(198.) In all these examples it will be observed that the axis of rotation passes through the centre of gravity. The general theorem, of which they are only particular instances, is, “if a body revolve on a principal axis, passing through the centre of gravity, the axis will sustain no pressure from the centrifugal force of the revolving mass.” This is a property in which the principal axes through the centre of gravity are unique. There is no other axis on which a body could revolve without pressure. If two of the principal axes through the centre of gravity have equal moments, every axis in their plane has the same moment, and is to be considered equally as a principal axis. In this case the body would revolve on any of these axes without pressure. A homogeneous spheroid furnishes an example of this. If any of the diameters of the earth’s equator were a fixed axis, the earth would revolve on it without producing pressure. If the three principal axes through the centre of gravity have equal moments, all axes through the centre of gravity are to be considered as principal axes. In this case the body would revolve without pressure on any axis through the centre of gravity. A globe, in which the density of the mass at equal distances from the centre is the same, is an example of this. Such a body would revolve without pressure on any axis through its centre. (199.) Since no pressure is excited on the axis in these cases, the state of the body will not be changed, if during its rotation the axis cease to be fixed. The body will notwithstanding continue to revolve round the axis, and the axis will maintain its position. Thus a spinning-top of homogeneous material and symmetrical form will revolve steadily in the same position, until the friction of its point with the surface on which it rests deprives it of motion. This is a phenomenon which can only be exhibited when the axis of rotation is a principal axis through the centre of gravity. (200.) If the body revolve round any axis through the centre of gravity, which is not a principal axis, the centrifugal pressure is represented by two forces, which are equal and parallel, but which act in opposite directions on different points of the axis. The effect of these forces is to produce a strain upon the axis, and give the body a tendency to move round another axis at right angles to the former. (201.) If the fixed axis on which a body revolves be a principal axis through any point different from the centre of gravity, then a pressure will be produced by the centrifugal force of the revolving mass, and this pressure will act at right angles to the axis on the point to which it is a principal axis, and in the plane through that axis and the centre of gravity. The amount of the pressure will be proportional to the mass of the body, the distance of the centre of gravity from the axis, and the square of the velocity of rotation.