Two random error grids were prepared using a set of 111 balls marked according to the Gaussian normal error law. For these grids, considered as grids of errors in gravity data, the second derivative values were computed and contoured. The resulting maps show strikingly the dangers in uncritical interpretations of second derivative maps based on insufficiently accurate data. Statistical checks were applied both to the random error grids and to the computed second derivative values. The check on the latter necessitated the development of a theory of the correlation between second derivative values which is also applicable to many other quantities, besides second derivatives, which are computed by coefficients.