In order to determine these effects, to predict the pressure produced by the weight if the body be quiescent, or the mixed effects of motion and pressure, if it be not so, it is necessary in all cases to be able to assign the place of the centre of gravity. When the magnitude and figure of the body, and the density of the matter which occupies its dimensions, are known, the place of the centre of gravity can be determined with the greatest precision by mathematical calculation. The process by which this is accomplished, however, is not of a sufficiently elementary nature to be properly introduced into this treatise. To render it intelligible would require the aid of some of the most advanced analytical principles; and even to express the position of the point in question, except in very particular instances, would be impossible, without the aid of peculiar symbols. (152.) There are certain particular forms of body in which, when they are uniformly dense, the place of the centre of gravity can be easily assigned, and proved by reasoning, which is generally intelligible; but in all cases whatever, this point may be easily determined by experiment. (153.) If a body uniformly dense have such a shape that a point may be found on either side of which in all directions around it the materials of the body are similarly distributed, that point will obviously be the centre of gravity. For if it be supported, the gravitation of the particles on one side drawing them downwards, is resisted by an effect of exactly the same kind and of equal amount on the opposite side, and so the body remains balanced on the point. The most remarkable body of this kind is a globe, the centre of which is evidently its centre of gravity. A figure, such as _fig. 38._, called an _oblate spheroid_, has its centre of gravity at its centre, C. Such is the figure of the earth. The same may be observed of the elliptical solid, _fig. 39._, which is called a prolate spheroid. A cube, and some other regular solids, bounded by plane surfaces, have a point within them, such as above described, and which is, therefore, their centre of gravity. Such are _fig. 40._ A straight wand of uniform thickness has its centre of gravity at the centre of its length; and a cylindrical body has its centre of gravity in its centre, at the middle of its length or axis. Such is the point C, _fig. 41._ A flat plate of any uniform substance, and which has in every part an equal thickness, has its centre of gravity at the middle of its thickness, and under a point of its surface, which is to be determined by its shape. If it be circular or elliptical, this point is its centre. If it have any regular form, bounded by straight edges, it is that point which is equally distant from its several angles, as C in _fig. 42._