GEOGRAPHY. 
S64 
the world, on the plane of the meridian. —With the chord 
of 6o degrees in the compafTes, defcribe a circle, as 
A C B D, in fig. i, Geography Plate IV. This circle 
may reprefent the meridian, or horizon, through which 
draw diameters at right angles, as A B, and C D ; then 
AB will reprefent the equator, and CD will reprefent 
the poles, and alfo the zenith and nadir; and CD the 
equinottial colure, and prime vertical circle ; and thus 
the circle will appear in quarters. Divide now the de¬ 
grees in a quadrant, viz. 90°, by the number of parts 
required, fuppofe 9, and the quotient fliows the number 
of degrees equal to each divifion, which in this cafe is 
10°. Apply this difiaitce taken from the firft part of 
the line of cltords, from D to A, as often as it will ad¬ 
mit, and it will divide the arc A^D into the number 
of parts required. 
It is necelTary to obferve, that, except the given circle 
is drawn with the cliord of 60°, the above rule is not 
applicable; in fuch cafes, proceed as follows: I'rom the 
centre of the given circle, as 0, with the chord of 60° 
defcribe another circle, (either within, or without the 
given circle,) to witich produce the diameters, and di¬ 
vide as above; transfer the divifions, found on the cir¬ 
cle defcribed by the chord of 60°, and they will in like 
manner divide the given circle into the parts required. 
Circles, or ajiy part thereof, may be more conveniently 
divided, by making the ceittre of the fernicircle coincide 
with the centre of the given circle, and its flat (ide with 
one end of the arc, to be divided ; then mark off tb.e 
degrees that each divifion contains, through which tranf- 
fer lines fro:ri the centre, as above. But the inftrument 
bell: calculated for inferibing polygons of any number 
of Tides into circles, or for dividing a circle, or an arc 
thereof, into any number of eqinil parts, is the feSlor, as it 
accommodates the divifions at once to any radius. Rule. 
Open the feiflor, until C—C, upon its fcale, is equal to 
the radius of the given circle, then find the degrees an- 
fvvering to each divifion on the fame lines, in the former 
Cafe lo—10, take the extent between them in the com- 
palfes, which apply to the arc, or circle, to be divided 
as often as it will admit, and it will point out the divi¬ 
fions, as required. 
To find the centres of the parallels of latitude. —Divide the 
arc AC, or A D, fig. 2, by either of the foregoing me¬ 
thods, into as many equal parts as the parall^s of lati¬ 
tude, to be projected in each hemifphere, require ; the 
ufual number is nine.—Then draw lines from the centre 
of the circle s, through each divifion on the divided arc 
of the horizon, and where thefe lines cut the horizon, 
raife perpendiculars towards the colure C D produced 
in y, which extend until they cut the colure produced, 
and their points of feCtion will be the centres required. 
For the tropics and polar circles : With 23^° in the 
compafles, from the line of chords, lay olf that extent 
from the equator, both ways, for the tropics; and alfo 
from the poles for the polar circles, and find their cen¬ 
tres as in the parallels of latitude ; then t will be the 
centre for the polar circle ; and x for parallels of lati- 
tude, &c. 
For the ecliptic: Join the extremity of the equator 
with the point where the tropics interfedt the equinoc¬ 
tial colure, as from r to B, bifect this line ; and through 
the feftions extend a line, until it cut the colure pro¬ 
duced in u, which will be its centre of projeflion re¬ 
quired. And thus the centres to any parallel, &c. found 
on one fide, will be the radius of the correfponding pa¬ 
rallel on the oppofite fide. 
Another method for deferibing the tropics, parallels 
of hititude, &c. is by fetting off the half-tangents of 
their refpedtive diftances, taken from the fcale of the 
feftor, on the line marked ST on the feflor, from the 
centre of the circle r, both ways on the colure, which 
will give the divifions through which the parallels. See-. 
are to pafs. Their centres are found by fetting off the 
taiigents of their refpedtive complements, each way, 
3 
from their points of fecHon, in the colure, on the co¬ 
lure produced ; or, by fetting off their co-fecants from 
the centre s, on the colure produced. 
To find the centres of the meridians. —Find the points if, 
30”, 45<’, 60°, 75°, and 90°, which will be hour-linss in 
the equator, by fetting off their half-tangents, taken 
from the line marked S T on the fcale of the fedlor, from 
the centre of the circle 0, both ways.—The centres are 
found by fetting off the co-fecants, of the diftances found 
in the equator, both ways, from their points of fedfion 
with the equator, in the equator produced; or, with 
their co-tangents, fet off both ways, from the centre of 
the circle on the equator produced, and the centre for 
the meridian will be t, as fhewn in fig. 3. 
The centres of the meridians, or Irour-lines, may be 
found, after tlie points are found in the equator, by fet¬ 
ting off the half-tangents, by the method ufed for 
finding the centres of the parallels of latitude ; tliat is, 
join C or D with each divifion, as 15 C, 30 C, See. bifedt 
thefe lines, and lines carried through the fedlions, as 
fig- 3> vvill cut the equator produced, in the centres 
required. 
This method of finding the points through which the 
meridians are to pafs, by fetting'off the half-tangents 
from the plane fcale, is only applicable when tlie radius 
of the fphere is taken from the line of chords. To find 
the points of fedtion for any given radius, open the fedlor 
until the diftance between C—C is equal to the given 
radius, then take the half tangents of their difiance from 
the lines on the fedlor marked T—T, which apply 
as before, and find their centres as directed above; 
tliat is, by joining the pole and each divifion, See .—On 
tlie fiereographic projedtion, moftof themaps in common 
u-fe are drawn ; the globular projedlion has been but re¬ 
cently introduced in England, by the ingenious Mr. 
Arrowfmith. 
To find the breadth of a degree, in any latitude. —With any 
convenient opening of the compalfes, defcribe the femi- 
circle A C B, as fliewn in the Plate at fig. 4; wliich di¬ 
vide into 90 equal parts. Join AB, to reprefent a de¬ 
gree on the equator, and divide it into 60 equal parts, 
to reprefent the miles in a degree. 
Application. —The extent from 90^, at B, to the pro- 
pofed parallel of latitude on the circular part, will 
reach from B to the number of miles, on the line AB, 
in a degree, in the propofed parallel of latitude. 
Example, for lat. 51° 30'.—The extentfrom 90°, at B, 
to 51° 30' on A C B, will reach from B towards A to 37I 
miles nearly, the breadth of a degree in the parallel of 
London. 
Example, for lat. 60°.—The extent from 90”, at B, 
to 60° on A C B, will reach from B to D, being 30 miles, 
the breadth of a degree in the latitude required. 
For drawing circles of longitude, and in many other ■ 
cafes where it is required to projefl a circle through any 
three points not fituated in a right line, the method is 
as follows : with any convenient opening of the com- 
pad'es, greater than half the diftance between A B and 
B C, and one point in A, as Ihewn in the Plate at fig. 5, 
defcribe an arc with the fame opening and one point in 
B ; crofs the former arc in n and m, with the point in 
B and C, defcribe fimilar arcs crofting each other in 0 r. 
Through the feftions nm, and or, draw lines which will 
crofs one another in s, the centre of the required circle. 
Then, with the diftance sA, sB, or sC, as a radius, 
defcribe a circle, and it will pafs through-the points 
ABC, as required. 
After all, though maps founded upon the llereogra. 
pliic projedtion, have for many years paft been in gene¬ 
ral eftimation, yet it muft: b? confeffed that by this con- 
ftrudlion, the true outline 6f diiTerent countries cann'ot 
be corredlly drawn; becaufe every part from the difle 
to the centre is gradually contradled by the parallels of 
longitude, as fhewn in Plate III. at fig. 4; and there, 
fore tliofe diltridts alone, which lie on the border of the 
map, 
