The velocities at which the precise form of definition becomes important are higher than can be reached in ordinary mechanical experiments. Such velocities can be attained in terrestrial laboratories only with electrified particles, as in experiments in high vacua or with radioactive disintegrations. It is interesting to notice that we very seldom attempt a direct measurement of velocity in such experiments by following a discrete particle in its flight and finding the time required to pass over a measured distance, but the velocities are measured indirectly, by calculation from the equations of electrodynamics and in terms of such immediately observed things as curvature of path. It is true that one or two experiments have attempted a more direct measure of velocity, but it seems there is room for more work here. THE CONCEPTS OF FORCE AND MASS Another concept of great importance is that of force. Since the usual analysis finds a connection between force and acceleration, and acceleration involves velocity, this is a natural place for the discussion of force. This concept has been subjected to much analysis by various writers. In origin the concept doubtless arises from the muscular sensations of resistance experienced from external bodies. This crude concept may at once be put on a quantitative basis by substituting a spring balance for our muscles, or instead of the spring balance we may use any elastic body, and measure the force exerted by it in terms of its deformation. Of course, the various precautions which must be taken in carrying out this idea physically are complex; the matter of precautions against temperature changes, for example, is one of the most easily understood. The concept of force so defined is limited to static systems; it is the task of statics to find the relation between the forces in systems at rest. We next extend the force concept to systems not in equilibrium, in which there are accelerations, and we must conceive that at first all our experiments are made in an isolated laboratory far out in empty space, where there is no gravitational field. We here encounter a new concept, that of mass, which as it is originally met is entangled with the force concept, but may later be disentangled by a process of successive approximations. The details of the various steps in the process of approximation are very instructive as typical of all methods in physics, but need not be elaborated here. Suffice it to say that we are eventually able to give to each rigid material body a numerical tag characteristic of the body, such that the product of this number and the acceleration it receives under the action of any given force applied to it by a spring balance is numerically equal to the force, the force being defined, except for a correction, in terms of the deformation of the balance, exactly as it was in the static case. In particularly, the relation found between mass, force, and acceleration