The book describes studies to determine the constant gravitation, mass and average density of the Earth. The first chapter describes the constant gravitation expressed in various systems of units. The second chapter begins with a statement of the idea of determining constant gravitation by means of torsional weights. The specific experiences of Cavendish, Reich, Bailey, Boyce, Etvesh, Brown, Hale, and Khrzhanovsky. are described below. The following chapter is devoted to the consideration of the weights experiments carried out by Yolly, Poynting, Rihartz and Krigar-Menzel. The fourth chapter contains a description of some of the original ideas of the experiences, both realized and unfulfilled. The fifth chapter of the book contains the theory of nonlinear oscillations in relation to the problem of determining the constant gravitation.