GEOGRAPHY. S(>3 
When tlic place is but fmall of which a map is to be 
made, as of a county for inlLuice, or of any portion of 
tlie earth of not more than one hundred miles in length 
and breadth, the meridians, as to Icnfe, are parallel to 
each otlier, and may be reprefented by llraight lines. 
But, the whole will differ fo little from a plane, that it 
will be fuliicient to meafure the diftances of places in 
miles, and fo lay them down in a plane right-lined map. 
In the projection of a quadrant of an hemifphere, ac¬ 
cording to this method, the parallels of latitude are all 
concentric circles, and the only difficulty is to find the 
common centre. 
In projecting a map for Afia, Plate II. fig'. 9, on the 
globular conltruCtion, the centre'of the parallel of 60 de¬ 
grees of latitude is found to be 30 degrees beyond the 
north pole, or at the I'ame diftance north of the parallel 
of 60 degrees, as the equator is fouth of it; and the cen¬ 
tre for this parallel is therefore tlie centre for all the 
others; and it is evident that in this map, the two dia¬ 
gonals of each figure arc equal to one another, lo that 
all the parts are of their proper magnitude. In project¬ 
ing the map of Europe, on this conltruCtion, it is found 
that the common centre for all the parallels of latitude 
is at fix degrees and ffieven tenths beyond the pole. 
Suppofe it be required to draw tlie meridians and pa¬ 
rallels for a map of Great Britain. This ifland lies be¬ 
tween 50 and 60 degrees nortli latitude, and between two 
degrees ealt and fix weft longitude. Having, therefore, 
chofen the length of the degrees of latitude, the degrees 
cf longitude muft be proportioned to it. By the table 
it appears, that in latitude 50°, the length of a degree 
of longitude is to one of latitude, as 38-57 is to 60 ; that 
is, the length of a degree of longitude is fomething 
more than half the length of a degree of latitude. The 
exaCl proportion may be liad by a diagonal line: after 
which feven or eight of thefe degrees are to be marked 
out upon a right line for the length of the intended map. 
On the extremities of this line raife two perpendiculars, 
upon which mark out ten degrees of latitude for tlie 
lieight of it. Then having completed the parallelogram, 
confult the table for the length of a degree of longitude, 
in latitude 60°, which is found to be very nearly one 
half of the length of a degree of latitude. It will always 
be necelfary, however, to draw' a vertical meridian ex- 
aClly in the middle of the parallelogram, to which the 
meridians on each fide may converge; and from this you 
are to fet off the'degrees of longitude on each fide : then 
having divided the lines bounding the map into as many 
parts as can conveniently be done, to ferve for a fcale, 
■ the longitudes and latitudes may by their means be fet 
off with much lefs trouble titan where curve lines are 
ufed. This method may be always followed w'here a 
particular kingdom is to be delineated, and will repre- 
fent the figure and fituationof the places with tolerable 
exaCfnefs. Towns and other places, whole bearings and 
fituation are known, may be accurately exprefied by 
this means; and this is the only kind of maps to which a 
I'cale of miles can be truly adapted. 
To projeEl maps upon the other pofitions of the fphere. —The 
circles upon which thefe projections are ufually made, 
are the equator, fome of the meridians, or the rational 
horizon of fome particular place. For maps of the 
world a meridian is generally chofen ; and it has been 
moll commonly that which palfes through Ferro, one of 
the Canary illands ; becaufe th'us Europe, Afia, and Af¬ 
rica, are conveniently delineated in one circle, and 
America in the other. To projebl, therefore, a map of 
the world ortkographically on the plane of any meridian, 
we have only to conlider, tiiat, as the eye is fuppofed to 
be at an infinite diltance, all the rays which come from 
thedilk of the earth are parallel; and confequently all 
lines drawn from the eye to the dific mult be perpendi¬ 
cular to the latter. Let A B C D, Geography Plate III. 
fig. I, repreTent the plane of one of the meridians. The 
equator, which cuts all the meridians in the centre, mull 
be reprefented by a number of points let fall upon the 
plane of projection, and dividing it exactly in the mid¬ 
dle : that is, by the right line B D. The parallels of 
latitude, being all'o perpendicular to the plane of the 
meridian, will be marked out by a number of right lines 
let fall from their peripheries upon tiiat plane, thus 
forming the right lines ab,cd. See. The meridians will 
likewil'e be reprefented on the dilk by a number of right 
lines let fall perpendicularly from their periplieries upon 
the plane ot projeftion, and thus will form the elliptic 
curves AioC, A20C, &c. From an infpeclion of the 
figure, therefore, it appears, that fn this projection 
both longitudes and latitudes are meafured by a line of 
fines, and both of them decreafe prodlgioufly as vve ap¬ 
proach the edges of the difk ; and hence the countries 
which lie at a diftance from the equator, or on the difl<, 
are exceedingly narrowed, fo that it is iiupoffible to draw 
tliem with any degree of accuracy. The orthographic 
projection on th.e plane of a meridian, therefore, is fel- 
dom ufed but for a map of the world. 
On the plane of the equator, the orthographic projec¬ 
tion reprefents the meridians as llraight lines diverging' 
from a centre, and the parallels of latitude as concentric 
circles. This projection is reprel'ented in the lame 
Plate at fig. 2. The latter, however, are by no means 
to be placed at equal dillances from each other ; for tiie 
meridians arc to be divided by the line of fines, as in 
the preceding ; and thus the eqtiatorial parts of the 
globe are as much narrowed and confufed as the polar 
ones are in the foregoing. This projection, therefore, 
is feldom ufed for a map of the whole world, though it 
anfwers extremely well for delineating the countries 
near the polar regions. 
On the horizon of any particular place, except either 
of the poles, or any point lying direCtly under the equa¬ 
tor, the orthographic projection reprefents both paral¬ 
lels and meridians by fegments of ellipfes. Fig. 3, in 
the engraving, reprefents a map executed on this princi¬ 
ple, on the horizon of Ur of the Chaldees ; it is obvious, 
however, that a confiderable degree of inequality takes 
place here alfo, though lefs than in the former cafes. 
Projections of this kind, therefore, are now ufed only 
for the conltruCtion of folar cclipfes. 
The flereographic projection of the fphere fuppofes 
the eye to be in the pole of the circle of projection. 
The laws of titis projection are, i. A right circle is pro¬ 
jected into a line of half-tangents. 2. The reprefen- 
tation of a right circle, perpendicularly oppofed to the 
eye, will be a circle in the plane of the projection. 
3. The reprefentation of a circle placed oblique to the 
eye will be a circle in the plane of tlie projection. 4, If 
a great circle is to be projected upon the plane of an¬ 
other great circle, its centre will lie in the line of mea- 
fures, diftant from the centre of the primitive by the 
tangent of its elevation above the plane of the pi imitive. 
5, If a lefler circle, whofe poles lie in the plane of the 
projection,' were to be projected, the centre of its re- 
prefentation would be in th.e line of meafures, difiant 
from the centre of the primitive, by the fecant of the 
leffer circle’s diltance from its pole, and its femidiameter 
or radius be equal to the tangent of that diftance. 6. If 
a Iclfer circle were to be projected, whole poles lie not 
in the plane of the projeCftion, its diameter in the pro¬ 
jection, if it falls on each fide of the pole of the primi¬ 
tive, will be equal to the fum of tlie half tangents of its 
greateft and neareft diftance from the pole of the primi¬ 
tive, fet each way from the centre of the primitive in 
the line of mealures. 7. If the lefter circle to be pro¬ 
jected fall entirely on one fide of tJie pole of tlie projec¬ 
tion, and do not encompafs it; then will its diameter be 
equal to the difference of the half-tangents of its greatell 
and neareft diftance from the pole of the primitive, fet 
off from the centre of the primitive one ; and the fame 
way in the line of mealures. 8. In the ftereographic 
projection; the angles made by the circles of the furface 
of the fphere are equal to the angles made by their re- 
prefentatives in the plane of their projection.—Thefe 
laws are demonftrated as follows : 
To draw the flereographic projeflion of the fphere^ or a map 
