Physical geography. By Mary Somerville ...

18 PHYSICAL GEOGRAPHY. CHAP. I.
tance; that is to say, an object a fathom or six feet high would be
hid by the curvature of the earth at the distance of three miles.
Since the dip increases as the square, a hill 100 fathoms high would
be hid at the distance of ten miles, and the top of Kunchinjunga,
the most elevated point of the Himalaya, hitherto measured 28,178
feet high, would be seen to sink beneath the horizon by a person
about 167 miles off; thus, when the height is known, an estimate can
be formed of the distance of a mountain.
The oscillations of the pendulum have afforded another method of
ascertaining the form of the earth. Like all heavy bodies, its descent
and consequently its oscillations are accelerated in proportion to the
force of gravitation, which increases from the equator to the poles.
In order, therefore, that the oscillations may be everywhere performed
in the same time, the length of the pendulum must be increased progressively in going from the equator to the poles, according to a
known law,' from whence the compression or flattening at the poles
may be deduced. Experiments for that purpose have been made in
a great number of places, but, as in the measurement of the arcs, no
two sets give exactly the same results; the mean of the whole, however, differs very little from that given by the degrees of the meridian
and the perturbations of the moon; and as the three methods are so
entirely independent of each other, the figure and dimensions of the
earth may be considered to be known. The sea has little effect on
these experiments, both because its mean density is less than that of
the earth, and that its mean depth of perhaps four miles is inconsiderable when compared with 3956 miles, the mean terrestrial
radius.2
1 A pendulum which oscillates 86,400 times in a mean clay at the equator,
will do the same at every point of the earth's surface if its length be increased progressively to the pole as the square of the sine of the latitude.
The sine of the latitude is a perpendicular line drawn from any point of a
terrestrial meridian to the equatorial radius of the earth. That line expressed in feet or miles, and multiplied by itself, is the square of the sine
of the latitude. Gravitation increases from the equator to the poles according to that law, and the length of the degrees augments very nearly in the
same ratio.
2 The compression deduced by M. Bessel from arcs of the meridian is
-; that deduced by Colonel Sabine from his experiments with the pen299
dulum is -. Other pendulum experiments have also given a compres288.7
1 1
sion of -- and -. The protuberant matter at the earth's equator
298-2 266.4
produces inequalities in the moon's motions, from whence the compression
1
of the earth is found to be -; and although the reciprocal action of the
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