“IbegantoattendtheSchoolofArtatDarlingtononthe6thofMarch，1872。Ifound，onattemptingtodraw，thatIhadnaturallyacorrecteyeandhand；andImadesuchprogress，thatwhenthestudents’drawingswereexamined，previouslytosendingthemuptoSouthKensington，allmyworkwasapproved。Iwasthensettodrawfromthecastinchalk，althoughIhadonlybeenattheschoolforamonth。ItriedforallthefoursubjectsattheMayexamination，andwasfortunateenoughtopassthreeofthem，andobtainedasaprizePackett’s’Sciography。’Iworkedhardduringthenextyear，andsentupseventeenworks；foroneofthese，the’VenusdeMilo，’Igainedastudentship。
“Ithencommencedthestudyofhumananatomy，andbeganwater-colourpainting，readingalltheworksuponartonwhichI
couldlaymyhand。AttheMayexaminationof1873，Icompletedmysecond-gradecertificate，andattheendoftheyearofmystudentship，IacceptedtheofficeofteacherintheSchoolofArt。Thisart-trainingcreatedinmeasortofdisgustforphotography，asIsawthatthescienceofphotographyhadreallyverylittlegenuineartinit，andwasmorealliedtoamechanicalpursuitthantoanartisticone。Now，whenIlookbackonmypastideas，Iclearlyseethatagreatdealofthisdisgustwasduetomyignoranceandself-conceit。
“In1874，Icommencedpaintingintempora，andtheninoil，copyingthepictureslenttotheschoolfromtheSouthKensingtonArtLibrary。Iworkedalsofromstilllife，andbegansketchingfromnatureinoilandwater-colours，sometimessellingmyworktohelpmetobuymaterialsforart-workandscientificexperiments。Iwas，however，abletodoverylittleinthefollowingyear，asIwasathomesufferingfromsciatica。ForninemonthsIcouldnotstanderect，buthadtohobbleaboutwithastick。Thisillnesscausedmetogiveupmyteachership。
“Earlyin1876IreturnedtoDarlington。Iwentonwithmyartstudiesandthescienceofchemistry；thoughIwentnofurtherinheliochromy。Ipushedforwardwithanatomy。IsentaboutfifteenworkstoSouthKensington，andgainedasmythird-gradeprizeinlistAthe’DictionaryofTermsusedinArt’byThomasFairholt，whichIfoundaveryusefulwork。Towardstheendoftheyear，myfather，whosehealthwasdeclining，sentformehometoassisthimintheschool。InowcommencedthestudyofAlgebraandEuclidingoodearnest，butfoundittoughwork。Myfather，thoughafairmathematician，wasunabletogivemeanyinstruction；forhehadbeenseizedwithparalysis，fromwhichheneverrecovered。Beforehedied，herecommendedmetotryforaschoolmaster’scertificate；andIpromisedhimthatIwould。I
obtainedasituationasmasterofasmallvillageschool，notunderGovernmentinspection；andIstudiedduringtheyear，andobtainedasecondclasscertificateattheDurhamDiocesanCollegeatChristmas，1877。Earlyinthefollowingyear，theschoolwasplacedunderGovernmentinspection，andbecamealittlemoreremunerative。
“Inowwentonwithchemicalanalysis，makingmyownapparatus。
Requiringanintenseheatonasmallscale，Iinventedafurnacethatburntpetroleumoil。Itwasblownbycompressedair。Aftermanyfailures，Ieventuallysucceededinbringingittosuchperfectionthatin71/2minutesitwouldbringfourouncesofsteelintoaperfectlyliquefiedstate。Inextcommencedthestudyofelectricityandmagnetism；andthenacoustics，light，andheat。Iconstructedallmyapparatusmyself，andacquiredtheartofglass-blowing，inordertomakemyownchemicalapparatus，andthussaveexpense。
“IthenwentonwithAlgebraandEuclid，andtookupplanetrigonometry；butIdevotedmostofmytimetoelectricityandmagnetism。Iconstructedvariousscientificapparatus——asyren，telephones，microphones，anEdison’smegaphone，aswellasanelectrometer，andamachineforcoveringelectricwirewithcottonorsilk。Afriendhavinglentmeaworkonartificialmemory，Ibegantostudyit；buttheworkledmeintonothingbutconfusion，andIsoonfoundthatifIdidnotgiveitup，I
shouldbeleftwithnomemoryatall。IstillwentansketchingfromNature，notsomuchasastudy，butasameansofrecruitingmyhealth，whichwasfarfrombeinggood。Atthebeginningof1881IobtainedmypresentsituationasassistantmasterattheYorebridgeGrammarSchool，ofwhichtheRev。W。Balderston，M。A。，isprincipal。
“SoonafterIbecamesettledhere，IspentsomeofmyleisuretimeinreadingEmerson’s’Optics，’aworkIboughtatanoldbookstall。Iwasnotverysuccessfulwithit，owingtomydeficientmathematicalknowledge。OntheMayScienceExaminationsof1881takingplaceatNewcastle-on-Tyne，appliedforpermissiontosit，andobtainedfourticketsforthefollowingsubjects:——Mathematics，ElectricityandMagnetism，Acoustics，LightandHeat，andPhysiography。DuringtheprecedingmonthIhadreadupthefirstthreesubjects，but，beingpressedfortime，Igaveuptheideaoftakingphysiography。However，onthelastnightoftheexaminations，I
hadsomeconversationwithoneofthestudentsastothesubjectsrequiredforphysiography。Hesaid，’Youwantalittleknowledgeofeverythinginascientificway，andnothingmuchofanything。’
Ideterminedtotry，for’nothingmuchofanything’suitedmeexactly。Iroseearlynextmorning，andassoonastheshopswereopenIwentandboughtabookonthesubject，’OutlinesofPhysiography，’byW。Lawson，F。R。G。S。Ireaditallday，andatnightsatfortheexamination。Theresultsofmyexaminationswere，failureinmathematics，butsecondclassadvancedgradecertificatesinalltheothers。Idonotattachanycredittopassinginphysiography，butmerelyrelatethecircumstanceascuriouslyshowingwhatcanbedonebyagood’cram。’
“Thefailureinmathematicscausedmetotakethesubject’bythehorns，’toseewhatIcoulddowithit。Ibeganbygoingoverquadraticequations，andIgraduallysolvedthewholeofthosegiveninTodhunter’slarger’Algebra。’ThenIre-readtheprogressions，permutations，combinations；thebinomialtheorem，withindicesandsurds；thelogarithmictheoremandseries，converginganddiverging。IgotTodhunter’slarger’PlaneTrigonometry，’andreadit，withthetheoremscontainedinit；
thenhis’SphericalTrigonometry；’his’AnalyticalGeometry，ofTwoDimensions，’and’Conics。’InextobtainedDeMorgan’s’DifferentialandIntegralCalculus，’thenWoolhouse’s，andlastly，Todhunter’s。Ifoundthisdepartmentofmathematicsdifficultandperplexingtothelastdegree；butImastereditsufficientlytoturnittosomeaccount。Thislastmathematicalcourserepresentseighteenmonthsofhardwork，andIoftensatupthewholenightthrough。Oneresultoftheapplicationwasapermanentinjurytomysight。
“Wantingsomeobjectonwhichtoapplymynewly-acquiredmathematicalknowledge，Ideterminedtoconstructanastronomicaltelescope。IgotAiry’s’GeometricalOptics，’andreaditthrough。ThenIsearchedthroughallmyEnglishMechanicascientificpaperthatItake，andpreparedformyworkbyreadingalltheliteratureonthesubjectthatIcouldobtain。I
boughttwodiscsofglass，of61/2inchesdiameter，andbegantogrindthemtoasphericalcurve12feetradius。Igotthemhollowedout，butfailedinfiningthemthroughlackofskill。
Thisoccurredsixtimesinsuccession；butattheseventhtimethepolishcameupbeautifully，withscarcelyascratchuponthesurface。Stoppingmyworkonenight，anditbeingstarlight，I
thoughtIwouldtrythemirroronastar。Ihadawoodenframereadyforthepurpose，whichthecarpenterhadmadeforme。
JudgeofmysurpriseanddelightwhenIfoundthatthestardiscenlargednearlyinthesamemannerfromeachsideofthefocalpoint，thusmakingitextremelyprobablethatIhadaccidentallyhitonanearapproachtotheparabolainthecurveofmymirror。
Andsuchprovedtobethecase。Ihavethemirrorstill，anditsperformanceisverygoodindeed。
“Iwentnofurtherwiththismirror，forfearorspoilingit。Itisveryslightlygreyinthecentre，butnotsufficientlysoastomateriallyinjureitsperformance。Imounteditinawoodentube，placeditonawoodenstand，anduseditforatimethusmounted；butgettingdisgustedwiththetremorandinconvenienceIhadtoputupwith，Iresolvedtoconstructforitanironequatorialstand。Imademypatterns，gotthemcast，turnedandfittedthemmyself，grindingalltheworkingpartstogetherwithemeryandoil，andfittedatangent-screwmotiontodrivetheinstrumentinrightascension。NowIfoundtheinstrumentapleasuretouse；andIdeterminedtoaddtoitdividedcircles，andtoaccuratelyadjustittothemeridian。Imademycirclesofwell-seasonedmahogany，withslipsofpaperontheiredges，dividingthemwithmydrawinginstruments，andvarnishingthemtokeepoutthewet。IshallneverforgetthatsunnyafternoonuponwhichIcomputedthehour-angleforJupiter，andsettheinstrumentsothatbycalculationJupitershouldpassthroughthefieldoftheinstrumentat1h。25m。15s。Withmywatchinmyhand，andmyeyetotheeye-piece，Iwaitedfortheorb。Whenhisgloriousfaceappeared，almostinadirectlineforthecentreofthefield，Icouldnotcontainmyjoy，butshoutedoutasloudlyasIcould，——greatlytotheastonishmentofoldGeorgeJohnson，themiller，whohappenedtobeinthefieldwhereIhadplantedmystand！
“Now，thoughIhadobtainedwhatIwanted——afairlygoodinstrument，——stillIwasnotquitesatisfied；asIhadproduceditbyafortunatechance，andnotbyskillalone。Ithereforesettoworkagainontheotherdiscofglass，totryifIcouldfinishitinsuchawayastoexcelthefirstone。Afternearlyayear’sworkIfoundthatIcouldonlysucceedinequallingit。
Butthen，duringthistime，Ihadremovedtheworkingofmirrorsfrommerechancetoafairamountofcertainty。Bybringingmymathematicalknowledgetobearonthesubject，Ihaddevisedamethodoftestingandmeasuringmyworkwhich，Iamhappytosay，hasbeenfairlysuccessful，andhasenabledmetoproducethespherical，elliptic，parabolic，orhyperboliccurveinmymirrors，withalmostunvaryingsuccess。Thestudyofthepracticalworkingofspeculaandlenseshasalsoabsorbedagooddealofmysparetimeduringthelasttwoyears，andtheworkinvolvedhasbeenscarcelylessdifficult。Altogether，I
considerthislastyear1882-3tomarkthebusiestperiodofmylife。
“ItwillbeobservedthatIhaveonlygivenanaccountofthosebranchesofstudyinwhichIhaveputtopracticaltestthedeductionsfromtheoreticalreasoning。Iamatpresentengagedonthetheoryoftheachromaticobject-glass，withregardtosphericalchromatism——asubjectuponwhich，Ibelieve，nearlyallourtext-booksaresilent，butoneneverthelessofvitalimportancetotheoptician。Icanonlyproceedveryslowlywithit，onaccountofhavingtogrindandfigurelensesforeverystepofthetheory，tokeepmyselfintherighttrack；asmeretheorizingisapttoleadoneverymuchastray，unlessitbecheckedbyconstantexperiment。Forthisparticularsubject，lensesmustbegroundfirstlytospherical，andthentocurvesofconicsections，soastoeliminatesphericalaberrationfromeachlens；sothatitwillbeobservedthatthissubjectisnotwithoutitsdifficulties。
“AboutamonthagoSeptember，1883，Ideterminedtoputtothetestthestatementofsomeofourtheorists，thatthesurfaceofarotatingfluidiseitheraparabolaorahyperbola。Ifoundbyexperimentthatitisneither，butanapproximationtothetractrixamodificationofthecatenary，ifanythingdefinite；
asindeedone，onthinkingoverthematter，mightfeelcertainitwouldbe——thetractrixbeingthecurveofleastfriction。
“Inastronomy，Ihavereallydoneverylittlebeyondmerealgebraicalworkingofthefundamentaltheorems，andalittlecasualobservationofthetelescope。Sofar，Imustown，Ihavetakenmorepleasureinthetheoryandconstructionofthetelescope，thaninitsuse。“
SuchisSamuelLancaster’shistoryofthegrowthanddevelopmentofhismind。Idonotthinkthereisanythingmoreinterestinginthe’PursuitofKnowledgeunderDifficulties。’Hislifehasbeenagallantendeavourtowinfurtherknowledge，thoughtoomuchattheexpenseofaconstitutionoriginallydelicate。Hepursuessciencewithpatienceanddetermination，andwooestruthwiththeardourofalover。Eulogyofhischaracterwouldherebeunnecessary；but，ifhetakesduecareofhishealth，weshallhearmoreofhim。[11]
Moreastronomersinhumblelife！Thereseemstotobenoendofthem。Theremustbeagreatfascinationinlookinguptotheheavens，andseeingthosewondrousworldscareeringinthefar-offinfinite。LetmelookbacktothenamesIhaveintroducedinthischapterofautobiography。First，therewasmyworthyporterfriendatCouparAngusstation，enjoyinghimselfwithhisthree-inchobject-glass。Thentherewastheshoemakerandteacher，andeventuallythefirst-ratemakerofachromaticinstruments。Lookalsoatthepersonswhomhesuppliedwithhisbesttelescopes。Amongthemwefindprinces，baronets，clergymen，professors，doctors，solicitors，manufacturers，andinventors。Thenwecometotheportraitpainter，whoacquiredthehighestsupremacyintheartoftelescopemaking；thentoMr。
Lassell，theretiredbrewer，whosedaughterspresentedhisinstrumenttothenation；and，lastly，totheextraordinaryyoungschoolmasterofBainbridge，inYorkshire。AndnowbeforeI