On the distribution of the error of an interpolated value, and on the construction of tables

Before the introduction of interpolation formulae, beyond linear interpolation by proportional parts, the presentation of the numerical values of mathematical functions was much restricted, for the labour of computation and the cost of printing, to say nothing of the inconvenience of handling a bulky volume, had to be increased quite disproportionately with every increase in accuracy. A four-figure logarithm table occupies two small pages, Chambers's seven-figure table takes 150 pages, while Vega's ten figure table requires 300 pages twelve inches long.