In an earlier paper by one of the authors, it was pointed out that if the vertical component of a gravitational or magnetic field is known over a horizontal plane surface of sufficient extent, all other components and derivatives of the field can theoretically be calculated by surface integration of the vertical component. In this paper, examples are given to show that within certain limits such calculations are not only theoretically possible but practically so. Examples are given of the calculations of curvatures from observed gradients and of horizontal magnetic intensity from observed vertical intensity, and the calculated values are compared with those obtained by observation. Examples are also given, based on artificial data, of the calculation of plumb-line deflections from gravity and of the calculation of magnetic anomalies at a given elevation above the earth from data obtained at the surface. The purpose of these calculations is to demonstrate the nonindependence of the various derivatives of gravitational and magnetic potential.