<p>newsletter </p><p>OF THE <strong>James Clerk Maxwell Foundation </strong></p><p>Issue No.5 <em>Spring 2015 </em></p><p>Maxwell and the Rings of Saturn </p><p><strong>by Professor Andrew Whitaker, Emeritus Professor of Physics, Queen’s University, Belfast </strong></p><p>LeVerrier,ortobeworthyofthecredit bestowedonhimbyBritainand,in particular,Cambridge. </p><p>ThefundsfortheAdamsPrizewere </p><p>providedbyalumniofAdams’Cambridge </p><p>college,St.John’s,andtheprizewasin thegiftoftheUniversity.AiryandChallis </p><p><em>A v ie w o f t h e r ing s o f S atur n ( fro m G ribbin , J oh n a nd Goodwin , S imo n ( 1998) . E mpir e o f t h e S un : P lanets an d M oon s o f t h e S ola r S ystem . C onstable , L ondon.) </em></p><p>wereheavilyinvolvedinchoosingtopics </p><p>Againstthisbackground,whywas </p><p>MaxwellconsideredtheringsofSaturn </p><p>tobe‘<em>th e m os t r emarkabl e b odie s i n t he </em></p><p><em>heavens</em>’,secondonly,inhisopinion,to thespiralnebulae.Yetitseemsextremely unlikelythathewouldhavedevoted asubstantialamountoftimeand efforttodeterminingtheirstructure mathematicallyhadthetopicnotbeen chosenin1855asthesubjectofthe AdamsPrizeof1856. inthefirstfewyearsoftheprize,andin Maxwell’syearWilliamThomsonwas alsoanexaminer.Thomson,laterLord Kelvin,had,ofcourse,beenProfessorof NaturalPhilosophyatGlasgowUniversity since1846,butretainedverystronglinks withCambridgethroughouthiscareer. ThustheinstitutionoftheAdamsPrize andthequalityoftheprize-winning essaysmayberegardedasanelementof academicrivalrywithFrance,anditis quitelikelythatMaxwellsawhisheavy laboursinthisway. </p><p>Maxwellpreparedtoputinsomuchwork overseveralyearsontheringsofSaturn? Admittedlytheprizewassubstantial– £130,orperhaps£13,000intoday’sterms, andthiswasrathermorethanathirdof hisfullyear’ssalaryatAberdeen.Butitis morelikelythatthereasonsfortaking onthechallengewere,firstly, personal prestige,but,secondly,andevenmore importantly,thewishtomaintainor increasethescientificstatureofBritain andinparticularCambridgeUniversity. </p><p>Thedeadlineforsubmissionwas December1856,andMaxwellsubmitted hisattempt–theonlyone–justbefore thedeadline.Hewasawardedtheprize inJune1857,butcontinuedtoworkon thetopicforafurtheryear,finally <br>TheAdamsPrizewasinstitutedin recognitionforthecontributionofthe youngCambridgemathematicianJohn CouchAdams,madeonlyeightyears earlier,tothediscoveryofthenew planetNeptune.Hiscontribution, <br>Asearlyas1610,Galileohadobserved structureaboutSaturn,thoughitwas ChristianHuygensin1656whowasable toidentifyitsringnatureandJeanCassini, acenturylater,whodiscoveredthat therewere,infact,twoconcentricrings separatedbyadarkband.Shortlybefore thesettingoftheAdamsPrizetopic, severalastronomersidentifiedaninner darkring,whichwaspartiallytransparent. publishinghisresultsasabookin1859. ThiswasatatimewhenMaxwellhada greatrangeofotherinterestsandduties. FromMarch1855,hemustcertainlyhave beenabsorbedbyhisfirststudieson electromagnetism.InApril1856his fatherdied,andevenapartfromthetime requiredforgrieving,hespentmuch efforttakingoverthechargeofthefamily estate.Also,inFebruary1856,justbefore hisfatherdied,hehadappliedforthe vacantChairofNaturalPhilosophyat Aberdeen’sMarischalUniversity, requiringhimtotaketimerequesting testimonials.Hewasdulyappointedand tookuphispostinNovemberofthatyear, andthis,ofcourse,requiredhimto prepareteachingandalsotowriteand presentaninaugurallecture. though,wasdisputed,particularlyin France.Adamshadtoldthesenior Cambridgeobservationalastronomers, GeorgeBiddellAiryandJamesChallis, ofhispredictionofthepositionofthe planetasearlyasSeptember1844,buthe hadnotpublishedhiswork,andno searchhadbeenmadefortheplanet beforetheFrenchmathematicianUrbain LeVerrierpublishedasimilarprediction, andwasalsoabletopersuadethe GermanastronomerJohannGalleto searchfortheplanet.Gallespeedilymet withcompletesuccessinSeptember 1847.Toputitmildly,Frenchscientists werenotconvincedthatAdamsdeserved tosharethehonourofthediscoverywith </p><p>Therewere,ofcourse,manyideasabout thestructureoftherings,inparticular whethereachringwassolidorconsisted ofalargenumberofrocks.Howeverthere wasverylittlerigorousmathematical analysis,and,asAirypointedout,eventhe conclusionsofthegreatmathematician Pierre-SimonLaplacewere somewhat flawed,thoughmanyofhisarguments werevalid–heshowedthattherings couldnotbeauniformsolidbutclaimed theythereforemustbeanirregularsolid. </p><p>ꢀ</p><p>newsletter </p><p>OF THE <strong>James Clerk Maxwell Foundation </strong></p><p>SowemayconsiderMaxwell’sworkas detailedrigorousandcomprehensive neighbouringregions,thesystemmoving towardsequilibrium.YetMaxwell’s neareroneofitsneighbours,itwouldseem thatgravitationwouldacttodecrease furtherthedistancebetweenthetwo satellites.Butthereverseoccurs,andfor thesamereasondiscussedinthefluidcase. Whenasatellitespeedsup,itswingsout fromitsorbit,andsoessentiallyitsangular speeddecreases.Thesituationisindeed stable. mathematicsonanessentiallyblankcanvas. mathematicsshowstheoppositeeffect occurring. <br>Maxwell’smethodswerenotactuallyvery </p><p>advanced,consistingofpotentialtheory, mainlyusinglineardifferentialequations, TaylorseriesandFourieranalysis,butthe <br>Supposeaportionoffluidneedstoincrease itsspeedaroundtheplanetinorderthatthe systemshouldmovetowardsequilibrium. analysiswassophisticatedandexceptionally Asitincreasesitsspeed,thebalance sure-footed.Ingeneral,hesearchedfor equilibriumconfigurationsofplanetand ring,andthenusedTaylorseriestostudy whetheranysuchconfigurationmightbe stabletosmalldisturbances. betweengravitationalattractionand centrifugalforceisbroken,andthisportion offluidmovesoutwards.Thusitspathhas alargercircumferenceandsoitsangular speeddecreases. Socomparedtoadjacent portionsofthering,itisgoingbackwards, andtheexpectedcatchingupistotally stymied.Thusthedisturbancedoesnot <br>Itmustberememberedthatthereismore thanonering,andMaxwellproceededto investigateasystemoftworings,eachofthe sameformasthesingleringjustdiscussed. Complicatedphenomenamayoccur;if,for example,awaveinoneringisinresonance withadifferenttypeofwaveintheother <br>Maxwellwasfirstabletoshowthatthecases ofauniformringoranon-uniformringdid notleadtostablesolutions.Hedid,though, findahighlybizarrecaseofstability–a uniformringloadedataparticularpoint withaveryheavyweight.Theconditions forstabilityofthis,somewhatodd,type ofringwerestringent;theratioofthe displacementofthecentreofgravityofthe ringtoitsradiusmustbebetween0.8159 and0.8279,andtheweightatthespecial pointmustbebetween4.43and4.81times thatoftherestofthering.Amusingas thissolutionwas,itwasclearfromdirect observationthatitborenorelationtothe actualringsystem,soMaxwell’soverall conclusionwasthateachringwasnota solidsystem. </p><p>resultinarestoringeffectbutinanincreasing ring,acombinedwavemayincrease divergencefromequilibrium.Inotherwords afluidringsystemisintrinsicallyunstable. </p><p>Maxwellwastowritethat:“<em>Thi s e ffec t i s v ery remarkabl e a s s howin g t h e d estructiv e e ffec t o f a n a pparentlyconservativ e f orce.</em>” </p><p>withoutlimitleadingtocollapseofthering system.Maxwellargued,though,thatthe ringsystemcouldexistforaverylongtime withoutsuchdestruction. Maxwellknew,ofcourse,thathisregular ringswereanover-simplification,and attemptedtogeneralizetoanirregular distributionofsatellites;itseemslikelythat thesethoughtsledtohisimportantwork onkinetictheory. <br>AsMaxwellpointedout,thefactthatSaturn itselfcouldbeseenthroughtheinnerdark ringinitstruepositionindicatedthe correctnessofthissuggestion.Thelight mustbepassingthroughgapsinthering; iftheringwerefluidtheimagewouldbe refracted.Thustheonlypossibilityseems tobethateachringconsistsofavery largenumberofunconnectedsatellites. NowthechallengewasforMaxwellto showthestabilityofsuchasystem. <br>Maxwell’sexplanationhasbroadlybeen foundtobecorrectbytheVoyagermission ofthe1980sandtheCassiniprobeof2009. Eachringconsistsofanimmensenumber ofparticles–mostlyicebutsomerocks– eachrotatingattheappropriatespeedfor itsdistancefromSaturn.Eachring,though, consistsofmuchvariationofbrightness – maximaandminimawithtotalgapsand ringletsofveryhighdensity.Itisnicetonote </p><p>thatthereisa<em>Maxwel l g a p</em>anda<em>Maxwell ringlet. </em></p><p>Maxwellnowconsideredthepossibilitythat theringsystemwasfluid,whichinitially attractedhim.Naturallyinordertobalance centrifugaleffects,theringmustrotate.His methodwastoanalyzewavemotioninthe ringandtoconsiderwhethersuchwaves willbestable.Letusimagine,forexample, aplacewhere,aspartofthewavemotion aroundthering,theringisthick,andfor stability,fluidshouldmoveawaytothe <br>Maxwellmodelledthesituationwitha systemofequivalentrocksorsatellites spacedequallyroundthering,and calculatedwhetheranydisturbancewould leadtoawavetravellingroundtheringora totaldisruptionofthesystem.Atfirstsight, thesecondpossibilityseemedlikely,forifa particularsatelliteisdisturbedsoastobe </p><p>William Dyce Cay (1838-1925), Civil Engineer </p><p><em>James Clerk Maxwell’s mathematical cousin </em></p><p><strong>by Professor Roland Paxton, MBE, FICE,&nbsp;FRSE, Hon. Professor Heriot-Watt University; Vice-Chair, Institution of Civil Engineers (ICE) Panel For Historical Engineering Works ; Trustee of the James Clerk Maxwell Foundation </strong></p><p>WilliamDyceCay,secondsonofRobertDundas Cay,W.S.,lawyerandbrotherofFrancesCaythe motherofJamesClerkMaxwell(1831–79)was bornon28March1838at18RutlandSt.Edinburgh. HewaseducatedattheRev.Wm.Bliss’sschool, Peeblesfrom1844–53andEdinburghUniversity where,in1856,heobtaineditshighest mathematicalprize,theStraitonGoldMedal and1stprizeinthe2ndDivisionoftheNatural Philosophyclass. <br>Inobtainingtheseawards,Cayacknowledgedthat </p><p>the‘<em>tuitio n a n d e xample</em>’gainedfromhiscousin </p><p>(Maxwell)onlongwalksfromtheestateatGlenlair, </p><p>Kirkcudbrightshire,in1855had‘<em>ha d g oo d e ffect</em>’. Thiswaseventhough‘<em>befor e I h a d g o t t o t he bottom o f o n e e xampl e h e h a d r ushe d o f f i nt o a nother</em>’!In1856 </p><p>MaxwellwentwithCaytoBelfastandintroduced himtohisfriendJamesThomson(elderbrother of William,laterLordKelvin),Engineerto BelfastWaterworksand,from1857,Professor of EngineeringatQueensCollege,Belfast. </p><p><em>Willia m D yc e C a y © I C E A rchives </em></p><p>newsletter </p><p>OF THE <strong>James Clerk Maxwell Foundation </strong></p><p><em>Cay’ s G lenlai r r oa d b ridg e – 4 5f t s pa n © K . M cCrae </em><br><em>Aberdee n H arbou r a fte r i mprovement </em>Groome’s Gazetteer 1882 </p><p>CayservedasapupilunderThomson from1856–58,completinghisfour-year apprenticeshipinNovember1860asan assistantresidentengineerwithleading EdinburghconsultingengineersB.andE. Blyth.Heworkedontheconstructionof the60-milePortpatrickRailway(from CastleDouglas)fromthefirm’sCreetown siteofficeandafterwardsinitsEdinburgh office.Interestingly,aresidentengineer contemporaryonthisprojectwas Maxwell’sfellowEdinburghAcademical, AllanD.Stewart(1831–94–aCambridge University9thwranglerin1853,theyear beforeMaxwellbecame2ndwrangler). Stewartlatercontributedsignificantlyto thedesignoftheTayandForthBridges, includingtheForthsuspensionbridge (abandonedinthewakeoftheTayBridge failure)inthefeasibilityreportonwhich itwasnotedthatheapplied<em>‘Professor </em></p><p><em>Cler k M axwell’ s d iagram s o f f orce s … w ith muc h s kill’. </em></p><p></p><ul style="display: flex;"><li style="flex:1">Caythenembarkedonhismost </li><li style="flex:1">Inconstructingtheharbourentrance, </li></ul><p>importantcivilengineeringworkas ResidentHarbourEngineeratAberdeen from1867–80.Hisdirectionofmajor improvementstotheharbour(seemap) includedchannelizingaboutamileofthe riverDeeandconstructionofthepresent SouthBreakwater(1050ftlong)–see illustrations. stillinservice,Cayadoptedconcrete, inpreferencetotraditionalrubbleand masonry,usingabout15,000tonsof PortlandCementinliquidconcreteand largeblocks.Fullwidthsinglepours rangeduptoathenremarkable1,300 tons.Hedesignedtheplantandstaging andimplemented,from1872,anew modeofdepositingliquidconcretefrom ahopperbargeto20ftbelowLowWater injutebagsholdingupto100tons. </p><p>Cayalsodesignedsteam-operated bargesforcarryingdredgedmaterial andaconcretemixingmachine.His experimentalworkincludedquantifying theincreasedearlystrengthofcement briquettesmadewithsaltwater. Althoughhedidnotinventtheconcrete bagtechnique,hewasthefirsttouseiton alargescaletofitabreakwatersoleneatly toanundressedfirmfoundation, minimisingcostlyexcavation.Cay’s achievementatAberdeenwasillustrated inVernon-Harcourt’sHarboursand Docksclassictextbookand,thathe </p><p>deserved<em>‘grea t c redit’</em>,wasalsopublicly </p><p>acknowledgedbyothereminent <br>FromJune1862toAugust1863Cay workedasresidentengineerontheTurin andSavonaRailwayunderitschief engineerJamesAbernethy,thenfortwo yearsinLondonasanassistanttoA.M. Rendel,returningtoScotlandfrom 1865–67aschiefassistanttoJames Leslie,EdinburghWaterworksEngineer. InatestimonialtoLeslie,Maxwell,who hadreturnedtoGlenlairafterresigning hisNaturalPhilosophychairatKing’s College,London,wroteofCay: </p><p><em>Sout h B reakwate r b ein g b uil t u nder Cay’ s d irection </em>MPICE 39 </p><p>engineersincludingAbernethyand SirJohnHawkshaw. </p><p>Cay’sinnovationsearnedhimabronze medalattheRoyalMiningEngineering andIndustrialExhibitionatNewcastleupon-Tynein1887andaBrisbaneMedal fromtheRoyalScottishSocietyofArts in1888.Bythenhisconcreteinbags technique(althoughoflimitedlater applicationassheetsteelandtheuseof compressedairdeveloped)hadbeenused atBuckie,Lerwick,Arbroath,Fraserburgh andNewhaven(Sussex)harbours,and NewPlymouthBreakwater(Ngamotu), NewZealand. </p><p><em>‘Hi s m athematica l k nowledg e i s s oun d a nd h e h a s m ad e a s pecia l s tud y o f i ro n a n d s tone bridges , s om e o f t h e r esult s o f w hic h h e h as bee n i n t h e h abi t o f c ommunicatin g t o m e … A s ke w b ridg e h a d t o b e e rected , b u t s om e o f th e s tones … were not properly shaped. Mr . C a y h oweve r d esigne d t h e c orrec t f orm … a n d t h e b ridg e w a s e recte d a ccordin g t o hi s p lans . M r . C a y h a s m ad e a d esign of a bridg e f o r m e a cros s t he th e R ive r U r r w hich I i nten d t o h av e e xecute d n ex t S pring ’</em>(1866 </p><p>–stillinservice,seeabove). <br>Bythe1870sCayhadbecomealeading memberofhisprofession. </p><p><em>Breakwate r e n d a n d L ighthouse </em></p><p>ꢀ</p><p>HewaselectedtotheInstitutionofCivilEngineers(AM,1864;M, 1872);FRSSA(1867)andFRSE(1882).From1880–1907hepractised inEdinburghasaconsultingengineer,firstlyat8SouthCharlotte Street,from1882–98at107APrincesStreetandthenfrom1Albyn Place.WorkonwhichhewasengagedincludedharboursatBuckie andLerwick,reconstructionofthedockentranceatArbroathand advisingonRoyalBridgeovertheDeeatBallater.In1908hewentto Londonand,forabouttenyears,tookanofficeat39VictoriaStreet. </p><p>Cay’sprogressivepracticeformedthesubjectofhisinfluential paperspublishedbytheInstitutionofCivilEngineers(ICE)and RoyalScottishSocietyofArts.Hiscareerwasalsoremarkableforthe largenumberofvaluablecontributionshemadetoICEProceedings from1873–1922.Subjectsincludedstabilityofchannelsandwalls, sandtravel,trainingofrivers,barsatmouthsoftidalestuaries, reductionofwaveaction,coasterosion,useandtestingofconcrete, groynes,harbourlayoutanddredging.Manyrelatedtospecific projectsathome,alsoinHolland,France,Panama,Japan,South Africa,Ceylon,BurmaandIndiaincludinga£760,000proposalfor anouterharbouratMadras.Healsowrotetechnicalarticlesfor Chambers’Encyclopaedia. </p><p><em>Cay’ s B reakwate r s til l p rotect s A berdee n H arbou r a fte r 1 4 0 y ears Postcar d 1 910 </em></p><p>Caynevermarriedandlivedduringthelatterpartofhislifeatthe JuniorCarltonClubinLondonorathotelsinvariousplaces.Hewas amemberofthisandnumerousotherclubsincludingtheOriental Club,London;theUniversityClub,Edinburgh;theRoyalNorthern Club,Aberdeen;theHon’bleCompanyofEdinburghGolfers, Musselburgh;theAberdeenGolfClub;andoftheCasino,Savona. Hediedonthe2December1925inanursinghomeatFolkestone afterashortillness. </p><p>Inhis‘Recollections’ofMaxwell,Caynotesthathe(Maxwell)was </p><p>‘<em>ver y f on d o f societ y a n d c onversatio n … H e t oo k m uc h p leasur e i n m y studyin g a n d w a s u nwearie d i n e xplainin g d ifficultie s a n d w rot e o u t f or m e a t reatis e o n h ydrostatics , h ydrodynamics , s tatics , d ynamic s a nd soli d g eometr y … A lthoug h c lea r o n p ape r h e w a s n o t s o i n v iva-voce explanations’ . ‘ 1857 , I w en t t o b e b es t m a n a t h i s m arriag e a t A berdeen’. ‘Whe n h e w a s p rofesso r a t K ing’ s C ollege , L ondon , I r emembe r h is explainin g t o m e t h e r eason s w hic h m ad e h i m g iv e u p t ha t p os t v iz . t hat th e s tudent s d i d n o t c ar e f o r i nstructio n e xcep t i n e ngineerin g o r p ractical mathematica l s ubjects’. </em></p><p><strong>Mainsources:</strong>ICEArchives;MS.AbstractfromCay’s‘Family </p><p>Book’(1865),TestimonialbyMaxwellforW.D.Cay,26Sept.1865, ‘RecollectionsofJamesClerkMaxwell(1854-64)byW.D.Cay, 30April1881’,forcopiesofwhichtheauthorthanksJamesBrown </p><p>(Cayrelative);<em>Th e T ime s</em>4Dec.1925,1;<em>Engineerin g</em>11Dec.1925, 749;<em>PRS E</em>XLVI(1925–26);<em>TRSS A</em>XII(1891);<em>MPIC E</em>37-212 </p><p>(1873–1922);Vernon-HarcourtL.V.<em>Harbour s</em>…,1885;PaxtonR. </p><p>&amp;ShipwayJ.<em>Civi l E ngineerin g H eritag e S cotland</em>,2007. </p><p><strong>Book Review: Faraday, Maxwell and the Electromagnetic Field </strong></p><p>by Forbes N. &amp; Mahon. B. (2014),&nbsp;Prometheus books, Amherst, New York. </p><p>Thisexcellentbookweavestogetherthehistoryof FaradayandMaxwellandthegradualuncovering ofthesecretsofmagnetismandelectricity.Today, wetakeforgrantedradio,televisionandmobile phonesbutitistooeasilyforgottenthat,inthe past,thesecretsofmagnetismandelectricity werenotknownand,asthebookshows,it requiredtheimmensecreativeeffortsofmany scientificmentouncoverthesecrets(e.g.Gilbert, Coulomb,Volta,Davy,Oersted,Ampère,Faraday, Kelvin(Thomson),Maxwell,Hertz,Heaviside, Fitzgerald,Lodge,Marconi).Thestoryofthe discoveryofthesecretsofelectricityand <br>AlthoughFaradaywasignorantofmathematics, </p>