The excellence of Mr. Clement's tools, and his well-known skill in designing and executing work requiring unusual accuracy and finish, led to his being employed by Mr. Babbage to make his celebrated Calculating or Difference Engine. The contrivance of a machine that should work out complicated sums in arithmetic with perfect precision, was, as may readily be imagined, one of the most difficult feats of the mechanical intellect. To do this was in an especial sense to stamp matter with the impress of mind, and render it subservient to the highest thinking faculty. Attempts had been made at an early period to perform arithmetical calculations by mechanical aids more rapidly and precisely than it was possible to do by the operations of the individual mind. The preparation of arithmetical tables of high numbers involved a vast deal of labour, and even with the greatest care errors were unavoidable and numerous. Thus in a multipltcation-table prepared by a man so eminent as Dr. Hutton for the Board of Longitude, no fewer than forty errors were discovered in a single page taken at random. In the tables of the Nautical Almanac, where the greatest possible precision was desirable and necessary, more than five hundred errors were detected by one person; and the Tables of the Board of Longitude were found equally incorrect. But such errors were impossible to be avoided so long as the ordinary modes of calculating, transcribing, and printing continued in use. The earliest and simplest form of calculating apparatus was that employed by the schoolboys of ancient Greece, called the Abacus; consisting of a smooth board with a narrow rim, on which they were taught to compute by means of progressive rows of pebbles, bits of bone or ivory, or pieces of silver coin, used as counters. The same board, strewn over with sand, was used for teaching the rudiments of writing and the principles of geometry. The Romans subsequently adopted the Abacus, dividing it by means of perpendicular lines or bars, and from the designation of calculus which they gave to each pebble or counter employed on the board, we have derived our English word to calculate. The same instrument continued to be employed during the middle ages, and the table used by the English Court of Exchequer was but a modified form of the Greek Abacus, the chequered lines across it giving the designation to the Court, which still survives. Tallies, from the French word tailler to cut, were another of the mechanical methods employed to record computations, though in a very rude way. Step by step improvements were made; the most important being that invented by Napier of Merchiston, the inventor of logarithms, commonly called Napier's bones, consisting of a number of rods divided into ten equal squares and numbered, so that the whole when placed together formed the common multiplication table. By these means various operations in multiplication and division were performed. Sir Samuel Morland,