Viewing the infinite extent and variety of the tables which have been calculated and printed, from the earliest periods of human civilisation to the present time, we feel embarrassed with the difficulties of the task which we have imposed on ourselves;--that of attempting to convey to readers unaccustomed to such speculations, any thing approaching to an adequate idea of them. These tables are connected with the various sciences, with almost every department of the useful arts, with commerce in all its relations; but above all, with Astronomy and Navigation. So important have they been considered, that in many instances large sums have been appropriated by the most enlightened nations in the production of them; and yet so numerous and insurmountable have been the difficulties attending the attainment of this end, that after all, even navigators, putting aside every other department of art and science, have, until very recently, been scantily and imperfectly supplied with the tables indispensably necessary to determine their position at sea. The first class of tables which naturally present themselves, are those of Multiplication. A great variety of extensive multiplication tables have been published from an early period in different countries; and especially tables of _Powers_, in which a number is multiplied by itself successively. In Dodson's _Calculator_ we find a table of multiplication extending as far as 10 times 1000.[2] In 1775, a still more extensive table was published to 10 times 10,000. The Board of Longitude subsequently employed the late Dr Hutton to calculate and print various numerical tables, and among others, a multiplication table extending as far as 100 times 1000; tables of the squares of numbers, as far as 25,400; tables of cubes, and of the first ten powers of numbers, as far as 100.[3] In 1814, Professor Barlow, of Woolwich, published, in an octavo volume, the squares, cubes, square roots, cube roots, and reciprocals of all numbers from 1 to 10,000; a table of the first ten powers of all numbers from 1 to 100, and of the fourth and fifth powers of all numbers from 100 to 1000. [Footnote 2: Dodson's _Calculator_. 4to. London: 1747.] [Footnote 3: Hutton's _Tables of Products and Powers_. Folio. London; 1781.]