The gravitational constant G is the least-well measured fundamental constant in Nature. Several recent determinations have not reduced the uncertainty, and some measurements are in severe disagreement with the accepted value. Among others, the most common characteristic of the experiments performed is the fact that the ?source' masses of the measured gravitational field are much larger then the ?test' masses. So far, no report on the determination of G for interaction between commensurable masses can be found in the literature. Over the last few years in Hungary, a very simple but highly sensitive method has been developed for investigating gravity by using relatively large physical pendulum. This new measuring system is readily applicable to the study of the gravitational interaction between equal or nearly equal masses. From such experiments, it has become obvious that the gravitational force is nearly proportional to the difference between the interacting masses. Particularly, we have observed a well-defined minimum in the gravitational interaction energy of two equal masses.