Mathemati- 
164 
tion of the north pole. From P’ draw. the diameter 
cal Geogra- pic P's and at right angles to this diameter draw ano- 
phy. 
PLATE 
CCLXVI. 
Fig. 6 
ther «’ Cg. From W_ through the-extremities of this 
diameter, draw Wg and W @, intersecting CS in Q and 
CN produced in @, and bisect @Q; the point of bisec- 
tion will be AE the centre, and half the line bisected 
will be EQ the radius of the equator WQE. To. find 
the centres of the meridians, join Wp’, and produce 
the line till it meet CS produced in.p ; bisect Pp, and 
the point of bisection will be A the centre; and half 
the line bisected will be AP, the radius of the meri- 
dian WPE at right angles to the first meridian NPS. 
The centres of the other meridians are found as be- 
fore in BD, drawn through A, at right angles to AN. 
In this, as in the equatorial projection, it becomes 
difficult to describe the meridians that make small angles 
withthe first meridian, their centres being ata great 
distance from the point A. This inconvenience, how- 
ever, will be in a great measure remedied by the fol- 
lowing construction. 
From C, (Fig. 6.) describe WNES, find #, P, Q 
and A, and draw P’ p' and BD, all asin Fig.)5.. From 
A draw Af perpendicular ‘to P’p’, and on AC set off 
Ag, equal to Af. From g asa centre, with any radius 
as gA, describe a quadrant AG, and divide it into de. 
ees from A towardsG. Through g, and every tenth 
poe of AG, draw straight lines intersecting AD 
in:a, 6,-¢, d, &c. and from these points draw straight 
lines through C: these lines will intersect the primitive 
in the points through which the corresponding meridian 
is to.pass._ Now, as every meridian must, pass through 
P, there will be given three points in» each, viz. 10, P5 
170 in the meridian 10° from NS, 20, P, 160.in the next, 
and so on; the circle may therefore be described |. by 
the instrument formerly mentioned in the equatorial 
projection. In this construction, the pointin| AD, next 
to A, gives the intersections.of the meridian:nearest to 
NS, and in the method explained in last paragraph the 
next to A is the.centre.of the meridian farthest 
_NS. By a combination of the .two methods 
therefore, all the meridians may be determined by 
means of points at a moderate distance from A. 
To project the ,parallels of latitude, set off from ,C, 
(Fig. 5.) on NS, the semitangents of the greatest and least 
distances of the.parallel from C, and bisect the part.of 
NS contained. between these. points; the point of bi- 
section will be the centre, and half the line bisected 
will be the radius of the.parallel. Thus let it be re- 
quired first to project a parallel to the north of the 
ape place, as of 70° north latitude. _ Since.the paral- 
el extends 20° on each side of the pole P,\and.C is 34° 
distant from P, the nearest point of the parallel to.C.is 
between C and P 34°—20°=14° from the former, and 
the opposite or.most distant 34°4.20°= 54°... From)C 
therefore, set.off towards.N the semitangents of 14° and 
54° to r ands, and bisect 7s; then the middle, point. of 
x s will be the centre, and half the line will be-the radi- 
us of the: parallel required. Secondly, let the parallel 
to be projected be.the 56th, or that whose distance'from 
the pole is equal to the co-latitude of the place. Inthis 
case it is obvious, that the circle must pass through-C 
on the one side, and on.the opposite it will .cut/CN in 
LE, at the distance of the semitangent of 34°--.34°=68°. 
‘The distance therefore between C and that point-being 
bisected, it will give the centre of th allel. Lastly, 
let the.parallel be tothe south asain A 
.of the.given :place, as, 
for example, that of 80°. Hereithe distin of the’eir- 
cle from P'is greater than PC by 60°24°26°, or its 
nearest distance from C is 26° towards S, while its 
greatest distance is 60°4.34°=94°, -From C therefore, 
GEOGRAPHY. 
_ usually employed by geographers, for delineating en's 
set off towards S the semitangent of 26° Cf, and from Mathe 
C towards N the semitangent of 914°C g, and bisect the * : 
distance between these pointsas before. 
Parallels. of latitude may also-be projected,. without 
the line of semitangents, thus: Divide the primitive © 
into degrees from P’ (Lig. 6.) in both directions, and 
through the degree‘denoting the co-latitude of the pa- 
rallel to be projected, draw lines to. W, intersecting 
NS or NS produced in. two points. Bisect the portion 
of NS contained between these intersections, and the 
circle deseribed from the point of bisection with a radius 
equal to half the line bisected, will be the parallel:re- 
quired. Thus, if straight lines be drawn from the 20th 
degree on each side of P’ to W, the intersection of these 
lines with NS, will give the points 7 ands, asin Fig. 5. 
IV. By Globular Projection. 
~ Though we have classed this method of projection Genera 
under a separate head, sit is, «strictly. *to be P 
considered:as a se be ee i nae ee 
originally proposed by its inventor: ire, it is mot CCLX 
indeed err remade employed, ‘but it :has giv crise Fig- 
to a mechanical). me |. which, from: ithe» of 
construction, is likely to. become more and more:com~ 
mon. in projecting maps)of the world, on the:plane ofa 
meridian, According to Lahire’sumethod, the: 
ing point, as was formerly observed, is distant :from the 
surface of the sphere, the ‘sine of 45°, that ‘is, if othe 
diameter.or meridian NS (Fig.:7.) be equal to 200, ‘the ti 
distance .N.P.of -the » cpectines oat P is equal \to°70. 
Having determined .P, divide “SW, SE enemies : 
and from P draw oe lines to every h di» % 
vision, intersecting BW and HE. Through ‘these 
points of intersection, and the two poles \N,'8, deseribe 
ellipses, and they will be projections) of meridians. — 
this construction, it is found, thatthe straight:dine fro 
P to 45 in the quadrant SW. or SE :divides :the wadius 
ZEW or ZEE into two-equal parts ; /buttowender the 
other division of these radii nearly equal, 
point P must be only at the distance of 59} fromiN; ? 
being equal'to 200. This -equality, however, may be _ 
caesar pipe rece thus, without regard:to the pos 
sition of the projecting point. to ; 
From C, (Rig. 8.) with \60 from \the line of chords; constr 
describe the primitive WINES representing‘a meridian, tion of a 
and draw the diameters NS, WE at right/angles:to ‘one globula 
another, the former representing a meridian 
angles) to the primitive, and »the latter the» Y 
From W and.E set-off in both directionstowards d Fig. 8. 
S; the chords of 10°, 20°,/80°,,&e.and divide eachofithe 
semidiameters CN, CE, CS, C sinorqihase 
ints. 10,-20,'30, &¢, ‘then: eircles pas through 
po N,,.S, and the divisions of the senticiametersOW, 
CE, will be meridians 10° distant from-each other,<and 
circles passing through the divisions of the quadrants 
WN, EN, and the semidiameter’ ON, «or ‘through “the 
divisions:of WS, ES, and the semidiameter°CS, will‘be 
parallels, the former of north and the latter of southrla- 
titude, 10° distant from sone another. ‘These ‘circlés. 
may be described, either by ae ithe centres, ‘whicl 
will always be in the diameters ‘WE, NS, or in these di- 
ameters produced, and which may be determined. from 
the three given points in the circumference; or'ifthe 
centres be at a great distance from ©, by employing 
the instrument formerly mentionedin g aphic 
rejection. Upon this. principle is. « cted ‘the Pea 
planisphere, Plate CCLXVIIL. “ . 
Haying thus. briefly explained the various:methods 
