The small oscillations of a simple pendulum in a vertical plane also come under equation (5).
This coincides with the equation of motion of a simple pendulum [E 13 (15)] of length 1, provided 1= hf/h.
If we produce OG to P, making OP =1, the point P is called the centre of oscillation; the bob of a simple pendulum of length OP suspended from 0 will keep step with the motion of P, if properly started.
If it could be arranged that the period of a small oscillation should be exactly the same about either edge, the two knifeedges would in general occupy the positions of conjugate centres of suspension and oscillation; and the distances between them would be the length 1 of the equivalent simple pendulum.
In these researches he skilfully took advantage of the well-known property of reciprocity between the centres of suspension and oscillation of an oscillating body, so as to determine experimentally the precise position of the centre of oscillation; the distance between these centres was then the length of the ideal simple pendulum having the same time of oscillation.
