Fig. 51.
Fig. 52.
103. Stability of Bodies.—The firmness with which a body stands depends upon two circumstances—the height of its centre of gravity, and the extent of its base. The lower the centre of gravity, and the broader the base, the firmer does the body stand. A cube, represented in Fig. 48, is more stable, that is, less easily turned over, than a body shaped as Fig. 49, because it has a larger base. The contrast is still greater between Figs. 48 and 50. The reason of the stability of a body with a broad base is found in the fact, that in turning it over the centre of gravity must be raised more than in turning over one of a narrower base. The curved lines indicate the paths of the centres of gravity as the bodies are turned over. In the case of a perfectly round ball, the base is a mere point, and therefore the least touch turns it over. Its centre of gravity does not rise at all, but moves in a horizontal line, as shown in Fig. 51. The pyramid is the firmest structure in the world, because it possesses in the highest degree the two elements—a broad base, and a low position of the centre of gravity. On both these accounts the centre of gravity must ascend considerably when the body is turned over, as seen in Fig. 52.
Fig. 53.
Fig. 54.
104. Bodies not Upright Unstable.—When a body does not stand upright, its stability is diminished simply because only a portion of the base is concerned in its support. In Fig. 53 the base is broad, but the body is so far from being upright that the centre of gravity bears upon the very extremity of the base on one side, as the perpendicular line from it indicates. The least jostle will turn it over, because the centre of gravity need not ascend the least when this is done. You see, then, that the less upright a body is, the less of the base is of service in its support, because the farther is the line of direction of the downward pressure of the centre of gravity from the centre of the base. The famous tower of Pisa, Fig. 54, one hundred and thirty feet high, overhangs its base fifteen feet. It was undoubtedly built intentionally in this way to excite wonder and surprise, for what would otherwise have been a very unsafe structure is rendered stable and safe by the arrangement of its materials. Its lower portion is built of very dense rock, the middle of brick, and the upper of a very light porous stone. In this way the centre of gravity of the whole structure is made to have a very low position.
