An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

FIGURE, AND DIMENSIONS. 5
the height of a mountain, ZO the direction of the plumb-line,
HIOR a line passing through the station 0, and at right angles
to the plumb-line, C the center of the earth, DAE the portion
of the earth's surface seen from 0; OD, OE, lines drawn from
the place of the spectator to the most distant parts of the
horizon, and CD a radius of the earth. The dip of the horizon
is the angle HOD or ROE. Now the angle made between
the direction of the plumb-line and that of the extreme line of
the horizon or the surface of the sea, namely, the angle ZOD,
can be easily measured; and subtracting the right angle ZOH
fiom ZOD, the remainder is the dip of the horizon, from which
the length of the line OD may be calculated (see Art. 10), the
height of the spectator, that is, the line OA, being known.
This length, to whatever point of the horizon the line is drawn,
is always found to be the same; and hence it is inferred, that
the boundary which limits the view on all sides is a circle.
Moreover, at whatever elevation the dip of the horizon is taken,
in any part of the earth, the space seen by the spectator is
always circular. Hence the surface of the earth is spherical.
10. The earth being a sphere, the dip of the horizon HOD
= OCD. Therefore, to find the dip of the horizon corresponding to any given height AO* (the diameter of the earth being
known), we have in the triangle OCD, the right angle at D,
and the two sides CD, CO, to find the angle OCD. Therefore,
CO: rad.:: CD: cos. OCD.
Learning the dip corresponding to different altitudes, by
giving to the line AO different values, we may arrange the
results in a table.
i The learner will remark that the line AO, as drawn in the figure, is much
larger in proportion to CA than is actually the case, and that the angle HOD is
much too great for the reality. Such disproportions are very frequent in astronomical diagrams, especially when some of the parts are exceedingly small com-n
pared with others; and hence the diagrams employed in astronomy are not to be
regarded as true pictures of the magnitudes concerned, but merely as representing
their abstract geonmetrical relations.