Page:Elementary Text-book of Physics (Anthony, 1897).djvu/66

 well illustrated by the instrument called the Foucault pendulum. This pendulum is a heavy spherical bob suspended by a long cylindrical wire, so clamped that it is perfectly free to swing in any plane. If such a pendulum were set up at the equator and started swinging in a north and south line, it would be carried around by the earth in its rotation and would evidently continue to swing in the same line on the earth's surface. If, on the other hand, it were set up at the pole and set swinging along any line traced on the earth's surface, the oscillations of the pendulum would persist in the same plane in space, and the earth would turn around under it, so that the oscillations of the pendulum would immediately begin to deviate from the line on the earth along which the first oscillation took place; and if the oscillations were continued the extremities of the paths of the pendulum would describe the arc of a circle, and at the end of a day the pendulum would again swing in the line in which it started. If now the pendulum be swung at some intermediate point on the earth's surface the angular velocity of the earth can be resolved into two component angular velocities—one about the axis $$OA$$ (Fig. 18), which coincides with the length of the pendulum when it is at rest, and the other about an axis $$OB$$ at right angles to this. The angular velocity about the latter axis will have no effect on the line traced out by the swinging pendulum; the angular velocity about the former axis will occasion an apparent angular displacement. By the parallelogram law this angular velocity equals $$\omega \sin{\phi}$$, where $$\omega$$ is the angular velocity of the earth about its axis, and $$\phi$$ is the latitude. By experiments with such a pendulum this formula is verified and the rotation of the earth established by direct experiment, and by assuming the validity of this formula and determining the angular displacement of the pendulum an approximate value of the length of the day has been obtained.