We discuss whether the torsion balance can again become a key tool for geophysical prospecting. We outline the acknowledged disadvantages of the Eötvös torsion balance and seek designs of a torsion balance beam that would enable the torsion balance to be used on moving platforms. A key result is that torsion balance beams designed to be insensitive to the curvature and horizontal gradients of the gravity field are insensitive to the angular motion of the platform about horizontal axes. We suggest that a double torsion balance using these balance beam designs could be used on moving platforms. We point out that second gradients of the gravitational field (third derivatives of the potential) can be determined with reasonable sensitivity with current technology. We describe double torsion balance schemes where the mass, range, and azimuth of localized mass anomalies could be estimated or where local anomalies could be rejected using information from the second gravity gradient.