e the imaginary lines with which they suppose the 
fe of Ge math to be intersected, we might go on 
to apply the same principles to the a oh tig of the ce. 
; Jestial sphere, or the construction ofa map of the hea- 
_ yens. As this, however, does not properly apply to 
_ geography, we shall proceed to:take a short view of the 
comparative defects and merits of the projections now 
explained, as applicable to the construction of terrestri- 
al maps. 
As the principal object of a planisphere, or map of 
therwerld, iat to acon the Arm eand latitude of 
particular places, with their distances and bearings from 
each other, and to exhibit a view of the figure, extent, 
and_ relative positions of the different countries, that 
projection is to be preferred, which determines all these 
i most-accurately, and with the greatest ‘faci- 
ty. In none of the preceding methods, however, nor 
indeed -in Tr: other method, are ‘all these ‘properties 
united. Jn the gnomonic polar projection, °as we for- 
merly observed, ‘the position of any place to be project- 
ed, and consequently the situation of a place after it has 
been projected, is easily determined, by applying a line 
of tangents to the centre, and making its graduated 
edge fall onthe degree of the primitive denoting the 
longitude. The distance-between two places that are 
in the same meridian, or under the same parallel of la- 
_ titude, may also be easily and accurately determined 
from this projection. In the former-case, lay the extre- 
mity of the line of tangents on the centre, and make its 
grachated ede passthrough 
erence of the numbers on the scale‘bétween' the two 
distance in miles may ‘be easily ascer- 
tained. “Inthe “Second case, when the places are under 
the same‘parallél of latitude, by laying the ruler suc- 
cessively oyereach, and referring to the divisions in the 
primitive, the;arch of the parallel of latitude intercept- 
ed between them will:he.determined, ‘and the latitude 
being known, the length of that arch may be found in 
miles by-means of the-Iable,iat page 151. “OF the latter, 
indeed, .it is to’ be observed, that therule holds only: in 
the case-of short ‘distanees, when ‘the arch:of a parallel 
sensibly | differ (from jan arch /of a grat cirele «inter- 
pon inant points. — these advan- 
tages, however, the projection is in other res v 
detective. “The;distance between suianeihacih; cht dames 
__ found.-by .an operation far too tedious :and complicated 
use, while,countries at a distance the 
_ polevare very. much extended beyond their true figure 
~ ensions. A 
Inthe, ortho ic, Y) projection, the advantages 
dtbeautenes are wiapedbcneee in ates pss 
monic. The situation of places, and their distance from 
each other, when under the’ same.meridian or parallel 
means .of a line of'sines in- 
___ Countries at a distance from the pole,, are.a8-much con- 
___ tracted below-the truth, as in the former case they were 
_- maine the longitude of an given point, the circles of 
itude or meritlians being ell ses. To the young 
Sear ch ee sy will be found ex- 
_ tremely useful, as calculated to convey distinct 
7 f the earth’s sphericity. atpindiad 
facility of finding the positions of places,.by means of a 
GEOGRAPHY. 
of latitude intercepted between two -points does not 
the same meridian or parallel of latitude, can ‘only be- 
ne ree polar. projection affords the same per 
165 
line of semitangents, that the gnomonic and orthogra- Mathemati: 
phic polar projections do, by means of tangents and “! ~ Bs 
sines, By the former may also be readily found the . Phy 
distance between places under the same meridian, or if 
they are not far from each other, under the same paral- 
lel of latitude, and it possesses the additional advan- 
tage of representing the different countries more nears 
ly, according to their true figure and dimensions. In 
other respects, it does not materially differ from the 
other polar projections. 
In the stereographic projection on the plane of a me- 
ridian, the principal advantages compared with the cor- 
res ing orthographic projection, are the simplicity 
of its construction, and greater accuracy of its repre- 
sentations. In neither, however, is it easy to find the 
distance between places not under the same meridian ; 
nor is it possible to exhibit exactly the different por. 
tions.of the globe according to their true figure and di- 
mensions. In the orthographic, the countries at a dis- 
tance from the centre of the map are very much con- 
tracted, and in the stereographie they are considerably, 
though uot in the same ‘proportion, expanded. The 
convenience formerly mentioned regarding the divi- 
sion of the-globe into the eastern ‘and’ western hemi- 
spheres, is common’to both ; and, indeed, to all projec- 
tions in which: the ‘primitive coincides with the plane- 
of a meridian. 
‘The principal recommendation of the stereographic Horizontal. 
projection-on the plane of: the“horizon, is the facility it 
affords of -solving’a problem which, in all the preced- 
ing methods, can only be effected by an operation too 
abstruse for the purposes of practical geography. ~The 
problem alluded to is, to.find the distance between any 
two places on the surface of the globe, whatever ma 
be their positions relatively.to oné ariother. Thus, if it- 
were required to find the distance between Edinburgh. 
and any other place, project the sphere on the horizon 
of Edinburgh, .and .construct. a line. of semitangents" 
to the radius .of the projection ; then laying the extre-. 
mity of the scale on the centre of the map, with its. 
graduated edge.on the given place, the number of the - 
seale over the place will-be the distance required in de- 
grees of a greaticircle. If the place does not lie with- 
in the primitive, that is if it be more than'g0° distant 
from Edinburgh, the map may be extended beyond the 
primitive so far as to.include it; or; what is:perhaps bet~ 
ter, the opposite hemisphere may eee ee, andthe - 
distance of the place from. the centre of is hhemisphere- 
subtracted from 180, will give the distance required. 
By this projection: may also be found the «angle of po- 
sition which given -place makes -with the place in: 
the centre, thus: Divide the primitive or horizon into 
degrees.from the north and south | points «towards the 
east. and west ; then applying the scale as before, ‘its 
graduated edge will cut the horizon. in the:angle re- 
quired, But.though the solution of these problems may 
im some.cases'be very desirable, the horizontal projec- 
tion.is, upon the whole, very inconvenient. for a map 
of the world, = Oba from the difficulty of deter- 
mining, on.such a «map, the -longitude.and latitude of: 
places which do not happen to lie under-any ‘ofthe 
meridians,or parallels of latitude. This defeet, indeed, 
is, common. to it-with the equatorial: projections, ‘and it 
may be. observed. of them all ‘in general, “thats itis 
impossible to combine ‘in .one' the whole, or even'the 
principal properties of each, we'must be satisfied with 
gaining one advantage by the saerifice-of another. For Globular, 
ordinary purposes, the globular projection is, after all, 
ha the best in constructing a map of the world, 
Simpheity of construction, tolerable accuracy in the 
Equatorial. 
