Chap. 2. PHILOSOPHY. 97

portion to L H, as the line C H bears to K ; and L shall bethe center of oscillation of the whole pendulum.

71. This computation is made upon supposition,that thecenter of oscillation of the rod C D, if that were to swing alonewithout any other weight annexed, would be the point I.And this point would be the true center of oscillation, so faras the thickness of the rod is not to be regarded. If any onechuses to take into consideration the thickness of the rod, hemust place the center of oscillation thereof so much belowthe point I, that eight times the distance of the center fromthe point I shall bear the fame proportion to the thickness ofthe rod, as the thickness of the rod bears to its length CD a .

72. It has been observed above, that when a pendulumswings in an arch of a circle, as here in fig. y8, the pendu-lum AB swings in the circular arch CD; if you draw an ho-rizontal line, as E F, from the place whence the pendulum islet fall, to the line A G, which is perpendicular to the horizon:then the velocity, which the pendulum will acquire in com-ing to the point G, will be the fame, as any body would ac-quire in falling directly down from F to G. Now this is to beunderstood of the circular arch, which is described by the cen-ter of oscillation of the pendulum. I shall here farther ob-serve, that is the straight line E G be drawn from the point,whence the pendulum falls, to the lowest point of the arch ;in the fame or in equal pendulums the velocity, which the

2 See Hugen Korolog. Oscilkt. p. 142.

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pendulum