MATHEMATICAL GEOGRAPHY. 18

 

The straight line that runs through the centre
of a sphere or spheroid and terminates at the cir-
cumference is called the diameter. If the sphere
rotates—that is, moves around like a top—the

  

Fig. 4, Oblate Spheroid,

diameter on which it turns is called its awis. In
the oblate spheroid the axis is the shorter diam-
eter ; in the prolate spheroid the axis is the longer
diameter.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig, 6, Curvature of the Harth’s Surface.

The shape of our earth is that of an oblate
spheroid. The polar diameter is 26.47 miles
shorter than the equatorial diameter.

14. Proofs of the Rotundity of the Earth—

 

 

The earth is so large a sphere that its surface
everywhere appears flat. The following simple
considerations will prove, however, that its form
is nearly spherical:

(1.) Appearance of Approaching Objects —If
the earth were flat, as soon as an object appeared
on the horizon we would see the upper and lower
parts at the same time; but if it were curved, the
top parts would first be seen. Now, when a ship
is coming into port we see first the topmasts, then
the sails, and finally the hull; hence the earth
must be curved; and, since the appearance is the
same no matter from what direction the ship is
approaching, we infer that the earth is evenly
curved, or spherical.

(2.) Circular Shape of the Horizon.—The hori-
zon—or, as the word means, the boundary—is the
line which limits our view when nothing inter-
venes. The fact that this is always a circle fur-
nishes another proof that the earth is spherical.

The horizon would still be a circle if the earth were
perfectly flat, for we would still see equally far in all di-
rections; but it would not everywhere be so, since to an
observer near the edges some other shape would appear.
It is on account of the spherical form of the earth that our
field of view on a plain is so soon limited by the apparent
meeting of the earth and sky. As we can see only in
straight lines, objects continue visible until they reach
such a distance as to sink below the horizon, so that a
straight line from the eye will pass above them, meeting
the sky far beyond, on which, as a background, the objects
on the horizon are projected.

(8.) Shape of the Earth’s Shadow.—We can
obtain correct ideas of the shape of a body by
the shape of the shadow it casts. Now, the
shadow which the earth casts on the moon dur-
ing an eclipse of the moon is always circular,
and as only spherical bodies cast circular shad-
ows in all positions, we infer that the earth is
spherical.

(4.) Measurement.—The shape of the earth has
been accurately ascertained by calculations based
on the measurement of an arc of a meridian. We
therefore not only know that the earth is oblately
spheroidal, but also approximately the amount of
its oblateness.

(5.) The Shape of the Great Circle of Ilumi-
nation, or the line separating the portions of the
earth’s surface lighted by the sun’s rays from
those in the shadow, is another evidence of the
rotundity of the earth. rs
\ 15. The Dimensions of the Earth.—The equa-
torial diameter of the earth, or the distance
through at the equator, is, approximately, 7926