Menage neral, referring for a demonstration of these properties 
cal Geogra- ' 
phy. 
Definition 
of a sphere. 
Diameter. 
Axis. 
Circle of 
the sphere. 
Pole of.a 
circle. 
Great circle. 
Small 
circle. 
Division of 
a circle. 
‘Length of 
an arch. 
Distance 
between 
two points. 
‘Great cir- 
cles equal. 
Measure of 
an angle 
formetl by 
two great 
circles. 
General 
view of the 
celestial 
phere, 
Diurnal 
revolution, 
146 
to the article T'ricoNomeTRy. 
A sphere is an uniformly round body, every point of 
whose surface, is equally distant from a point within 
the body, called the centre. Hence, ; sieht 
Ifa circle is made to revolve about its diameter, 
which remains fixed, its circumference will describe or 
trace out the surface of a sphere. . The’ circle thus re- 
volving is called the generating circle. 
The diameter of a sphere is a straight line passing 
through the centre, and terminated both ways by the 
surface. 
The axis of a sphere is that: diameter about which 
‘the generating circle, or sphere itself, is supposed to re~ 
volve. 
If an indefinitely thin plane or flat surface cut or 
pass ‘through a sphere, the part of the plane that lies 
within the sphere will be a circle, whose circumference 
appears on the surface, and is called a circle of the 
sphere. tt 
The pole of a circle of the sphere, is a point on the 
surface, from which every point in the circle is equally 
distant. Hence 
Every circle of the sphere has two poles, diametri-+ 
cally opposite to one another. 
A great circle of the sphere, is that whose plane*pas- 
ses through the centre, and consequently divides the 
sphere into two equal parts or hemispheres, 
A small circle of the sphere is that whose plane does 
not pass through the centre, but divides the sphere into 
two unequal parts. 
Every circle is supposed to be divided into 360 
equal parts, called degrees; each degree into 60 equal 
parts, called minutes ; and each minute into 60 equal 
parts called seconds. These different subdivisions are 
denoted by the signs ° ’ ”, thus 12° 15’ 10” mean 12 
degrees, 15 minutes, and 10 seconds. 
The length of an arch is expressed by the number of 
degrees, minutes, and seconds which it contains; thus 
the fourth part of a circle, or a quadrant, is said to be 
equal to 90°. 
The distance between two points, on the surface of a 
sphere, is measured by an arch of a great circle inter- 
cepted between them. 
All great circles of a sphere are equal, and intersect 
one another in two points diametrically opposite. 
The angle formed by the intersection of two at 
circles, is measured by the arch of another great circle, 
cutting the other two at the distance of 90° from the 
point of intersection in each. 
When two great circles make with one another an 
angle of 90°, that is, when their planes are at right 
angles to one another, they pass through each others 
poles, the poles of a great circle being 90° distant from 
its circumference. 
Sect. II. Of the Celestial Sphere. 
Tux heavenly bodies as seen from the earth, appear 
to be placed in the concave surface of a hollow sphere, 
having the earth in its centre, and seem to describe 
circles every 24 hours of a greater or less circumference, 
cording as they are farther from, or nearer to a cer- 
tain point, that appears fixed. Diametrically opposite 
to this point is another, about which also the heavenly 
bodies seem to describe circles, thus exhibiting the 
same appearance, as if the whole celestial sphere revol« 
ved about a diameter from east to west. In this mo- 
tion, which is called the diurnal revolution of the sphere, 
all the heavenly bodies seem to participate, but the 
GEOGRAPHY. | 
sun, with others of them called.planets, have alsoa a 
r+ motion of their own in a contrary direction, by 
which, ina certain time, they performacomplete revo- 
lution. of the sphere, though this is gene avery long 
yout compared with, that of their diurnal revolution. 
hus the sun, by-his proper, motion from west to east, 
describes a circle of the: celestial sphere in 365 days, | 
the moon in, 27, and the other planets in different 
riods between 87. and 30689 days. In order to ‘lines 
trate these motions, as well as to determine the relative 4 
positions of the bodies themselves, certain imaginary 
points and lines are supposed to be marked or traced 
out on the surface of the celestial sphere. The most 
important of these we now proceed to explain, . .. — 
The north and south.poles of the world, are those Defini 
points in the pretest that appear to be fixed. 
The poles arealso termed arctic and antarctic’; the arctic Poles 
or north pole being that which is visible in this.as well *°™ 
as in es other country of Europe. ; , 
The axis of the world is that diameter of the sphere Axis, 
which connects;the poles, and about which the whole > 
sphere seems: to revolve. | | ‘ s whee “a 
The zenith of any place on the earth, is that point in Zen 
the celestial sphere which is directly over the or 
itis a in which the plumb+line at that place, if 
produced upwards, would meet the celestial sphere, 
When the sun or any other heavenly body is in the 
zenith of a place, it is said to be vertical, to anes 
_ The nadir is a point in the sphere diametrically op- Nadir, 
Pith egeisbetlebice, peauisuacleatisherihorencteny Bed 
: inoctial is a ircle o w Equin 
poles tointide with the poles of the world... tal 
The horizon is a great circle whose \poles. are the Horiz 
zenith and nadir. ; : 
The cardinal points of the horizon are its north, south, Cardir 
east, and west points, which divide it into four qua- points 
drants, the two first being opposite to each other, as poh 
also the two last. Thé point of the horizon nearest the 
north pole is called the north point. 
Meridians, called also hour circles and circles of right Meri¢ 
ascension, are great circles perpendicular to the equi- 
noctial, and consequently passing through the poles of 
the world. _ 
The meridian of the , or the twelve o’clock hour Me 
circle, is the meridian cuts the horizon in the north of th 
and south points. se 
The six o’clock hour circle, is the meridian at right Six ¢ 
angles to the meridian of the place, __, hour 
An azimuth or vertical circle, is a great circle per- Azin 
pendicular to-the horizon, and consequently passing 
through the zenith oe nadir, ig og 2 
The prime vertical, is a vertical.circle passing im 
the motaaeee ints of the horizon, and consequently tical. 
cutting the meridian of the at right sale 
The ecliptic is a great circle representing the sun’s Ecli 
annual oy and cutting the equinoctial at an angle of 
about 23° 28’, Hence the poles of the ecliptic are 
about 23° 28’ distant from the corresponding poles of 
the world. ss j : ‘ iat 
The signs are the twelve equal parts into which the Si 
ecliptic-is divided, each consisting of 30°. They are 
written and named as follows : 
oy Aries, < Libra. 
& Taurus m Scorpio, 
a Gemini f Sagittarius. 
gs Cancer vs Capricornus. 
SK Leo. ae Aquarius, - 
Pisces. 
