ray ray tool identifying atomic molecular structure crystal cause beam incident rays specific directions measuring angles beams produce dimensional picture density crystal electron density mean positions crystal determined chemical bonds disorder information materials form crystals metals minerals organic biological molecules ray fundamental development scientific fields decades use method determined size lengths types chemical bonds atomic scale differences materials especially minerals method revealed structure function biological molecules including drugs proteins dna ray chief method atomic structure new materials materials appear similar experiments ray crystal structures account unusual electronic elastic properties material shed light chemical interactions processes serve basis designing diseases single crystal ray measurement crystal mounted position crystal selected crystal illuminated finely focused beam rays producing pattern regularly spaced spots known reflections dimensional images taken different converted dimensional model density crystal mathematical method transforms combined chemical data known sample poor resolution errors result crystals small uniform internal makeup ray related methods determining atomic structures similar patterns produced scattering likewise interpreted transformation single crystals sufficient size obtained ray methods applied obtain detailed information methods include fiber powder sample small angle ray scattering material investigation available form suffers poor methods electron applied determining atomic structure mentioned ray methods scattering elastic scattered rays incoming ray contrast ray scattering methods useful studying sample distribution history early scientific history crystals rays crystals long admired symmetry investigated scientifically 17th century work new year gift snow symmetry crystals regular packing spherical water particles danish scientist pioneered experimental investigations crystal symmetry showed angles faces particular type crystal discovered face crystal described simple patterns blocks shape size william miller able face unique label small miller remain use today identifying crystal faces study led correct idea crystals regular dimensional array molecules single unit cell repeated indefinitely principal directions necessarily perpendicular 19th century complete catalog possible crystal worked arthur william available data physical reasoning proposed crystal structures 1880s later ray available data scarce 1880s accept models conclusive discovered rays studies crystal symmetry concluded initially uncertain nature rays soon suspected correctly waves electromagnetic radiation words form light time wave model light specifically theory electromagnetic radiation accepted scientists experiments charles showed rays exhibited phenomena associated electromagnetic waves including transverse lines akin observed visible single experiments laboratory arnold suggested rays rays composed waves electromagnetic radiation exhibit particle like properties albert introduced concept broadly accepted arthur confirmed scattering rays particle like properties rays gases caused william henry argue rays electromagnetic radiation view broadly accepted observation ray max von confirmed scientists rays form electromagnetic radiation ray crystals regular rays considered waves electromagnetic radiation ray waves primarily ocean wave striking lighthouse produces secondary circular waves lighthouse ray striking electron produces secondary spherical waves electron phenomenon known elastic scattering electron lighthouse known regular array produces regular array spherical waves waves cancel directions destructive interference add specific directions determined law formula planes formula incident angle beam specific directions appear spots pattern called reflections ray results electromagnetic wave ray regular array repeating arrangement crystal rays produce pattern typically order magnitude planes crystal principle wave regular array produces predicted maria produce significant wave similar size illustration sunlight bird feather reported james gregory later 17th century artificial visible light constructed david joseph von visible light long typically observe crystals prior ray experiments planes crystal known certainty idea crystals rays arose conversation paul peter max von english garden munich proposed model crystals thesis model visible light larger von realized electromagnetic radiation shorter needed observe small suggested rays comparable unit cell crystals von worked technicians walter friedrich assistant paul shine beam rays copper crystal record photographic plate developed plate showed large number defined spots arranged pattern intersecting circles spot produced central beam von developed law connects scattering angles size orientation unit cell crystal awarded nobel prize physics scattering described mathematical ray scattering determined density crystal energy ray greater electron scattering modeled scattering interaction electromagnetic ray free electron model generally adopted describe scattered radiation intensity scattering particle mass charge formula atomic heavier electron contribute scattered rays development von pioneering research field developed rapidly notably william lawrence father william henry younger developed law connects observed scattering reflections evenly spaced planes crystal father son shared nobel prize physics work earliest structures generally simple marked dimensional symmetry experimental methods improved decades feasible reliable atomic positions complicated dimensional arrangements unit cell potential ray determining structure molecules minerals known chemical experiments realized immediately earliest structures simple crystals minerals revealed fundamental laws physics chemistry atomic resolution structure solved determined table salt distribution table salt structure showed crystals necessarily composed molecules proved existence compounds structure diamond solved year proving arrangement chemical bonds showing length single bond early structures included copper calcium known forms dioxide extension determined walter structure known structure solved related method powder developed peter paul independently albert hull structure determined single crystal groups independently hull powder method determine structures metals iron cultural aesthetic importance ray called scientific autobiography development ray analysis sir william lawrence mentioned believed field particularly welcoming women techno aesthetics molecular structures resembled household objects known compare crystal formation roses festival pattern group festival britain hosted collaborative group textile manufacturers experienced design lace prints based ray china clay leading scientists project helen assistant director research laboratory cambridge time credited central figures took inspiration crystal saw potential design collection london exhibition festival pattern group called patterns contributions chemistry material science ray led better understanding chemical bonds non interactions initial studies revealed typical confirmed theoretical models chemical bonding bonding carbon diamond structure bonding metals observed resonance observed group molecules structure established symmetry showed clear difference bond length bonds bonds finding led idea resonance chemical bonds profound consequences development chemistry conclusions anticipated william henry published models based molecules early form molecular replacement 1920s victor later developed rules eliminating unlikely structures determining relative sizes rules led structure understanding relative stability forms dioxide distance sensitive measure bond strength bond order ray studies led discovery exotic types bonding chemistry metal metal double bonds metal metal quadruple bonds center electron bonds ray strictly speaking scattering experiment provided evidence partly character hydrogen bonds field chemistry ray structure initiated scientific studies sandwich compounds salt stimulated research bonding metal complexes finally ray pioneering role development chemistry particularly structures crown principles host guest chemistry material sciences complicated systems analyzed single crystal methods complicated compounds single crystal industry recent problems major factors affecting quality single crystal structures crystal size commonly technique improve factors small crystals cambridge structural database contains structures structures determined ray 1920s ray principal method determining arrangement minerals metals application ray began structure determined systematic ray study undertaken 1920s study showed ratio altered crystals exhibit significant changes atomic arrangements extended insights minerals aluminium application ray likewise occurred notably structure led theory stability structure complex crystals october curiosity planet mars performed ray analysis soil results revealed presence minerals including suggested soil sample similar soils hawaiian early organic small biological molecules structure organic compound solved followed studies long chain important component biological membranes 1930s structures larger molecules dimensional complexity began solved significant advance structure large closely related molecules important biology ray biological molecules took solved structures awarded nobel prize chemistry succeeded solving structure worked thirty years biological crystal structures proteins irregular hundreds times larger began solved late 1950s beginning structure sperm whale sir john shared nobel prize chemistry max success ray crystal structures proteins biological molecules determined comparison nearest competing method terms structures analyzed nuclear magnetic resonance resolved chemical structures solve structures large molecules solution state restricted relatively small ones ray routinely scientists determine drug protein target changes improve membrane proteins remain challenging require means isolation interfere membrane proteins large component include proteins great importance channels prevent radiation damage protein crystals end size scale relative small molecules able lure resolving power ray structure assigned isolated marina organism proved incorrect classical proof structure synthetic sample identical natural product mistake possible inability ray distinguish correct groups incorrect structure relationship scattering techniques elastic scattering ray form elastic scattering outgoing rays energy incoming rays altered direction contrast scattering occurs energy transferred incoming ray crystal exciting inner shell electron higher energy level scattering reduces energy increases outgoing beam scattering useful matter determining distribution matter goal ray rays range typical scale chemical bonds radius single longer radiation sufficient resolution determine atomic positions extreme shorter gamma rays difficult produce large numbers difficult focus interact strongly matter producing particle pairs rays determining atomic resolution structures scattering electromagnetic radiation ray techniques forms elastic ray scattering include powder small angle ray scattering types ray fiber franklin determining double structure dna general single crystal ray offers structural information techniques requires sufficiently large regular crystal available scattering methods generally use rays restricted single minor broad spectrum rays blend rays different carry ray technique known method method original discovery ray scattering provides structural information short exposure ray beam structural studies rapid events time resolved suited scattering determining atomic structure crystal works better crystals relatively simple atomic arrangements reflection mode records rays scattered backwards broad spectrum source useful sample thick rays transmit planes crystal determined knowing normal plane angle incident beam beam chart interpret reflection photograph electron particles produce pattern electron ray scattering based different physical processes resulting patterns analyzed coherent imaging techniques derived electron density crystal patterns related simple mathematical method transform allows density calculated relatively easily patterns works scattering weak scattered beams intense incoming beam weakly scattered beams pass remainder crystal undergoing second scattering event scattered waves called secondary scattering hinder analysis sufficiently thick crystal produce secondary scattering rays interact relatively weakly generally significant concern contrast electron beams produce strong secondary scattering relatively thin crystals thickness corresponds diameter promising direction electron isolated assemblies viral molecular machines carried electron microscope strong interaction matter times stronger rays allows determination atomic structure extremely small volumes field applications electron ranges molecules like membrane proteins organic thin films complex structures compounds excellent method structure determination difficult obtain intense beams sufficient quantities traditionally nuclear sources producing increasingly available readily atomic scattering useful observing positions light especially hydrogen essentially invisible ray scattering remarkable property invisible adjusting ratio normal water heavy water methods overview single crystal ray oldest precise method ray single crystal ray beam rays strikes single crystal producing scattered beams land piece film beams pattern spots strengths angles beams recorded crystal gradually rotated spot called reflection corresponds reflection rays set evenly spaced planes crystal single crystals sufficient purity ray data determine mean chemical bond lengths angles tenths degree respectively crystal static mean positions usually tenths ray allows measuring size procedure technique single crystal ray basic steps difficult step obtain adequate crystal material study crystal sufficiently large typically larger dimensions pure composition regular structure significant internal cracks second step crystal placed intense beam rays usually single rays producing regular pattern reflections crystal gradually rotated previous reflections disappear new ones appear intensity spot recorded orientation crystal multiple data sets collected set covering slightly half rotation crystal typically containing tens thousands reflections step data combined chemical information produce model arrangement crystal final refined model atomic arrangement called crystal structure usually stored public database limitations crystal repeating unit unit cell larger complex atomic level picture provided ray resolved given number observed reflections limiting cases ray small small typically involves crystals fewer unit crystal structures usually resolved isolated electron density contrast involves tens thousands unit cell crystal structures generally resolved chemical bonds appear tubes electron density isolated general small molecules easier ray proven possible hundreds thousands normally ray performed sample crystal form new research sampling non forms samples characterize disorder irregular crystal generally requires pure crystal high solve structure complicated arrangement pure regular crystals obtained natural synthetic materials samples metals minerals materials crystals improved crystal methods cases obtaining quality crystal chief barrier solving atomic resolution structure small differ range possible techniques produce quality crystals small molecules generally degrees freedom wide range methods chemical deposition contrast generally degrees freedom carried maintain stable structure example proteins larger molecules structure range conditions restricted solution conditions molecules remain folded protein crystals grown solution common approach lower component molecules gradually quickly molecules solution forming useless dust container crystal growth solution characterized steps microscopic possibly having molecules followed growth quality crystal solution conditions favor step conditions favor second step subsequent growth goal identify solution conditions favor development single large crystal larger crystals offer improved resolution consequently solution conditions step favor second growth large crystal forms favored shower small form large crystal favored little crystal form whatsoever approaches involves proteins oil protein solutions liquid oil water layer oil different different yielding changes concentration rates different protein mixture technique relies bringing protein directly zone mixing protein appropriate prevent water drop extremely difficult predict good conditions growth ordered crystals practice favorable conditions identified screening large batch molecules prepared wide variety solutions tested hundreds thousands solution conditions generally tried finding successful conditions use physical mechanisms lower example change contain series chemicals lower constant solution contain large drive solution effects common try temperatures encouraging gradually lower temperature solution methods require large amounts target use high concentration difficulty obtaining large quantities grade protein robots developed capable accurately trial drops order volume means fold protein experiment compared trials set hand order factors known growing crystals generally held constant temperature protected vibrations molecules solutions flexibility tends likely ironically molecules tend self assemble regular unwilling assemble crystals crystals marred occur unit cell pack equally favorably multiple recent advances methods allow solving structure crystals having failed target try slightly modified version small changes molecular properties lead large differences behavior data collection mounting crystal crystal mounted measurements held ray beam rotated methods mounting past crystals loaded glass solution mother liquor crystals small molecules typically attached oil glass fiber loop plastic attached solid rod protein crystals loop flash frozen liquid nitrogen freezing reduces radiation damage rays noise peaks thermal motion effect protein crystals crack flash frozen generally pre soaked solution freezing unfortunately pre cause crystal crack generally successful conditions identified trial error loop mounted allows positioned accurately ray beam rotated crystal beam small crystal centered beam accuracy aided camera focused crystal common type offers angles rotation angle axis perpendicular beam angle axis axis finally angle loop axis angle zero axes aligned rotation allows convenient mounting crystal arm crystal mounted swung carried data collection mentioned involve axis older type circle relatives circle rotating small scale local ray tube source typically coupled image plate advantage relatively inexpensive easy maintain allow quick screening collection samples light produced limited material typically copper intensity limited power applied cooling capacity available avoid melting systems boiled accelerated strong electric potential having reached high speed metal plate strong lines corresponding inner shell metal common metal copper kept cool easily high thermal produces strong lines line suppressed thin foil simplest variety sealed ray tube stationary tube run electron beam power expensive variety rotating type source run beam power rays generally filtered use ray filters single single direction allowed strike crystal data analysis removes radiation crystal contributing useful information basically long tube clever arrangement gently curved mirrors mirror systems preferred small crystals large unit cells radiation radiation lights earth single powerful tool available ray ray beams generated large machines called machines accelerate electrically charged particles nearly speed light roughly circular loop magnetic fields generally national facilities dedicated data collected originally designed use high energy studying particles cosmic phenomena largest component electron storage ring ring actually perfect circle sided corner sector precisely aligned bend electron stream path bent bursts energy form rays radiation frequently specific requirements ray intense radiation cause radiation damage samples particularly crystals protects sample radiation damage freezing crystal liquid nitrogen temperatures radiation frequently advantage user allowing scattering experiments signal critical experiments sad mad free electron laser recently free electron developed use ray ray sources currently available rays coming bursts intensity source atomic resolution patterns resolved crystals small collection intense light source destroys sample requiring multiple crystals shot crystal randomly oriented beam hundreds thousands individual images collected order complete data set method serial solving structure number protein crystal structures noting differences equivalent structures collected sources recording reflections crystal mounted exposed intense beam rays rays pattern spots reflections observed screen crystal similar pattern seen shining laser compact disc relative spots provide information determine arrangement molecules crystal atomic detail reflections recorded photographic film area charge coupled device image peaks small angles correspond low resolution data high angles represent high resolution data upper limit eventual resolution structure determined images measures quality determined point crystal overall disorder observed peak crystal render unfit solving structure diagnosed quickly point image spots insufficient reconstruct crystal represents small slice transform collect necessary information crystal rotated step step image recorded step actually slightly required cover space sphere crystal higher symmetry smaller angular range recorded rotation axis changed avoid developing blind spot space close rotation axis customary rock crystal slightly catch broader region space multiple data sets necessary certain methods example mad requires scattering recorded usually incoming ray radiation single crystal collection data set owing radiation damage cases data sets multiple crystals taken data analysis crystal symmetry unit cell image scaling recorded series dimensional patterns corresponding different crystal orientation converted dimensional model electron density conversion uses mathematical technique transforms explained spot corresponds different type variation electron density determine variation corresponds spot relative strengths spots different images merging scaling variations combined yield total electron density data processing begins reflections means identifying dimensions unit cell image peak corresponds position space determine symmetry crystal space group space groups eliminated beginning example reflection observed molecules space groups possible allowed protein molecules generally accomplished routine having assigned symmetry data integrated converts hundreds images containing thousands reflections single file consisting records miller index reflection intensity reflection state file includes error estimates measures given reflection recorded image data set consist hundreds separate images taken different crystal step merge scale images identify peaks appear images merging scale relative images consistent intensity scale intensity scale critical relative intensity peaks key information structure determined repetitive technique data collection high symmetry materials cause record symmetry equivalent reflections multiple times allows calculating symmetry related factor reliability index based similar measured symmetry equivalent reflections assessing quality data initial data collected experiment space representation crystal position spot governed size shape unit cell inherent symmetry crystal intensity spot recorded intensity proportional square structure factor structure factor complex number containing information relating phase wave order obtain electron density map phase known electron density map allows build starting model phase directly recorded experiment known phase problem initial phase estimates obtained variety ways direct methods usually method choice small molecules non hydrogen successfully solve phase problems small proteins resolution data better direct methods obtain phase information exploiting known phase relationships certain groups reflections molecular replacement related structure known search model molecular replacement determine orientation position molecules unit cell phases obtained way generate electron density maps ray scattering mad sad ray past absorption edge changes scattering known way recording sets reflections different far far middle absorption edge solve structure popular method incorporating scattering proteins express protein host incapable media rich contains mad experiment conducted absorption edge yield position protein providing initial phases heavy methods multiple replacement electron dense metal introduced crystal direct methods space methods determine location obtain initial phases heavy introduced crystal heavy containing solution growing crystals presence heavy mad changes scattering interpreted yield phases original method protein crystal structures solved largely superseded mad model building phase having obtained initial phases initial model built model phases leading improved model given model atomic positions positions respective factors factors accounting thermal motion refined fit observed data yielding better set phases new model fit new electron density map round carried continues data model agreement measured factor defined formula structure factor similar quality criterion calculated reflections included structure factors depend resolution data rule thumb approximately resolution divided data set resolution yield final chemical bonding features hydrogen bonding distribution bond lengths angles measures model quality phase bias problem model building maps common technique check possible observe remembered resulting electron density average molecules crystal cases disorder resulting electron density existing extent longer electron density map weakly scattering hydrogen routinely invisible possible single appear multiple times electron density map protein multiple allowed cases detect structure incorrect changed example proteins undergo post modifications detected prior deposition structure model structure finalized deposited database cambridge structural database small molecules crystal structure database compounds protein data bank protein structures structures obtained private commercial ventures relevant proteins deposited public theory main goal ray determine density crystal represents dimensional position crystal ray scattering collect data transform inverted obtain density defined real space formula formula integral taken values dimensional real represents point space particular electron density moves direction points length corresponds formula divided corresponding formula transform formula integral summed possible values position crystal transform generally complex number magnitude phase related equation formula reflections observed ray phases obtain phases sets reflections collected known alterations scattering past certain absorption edge adding strongly scattering electron dense metal mercury combining phases yields transform inverted obtain electron density crystals perfectly periodic ideal case positioned perfect electron density perfectly periodic transform zero belongs called peaks reality crystals perfectly periodic mean position disorder types point defects molecules peaks finite width significant scattering scattered rays fall peaks intuitive understanding law intuitive understanding ray obtained model model given reflection associated set evenly spaced sheets running crystal usually passing centers crystal orientation particular set sheets identified miller let noted william lawrence proposed model incoming rays scattered mirror like plane assumption rays scattered adjacent planes combine interference angle plane ray results path length difference multiple ray formula reflection said miller correctly components identified known scattering angle gives unit cell parameters lengths angles unit cell space group law interpret relative reflections generally inadequate solve arrangement unit cell transform method carried scattering transform incoming ray beam represented wave simplicity let represented wave ignore time dependence wave concentrate wave spatial dependence plane waves represented wave strength incoming wave time given formula position sample let density produce scattered spherical wave proportional local incoming wave times number small volume formula constant let consider fraction scattered waves leave outgoing wave strike screen energy lost elastic scattering wave time scattered absorbed undergoes change phase formula net radiation arriving sum scattered waves crystal formula written transform formula measured intensity reflection square formula mates reflection corresponding point space reflection intensity opposite point opposite reflection known mate original reflection symmetry results mathematical fact density position real number noted transform transform transform complex number general ensure real transform mates complex magnitude opposite phase formula equality ensures mates intensity symmetry allows measure transform half space rotating crystal slightly instead revolution crystals significant symmetry reflections intensity mates cases space need measured favorable cases high symmetry data required completely explore space mate derived definition transform formula formula states sin transform separated sum purely real purely imaginary formula function real second integral zero values turn true satisfied formula implies sphere ray image represents slice spherical slice space seen sphere construction length elastic scattering changed represented radial sphere space shows values sampled given image slight spread incoming incoming ray beam values measured located spheres corresponding obtain set transform data necessary rotate crystal slightly sufficient symmetry present rotation needed symmetry transforms real functions electron density slightly needed cover space given resolution sphere practice crystal small incorporate reflections near boundaries spherical shells function known result transforms states function formula transform squared magnitude formula function electron density known function directly reflection computing phases principle determine crystal structure directly difficult realize practice function corresponds distribution crystal crystal unit cell peaks function given inevitable errors measuring mathematical difficulties atomic positions technique rarely solve structures simplest crystals advantages crystal principle atomic structure determined applying ray scattering non samples single crystals offer stronger signal sample definition periodic crystal composed unit cells repeated indefinitely independent directions periodic systems transform concentrated periodically repeating points space known peaks peaks correspond reflection spots observed image reflections grows number observed intensity spots grow like words crystal weak scattering individual unit cells powerful coherent reflection observed noise example interference liquid powder sample molecules sample random samples continuous spectrum uniformly spreads reducing measured signal intensity observed importantly information lost theoretically possible difficult obtain atomic resolution structures complicated molecules averaged data intermediate case fiber arranged periodically dimension nobel prizes ray international tables international tables volume space group symmetry 5th academic publishers international union isbn michael arnold international tables volume biological molecules academic publishers international union isbn international tables brief teaching edition volume space group symmetry 4th academic publishers international union isbn bound collections articles charles carter robert sweet methods san_diego academic press isbn charles carter robert sweet methods san_diego academic press isbn proteins practical approach 2nd oxford oxford_university press isbn textbooks warren ray new_york isbn blow outline oxford oxford_university press isbn burns space groups scientists engineers 2nd boston academic press inc isbn crystal structure determination oxford chemistry oxford oxford_university press isbn elements ray 2nd reading massachusetts publishing company isbn principles protein ray new_york isbn oxford oxford_university press isbn lewis crystal structure analysis new_york publishers isbn crystal structure determination berlin isbn biological cold spring harbor cold spring harbor laboratory press isbn introduction john sons isbn practical protein san_diego academic press isbn crystal structures patterns symmetry washington society america monograph series isbn rhodes crystal clear san_diego academic press isbn copy select chapters principles practice application structural biology new_york science isbn theory ray crystals new_york dover publications applied data analysis young method oxford oxford_university press international union isbn historical early papers rays crystals published international union early papers rays crystals published international union phillips development ray analysis new_york dover isbn numerous years ray published international union isbn editor years ray reprinted format congress glasgow scotland international union friedrich die der der die crystals rays new_york van structures life department health human services learning simple non technical introduction collection video series royal institution small illinois institute technology website international union interactive structure factor demonstrating properties pattern crystal transforms illustrating relationship crystal pattern lecture notes ray structure determination online lecture modern ray scattering methods materials analysis richard interactive timeline royal institution primary open database protein data bank acid cambridge structural database crystal structure database biological database derivative collaborative encyclopedia proteins molecules database structural classification proteins database protein structure classification list proteins known structure proteins membranes database structural structural suite web check unfavorable identifies proteins similar given protein


croatian patrol boat pennant number class patrol boat service croatian navy completed 1980s sixth ship class built yugoslav navy shipyard croatian war independence tactical group tasked enforcing naval blockade city split november croatian navy disabled vessel improvised torpedo leaving vessel drifting abandoned crew crippled ship away croatian locals nearby island subsequently repaired entered service croatian navy remains service croatian coast guard integral navy design construction laid shipyard sixth ship class patrol boats built yugoslav navy launched november measures length draught beam standard displacement tonnes long tons tonnes long tons powered diesel engines spin propellers maximum speed knots mph continuous speed knots mph range nautical miles knots mph autonomy days extended days wartime ship original armament consisted single gun mounted ship bow quadruple bridge gun stern depth charges carried anti submarine warfare duties located sides double barrel illumination launchers sensors included surface search radar service service yugoslav navy border patrol detachment november croatian war independence tactical group tasked enforcing naval blockade port split surrounding islands november patrol split islands hit improvised torpedo launched special forces croatian navy effectively starting battle channels command constructed torpedo small motor boat loaded explosives missile technician navy receiving training missiles sweden picked remote control plane parts hobby store handed gear yielded ability remotely control vessel explosion ripped hole forward section hull causing bow flood killing crew members remaining crew rescued class torpedo boat left evening november ship away croatian fishing ship nearby cove vessel beached prevent sinking early hours day remaining ships opened fire retaliation damaging yugoslav forces left area ship towed shipyard night november salvaged divers help ship repaired renamed entering service mile command croatian coast guard formed october assigned 1st division based split year ship underwent included installation new marine radar gps second refit occurred included stern gun create space needed hydraulic crane lower sea pennant number changed


croatian submarine pennant number modified class submarine submarine service croatian navy built yugoslav navy 1980s named outbreak croatian war independence overhauled division shipyard split croatia stripped equipment preserved retreating yugoslav forces shipyard workers modifications aimed improving ships endurance including diesel generator launched years later service need acquire new set batteries turn happened unsuccessful attempts selling foreign buyer offered museums croatia final destination pending design construction completed division shipyard split croatia fourth boat class measures metres feet length draft beam tonnes long tons surfaced tonnes long tons submerged constructed single hull design internal compartment divided sections forward command steering position exit chamber propulsion section underwater operations battery groups total cells power electric motors mounted single shaft spins blade propeller surface propulsion battery provided single diesel generator maximum speed knots kilometres hour miles hour underwater seven knots kilometres hour miles hour surfaced boat range nautical miles kilometres miles speed knots kilometres hour miles hour underwater endurance days improvement compared hours class boats maximum diving depth metres class designed reconnaissance small scale special operations mind possess offensive weapons torpedoes submarine use small dimensions easily maneuver relatively shallow waters adriatic_sea staying transporting special forces personnel mines aim mines disposal crew service croatian war independence served submarine flotilla yugoslav navy entering service late 1980s named like class submarines named rivers yugoslavia overhauled beginning war croatian forces captured started modification program improve operational capabilities submarine captured years earlier hull create space needed installation single diesel generator feature original class design lacked new steering system developed installed recommissioned according edition naval institute guide combat fleets world fitted active passive portable navigational radar board gps claim contradicted sources news reports stating submarine completed active effectively blind underwater 1990s pennant number painted existing battery set needed underwater propulsion expired needed replacement crew training boat operations limited surface drives aftermath february raised sea placed small platform naval base remained june croatian ministry defence released croatian armed forces long term development plan croatian plan stated croatian navy possess anti submarine warfare capabilities possesses submarine operationally usable designed offensive transporting underwater special forces armed forces croatia submarine capabilities submarine decommissioned croatian armed forces long term development plan defence minister time explained croatia join nato spring collective defense entire alliance need develop aspects defence system including submarine force unnecessary confirmed submarine sale state owned agency deals weapons sales starting price million croatian approximately million acting commander croatian navy time mentioned possibility installing new set batteries submarine fully operational sold higher price million considering potential overhaul sale didn happen decision donate submarine museum appeared submarine given technical museum agreement mayor milan government agencies project canceled difficulty transporting metres feet tall submarine city center museum croatian maritime museum split expressed interest obtaining display especially considering built split city service career main obstacle option maritime museum located fortress plans moving maritime museum port split hold new option includes moving military museum created appeared november final location decided


camouflage camouflage known usa painting family ship camouflage extensively world war lesser extent world war credited british marine artist norman rejected prior claim zoologist john graham consisted complex patterns geometric shapes contrasting colours intersecting unlike forms camouflage intention conceal difficult estimate target range speed heading norman explained intended enemy ship course poor firing position actually cause enemy miss shot firing adopted admiralty britain united_states_navy little evaluation ship pattern unique avoid making classes ships instantly enemy result schemes tried evidence success best mixed factors involved impossible determine important colour schemes effective attracted notice artists claimed like invented edward supervised ships world war painted series ships war based wartime work arthur similarly painted series ship intended purposes unlikely form camouflage drawing attention ship hiding approach developed allied navies unable develop effective means hide ships weather conditions british zoologist john graham proposed application camouflage british warships world war outlining believed applicable principle camouflage letter winston_churchill explaining goal confuse conceal disrupting ship outline compared effect created patterns series land animals jaguar taking example proposed vertical lines ships masts disrupted irregular white bands hiding ships conspicuous greatly increase difficulty accurate range finding letter calls use paint self appearance solid shapes example proposes paint ships guns grey grading white guns disappear grey background similarly advised painting shaded parts ship white brightly lit parts grey smooth grading making shapes structures invisible hoping achieve measure degree confusion enemy rangefinder mixing goals admiralty skepticism theory based analogy animals admiralty claimed july conducted trials decided paint ships grey adopting suggestions mind subsequent letters achieved american artist developed theory camouflage based coloration published controversial book coloration animal kingdom seeing opportunity theory service wrote churchill february proposing camouflage submarines like fish advocating painting ships white invisible ideas considered admiralty rejected proposals freak methods painting ships academic interest practical advantage admiralty noted required camouflage vary depending light changing colours sea sky time day angle sun repeated desperate efforts persuade authorities november travelled england gave demonstrations theory country warm welcome glasgow support avoided meeting war office intending win instead sailed home continuing write ineffective letters british american authorities marine artist royal naval volunteer reserve officer norman agreed aim confusion disagreed type confusion enemy mind wanted difficult enemy estimate ship type size speed heading confuse enemy ship commanders taking mistaken poor firing positions observer find difficult know exactly stern bow view difficult estimate observed vessel moving away observer position advocated masses strongly contrasted colour confuse enemy ship heading lighting conditions close ranges actually increase ship visibility conspicuous patterns obscure outlines ship hull superstructure ship correct heading making harder hit created response extreme need hosted organisation admiralty rejected approach supported scientific theory proposal use based known camouflage methods coloration dropped favour non scientific led socially connected explanations principles clear logical based years study simple inspirational based artist perception decision likely admiralty felt comfortable sharp contrast awkward relationship claimed known theories camouflage admitting having heard old idea roman times possible mechanisms naval museum curator robert suggested mechanism camouflage kind confusion intended coincidence naval artillery optical mechanism operated human range operator adjusted mechanism half images target lined complete picture argued intended hard patterns looked abnormal halves aligned important submarine included patterns included false bow wave difficult enemy estimate ship speed historian sam argued knew impossible ship invisible paint extreme opposite answer conspicuous shapes violent colour contrasts confuse enemy submarine commanders pointed olympic scheme example different mechanisms work contradictory patterns ship funnels imply ship different heading curve hull funnel false bow wave creating misleading impression ship speed striped patterns bow stern create confusion end ship work lines suggested testimony boat captain half mile ship steering course right angles crossing starboard port dark painted stripes stern appear bow broad cut green paint amidships looks like patch water weather bright visibility good best camouflage seen scientist nicholas scott samuel colleagues presented evidence moving patterns computer human perception speed distorted patterns speeds required larger available world war ships scott samuel notes targets experiment correspond patterned land vehicle range metres travelling kilometres hour confusion aiming observed size rocket propelled grenade travelling metres seconds distance moved target centimetres save life situation world war persuaded lord admiralty winston_churchill adopt form military camouflage called argued following american artist coloration animals general order british fleet issued november advocated use approach applied ways british warships hms officers noted pattern increased difficulty accurate range finding following churchill departure admiralty royal_navy reverted plain grey paint schemes informing july trials undertaken range conditions light surroundings rendered necessary modify considerably theory based analogy colours patterns animals british_army inaugurated camouflage section land use end sea heavy losses merchant ships germany submarine warfare campaign led new desire camouflage marine painter norman promoted system stripes broken lines external shape violent colour contrasts confuse enemy speed dimensions ship lieutenant commander royal_navy patrol duty implemented precursor beginning industry charge camouflage unit technique large groups merchant ships british merchant ships painted came known camouflage applied naval vessels starting august british patterns different tested small wooden models viewed studio model designs painted women london royal academy arts scaled designs real thing painters project creative people including artists set designers designed camouflage camouflage accepted admiralty practical visual assessment improving performance modifying designs colours camouflage strategy adopted navies led scientific studies colour options enhance camouflage effectiveness war starting october admiralty committee met determine priority invention asked thought personally benefited written avoided question implying said claim invented principle principle course invented nature agreed suggested letters system create illusion course vessel painted october admiralty told seen responsible painting awarded sum invention effectiveness effectiveness highly uncertain time world war nonetheless adopted britain america admiralty analysed shipping losses unable draw clear conclusions ships attacked compared ships suggesting increased visibility argued attempting ships hard ships struck torpedoes ships sank compared similarly ships struck amidships compared comparisons taken imply submarine commanders difficulty deciding ship heading aim ships painted larger ships tons compared ships making comparisons unreliable factors choice colour scheme size speed ships tactics varied possible determine factors significant schemes worked best carry experiment camouflage failed reliable advantage plain american data analysed van ships painted march end war november year american tons ships sunk ships sunk torpedoes collisions mines navy ships sunk period world war effective camouflage world war useful especially aircraft advanced time use world war radar reduced effectiveness enemy submarines royal_navy paint schemes reappeared january unofficial competitions held ships best camouflage patterns royal_navy camouflage department came scheme devised young naval officer peter scott wildlife artist developed western approaches schemes admiralty intermediate pattern came use followed admiralty standard schemes united_states_navy implemented camouflage painting program world war applied ship classes patrol craft battleships essex class aircraft carriers designs known measures identified number arbitrary process involved planning stage review fleet wide implementation united_states_navy measures involved patterns simple totally false bow wave traditional grey deck blue replacing grey ship counter threat measures february united_states_navy pacific fleet decided ships non measures threat atlantic fleet continued use ships transferred pacific nazi_germany kriegsmarine camouflage norwegian campaign wide range patterns authorised commonly black white diagonal stripes patterns designed hide ships harbour near coast painted plain grey operating atlantic arts abstract patterns camouflage inspired artists including characteristic claimed credit camouflage experiments technique conversation shortly saw painted cannon streets paris remarked yes britain edward supervised camouflage painting war created series war based work ships canada arthur ships wartime compositions america painted united_states_navy ships camouflage sea historian camouflage peter forbes comments ships modernist look designs succeeding avant garde art art camouflage including evolution featured theme imperial war museum fleet library rhode_island school design exhibited rediscovered collection printed plans camouflage american world war merchant ships exhibition titled centenary art commission backed camouflage installations britain covered pilot ship liverpool canning dock bright multi coloured artwork city liverpool art festival painted hms president anchored bridge london commemorate use century peter blake commissioned design exterior ferry called everybody combining trademark motifs stars targets etc world war designs uses patterns reminiscent camouflage mask test cars trials formula testing period red bull car painted scheme intended rival teams ability designer adam harvey similarly proposed form camouflage reminiscent personal camouflage face detection technology attempts block detection facial recognition technologies creating anti face uses covering certain facial features transformation altering shape colour parts face combination sea shepherd conservation society patterns fleet similarities drawn modern usage short production intent cars released tested public roads kind pattern prevents design style photographs released car taken


ship camouflage ship camouflage form military deception ship painted colors order obscure confuse enemy visual observation types marine camouflage blending paint scheme attempts hide ship view deception ship look smaller ships mimic chaotic paint scheme tries confuse estimate distance direction heading hide ship slightly brighter night sky royal canadian navy lighting camouflage ships classical times mediterranean pirate ships painted blue gray records scout ships painted bluish green gathering intelligence coast britain wars ships painted age sail sides american_civil_war ships run night reconnaissance ship camouflage earnest british admiralty world war marine artist norman led research camouflage resulting painting thousands british later american ships patterns intended ships invisible cause enemy miss shot taking poor firing position second world war revisited royal_navy united_states_navy applied limited extent navies second world war radar painted camouflage effective craft continue use camouflage schemes alongside anti radar stealth early use ship camouflage occasionally ancient times 3rd century book notes mediterranean pirate ships painted blue gray writing 4th century says venetian blue bluish green color sea years wars sent scout ships gather intelligence coast britain ships painted entirely bluish green wax sails ropes color sailors marines dressed venetian blue age sail deception ships paint applied hoc ships captains temporary tactical advantage ship painted look like cannon ports hidden painted canvas look harmless additional cannon ports painted appear powerful example battles american hid guns ship general appear slow merchant ship allowed ship approached close range faster british quickly pulled painted canvas away delivered broadside capturing enemy american_civil_war camouflage paint applied sides union blockade blockade runners aiding painted ships mist gray hide coastal fog union blockade crew painted white wore white clothing night reconnaissance patrol enemy held river 1890s german french fighting ships painted gray american interest ship camouflage given official funding spanish american war white light gray medium gray paint schemes evaluated ability hide ship seen distant sky horizon artist investigated color schemes paint natural shadows united_states_navy switched gray white 1900s great white fleet set globe white hulls white paint proved unsuccessful return great white fleet ships painted gray british ships began painted gray lighter shades preferred minimize solar heating warmer climates world war world war increasing range naval guns great fear high speed long range torpedoes warships merchant ships caused significant increase use ship camouflage royal_navy patterned ship camouflage pioneered britain early world war zoologist john graham advised winston_churchill use camouflage break ships outlines appear solid following american artist beliefs effective political ideas abandoned churchill departure admiralty postwar legal action claim credit ship camouflage failed successor marine artist norman successfully promoted idea camouflage sought image disruption admiralty researched issued large number designs known simply counter threat submarines models painted women artists tested laboratory viewing trials october admiralty ordered merchant ships painted patterns purpose camouflage motion visual deception later explained primary object scheme cause enemy miss shot actually firing position ship sighted correct position making matter difficulty submarine decide exact course vessel attacked british merchant ships naval vessels painted camouflage measures included fitting anti rangefinder masts yards battleships hms emperor india practised heavily armed ships disguised merchant ships german_imperial_navy german_navy little emphasis camouflage battle jutland german naval effort case went submarine warfare germany use disguise painting ships colour schemes british neutral shipping example painted resemble british liner olympic managed reach america british blockade germans use commerce raiders converted hidden weapons long range able slip british blockade attack shipping far away south atlantic german world war merchant ships rarely use ships allied navies attack merchant shipping navies allied navies france italy essentially followed admiralty camouflage practice american camouflage experiments included submarine painted color pattern broad vertical stripes designed william white stripes separate green blue stripes visited united_states advise navy ship camouflage schemes merchant ships naval transports smaller warships battleships variety patterns second world war color paint schemes attempted sea sky near horizon navy painted ships dark gray white structures bridge level navy royal_navy painted ships dark gray hull light gray superstructure turrets measure graded system sea blue low hull continuous deck ocean gray masts painted gray measure modified ocean gray navy blue low hull continuous deck painted parallel waterline main deck bold contrast horizontal line near horizon reduced visibility surface observers created illusion greater range camouflage considered effective gunnery engagements surface units shore batteries areas aerial observation unlikely atlantic european coastal waters end end world war worn shore bombardment ships pacific late destruction japanese naval aviation capability battle philippine sea similar admiralty standard schemes applied beginning assumed enemy forces radar ships painted light gray overall sea blue patch low hull main gun turrets entire length hull united_states_navy united_states_navy naval research laboratory began studies tests low visibility camouflage ships measures like false painted bow wave impression high speed times measures making cruisers resemble destroyers discontinued causing station keeping confusion ships operating formation color schemes included light gray gray ocean gray black gray found provide reasonable protection widest range conditions standard navy paint scheme world war ocean gray standard paint scheme war black submarines discontinued destroyers determined black ships remained noticeable gray ships nights navy painted ships sea blue overall aircraft battle coral sea battle midway ships painted completely blue came attack ships wearing color schemes advice united_states blue color extensively western southern pacific minimize detection identification enemy aircraft dark blue proved effective artificial illumination night actions upper surfaces aircraft operating carrier decks painted similar shade blue sailors ordered wear white uniforms system white large patches light sea blue called blue measure useful arctic latitudes extended twilight frequent fog cloud cover purity color important realization effect colors appear lighter appear darker low levels illumination pattern increased course deception increased visibility night measure medium pattern navy blue black background lighter measure emphasized mistaken identity course deception submarine attack patterns carried bow light gray aft blend wake measure based world war system modified observations western pacific applied surface ships pacific different patterns devised classes large numbers ships pattern identify class ship royal_navy world wars royal_navy ships painted dark gray home_fleet light gray mediterranean caribbean seas white indian_ocean western pacific home_fleet ships painted medium gray decrease visibility peacetime dark gray year war british captains largely painted ships saw fit hms believed ship adopt camouflage paint scheme december class destroyers flotilla similar scheme contrasting stone colored concern arose german aerial reconnaissance scapa_flow home_fleet ships painted schemes dark brown light gray light green april august identity confusion port home_fleet ships medium gray december royal_navy painted mediterranean submarines dark blue reduce submerged visibility aircraft captain louis 5th flotilla class destroyers painted pink observed union castle liner disappear convoy autumn sunset company unusual gray hull color reasoned color effective camouflage dawn dusk periods devised similar shade mixing medium gray small venetian red effectiveness disputed applied destroyers cruisers numerous small warships maintained scheme use coastal waters admiralty camouflage section established october admiralty camouflage schemes universally adopted difficulties operating schedules shortages paint nearly destroyers larger ships wore admiralty camouflage scheme late commonwealth captains executed official camouflage schemes greater variation customary american measures initial admiralty camouflage schemes employed varying shades gray blue green colors blend background sea sky different light conditions schemes devised capital ships emphasized identity confusion hms queen elizabeth ship receive official camouflage scheme january ships received similar schemes evident small differentiated effective camouflage ranges simplified admiralty light dark schemes use larger simpler colors light schemes intended use higher latitudes skies overcast dark schemes darker colors providing effective disruption bright sunlight expected admiralty western approaches scheme evolved camouflage scheme applied hms broke june suggestion naturalist peter scott serving aboard ship broke painted white large patches light gray light sea blue light sea green broke achieved notoriety collision captain ship claimed unable broke escort captains observing broke experimented similar schemes including dark gray dark blue increased contrast tried painting ships entirely white emphasize admiralty omitted light gray peter scott scheme white large patches light sea blue light sea green adopted use exclusively destroyers smaller ships engaged anti submarine operations effective scheme typical north_atlantic weather conditions fog overcast captain class frigates delivered painted white pattern sea blue light grey american western approaches variant colors american camouflage measures pattern unique ships produced royal_navy replaced admiralty schemes colors refit home_fleet destroyer scheme similar western approaches scheme darker shades blue gray rear ship assist station keeping british decks usually dark gray admiralty informal approach changed branch naval research laboratory established spa commander james test ship camouflage schemes painted models floated large tank examined different backgrounds theater lamps simulate varying lighting conditions experimental coating able change color tested royal_navy submarines suggestion professor lead applied hull enabling black application solution sea water night operation day sailing solution hydrogen sea water applied producing returning hull white colour desirable daytime conditions german kriegsmarine german kriegsmarine ships second world war light gray overall dark gray hulls retained scheme war cruiser instance gray hull light gray superstructure camouflage usually combinations pale gray dark gray sea blue example hull battleship pattern stripes gray background later painted bows forward main guns painted black air observation decks fore aft bearing large black white red field main gun turrets red baltic yellow tops air recognition battleship set norway camouflage painted gray final trip atlantic cruiser admiral wore low contrast pattern irregular dark gray marks light grey superstructure dark gray hull black waterline away air support raiding dark gray turret tops larger ships false bows painted different shade rest hull create impression ship greater range observer german decks dark gray smaller ships operating north_sea baltic_sea painted white pale gray blend daytime mist nighttime organisms world war germans employed disguised commerce raiders atlantis ships able modify appearance throw searching allied cruisers royal canadian navy lighting camouflage project royal canadian navy experimented variable counter illumination camouflage match horizon light levels minimize ships prolonged arctic twilight experiments test ship illuminated mounted results improved use blue green filters measure night sky ship visibility reduced technology adopted practice navies italian ships navy retained pre war scheme light gray overall smaller ships larger units camouflage dark gray light sea blue light sea green light gray italian high visibility pattern red white diagonal stripes aircraft attack japanese ships generally special tactical situations camouflage improvised battleships decks mixture help hide passing san night october battle gulf japanese ships largely retained pre war dark gray paint scheme major units like aircraft carriers changed dark sea green aircraft carriers flight decks painted camouflage ineffective remnants japanese navy seeking hide american air power battleships painted variety camouflage measures example wore olive green overall turrets painted light green gray stripes olive dress broken patches gray red brown yellow dark green soviet ships dark gray overall medium gray french_navy light gray war regime free french ships operated british adopted british schemes refitted american shipyards usually american measure second world war coastal river boats second world war universal adoption radar traditional camouflage generally effective led development stealth ships form radar camouflage camouflage helped united_states warships avoid hits vietnamese shore batteries optical navy boats green overall broken patterns gray black uss freedom combat ship said navy ship camouflage reminiscent world wars


latin art book mathematical probability written jacob published years death nephew seminal work consolidated apart topics central ideas probability theory version law large numbers widely regarded founding work subject addressed problems today classified way added subjects consequently dubbed important historical landmark probability mathematical historians importance early work large impact contemporary later example wrote text including work incorporated fundamental topics theory combinations aforementioned problems way connected burgeoning subject properties eponymous numbers instance core topics probability expected value significant portion important work background europe subject probability formally developed 16th century work interest branch mathematics largely habit gambling called classical definition probability event possible outcomes select probability occurring formula actual influence mathematical scene great wrote light subject titled book games chance published posthumously date historians cite beginning development modern probability theory known time began correspondence discussing subject initiated communication earlier year paris named sent questions practical applications theories particular posed problem points concerning theoretical player game prize divided players external circumstances halting game fruits correspondence interested including calculations games chance appeared final chapter van posthumously published results eponymous triangle important concept referred triangle work triangle traits triangle triangle book art published anonymously paris authors presumably leading worked latin title book successful book logic time consists books fourth dealing decision making uncertainty considering analogy gambling introducing explicitly concept probability field statistics applied probability john published natural political observations bills mortality initiating discipline work things gave statistical estimate population london produced life table gave survival different age groups examined different causes death noting annual rate suicide accident constant commented level stability sex ratio interpretation tables discussed series brothers realized difference mean median estimates christian life table smooth curve creating continuous probability distribution published later prime minister dutch republic published similar material work van treatise life statistical concepts determine life practical political purposes demonstration fact branch mathematics significant pragmatic applications work widely distributed dutch republic fall power execution mob apart practical contributions work exposed fundamental idea probability assigned events inherent physical symmetry chances dying certain age unlike rolling coin simply counting frequency occurrence probability mere development wake pioneers produced results contained recorded diary began work age intrigued problems read work triangle work applications probability theory earlier requested copy acquaintance failed provide manage provide work largely foundations constructed apart works certainly possessed knew contents secondary sources art bills mortality makes explicit reference works progress time pursued means working periods respect discovery distinguished aims times period lasts devoted study problems games chance posed second period investigations extended cover processes known determined finally period problem measuring solved publication produced number treaties related probability journal des appear problems concerning probability players winning game solutions published article cum addition published solution journal pages public lecture delivered february related theory probability letter amy sur les parties letter friend sets game tennis published corresponded learning discoveries probability brother managed provide thoughtful criticisms law large number failed provide work desired outset wished work demonstrate probability theory numerous real world applications society line work serve rigorous method logical reasoning insufficient evidence moral hoped theory probability provide comprehensive consistent method reasoning ordinary reasoning overwhelmed complexity situation title chosen link concept provided symbolic link desired extension prior words art defined chapter art measuring precisely possible things goal able choose follow actions course determined better satisfactory safer development book terminated death book essentially incomplete compared original vision quarrel younger brother competent person fulfilled jacob project prevented hold manuscript jacob children task editing publishing manuscript finally jacob nephew years jacob death managed publish manuscript contents work originally published latin divided parts covers notably theory combinations standard foundations today problems today known way discusses motivation applications sequence numbers closely related number theory probability numbers bear today notable achievements depth provides section solutions problems posed end work particularly develops concept expected value weighted average possible outcomes event developed following formula formula formula expected value attaining value values expected value assuming outcomes value implying key theory developed probability achieving certain number successes number events today named trials given probability success event shows mathematical induction given number favorable outcomes event number total outcomes event desired number successful outcomes number events probability successes formula concludes known distribution second expands systematic objects important ways combinations form basis subject introduced earlier purposes probability theory gives non proof expansion arguments note related second section discusses general formula sums powers free formula called numbers influenced work later proven numerous applications number theory applies probability techniques section common chance games played playing cards feel necessity describe rules objectives card games presents probability problems related games method established posed example problem involving expected number court cards jack queen king pick card hand standard deck cards containing court cards deck cards contained court cards card hand fourth section continues trend practical applications discussing applications probability personal judicial financial decisions section differs school thought known defined probability sense counter produces result resembling law large numbers describes predicting results observation approach theoretical probability trials held contrast defined probability terms proud result referring golden remarked problem engaged years early version law known today weak law large numbers rigorous general modern version primary sections tract concerned infinite series reprint published legacy considered landmark work founding work mathematical probability anthology great mathematical writings published edited historian describes studies set work occupying 18th 19th centuries influence lasting centuries anthony edwards praised book groundbreaking content writing demonstrated thorough familiarity form written book constructed recently notable popular mathematical historian william called paper milestone probability theory work masterpiece greatly aided describes long established reputation work influenced contemporary subsequent like tract quoted frequently notably scottish mathematician jacob program applying art matters practical life terminated death continued nephew having taken parts entitled published finally edited assisted publication later edited jacob complete works supplemented results taken jacob diary collaboration wrote book probability essay sur les hazard appeared seen extension iii applies probability analyze games chance commonly played time wrote extensively subject extension doctrine chances method calculating probability events play notable achievement probability discovery instance central limit able approximate distribution normal distribution achieve developed sequence function refer formula sum powers numbers adopted term probability jacob previous publications gambling works enormously popular golden convergence theoretical probability probability taken notable later day like complete proof law large numbers arbitrary random finally provided half 20th century significant indirect influence thomas simpson achieved result closely resembled according simpsons work preface work depended greatly fact described simpson work version finally thomas wrote essay discussing theological implications results solution problem determining probability event relative frequency taken proof existence god finally simon published des consolidated laid fundamental results probability statistics moment generating function method squares probability hypothesis testing completing final phase development classical probability light good reason work hailed seminal event influences direct indirect set mathematical study spinning theology impacted