the pendulum, and _vice versâ_. So long as the rods are horizontal and in the same straight line their centre of gravity is in the crutch axis, and they are therefore balanced in every position; they therefore only retard the pendulum by their inertia; but when the ends are bent down the centre of gravity is lowered, and they have a tendency to come to a horizontal position and to balance each other like a scale beam, and so swing with the pendulum and overcome its retardation. It is obvious that they would, if alone, swing in a shorter time than the pendulum and so, being connected, they increase its rate. When the rods are vertical they have no compensating action, for the centre of gravity is simply thrown sidewise, and acts as a continuous force tending to make the pendulum oscillate further on one side than on the other; and in the intermediate positions of the rods their action varies, and a consideration of the position of their centre of gravity will give the intensity of the compensating action. In order to make a small change in the rate of the clock without stopping it to turn the screw at the bottom of the pendulum, the following contrivance is adopted. A weight _k_ slides freely on the crutch rod, but is tapped to receive the screw cut on the lower portion of the spindle _l_, the upper end of which terminates in a nut _m_ at the crutch axis. By turning this nut the position of the small weight on the crutch rod is altered, and the clock rate correspondingly changed. To make the clock lose, the weight must be raised. There is also another method of compensation, depending on differential expansion. Attached to an ordinary pendulum just above the bob, and at right angles to it, is a composite rod, made of copper and iron, the lower half being copper; then, as the pendulum rod lengthens and lets down the bob, the copper expands more than the iron, and causes the rod to bend, like a piece of wood wetted on one side, and by this bending or warping the weights at either end are raised as the bob is lowered, so the centre of oscillation keeps at the same height at all temperatures. We have dealt with clocks and pendulums somewhat in the order of their invention. We may add that the great majority of clocks of modern manufacture of any pretention to time-keepers are constructed with the dead beat escapement of Graham or a modification of it, combined with a mercurial or gridiron pendulum. For the best Observatory clocks of the more expensive kind other more elaborate forms of escapement are sometimes used, as, for example, that in the clock at the Royal Observatory, Greenwich, which we shall refer to in detail further on, on account of other new points in its construction.