A pendulous body being of determinate magnitude, its several parts will be situated at different distances from the axis of suspension. If each component part of such a body were separately connected with the axis of suspension by a fine thread, it would, being unconnected with the other particles, be an independent simple pendulum, and would oscillate according to the laws already explained. It therefore follows that those particles of the body which are nearest to the axis of suspension would, if liberated from their connection with the others, vibrate more rapidly than those which are more remote. The connection, however, which the particles of the body have, by reason of their solidity, compels them all to vibrate in the same time. Consequently, those particles which are nearer the axis are retarded by the slower motion of those which are more remote; while the more remote particles, on the other hand, are urged forward by the greater tendency of the nearer particles to rapid vibration. This will be more readily comprehended, if we conceive two particles of matter A and B, _fig. 75._, to be connected with the same axis O by an inflexible wire O C, the weight of which may be neglected. If B were removed, A would vibrate in a certain time depending upon the distance O A. If A were removed, and B placed upon the wire at a distance B O equal to four times A O, B would vibrate in twice the former time. Now if both be placed on the wire at the distances just mentioned, the tendency of A to vibrate more rapidly will be transmitted to B by means of the wire, and will urge B forward more quickly than if A were not present: on the other hand, the tendency of B to vibrate more slowly will be transmitted by the wire to A, and will cause it to move more slowly than if B were not present. The inflexible quality of the connecting wire will in this case compel A and B to vibrate simultaneously, the time of vibration being greater than that of A, and less than that of B, if each vibrated unconnected with the other. If, instead of supposing two particles of matter placed on the wire, a greater number were supposed to be placed at various distances from O, it is evident the same reasoning would be applicable. They would mutually affect each other’s motion; those placed nearest to point O accelerating the motion of those more remote, and being themselves retarded by the latter. Among these particles one would be found in which all these effects would be mutually neutralised, all the particles nearer O being retarded in reference to that motion which they would have if unconnected with the rest, and those more remote being in the same respect accelerated. The point at which such a particle is placed is called _the centre of oscillation_.