the surface may be exactly calculated. The time required for the vibration of the pendulum is, in consequence of the same law, longer at heights above, shorter at points below the surface of the earth, than at the surface itself; hence it is easy to calculate the time of an oscillation at any given elevation. It is necessary, however, in order that the time calculated in this manner may agree with the result actually observed, that the surface of the earth at the given point shall be plane, and form part of an exact sphere. Mountains near the place of observation cause the attraction on the ball to be stronger than is contemplated in the calculation, and make the oscillations more rapid. The difference between the calculated and observed rate of oscillation will give the amount of influence which the mountain exerts. From this, the relative masses of the mountain and the earth being known, the mean density of the earth may be calculated by a series of formulas similar to those by which it is computed in the method just described. This method is liable to the same defects as the former one; that is, that the elements of the mountain on which the calculations are based are estimated, not accurately measured.
Carlini, Biot, and Matthieu employed it in 1824, Carlini selecting Mont Cenis as his point of observation, the other philosophers performing their experiments at Bordeaux. Their calculations gave a mean density of 4·83. Two other philosophers, Julius and E. Schmidt, calculating from the same observations, obtained, the former 4·95, the latter 4·84. Adopting a converse method from that of Carlini, Drobish, in 1826, measured the duration of the oscillations of the pendulum in a mining-shaft at Dolcoath, in Cornwall, and obtained 5·43.
Determination by Means of the Torsion Balance.—The torsion balance employed in measuring the density of the earth consists
of a straight rod a b (Fig. 3) of as uniform dimensions as possible, made of wood or metal, hanging by the cord c d, and supporting at its ends the balls a and b. A small mirror at d, in the middle of the