The essential character of all tabular aids to computation is, that the results of many operations are recorded in some systematic way for easy reference, and that thereby the computer is spared the toil of obtaining these results for himself.

In many cases this constitutes almost the whole advantage of the table. Thus when, instead of extracting the cube root of some number, we take it from a printed book, we are merely using another's labour. The gain to the calculating community is, that the oft-repeated extraction of the same root is avoided. We also gain by the facility of systematic calculation; the labour of computing a series of successive results being in general only a small fraction of that which would have attended the same work performed in a desultory manner.