The advent of high-speed digital computing machines requires extrapolation and interpolation methods which do not involve central differences and time-consuming tabular information. Extrapolation and interpolation formulae meeting these requirements are developed. These formulae are applicable to the desk calculator as well as to punched-card programming systems for electronic-digital computors. Some applications of the usefulness of these formulae are noted in connection with the preparation of gravity and magnetic maps. Their usefulness may likewise be extended to other types of geophysical and experimental data where the time required to obtain computed results is an economic factor.