Neither must the effects of friction or other resistances be con founded with those of a stable or unstable disposition. A ladder rest ing against horizontal ground and a vertical wall is maintained by friction ; were it not for friction, there would not be rest in any posi tion; and as it is, the angle which the ladder makes with the ground must not be too small. There is thus a set of positions, from the vertical one to a certain inclination, depending on the amount of friction, in all of which there is equilibrium ; while in every other position there is no equilibrium. In no case must the words stability and instability be used in such manner as to confuse their popular with their technical sense.
Under SOLAR SYSTEM is pointed out what is meant by the stability of that system. When a system has a motion of a permanent charac ter, it is stable if a small disturbance only produce oscillations in that motion, or make permanent alterations of too slight a character to allow the subsequent mutual actions of the parts to destroy the per manent character of the motion. Suppose a material body, for instance, to revolve about an axis passing through the centre of gravity enacted on by any forces except the weight of its parts. If this
axis be one of the principal axes, the rotation on it is permanent, that Li, the axis of rotation will continue unaltered, even though that axis be not fixed. The rotation however, though permanent, is not stable about more than two out of the three principal axes. Let the first rotation be established about the axis which has the greatest moment of rotation, or the least, and if a slight displacement or disturbance be given, which has the effect of producing a little alteration of the axis of rotation, that alteration will not increase indefinitely, but will only occasion a perpetual transmission of the rotation from axis to axis, all the lines lying near to the principal axis first mentioned. But if that axis be chosen about which the moment of inertia is neither greatest nor least, any disturbance, however slight, will continually remove the axis of rotation farther and farther from the first axis, near which it will not return until it has made a circuit about one of the other two principal axes.
For the mathematical part of this subject, so far as we give it, see VIRTUAL VELOCITIES.