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heavy blocks； the support at all points being so complete as
effectually to destroy all tendency to vibration； with the object of
securing full； round； and quiet cuts。 The rollers on which the
planing…machine travelled were so true； that Clement himself used to
say of them； 〃If you were to put but a paper shaving under one of the
rollers； it would at once stop all the rest。〃 Nor was this any
exaggerationthe entire mechanism； notwithstanding its great size；
being as true and accurate as that of a watch。
By an ingenious adaptation of the apparatus； which will also be found
described in the Society of Arts paper； the planing machine might be
fitted with a lathe…bed； either to hold two centres； or a head with a
suitable mandrill。 When so fitted； the machine was enabled to do the
work of a turning…lathe； though in a different way； cutting cylinders
or cones in their longitudinal direction perfectly straight； as well
as solids or prisms of any angle； either by the longitudinal or
lateral motion of the cutter； whilst by making the work revolve； it
might be turned as in any other lathe。 This ingenious machine； as
contrived by Mr。 Clement； therefore represented a complete union of
the turning…lathe with the planing machine and dividing engine； by
which turning of the most complicated kind might readily be executed。
For ten years after it was set in motion； Clement's was the only
machine of the sort available for planing large work； and being
consequently very much in request； it was often kept going night and
day；the earnings by the planing machine alone during that time
forming the principal income of its inventor。 As it took in a piece
of work six feet square； and as his charge for planing was
three…halfpence the square inch； or eighteen shillings the square
foot； he could thus earn by his machine alone some ten pounds for
every day's work of twelve hours。 We may add that since planing
machines in various forms have become common in mechanical workshops；
the cost of planing does not amount to more than three…halfpence the
square foot。
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； 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。
This intricate subject was taken up by Mr。 Babbage in 1821； when he
undertook to superintend for the British government the construction
of a machine for calculating and printing mathematical and
astronomical tables。 The model first constructed to illustrate the
nature of his invention produced figures at the rate of 44 a minute。
In 1823 the Royal Society was requested to report upon the invention；
and after full inquiry the committee recommended it as one highly
deserving of public encouragement。 A sum of 1500L。 was then placed at
Mr。 Babbage's disposal by the Lords of the Treasury for the purpose
of enabling him to perfect his invention。 It was at this time that he
engaged Mr。 Clement as draughtsman and mechanic to embody his ideas
in a working machine。 Numerous tools were expressly contrived by the
latter for executing the several parts； and workmen were specially
educated for the purpose of using them。 Some idea of the elaborate
character of the drawings may be formed from the fact that those
required for the calculating machinery alonenot to mention the
printing machinery； which was almost equally elaboratecovered not
less than four hundred square feet of surface！ The cost of executing
the calculating machine was of course very great； and the progress of
the work was necessarily slow。 The consequence was that the
government first became impatient； and then began to grumble at the
expense。 At the end of seven years the engineer's bills alone were
found to amount to nearly 7200L。； and Mr。 Babbage's costs out of
pocket to 7000L。 more。 In order to make more satisfactory progress；
it was determined to remove the works to the neighbourhood of Mr。
Babbage's own residence； but as Clement's claims for conducting the
operations in the new premises