Inthesameyear1828Mr。Clementbeganthemakingofflutedtapsanddies，andheestablishedamechanicalpracticewithreferencetothepitchofthescrew，whichprovedofthegreatestimportanceintheeconomicsofmanufacture。Beforehistime，eachmechanicalengineeradoptedathreadofhisown；sothatwhenapieceofworkcameunderrepair，thescrew-hobhadusuallytobedrilledout，andanewthreadwasintroducedaccordingtotheusagewhichprevailedintheshopinwhichtheworkwasexecuted。Mr。Clementsawagreatwasteoflabourinthispractice，andhepromulgatedtheideathateveryscrewofaparticularlengthoughttobefurnishedwithitsappointednumberofthreadsofasettledpitch。Takingtheinchasthebasisofhiscalculations，hedeterminedthenumberofthreadsineachcase；andthepracticethusinitiatedbyhim，recommendedasitwasbyconvenienceandeconomy，wasveryshortlyadoptedthroughoutthetrade。ItmaybementionedthatoneofClement’sablestjourneymen，Mr。Whitworth，has，sincehistime，beenmainlyinstrumentalinestablishingthesettledpractice；andWhitworth’sthreadinitiatedbyClementhasbecomerecognisedthroughoutthemechanicalworld。Tocarryouthisidea，Clementinventedhisscrew-enginelathe，withgearing，mandrill，andsliding-tablewheel-work，bymeansofwhichhefirstcuttheinsidescrew-toolsfromtheleft-handedhobs——thereversemodehavingbeforebeenadopted，——whileinshapingmachineshewasthefirsttousetherevolvingcutterattachedtothesliderest。Then，in1828，heflutedthetapsforthefirsttimewitharevolvingcutter，——othermakershavinguptothattimeonlynotchedthem。Amonghisotherinventionsinscrewsmaybementionedhisheadlesstap，which，accordingtoMr。
Nasmyth，issovaluableaninvention，that，”ifhehaddonenothingelse，itoughttoimmortalizehimamongmechanics。Itpassedrightthroughtheholetobetapped，andwasthusenabledtodothedutyofthreeordinaryscrews。”Bytheseimprovementsmuchgreaterprecisionwassecuredinthemanufactureoftoolsandmachinery，accompaniedbyagreatlyreducedcostofproduction；theresultsofwhicharefelttothisday。
AnotherofMr。Clement’singeniousinventionswashisPlaningMachine，bymeansofwhichmetalplatesoflargedimensionswereplanedwithperfecttruthandfinishedwithbeautifulaccuracy。Thereisperhapsscarcelyamachineaboutwhichtherehasbeenmorecontroversythanthis；andwedonotpretendtobeabletodeterminetherespectivemeritsofthemanyablemechanicswhohavehadahandinitsinvention。ItisexceedinglyprobablethatothersbesidesClementworkedouttheproblemintheirownway，byindependentmethods；andthisisconfirmedbythecircumstancethatthoughtheresultsachievedbytherespectiveinventorswerethesame，themethodsemployedbythemwereinmanyrespectsdifferent。AsregardsClement，wefindthatprevioustotheyear1820hehadamachineinregularuseforplaningthetriangularbarsoflathesandthesidesofweaving-looms。Thisinstrumentwasfoundsousefulandsoeconomicalinitsworking，thatClementproceededtoelaborateaplaningmachineofamorecompletekind，whichhefinishedandsettoworkintheyear1825。Hepreparednomodelofit，butmadeitdirectfromtheworkingdrawings；anditwassonicelyconstructed，thatwhenputtogetheritwentwithoutahitch，andhascontinuedsteadilyworkingformorethanthirtyyearsdowntothepresentday。
Clementtookoutnopatentforhisinvention，relyingforprotectionmainlyonhisownandhisworkmen’sskillinusingit。WethereforefindnospecificationofhismachineatthePatentOffice，asinthecaseofmostothercapitalinventions；butaverycompleteaccountofitistobefoundintheTransactionsoftheSocietyofArtsfor1832，asdescribedbyMr。Varley。ThepracticalvalueofthePlaningMachineinducedtheSocietytoapplytoMr。Clementforlibertytopublishafulldescriptionofit；andMr。Varley’spaperwastheresult。*
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TransactionsoftheSocietyfortheEncouragementofArts，vol。xlix。
p。157。
Itmaybebrieflystatedthatthisengineer’splanediffersgreatlyfromthecarpenter’splane，thecutterofwhichisonlyallowedtoprojectsofarastoadmitofathinshavingtobeslicedoff，——theplaneworkingflatinproportiontothewidthofthetool，anditslengthandstraightnesspreventingthecutterfromdescendingintoanyhollowsinthewood。Theengineer’splanemoreresemblestheturning-lathe，ofwhichindeeditisbutamodification，workinguponthesameprinciple，onflatsurfaces。ThetoolsorcuttersinClement’smachineweresimilartothoseusedinthelathe，varyinginlikemanner，butperformingtheirworkinrightlines，——thetoolbeingstationaryandtheworkmovingunderit，thetoolonlytravellingwhenmakinglateralcuts。Tosavetimetwocuttersweremounted，onetocuttheworkwhilegoing，theotherwhilereturning，bothbeingsoarrangedandheldastobepresentedtotheworkinthefirmestmanner，andwiththeleastpossiblefriction。Thebedofthemachine，onwhichtheworkwaslaid，passedunderthecuttersonperfectlytruerollersorwheels，lodgedandheldintheirbearingsasaccuratelyasthebestmandrillcouldbe，andhavingset-screwsactingagainsttheirendstotallypreventingallend-motion。Themachinewasbeddedonamassiveandsolidfoundationofmasonryinheavyblocks，thesupportatallpointsbeingsocompleteaseffectuallytodestroyalltendencytovibration，withtheobjectofsecuringfull，round，andquietcuts。Therollersonwhichtheplaning-machinetravelledweresotrue，thatClementhimselfusedtosayofthem，”Ifyouweretoputbutapapershavingunderoneoftherollers，itwouldatoncestopalltherest。”Norwasthisanyexaggeration——theentiremechanism，notwithstandingitsgreatsize，beingastrueandaccurateasthatofawatch。
Byaningeniousadaptationoftheapparatus，whichwillalsobefounddescribedintheSocietyofArtspaper，theplaningmachinemightbefittedwithalathe-bed，eithertoholdtwocentres，oraheadwithasuitablemandrill。Whensofitted，themachinewasenabledtodotheworkofaturning-lathe，thoughinadifferentway，cuttingcylindersorconesintheirlongitudinaldirectionperfectlystraight，aswellassolidsorprismsofanyangle，eitherbythelongitudinalorlateralmotionofthecutter；whilstbymakingtheworkrevolve，itmightbeturnedasinanyotherlathe。Thisingeniousmachine，ascontrivedbyMr。Clement，thereforerepresentedacompleteunionoftheturning-lathewiththeplaningmachineanddividingengine，bywhichturningofthemostcomplicatedkindmightreadilybeexecuted。
Fortenyearsafteritwassetinmotion，Clement’swastheonlymachineofthesortavailableforplaninglargework；andbeingconsequentlyverymuchinrequest，itwasoftenkeptgoingnightandday，——theearningsbytheplaningmachinealoneduringthattimeformingtheprincipalincomeofitsinventor。Asittookinapieceofworksixfeetsquare，andashischargeforplaningwasthree-halfpencethesquareinch，oreighteenshillingsthesquarefoot，hecouldthusearnbyhismachinealonesometenpoundsforeveryday’sworkoftwelvehours。Wemayaddthatsinceplaningmachinesinvariousformshavebecomecommoninmechanicalworkshops，thecostofplaningdoesnotamounttomorethanthree-halfpencethesquarefoot。
TheexcellenceofMr。Clement’stools，andhiswell-knownskillindesigningandexecutingworkrequiringunusualaccuracyandfinish，ledtohisbeingemployedbyMr。BabbagetomakehiscelebratedCalculatingorDifferenceEngine。Thecontrivanceofamachinethatshouldworkoutcomplicatedsumsinarithmeticwithperfectprecision，was，asmayreadilybeimagined，oneofthemostdifficultfeatsofthemechanicalintellect。Todothiswasinanespecialsensetostampmatterwiththeimpressofmind，andrenderitsubservienttothehighestthinkingfaculty。Attemptshadbeenmadeatanearlyperiodtoperformarithmeticalcalculationsbymechanicalaidsmorerapidlyandpreciselythanitwaspossibletodobytheoperationsoftheindividualmind。Thepreparationofarithmeticaltablesofhighnumbersinvolvedavastdealoflabour，andevenwiththegreatestcareerrorswereunavoidableandnumerous。Thusinamultipltcation-tablepreparedbyamansoeminentasDr。HuttonfortheBoardofLongitude，nofewerthanfortyerrorswerediscoveredinasinglepagetakenatrandom。InthetablesoftheNauticalAlmanac，wherethegreatestpossibleprecisionwasdesirableandnecessary，morethanfivehundrederrorsweredetectedbyoneperson；andtheTablesoftheBoardofLongitudewerefoundequallyincorrect。Butsucherrorswereimpossibletobeavoidedsolongastheordinarymodesofcalculating，transcribing，andprintingcontinuedinuse。
TheearliestandsimplestformofcalculatingapparatuswasthatemployedbytheschoolboysofancientGreece，calledtheAbacus；
consistingofasmoothboardwithanarrowrim，onwhichtheyweretaughttocomputebymeansofprogressiverowsofpebbles，bitsofboneorivory，orpiecesofsilvercoin，usedascounters。Thesameboard，strewnoverwithsand，wasusedforteachingtherudimentsofwritingandtheprinciplesofgeometry。TheRomanssubsequentlyadoptedtheAbacus，dividingitbymeansofperpendicularlinesorbars，andfromthedesignationofcalculuswhichtheygavetoeachpebbleorcounteremployedontheboard，wehavederivedourEnglishwordtocalculate。Thesameinstrumentcontinuedtobeemployedduringthemiddleages，andthetableusedbytheEnglishCourtofExchequerwasbutamodifiedformoftheGreekAbacus，thechequeredlinesacrossitgivingthedesignationtotheCourt，whichstillsurvives。Tallies，fromtheFrenchwordtaillertocut，wereanotherofthemechanicalmethodsemployedtorecordcomputations，thoughinaveryrudeway。Stepbystepimprovementsweremade；themostimportantbeingthatinventedbyNapierofMerchiston，theinventoroflogarithms，commonlycalledNapier’sbones，consistingofanumberofrodsdividedintotenequalsquaresandnumbered，sothatthewholewhenplacedtogetherformedthecommonmultiplicationtable。Bythesemeansvariousoperationsinmultiplicationanddivisionwereperformed。SirSamuelMorland，Gunter，andLambintroducedothercontrivances，applicabletotrigonometry；Gunter’sscalebeingstillincommonuse。ThecalculatingmachinesofGerstenandPascalwereofadifferentkind，workingoutarithmeticalcalculationsbymeansoftrainsofwheelsandotherarrangements；andthatcontrivedbyLordStanhopeforthepurposeofverifyinghiscalculationswithrespecttotheNationalDebtwasoflikecharacter。ButnoneofthesewillbearforamomenttobecomparedwiththemachinedesignedbyMr。
Babbageforperformingarithmeticalcalculationsandmathematicalanalyses，aswellasforrecordingthecalculationswhenmade，therebygettingridentirelyofindividualerrorintheoperationsofcalculation，transcription，andprinting。
TheFrenchgovernment，intheirdesiretopromotetheextensionofthedecimalsystem，hadorderedtheconstructionoflogarithmicaltablesofvastextent；butthegreatlabourandexpenseinvolvedintheundertakingpreventedthedesignfrombeingcarriedout。ItwasreservedforMr。BabbagetodevelopetheideabymeansofamachinewhichhecalledtheDifferenceEngine。Thismachineisofsocomplicatedacharacterthatitwouldbeimpossibleforustogiveanyintelligibledescriptionofitinwords。AlthoughDr。Lardnerwasunrivalledintheartofdescribingmechanism，heoccupiedtwenty-fivepagesofthe’EdinburghReview’vol。59inendeavouringtodescribeitsaction，andtherewereseveralfeaturesinitwhichhegaveupashopeless。Somepartsoftheapparatusandmodesofactionareindeedextraordinaryandperhapsnonemoresothanthatforensuringaccuracyinthecalculatedresults，——themachineactuallycorrectingitself，andrubbingitselfbackintoaccuracy，whenthedispositiontoerroccurs，bythefrictionoftheadjacentmachinery！Whenanerrorismade，thewheelsbecomelockedandrefusetoproceed；thusthemachinemustgorightlyornotatall，——anarrangementasnearlyresemblingvolitionasanythingthatbrassandsteelarelikelytoaccomplish。
ThisintricatesubjectwastakenupbyMr。Babbagein1821，whenheundertooktosuperintendfortheBritishgovernmenttheconstructionofamachineforcalculatingandprintingmathematicalandastronomicaltables。Themodelfirstconstructedtoillustratethenatureofhisinventionproducedfiguresattherateof44aminute。
In1823theRoyalSocietywasrequestedtoreportupontheinvention，andafterfullinquirythecommitteerecommendeditasonehighlydeservingofpublicencouragement。Asumof1500L。wasthenplacedatMr。Babbage’sdisposalbytheLordsoftheTreasuryforthepurposeofenablinghimtoperfecthisinvention。ItwasatthistimethatheengagedMr。Clementasdraughtsmanandmechanictoembodyhisideasinaworkingmachine。Numeroustoolswereexpresslycontrivedbythelatterforexecutingtheseveralparts，andworkmenwerespeciallyeducatedforthepurposeofusingthem。Someideaoftheelaboratecharacterofthedrawingsmaybeformedfromthefactthatthoserequiredforthecalculatingmachineryalone——nottomentiontheprintingmachinery，whichwasalmostequallyelaborate——coverednotlessthanfourhundredsquarefeetofsurface！Thecostofexecutingthecalculatingmachinewasofcourseverygreat，andtheprogressoftheworkwasnecessarilyslow。Theconsequencewasthatthegovernmentfirstbecameimpatient，andthenbegantogrumbleattheexpense。Attheendofsevenyearstheengineer’sbillsalonewerefoundtoamounttonearly7200L。，andMr。Babbage’scostsoutofpocketto7000L。more。Inordertomakemoresatisfactoryprogress，itwasdeterminedtoremovetheworkstotheneighbourhoodofMr。
Babbage’sownresidence；butasClement’sclaimsforconductingtheoperationsinthenewpremiseswerethoughtexorbitant，andashehimselfconsideredthattheworkdidnotyieldhimtheaverageprofitofordinaryemploymentinhisowntrade，heeventuallywithdrewfromtheenterprise，takingwithhimthetoolswhichhehadconstructedforexecutingthemachine。Thegovernmentalsoshortlyafterwithdrewfromit，andfromthattimetheschemewassuspended，theCalculatingEngineremainingabeautifulbutunfinishedfragmentofagreatwork。
Thoughoriginallyintendedtogoasfarastwentyfigures，itwasonlycompletedtotheextentofbeingcapableofcalculatingtothedepthoffivefigures，andtwoordersofdifferences；andonlyasmallpartoftheproposedprintingmachinerywasevermade。TheenginewasplacedinthemuseumofKing’sCollegein1843，enclosedinaglasscase，untiltheyear1862，whenitwasremovedforatimetotheGreatExhibition，whereitformedperhapsthemostremarkableandbeautifullyexecutedpieceofmechanismthecombinedresultofintellectualandmechanicalcontrivance——intheentirecollection。*
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Acompleteaccountofthecalculatingmachine，aswellasofananalyticalengineafterwardscontrivedbyMr。Babbage，ofstillgreaterpowerthantheother，willbefoundintheBibliothequeUniverselledeGeneve，ofwhichatranslationintoEnglish，withcopiousoriginalnotes，bythelateLadyLovelace，daughterofLordByron，waspublishedinthe3rdvol。ofTaylor’sScientificMemoirsLondon，1843。Ahistoryofthemachine，andofthecircumstancesconnectedwithitsconstruction，willalsobefoundinWeld’sHistoryoftheRoyalSociety，vol。ii。369-391。Itremainstobeadded，thattheperusalbyMessrs。ScheutzofStockholmofDr。Lardner’saccountofMr。Babbage’sengineintheEdinburghReview，ledthoseclevermechanicstoenterupontheschemeofconstructingandcompletingit，andtheresultis，thattheirmachinenotonlycalculatesthetables，butprintstheresults。Ittookthemnearlytwentyyearstoperfectit，butwhencompletedthemachineseemedtobealmostcapableofthinking。TheoriginalwasexhibitedattheParisExhibitionof1855。
AcopyofithassincebeensecuredbytheEnglishgovernmentatacostof1200L。，anditisnowbusilyemployedatSomersetHouseinworkingoutannuityandothertablesfortheRegistrar-General。Thecopywasconstructed，withseveraladmirableimprovements，bytheMessrs。Donkin，thewell-knownmechanicalengineers，aftertheworkingdrawingsoftheMessrs。Scheutz。