rately defined, and it enables us to state with the utmost
precision the relation between the pole and the latitude. The statement
is, that the elevation of the pole above the horizon is equal to the
latitude of the place.

The astronomer stationed at one end of the long line measures the
elevation of the pole above the horizon. This is an operation of some
delicacy. In the first place, as the pole is invisible, he has to obtain
its position indirectly. He measures the altitude of the Pole Star when
that altitude is greatest, and repeats the operation twelve hours later,
when the altitude of the Pole Star is least; the mean between the two,
when corrected in various ways which it is not necessary for us now to
discuss, gives the true altitude of the pole. Suffice it to say that by
such operations the latitude of one end of the line is determined. The
astronomer then, with all his equipment of instruments, moves to the
other end of the line. He there repeats the process, and he finds that
the pole has now a different elevation, corresponding to the different
latitude. The difference of the two elevations thus gives him an
accurate measure of the number of degrees and fractional parts of a
degree between the latitudes of the two stations. This can be compared
with the actual distance in miles between the two stations, which has
been ascertained by the trigonometrical survey. A simple calculation
will then show the number of miles and fractional parts of a mile
corresponding to one degree of latitude--or, as it is more usually
expressed, the length of a degree of the meridian.

This operation has to be repeated in different parts of the earth--in
the northern hemisphere and in the southern, in high latitudes and in
low. If the sea-level over the entire earth were a perfect sphere, an
important consequence would follow--the length of a degree of the
meridian would be everywhere the same. It would be the same in Peru as
in Sweden, the same in India as in England. But the lengths of the
degrees are not all the same, and hence we learn that our earth is not
really a sphere. The measured lengths of the degrees enable us to see to
what extent the shape of the earth departs from a perfect sphere. Near
the pole the length of a degree is longer than near the equator. This
shows that the earth is flattened at the poles and protuberant at the
equator, and it provides the means by which we may calculate the actual
lengths of the pola