This stationary position of the plane of vibration at the pole seems
to present little difficulty. We impress a peculiar motion on the
pendulum in setting it a going. The Earth is at the same time carrying
the pendulum eastward, but _at the pole_ the one motion will not
interfere with the other. The only action of the Earth on the pendulum
there is that of attracting it towards its own (the Earth’s) centre.
But this attraction is exactly in the plane of vibration and merely
tends to continue the oscillatory motion without disturbing it. It
is otherwise if the experiment is made at some other point, say 20
degrees distant from the pole. Supposing the vibrations to commence in
the plane of the meridian, then as the tendency of the pendulum is to
continue its vibrations in planes absolutely parallel to the original
plane, it will be seen, if we trace both motions, that, while it is
carried eastward with the Earth along a parallel of latitude, this
tendency will operate to draw the plane of vibration away from a ‘great
circle’ into a ‘small circle’ (that is, from a circle dividing the
globe into two _equal_ parts, into one dividing it into two _unequal_
parts). But the pendulum _must_ necessarily move in a ‘great circle,’
and hence to counteract its tendency to deviate into a ‘small circle,’
a correctory movement is constantly going on, to which the lengthening
of the period necessary to complete a revolution must be ascribed. At
Edinburgh the period is about 29 hours, at Paris 32, at Cairo 48, at
Calcutta 63. At the Equator, the period stretches out to infinity. M.
Foucault’s rule is, that the angular space passed over by the pendulum
at any latitude in a given time, is equal to the angular motion of
the Earth in the period, multiplied by the sine of the latitude.
The angular motion of the Earth is 15 degrees per hour; and at the
latitude of 30, for example, the sine being to radius as 500 to 1000,
the angular motion of the pendulum will consequently be 7¹⁄₂ degrees per
hour. It is, therefore, easily found. It follows that the motions of
the pendulum may be employed in a rough way to indicate the latitude of
a place.”[37]
[37] Supplement of the _Manchester Examiner_, of May 24, 1851.
Public-domain text, read in full here on John Shaqi.
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