deter:\iinatiox of the mean density of the earth 

 by means of a pendulum principle. 



By J. WiLSING. 



Translated and condensed by Prof. J. Howard Gore, Ph. D.* 



Four different methods have been used in the deteruiinafciou of the 

 mean density of the earth. The* first is based upon the measurement 

 of the deflection of the plumb-line in the ueij^hborhood of great mount- 

 ain masses; the second upon the determination of the length of the 

 second's pendulum at various distances from the earth's center. Accord- 

 ing to the third and fourth methods, the attraction of a body of known 

 mass, usually of a globular shape, is ascertained by means of the torsion 

 balance, or directly with an ordinary balance and compared with the 

 constants of gravity. 



The first attempts towards the solution of this problem were by Mas- 

 kelyue, receiving a new discussion at the hand of Hutton a few years 

 later. Maskelyne's results depended upon the measurement of the de- 

 flection of the plumb line caused by the attraction of Schehallien, in 

 connection with an approximated value for the density of the moun- 

 tain. This estimated density, derived from the superficial strata alone, 

 was so subject to uncertainties that the result can be regarded as 

 nothing more than a rough approximation. Later and more general 

 investigations have shown that local deflection may arise from a variety 

 of co-existing or conspiring causes, so that the attraction of elevations can 

 be accounted for by the presence of depressions or interior defects in 

 the earth's mass. In such a case, a value for the attracting mass which 

 is deduced from the exterior configuration alone, must lead to incorrect 

 results. Similar objections can be a])plied to the method of pendulum 

 swinging, which was made use of by Carlini and Airy, and more recently 

 by von Sterneck and Albrecht. 



Hence the invention by Coulomb of the torsion balance and its ap- 

 plication by Cavendish to the problem in question marked a great 

 advance towards its accurate solution. The great sensitiveness of this 

 instrument makes its possible to render measurable the attraction of 

 balls of a lew hundredweight, the mass of which can easily be ascer- 



* From Publicationea des astropLysikalischea Observatoriums zu Potsdam, vol. 

 VI, Potsdam, 1887, 1888. 



635 



