The word inertia occurs in compounds; viz., as in moment of inertia. The moment of in ertia of a body or a system of bodies upon or round an axis is the SUM of the products ob tained by multiplying each element of mass by the square of its distance from the axis. But with regard to a plane or point, the moment of inertia is the sum of the elements of mass each multiplied by the square of its distance from the given plane or point. There are other compounds, and phrases, in which the word inertia conveys a specific meaning. All, like the above, are defined in the better works on physics.
We gain our first of inertia by the attempts that we make to move bodies that are at rest, or to stop those that are in motion. As to the underlying notion of continuity in herent in the idea of inertia, we can hardly say more, philosophically speaking, than, that nothing in the known world is inconsistent with the hypothesis that all changes are really continuous. Indeed if the a priori belief in per manence or continuity had not existed the same laws which are now formulated in terms of, this belief might just as well have been formu lated without it. In a hypothetical sense con tinuity may be allowed to be the necessary condition if two appearances are to be classed as appearances of the same thing. Even if
bodies are suspended freely, so that fractional forces are negligible, we find that their state of rest or motion cannot be modified without the exercise of a certain amount of muscular force; and by abstracting our own personality in the case, we gradually come to the conception of inertia as a physical property inherent in all bodies. Inertia has been popularly described as a "passive resistance" to change of motion i but this expression is objectionable because it is entirely inaccurate. Freely suspended bodies (that is, bodies that are free from frictional force) cannot be said to "resist" forces that are applied to them. On the contrary, they yield instantly to the smallest force; but a small force, when exerted upon a given body, for a given length of time, does not produce as great a change of motion as would be produced by a large force acting upon the same body for. the same length of time. The conception of inertia shades insensibly into that of "mass"; the mass of a given body being proportional (by definition) to the velocity that is communi cated to the body by a force of standard in tensity, acting upon it for a standard length of time. See MASS; MATTER; MOLECULAR THEORY.