d more precise
than those of certain points on our minute planet. Hence, it is of
particular moment for us to give an exact account of the means employed
in determining them.

The calculation of these distances is made by "_triangulation_." This
process is the same that surveyors use in the measurement of terrestrial
distances. There is nothing very alarming about it. If the word repels
us a little at first, it is from its appearance only.

When the distance of an object is unknown, the only means of expressing
its apparent size is by measurement of the angle which it subtends
before our eyes.

We all know that an object appears smaller, in proposition with its
distance from us. This diminution is not a matter of chance. It is
geometric, and proportional to the distance. Every object removed to a
distance of 57 times its diameter measures an angle of 1 degree,
whatever its real dimensions. Thus a sphere 1 meter in diameter measures
exactly 1 degree, if we see it at a distance of 57 meters. A statue
measuring 1.80 meters (about 5 ft. 8 in.) will be equal to an angle of 1
degree, if distant 57 times its height, that is to say, at 102.60
meters. A sheet of paper, size 1 decimeter, seen at 5.70 meters,
represents the same magnitude.

In length, a degree is the 57th part of the radius of a circle, _i.e._,
from the circumference to the center.

The measurement of an angle is expressed in parts of the circumference.
Now, what is an angle of a degree? It is the 360th part of any
circumference. On a table 3.60 meters round, an angle of one degree is a
centimeter, seen from the center of the table. Trace on a sheet of paper
a circle 0.360 meters round--an angle of 1 degree is a millimeter.

[Illustration: FIG. 80.--Measurement of Angles.]

If the circumference of a circus measuring 180 meters be divided into
360 places, each measuring 0.50 meters in width, then when the circus is
full a person placed at the center will see each spectator occupying an
angle of 1 degree. The angle does not alter with the distance, and
whether it be measured at 1 meter, 10 meters, 100 kilometers, or in the
infinite spaces of Heaven, it is always the same angle. Whether a degree
be represented by a meter or a kilometer, it always remains a degree. As
angles measuring less than a degree often have to be calculated, this
angle has been subdivided into 60 parts, to which the name of _minutes_
has been given, and each minute into 60 parts or _sec