In ascending a hill, we appear to incline forward; and in descending, to lean backward, but in truth, we are standing upright with respect to a level plane. This is necessary to keep the line of direction between the feet, as is evident from _fig. 65._ A person sitting on a chair which has no back cannot rise from it without either stooping forward to bring the centre of gravity over the feet, or drawing back the feet to bring them under the centre of gravity. A quadruped never raises both feet on the same side simultaneously, for the centre of gravity would then be unsupported. Let A B C D, _fig. 66._, be the feet. The base on which it stands is A B C D, and the centre of gravity is nearly over the point O, where the diagonals cross each other. The legs A and C being raised together, the centre of gravity is supported by the legs B and D, since it falls between them; and when B and D are raised it is, in like manner, supported by the feet A and C. The centre of gravity, however, is often unsupported for a moment; for the leg B is raised from the ground before A comes to it, as is plain from observing the track of a horse’s feet, the mark of A being upon or before that of B. In the more rapid paces of all animals the centre of gravity is at intervals unsupported. The feats of rope-dancers are experiments on the management of the centre of gravity. The evolutions of the performer are found to be facilitated by holding in his hand a heavy pole. His security in this case depends, not on the centre of gravity of his body, but on that of his body and the pole taken together. This point is near the centre of the pole, so that, in fact, he may be said to hold in his hands the point on the position of which the facility of his feats depends. Without the aid of the pole the centre of gravity would be within the trunk of the body, and its position could not be adapted to circumstances with the same ease and rapidity. (170.) The centre of gravity of a mass of fluid is that point which would have the properties which have been proved to belong to the centre of gravity of a solid, if the fluid were solidified without changing in any respect the quantity or arrangement of its parts. This point also possesses other properties, in reference to fluids, which will be investigated in HYDROSTATICS and PNEUMATICS. (171.) The centre of gravity of two bodies separated from one another, is that point which would possess the properties ascribed to the centre of gravity, if the two bodies were united by an inflexible line, the weight of which might be neglected. To find this point mathematically is a very simple problem. Let A and B, _fig. 67._, be the two bodies, and _a_ and _b_ their centres of gravity. Draw the right line _a b_, and divide it at C, in such a manner that _a_ C shall have the same proportion to _b_ C as the mass of the body B has to the mass of the body A.