its connection with A were invisible so that all we could observe was the motion of A, we should ascribe the deviation of A's path from a straight line to the action of a force, and the changes in its kinetic energy to changes in the potential energy of A as it moved from place to place. This method is, however, the result of our regarding A as the sole member of the system under observation, whereas A is in reality only a part of a larger system; when we consider the system as a whole we see that it behaves as if it were free from the action of external forces and that its kinetic energy remains constant; what on our restricted view we regarded as the potential energy of A is seen on the more general view to be the kinetic energy of the system B. It is now many years ago since I showed that the effects of force and the existence of potential energy may be regarded as due to the connection of the primary system with secondary systems, the kinetic energy of these systems being the potential energy of the primary, the complete system having no energy other than the kinetic energy of its constituents; a similar view is the foundation of Hertz's system of Mechanics.
Let us consider one or two simple mechanical systems in which the motion of matter attached to the system produces the same effect as a force. Suppose A and B (Fig. 1) are two bodies attached to tubes which can slide vertically up and down the rod E F, and that two balls C and D are attached to A and B by rods hinged at A and B, then if the balls rotate about the rod they will tend to fly apart, and as the balls move further from the rod their points of attachment A and B must approach each other; thus A and B will tend to move towards each other, i.e., they will behave as if there were an attractive force acting between; the velocities of A and B, and therefore their kinetic energy will change from time to time; the kinetic energy lost by A and B will really have gone to increase the kinetic energy of the balls. If the rotating system C and D had been invisible we should have
