now THE EARTH IS WEIGHED, 



747 



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 oscilla- 

 tion at any given elevation. It is necessary, however, in order that the 

 time calculated in this manner may agree with the result actually ob- 

 served, 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 ob- 

 servation cause the attraction on the ball to be stronger than is con- 

 templated 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 formu- 

 las similar to those by which it is computed in the method just de- 

 scribed. 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 per- 

 forming 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 Car- 

 lini, Drobish, in 1826, measured the duration of the oscillations of 

 the pendulum in a mining-shaft at Dolcoath, in Cornwall, and ob- 

 tained 5*43. 



Determination by Means of the Torsion Balance. The tor- 

 sion balance employed in measuring the density of the earth consists 



Fig. 3. 



of a straight rod a h (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 h. A small mirror at d, in the middle of the 



