h, 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 improvemen