describe concentric 
circles about the centre P. ‘Thus the tangent of 10°, 
: is the radius of the parallel of: 80°, the tangent’ of 
20°, is the radius of the parallel of 70°, &c.; that 
| ‘is, PM se = tae the intersections of the par- 
2 allels into a line of tangents to radins PM: The par- 
allel of 145° corr | Ag 
implies, constitutes the 
all esponds with the primitive WLEM, af- 
ter which’ the radii increase with great rapidity as they 
VOL. X. PART 1, i Mi 
GEOGRAPHY. 
161 
approach the equator, which becomes infinite. Hence, Mathematt. 
a whole hcutlegugs cannot be projected by this me- dl = 
thod, and it is obvious from inspection, that of what _P®Y- 
can be projected, the countries farther from the pole 
than the 60th parallel of latitude, must be very inac- 
curately represented. 
Havin {sete the meridians, and described the pa- 
rallels of latitude as above, the continents, seas, islands, 
&c, which it is intended to represent, are to be deli. 
neated according to their relative situations and extent, 
the position of every point being determined by the in- 
tersection of its meridian and ss of latitude. This 
may be considered asa ape tule for determining the 
position of places in all projections ; but as meridians 
and parallels of latitude cannot be described through 
every degree, the position of any intermediate point in 
the preceding method, may be found readily thus: 
Transfer to the edge of a flat ruler the divisions of the 
line of ts, then by laying the commencement of 
this scale on P, and the graduated edge on the degree of 
the primitive denoting the longitude, the division of 
the scale corresponding to the co-latitude of the place, 
will shew the position required. 
II. By Orthographic Projection. 
Though this method of projection is more frequently General 
employed in geography than the preceding, it affords Properties. 
but a very imperfect and inaccurate representation of 
the whole hemisphere. From the position of the eye, 
the parts of the sphere are seen more and more oblique- 
ly as they approach the primitive, and consequently the 
countries at a distance from the centre of projection are 
contracted. far below their natural limits. ‘The ortho- 
graphic projection, therefore, though the reverse of the 
gnomonic as to its defects, is like the latter best adapt~ 
ed for representing countries at a moderate distance 
from the centre of projection. The representations of 
the hemisphere on orthographic principles, usually em- 
ployed in geography, are the polar and equatorial, which 
are constructed as follows: 
1. The Polar. From the centre P, (Fig. 11.) with Construc- 
60° from the line of chords, describe the primitive tion of an 
WLEM, which will represent the equator, and draw —T 
the meridians as in Fig. 10. To find the parallels of i a 
latitude, take the sines of their respective co-latitudes, p,.+. 
and with these radii describe circles about the centre CCLXV. 
P. Thus the sine of 10° is the radius of the paralle] Fig. 11. 
of 80°, the sine of 20° is the radius of the parallel of 
70°, &c: or PM is converted by the intersections of 
the parallels into a line of sines to radius PM. Hence, 
to find the radii of the parallels without the help of 
lines previously constructed, divide ME into as many 
equal parts as the parallels wanted, and let fall en 
diculars from these divisions on MP ; the distances 
between P and these perpendiculars will be the radii 
uired. 
n this projection, the whole hemisphere is repre~ 
sented within the primitive, which in the snomonic is 
occupied by the zone of 45° round the pole ; but the 
countries near the equator are very much distorted from 
their true dimensions, , 
2. The Equatorial. From # (Fig. 1. Plate CCLXVT.), -An ortho- 
with the chord of 60°, describe the meridian WN ES for graphic e~ 
the primitive, and draw the diameters WE,NS at right quatorial 
x 
