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