1。Mydesignistoshewthemannerwhereinweperceivebysightthedistance，magnitude，andsituationofobjects。Alsotoconsiderthedifferencethereisbetwixttheideasofsightandtouch，andwhethertherebeanyideacommontobothsenses。
2。Itis，Ithink，agreedbyallthatdistance，ofitselfandimmediately，cannotbeseen。FordistancebeingaLinedirectedend—wisetotheeye，itprojectsonlyonepointinthefundoftheeye，whichpointremainsinvariablythesame，whetherthedistancebelongerorshorter。
3。Ifinditalsoacknowledgedthattheestimatewemakeofthedistanceofobjectsconsiderablyremoteisratheranactofjudgmentgroundedonexperiencethanofsense。Forexample，whenIperceiveagreatnumberofintermediateobjects，suchashouses，fields，rivers，andthelike，whichIhaveexperiencedtotakeupaconsiderablespace，IthenceformajudgmentorconclusionthattheobjectIseebeyondthemisatagreatdistance。
Again，whenanobjectappearsfaintandsmall，whichataneardistanceIhaveexperiencedtomakeavigorousandlargeappearance，Iinstantlyconcludeittobefaroff：Andthis，’tisevident，istheresultofexperience；
withoutwhich，fromthefaintnessandlittlenessIshouldnothaveinferredanythingconcerningthedistanceofobjects。
4。Butwhenanobjectisplacedatsonearadistanceasthattheintervalbetweentheeyesbearsanysensibleproportiontoit，theopinionofspeculativemenisthatthetwoopticaxes（thefancythatweseeonlywithoneeyeatoncebeingexploded）concurringattheobjectdotheremakeanangle，bymeansofwhich，accordingasitisgreaterorlesser，theobjectisperceivedtobenearerorfartheroff。[1]
5。Betwixtwhichandtheforegoingmannerofestimatingdistancethereisthisremarkabledifference：thatwhereastherewasnoapparent，necessaryconnexionbetweensmalldistanceandalargeandstrongappearance，orbetweengreatdistanceandalittleandfaintappearance，thereappearsaverynecessaryconnexionbetweenanobtuseangleandneardistance，andanacuteangleandfartherdistance。Itdoesnotintheleastdependuponexperience，butmaybeevidentlyknownbyanyonebeforehehadexperiencedit，thatthenearertheconcurrenceoftheopticaxes，thegreatertheangle，andtheremotertheirconcurrenceis，thelesserwillbetheanglecomprehendedbythem。
6。Thereisanotherwaymentionedbyopticwriters，wherebytheywillhaveusjudgeofthosedistances，inrespectofwhichthebreadthofthepupilhathanysensiblebigness：Andthatisthegreaterorlesserdivergencyoftherays，whichissuingfromthevisiblepointdofallonthepupil，thatpointbeingjudgednearestwhichisseenbymostdivergingrays，andthatremoterwhichisseenbylessdivergingrays：andsoon，theapparentdistancestillincreasing，asthedivergencyoftheraysdecreases，tillatlengthitbecomesinfinite，whentheraysthatfallonthepupilaretosenseparallel。Andafterthismanneritissaidweperceivedistancewhenwelookonlywithoneeye。
7。Inthiscasealsoitisplainwearenotbeholdingtoexperience：
itbeingacertain，necessarytruththatthenearerthedirectraysfallingontheeyeapproachtoaparallelism，thefartheroffisthepointoftheirintersection，orthevisiblepointfromwhencetheyflow。
8。Nowthoughtheaccountsheregivenofperceivingneardistancebysightarereceivedfortrue，andaccordinglymadeuseofindeterminingtheapparentplacesofobjects，theydoneverthelessseemveryunsatisfactory：
andthatforthesefollowingreasons。
9。Itisevidentthatwhenthemindperceivesanyidea，notimmediatelyandofitself，itmustbebythemeansofsomeotheridea。Thus，forinstance，thepassionswhichareinthemindofanotherareofthemselvestomeinvisible。
Imayneverthelessperceivethembysight，thoughnotimmediately，yetbymeansofthecolourstheyproduceinthecountenance。Weoftenseeshameorfearinthelooksofaman，byperceivingthechangesofhiscountenancetoredorpale。
10。Moreoveritisevidentthatnoideawhichisnotitselfperceivedcanbethemeansofperceivinganyotheridea。IfIdonotperceivetherednessorpalenessofaman’sfacethemselves，itisimpossibleIshouldperceivebythemthepassionswhichareinhismind。
11。Nowfromsect。2itisplainthatdistanceisinitsownnatureimperceptible，andyetitisperceivedbysight。Itremains，therefore，thatitbebroughtintoviewbymeansofsomeotherideathatisitselfimmediatelyperceivedintheactofvision。
I2。Butthoselinesandangles，bymeanswhereofsomemenpretendtoexplaintheperceptionofdistance，arethemselvesnotatallperceived，noraretheyintrutheverthoughtofbythoseunskilfulinoptics。Iappealtoanyone’sexperiencewhetheruponsightofanobjecthecomputesitsdistancebythebignessoftheanglemadebythemeetingofthetwoopticaxes？Orwhetherheeverthinksofthegreaterorlesserdivergencyoftherays，whicharrivefromanypointtohispupil？Everyoneishimselfthebestjudgeofwhatheperceives，andwhatnot。invainshallanymantellmevariousideasofdistance，solongasImyselfamconsciousofnosuchthing。
13。Since，therefore，thoseanglesandlinesarenotthemselvesperceivedbysight，itfollowsfromsect。10thattheminddothnotbythemjudgeofthedistanceofobjects。
14。Thetruthofthisassertionwillbeyetfartherevidenttoanyonethatconsidersthoselinesandangleshavenorealexistenceinnature，beingonlyanhypothesisframedbythemathematicians，andbythemintroducedintooptics，thattheymighttreatofthatscienceinageometricalway。
15。ThelastreasonIshallgiveforrejectingthatdoctrineis，thatthoughweshouldgranttherealexistenceofthoseopticangles，etc。，andthatitwaspossibleforthemindtoperceivethem，yettheseprincipleswouldnotbefoundsufficienttoexplainthephenomenaofdistance，asshallbeshewnhereafter。
16。Now，itbeingalreadyshewnthatdistanceissuggestedtothemindbythemediationofsomeotherideawhichisitselfperceivedintheactofseeing，itremainsthatweinquirewhatideasorsensationstherebethatattendvision，untowhichwemaysupposetheideasofdistanceareconnected，andbywhichtheyareintroducedintothemind。Andfirst，itiscertainbyexperiencethatwhenwelookatanearobjectwithbotheyes，accordingasitapproachesorrecedesfromus，wealterthedispositionofoureyes，bylesseningorwideningtheintervalbetweenthepupils。Thisdispositionorturnoftheeyesisattendedwithasensation，whichseemstometobethatwhichinthiscasebringstheideaofgreaterorlesserdistanceintothemind。
17。Notthatthereisanynaturalornecessaryconnexionbetweenthesensationweperceivebytheturnoftheeyesandgreaterorlesserdistance，butbecausethemindhasbyconstantexperiencefoundthedifferentsensationscorrespondingtothedifferentdispositionsoftheeyestobeattendedeachwithadifferentdegreeofdistanceintheobject，therehasgrownanhabitualorcustomaryconnexionbetweenthosetwosortsofideas，sothatthemindnosoonerperceivesthesensationarisingfromthedifferentturnitgivestheeyes，Inordertobringthepupilsnearerorfartherasunder，butitwithalperceivesthedifferentideaofdistancewhichwaswonttobeconnectedwiththatsensation；justasuponhearingacertainsound，theideaisimmediatelysuggestedtotheunderstandingwhichcustomhadunitedwithit。
18NordoIseehowIcaneasilybemistakeninthismatter。Iknowevidentlythatdistanceisnotperceivedofitself。Thatbyconsequenceitmustbeperceivedbymeansofsomeotherideawhichisimmediatelyperceived，andvarieswiththedifferentdegreesofdistance。Iknowalsothatthesensationarisingfromtheturnoftheeyesisofitselfimmediatelyperceived，andvariousdegreesthereofareconnectedwithdifferentdistances，whichneverfailtoaccompanythemintomymind，whenIviewanobjectdistinctlywithbotheyes，whosedistanceissosmallthatinrespectofittheintervalbetweentheeyeshasanyconsiderablemagnitude。
19。Iknowitisareceivedopinionthatbyalteringthedispositionoftheeyesthemindperceiveswhethertheangleoftheopticaxesorthelateralanglescomprehendedbetweentheintervaloftheeyesandtheopticaxesaremadegreaterorlesser；andthataccordinglybyakindofnaturalgeometryitjudgesthepointoftheirintersectiontobenearerorfartheroff。ButthatthisisnottrueIamconvincedbymyownexperience，sinceIamnotconsciousthatImakeanysuchuseoftheperceptionIhavebytheturnofmyeyes。Andformetomakethosejudgments，anddrawthoseconclusionsfromit，withoutknowingthatIdoso，seemsaltogetherincomprehensible。
20。Fromallwhichitfollowsthatthejudgmentwemakeofthedistanceofanobject，viewedwithbotheyes，isentirelytheresultofexperience。
Ifwehadnotconstantlyfoundcertainsensationsarisingfromthevariousdispositionoftheeyes，attendedwithcertaindegreesofdistance，weshouldnevermakethosesuddenjudgmentsfromthemconcerningthedistanceofobjects；nomorethanwewouldpretendtojudgeaman’sthoughtsbyhispronouncingwordswehadneverheardbefore。
21。Secondly，anobjectplacedatacertaindistancefromtheeye，towhichthebreadthofthepupilbearsaconsiderableproportion，beingmadetoapproach，isseenmoreconfusedly：andtheneareritisbroughtthemoreconfusedappearanceitmakes。Andthisbeingfoundconstantlytobeso，therearisethinthemindanhabitualconnexionbetweentheseveraldegreesofconfusionanddistance；thegreaterconfusionstillimplyingthelesserdistance，andthelesserconfusionthegreaterdistanceoftheobject。
22。Thisconfusedappearanceoftheobjectdoththereforeseemtobethemediumwherebythemindjudgethofdistanceinthosecaseswhereinthemostapprovedwritersofopticswillhaveitjudgebythedifferentdivergencywithwhichtheraysflowingfromtheradiatingpointfallonthepupil。Noman，Ibelieve，willpretendtoseeorfeelthoseimaginaryanglesthattheraysaresupposedtoformaccordingtotheirvariousinclinationsonhiseye。Buthecannotchooseseeingwhethertheobjectappearmoreorlessconfused。Itisthereforeamanifestconsequencefromwhatbathbeendemonstrated，thatinsteadofthegreaterorlesser—divergencyoftherays，themindmakesuseofthegreaterorlesserconfusednessoftheappearance，therebytodeterminetheapparentplaceofanobject。
23Nordothitavailtosaythereisnotanynecessaryconnexionbetweenconfusedvisionanddistance，greatorsmall。ForIaskanymanwhatnecessaryconnexionheseesbetweentherednessofablushandshame？Andyetnosoonershallhebeholdthatcolourtoariseinthefaceofanother，butitbringsintohisandtheideaofthatpassionwhichhathbeenobservedtoaccompanyit。
24。Whatseemstohavemisledthewritersofopticsinthismatteristhattheyimaginemenjudgeofdistanceastheydoofaconclusioninmathematics，betwixtwhichandthepremisesitisindeedabsolutelyrequisitetherebeanapparent，necessaryconnexion：butitisfarotherwiseinthesuddenjudgmentsmenmakeofdistance。Wearenottothinkthatbrutesandchildren，orevengrownreasonablemen，whenevertheyperceiveanobjecttoapproach，ordepartfromthem，doitbyvirtueofgeometryanddemonstration。
25。Thatoneideamaysuggestanothertotheminditwillsufficethattheyhavebeenobservedtogotogether，withoutanydemonstrationofthenecessityoftheircoexistence，orwithoutsomuchasknowingwhatitisthatmakesthemsotocoexist。Ofthisthereareinnumerableinstancesofwhichnoonecanbeignorant。
26。Thus，greaterconfusionhavingbeenconstantlyattendedwithnearerdistance，nosooneristheformerideaperceived，butitsuggeststhelattertoourthoughts。AndifithadbeentheordinarycourseofNaturethatthefartheroffanobjectwereplaced，themoreconfuseditshouldappear，itiscertaintheverysameperceptionthatnowmakesusthinkanobjectapproacheswouldthenhavemadeustoimagineitwentfartheroff。Thatperception，abstractingfromcustomandexperience，beingequallyfittedtoproducetheideaofgreatdistance，orsmalldistance，ornodistanceatall。
27。Thirdly，anobjectbeingplacedatthedistanceabovespecified，andbroughtnearertotheeye，wemayneverthelessprevent，atleastforsometime，theappearancesgrowingmoreconfused，bystrainingtheeye。
Inwhichcasethatsensationsuppliestheplaceofconfusedvisioninaidingthemindtojudgeofthedistanceoftheobject；itbeingesteemedsomuchthenearerbyhowmuchtheeffortorstrainingoftheeyeinordertodistinctvisionisgreater。
28。Ihaveheresetdownthosesensationsorideasthatseemtobetheconstantandgeneraloccasionsofintroducingintothemindthedifferentideasofneardistance。Itistrueinmostcasesthatdiversothercircumstancescontributetoframeourideaofdistance，towit，theparticularnumber，size，kind，etc。，ofthethingsseen。Concerningwhich，aswellasallothertheforementionedoccasionswhichsuggestdistance，Ishallonlyobservetheyhavenoneofthem，intheirownnature，anyrelationorconnexionwithit：norisitpossibletheyshouldeversignifythevariousdegreesthereof，otherwisethanasbyexperiencetheyhavebeenfoundtobeconnectedwiththem。
29。Ishallproceedupontheseprinciplestoaccountforaphenomenonwhichhashithertostrangelypuzzledthewritersofoptics，andissofarfrombeingaccountedforbyanyoftheirtheoriesofvisionthatitis，bytheirownconfession，plainlyrepugnanttothem；andofconsequence，ifnothingelsecouldbeobjected，werealonesufficienttobringtheircreditinquestion。ThewholedifficultyIshalllaybeforeyouinthewordsofthelearnedDr。Barrow，withwhichheconcludeshisopticlectures。
’Ihaveheredeliveredwhatmythoughtshavesuggestedtomeconcerningthatpartofopticswhichismoreproperlymathematical。Asfortheotherpartsofthatscience（whichbeingratherphysical，doconsequentlyaboundwithplausibleconjecturesinsteadofcertainprinciples），therehasinthemscarceanythingoccur’dtomyobservationdifferentfromwhathasbeenalreadysaidbyKepler，Scheinerus，Descartes，andothers。Andmethinks，Ihadbettersaynothingatall），thanrepeatthatwhichhasbeensooftensaidbyothers。Ithinkitthereforehightimetotakemyleaveofthissubject：butbeforeIquititforgoodandall，thefairandingenuousdealingthatIowebothtoyouandtotruthobligethmetoacquaintyouwithacertainuntowarddifficulty，whichseemsdirectlyoppositetothedoctrineIhavebeenhithertoinculcating，atleast，admitsofnosolutionfromit。Inshortitisthis。BeforethedoubleconvexglassorconcavespeculumEBF，letthepointAbeplacedatsuchadistancethattheraysproceedingfromA，afterrefractionorreflexion，bebroughttounitesomewhereintheAxAB。Andsupposethepointofunion（i。e。theimageofthepointA，ashathbeenalreadysetforth）tobeZ；betweenwhichandB，thevertexoftheglassorspeculum，conceivetheeyetobeanywhereplaced。Thequestionnowis，wherethepointAoughttoappear？ExperienceshewsthatitdoesnotappearbehindatthepointZ，anditwerecontrarytonaturethatitshould，sincealltheimpressionwhichaffectsthesensecomesfromtowardsA。Butfromourtenetsitshouldseemtofollowthatitwouldappearbeforetheeyeatavastdistanceoff，sogreatasshouldinsomesortsurpassallsensibledistance。Forsinceifweexcludeallanticipationsandprejudices，everyobjectappearsbysomuchthefartheroff，byhowmuchtheraysitsendstotheeyearelessdiverging。Andthatobjectisthoughttobemostremotefromwhichparallelraysproceeduntotheeye。Reasonwouldmakeonethinkthatobjectshouldappearatyetagreaterdistancewhichisseenbyconvergingrays。MoreoveritmayingeneralbeaskedconcerningthiscasewhatitisthatdeterminestheapparentplaceofthepointA，andmakethittoappearafteraconstantmannersometimesnearer，atothertimesfartheroff？TowhichdoubtIseenothingthatcanbeansweredagreeabletotheprincipleswehavelaiddownexceptonlythatthepointAoughtalwaystoappearextremelyremote。ButonthecontraryweareassuredbyexperiencethatthepointAappearsvariouslydistant，accordingtothedifferentsituationsoftheeyebetweenthepointsBandZ。Andthatitdothnever（ifatall）seemfartheroff，thanitwouldifitwerebeheldbythenakedeye，butonthecontraryitdothsometimesappearmuchnearer。
Nay，itisevencertainthatbyhowmuchtheraysfallingontheeyedomoreconvergebysomuchthenearerdoththeobjectseemtoapproach。FortheeyebeingplacedclosetothepointB，theobjectAappearsnearlyinitsownnaturalplace，ifthepointBistakenintheglass，oratthesamedistance，ifinthespeculum。TheeyebeingbroughtbacktoO，theobjectseemstodrawnear：andbeingcometoPitbeholdsitstillnearer。
Andsoonlittleandlittle，tillatlengththeeyebeingplacedsomewhere，supposeatQ，theobjectappearingextremelynear，beginstovanishintomereconfusion。Allwhichdothseemrepugnanttoourprinciples，atleastnotrightlytoagreewiththem。Norisourtenetalonestruckatbythisexperiment，butlikewiseallothersthatevercametomyknowledgeare，everywhitasmuch，endangeredbyit。Theancientoneespecially（whichismostcommonlyreceived，andcomesnearesttomine）seemstobesoeffectuallyoverthrowntherebythatthemostlearnedTacquethasbeenforcedtorejectthatprinciple，asfalseanduncertain，onwhichalonehehadbuiltalmosthiswholeCatoptrics；andconsequentlybytakingawaythefoundation，hathhimselfpulleddownthesuperstructurehehadraisedonit。Which，nevertheless，Idonotbelievehewouldhavedonehadhebutconsideredthewholemattermorethoroughly，andexaminedthedifficultytothebottom。
Butasforme，neitherthisnoranyotherdifficultyshallhavesogreataninfluenceonmeastomakemerenouncethatwhichIknowtobemanifestlyagreeabletoreason：especiallywhen，asitherefallsout，thedifficultyisfoundedinthepeculiarnatureofacertainoddandparticularcase。
Forinthepresentcasesomethingpeculiarlieshid，whichbeinginvolvedinthesubtiltyofnaturewill，perhaps，hardlybediscoveredtillsuchtimeasthemannerofvisionismoreperfectlymadeknown。Concerningwhich，Imustown，Ihavehithertobeenabletofindoutnothingthathastheleastshewofprobability，nottomentioncertainty。Ishall，therefore，leavethisknottobeuntiedbyyou，wishingyoumayhavebettersuccessinitthanIhavehad。’
30。Theancientandreceivedprinciple，whichDr。BarrowherementionsasthemainfoundationofTacquet’sCatoptrics，isthat：everyvisiblepointseenbyreflexionfromaspeculumshallappearplacedattheintersectionofthereflectedray，andtheperpendicularofincidence。Whichintersectioninthepresentcase，happeningtobebehindtheeye，itgreatlyshakestheauthorityofthatprinciple，whereontheaforementionedauthorproceedsthroughouthiswholeCatoptricsindeterminingtheapparentplaceofobjectsseenbyreflexionfromanykindofspeculum。
31。Letusnowseehowthisphenomenonagreeswithourtenets。TheeyetheneareritisplacedtothepointBintheforegoingfigures，themoredistinctistheappearanceoftheobject；butasitrecedestoOtheappearancegrowsmoreconfused；andatPitseestheobjectyetmoreconfused；andsoontilltheeyebeingbroughtbacktoZseestheobjectinthegreatestconfusionofall。Whereforebysect。21theobjectshouldseemtoapproachtheeyegraduallyasitrecedesfromthepointB，thatis，atOitshould（inconsequenceoftheprincipleIhavelaiddownintheaforesaidsection）
seemnearerthanitdidatB，andatPnearerthanat0，andatQnearerthanatP；andsoon，tillitquitevanishesatZ。Whichistheverymatteroffact，asanyonethatpleasesmayeasilysatisfyhimselfbyexperiment。
32。ThiscaseismuchthesameasifweshouldsupposeanEnglishmantomeetaforeignerwhousedthesamewordswiththeEnglish，butinadirectcontrarysignification。TheEnglishmanwouldnotfailtomakeawrongjudgmentoftheideasannexedtothosesoundsinthemindofhimthatusedthem。Justso，inthepresentcasetheobjectspeaks（ifImaysosay）withwordsthattheeyeiswellacquaintedwith，thatis，confusionsofappearance；butwhereasheretoforethegreaterconfusionswerealwayswonttosignifynearerdistances，theyhaveinthiscaseadirect，contrarysignification，beingconnectedwiththegreaterdistances。Whenceitfollowsthattheeyemustunavoidablybemistaken，sinceitwilltaketheconfusionsinthesenseithasbeenusedto，whichisdirectlyopposedtothetrue。
33。Thisphenomenonasitentirelysubvertstheopinionofthosewhowillhaveusjudgeofdistancebylinesandangles，onwhichsuppositionitisaltogetherinexplicable，soitseemstomenosmallconfirmationofthetruthofthatprinciplewherebyitisexplained。Butinordercoamorefullexplicationofthispoint，andtoshewhowfarthehypothesisofthemind’sjudgingbythevariousdivergencyofraysmaybeofuseindeterminingtheapparentplaceofanobject，itwillbenecessarytopremisesomefewthings，whicharealreadywellknowntothosewhohaveanyskillindioptrics。
34。First，anyradiatingpointisthendistinctlyseenwhentheraysproceedingfromitare，bytherefractivepowerofthecrystalline，accuratelyreunitedintheretinaorfundoftheeye：butiftheyarereunited，eitherbeforetheyarriveattheretina，oraftertheyhavepassedit，thenthereisconfusedvision。
35。Secondly，supposeintheadjacentfiguresNPrepresentaneyedulyframedandretainingitsnaturalfigure。InFig。1theraysfallingnearlyparallelontheeye，arebythecrystallineABrefracted，soastheirfocusorpointofunionFfallsexactlyontheretina：butiftheraysfallsensiblydivergingontheeye，asinFig。2，thentheirfocusfallsbeyondtheretina：oriftheraysaremadetoconvergebythelensQSbeforetheycomeattheeye，asinFig。3，theirfocusFwillfallbeforetheretina。Inwhichtwolastcasesitisevidentfromt[sic]theforegoingsectionthattheappearanceofthepointZisconfused。Andbyhowmuchthegreateristheconvergency，ordivergency，oftheraysfallingonthepupil，bysomuchthefartherwillthepointoftheirreunionbefromtheretina，eitherbeforeorbehindit，andconsequentlythepointZwillappearbysomuchthemoreconfused。Andthis，bythebye，mayshewusthedifferencebetweenconfusedandfaintvision。Confusedvisioniswhentheraysproceedingsfromeachdistinctpointoftheobjectarenotaccuratelyrecollectedinonecorrespondingpointontheretina，buttakeupsomespacethereon，sothatraysfromdifferentpointsbecomemixedandconfusedtogether。Thisisopposedtoadistinctvision，andattendsnearobjects。Faintvisioniswhenbyreasonofthedistanceoftheobjectorgrossnessoftheinterjacentmediumfewraysarrivefromtheobjecttotheeye。Thisisopposedtovigorousorclearvision，andattendsremoteobjects。Buttoreturn。
36。Theeye，or（tospeaktruly）themind，perceivingonlytheconfusionitself，withouteverconsideringthecausefromwhichitproceeds，dothconstantlyannexthesamedegreeofdistancetothesamedegreeofconfusion。
Whetherthatconfusionbeoccasionedbyconvergingorbydivergingrays，itmattersnot。WhenceitfollowsthattheeyeviewingtheobjectZthroughtheglassQS（whichbyrefractioncauseththeraysZQ，ZS，etc。，toconverge）
shouldjudgeittobeatsuchanearnessatwhichifitwereplaceditwouldradiateontheeyewithraysdivergingtothatdegreeaswouldproducethesameconfusionwhichisnowproducedbyconvergingrays，i。e。wouldcoveraportionoftheretinaequaltoDC（vid。Fig。3supra）。
Butthenthismustbeunderstood（touseDr。Barrow’sphrase）seclusispræ；notionibusetpræ；judiciis，incaseweabstractfromallothercircumstancesofvision，suchasthefigure，size，faintness，etc。ofthevisibleobjects；allwhichdoordinarilyconcurtoformourideaofdistance，themindhavingbyfrequentexperienceobservedtheirseveralsortsordegreestobeconnetedwithvariousdistances。
37Itplainlyfollowsfromwhathathbeensaidthatapersonperfectlypurblind（i。e。thatcouldnotseeanobjectdistinctlybutwhenplacedclosetohiseye）wouldnotmakethesamewrongjudgmentthatothersdointheforementionedcase。Fortohimgreaterconfusionsconstantlysuggestinggreaterdistances，hemust，asherecedesfromtheglassandtheobjectgrowsmoreconfused，judgeittobeatafartherdistance，contrarytowhattheydowhohavehadtheperceptionoftheobjectsgrowingmoreconfusedconnectedwiththeideaofapproach。
38。Hencealsoitdothappeartheremaybegooduseofcomputationbylinesandanglesinoptics；notthatthemindjudgethofdistanceimmediatelybythem，butbecauseitjudgethbysomewhatwhichisconnectedwiththem，andtothedeterminationwhereoftheymaybesubservient。Thusthemindjudgingofthedistanceofanobjectbytheconfusednessofitsappearance，andthisconfusednessbeinggreaterorlessertothenakedeye，accordingastheobjectisseenbyraysmoreorlessdiverging，itfollowsthatamanmaymakeuseofthedivergencyoftheraysincomputingtheapparentdistance，thoughnotforitsownsake，yetonaccountoftheconfusionwithwhichitisconnected。But，soitis，theconfusionitselfisentirelyneglectedbymathematiciansashavingnonecessaryrelationwithdistance，suchasthegreaterorlesseranglesofdivergencyareconceivedtohave。
Andthese（especiallyforthattheyfallundermathematicalcomputation）
arealoneregardedindeterminingtheapparentplacesofobjects，asthoughtheywerethesoleandimmediatecauseofthejudgmentsthemindmakesofdistance。Whereas，intruth，theyshouldnotatallberegardedinthemselves，oranyotherwise，thanastheyaresupposedtobethecauseofconfusedvision。
39。Thenotconsideringofthishasbeenafundamentalandperplexingoversight。Forproofwhereofweneedgonofartherthanthecasebeforeus。Ithavingbeenobservedthatthemostdivergingraysbroughtintothemindtheideaofnearestdistance，andthatstill，asthedivergencydecreased，thedistanceincreased：anditbeingthoughttheconnexionbetweenthevariousdegreesofdivergencyanddistancewasimmediate；thisnaturallyleadsonetoconclude，fromanill—groundedanalogy，thatconvergingraysshallmakeanobjectappearatanimmensedistance：andthat，astheconvergencyincreases，thedistance（ifitwerepossible）shoulddosolikewise。ThatthiswasthecauseofDr。Barrow’smistakeisevidentfromhisownwordswhichwehavequoted。Whereashadthelearneddoctorobservedthatdivergingandconvergingrays，howoppositesoevertheymayseem，doneverthelessagreeinproducingthesameeffect，towit，confusednessofvision，greaterdegreeswhereofareproducedindifferently，eitherasthedivergencyorconvergencyandtheraysincreaseth。Andthatitisbythiseffect，whichisthesameinboth，thateitherthedivergencyorconvergencyisperceivedbytheeye；Isay，hadhebutconsideredthis，itiscertainhewouldhavemadeaquitecontraryjudgment，andrightlyconcludedthatthoserayswhichfallontheeyewithgreaterdegreesofconvergencyshouldmaketheobjectfromwhencetheyproceedappearbysomuchthenearer。Butitisplainitwasimpossibleforanymantoattaintoarightnotionofthismattersolongashehadregardonlytolinesandangles，anddidnotapprehendthetruenatureofvision，andhowfaritwasofmathematicalconsideration。
40。Beforewedismissthissubject，itisfitwetakenoticeofaqueryrelatingthereto，proposedbytheingeniousMr。Molyneux，ishisTreatiseofDioptrics，[2]wherespeakingofthisdifficulty，hehasthesewords：
’Andsohe（i。e。Dr。Barrow）leavesthisdifficultytothesolutionofothers，whichI（aftersogreatanexample）shalldolikewise；butwiththeresolutionofthesameadmirableauthorofnotquittingtheevidentdoarinewhichwehavebeforelaiddown，fordeterminingthelocusobjecti，onaccountofbeingpressedbyonedifficultywhichseemsinexplicabletillamoreintimateknowledgeofthevisivefacultybeobtainedbymortals。
Inthemeantime，Iproposeittotheconsiderationoftheingenious，whetherthelocusapparensofanobjectplacedasinthis9thsectionbenotasmuchbeforetheeyeasthedistinctbaseisbehindtheeye!’Towhichquerywemayventuretoanswerinthenegative。Forinthepresentcasetherulefordeterminingthedistanceofthedistinctbase，orrespectivefocusfromtheglass，isthis：Asthedifferencebetweenthedistanceoftheobjectandfocusistothefocusorfocallength，sothedistanceoftheobjectfromtheglassistothedistanceoftherespectivefocusordistinctbasefromtheglass。[3]Letusnowsupposetheobjecttobeplacedatthedistanceofthefocallength，andonehalfofthefocallengthfromtheglass，andtheeyeclosetotheglass，henceitwillfollowbytherulethatthedistanceofthedistinctbasebehindtheeyeisdoublethetruedistanceoftheobjectbeforetheeye。IfthereforeMr。Molyneux’sconjectureheldgood，itwouldfollowthattheeyeshouldseetheobjecttwiceasfaroffasitreallyis；andinothercasesatthreeorfourtimesitsduedistance，ormore。Butthismanifestlycontradictsexperience，theobjectneverappearing，atfarthest，beyonditsduedistance。Whatever，therefore，isbuiltonthissupposition（vid。Corol。I。Prop。57，ibid。）comestothegroundalongwithit。
41。Fromwhathathbeenpremiseditisamanifestconsequencethatamanbornblind，beingmadetosee，would，atfirst，havenoideaofdistancebysight；thesunandstars，theremotestobjectsaswellasthenearer，wouldallseemtobeinhiseye，orratherinhismind。Theobjectsintromittedbysightwouldseemtohim（asintruththeyare）nootherthananewsetofthoughtsorsensations，eachwhereofisasneartohimastheperceptionsofpainorpleasure，orthemostinwardpassionsofhissoul。Forourjudgingobjectsprovidedbysighttobeatanydistance，orwithoutthemind，is（vid。sect。28）entirelytheeffectofexperience，whichoneinthosecircumstancescouldnotyethaveattainedto。
42。Itisindeedotherwiseuponthecommonsuppositionthatmenjudgeofdistancebytheangleoftheopticaxes，justasoneinthedark，orablind—manbytheanglecomprehendedbytwosticks，onewhereofheheldineachhand。Forifthisweretrue，itwouldfollowthatoneblindfromhisbirthbeingmadetosee，shouldstandinneedofnonewexperienceinordertoperceivedistancebysight。Butthatthisisfalsehas，Ithink，beensufficientlydemonstrated。
43。Andperhapsuponastrictinquiryweshallnotfindthateventhosewhofromtheirbirthhavegrownupinacontinuedhabitofseeingareirrecoverablyprejudicedontheotherside，towit，inthinkingwhattheyseetobeatadistancefromthem。Foratthistimeitseemsagreedonallhands，bythosewhohavehadanythoughtsofthatmatter，thatcolours，whicharetheproperandimmediateobjectofsight，arenotwithoutthemind。Butthenitwillbesaid，bysightwehavealsotheideasofextension，andfigure，andmotion；allwhichmaywellbethoughtwithout，andatsomedistancefromthemind，thoughcolourshouldnot。InanswertothisIappealtoanyman’sexperience，whetherthevisibleextensionofanyobjectdothnotappearasneartohimasthecolourofthatobject；nay，whethertheydonotbothseemtobeintheverysameplace。Isnottheextensionweseecoloured，andisitpossibleforus，somuchasinthought，toseparateandabstractcolourfromextension？Now，wheretheextensionistheresurelyisthefigure，andtherethemotiontoo。Ispeakofthosewhichareperceivedbysight。
44。Butforafullerexplicationofthispoint，andtoshewthattheimmediateobjectsofsightarenotsomuchastheideasorresemblancesofthingsplacedatadistance，itisrequisitethatwelooknearerintothematterandcarefullyobservewhatismeantincommondiscourse，whenonesaysthatwhichheseesisatadistancefromhim。Suppose，forexample，thatlookingatthemoonIshouldsayitwerefiftyorsixtysemidiametersoftheearthdistantfromme。Letusseewhatmoonthisisspokenof：itisplainitcannotbethevisiblemoon，oranythinglikethevisiblemoon，orthatwhichIsee，whichisonlyaround，luminousplaneofaboutthirtyvisiblepointsindiameter。ForincaseIamcarriedfromtheplacewhereIstanddirectlytowardsthemoon，itismanifesttheobjectvaries，stillasIgoon；andbythetimethatIamadvancedfiftyorsixtysemidiametersoftheearth，Ishallbesofarfrombeingnearasmall，round，luminousflatthatIshallperceivenothinglikeit；thisobjecthavinglongsincedisappeared，andifIwouldrecoverit，itmustbebygoingbacktotheearthfromwhenceIsetout。Again，supposeIperceivebysightthefaintandobscureideaofsomethingwhichIdoubtwhetheritbeaman，oratree，oratower，butjudgeittobeatthedistanceofaboutamile。ItisplainIcannotmeanthatwhatIseeisamileoff，orthatitistheimageorlikenessofanythingwhichisamileoff，sincethateverystepItaketowardsittheappearancealters，andfrombeingobscure，small，andfaint，growsclear，large，andvigorous。AndwhenIcometothemile’send，thatwhichIsawfirstisquitelost，neitherdoIfindanythinginthelikenessofit。
45。Intheseandthelikeinstancesthetruthofthematterstandsthus：
havingofalongtimeexperiencedcertainideas，perceivablebytouch，asdistance，tangiblefigure，andsolidity，tohavebeenconnectedwithcertainideasofsight，Idouponperceivingtheseideasofsightforthwithconcludewhattangibleideasare，bythewontedordinarycourseofNatureliketofollow。LookingatanobjectIperceiveacertainvisiblefigureandcolour，withsomedegreeoffaintnessandothercircumstances，whichfromwhatIhaveformerlyobserved，determinemetothinkthatifIadvanceforwardsomanypacesormiles，Ishallbeaffectedwithsuchandsuchideasoftouch：sothatintruthandstrictnessofspeechIneitherseedistanceitself，noranythingthatItaketobeatadistance。Isay，neitherdistancenorthingsplacedatadistancearethemselves，ortheirideas，trulyperceivedbysight。ThisIampersuadedof，astowhatconcernsmyself：
andIbelievewhoeverwilllooknarrowlyintohisownthoughtsandexaminewhathemeansbysayingheseesthisorthatthingatadistance，willagreewithmethatwhatheseesonlysuggeststohisunderstandingthatafterhavingpassedacertaindistance，tobemeasuredbythemotionofhisbody，whichisperceivablebytouch，heshallcometoperceivesuchandsuchtangibleideaswhichhavebeenusuallyconnectedwithsuchandsuchvisibleideas。Butthatonemightbedeceivedbythesesuggestionsofsense，andthatthereisnonecessaryconnexionbetweenvisibleandtangibleideassuggestedbythem，weneedgonofartherthanthenextlooking—glassorpicturestobeconvinced。NotethatwhenIspeakoftangibleideas，Itakethewordideaforanytheimmediateobjectofsenseorunderstanding，inwhichlargesignificationitiscommonlyusedbythemoderns。
46。Fromwhatwehaveshewnitisamanifestconsequencethattheideasofspace，outness，andthingsplacedatadistancearenot，strictlyspeaking，theobjectofsight；theyarenototherwiseperceivedbytheeyethanbytheear。SittinginmystudyIhearacoachdrivealongthestreet；Ilookthroughthecasementandseeit；Iwalkoutandenterintoit；thus，commonspeechwouldinclineonetothinkIheard，saw，andtouchedthesamething，towit，thecoach。Itisneverthelesscertain，theideasintromittedbyeachsensearewidelydifferentanddistinctfromeachother；buthavingbeenobservedconstantlytogotogether，theyarespokenofasoneandthesamething。BythevariationofthenoiseIperceivethedifferentdistancesofthecoach，andknowthatitapproachesbeforeIlookout。
ThusbytheearIperceivedistance，justafterthesamemannerasIdobytheeye。
47。IdonotneverthelesssayIheardistanceinlikemannerasIsaythatIseeit，theideasperceivedbyhearingnotbeingsoapttobeconfoundedwiththeideasoftouchasthoseofsightare。Solikewiseamaniseasilyconvincedthatbodiesandexternalthingsarenotproperlytheobjectofhearing；butonlysounds，bythemediationwhereoftheideaofthisorthatbodyordistanceissuggestedtohisthoughts。Butthenoneiswithmoredifficultybroughttodiscernthedifferencethereisbetwixttheideasofsightandtouch：thoughitbecertainamannomoreseesandfeelsthesamethingthanhehearsandfeelsthesamething。
48。Onereasonofwhichseemstobethis。Itisthoughtagreatabsurditytoimaginethatoneandthesamethingshouldhaveanymorethanoneextension，andonefigure。Buttheextensionandfigureofabody，beingletintothemindtwoways，andthatindifferentlyeitherbysightortouch，itseemstofollowthatweseethesameextensionandthesamefigurewhichwefeel。
49。Butifwetakeacloseandaccurateviewofthings，itmustbeacknowledgedthatweneverseeandfeeloneandthesameobject。Thatwhichisseenisonething，andthatwhichisfeltisanother。Ifthevisiblefigureandextensionbenotthesamewiththetangiblefigureandextension，wearenottoinferthatoneandthesamethinghasdiversextensions。Thetrueconsequenceisthattheobjectsofsightandtoucharetwodistinctthings。Itmayperhapsrequiresomethoughtrightlytoconceivethisdistinction。
Andthedifficultyseemsnotalittleincreased，becausethecombinationofvisibleideashathconstantlythesamenameasthecombinationoftangibleideaswherewithitisconnected：whichdothofnecessityarisefromtheuseandendoflanguage。
50。Inorderthereforetotreataccuratelyandunconfusedlyofvision，wemustbearinmindthattherearetwosortsofobjectsapprehendedbytheeye，theoneprimarilyandimmediately，theothersecondarilyandbyinterventionoftheformer。Thoseofthefirstsortneitherare，norappeartobe，withoutthemind，oratanydistanceoff；theymayindeedgrowgreaterorsmaller，moreconfused，ormoreclear，ormorefaint，buttheydonot，cannotapproachorrecedefromus。Wheneverwesayanobjectisatadistance，wheneverwesayitdrawsnear，orgoesfartheroff，wemustalwaysmeanitofthelattersort，whichproperlybelongtothetouch，andarenotsotrulyperceivedassuggestedbytheeyeinlikemannerasthoughtsbytheear。
51。Nosoonerdowehearthewordsofafamiliarlanguagepronouncedinourears，buttheideascorrespondingtheretopresentthemselvestoourminds：intheverysameinstantthesoundandthemeaningentertheunderstanding：socloselyaretheyunitedthatitisnotinourpowertokeepouttheone，exceptweexcludetheotheralso。Weevenactinallrespectsasifweheardtheverythoughtsthemselves。Solikewisethesecondaryobjects，orthosewhichareonlysuggestedbysight，dooftenmorestronglyaffectus，andaremoreregardedthantheproperobjectsofthatsense；
alongwithwhichtheyenterintothemind，andwithwhichtheyhaveafarmorestrictconnexion，thanideashavewithwords。Henceitiswefinditsodifficulttodiscriminatebetweentheimmediateandmediateobjectsofsight，andaresopronetoattributetotheformerwhatbelongsonlytothelatter。Theyare，asitwere，mostcloselytwisted，blended，andincorporatedtogether。Andtheprejudiceisconfirmedandrivetedinourthoughtsbyalongtractoftime，bytheuseoflanguage，andwantofreflexion。
However，Ibelieveanyonethatshallattentivelyconsiderwhatwehavealreadysaid，andshallsay，uponthissubjectbeforewehavedone（especiallyifhepursueitinhisownthoughts）maybeabletodeliverhimselffromthatprejudice。SureIamitisworthsomeattention，towhoeverwouldunderstandthetruenatureofvision。
52。Ihavenowdonewithdistance，andproceedtoshewhowitisthatweperceivebysightthemagnitudeofobjects。Itistheopinionofsomethatwedoitbyangles，orbyanglesinconjunctionwithdistance：butneitheranglesnordistancebeingperceivablebysight，andthethingsweseebeingintruthatnodistancefromus，itfollowsthataswehaveshewnlinesandanglesnottobethemediumthemindmakesuseofinapprehendingtheapparentplace，soneitheraretheythemediumwherebyitapprehendstheapparentmagnitudeofobjects。
53。Itiswellknownthatthesameextensionataneardistanceshallsubtendagreaterangle，andatafartherdistancealesserangle。Andbythisprinciple（wearetold）themindestimatesthemagnitudeofanobject，comparingtheangleunderwhichitisseenwithitsdistance，andthenceinferringthemagnitudethereof。Whatinclinesmentothismistake（besidethehumourofmakingoneseebygeometry）isthatthesameperceptionsorideaswhichsuggestdistancedoalsosuggestmagnitude。Butifweexamineitweshallfindtheysuggestthelatterasimmediatelyastheformer。
Isay，theydonotfirstsuggestdistance，andthenleaveittothejudgmenttousethatasamediumwherebytocollectthemagnitude；buttheyhaveascloseandimmediateaconnexionwiththemagnitudeaswiththedistance；
andsuggestmagnitudeasindependentlyofdistanceastheydodistanceindependentlyofmagnitude。Allwhichwillbeevidenttowhoeverconsiderswhathathbeenalreadysaid，andwhatfollows。
54。Ithathbeenshewntherearetwosortsofobjectsapprehendedbysight；eachwhereofhathitsdistinctmagnitude，orextension。Theone，properlytangible，i。e。tobeperceivedandmeasuredbytouch，andnotimmediatelyfallingunderthesenseofseeing：theother，properlyandimmediatelyvisible，bymediationofwhichtheformerisbroughtinview。Eachofthesemagnitudesaregreaterorlesser，accordingastheycontaininthemmoreorfewerpoints，theybeingmadeupofpointsorminimums。
For，whatevermaybesaidofextensioninabtract，itiscertainsensibleextensionisnotinfinitelydivisible。ThereisaMinimumTangibileandaMinimumVisibile，beyondwhichsensecannotperceive。
Thiseveryone’sexperiencewillinformhim。
55。Themagnitudeoftheobjectwhichexistswithoutthemind，andisatadistance，continuesalwaysinvariablythesame：butthevisibleobjectstillchangingasyouapproachto，orrecedefrom，thetangibleobject，ithathnofixedanddeterminategreatness。Whenever，therefore，wespeakofthemagnitudeofanything，forinstanceatreeorahouse，wemustmeanthetangiblemagnitude，otherwisetherecanbenothingsteadyandfreefromambiguityspokenofit。Butthoughthetangibleandvisiblemagnitudeintruthbelongtotwodistinctobjects：Ishallnevertheless（especiallysincethoseobjectsarecalledbythesamename，andareobservedtocoexist），toavoidtediousnessandsingularityofspeech，sometimesspeakofthemasbelongingtooneandthesamething。
56。Nowinordertodiscoverbywhatmeansthemagnitudeoftangibleobjectsisperceivedbysight。Ineedonlyreflectonwhatpassesinmyownmind，andobservewhatthosethingsbewhichintroducetheideasofgreaterorlesserintomythoughts，whenIlookonanyobject。AndtheseIfindtobe，first，themagnitudeorextensionofthevisibleobject，whichbeingimmediatelyperceivedbysight，isconnectedwiththatotherwhichistangibleandplacedatadistance。Secondly，theconfusionordistinctness。Andthirdly，thevigorousnessorfaintnessoftheaforesaidvisibleappearance。Ceterisparibus，byhowmuchthegreaterorlesserthevisibleobjectis，bysomuchthegreaterorlesserdoI
concludethetangibleobjecttobe。But，betheideaimmediatelyperceivedbysightneversolarge，yetifitbewithalconfused，Ijudgethemagnitudeofthethingtobebutsmall。Ifitbedistinctandclear，Ijudgeitgreater。
Andifitbefaint，Iapprehendittobeyetgreater。Whatisheremeantbyconfusionandfaintnesshathbeenexplainedinsect。35。
57。Moreoverthejudgmentswemakeofgreatnessdo，inlikemannerasthoseofdistance，dependonthedispositionoftheeye，alsoonthefigure，number，andsituationofobjectsandothercircumstancesthathavebeenobservedtoattendgreatorsmalltangiblemagnitudes。Thus，forinstance，theverysamequantityofvisibleextension，whichinthefigureofatowerdothsuggesttheideaofgreatmagnitude，shallinthefigureofamansuggesttheideaofmuchsmallermagnitude。Thatthisisowingtotheexperiencewehavehadoftheusualbignessofatowerandamannoone，Isuppose，needbetold。
58。Itisalsoevidentthatconfusionorfaintnesshavenomoreanecessaryconnexionwithlittleorgreatmagnitudethantheyhavewithlittleorgreatdistance。Astheysuggestthelatter，sotheysuggesttheformertoourminds。Andbyconsequence，ifitwerenotforexperience，weshouldnomorejudgeafaintorconfusedappearancetobeconnectedwithgreatorlittlemagnitude，thanweshouldthatitwasconnectedwithgreatorlittledistance。
59。Norwillitbefoundthatgreatorsmallvisiblemagnitudehathanynecessaryrelationtogreatorsmalltangiblemagnitude：sothattheonemaycertainlybeinferredfromtheother。Butbeforewecometotheproofofthis，itisfitweconsiderthedifferencethereisbetwixttheextensionandfigurewhichistheproperobjectoftouch，andthatotherwhichistermedvisible；andhowtheformerisprincipally，thoughnotimmediatelytakennoticeof，whenwelookatanyobject。Thishasbeenbeforementioned，butweshallhereinquireintothecausethereof。Weregardtheobjectsthatenvironusinproportionastheyareadaptedtobenefitorinjureourownbodies，andtherebyproduceinourmindsthesensationofpleasureorpain。Nowbodiesoperatingonourorgans，byanimmediateapplication，andthehurtoradvantagearisingtherefrom，dependingaltogetheronthetangible，andnotatallonthevisible，qualitiesofanyobject：thisisaplainreasonwhythoseshouldberegardedbyusmuchmorethanthese：andforthisendthevisivesenseseemstohavebeenbestowedonanimals，towit，thatbytheperceptionofvisibleideas（whichinthemselvesarenotcapableofaffectingoranywisealteringtheframeoftheirbodies）
theymaybeabletoforesee（fromtheexperiencetheyhavehadwhattangibleideasareconnectedwithsuchandsuchvisibleideas）anddamageorbenefitwhichisliketoensue，upontheapplicationoftheirownbodiestothisorthatbodywhichisatadistance。Whichforesight，hownecessaryitistothepreservationofananimal，everyone’sexperiencecaninformhim。
Henceitisthatwhenwelookatanobject，thetangiblefigureandextensionthereofareprincipallyattendedto；whilstthereissmallheedtakenofthevisiblefigureandmagnitude，which，thoughmoreimmediatelyperceived，dolessconcernus，andarenotfittedtoproduceanyalterationinourbodies。
60。Thatthematteroffactistruewillbeevidenttoanyonewhoconsidersthatamanplacedattenfootdistanceisthoughtasgreatasifhewereplacedatadistanceonlyoffivefoot：whichistruenotwithrelationtothevisible，buttangiblegreatnessoftheobject：thevisiblemagnitudebeingfargreateratonestation：thanitisattheother。
61。Inches，feet，etc。，aresettledstatedlengthswherebywemeasureobjectsandestimatetheirmagnitude：wesay，forexample，anobjectappearstobesixinchesorsixfootlong。Now，thatthiscannotbemeantofvisibleinches，etc。，isevident，becauseavisibleinchisitselfnoconstant，determinatemagnitude，andcannotthereforeservetomarkoutanddeterminethemagnitudeofanyotherthing。Takeaninchmarkeduponaruler：viewit，successively，atthedistanceofhalfafoot，afoot，afootandahalf，etc。，fromtheeye：ateachofwhich，andatalltheintermediatedistances，theinchshallhaveadifferentvisibleextension，i。e。thereshallbemoreorfewerpointsdiscernedinit。NowIaskwhichofallthesevariousextensionsisthatstated，determinateonethatisagreedonforacommonmeasureofothermagnitudes？Noreasoncanbeassignedwhyweshouldpitchononemorethananother：andexcepttherebesomeinvariable，determinateextensionfixedontobemarkedt~thewordinch，itisplainitcanbeusedtolittlepurpose；andtosayathingcontainsthisorthatnumberofinchesshallimplynomorethanthatitisextended，withoutbringinganyparticularideaofthatextensionintothemind。Farther，aninchandafoot，fromdifferentdistances，shallbothexhibitthesamevisiblemagnitude，andyetatthesametimeyoushallsaythatoneseemsseveraltimesgreaterthantheother。Fromallwhichitismanifestthatthejudgmentswemakeofthemagnitudeofobjectsbysightarealtogetherinreferencetotheirtangibleextension。Wheneverwesayanobjectisgreat，orsmall，ofthisorthatdeterminatemeasure，Isayitmustbemeantofthetangible，andnotthevisibleextension，which，thoughimmediatelyperceived，isneverthelesslittletakennoticeof。
62。Now，thatthereisnonecessaryconnexionbetweenthesetwodistinctextensionsisevidentfromhence：becauseoureyesmighthavebeenframedinsuchamannerastobeabletoseenothingbutwhatwerelessthantheminimumtangibile。Inwhichcaseitisnotimpossiblewemighthaveperceivedalltheimmediateobjectsofsight，theverysamethatwedonow：butuntothosevisibleappearancestherewouldnotbeconnectedthosedifferenttangiblemagnitudesthatarenow。Whichshewsthejudgmentswemakeofthcmagnitudeofthingsplacedatadistancefromthevariousgreatnessoftheimmediateobjectsofsightdonotarisefromanyessentialornecessarybutonlyacustomarytie，whichhasbeenobservedbetweenthem。
63。Moreover，itisnotonlycertainthatanyideaofsightmightnothavebeenconnectedwiththisorthatideaoftouch，whichwenowobservetoaccompanyit：butalsothatthegreatervisiblemagnitudesmighthavebeenconnectedwith，andintroducedintoourmindslessertangiblemagnitudesandthelesservisiblemagnitudesgreatertangiblemagnitudes。Nay，thatitactuallyissowehavedailyexperience；thatobjectwhichmakesastrongandlargeappearance，notseemingnearsogreatasanother，thevisiblemagnitudewhereofismuchless，butmorefaint，andtheappearanceupper，orwhichisthesamethingpaintedlowerontheretina，whichfaintnessandsituationsuggestbothgreatermagnitudeandgreaterdistance。
64。Fromwhich，andfromsect。57and58，itismanifestthataswedonotperceivethemagnitudesofobjectsimmediatelybysight，soneitherdoweperceivethembythemediationofanythingwhichhasanecessaryconnexionwiththem。Thoseideasthatnowsuggestuntousthevariousmagnitudesofexternalobjectsbeforewetouchthem，mightpossiblyhavesuggestednosuchthing：ortheymighthavesignifiedtheminadirectcontrarymanner：
sothattheverysameideas，ontheperceptionwhereofwejudgeanobjecttobesmall，mightaswellhaveservedtomakeusconcludeitgreat。Thoseideasbeingintheirownnatureequallyfittedtobringintoourmindstheideaofsmallorgreat，ornosizeatallofoutwardobjects；justasthewordsofanylanguageareintheirownnatureindifferenttosignifythisorthatthingornothingatall。
65。Asweseedistance，soweseemagnitude。Andweseebothinthesamewaythatweseeshameorangerinthelooksofaman。Thosepassionsarethemselvesinvisible，theyareneverthelessletinbytheeyealongwithcoloursandalterationsofcountenance，whicharetheimmediateobjectofvision：andwhichsignifythemfornootherreasonthanbarelybecausetheyhavebeenobservedtoaccompanythem。Withoutwhichexperienceweshouldnomorehavetakenblushingforasignofshamethanofgladness。
66。Weareneverthelessexceedingpronetoimaginethosethingswhichareperceivedonlybythemediationofotherstobethemselvestheimmediateobjectsofsight；or，atleast，tohaveintheirownnatureafitnesstobesuggestedbythem，beforeevertheyhadbeenexperiencedtocoexistwiththem。Fromwhichprejudiceeveryone，perhaps，willnotfinditeasytoemancipatehimself，byany[but]theclearestconvictionsofreason。
Andtherearesomegroundstothinkthatiftherewasoneonlyinvariableanduniversallanguagesintheworld，andthatmenwerebornwiththefacultyofspeakingit，itwouldbetheopinionofmanythattheideasofothermen’smindswereproperlyperceivedbytheear，orhadatleastanecessaryandinseparabletiewiththesoundsthatwereaffixedtothem。Allwhichseemstoarisefromwantofadueapplicationofourdiscerningfaculty，therebytodiscriminatebetweentheideasthatareinourunderstandings，andconsiderthemapartfromeachother；whichwouldpreserveusfromconfoundingthosethataredifferent，andmakeusseewhatideasdo，andwhatdonotincludeorimplythisorthatotheridea。
67。Thereisacelebratedphenomenon，thesolutionwhereofIshallattempttogivebytheprinciplesthathavebeenlaiddown，inreferencetothemannerwhereinweapprehendbysightthemagnitudeofobjects。Theapparentmagnitudeofthemoonwhenplacedinthehorizonismuchgreaterthanwhenitisinthemeridian，thoughtheangleunderwhichthediameterofthemoonisseenbenotobservedgreaterintheformercasethaninthelatter：
andthehorizontalmoondothnotconstantlyappearofthesamebigness，butatsometimesseemethfargreaterthanatothers。
68。Nowinordertoexplainthereasonofthemoon’sappearinggreaterthanordinaryinthehorizon，itmustbeobservedthattheparticleswhichcomposeouratmosphereintercepttheraysoflightproceedingfromanyobjecttotheeye；andbyhowmuchthegreateristheportionofatmosphereinterjacentbetweentheobjectandtheeye，bysomuchthemorearetheraysintercepted；andbyconsequencetheappearanceoftheobjectrenderedmorefaint，everyobjectappearingmorevigorousormorefaintinproportionasitsendethmoreorfewerraysintotheeye。Nowbetweentheeyeandthemoon，whensituatedinthehorizon，thereliesafargreaterquantityofatmospherethantheredoeswhenthemoonisinthemeridian。Whenceitcomestopassthattheappearanceofthehorizontalmoonisfainter，andthereforebysect。56itshouldbethoughtbiggerinthatsituationthaninthemeridian，orinanyotherelevationabovethehorizon。
