Geometrical geodesy, which was based on astronomical-geodetic methods, could give information only concerning the external form of the figure of the earth. The gravimetric methods of physical geodesy, in conjunction with methods such as those of seismology, enable scientists to test hypotheses concerning the internal structure of the earth. Heiskanen and Vening Meinesz summarize the present-day achievements of the gravimetric method of physical geodesy by stating[113] that it alone can give: 1. The flattening of the reference ellipsoid. 2. The undulations N of the geoid. 3. The components of the deflection of the vertical [xi] and [eta] at any point, oceans and islands included. 4. The conversion of existing geodetic systems to the same world geodetic system. 5. The reduction of triangulation base lines from the geoid to the reference ellipsoid. 6. The correction of errors in triangulation in mountainous regions due to the effect of the deflections of the vertical. 7. Geophysical applications of gravity measurements, e.g., the isostatic study of the earth's interior and the exploration of oil fields and ore deposits. With astronomical observations or with existing triangulations, the gravimetric method can accomplish further results. Heiskanen and Vening Meinesz state: It is the firm conviction of the authors that the gravimetric method is by far the best of the existing methods for solving the main problems of geodesy, i.e., to determine the shape of the geoid on the continents as well as at sea and to convert the existing geodetic systems to the world geodetic system. It can also give invaluable help in the computation of the reference ellipsoid.[114] Summary Since the creation of classical mechanics in the 17th century, the pendulum has been a basic instrument for the determination of the intensity of gravity, which is expressed as the acceleration of a freely falling body. Basis of theory is the simple pendulum, whose time of swing under gravity is proportional to the square root of the length divided by the acceleration due to gravity. Since the length of a simple pendulum divided by the square of its time of swing is equal to the length of a pendulum that beats seconds, the intensity of gravity also has been expressed in terms of the length of the seconds pendulum. The reversible compound pendulum has served for the absolute determination of gravity by means of a theory developed by Huygens. Invariable compound pendulums with single axes also have been used to determine relative values of gravity by comparative times of swing.