the mountain at N and S would have been about

part of gravity. But the observed sum of effects was 12 seconds, which corresponds to part of gravity. Hence the density of the mountain is only about of the earth's mean density; or the earth's mean density is nearly double of the mountain's density. The nature of the rocks composing the mountain was carefully examined, and their density as compared with that of water was ascertained; and thus the mean density of the earth was found to be something less than five times the density of water : a result agreeing nearly with that found from the assumption of the law of density of the earth's strata, connected with the observed variation of gravity, and observed ellipticity.

This was the nature of the celebrated Schehallien experiment, which was so extremely creditable to the parties by whom it was promoted and undertaken, and so important in its results.

After this another set of experiments was made; first by Mr. Henry Cavendish, a rich man, much attached to science, and who made many important contributions to chemistry, and other branches of natural philosophy (from whom the experiment of which I am speaking received the name of the Cavendish Experiment); afterwards by a Dr. Reich; and finally, in a very much more complete way, by Mr. Francis Baily, as the active member of a committee of the Astronomical Society of London, to whom funds were supplied by the British Government. It is an experiment of a different kind—a sort of domestic experiment-one of those experiments which can be made in your own observing rooms at home, and which are, in many respects, preferable to those made on the hill sides of Scotland.

The shape in which the apparatus is represented in Figure 64, is that in which it was used by Mr. Baily. There are two small balls A,B, (generally

about two inches in diameter,) carried on a rod ACB, suspended by a single wire DE, or by two wires at a small distance from each other. By means of a telescope, the positions of these balls were observed from a distance. It was of the utmost consequence that the observer should not go near, not only to prevent his shaking the apparatus, but also because the warmth of the body would create currents of air that would disturb everything very much, even though the balls were enclosed in double boxes, lined with gilt paper, to prevent as much as possible the influence of such currents. When the position of the small balls had been observed, large balls of lead F,G, about twelve inches in diameter, which moved upon a turning frame, were brought near to them; but still they were separated from each other

by half-a-dozen thicknesses of deal boxes, so that no effect could be produced except by the attraction of the large balls. Observations were then made to see how much these smaller balls were attracted out of their places by the large ones. By another movement of the turning frame, the larger balls could be brought to the position HK. In every case, the motion of the small balls produced by the attraction of the larger ones, was undeniably apparent. The small balls were always put into a state of vibration by this attraction; then by observing the extreme distances to which they swing both ways, and taking the middle place between those extreme distances, we find the place at which the attraction of the large balls would hold them steady.

Suppose, now, the attraction of the large balls was found to pull the small balls an inch away from their former place of rest: then comes the question-what amount of dead pull does that show? The steps by which this is computed are curious.

First I must tell you that it has long been known (from experiment), that when a rod carrying balls is suspended in this manner by a wire, the space through which the balls will be pulled sideways is exactly in proportion to the force which pulls them sideways. In this respect, the law of forces acting on the suspended rod, is exactly similar to the law of forces acting sideways on a pendulum vibrating in a moderately small arc, for the motion of a pendulum is thus produced. If the pressure caused by the weight of the pendulum-bob, which acts vertically, is resolved into two parts, of which one part is in the direction of the pendulum rod, and the other acts sideways upon the pendulum, the former does not affect the movement of the pendulum at all, and the

latter, which produces the movement, is proportional to the distance of the pendulum from its place of rest, and therefore is similar in its law to the law of the force of twist of the suspending wire by which a rod with balls is supported (which force of twist is the same thing as the force which pulls the balls aside, because it exactly resists that force). Moreover, the force which acts sideways on the pendulumbob, is in the same proportion to the whole weight of the bob, as the displacement sideways is to the length of the pendulum. Now the length of a pendulum which vibrates in a second, is 39 139 inches; and for such a pendulum, if it is pulled one inch sideways, the dead pull sideways (as I have just explained) will be part of its weight and thus we know that, for any balls or other things which vibrate in one second, the dead pull sideways corresponding to an inch of displacement is part of their weight.

Then it is known as a general theorem regarding vibrations, that to make the vibrations twice as slow, we must have forces (for the same distances of displacement) four times as small; and so in proportion to the inverse square of the times of vibration. Thus if balls or anything else vibrate once in ten seconds, the dead pull sideways corresponding to an inch of displacement is of their weight. So that, in fact, all that we now want for our calculation, is the time of vibration of the suspended balls. This is very easily observed; and then on the principles already explained, there is no difficulty in computing the dead pull sideways corresponding to a sideways displacement of one inch; and then (by altering this in the proportion of the observed displacement, whatever it may be) the sideways dead pull or attraction

corresponding to any observed displacement is readily found. The delicacy of this method of observing and computing the attraction of the large balls may be judged from this circumstance: that the whole attraction amounted to only about 20,000,000 part of the weight of the small balls, and that the uncertainty in the measure of this very small quantity did not amount probably toor of the whole.

Then the next step was this: knowing the size of the large balls and their distances from the small balls in the experiment, and knowing also the size of the earth, and the distance of the small balls from the centre of the earth, we can calculate what would be the proportion of the attraction of the large balls on the small balls to the attraction of the earth on the small balls (that is the weight of the small balls), if the leaden balls had the same density as the mean density of the earth. It was found that this would produce a smaller attraction than that computed from the observations. Consequently, the mean density of the earth is less than the density of lead in the same proportion; and thus the mean density of the earth is found to be 5.67 times the density of water.

The near agreement of this result with that found from the Schehallien experiment, and that found from the theory of the figure of the earth, (taking the observed ellipticity of the earth in combination with such a law of density as would produce that ellipticity,) shows, beyond doubt, that the same law of gravitation which regulates the attraction of the sun upon the planets, and the attraction of the earth upon the moon, does also apply to the attraction of a leaden ball upon another ball within a foot of it. In regard to the slight difference of results, it is probable that the result of the Cavendish experiment is the more