On Interpolation, Summation and the Adjustment of Numerical Tables

The three heads, into which it has been found expedient to divide the general subject of the present paper, all relate to the consideration of a series of numerical quantities which are supposed to represent, either accurately or approximately, some known or implied law which necessarily has an influence in regulating their progression. Assuming that we only know the values of certain terms of the series of quantities, distributed at stated equidistant intervals, it has been shown that all the intermediate or absent terms are most accurately and expeditiously determined by the process of interpolation, already discussed and practically developed.