The Eötvös “Tour de Force”

Abstract

MAY I add to my article in NATURE of March 21, on the revolving balance of Baron Eötvös, that the method lends itself to determine the mass of the earth, or, more directly, the Newtonian constant of gravitation, with the same simplicity as it does to find the rotation of the earth. For this purpose it is merely necessary to place a large mass above the balance, say at the north end, and below the balance at the south end. Then if the direction of rotation is such that the north end is moving in the same direction as the earth the gravitational couple will act in the same direction as the 4 Vv difference of centrifugal force, whereas if it turns in the opposite direction, the gravitational couple will be opposed to the centrifugal couple. If the large masses of radius c are spherical and are made of material of density d, and the fictitious distances of their centres vertically above and below the small masses at the ends of the balance-arms are also equal to c, the arm lengths being r, then the time of rotation necessary to make the one action equal to the other is given by the equation—