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knife-edge correction

The amount by which the observed period P of a pendulum must be increased because the knife edge on which the pendulum swings has a circular rather than V-shaped cross section. The correction amounts to about P/2s, in which s is the quantity √(1 + (d/r)² - 2 (d/r)cos α). r is the radius of curvature of the cross section, d is the distance from the center of gravity to the center of curvature and á is half the angle through which the pendulum swings from side to side. In practice, the radius r may not be measurable; the correction must then be determined empirically.

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