HORIZONTAL PENDULUM w FIG. 1. in direct proportion to the square of the dis- tance. In the torsion balance (see BALANCE) these relations are reversed ; it is a lever with two arms, and is retained in its position of rest only by the force of torsion, which can easily be reduced to a very minute quantity ; hence it readily obeys attractive and repulsive forces to which the common pendulum is abso- lutely insensitive. But the point from which the force emanates must be in the immediate neighborhood of the end of one of its arms ; for if it is situated at a great distance from the balance, it will act with equal power on both arms, and these actions, being contrary and op- posed, will neutralize each other, and no effect will be observed. The horizontal pendulum combines the advantages of the ordinary pen- dulum and of the torsion balance. Let R R represent an in- flexible rod of steel placed horizontally, and supported at its extremities by pivots on which it turns freely, and let W be a weight inflexibly at- tached to the rod, as indicated in fig. 1 . It is evident that W A when left to itself will assume a vertical position, and that the whole apparatus will essentially con- stitute an ordinary pendulum. If now an at- tractive or repulsive force be made to act on W, the pendulum will tend to be deflected from its vertical position ; and if the force is suffi- ciently powerful, a sensible deflection will be observed. In an arrangement of this kind, aside from friction, the opposing force to be overcome will of course be the attraction of gravitation ; if however we gradually elevate the rod R R by one end, the gravity com- ponent will diminish, and finally become zero when R R is ver- tical, and consequent- ly A "W horizontal. Zollner has shown ex- perimentally how this may be accomplished to an almost incredi- ble extent, so that an apparatus of this gen- eral nature in his hands became capa- ble of obeying even the feeble attractive force of the moon. Fig. 2 represents Zollner's horizontal pendu- lum. At W is the weight, the inflexible rod being replaced by fine steel wire or watch spring, stretched as shown on the vertical col- umn C C, the whole being supported by a tri- pod provided with levelling screws. P is a counterpoise, and M a mirror for reflecting the divisions of a distant scale to a telescope, to- FIG. 2. Zollner's Horizontal Pendulum. gether constituting an arrangement for magni- fying the motion of the pendulum. The appa- ratus shown in fig. 2 was made of brass, its height being about 30 in. ; it was mounted on a pier like an astronomical instrument, and enclosed in a small separate building by itself, the observations being made from without. An inspection of the drawing shows that by turning the levelling screw L it is possible to bring the line joining R and R' more and more into a vertical position, and that when this has been accomplished the pendulum will be con- trolled only by the torsion of the suspension springs. In practice this state of things is never actually realized, but may be closely approximated to, so that by the extreme sen- sitiveness to attraction of this instrument it becomes possible to obtain measures of the masses and distances of the sun and moon, ex- pressed in units of the mass and semi-diameter of the earth. Zollner has also suggested that since this pendulum obeys the action of the sun, or moves with it, it may in this way be possible to determine whether the pendulum keeps accurate pace with the apparent motion of the sun ; that is, whether the attraction of gravitation requires time for propagation. Thus, for example, if it is found practicable to determine the position of the pendulum when on the meridian accurately to a minute of time, this would furnish the astronomer with a means of measuring the velocity of gravitation, even if it were eight times as great as that of light. Up to the present time he has published only a few observations made with his apparatus ; the most important were taken on the evening of Sept. 18, 1870, from 6h. 35m. to lOh. 35m. ; during the first hour the pendulum moved over 2 T 8 scale divi- sions, and during the remaining three hours over 3 T V In these observations the gravity com- ponent was still considerable, the pendulum consuming only 14'44 seconds for one oscilla- tion ; still they point to an important future for the new instrument, and prove incidentally that with it even in its present state it is pos- sible to observe a change in level as small as T1 i_ Tr of a second of arc, an achievement the magnitude of which becomes evident when we remember that with the best spirit level one can barely estimate T V of a second. ^ Vibra- tions are a source of great difficulty in using this instrument, and in the experiments above referred to prevented Zollner from rendering it more sensitive ; as he remarks, observations of this character would best be conducted un- der the surface of the earth, as in a mine, where the temperature would remain constant, and the support be free from tremors; so that, paradoxical as it at first sight may appear, it really is possible to have a useful subterranean astronomical observatory. As Zollner was in the act of printing his first description of the horizontal pendulum, he found that an instru- ment of the same kind had been described ten years previously by a French physicist, M. Per-
