instant CC' points to a fixed star, it continues to do so while the disc rotates, and thus appears to an observer to change its position relative to the surface of the earth; unless, indeed, the star be the pole star, in which case the observer will not notice any apparent change in its direction.

This instrument is called the " Gyroscope."

III.

THE DENSITY OF THE EARTH.

It is stated in the lectures, (page 222,) that if the law of universal gravitation be true, it is found (by a difficult mathematical investigation) that the attraction of the whole earth, considered as a sphere, on a body at its surface is the same as if the whole matter of the earth were collected at its centre. It is also found that the attraction of the earth on a body within its surface is the same as if the spherical shell situated between the body and the earth's surface were removed; or is the same as if all the matter situated nearer to the earth's centre than the body were collected at the centre, and all the matter situated at a greater distance were removed.

If the earth were of uniform density throughout, it would follow from these propositions that the force

of gravity at the bottom of a mine would be less than the force at the top. To shew this, suppose that the mine reached half-way to the centre of the earth. Then (since the volumes of spheres vary as the cubes of their diameters) the quantity of matter nearer to the earth's centre than the bottom of the mine would be only one-eighth of the whole quantity of matter in the earth. But the attraction of a quantity of matter at the earth's centre would be more powerful on a body at the bottom of a mine than on one at the top, in the inverse ratio of the squares of the distances of the bodies from the earth's centre that is in the present case in the ratio of four to one. Hence the attraction on a body at the bottom of the mine would be, on the whole, less than the attraction on a body on the top in the ratio of one to two.

If, however, the earth be not of uniform density, but its density increase towards the centre, then though the attracting mass which acts on a body at the bottom of the mine be smaller, yet the diminution in the force of gravity so occasioned may be more than compensated by the comparative nearness of the attracted body to the denser parts of the earth. From the two laws of the attraction of spheres, which have been stated above, it is possible to calculate the ratio which the force of gravity at the bottom of the mine would bear to that at the top on any supposition we choose to make as to the ratio which subsists between the mean density of the earth and the density of the surface; so that if we know one ratio we can immediately infer the other. Now, pendulum observations afford us the means of determining the force of gravity at any place, (page 248,) and therefore, if the times of vibration of a

pendulum at the top and bottom of a mine be found, the ratio of the force of gravity at the top to that at the bottom may be calculated, and thence the ratio of the mean density of the earth to that of its surface.

This mode of determining the mean density was put in practice by the Astronomer Royal, at the Harton Coal Pit, near South Shields, in the year 1854. The mean density deduced from his observations is 6.565: a value considerably exceeding that found from the Schehallien and Cavendish experi

ments.

THE END.

INDEX.