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Fig. 27.

99. We proceed to an experiment which will give an insight into a curious property of gravity. I have here a plate of sheet iron; it has the irregular shape shown in Fig. 27. Five small holes a b c d e are punched at different positions on the margin. Attached to the framework is a small pin from which I can suspend the iron plate by one of its holes a: the plate is not supported in any other way; it hangs freely from the pin, around which it can be easily turned. I find that there is one position, and one only, in which the plate will rest; if I withdraw it from that position it returns there after a few oscillations. In order to mark this position, I suspend a line and plummet from the pin, having rubbed the line with chalk. I allow the line to come to rest in front of the plate. I then flip the string against the plate, and thus produce a chalked mark: this of course traces out a vertical line a p on the plate.

I now remove the plummet and suspend the plate from another of its holes b, and repeat the process, thus drawing a second chalked line b p across the plate, and so on with the other holes: I thus obtain five lines across the plate, represented by dotted lines in the figure. It is a very remarkable circumstance that these five lines all intersect in the same point p; and if additional holes were bored in the plate, whether in the margin or not, and the chalk line drawn from each of them in the manner described, they would one and all pass through the same point. This remarkable point is called the centre of gravity of the plate, and the result at which we have arrived may be expressed by saying that the vertical line from the point of suspension always passes through the centre of gravity.

100. At the centre of gravity p a hole has been bored, and when I place the supporting pin through this hole you see that the plate will rest indifferently in all positions: this is a curious property of the centre of gravity. The centre of gravity may in this respect be contrasted with another hole q, which is only an inch distant: when I support the plate by this hole, it has only one position of rest, viz. when the centre of gravity p is vertically beneath q. Thus the centre of gravity differs remarkably from any other point in the plate.

101. We may conceive the force of gravity on the plate to act as a force applied at p. It will then be easily seen why this point remains vertically underneath the point of suspension when the body is at rest. If I attached a string to the plate and pulled it, the plate would evidently place itself so that the direction of the string would pass through the point of suspension; in like manner gravity so places the plate that the direction of its force passes through the point of suspension.

102. Whatever be the form of the plate it always contains one point possessing these remarkable properties, and we may state in general that in every body, no matter what be its shape, there is a point called the centre of gravity, such that if the body be suspended from this point it will remain in equilibrium indifferently in any position, and that if the body be suspended from any other point, then it will be in equilibrium when the centre of gravity is directly underneath the point of suspension. In general, it will be impossible to support a body exactly at its centre of gravity, as this point is within the mass of the body, and it may also sometimes happen that the centre of gravity does not lie in the substance of the body at all, as for example in a ring, in which case the centre of gravity is at the centre of the ring. We need not, however, dwell on these exceptional cases, as sufficient illustrations of the truth of the laws mentioned will present themselves subsequently.