HKB
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, Gunter, and Lamb introduced other contrivances, applicable to trigonometry; Gunter's scale being still in common use. The calculating machines of Gersten and Pascal were of a different kind, working out arithmetical calculations by means of trains of wheels and other arrangements; and that contrived by Lord Stanhope for the purpose of verifying his calculations with respect to the National Debt was of like character. But none of these will bear for a moment to be compared with the machine designed by Mr. Babbage for performing arithmetical calculations and mathematical analyses, as well as for recording the calculations when made, thereby getting rid entirely of individual error in the operations of calculation, transcription, and printing.
The French government, in their desire to promote the extension of the decimal system, had ordered the construction of logarithmical tables of vast extent; but the great labour and expense involved in the undertaking prevented the design from being carried out. It was reserved for Mr. Babbage to develope the idea by means of a machine which he called the Difference Engine. This machine is of so complicated a character that it would be impossible for us to give any intelligible description of it in words. Although Dr. Lardner was unrivalled in the art of describing mechanism, he occupied twenty-five pages of the 'Edinburgh Review' (vol.59) in endeavouring to describe its action, and there were several features in it which he gave up as hopeless. Some parts of the apparatus and modes of action are indeed extraordinary and perhaps none more so than that for ensuring accuracy in the calculated results,--the machine actually correcting itself, and rubbing itself back into accuracy, when the disposition to err occurs, by the friction of the adjacent machinery! When an error is made, the wheels become locked and refuse to proceed; thus the machine must go rightly or not at all,--an arrangement as nearly resembling volition as anything that brass and steel are likely to accomplish.