Horizontal Pendulum, an instrument for measuring very weak attractive or repulsive forces; it can also be used for measuring slight changes of level, or minute variations in the dimensions of solid bodies. It combines the advantages of the ordinary pendulum with those of the torsion balance. The former instrument may be considered as a one-armed lever, which is retained in a vertical position by the attraction of gravitation; when acted on by an attractive or repulsive force in any except a vertical direction, it tends to be deflected from its normal position, and if the force be sufficiently powerful, an actual change of position will be observed. But this deflection can be accomplished only by lifting the pendulum bodily through a distance measured by the versed sine of the arc of deflection, and it is this fact which deprives the ordinary pendulum of sensitiveness to the action of weak attractive or repulsive forces. On the other hand, the ordinary pendulum obeys equally well a force emanating from a point in its immediate neighborhood, and that of one proceeding from an infinite distance, provided only these forces are virtually equal with respect to it; in other words, the distance of the point from which the force emanates exercises no effect on the final action, except to weaken it in direct proportion to the square of the distance.

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 absolutely 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 opposed, will neutralize each other, and no effect will be observed. - The horizontal pendulum combines the advantages of the ordinary pendulum and of the torsion balance. Let R R represent an inflexible rod of steel placed horizontally, and supported at its extremities by pivots on which it turns freely, and let W be a weight inflexibly attached 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 constitute an ordinary pendulum.

If now an attractive 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 sufficiently 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 component will diminish, and finally become zero when R R is vertical, and consequently A W horizontal. Zollner has shown experimentally how this may be accomplished to an almost incredible extent, so that an apparatus of this general nature in his hands became capable of obeying even the feeble attractive force of the moon. Fig. 2 represents Zollner's horizontal pendulum. At W is the weight, the inflexible rod being replaced by fine steel wire or watch spring, stretched as shown on the vertical column 0 0, the whole being supported by a tripod provided with levelling screws. P is a counterpoise, and M a mirror for reflecting the divisions of a distant scale to a telescope, together constituting an arrangement for magnifying the motion of the pendulum.

The apparatus 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 controlled 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 sensitiveness to attraction of this instrument it becomes possible to obtain measures of the masses and distances of the sun and moon, expressed 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 8/10 scale divisions, and during the remaining three hours over 3 9/10. In these observations the gravity component was still considerable, the pendulum consuming only 14.44 seconds for one oscillation; still they point to an important future for the new instrument, and prove incidentally that with it even in its present state it is possible to observe a change in level as small as 1/1000 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 1/10 of a second.

Vibrations 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 under 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 instrument of the same kind had been described ten years previously by a French physicist, M. Perrot, in the Comptes rendus; and further investigation brought to light the curious fact that as far back as 1832 a German, Lorenz Hengler, subsequently a Catholic priest, had not only invented and described the horizontal pendulum in Dingler's PolytechniscJies Journal, but had also made with it a series of observations on the attractive force of the moon.

This publication attracted no attention owing to the backward condition of physical astronomy at that period, and was soon entirely forgotten. - The writer of this article, by suitable alterations and additions, has converted the horizontal pendulum into an instrument of unprecedented delicacy for measuring minute changes in the dimensions of solid bodies. By the application of braces the natural tendency of Zollner's instrument to vibrate has been greatly reduced, and it has been provided with a means of bringing the pendulum to rest without friction; spring stops, an index, and micrometer have also been added, and the size diminished. The reach of the most powerful microscope is hardly more than 1/150,000 of an inch, and the best mechanical means scarcely reach beyond 1/200,000 of an inch,but in a set of linear determinations made with this modified pendulum, the probable error of the measurements proved to be only 1/36,204,000 of an inch. - For further details, see Poggendorff's Annalen for November, 1873, and the " American Journal of Science" for June, 1875.

Fig. 1.

Fig. 2. - Zollner's Horizontal Pendulum.