| is.to pass, draw a 
_ 60 in each of the quadrants EN,WN, puineney iE 
~ angle ABC 
the atch to 
touch th 
codes aie fe Point at B describes the arch required. 
GEOGRAPHY. 
the projection may be performed without the assist- 
ei of tine lines. nd pe the first method, divide 
the quadrants WN and ES, Fig. 3: into degrees, and 
from S, through every tenth degree of each, draw 
straight lines’ intersecting WE on both sides of Al; then 
*_ the parts of WE contained between ‘every two corre- 
ding points of intersection; will be the projected 
Kaige’ of the meridians, whose distance fede first 
meridian, is equal to the distance of the points in the 
uadrants from the poles. ‘Thus the straight line drawn 
S to 10 in the quadrant WN, will intersect AZ! W 
in’m, and the line joining S and 10 in the quadrant ES, 
will intersect ALE produced in e, wherefore me is the 
1 ay diameter of the meridian, 80° distant’ from 
ES. If thenm e be bisected, the point of bisection 
will be the centre, and half the line bisected will be the 
radius of the meridian N mS. In the same manner may 
be described the other meridians on either side of NES. 
In the second method, where it is required to find the 
points of the equator through which any given meridian 
t ight line from 8, Fig.4. tothe 
pores of the quadrant WN, or EN, whose distance from 
is equal to the distance of the given meridian from 
‘the first meridian, and it will intersect AZW or EE in 
the point required... Thus the line joining S and 10 in 
the quadrant WN will intersect EW in 80, the point 
through which the meridian’ must pass, whose distance 
from the first meridian is 80°. This point being deter- 
mined, the centre may be found as’before.’ 9 9 | 
In jecting maps.on a large scale, it’ becomes ex- 
tremely difficult to determine the centres, and still more 
so to describe, with accuracy, the arches of meridians at 
small distances from the first meridian. To remedy 
this inconvenience, an instrument has been invented of 
a very simple construction, by which these arches may 
readily be described, the extremities and one interme- 
diate point being given. * | When this intermediate point 
is determined, as in the preceding paragraph, and the 
circle described by means of the instrument now men- 
tioned, the operation is perhaps as much simplified as 
the nature of the subject will admit of. fio 
» To describe the parallels of latitude in this projection, 
set off from AZ (Fig. 3.) on Z2N produced, the secants 
of the co-latitudes of the parallels, and from these points 
_ as centres, with radii a to the distances between 
them and the points in the quadrants WN, EN, derio- 
ting the latitudes, describe arches, and they will be the 
parallels required. _ Thus the secant of 30°'set. off from 
_ ££ to f, on ZEN produced, will be the centre of the paz 
 rallel of 60° no: saat ~ 
f latitude, and the distance between 
that point and 60 in the quadrant WN, or EN will be 
ee: patie of the parallel. 
_ fhe centre of any given parallel, as 60, may also be 
determined thus: i rom E, draw straight lines through 
and ZEN produced, in the points ¢ and fh then the part 
of ZEN contained between these points will be the oro. 
jected diameter of the parallel of 60. If, th re, 
this line be bisected, the ty of bisection will be f, 
the centre ; and’half the line bisected’ will be the ra~ 
igi the parallel. : 
‘ € semi-tangents of 10°, 20°; 30°, &c. be set off 
from towards N, they willgive the points in which the 
parallels of 10°, 20°, 30°, must intersect AUN. \ Thus 
| © This i 
to bed, and pins bei 
same segment are equal to one another. 
-NP’ 
being fixed, or weights laid at the extremities of the arch, 
163 
the semitangent of 60° set off from JE towards N, gives 
the point g. In every parallel, there will thus be given 
three points, viz. the extremities in the quadrants WN 
and EN, and an intermediate Pore in ZEN ; and con- 
sequently the parallel may be described either by find- 
ing its‘ centre, or applying the instrument formerly men- 
tioneil, in the projection of meridians, The interme- 
diate points in ASN may also be found without a line 
of semitangents, as in the last paragraph, viz. by draw- 
ing lines from E to every tenth degree of WN. In the 
same manner may be described the parallels ‘on the 
other side of the equator. 
8: The Horizontal. Though this projection is not so 
frequently used as the preceding in constructing a map 
of the world, it is more convenient, as we shall after- 
wards shew, for some particular purposes, and is there- 
fore not to be omitted in a system of mathematical geo- 
graphy. The projection of the equator, meridians, and 
parallels of latitude on the horizon of any given place, 
as Edinburgh, Lat. 56° N. is as follows. : 
From C (Fig. 5. 
describe the circle 
with 60 from the line of chords, A stereogra- 
NES for the primitive or horizon phic hori- 
of the place C, and draw NCS, WCE at right angles 70‘! map. 
to: each other, the former representing the meridian Prater 
of the place, and the other a great circle 90° distant CCLXVL. 
from it, and which, on the celestial sphere, is called 
the Prime vertical. From C set off on CN, the semi- 
tangent CP of the co-latitude, in this case 34°, and P 
will be’ the projection of the north pole.. From the 
same point set off on CN and CS, CH equal to the tan- 
gent of the co-latitude (34°), and CQ equal to the semi+ 
tangent of the latitude (56°); then a circle described from 
Bas a centre with the radius Q will pass through W, E, 
and represent the equator. sb the meridians, 
set off from C on CS, or CS produced, CA equal to the 
tangent of the latitude (56°), and through A draw BD 
at right angles to CA. From P, with 60 from the lite 
of chords, describe the quadrant vw, and from v set 
off on this arch the chords of 10, 20, 30, &c.; then a 
ruler laid between P’and each’ of these divisions, will 
intersect AD in a, b, c, d, &c. the ceritres of the me. 
ridians between S and W. Thus’ AP will be the ra- 
dius of the meridian WPE, 90° distant from the first 
meridian NPS ; a P will be the radius of 80 P 100, the 
meridian 10° distant from the last, ox 80° from the 
first meridian, and so of the others. In the samme man- 
ner may be described the meridians on the other side of 
NS from ‘centres’ in- the line AB. In determining the 
centres of the meridian, it is convenient to describe the 
uadrant vw with 60 from the line of chords, because 
the chords of 10, 20, 30, &c. maybe set off from the 
same line, without the trouble of dividing the quadrant, 
It is not necessary, however, nor indeed is it rhe 
proper, to take that particular radius, as any other wi 
answer the same purpose ; and the greater it is, the 
more accurately will the points in BD be determined, 
particularly such as are at a great distance from A. 
In the preceding method, the points P, Q, JE, A, 
are determined by the lines of tangents and semitan- 
ts; but they may also be found without the help of 
ese lines thus: Having described WNES, and drawn 
NS, WE as before} set off from N towards E, the arch 
equal to the latitude of the place (56°), and join 
P’W;; the line P’W will intersect CN in P, the projec- 
it consists of two rulers AB, CB Fig. 12. Plate CCLXV.) fastened together by a joint B, so as to form any required 
pen or peneil being fixed in. the angular point B. In using the instrument, this é 
a 
be 
ese pins or weights. In this state the whole instrument is moved round, the two sides being. always pressed 
The principle of the instrument depends on the property of the circle, that all 
See GromErhy, SECT. 11, PRor. XVIL and Drawine IysTRUMENTS, 
is placed on the intermediate point of 
limbs AB, CB are extended so as to 
against the pins or 
