In the instruments of Wagener and Ewing, the clockwork and moving surface do not form part of the pendulum, but rest independently on a support rigidly attached to the earth. In Wagener’s instrument one index only is used, while in Ewing’s two are used for writing the record of the motion. A difficulty which is apparent in all pendulum machines is that when the bob of such a pendulum is deflected it tends to fall back to its normal position. To make a pendulum perfect it therefore requires some compensating arrangement, so that the pendulum, for small displacements, shall be in neutral equilibrium, and the errors due to swinging shall be avoided. Several methods have been suggested for making the bob of an ordinary pendulum astatic for small displacements. One method proposed by Gray consists in fixing in the bob of a pendulum a circular trough of liquid, the curvature of this trough having a proper form. Another method which was suggested, was to attach a vertical spiral spring to a point in the axis of the pendulum a little below the point of suspension, and to a fixed point above it, so that when the pendulum is deflected it would introduce a couple. Professor Ewing has suggested an arrangement so that the bob of the pendulum shall be partly suspended by a stretched spiral spring, and at the same time shall be partly held up from below by a vertically placed strut, the weight carried by the strut being to the weight carried by the spring in the ratio of their respective lengths. As to how these arrangements will act when carried into practice yet remains to be seen. Another important class of instruments are _inverted pendulums_. These are vertical springs made of metal or wood loaded at their upper end with a heavy mass of metal. An arrangement of this sort, provided at its upper end with a pencil to write on a concave surface, was employed in 1841 to register the earthquakes at Comrie in Scotland. In Japan they were largely employed in series, each member of a series having a different period of vibration. The object of these arrangements was to determine which of the pendulums, with a given earthquake, recorded the greatest motion, it being assumed that the one which was thrown into the most violent oscillation would be the one most nearly approximating with the period of the earthquake. The result of these experiments showed that it was usually those with a slow period of vibration which were the most disturbed.