160 
Mat'emati- 
eal Geogra- 
phy. 
General de- 
finition. 
‘Different 
kinds of 
maps, 
Plani- 
sphere. 
To - 
»phical. 
Mineralogi- 
cal 
Nautical. 
made by the other hour lines, after which the dial is 
to be constructed according to the directions given un- 
der.the article Diatuine, § 40. vol. vii. p. 697. 
The lines for half hours and quarters may be found 
‘in the same way as the hour lines, if meridians be de- 
scribed on the globe, dividing every 15° of the equator, 
into four equal parts, that is at the distance of 3° 45’ 
from each other. But as globes have seldom so many 
meridians, the half hours and quarters may be found 
thus : 
Having disposed the globe as directed above, turn it 
‘in either direction, till the brazen meridian intersect the 
equator in $° 45’, and the arch of the horizon, intercept- 
od between the brazen meridian, and. the first meridian, 
will be the measure of the angle, which the line of three 
uarters past 11, or a quarter past 12 must make with 
ihe meridian line. Turn the globe in the same direc- 
“tion, till the brazen meridian intersect the equator in 
7° 30’, and the arch of the horizon intercepted between 
.the brazen meridian, and the first meridian, will measure 
the angle which the line of half past 11, or half past 12, 
must make with the meridian line, and thus every other 
quarter and half hour line may be found, by bringing 
successively to the brazen meridian every 3° 45’ of the 
equator. If the globe.ismoved only 1° 15’ at once, the 
successive arches of the horizon, intercepted between 
the brazen meridian and first meridian, will measure 
‘the angles which the lines of every 5 minutes must 
make with the meridian line, and so of any other sub- 
division. 
To construct a vertical south or north dial, rectify the 
globe for the co-latitude of the place, and proceed as 
in the case of a horizontal dial. See Diauuine, § 51, 
‘vol. vii. p. 700.—The application of the armillary sphere 
‘to the solution of problems, is the same in principle 
with that of the globes. 
CHAP. III. 
Or Maps. 
Secr. I. Of Maps in General. 
Tuoven the representation of the terrestrial sphere, 
by means of a globe, is the simplest as well as the most 
accurate, it has been found in many respects deficient 
for the purposes of geography. If the globe be made 
very large, it becomes -expensive and incommodious ; if 
small, the places which it ought to represent are either 
too much crowded, or altogether omitted. To remedy 
these defects, geographers have contrived to delineate 
the earth’s surface on a plane, ‘by which means the 
whole or any portion -may be easily represented, on a 
greater or less scale, according to circumstances. Such 
representations are in general denominated maps, and 
are aiso distinguished by particular names, ‘according 
to their nature or use. Thus a map representing the 
whole world is called a planisphere ; if it represent a 
considerable portion of the globe, it is called a gene- 
ral map, and ‘a particular map ‘if it contains only a 
country. “When a portion of a country is represented 
on a large scale, with the direction of roads, the course 
of small rivulets, and the position of villages. and single 
houses, it is called a topographical map. ‘Hence also 
mineralogical maps, intended to illustrate the geological 
structure of a country; and nautical maps or charts, used 
for the purposes ofnavigation. With regard to the po- 
sition of maps, it may be observed, that whatever be 
GEOGRAPHY. 
their nature or use, the north is: generally at the 
the east on the right hand, the south at the bottom, 
the west on the left hand. The graduation of the 
tor, or degrees of longitude, are marked at the top and 
bottom, and the graduations of the meridian, or degrees 
of latitude, on the right and left sides. __ arspet 
The various, methods adopted by hers in the 
construction of maps, may be referred to two principles, 
Prosection and DeyeLrorement. By jection is 
meant, a representation of the surface of the sphere on 
, Mat 
od oa 
a plane, as it, appears to the eye situated at a particular 
int and by developement is to be understood the un- q 
folding, or spreading out, of a ical surface on a 
plane. We are now to explain briefly, the construction : 
of maps according to both of these principles ; but as we "4 
shall frequently have occasion to employ lines of chords, 
sines, tangents, secants, &c. we here show the me- _ q 
thod of constructing these lines, and explainsomuch __ 
of their nature and use, as may be necessary for our uF 
present purpose. sits Pi 
From any point C, (Fig. 9.) draw CA, CD at right prs 
angles to one another, and with any convenient ra cc 
CA, describe a quadrant ABD. Join AD, and from A Fig. 
as a centre, through every degree of the arch ABD, 
describe arches intersecting AD, marking these inters 
sections with the corresponding degrees of the qua- 
drant. Then AD will be a line of chords. From each 
degree of the quadrant let fall perpendiculars on AC, 
and it will be a line of sines. Produce pe art: | 
towards E, and through A draw AF parallel to C 
Through the centre C, and each of the qua- 
Sap draw lines nnerseging AF, and it will become a 
ine of tangents. From C as acentre through every in- 
ee AF, describe arches intersecting DE. and 
CE will bea line of secants, And lastly, through every 
half degree in the line of tangents, draw to CD, 
and it will be a line of semitangents. 
For practical purposes, the lines, after being divided 
in this manner, are transferred to flat rulers of different 
sizes, where they are drawn parallel to one another, 
generally in the following order, chords, sines and se- 
cants in one line, tangents, and semitangents. In using 
them, nothing more is necessary, than to extend the 
compasses from the extremity of the line, to the number 
denoting the degrees of the given arch: thus the dis- 
tances from A to 40 on AD, C to 40 on AC, from 
At $098 SF foe frase on DE. 97 from C to 
40 on CD, will give respective e chord, sine, tangent, 
secant, and ee, t of pe arch of 40°, the radius 
of the arch being equal to AC. In any set of lines, the 
chord of 60°, is always equal to the radius of the quas 
Arant, from which the lines are constructed, 
‘Secr. II. Construction of Maps by Projection. .. 
In projecting an object upon a plane, according to 
the rules of perspective, the plane of projection, or that prit 
on which the object is to be delineated, is generally 
supposed to ‘be transparent, and situated between the 
eye and eae ok i to be projected. The man 
the eye is rojectt int, and i 
line drawn from this Sane, Habit 4s Do to the plane 
of projection, is termed the axis of that plane. The 
projection of any point of the object, is the point which 
it is to occupy, when transferred to the plane of projec- 
tion, and is always determined from the intersection of _ 
that plane, by the ray of light coming from the given _ 
point to the eye, eat 4 
