similar to those of the external air, whose average temperature for each interval is given in the table.
The compensating action of the pendulum evidently depends upon the relative lengths of steel and zinc, and it is easily possible that great difficulty would be experienced in cutting and fitting tubes of exactly the right length; to complete the adjustment a very delicate contrivance is added.
Two compound bars of brass and steel (h and i, Fig. 1), with small weights at their ends, are hung to the crutch-axis by means of a collar loose enough to be easily turned. The rods are so made that under normal conditions the brass and steel are of the same length, and the two bars are in the same straight line; the center of gravity of the rods and the weights (regarded as one body) is therefore in the axis, and the weights are balanced in every position, no matter what angle the line of the rods makes with the plane of the horizon; they affect the pendulum only by their inertia. But, when a change in temperature occurs, the brass and steel become of unequal length, owing to a difference in the co-efficients of expansion of the two metals, the rods are bent, and the center of gravity of the rods and weights is no longer in the axis, nor is it in the same vertical plane as the axis except when the weights are in a horizontal line; so that an unbalanced force is introduced whose compensating action varies from a maximum when the weights are in a horizontal line, to zero when the weights "are in a vertical line. To be explicit, suppose the rods to be horizontal and the brass uppermost, and let there be an increase of temperature. The brass will expand more than the steel, and, the rods being bent downward, the weights will be lowered. As the pendulum swings the weights swing with it, and are continually trying to get back to a horizontal position where they would balance each other; if they were swinging alone, they would evidently swing faster than the pendulum, and therefore, being attached, they accelerate its motion. If the steel were uppermost, the weights would be raised with an increase of temperature and the pendulum retarded. If the rods were both vertical, a change of temperature would only throw the center of gravity of the two weights to one side or the other of the axis, but would not raise or lower it; this would only introduce a continuous force tending to make the pendulum oscillate farther on one side than the other, but not affecting its rate. At intermediate positions between the vertical and horizontal, the change in the position of the center of gravity due to a change of temperature would vary with the angle made by the line joining the centers of gravity of the two weights with the plane of the horizon; any required compensating action, between the limits above mentioned, for a known change of temperature, can therefore be obtained by setting the rods at the proper angle.
In order to make a small change in the rate without stopping the pendulum, the device shown in Fig. 1 has been employed: A weight