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HISTORY OF PHYSICAL ASTRONOMY.

approximation to the truth which has yet been arrived at by philosophers *.It is remarkable that Newton conjectured that the mean density of theearth is about five or six times the density of waterf.

The Schehallien experiment for determining the mean density of theearth is purely statical; on the other hand, the experiment with thetorsion balance is founded on dynamical principles, being in fact a case ofthe horizontal pendulum. The vertical pendulum has also been em-ployed for a similar purpose. The attraction on the top of a highmountain may be decomposed into two parts; one of which is theattraction at the level of the sea diminished in the inverse ratio of thesquare of the distance, and the other is the attraction of the mountainitself. Hence, if the intensities of gravity on the mountain and at the levelof the sea be determined by observation, the difference of the two forceswill indicate the attraction due to the mountain, and, by a process similarto that employed in the Schehallien experiment, we shall be enabled toascertain the mean density of the earth. Experiments for this purposewere made by Carlini at the hospice of Mount Cenis, which has anelevation of 6375 feet above the level of the sea; and the conclusion atwhich he arrived was that the mean density of the earth is 4.39, that ofwater being unity.

We have mentioned already that D’Alembert succeeded in accountingcompletely for the motion of the earth’s axis in space, arising from the actionof the sun and moon upon the redundant matter accumulated round the equa-tor. It still remained, however, for geometers to ascertain whether the dis-turbing forces affected the position of the axis relative to the surface of theterrestrial spheroid, or whether they occasioned any change in the velocityof rotation. Observation, indeed, gave a negative answer to both of thesequestions; for neither the latitudes of places on the earth’s surface northe length of the day appeared to have undergone any variation from theearliest period of history. It was desirable, however, to establish thesefacts by demonstrative reasoning founded on the theory of gravitation;for, in the absence of such conclusive evidence, there existed no groundsfor supposing that the position of the axis and the velocity of rotationmight not he affected by secular inequalities, which, though slow in theirdevelopement, would in the lapse of ages become sensible by continualaccumulation. If the axis experienced any such displacement, theposition of the equator would be constantly shifting with inconceivableslowness, and the sea, by always flowing towards the new position torestore the equilibrium of the particles, would eventually occasion a totalchange in the relation of land and water on the earth’s surface. It isclear also that the latitudes of places would be ultimately affected by thedisplacement, and hence would ensue a corresponding alteration of theseasons. Poisson first examined this point with all the attention due toits importance. In an admirable paper, which was published in the

* Notwithstanding all the precautions used by Mr. Baily, he found that the restingpoints of the balls and the times of oscillation were subject to disturbances, the cause ofwhich he was unable to explain. In the Philosophical Transactions for 1847, there is apaper by Mr. Herne, of the Royal Military College of Sandhurst, in which he attemptsto account for these anomalies by the supposition of a magnetic state of the masses andballs.

t Verisimile est quod copia materiae totius in Terra quasi quintuplo vel sextuplo major sitquam sit tota ex aqua constaret.—Princip., lib. iii. prop. 10.