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。