The presence of an extra‐heavy (or light) body in the sub‐surface warps the level surfaces up (down) over the body and the lines of the vertical toward or into (away from) itself. The Eo¨tvo¨s torsion balance consists of a calibrated platinum‐iridium torsion wire which supports a beam of negligible weight; a weight is attached to one end of the beam and a second weight is suspended from the other end. Curvature of the level surfaces and curvature of the vertical each produce at the two weights horizontal components of gravity which are respectively equal and opposite in actual but the same in rotational direction. The torque produced by the curvature of the vertical is a function of the difference of the radii of curvature of the level surface in the directions of major and minor curvature. There has been only one slight important improvement of the torsion balance in the past twenty‐five years. There is room for improvement in the avoidance of temperature effects and in speeding up in the time necessary for observation. The mathematics of the torsion balance and of the gravitational effects of simple geometrical bodies is simple and developed. The main field of research with the torsion balance lies mainly in the geological‐geophysical field of interpretation, although there are still unsolved problems in the mathematics of interpretation.