,/>s & ,atoms ,illu/ration ,illu/ration3 ,fig4 #a4 ,,! ,,sun4 ,hydrog5 photograph ,,/>s ,,& ,,atoms ,,by ,a4 ,s4 ,,edd+ton ,m4,a41 ,d4,sc41 ,,ll4,d41 ,f4,r4,s41 ,plumian ,pr(essor ( ,a/ronomy 9 ! ,univ]sity ( ,cambridge ,,new ,,hav53 ,,yale ,,univ]sity ,,press ,,london3 ,,humphrey ,,mil=d1 ,,ox=d ,,univ]sity ,,press #aibg ,i* hufe ungeheure ,zahl51 ,gebrge ,million5 auf1 ,i* setze ,zeit auf ,zeit und ,welt auf ,welt zu ,hauf4 ,a4 ,,von ,,hall]4 ,,preface #8,,/>s & ,atoms' 0 ! title ( an ,ev5+ ,disc\rse giv5 at ! meet+ ( ! ,briti% ,association 9 ,ox=d 9 ,augu/ #aibf4 ,9 adapt+ x = publication ! re/rictions ( a "t limit are remov$1 & accord+ly x appe>s 9 ?is book z ?ree lectures4 ,e>li] 9 ! ye> ,i _h giv5 a c\rse ( ?ree lectures 9 ,k+'s ,college1 ,london1 on ! same topics2 ^! h be5 comb9$ ) ! ,ox=d lecture & are ! orig9 ( mo/ ( ! additions4 ,a full acc\nt ( ! subject1 includ+ ! ma!matical !ory1 is giv5 9 my l>g] book1 ,! ,int]nal ,con/itution ( ! ,/>s 7,camb4 ,univ4 ,press1 #aibf74 ,"h ,i only aim at exposition ( "s ( ! lead+ ideas & results4 ,! advance 9 our k ( atoms & radiation has l$ to _m int]e/+ developm5ts 9 a/ronomy2 & reciprocally ! /udy ( matt] 9 ! extreme conditions prevail+ 9 />s & nebulae has play$ no mean "p 9 ! progress ( atomic physics4 ,?is is ! g5]al !me ( ! lectures4 ,selection has be5 made ( ! advances & discov]ies :i* admit ( comp>atively elem5t>y exposition2 b x is (t5 necess>y to dem& f ! read] a conc5tration ( ?\ght :i*1 x is hop$1 w be repaid by ! fasc9ation ( ! subject4 ,! treatm5t 0 meant to be discursive r ?an sy/ematic2 b habits ( m9d refuse to be suppress$ entirely & a c]ta9 am\nt ( sy/em has crept 94 ,9 ^! problems :]e our ?\ght fluctuates cont9ually f ! excessively great to ! excessively small1 f ! /> to ! atom & back to ! />1 ! /ory ( progress is ri* 9 v>iety2 if x has n lo/ too mu* 9 ! tell+1 x %\ld convey 9 full measure ! delights--& ! tr\bles--( sci5tific inve/igation 9 all its phases4 ,temp]atures are express$ ?r\gh\t 9 degrees ,c5tigrade4 ,! ,engli% billion1 trillion1 c4 7#ajab1 #ajah1 c47 are us$4 ,a4 ,s4 ,e4 ,,cont5ts ,,lecture ,i4 ,,! ,,int]ior ,,( ,a ,,/> #i ,temp]ature 9 ! ,int]ior #aa ,ionization ( ,atoms #ag ,radiation ,pressure & ,mass #bd ,! ,int]ior ( a ,/> #bf ,opacity ( ,/ell> ,matt] #bh ,! ,relation ( ,brightness to ,mass #ca ,d5se ,/>s #cf ,,lecture ,,ii4 ,,"s ,,rec5t ,,inve/igations #db ,! ,/ory ( ,algol #db ,! ,/ory ( ! ,companion ( ,sirius #dh ,unkn[n ,atoms & ,int]pretation ( ,spectra #ec ,spectral ,s]ies #ei ,! ,cl\d 9 ,space #fc ,! ,sun's ,*romosph]e #gj ,! ,/ory ( ,betelgeuse #gf ,,lecture ,,iii4 ,,! ,,age ,,( ,,! ,,/>s #he ,pulsat+ ,/>s #he ,! ,cepheid z a #8,/&>d ,c&le' #ij ,! ,contraction ,hypo!sis #id ,subatomic ,en]gy #ii ,evolution ( ! ,/>s #ajf ,radiation ( ,mass #aac ,,app5dix ,fur!r ,rem>ks on ! ,companion ( ,sirius #abb ,,li/ ,,( ,,illu/rations ,,fig4 #a4 ,! ,sun4 ,hydrog5 ,spectroheliogram4 7,j4 ,ev]%$7 #b4 ,sol> ,vortices4 ,hydrog5 ,spectroheliogram4 7,m\nt ,wilson ,obs]vatory7 #c4 ,tracks ( ,alpha ,p>ticles 7helium atoms74 7,c4 ,t4 ,r4 ,wilson7 #d4 ,tracks ( ,beta ,p>ticles 7electrons74 7,c4 ,t4 ,r4 ,wilson7 #e4 ,ionization by ,x-rays4 7,c4 ,t4 ,r4 ,wilson7 #f4 ,ions produc$ by ,collision ( a ,beta p>ticle4 7,c4 ,t4 ,r4 ,wilson7 #g4 ,! ,mass-lum9osity ,curve4 #h4 ,! ,r+ ,nebula 9 ,lyra4 ,slitless ,spectrogram4 7,w4 ,h4 ,wright7 #i4 ,fla% ,spectrum ( ,*romosph]e %[+ ,head ( ! ,balm] ,s]ies4 7,briti% ,eclipse ,exp$ition1 #ad ,jan4 #aibf7 #aj4 ,sol> ,prom95ce4 7,briti% ,eclipse ,exp$ition1 #bi ,may #aiai7 #aa4 ,/> ,clu/] ,c5tauri4 7,cape ,obs]vatory7 ,,lecture ,i ,,! ,,int]ior ,,( ,a ,,/> ,,! sun belongs to a sy/em conta9+ "s #c1jjj million />s4 ,! />s are globes comp>able 9 size ) ! sun1 t is to say1 ( ! ord] ( a million miles 9 diamet]4 ,! space = _! accommodation is on ! mo/ lavi% scale4 ,imag9e ?irty cricket balls roam+ ! :ole int]ior ( ! e>?2 ! />s roam+ ! heav5s are j z little cr[d$ & run z little risk ( collision z ! cricket balls4 ,we m>vel at ! gr&eur ( ! /ell> sy/em4 ,b ?is probably is n ! limit4 ,evid5ce is gr[+ t ! spiral nebulae are #8isl& univ]ses' outside our own /ell> sy/em4 ,x may well be t our survey cov]s only "o unit ( a va/] organization4 ,a drop ( wat] conta9s sev]al ?\s& million million million atoms4 ,ea* atom is ab\t "o hundr$-million? ( an in* 9 diamet]4 ,"h we m>vel at ! m9ute delicacy ( ! workman%ip4 ,b ?is is n ! limit4 ,)9 ! atom are ! mu* small] electrons pursu+ orbits1 l planets r\nd ! sun1 9 a space :i* relatively to _! size is no less roomy ?an ! sol> sy/em4 ,ne>ly midway 9 scale betwe5 ! atom & ! /> !re is ano!r /ructure no less m>vell\s--! human body4 ,man is slightly ne>] to ! atom ?an to ! />4 ,ab\t #ajbg atoms build 8 body2 ab\t #ajbh human bodies con/itute en\gh mat]ial to build a />4 ,f 8 c5tral position man c survey ! gr&e/ works ( ,nature ) ! a/ronom]1 or ! m9ute/ works ) ! physici/4 ,to-night ,i ask y to look bo? ways4 ,= ! road to a k ( ! />s leads ?r\gh ! atom2 & important k ( ! atom has be5 rea*$ ?r\gh ! />s4 99 99 99 99 99 ,! /> mo/ famili> to u is ! sun4 ,a/ronomically speak+1 x is close at h&4 ,we c measure its size1 weigh x1 take its temp]ature1 & s on1 m easily ?an ! o!r />s4 ,we c take photographs ( its surface1 :]eas ! o!r />s are s di/ant t ! l>ge/ telescope 9 ! _w does n magnify !m into any?+ m ?an po9ts ( light4 ,figs4 #a & #ba %[ rec5t pictures ( ! sun's surface4 ,no d\bt ! />s 9 g5]al w\ld %[ simil> features if !y 7 ne> en\gh to be exam9$4 ,i mu/ fir/ expla9 t ^! are n ! ord9>y photographs4 ,simple photographs %[ v well ! d>k blot*es call$ sunspots1 b o!rwise !y are r flat & un9t]e/+4 ,! pictures "h %[n 7 tak5 ) a spectroheliograph1 an in/rum5t :i* looks out = light ( j "o v>iety 7wave-l5g?7 & ignores all ! re/4 ,! ultimate effect ( ?is selection is t ! in/rum5t sorts out ! diff]5t levels 9 ! sun's atmosph]e & %[s :at is go+ on at "o level1 in/ead ( giv+ a s+le blurr$ impression ( all levels sup]pos$4 ,fig4 #b1 :i* ref]s to a high level1 gives a wond]ful picture ( :irlw9ds & commotion4 ,i ?9k t ! sol> meteorologi/s w\ld be likely to describe ^! vortices 9 t]ms n unfamili> to u--#8,a deep depression ) second>ies is approa*+1 & a r5ewal ( unsettl$ conditions is probable4' ,h[ev] t may be1 !re is always "o safe wea!r =eca/ on ! sun2 cyclone or anticyclone1 ! temp]ature w be v w>m--ab\t #f1jjj 9 fact4 ,illu/ration3 ,fig4 #b4 ,,! ,,sun4 ,hydrog5 photograph ,b j n[ ,i d n wi% to l+] ov] ! surface lay]s or atmosph]e ( ! sun4 ,a great _m new & int]e/+ discov]ies h rec5tly be5 made 9 ?is region1 & mu* ( ! new k is v g]mane to my subject ( #8,/>s & ,atoms'4 ,b p]sonally ,i am m at home und]nea? ! surface1 & ,i am 9 a hurry to dive bel[4 ,!re=e ) ?is brief glance at ! sc5]y t we pass we %all plunge into ! deep int]ior--:]e ! eye _c p5etrate1 b :]e x is yet possible by sci5tific reason+ to le>n a great deal ab\t ! conditions4 ,temp]ature 9 ! ,int]ior ,by ma!matical me?ods x is possible to "w out h[ fa/ ! pressure increases z we g d[n into ! sun1 & h[ fa/ ! temp]ature mu/ increase to )/& ! pressure4 ,! ar*itect c "w out ! /resses inside ! pi]s ( 8 build+2 he does n ne$ to bore holes 9 !m4 ,likewise ! a/ronom] c "w out ! /ress or pressure at po9ts inside ! sun )\t bor+ a hole4 ,p]haps x is m surpris+ t ! temp]ature c be f\nd by pure calculation4 ,x is natural t y %\ld feel r sceptical ab\t our claim t we "k h[ hot x is 9 ! v middle ( a />--& y may be /ill m sceptical :5 ,i divulge ! actual figures6 ,!re=e ,i _h bett] describe ! me?od z f> z ,i c4 ,i %all n attempt to g into detail1 b ,i hope to %[ y t !re is a clue :i* might be foll[$ up by appropriate ma!matical me?ods4 ,i mu/ premise t ! heat ( a gas is *iefly ! en]gy ( motion ( its p>ticles ha/5+ 9 all directions & t5d+ to scatt] ap>t4 ,x is ?is :i* gives a gas its ela/icity or expansive =ce2 ! ela/icity ( a gas is well kn[n to e "o ?r\gh its practical application 9 a pneumatic tyre4 ,n[ imag9e y\rself at "s po9t deep d[n 9 ! /> :]e y c look upw>ds t[>ds ! surface or d[nw>ds t[>ds ! c5tre4 ,:]ev] y are1 a c]ta9 condition ( balance mu/ be rea*$2 on ! "o h& !re is ! weight ( all ! lay]s above y press+ d[nw>ds & try+ to squeeze clos] ! gas b5ea?2 on ! o!r h& !re is ! ela/icity ( ! gas bel[ y try+ to exp& & =ce ! sup]9cumb5t lay]s outw>ds4 ,s9ce nei!r "o ?+ nor ! o!r happ5s & ! /> rema9s practically un*ang$ = hundr$s ( ye>s1 we mu/ inf] t ! two t5d5cies j balance4 ,at ea* po9t ! ela/icity ( ! gas mu/ be j en\gh to balance ! weight ( ! lay]s above2 & s9ce x is ! heat :i* furni%es ! ela/icity1 ?is requirem5t settles h[ mu* heat ! gas mu/ h4 ,& s we f9d ! degree ( heat or temp]ature at ea* po9t4 ,! same ?+ c be express$ a little diff]5tly4 ,z be=e1 fix att5tion on a c]ta9 po9t 9 a /> & consid] h[ ! matt] above x is support$4 ,if x 7 n support$ x w\ld fall to ! c5tre "u ! attractive =ce ( gravitation4 ,! support is giv5 by a succession ( m9ute bl[s deliv]$ by ! p>ticles und]nea?2 we h se5 t _! heat en]gy causes !m to move 9 all directions1 & !y keep on /rik+ ! matt] above4 ,ea* bl[ gives a slight boo/ upw>ds1 & ! :ole succession ( bl[s supports ! upp] mat]ial 9 %uttlecock fa%ion4 7,?is process is n conf9$ to ! />s2 = in/ance1 x is 9 ?is way t a motor c> is support$ by its tyres47 ,an increase ( temp]ature w\ld mean an increase ( activity ( ! p>ticles1 & !re=e an increase 9 ! rapidity & /r5g? ( ! bl[s4 ,evid5tly we h to assign a temp]ature su* t ! sum total ( ! bl[s is nei!r too great nor too small to keep ! upp] mat]ial /eadily support$4 ,t 9 pr9ciple is our me?od ( calculat+ ! temp]ature4 ,"o obvi\s difficulty arises1 ,! :ole support+ =ce w dep5d n only on ! activity ( ! p>ticles 7temp]ature7 b also on ! numb] ( !m 7d5sity74 ,initially we d n "k ! d5sity ( ! matt] at an arbitr>y po9t deep )9 ! sun4 ,x is 9 ?is connexion t ! +5uity ( ! ma!matician is requir$4 ,he has a def9ite am\nt ( matt] to play )1 viz4 ! kn[n mass ( ! sun2 s ! m he uses 9 "o "p ( ! globe ! less he w h to sp>e = o!r p>ts4 ,he might say to himself1 #8,i d n want to exagg]ate ! temp]ature1 s ,i w see if ,i c manage )\t go+ beyond #aj1jjj1jjj4' ,t sets a limit to ! activity to be ascrib$ to ea* p>ticle2 !re=e :5 ! ma!matician rea*es a great dep? 9 ! sun & accord+ly has a heavy weight ( upp] mat]ial to su/a91 8 only res\rce is to use l>ge numb]s ( p>ticles to give ! requir$ total impulse4 ,he w !n f9d t he has us$ up all 8 p>ticles too fa/1 & has no?+ left to fill up ! c5tre4 ,( c\rse 8 /ructure1 support$ on no?+1 w\ld come tumbl+ d[n into ! holl[4 ,9 t way we c prove t x is impossible to build up a p]man5t /> ( ! dim5sions ( ! sun )\t introduc+ an activity or temp]ature exce$+ #aj1jjj1jjj4 ,! ma!matician c g a /ep beyond ?is2 in/ead ( m]ely f9d+ a l[] limit1 he c asc]ta9 :at mu/ be ne>ly ! true temp]ature di/ribution by tak+ into acc\nt ! fact t ! temp]ature mu/ n be #8pat*y'4 ,heat fl[s f "o place to ano!r1 & any pat*9ess w\ld soon be ev5$ out 9 an actual />4 ,i w leave ! ma!matician to deal m ?or\ghly ) ^! consid]ations1 :i* belong to ! foll[+ up ( ! clue2 ,i am cont5t if ,i h %[n y t !re is an op5+ = an attack on ! problem4 ,?is k9d ( inve/igation 0 />t$ m ?an fifty ye>s ago4 ,x has be5 gradually develop$ & correct$1 until n[ we believe t ! results mu/ be ne>ly "r--t we really "k h[ hot x is inside a />4 ,i m5tion$ j n[ a temp]ature ( #f1jjj2 t 0 ! temp]ature ne> ! surface--! region :i* we actually see4 ,!re is no s]i\s difficulty 9 det]m9+ ?is surface temp]ature by obs]vation2 9 fact ! same me?od is (t5 us$ comm]cially = f9d+ ! temp]ature ( a furnace f ! outside4 ,x is = ! deep regions out ( sight t ! highly !oretical me?od ( calculation is requir$4 ,?is #f1jjj is only ! m>g9al heat ( ! great sol> furnace giv+ no idea ( ! t]rific int5sity )94 ,go+ d[n into ! int]ior ! temp]ature rises rapidly to above a million degrees1 & goes on increas+ until at ! sun's c5tre x is ab\t #dj1jjj1jjj4 ,d n imag9e t #dj1jjj1jjj is a degree ( heat s extreme t temp]ature has become mean+less4 ,^! /ell> temp]atures are to be tak5 q lit]ally4 ,heat is ! en]gy ( motion ( ! atoms or molecules ( a sub/ance1 & temp]ature :i* indicates ! degree ( heat is a way ( /at+ h[ fa/ ^! atoms or molecules are mov+4 ,= example1 at ! temp]ature ( ?is room ! molecules ( air are ru%+ ab\t ) an av]age spe$ ( #ejj y>ds a second2 if we heat$ x up to #dj1jjj1jjj ! spe$ w\ld be j ov] #ajj miles a second4 ,t is no?+ to be al>m$ ab\t2 ! a/ronom] is q accu/om$ to spe$s l t4 ,! velocities ( ! />s1 or ( ! meteors ent]+ ! e>?'s atmosph]e1 are usually betwe5 #aj & #ajj miles a second4 ,! velocity ( ! e>? travell+ r\nd ! sun is #bj miles a second4 ,s t = an a/ronom] ?is is ! mo/ ord9>y degree ( spe$ t c\ld be sugge/$1 & he naturally consid]s #dj1jjj1jjj a v com=table sort ( condition to deal )4 ,& if ! a/ronom] is n fright5$ by a spe$ ( #ajj miles a second1 ! exp]im5tal physici/ is q contemptu\s ( x2 = he is us$ to h&l+ atoms %ot (f f radium & simil> sub/ances ) spe$s ( #aj1jjj miles a second4 ,accu/om$ z he is to wat*+ ^! express atoms & te/+ :at !y are capable ( do+1 ! physici/ consid]s ! jog-trot atoms ( ! />s v commonplace4 ,besides ! atoms ru%+ to & fro 9 all directions we h 9 ! int]ior ( a /> great quantities ( e!r waves also ru%+ 9 all directions4 ,e!r waves are call$ by diff]5t names accord+ to _! wave-l5g?4 ,! longe/ are ! ,h]tzian waves us$ 9 broadca/+2 !n come ! infra-r$ heat waves2 next come waves ( ord9>y visible light2 !n ultra-violet photographic or *emical rays2 !n ,x-rays2 !n ,gamma rays emitt$ by radio-active sub/ances4 ,probably ! %orte/ ( all are ! rays con/itut+ ! v p5etrat+ radiation f\nd 9 our atmosph]e1 :i* accord+ to ! inve/igations ( ,kohlhr/] & ,millikan are believ$ to rea* u f int]/ell> space4 ,^! are all fundam5tally ! same b correspond to diff]5t octaves4 ,! eye is attun$ to only "o octave1 s t mo/ ( !m are invisible2 b ess5tially !y are ( ! same nature z visible light4 ,! e!r waves inside a /> belong to ! division call$ ,x-rays4 ,!y are ! same z ! ,x-rays produc$ artificially 9 an ,x-ray tube4 ,on ! av]age !y are #8s(t]' 7i4e4 long]7 ?an ! ,x-rays us$ 9 hospitals1 b n s(t] ?an "s ( ^? us$ 9 laboratory exp]im5ts4 ,?us we h 9 ! int]ior ( a /> some?+ famili> & ext5sively /udi$ 9 ! laboratory4 ,besides ! atoms & e!r waves !re is a ?ird population to jo9 9 ! dance4 ,!re are multitudes ( free electrons4 ,! electron is ! lighte/ ?+ kn[n1 weigh+ no m ?an ( ! lighte/ atom4 ,x is simply a *>ge ( negative electricity w&]+ ab\t alone4 ,an atom consi/s ( a heavy nucleus :i* is usually surr\nd$ by a girdle ( electrons4 ,x is (t5 comp>$ to a m9iature sol> sy/em1 & ! comp>ison gives a prop] idea ( ! empt9ess ( an atom4 ,! nucleus is comp>$ to ! sun1 & ! electrons to ! planets4 ,ea* k9d ( atom--ea* *emical elem5t--has a diff]5t quorum ( planet electrons4 ,our own sol> sy/em ) eight planets might be comp>$ especially ) ! atom ( oxyg5 :i* has eight circulat+ electrons4 ,9 t]re/rial physics we usually reg>d ! girdle or cr9ol9e ( electrons z an ess5tial "p ( ! atom because we r>ely meet ) atoms incompletely dress$2 :5 we d meet ) an atom :i* has lo/ "o or two electrons f its sy/em1 we call x an #8ion'4 ,b 9 ! int]ior ( a />1 ow+ to ! great commotion go+ on1 x w\ld be absurd to exact su* a meticul\s /&>d ( attire4 ,all our atoms h lo/ a consid]able proportion ( _! planet electrons & are !re=e ions accord+ to ! /rict nom5clature4 ,ionization ( ,atoms ,at ! high temp]ature inside a /> ! batt]+ ( ! p>ticles by "o ano!r1 & m especially ! collision ( ! e!r waves 7,x-rays7 ) atoms1 cause electrons to be brok5 (f & set free4 ,^! free electrons =m ! ?ird population to :i* ,i h ref]r$4 ,= ea* individual ! fre$om is only tempor>y1 because x w pres5tly be captur$ by "s o!r mutilat$ atom2 b mean:ile ano!r electron w h be5 brok5 (f some:]e else to take its place 9 ! free population4 ,?is break+ away ( electrons f atoms is call$ ionization1 & z x is extremely important 9 ! /udy ( ! />s ,i w pres5tly %[ y photographs ( ! process4 ,my subject is #8,/>s & ,atoms'2 ,i h already %[n y photographs ( a />1 s ,i ought to %[ y a photograph ( an atom4 ,n[adays t is q easy4 ,s9ce !re are "s trillions ( atoms pres5t 9 ! t9ie/ piece ( mat]ial x w\ld be v confus+ if ! photograph %[$ !m all4 ,happily ! photograph ex]cises discrim9ation & %[s only #8express tra9' atoms :i* fla% pa/ l meteors1 ignor+ all ! o!rs4 ,we c arrange a p>ticle ( radium to %oot only a few express atoms across ! field ( ! cam]a1 & s h a cle> picture ( ea* ( !m4 ,fig4 #cb is a photograph ( ?ree or f\r atoms :i* h fla%$ across ! field ( view--giv+ ! broad /raight tracks4 ,^! are atoms ( helium dis*>g$ at high spe$ f a radio-active sub/ance4 ,i wond] if !re is an "u-curr5t ( suspicion 9 y\r m9ds t !re mu/ be some?+ ( a fake ab\t ?is photograph4 ,are ^! really ! s+le atoms t are %[+ !mselves--^? inf9itesimal units :i* n _m ye>s ago seem$ to be !oretical concepts f> outside any practical appreh5sion8 ,i w answ] t "q by ask+ y "o4 ,y see a dirty m>k on ! picture4 ,is t somebody's ?umb8 ,if y say ,yes1 !n ,i assure y unhesitat+ly t ^! /reaks are s+le atoms4 ,b if y are hyp]critical & say #8,no4 ,t is n anybody's ?umb1 b x is a m>k t %[s t somebody's ?umb has be5 !re'1 !n ,i mu/ be equally cauti\s & say t ! /reak is a m>k t %[s :]e an atom has be54 ,! photograph in/ead ( be+ ! impression ( an atom is ! impression ( ! impression ( an atom1 j z x is n ! impression ( a ?umb b ! impression ( ! impression ( a ?umb4 ,i don't see t x really matt]s t ! impression is second-h& in/ead ( fir/-h&4 ,i d n ?9k we h be5 guilty ( any m fak+ ?an ! crim9ologi/ :o scatt]s p[d] ov] a f+]-pr9t to make x visible1 or a biologi/ :o /a9s 8 prep>ations ) ! same object4 ,! atom 9 its passage leaves :at we might call a #8sc5t' along its trail2 & we owe to ,pr(essor ,c4 ,t4 ,r4 ,wilson a mo/ +5i\s device = mak+ ! sc5t visible4 ,pr(essor ,wilson's #8pack ( h\nds' consi/s ( wat] vap\r :i* flocks to ! trail & !re cond5ses into t9y drops4 ,y w next want to see a photograph ( an electron4 ,t also c be manag$4 ,! brok5 wavy trail 9 ,fig4 #c is an electron4 ,ow+ to its small mass ! electron is m easily turn$ aside 9 its c\rse ?an ! heavy atom :i* ru%es bull-head$ ?r\gh all ob/acles4 ,fig4 #d %[s num]\s electrons1 & x includes "o ( v high spe$ :i* on t acc\nt 0 able to make a /raight track4 ,incid5tally x gives away ! device us$ = mak+ ! tracks visible1 because y c see ! t9y drops ( wat] sep>ately4 ,illu/ration3 ,fig4 #c ,illu/ration3 ,fig4 #d4 ,,fa/-,,mov+ ,,atoms ,,& ,,electrons ,we h se5 photographs ( atoms & free electrons4 ,n[ we want a photograph ( ,x-rays to complete ! /ell> population4 ,we _c q manage t1 b we c v ne>ly4 ,photographs by ,x-rays are common en\gh2 b a photograph ( ,x-rays is a diff]5t matt]4 ,i h already said t electrons c be brok5 away f atoms by ,x-rays collid+ ) !m4 ,:5 ?is happ5s ! free electron is usually %ot (f ) high velocity s t x is "o ( ! express electrons :i* c be photograph$4 ,9 ,fig4 #e y see f\r electrons %ot (f 9 ?is way4 ,y notice t !y all />t f po9ts 9 ! same l9e1 & x does n require mu* imag9ation to see 9 y\r m9d a my/]i\s p[] travell+ along ?is l9e & creat+ ! explosions4 ,t p[] is ! ,x-rays :i* 7 direct$ 9 a n>r[ beam along ! l9e 7f "r to left7 :5 ! photograph 0 tak54 ,al?\gh ! ,x-rays are left to y\r imag9ation1 ! photograph at any rate %[s ! process ( ionization :i* is s important 9 ! /ell> int]ior--! free+ ( electrons f ! atoms by ! incid5ce ( ,x-rays4 ,y notice t x is j a *ance :e!r ! ,x-ray ionizes an atom :5 x meets x4 ,!re are trillions ( atoms ly+ ab\t 7( :i* ! photograph takes no notice72 b1 nev]!less1 ! ,x-rays travel a long way be=e meet+ ! atom :i* !y *oose to op]ate on4 ,f9ally ,i c %[ y ! o!r me?od ( ioniz+ atoms by batt]+ ( a m me*anical k9d--9 ?is case by ! collision ( a fa/ electron4 ,9 ,fig4 #f a fa/ electron 0 travell+ ne>ly horizontally1 b ! t9y wat]-drops t %\ld m>k its track are s spread out t y d n at fir/ trace ! connexion4 ,notice t ! drops occur 9 pairs4 ,?is is because ! fa/ electron batt]$ "s ( ! atoms along its track1 wr5*+ away an electron f ea*4 ,y see at int]vals along ! track a brok5 atom & a free electron ly+ side by side1 ?\gh y _c tell :i* is :i*4 ,occasionally ! orig9al fa/ electron 0 too vigor\s & !re is m ( a mix up1 b usually y c see cle>ly ! two fragm5ts result+ f ! sma%4#c ,a cynic might rem>k t ! int]ior ( a /> is a v safe subject to talk ab\t because no "o c g !re & prove t y are wrong4 ,i w\ld plead 9 reply t at lea/ ,i am n abus+ ! unlimit$ opportunity = imag9ation2 ,i am only ask+ y to all[ 9 ! int]ior ( ! /> q homely objects & processes :i* c be photograph$4 ,p]haps n[ y w turn r\nd on me & say1 #8,:at "r h y to suppose t ,nature is z b>r5 ( imag9ation z y are8 ,p]haps %e has hidd5 9 ! /> some?+ novel :i* w upset all y\r ideas4' ,b ,i ?9k t sci5ce w\ld nev] h a*iev$ mu* progress if x _h always imag9$ unkn[n ob/acles hidd5 r\nd e corn]4 ,at lea/ we may pe] g+]ly r\nd ! corn]1 & p]haps we %all f9d !re is no?+ v =midable aft] all4 ,our object 9 div+ into ! int]ior is n m]ely to admire a fanta/ic _w ) conditions transc5d+ ord9>y exp]i5ce2 x is to get at ! inn] me*anism :i* makes />s behave z !y d4 ,if we are to und]/& ! surface manife/ations1 if we are to und]/& :y #8"o /> diff]e? f ano!r /> 9 glory'1 we mu/ g bel[--to ! eng9e-room--to trace ! beg9n+ ( ! /ream ( heat & en]gy :i* p\rs out ?r\gh ! surface4 ,f9ally1 !n1 our !ory w take u back to ! surface & we %all be able to te/ by comp>ison ) obs]vation :e!r we h be5 badly misl$4 ,mean:ile1 al?\gh we naturally _c prove a g5]al negative1 !re is no reason to anticipate any?+ :i* our laboratory exp]i5ce does n w>n u (4 ,! ,x-rays 9 a /> are ! same z ! ,x-rays exp]im5t$ on 9 a laboratory1 b !y are enorm\sly m abundant 9 ! />4 ,we c produce ,x-rays l ! /ell> ,x-rays1 b we _c produce !m 9 any?+ l /ell> abundance4 ,! photograph 7,fig4 #e7 %[$ a laboratory beam ( ,x-rays :i* _h wr5*$ away f\r electrons f diff]5t atoms2 ^! w\ld be spe$ily recaptur$4 ,9 ! /> y mu/ imag9e ! int5sity multipli$ _m million-fold1 s t electrons are be+ wr5*$ away z fa/ z !y settle & ! atoms are kept /ripp$ almo/ b>e4 ,! ne>ly complete mutilation ( ! atoms is important 9 ! /udy ( ! />s = two ma9 reasons4 ,! fir/ is ?is4 ,an ar*itect be=e pron\nc+ an op9ion on ! plans ( a build+ w want to "k :e!r ! mat]ial %[n 9 ! plans is to be wood or /eel or t9 or pap]4 ,simil>ly x w\ld seem ess5tial be=e work+ out details ab\t ! int]ior ( a /> to "k :e!r x is made ( heavy /uff l lead or light /uff l c>bon4 ,by means ( ! spectroscope we c f9d out a great deal ab\t ! *emical composition ( ! sun's atmosph]e2 b x w\ld n be fair to take ?is z a sample ( ! composition ( ! sun z a :ole4 ,x w\ld be v risky to make a guess at ! elem5ts prepond]at+ 9 ! deep int]ior4 ,?us we seem to h rea*$ a deadlock4 ,b n[ x turns out t :5 ! atoms are ?or\ghly sma%$ up1 !y all behave ne>ly alike--at any rate 9 ^? prop]ties ) :i* we are conc]n$ 9 a/ronomy4 ,! high temp]ature--:i* we 7 incl9$ to be afraid ( at fir/--has simplifi$ ?+s = u1 because x has to a l>ge ext5t elim9at$ diff]5ces betwe5 diff]5t k9ds ( mat]ial4 ,! /ructure ( a /> is an unusually simple physical problem2 x is at l[ temp]atures su* z we exp]i5ce on ! e>? t matt] beg9s to h tr\blesome & complicat$ prop]ties4 ,/ell> atoms are nude savages innoc5t ( ! class di/9ctions ( our fully array$ t]re/rial atoms4 ,we are ?us able to make progress )\t guess+ at ! *emical composition ( ! int]ior4 ,x is necess>y to make "o res]vation1 viz4 t !re is n an excessive proportion ( hydrog54 ,hydrog5 has its own way ( behav+2 b x makes v little diff]5ce :i* ( ! o!r #ia elem5ts pr$om9ate4 ,! o!r po9t is "o ab\t :i* ,i %all h m to say lat]4 ,x is t we mu/ realize t ! atoms 9 ! />s are mutilat$ fragm5ts ( ! bulky atoms ) ext5d$ electron sy/ems famili> to u on ! e>?2 & !re=e ! behavi\r ( /ell> & t]re/rial gases is by no means ! same 9 reg>d to prop]ties :i* conc]n ! size ( ! atoms4 ,to illu/rate ! effect ( ! *emical composition ( a />1 we rev]t to ! problem ( ! support ( ! upp] lay]s by ! gas und]nea?4 ,at a giv5 temp]ature e indep5d5t p>ticle contributes ! same am\nt ( support no matt] :at its mass or *emical nature2 ! light] atoms make up = _! lack ( mass by mov+ m actively4 ,?is is a well-kn[n law orig9ally f\nd 9 exp]im5tal *emi/ry1 b n[ expla9$ by ! k9etic !ory ( ,maxwell & ,boltzmann4 ,suppose we _h orig9ally assum$ ! sun to be compos$ entirely ( silv] atoms & _h made our calculations ( temp]ature accord+ly2 aft]w>ds we *ange our m9ds & sub/itute a light] elem5t1 alum9ium4 ,a silv] atom weighs j f\r times z mu* z an alum9ium atom2 h5ce we mu/ sub/itute f\r alum9ium atoms = e silv] atom 9 ord] to keep ! mass ( ! sun un*ang$4 ,b n[ ! support+ =ce w ev]y:]e be quadrupl$1 & all ! mass w be heav$ outw>ds by x if we make no fur!r *ange4 ,9 ord] to keep ! balance1 ! activity ( ea* p>ticle mu/ be r$uc$ 9 ! ratio 2 t means t we mu/ assign ?r\gh\t ! alum9ium sun temp]atures ( ^? assign$ to ! silv] sun4 ,?us = unsma%$ atoms a *ange 9 ! assign$ *emical composition makes a big *ange 9 our inf]5ce z to ! int]nal temp]ature4 ,b if electrons are brok5 away f ! atom ^! also become indep5d5t p>ticles r5d]+ support to ! upp] lay]s4 ,a free electron gives j z mu* support z an atom does2 x is ( mu* small] mass1 b x moves ab\t a hundr$ times z fa/4 ,! sma%+ ( "o silv] atom provides #dg free electrons1 mak+ ) ! residual nucleus ( ! atom #dh p>ticles 9 all4 ,! alum9ium atom gives #ac electrons or #ad p>ticles 9 all2 ?us #d alum9ium atoms give #ef indep5d5t p>ticles4 ,! *ange f sma%$ silv] to an equal mass ( sma%$ alum9ium only means a *ange f #dh to #ef p>ticles1 requir+ a r$uction ( temp]ature by #ad p] c5t4 ,we c tol]ate t degree ( unc]ta9ty 9 our e/imates ( int]nal temp]ature2#d x is a great improvem5t on ! correspond+ calculation = unsma%$ atoms :i* 0 unc]ta9 by a factor #d4 ,besides br++ clos] toge!r ! results = diff]5t v>ieties ( *emical con/itution1 ionization by increas+ ! numb] ( support+ p>ticles l[]s ! calculat$ temp]atures consid]ably4 ,x is sometimes ?\ght t ! exce$+ly high temp]ature assign$ to ! int]ior ( a /> is a mod]n s5sationalism4 ,t is n s4 ,! e>ly inve/igators1 :o neglect$ bo? ionization & radiation pressure1 assign$ mu* high] temp]atures ?an ^? n[ accept$4 ,radiation ,pressure & ,mass ,! />s diff] f "o ano!r 9 mass1 t is to say1 9 ! quantity ( mat]ial ga!r$ toge!r to =m !m2 b ! diff]5ces are n s l>ge z we might h expect$ f ! great v>iety 9 brightness4 ,we _c always f9d out ! mass ( a />1 b !re are a fair numb] ( />s = :i* ! mass has be5 det]m9$ by a/ronomical measurem5ts4 ,! mass ( ! sun is--,i w write x on ! blackbo>d-- #bjjjjjjjjjjjjjjjjjjjjjjjjjjj tons ,i hope ,i h c\nt$ ! #j's rightly1 ?\gh ,i d>e say y w\ld n m9d mu* if !re 7 "o or two too _m or too few4 ,b ,nature does m9d4 ,:5 %e made ! />s %e evid5tly atta*$ great importance to gett+ ! numb] ( #j's "r4 ,%e has an idea t a /> %\ld conta9 a p>ticul> am\nt ( mat]ial4 ,( c\rse %e all[s :at ! (ficials at ! m9t w\ld call a #8rem$y'4 ,%e may ev5 pass a /> ) "o #j too _m & give u an exceptionally l>ge />1 or ) "o #j too few1 giv+ a v small />4 ,b ^! deviations are r>e1 & a mi/ake ( two #j's is almo/ unhe>d (4 ,usually %e adh]es mu* m closely to h] patt]n4 ,illu/ration3 ,fig4 #e4 ,,ionization ,,by ,x-,,rays ,illu/ration3 ,fig4 #f4 ,,ionization ,,by ,,collision ,h[ does ,nature keep c\nt ( ! #j's8 ,x seems cle> t !re mu/ be some?+ inside ! /> itself :i* keeps *eck &1 s to speak1 makes a w>n+ prote/ z soon z ! "r am\nt ( mat]ial has be5 ga!r$ toge!r4 ,we ?9k we "k h[ x is done4 ,y rememb] ! e!r waves inside ! />4 ,^! are try+ to escape outw>ds & !y ex]t a pressure on ! matt] :i* is cag+ !m 94 ,?is outw>d =ce1 if x is suffici5tly p[]ful to be wor? consid]+ 9 comp>ison ) o!r =ces1 mu/ be tak5 into acc\nt 9 any /udy ( ! equilibrium or /ability ( ! />4 ,n[ 9 all small globes ?is =ce is q trivial2 b its importance increases ) ! mass ( ! globe1 & x is calculat$ t at j ab\t ! above mass x rea*es equal /atus ) ! o!r =ces gov]n+ ! equilibrium ( ! />4 ,if we _h nev] se5 ! />s & 7 simply consid]+ z a curi\s problem h[ big a globe ( matt] c\ld possibly hold toge!r1 we c\ld calculate t !re w\ld be no difficulty up to ab\t two ?\s& quadrillion tons2 b beyond t ! conditions are entirely alt]$ & ?is new =ce beg9s to take control ( ! situation4 ,"h1 ,i am afraid1 /rict calculation /ops1 & no "o has yet be5 able to calculate :at ! new =ce w d ) ! /> :5 x does take control4 ,b x c sc>cely be an accid5t t ! />s are all s ne> to ?is critical mass2 & s ,i v5ture to conjecture ! re/ ( ! /ory4 ,! new =ce does n prohibit l>g] mass1 b x makes x risky4 ,x may help a mod]ate rotation ab\t ! axis to break up ! />4 ,consequ5tly l>g] masses w survive only r>ely2 = ! mo/ "p />s w be kept d[n to ! mass at :i* ! new =ce fir/ becomes a s]i\s m5ace4 ,! =ce ( gravitation collects toge!r nebul\s & *aotic mat]ial2 ! =ce ( radiation pressure *ops x (f into suitably siz$ lumps4 ,?is =ce ( radiation pressure is bett] kn[n to _m p "u ! "n #8pressure ( light'4 ,! t]m #8radiation' comprises all k9ds ( e!r-waves includ+ light1 s t ! mean+ is ! same4 ,x 0 fir/ %[n !oretically & aft]w>ds v]ifi$ exp]im5tally t light ex]ts a m9ute pressure on any object on :i* x falls4 ,!oretically x w\ld be possible to knock a man ov] by turn+ a se>*light on him--only ! se>*light w\ld h to be excessively int5se1 & ! man w\ld probably be vaporiz$ fir/4 ,pressure ( light probably plays a great "p 9 _m cele/ial ph5om5a4 ,"o ( ! e>lie/ sugge/ions 0 t ! m9ute p>ticles =m+ ! tail ( a comet are driv5 outw>ds by ! pressure ( sunlight1 ?us acc\nt+ = ! fact t a comet's tail po9ts away f ! sun4 ,b t p>ticul> application mu/ be consid]$ d\btful4 ,inside ! /> ! int5se /ream ( light 7or r ,x-rays7 is l a w9d ru%+ outw>ds & di/5d+ ! />4 ,! ,int]ior ( a ,/> ,we c n[ =m "s k9d ( a picture ( ! inside ( a />--a hurly-burly ( atoms1 electrons1 & e!r-waves4 ,di%evell$ atoms te> along at #ajj miles a second1 _! normal array ( electrons be+ torn f !m 9 ! scrimmage4 ,! lo/ electrons are spe$+ #ajj times fa/] to f9d new re/+ places4 ,let u foll[ ! progress ( "o ( !m4 ,!re is almo/ a collision z an electron approa*es an atomic nucleus1 b putt+ on spe$ x sweeps r\nd 9 a %>p curve4 ,sometimes !re is a side-slip at ! curve1 b ! electron goes on ) increas$ or r$uc$ en]gy4 ,aft] a ?\s& n>r[ %aves1 all happ5+ )9 a ?\s& million? ( a second1 ! hectic c>e] is end$ by a worse side-slip ?an usual4 ,! electron is fairly caught1 & atta*$ to an atom4 ,b sc>cely has x tak5 up its place :5 an ,x-ray bur/s into ! atom4 ,suck+ up ! en]gy ( ! ray ! electron d>ts (f aga9 on its next adv5ture4 ,i am afraid ! knockab\t com$y ( mod]n atomic physics is n v t5d] t[>ds our ae/hetic ideals4 ,! /ately drama ( /ell> evolution turns out to be m l ! hair-bread? escapades on ! films4 ,! music ( ! sph]es has almo/ a sugge/ion (--jazz4 ,& :at is ! result ( all ?is bu/le8 ,v little4 ,! atoms & electrons = all _! hurry nev] get any:]e2 !y only *ange places4 ,! e!r-waves are ! only "p ( ! population :i* accompli% any?+ p]man5t4 ,al?\gh app>5tly d>t+ 9 all directions indiscrim9ately1 !y d on ! av]age make a sl[ progress outw>ds4 ,!re is no outw>d progress ( ! atoms & electrons2 gravitation sees to t4 ,b sl[ly ! encag$ e!r-waves leak outw>ds z ?r\gh a sieve4 ,an e!r-wave hurries f "o atom to ano!r1 =w>ds1 backw>ds1 n[ absorb$1 n[ flung out aga9 9 a new direction1 los+ its id5tity1 b liv+ aga9 9 its successor4 ,) any luck x w 9 no unduly long "t 7t5 ?\s& to t5 million ye>s accord+ to ! mass ( ! />7 f9d itself ne> ! b\nd>y4 ,x *anges at ! l[] temp]ature f ,x-rays to light-rays1 be+ alt]$ a little at ea* re-bir?4 ,at la/ x is s ne> ! b\nd>y t x c d>t outside & travel =w>d 9 peace = a few hundr$ ye>s4 ,p]haps x may 9 ! end rea* "s di/ant _w :]e an a/ronom] lies 9 wait to trap x 9 8 telescope & extort f x ! secrets ( its bir?-place4 ,x is ! leakage t we p>ticul>ly want to det]m9e2 & t is :y we h to /udy pati5tly :at is go+ on 9 ! turbul5t cr[d4 ,to put ! problem 9 ano!r =m2 ! waves are urg$ to fl[ out by ! temp]ature gradi5t 9 ! />1 b are h9d]$ & turn$ back by _! adv5tures ) ! atoms & electrons4 ,x is ! task ( ma!matics1 aid$ by ! laws & !ories develop$ f a /udy ( ^! same processes 9 ! laboratory1 to calculate ! two factors--! factor urg+ & ! factor h9d]+ ! outw>d fl[--& h5ce to f9d ! leakage4 ,?is calculat$ leakage %\ld1 ( c\rse1 agree ) a/ronomical measurem5ts ( ! en]gy ( heat & light p\r+ out ( ! />4 ,& s f9ally we arrive at an obs]vational te/ ( ! !ories4 ,opacity ( ,/ell> ,matt] ,let u consid] ! factor :i* h9d]s ! leakage--! turn+ back ( ! e!r-waves by _! enc\nt]s ) atoms & electrons4 ,if we 7 deal+ ) light waves we %\ld call ?is ob/ruction to _! passage #8opacity'1 & we may conv5i5tly use ! same t]m = ob/ruction to ,x-rays4 ,we soon realize t ! mat]ial ( ! /> mu/ be decid$ly opaque4 ,! quantity ( radiation 9 ! int]ior is s great t unless x 7 v sev]ely conf9$ ! leakage w\ld be mu* great] ?an ! am\nt :i* we obs]ve com+ out ( ! />s4 ,! foll[+ is an illu/ration ( ! typical degree ( opacity requir$ to agree ) ! obs]v$ leakage4 ,let u ent] ! /> ,capella & f9d a region :]e ! d5sity is ! same z t ( ! atmosph]e ar\nd u2#e a slab ( ! mat]ial only two in*es ?ick w\ld =m a scre5 s opaque t only "o-?ird ( ! e!r-waves fall+ on "o side w\ld get ?r\gh to ! o!r side1 ! re/ be+ absorb$ 9 ! scre54 ,a foot or two ( ! mat]ial w\ld be practically a p]fect scre54 ,if we are ?9k+ ( light-waves ?is seems an a/oni%+ opacity = mat]ial z t5u\s z air2 b we h to rememb] t x is an opacity to ,x-rays1 & ! practical physici/ kn[s well ! difficulty ( gett+ ! s(t] k9ds ( ,x-rays to pass ?r\gh ev5 a few millimetres ( air4 ,!re is a gratify+ accordance 9 g5]al ord] ( magnitude betwe5 ! opacity inside ! />1 det]m9$ f a/ronomical obs]vation ( leakage1 & ! opacity ( t]re/rial sub/ances to ,x-rays ( m or less ! same wave-l5g?4 ,?is gives u "s assurance t our !ory is on ! "r track4 ,b a c>eful comp>ison %[s u t !re is "s important diff]5ce betwe5 ! /ell> & t]re/rial opacity4 ,9 ! laboratory we f9d t ! opacity increases v rapidly ) ! wave-l5g? ( ! ,x-rays t are us$4 ,we d n f9d any?+ l ! same diff]5ce 9 ! />s al?\gh ! ,x-rays 9 ! cool] />s mu/ be ( consid]ably great] wave-l5g? ?an ^? 9 ! hott] />s4 ,also1 tak+ c>e to make ! comp>ison at ! same wave-l5g? = bo?1 we f9d t ! /ell> opacity is less ?an ! t]re/rial opacity4 ,we mu/ foll[ up ?is div]g5ce4 ,!re is m ?an "o way 9 :i* an atom c ob/ruct e!r-waves1 b !re seems to be no d\bt t = ,x-rays bo? 9 ! />s & 9 ! laboratory ! ma9 "p ( ! opacity dep5ds on ! process ( ionization4 ,! e!r-wave falls on an atom & its en]gy is suck$ up by "o ( ! planet electrons :i* uses x to escape f ! atom & travel away at high spe$4 ,! po9t to notice is t 9 ! v act ( absorption ! absorb+ me*anism is brok51 & x _c be us$ aga9 until x has be5 repair$4 ,to repair x ! atom mu/ capture "o ( ! free electrons w&]+ ab\t1 induc+ x to take ! place ( ! lo/ electron4 ,9 ! laboratory we c only produce ?9 /reams ( ,x-rays s t ea* wave-trap is only call$ ^u to act occasionally4 ,!re is pl5ty ( "t to repair x be=e ! next "t x has a *ance ( cat*+ any?+2 & !re is practically no loss ( effici5cy ?r\gh ! traps be+ out ( ord]4 ,b 9 ! />s ! /ream ( ,x-rays is exce$+ly int5se4 ,x is l an army ( mice m>*+ ?r\gh y\r l>d] spr++ ! m\se-traps z fa/ z y c set !m4 ,"h x is ! "t wa/$ 9 resett+ ! traps--by captur+ electrons--:i* c\nts1 & ! am\nt ( ! cat* dep5ds almo/ entirely on ?is4 ,we h se5 t ! /ell> atoms h lo/ mo/ ( _! electrons2 t means t at any mom5t a l>ge proportion ( ! absorption traps are await+ repair4 ,= ?is reason we f9d a small] opacity 9 ! />s ?an 9 t]re/rial mat]ial4 ,! l[]$ opacity is simply ! result ( ov]work+ ! absorb+ me*anisms--!y h too mu* radiation to deal )4 ,we c also see :y ! laws ( /ell> & t]re/rial opacity are some:at diff]5t4 ,! rate ( repair1 :i* is ! ma9 consid]ation 9 /ell> opacity1 is increas$ by compress+ ! mat]ial1 because !n ! atom w n h to wait s long to meet & capture a free electron4 ,consequ5tly ! /ell> opacity w increase ) ! d5sity4 ,9 t]re/rial conditions !re is no advantage 9 accel]at+ ! repair :i* w 9 any case be complet$ 9 suffici5t "t2 ?us t]re/rial opacity is indep5d5t ( ! d5sity4 ,! !ory ( /ell> opacity ?us r$uces ma9ly to ! !ory ( ! capture ( electrons by ioniz$ atoms2 n t ?is process is att5d$ by absorption ( ,x-rays--x is actually att5d$ by emission--b x is ! necess>y prelim9>y to absorption4 ,! physical !ory ( electron-capture is n yet fully def9itive2 b x is suffici5tly advanc$ = u to make use ( x provisionally 9 our calculations ( ! h9d]+ factor 9 ! leakage ( radiation f ! />s4 ,! ,relation ( ,brightness to ,mass ,we d n want to tackle too difficult a problem at fir/1 & s we %all deal ) />s compos$ ( p]fect gas4 ,if y d n l ! te*nical phrase #8p]fect gas' y c call x simply #8gas'1 because all ! t]re/rial gases t y are likely to ?9k ( are )\t s5sible imp]fection4 ,x is only "u high compression t t]re/rial gases become imp]fect4 ,i %\ld m5tion t !re are pl5ty ( examples ( gase\s#f />s4 ,9 _m />s ! mat]ial is s inflat$ t x is m t5u\s ?an ! air ar\nd u2 = example1 if y 7 inside ,capella y w\ld n notice ! mat]ial ( ,capella any m ?an y notice ! air 9 ?is room4 ,= gase\s />s1 !n1 ! inve/igation w give =mulae by :i*1 giv5 ! mass ( ! />1 we c calculate h[ mu* en]gy ( heat & light w leak out ( x--9 %ort1 h[ bright x w be4 ,9 ,fig4 #g a curve is drawn giv+ ?is !oretical relation betwe5 ! brightness & mass ( a />4 ,/rictly speak+1 !re is ano!r factor besides ! mass :i* affects ! calculat$ brightness2 y c h two />s ( ! same mass1 ! "o d5se & ! o!r puff$ out1 & !y w n h q ! same brightness4 ,b x turns out 7r unexpect$ly7 t ?is o!r factor1 d5sity1 makes v little diff]5ce to ! brightness1 always provid$ t ! mat]ial is n too d5se to be a p]fect gas4 ,i %all !re=e say no m ab\t d5sity 9 ?is brief summ>y4 99 99 99 99 99 ,"h are a few details ab\t ! scale ( ! diagram4 ,! brightness is measur$ 9 magnitudes1 a r te*nical unit4 ,y h to rememb] t /ell> magnitude is l a golf]'s h&icap--! bigg] ! numb]1 ! worse ! p]=mance4 ,! diagram includes practically ! :ole range ( /ell> brightness2 at ! top -#d repres5ts almo/ ! brighte/ />s kn[n1 & at ! bottom #ab is ne>ly ! fa9te/ limit4 ,! diff]5ce f top to bottom is ab\t ! same z ! diff]5ce betwe5 an arc light & a gl[ worm4 ,! sun is ne> magnitude #e4 ,^! magnitudes ref]1 ( c\rse1 to ! true brightness1 n to ! app>5t brightness affect$ by di/ance2 also1 :at is repres5t$ "h is ! #8heat brightness' or heat int5sity1 :i* is sometimes a little diff]5t f ! light int5sity4 ,a/ronomical in/rum5ts h be5 made :i* measure directly ! heat in/ead ( ! light receiv$ f a />4 ,^! are q successful2 b !re are tr\blesome corrections on acc\nt ( ! l>ge absorption ( heat 9 ! e>?'s atmosph]e1 & x is 9 mo/ cases easi] & m accurate to inf] ! heat brightness f ! light brightness1 mak+ all[ance = ! col\r ( ! />4 ,illu/ration3 ,fig4 #g4 ,! ,mass-lum9osity ,curve4 ,! horizontal scale ref]s to mass1 b x is graduat$ accord+ to ! log>i?m ( ! mass4 ,at ! extreme left ! mass is ab\t x sun1 & on ! extreme "r ab\t #cj x sun2 !re are v few />s ) masses outside ^! limits4 ,! sun's mass corresponds to ! division labell$ #jj4 ,hav+ obta9$ our !oretical curve1 ! fir/ ?+ to d is to te/ x by obs]vation4 ,t is to say1 we ga!r toge!r z _m />s z we c lay h&s on = :i* bo? ! mass & absolute brightness h be5 measur$4 ,we plot ! correspond+ po9ts 7opposite to ! appropriate horizontal & v]tical graduations7 & see :e!r !y fall on ! curve1 z !y ought to d if ! !ory is "r4 ,!re are n _m /ell> masses det]m9$ ) mu* precision4 ,ev]y?+ t is reasonably tru/wor?y has be5 includ$ 9 ,fig4 #g4 ,! circles1 crosses1 squ>es1 & triangles ref] to diff]5t k9ds ( data--"s good1 "s bad1 "s v bad4 ,! circles are ! mo/ tru/wor?y4 ,let u run ?r\gh !m f "r to left4 ,fir/ comes ! bright compon5t ( ,capella1 ly+ beautifully on ! curve--because ,i drew ! curve ?r\gh x4 ,y see1 !re 0 "o num]ical con/ant :i* 9 ! pres5t /ate ( our k ( atoms & e!r-waves1 c41 x 0 n possible to det]m9e ) any confid5ce f pure !ory4 ,s ! curve :5 x 0 obta9$ 0 loose 9 "o direction & c\ld be rais$ or l[]$4 ,x 0 an*or$ by mak+ x pass ?r\gh ! bright compon5t ( ,capella :i* seem$ ! be/ /> to tru/ to = ?is purpose4 ,aft] t !re c\ld be no fur!r tamp]+ ) ! curve4 ,cont9u+ to ! left we h ! fa9t] compon5t ( ,capella2 next ,sirius2 !n1 9 a bun*1 two compon5ts ( ,c5tauri 7! ne>e/ fix$ />7 ) ! ,sun betwe5 !m1 &--ly+ on ! curve--a circle repres5t+ ! mean ( six d\ble />s 9 ! ,hyades4 ,f9ally1 f> on ! left !re are two compon5ts ( a well-kn[n d\ble /> call$ ,krueg] #fj4 ,! obs]vational data = te/+ ! curve are n s ext5sive & n s tru/wor?y z we c\ld wi%2 b /ill ,i ?9k x is pla9 f ,fig4 #g t ! !ory is sub/antially confirm$1 & x really does enable u to pr$ict ! brightness ( a /> f its mass1 or vice v]sa4 ,t is a useful result1 because !re are ?\s&s ( />s ( :i* we c measure ! absolute brightness b n ! mass1 & we c n[ inf] _! masses ) "s confid5ce4 ,s9ce ,i h n be5 able to give "h ! details ( ! calculation1 ,i %\ld make x pla9 t ! curve 9 ,fig4 #g is trac$ by pure !ory or t]re/rial exp]im5t except = ! "o con/ant det]m9$ by mak+ x pass ?r\gh ,capella4 ,we c imag9e physici/s work+ on a cl\d-b\nd planet su* z ,jupit] :o h nev] se5 ! />s4 ,!y %\ld be able to d$uce by ! me?od expla9$ on p4 #be t if !re is a univ]se exi/+ beyond ! cl\ds x is likely to aggregate prim>ily into masses ( ! ord] a ?\s& quadrillion tons4 ,!y c\ld !n pr$ict t ^! aggregations w be globes p\r+ out light & heat & t _! brightness w dep5d on ! mass 9 ! way giv5 by ! curve 9 ,fig4 #g4 ,all ! in=mation t we h us$ = ! calculations w\ld be accessible to !m b5ea? ! cl\ds1 except t we h /ol5 "o advantage ov] !m 9 utiliz+ ! bright compon5t ( ,capella4 ,ev5 )\t ?is =bidd5 peep1 pres5t-day physical !ory w\ld enable !m to assign a brightness to ! invisible /ell> ho/ :i* w\ld n be absurdly wrong4 ,unless !y 7 wis] ?an u !y w\ld probably ascribe to all ! />s a brilliance ab\t t5 times too great#g--n a bad error = a fir/ attempt at s transc5d5t a problem4 ,we hope to cle> up ! discrepant factor #aj ) fur!r k ( atomic processes2 mean:ile we %elve x by fix+ ! d\btful con/ant by a/ronomical obs]vation4 ,d5se ,/>s ,! agreem5t ( ! obs]vational po9ts ) ! curve is rem>kably close1 consid]+ ! r\gh nature ( ! obs]vational measurem5ts2 & x seems to af=d a r /rong confirmation ( ! !ory4 ,b !re is "o awful confession to make--we h comp>$ ! !ory ) ! wrong />s4 ,at lea/ :5 ! comp>ison 0 fir/ made at ! beg9n+ ( #aibd no "o ent]ta9$ any d\bt t !y 7 ! wrong />s4 ,we mu/ recall t ! !ory 0 develop$ = />s 9 ! condition ( a p]fect gas4 ,9 ! "r half ( ,fig4 #g ! />s repres5t$ are all diffuse />s2 ,capella ) a mean d5sity ab\t equal to t ( ! air 9 ?is room may be tak5 z typical4 ,mat]ial ( ?is t5uity is evid5tly a true gas1 & 9 s f> z ^! />s agree ) ! curve ! !ory is confirm$4 ,b 9 ! left half ( ! diagram we h ! ,sun ^: mat]ial is d5s] ?an wat]1 ,krueg] #fj d5s] ?an iron1 & _m o!r />s ( ! d5sity usually associat$ ) solid or liquid matt]4 ,:at bus9ess h !y on ! curve res]v$ = a p]fect gas8 ,:5 ^! />s 7 put into ! diagram x 0 n ) any expectation t !y w\ld agree ) ! curve2 9 fact1 ! agreem5t 0 mo/ annoy+4 ,some?+ v diff]5t 0 be+ s\ght =4 ,! idea 0 t ! !ory might p]haps be tru/$ on its own m]its ) su* confirmation z ! diffuse />s _h already af=d$2 !n by measur+ h[ f> ^! d5se />s fell bel[ ! curve we %\ld h def9ite in=mation z to h[ great a deviation f a p]fect gas occurr$ at any giv5 d5sity4 ,accord+ to curr5t ideas x 0 expect$ t ! sun w\ld fall ?ree or f\r magnitudes bel[ ! curve1 & ! /ill d5s] ,krueg] #fj %\ld be ne>ly t5 magnitudes bel[4#h ,y see t ! expectation 0 entirely unfulfill$4 ,! %ock 0 ev5 great] ?an ,i c well indicate to y1 because ! great drop 9 brightness :5 ! /> is too d5se to behave z a true gas 0 a fundam5tal t5et 9 our conception ( /ell> evolution4 ,on ! /r5g? ( x ! />s _h be5 divid$ into two gr\ps kn[n z giants & dw>fs1 ! =m] be+ ! gase\s />s & ! latt] ! d5se />s4 ,two alt]natives n[ lie be=e u4 ,! fir/ is to assume t some?+ mu/ h gone wrong ) our !ory2 t ! true curve = gase\s />s is n z we h drawn x1 b runs high up on ! left ( ! diagram s t ! ,sun1 ,krueg] #fj1 c41 are at ! appropriate di/ances bel[ x4 ,9 %ort1 our imag9>y critic 0 "r2 ,nature _h hidd5 some?+ unexpect$ inside ! /> & s fru/rat$ our calculations4 ,well1 if ?is 7 s1 x w\ld be some?+ to h f\nd x out by our inve/igations4 ,! o!r alt]native is to consid] ?is "q--,is x impossible t a p]fect gas %\ld h ! d5sity ( iron8 ,! answ] is r surpris+4 ,!re is no e>?ly reason :y a p]fect gas %\ld n h a d5sity f> exce$+ iron4 ,or x w\ld be m accurate to say1 ! reason :y x %\ld n is e>?ly & does n apply to ! />s4 ,! sun's mat]ial1 9 spite ( be+ d5s] ?an wat]1 really is a p]fect gas4 ,x s\nds incr$ible1 b x mu/ be s4 ,! feature ( a true gas is t !re is pl5ty ( room betwe5 ! sep>ate p>ticles--a gas conta9s v little sub/ance & lots ( empt9ess4 ,consequ5tly :5 y squeeze x y d n h to squeeze ! sub/ance2 y j squeeze out "s ( ! wa/e space4 ,b if y g on squeez+1 !re comes a "t :5 y h squeez$ out all ! empty space2 ! atoms are !n jamm$ 9 contact & any fur!r compression means squeez+ ! sub/ance itself1 :i* is q a diff]5t proposition4 ,s z y approa* t d5sity ! compressibility *>act]i/ic ( a gas is lo/ & ! matt] is no long] a prop] gas4 ,9 a liquid ! atoms are ne>ly 9 contact2 t w give y an idea ( ! d5sity at :i* ! gas loses its *>act]i/ic compressibility4 ,! big t]re/rial atoms :i* beg9 to jam at a d5sity ne> t ( ! liquid /ate d n exi/ 9 ! />s4 ,! /ell> atoms h be5 trimm$ d[n by ! break+ (f ( all _! out] electrons4 ,! light] atoms are /ripp$ to ! b>e nucleus--( q insignificant size4 ,! heavi] atoms reta9 a few ( ! clos] electrons1 b h n mu* m ?an a hundr$? ( ! diamet] ( a fully array$ atom4 ,consequ5tly we c g on squeez+ ev] s mu* m be=e ^! t9y atoms or ions jam 9 contact4 ,at ! d5sity ( wat] or ev5 ( plat9um !re is /ill any am\nt ( room betwe5 ! trimm$ atoms2 & wa/e space rema9s to be squeez$ out z 9 a p]fect gas4 ,our mi/ake 0 t 9 e/imat+ ! conge/ion 9 ! /ell> ball-room we _h =gott5 t cr9ol9es are no long] 9 fa%ion4 ,x 01 ,i suppose1 v bl9d ( u n to h =ese5 ?is result1 consid]+ h[ mu* att5tion we _h be5 pay+ to ! mutilation ( ! atoms 9 o!r bran*es ( ! inve/igation4 ,by a r\ndab\t r\te we h rea*$ a conclusion :i* is really v obvi\s4 ,& s we conclude t ! />s on ! left ( ! diagram are aft] all n ! #8wrong' />s4 ,! sun & o!r d5se />s are on ! p]fect gas curve because _! mat]ial is p]fect gas4 ,c>eful inve/igation has %[n t 9 ! small />s on ! extreme left ( ,fig4 #g ! electric *>ges ( ! atoms & electrons br+ ab\t a slight deviation f ! ord9>y laws ( a gas2 x has be5 %[n by ,r4 ,h4 ,f[l] t ! effect is to make ! gas n imp]fect b sup]p]fect--x is m easily compress$ ?an an ord9>y gas4 ,y w notice t on ! av]age ! />s run a little above ! curve on ! left ( ,fig4 #g4 ,x is probable t ! deviation is g5u9e & is p>tly due to sup]p]fection ( ! gas2 we h already se5 t imp]fection w\ld h br\ght !m bel[ ! curve4 ,ev5 at ! d5sity ( plat9um !re is pl5ty ( wa/e space1 s t 9 ! />s we might g on squeez+ /ell> matt] to a d5sity transc5d+ any?+ kn[n on ! e>?4 ,b t's ano!r /ory--,i w tell x lat] on4 99 99 99 99 99 ,! g5]al agreem5t betwe5 ! obs]v$ & pr$ict$ brightness ( ! />s ( v>i\s masses is ! ma9 te/ ( ! correctness ( our !ories ( _! int]nal con/itution4 ,! incid5ce ( _! masses 9 a range :i* is especially critical = radiation pressure is also valuable confirmation4 ,x w\ld be an exagg]ation to claim t ?is limit$ success is a pro( t we h rea*$ ! tru? ab\t ! /ell> int]ior4 ,x is n a pro(1 b x is an enc\ragem5t to "w f>!r along ! l9e ( ?\ght :i* we h be5 pursu+4 ,! tangle is beg9n+ to loos54 ,! m optimi/ic may assume t x is n[ /raight5$ out2 ! m cauti\s w make ready = ! next knot4 ,! "o reason = ?9k+ t ! real tru? _c be s v f> away is t 9 ! int]ior ( a />1 if any:]e1 ! problem ( matt] is r$uc$ to its utmo/ simplicity2 & ! a/ronom] is engag$ on :at is ess5tially a less ambiti\s problem ?an t ( ! t]re/rial physici/ to :om matt] always appe>s 9 ! guise ( electron sy/ems ( ! mo/ complex organization4 ,we h tak5 ! pres5t-day !ories ( physics & press$ !m to _! remote/ conclusions4 ,!re is no dogmatic int5tion 9 ?is2 x is ! be/ means we h ( te/+ !m & reveal+ _! weaknesses if any4 ,9 anci5t days two aviators procur$ to !mselves w+s4 ,da$alus flew safely ?r\gh ! middle air & 0 duly hon\r$ on 8 l&+4 ,ic>us so>$ upw>ds to ! sun till ! wax melt$ :i* b\nd 8 w+s & 8 flight end$ 9 fiasco4 ,9 weigh+ _! a*ievem5ts1 !re is some?+ to be said = ,ic>us4 ,! classical au?orities tell u t he 0 only #8do+ a /unt'1 b ,i pref] to ?9k ( him z ! man :o br\ght to light a s]i\s con/ructional defect 9 ! fly+-ma*9es ( 8 day4 ,s1 too1 9 ,sci5ce4 ,cauti\s ,da$alus w apply 8 !ories :]e he feels confid5t !y w safely g2 b by 8 excess ( caution _! hidd5 weaknesses rema9 undiscov]$4 ,ic>us w /ra9 8 !ories to ! break+-po9t till ! weak jo9ts gape4 ,= ! m]e adv5ture8 ,p]haps p>tly2 t is human nature4 ,b if he is de/9$ n yet to rea* ! sun & solve f9ally ! riddle ( its con/itution1 we may at lea/ hope to le>n f 8 j\rney "s h9ts to build a bett] ma*9e4 ,,lecture ,,ii ,,"s ,,rec5t ,,inve/igations ,,x w help u to appreciate ! a/ronomical significance ( :at we h le>nt 9 ! previ\s lecture if we turn f ! g5]al to ! p>ticul> & see h[ x applies to individual />s4 ,i w take two />s r\nd :i* c5tre /ories ( special int]e/1 & relate ! hi/ory ( our k ( !m4 ,! ,/ory ( ,algol ,?is is a detective /ory1 :i* we might call #8,! ,miss+ ,^w & ! ,false ,clue'4 ,9 a/ronomy1 unlike _m sci5ces1 we _c h&le & probe ! objects ( our /udy2 we h to wait passively & receive & decode ! messages t !y s5d to u4 ,! :ole ( our in=mation ab\t ! />s comes to u along rays ( light2 we wat* & try to und]/& _! signals4 ,!re are "s />s :i* seem to be s5d+ u a regul> s]ies ( dots & da%es--l ! int]mitt5t light f a ligh?\se4 ,we _c translate ?is z a morse code2 nev]!less1 by c>eful measurem5t we dis5tangle a great deal ( in=mation f ! messages4 ,! /> ,algol is ! mo/ fam\s ( ^! #8v>iable />s'4 ,we le>n f ! signals t x is really two />s revolv+ r\nd ea* o!r4 ,sometimes ! bright] ( ! two />s is hidd51 giv+ a deep eclipse or #8da%'2 sometimes ! fa9t /> is hidd51 giv+ a #8dot'4 ,?is recurs 9 a p]iod ( #b days #ba h\rs--! p]iod ( revolution ( ! two />s4 ,!re 0 a great deal m in=mation 9 ! message1 b x 0 r tantaliz+4 ,!re 01 s to speak1 j "o ^w miss+4 ,if we c\ld supply t ^w ! message w\ld give full & accurate p>ticul>s z to ! size ( ! sy/em--! diamet]s & masses ( ! two compon5ts1 _! absolute brightness1 ! di/ance betwe5 !m1 _! di/ance f ! sun4 ,lack+ ! ^w ! message told u no?+ really def9ite ab\t any ( ^! ?+s4 ,9 ^! circum/ances a/ronom]s w\ld sc>cely h be5 human if !y _h n tri$ to guess ! miss+ ^w4 ,! ^w %\ld h told u h[ mu* bigg] ! bright /> 0 ?an ! fa9t]1 t is to say1 ! ratio ( ! masses ( ! two />s4 ,"s ( ! less fam\s v>iable />s give u complete messages4 7,^! c\ld accord+ly be us$ = te/+ ! relation ( mass & absolute brightness1 & are repres5t$ by triangles 9 ,fig4 #g47 ,! difficulty ab\t ,algol arose f ! excessive brightness ( ! bright compon5t :i* swamp$ & made illegible ! m delicate signals f ! fa9t compon5t4 ,f ! o!r sy/ems we c\ld f9d ! mo/ usual value ( ! mass ratio1 & base on t a guess z to its probable value = ,algol4 ,diff]5t au?orities pref]r$ slightly diff]5t e/imates1 b ! g5]al judgem5t 0 t 9 sy/ems l ,algol ! bright compon5t is twice z massive z ! fa9t compon5t4 ,& s ! miss+ ^w 0 assum$ to be #8two'2 on ?is assumption ! v>i\s dim5sions ( ! sy/em 7 work$ out & came to be g5]ally accept$ z ne> ! tru?4 ,t 0 sixte5 ye>s ago4#i ,9 ?is way ! s5se ( ! message 0 made out to be t ! bright] /> _h a radius ( #a1ajj1jjj kilometres 7"o & a half times ! sun's radius71 t x _h half ! mass ( ! sun1 & ?irty times ! sun's light-p[]1 c4 ,x w be se5 at once t ?is w n fit our curve 9 ,fig4 #g2 a /> ( half ! sun's mass ought to be v mu* fa9t] ?an ! sun4 ,x 0 r disconc]t+ to f9d s fam\s a /> prote/+ aga9/ ! !ory2 b aft] all ! !ory is to be te/$ by comp>ison ) facts & n ) guesses1 & ! !ory might well h a s\nd] basis ?an ! conjecture z to ! miss+ ^w4 ,moreov]1 ! spectral type ( ,algol is "o t is n usually associat$ ) l[ mass1 & ?is ca/ "s suspicion on ! accept$ results4 ,if we are will+ to tru/ ! !ory giv5 9 ! la/ lecture we c d )\t ! miss+ ^w4 ,or1 to put x ano!r way1 we c try 9 succession v>i\s guesses in/ead ( #8two' until we rea* "o t gives ! bright compon5t a mass & lum9osity agree+ ) ! curve 9 ,fig4 #g4 ,! guess #8two' gives1 z we h se51 a po9t :i* falls a long way f ! curve4 ,alt] ! guess to #8?ree' & recalculate ! mass & brightness on ?is assumption2 ! correspond+ po9t is n[ some:at ne>] to ! curve4 ,cont9ue ) #8f\r'1 #8five'1 c42 if ! po9t crosses ! curve we "k t we h gone too f> & mu/ take an int]m$iate value 9 ord] to rea* ! desir$ agreem5t4 ,?is 0 done 9 ,novemb] #aibe1 & x appe>$ t ! miss+ ^w mu/ be #8five'1 n #8two'--a r />tl+ *ange4 ,& n[ ! message ran-- ,radius ( bright compon5t #b1adj1jjj kilometres4 ,mass ( bright compon5t #dc x sun's mass4 ,if y comp>e ^! ) ! orig9al figures y w see t !re is a great alt]ation4 ,! /> is n[ assign$ a l>ge mass mu* m appropriate to a ,b-type />4 ,x also turns out t ,algol is m ?an a hundr$ times z bright z ! sun2 & its p>allax is #jjbh--twice ! di/ance previ\sly suppos$4 ,at ! "t !re seem$ little likelihood t ^! conclusions c\ld be te/$4 ,possibly ! pr$iction z to ! p>allax might be prov$ or disprov$ by a trigonometrical det]m9ation2 b x is s small z to be almo/ out ( range ( reasonably accurate measurem5t4 ,we c\ld only adopt a #8take x or leave x' attitude--#8,if y accept ! !ory1 ?is is :at ,algol is l2 if y di/ru/ ! !ory1 ^! results are ( no int]e/ to y4' ,b mean:ile two a/ronom]s at ,ann ,arbor ,obs]vatory _h be5 mak+ a se>* = ! miss+ ^w by a rem>kable new me?od4 ,!y _h 9 fact f\nd ! ^w & publi%$ x a ye> be=e1 b x _h n become widely kn[n4 ,if a /> is rotat+1 "o edge or #8limb' is com+ t[>ds u & ! o!r go+ away f u4 ,we c measure spe$s t[>ds u or away f u by means ( ! ,doppl] effect on ! spectrum1 obta9+ a def9ite result 9 miles p] second4 ,?us we c & d measure ! equatorial spe$ ( rotation ( ! sun by obs]v+ fir/ ! ea/ limb !n ! we/ limb & tak+ ! diff]5ce ( velocity %[n4 ,t is all v well on ! sun1 :]e y c cov] up ! disk except ! special "p t y want to obs]ve2 b h[ c y cov] up "p ( a /> :5 a /> is a m]e po9t ( light8 ,y _c2 b 9 ,algol ! cov]+ up is done = y4 ,! fa9t compon5t is y\r scre54 ,z x passes 9 front ( ! bright /> !re is a mom5t :5 x leaves a ?9 cresc5t %[+ on ! ea/ & ano!r mom5t :5 a ?9 cresc5t on ! we/ is uncov]$4 ,( c\rse1 ! /> is too f> away = y actually to see ! cresc5t %ape1 b at ^! mom5ts y receive light f ! cresc5ts only1 ! re/ ( ! disk be+ hidd54 ,by seiz+ ^! mom5ts y c make ! measurem5ts j z ?\gh y _h manipulat$ ! scre5 y\rself4 ,=tunately ! spe$ ( rotation ( ,algol is l>ge & s c be measur$ ) relatively small error4 ,n[ multiply ! equatorial velocity by ! p]iod ( rotation2#aj t w give y ! circumf]5ce ( ,algol4 ,divide by #fbh1 & y h ! radius4 ,t 0 ! me?od develop$ by ,rossit] & ,mc,laughlin4 ,! latt] :o appli$ x to ,algol f\nd ! radius ( ! bright compon5t to be #b1ahj1jjj kilometres4 ,s f> z c be judg$ 8 result has consid]able accuracy2 inde$ x is probable t ! radius is n[ bett] kn[n ?an t ( any o!r /> except ! sun4 ,if y w n[ turn back to p4 #dd & comp>e x ) ! value f\nd f ! !ory y w see t !re is cause = satisfaction4 ,mc,laughlin evaluat$ ! o!r con/ants & dim5sions ( ! sy/em2 ^! agree equally well1 b t foll[s automatically because !re 0 only "o miss+ ^w to be suppli$4 ,9 bo? det]m9ations ! miss+ ^w or mass ratio turn$ out to be #ej4 ,?is is n q ! end ( ! /ory4 ,:y _h ! fir/ guess at ! mass ratio gone s badly wrong8 ,we und]/& by n[ t a disp>ity 9 mass is closely associat$ ) a disp>ity 9 brightness ( ! two />s4 ,! disp>ity 9 brightness 0 giv5 9 ,algol's orig9al message2 x in=m$ u t ! fa9t compon5t gives ab\t "o-?irte5? ( ! light ( ! bright "o4 7,at lea/ t 0 h[ we int]pret$ x47 ,accord+ to our curve ?is corresponds to a mass ratio #b1 :i* is n mu* improvem5t on ! orig9al guess #b4 ,= a mass ratio #e ! companion ought to h be5 mu* fa9t]--9 fact its light %\ld h be5 undetectable4 ,al?\gh consid]ations l ^! c\ld n h _h mu* influ5ce on ! orig9al guess1 !y seem$ at fir/ to reassure u t !re 0 n v mu* wrong ) x4 ,let u call ! bright compon5t ,algol ,a & ! fa9t compon5t ,algol ,b4 ,"s ye>s ago a new discov]y 0 made1 namely ,algol ,c4 ,x 0 f\nd t ,algol ,a & ,b toge!r travel 9 an orbit r\nd a ?ird /> 9 a p]iod ( j "u two ye>s--at lea/ !y are travell+ r\nd 9 ?is p]iod1 & we mu/ suppose t !re is some?+ pres5t = !m to revolve ar\nd4 ,hi!rto we _h believ$ t :5 ,algol ,a 0 ne>ly hidd5 at ! "t ( deepe/ eclipse all ! rema9+ light mu/ come f ,algol ,b2 b n[ x is cle> t x belongs to ,algol ,c1 :i* is always %9+ )\t int]f]5ce4 ,consequ5tly ! mass ratio #b is t ( ,algol ,a to ,algol ,c4 ,! light f ,algol ,b is inappreciable z x %\ld be = a mass ratio #e4aa ,! message f ,algol ,a & ,b 0 confus$1 n only on acc\nt ( ! miss+ ^w1 b because a ^w or two ( ano!r message f ,algol ,c _h got mix$ up ) x2 s t ev5 :5 ! miss+ ^w 0 f\nd to be #8five' & confirm$ 9 two ways1 ! message 0 n q coh]5t4 ,9 ano!r place ! message seem$ to wav] & read #8two-&-a-half'4 ,! f9i%+ /ep is ! discov]y t #8two-&-a-half' belongs to a diff]5t message f a previ\sly unsuspect$ />1 ,algol ,c4 ,& s x all ends happily4 ,! be/ detective is n infallible4 ,9 ?is /ory our a/ronomical detective made a reasonable b unsuccessful guess ne> ! beg9n+ ( ! case4 ,he might h se5 8 error e>li]1 only !re 0 a false clue dropp$ by a ?ird p>ty :o happ5$ to be pres5t at ! crime1 :i* seem$ to confirm ! guess4 ,?is 0 v unlucky4 ,b x makes all ! bett] detective /ory ( x4 ,! ,/ory ( ! ,companion ( ,sirius ,! title ( ?is detective /ory is #8,! ,nons5sical ,message'4 ,sirius is ! mo/ conspicu\s /> 9 ! sky4 ,naturally x 0 obs]v$ v (t5 9 e>ly days1 & x 0 us$ by a/ronom]s along ) o!r bright />s to det]m9e "t & set ! clocks by4 ,x 0 a clock />1 z we say4 ,b x turn$ out t x 0 n at all a good clock2 x w\ld ga9 /eadily = "s ye>s1 & !n lose4 ,9 #ahdd ,bessel f\nd out ! cause ( ?is irregul>ity2 ,sirius 0 describ+ an elliptic orbit4 ,obvi\sly !re mu/ be some?+ = x to move ar\nd1 & s x came to be recogniz$ t !re 0 a d>k /> !re :i* no "o _h ev] se54 ,i d\bt :e!r any "o expect$ x w\ld ev] be se54 ,! ,companion ( ,sirius 01 ,i believe1 ! fir/ invisible /> to be regul>ly recogniz$4 ,we ought n to call su* a /> hypo!tical4 ,! me*anical prop]ties ( matt] are mu* m crucial ?an ! accid5tal prop]ty ( be+ visible2 we d n consid] a transp>5t pane ( glass #8hypo!tical'4 ,!re 0 ne> ,sirius some?+ :i* exhibit$ ! mo/ univ]sal me*anical prop]ty ( matt]1 namely1 ex]t+ =ce on neighb\r+ matt] accord+ to ! law ( gravitation4 ,t is bett] evid5ce ( ! exi/5ce ( a mat]ial mass ?an ocul> evid5ce w\ld be4 ,h[ev]1 eighte5 ye>s lat] ! ,companion ( ,sirius 0 actually se5 by ,alvan ,cl>k4 ,?is discov]y 0 unique 9 its way2 ,cl>k 0 n look+ at ,sirius because he 0 int]e/$ 9 x1 b because ,sirius 0 a nice bright po9t ( light ) :i* to te/ ! optical p]fection ( a l>ge new object-glass t 8 firm _h made4 ,i d>e say t :5 he saw ! little po9t ( light close to ,sirius he 0 disappo9t$ & tri$ to poli% x away4 ,h[ev]1 x /ay$1 & prov$ to be ! already kn[n b hi!rto unse5 ,companion4 ,! big mod]n telescopes easily %[ ! /> & r spoil ! romance2 b z romance fad$1 k grew1 & we n[ "k t ! ,companion is a /> n mu* less massive ?an ! sun4 ,x has ?s ( ! mass ( ! sun1 b gives out only ? ( ! sun's light4 ,! fa9tness did n p>ticul>ly surprise u2#aa presumably !re %\ld be :ite-hot />s gl[+ v brightly & r$-hot />s gl[+ feebly1 ) all sorts ( int]m$iate degrees ( brightness4 ,x 0 assum$ t ! ,companion 0 "o ( ! feeble />s only j r$ hot4 ,9 #aiad ,pr(essor ,adams at ! ,m\nt ,wilson ,obs]vatory f\nd t x 0 n a r$ />4 ,x 0 :ite--:ite hot4 ,:y1 !n1 0 x n %9+ brilliantly8 ,app>5tly ! only answ] 0 t x mu/ be a v small />4 ,y see1 ! nature & col\r ( ! light %[ t its surface mu/ be gl[+ m int5sely ?an ! sun's2 b ! total light is only ? ( ! sun's2 !re=e ! surface mu/ be less ?an ? ( ! sun's4 ,t makes ! radius less ?an ? ( ! sun's radius1 & br+s ! globe d[n to a size :i* we ord9>ily associate ) a planet r ?an ) a />4 ,work+ out ! sum m accurately we f9d t ! ,companion ( ,sirius is a globe int]m$iate 9 size betwe5 ! e>? & ! next l>g] planet ,uranus4 ,b if y are go+ to put a mass n mu* less ?an t ( ! sun into a globe n v mu* l>g] ?an ! e>?1 x w be a tight squeeze4 ,! actual d5sity works out at #fj1jjj times t ( wat]--j ab\t a ton to ! cubic in*4 ,we le>n ab\t ! />s by receiv+ & int]pret+ ! messages :i* _! light br+s to u4 ,! message ( ! ,companion ( ,sirius :5 x 0 decod$ ran3 #8,i am compos$ ( mat]ial #c1jjj times d5s] ?an any?+ y h ev] come across2 a ton ( my mat]ial w\ld be a little nugget t y c\ld put 9 a mat*-box4' ,:at reply c "o make to su* a message8 ,! reply :i* mo/ ( u made 9 #aiad 0--#8,%ut up4 ,don't talk nons5se4' ,b 9 #aibd ! !ory describ$ 9 ! la/ lecture _h be5 develop$2 & y w rememb] t at ! end x po9t$ to ! possibility t matt] 9 ! />s might be compress$ to a d5sity mu* transc5d+ our t]re/rial exp]i5ce4 ,?is call$ back to m9d ! /range message ( ! ,companion ( ,sirius4 ,x c\ld no long] be dismiss$ z obvi\s nons5se4 ,t does n mean t we c\ld imm$iately assume x to be true2 b x mu/ be weigh$ & te/$ ) a caution :i* we %\ld n c>e to wa/e ov] a m]e nons5se j+le4 ,x %\ld be und]/ood t x 0 v difficult to expla9 away ! orig9al message z a mi/ake4 ,z to ! mass be+ ?s ( ! sun's mass !re c be no s]i\s d\bt at all4 ,x is "o ( ! v be/ det]m9ations ( /ell> mass4 ,moreov]1 x is obvi\s t ! mass mu/ be l>ge if x is to sway ,sirius out ( its c\rse & upset its punctuality z a clock4 ,! det]m9ation ( ! radius is less direct1 b x is made by a me?od :i* has _h conspicu\s success :5 appli$ to o!r />s4 ,= example1 ! radius ( ! huge /> ,betelgeuse 0 fir/ calculat$ 9 ?is way2 aft]w>ds x 0 f\nd possible to measure directly ! radius ( ,betelgeuse by means ( an int]f]omet] devis$ by ,mi*elson1 & ! direct measurem5t confirm$ ! calculat$ value4 ,aga9 ! ,companion ( ,sirius does n /& alone 9 its peculi>ity4 ,at lea/ two o!r />s h s5t u messages proclaim+ incr$ibly high d5sity2 & consid]+ our v limit$ opportunities = detect+ ?is condition1 !re c be little d\bt t ^! #8:ite dw>fs'1 z !y are call$1 are comp>atively abundant 9 ! /ell> univ]se4 ,b we d n want to tru/ entirely to "o clue le/ x prove false 9 "s unsuspect$ way4 ,!re=e 9 #aibd ,pr(essor ,adams set to "w aga9 to apply to ! message a te/ :i* ought to be crucial4 ,e9/e9's !ory ( gravitation indicates t all ! l9es ( ! spectrum ( a /> w be slightly displac$ t[>ds ! r$ end ( ! spectrum z comp>$ ) ! correspond+ t]re/rial l9es4 ,on ! sun ! effect is almo/ too small to be detect$ hav+ reg>d to ! _m causes ( slight %ift :i* h to be dis5tangl$4 ,to me p]sonally ,e9/e9's !ory gives mu* /rong] assurance ( ! real exi/5ce ( ! effect ?an does ! obs]vational evid5ce available4 ,/ill x is a /rik+ fact t ^? :o h made ! inve/igation are n[ unanim\s 9 _! judgem5t t ! effect really occurs on ! sun1 al?\gh "s ( !m at fir/ ?\ght t !y _h evid5ce aga9/ x4 ,hi!rto ,e9/e9's !ory has be5 *iefly reg>d$ by ! practical a/ronom] z some?+ he is ask$ to te/2 b n[ ! !ory has a *ance to %[ its mettle by help+ u to te/ some?+ mu* m d\btful ?an itself4 ,! ,e9/e9 effect is proportional to ! mass divid$ by ! radius ( ! />2 & s9ce ! radius ( ! ,companion ( ,sirius is v small 7if ! message is "r7 ! effect w be v l>ge4 ,x %\ld 9 fact be ?irty times z l>ge z on ! sun4 ,t lifts x mu* above all ! second>y causes ( %ift ( ! l9es :i* made ! te/ on ! sun s unc]ta94 ,! obs]vation is v difficult because ! ,companion ( ,sirius is fa9t = "w ( ?is k9d1 & scatt]$ light f its ov]p[]+ly brilliant neighb\r causes mu* tr\ble4 ,h[ev]1 aft] a ye>'s ef=t ,pr(essor ,adams made satisfactory measurem5ts1 & he f\nd a l>ge %ift z pr$ict$4 ,express+ ! results 9 ! usual unit ( kilometres p] second1 ! mean ( 8 measurem5ts came to #ai1 :il/ ! pr$ict$ %ift 0 #bj4 ,pr(essor ,adams has ?us kill$ two birds ) "o /one4 ,he has c>ri$ out a new te/ ( ,e9/e9's g5]al !ory ( relativity1 & he has %[n t matt] at lea/ #b1jjj times d5s] ?an plat9um is n only possible b actually exi/s 9 ! /ell> univ]se4#ac ,?is is ! be/ confirmation we c\ld h = our view t ! sun ) a d5sity #a times t ( wat] is /ill v f> inde$ f ! maximum d5sity ( /ell> matt]2 & x is !re=e entirely reasonable t we %\ld f9d x behav+ l a p]fect gas4 ,i h said t ! obs]vation 0 exce$+ly difficult4 ,h[ev] exp]i5c$ ! obs]v]1 ,i d n ?9k we ought to put implicit tru/ 9 a result :i* /ra9s 8 skill to ! utmo/ until x has be5 v]ifi$ by o!rs work+ indep5d5tly4 ,!re=e y %\ld = ! pres5t make ! usual res]vations 9 accept+ ^! conclusions4 ,b sci5ce is n j a catalogue ( asc]ta9$ facts ab\t ! univ]se2 x is a mode ( progress1 sometimes tortu\s1 sometimes unc]ta94 ,& our int]e/ 9 sci5ce is n m]ely a desire to he> ! late/ facts add$ to ! collection2 we l to discuss our hopes & fe>s1 probabilities & expectations4 ,i h told ! detective /ory s f> z x has yet unroll$ itself4 ,i d n "k :e!r we h rea*$ ! la/ *apt]4 ,unkn[n ,atoms & ,int]pretation ( ,spectra ,x %\ld be und]/ood t ?is matt] ( enorm\s d5sity is n suppos$ to be any /range sub/ance--a new *emical elem5t or elem5ts4 ,x is j ord9>y matt] sma%$ ab\t by ! high temp]ature & s capable ( be+ pack$ m tightly--j z m p c\ld be squeez$ into a room if a few bones 7 brok54 ,x is "o ( ! features ( a/ronomical physics t x %[s u ! ord9>y elem5ts ( ! e>? 9 an extraord9>y /ate--sma%$ or ioniz$ to a degree t has ei!r n be5 reproduc$ or has be5 reproduc$ ) great difficulty 9 ! laboratory4 ,x is n only 9 ! inaccessible int]ior ( ! /> t we f9d matt] 9 a /ate outside t]re/rial exp]i5ce4 ,"h is a picture ( ! ,r+ ,nebula 9 ,lyra 7,fig4 #h74ad ,x is tak5 ?r\gh a prism s t we see n "o r+ b a numb] ( r+s correspond+ to diff]5t l9es ( ! spectrum & repres5t+ ! diff]5t k9ds ( atoms :i* are at "w produc+ ! light ( ! nebula4 ,! smalle/ r+1 :i* is r fa9t 7m>k$ by an arr[71 consi/s ( light produc$ by ! helium atoms 9 ! nebula--n ord9>y helium b sma%$ helium atoms4 ,x 0 "o ( ! great laboratory a*ievem5ts ( rec5t times :5 ,pr(essor ,a4 ,f[l] 9 #aiab succe$$ 9 batt]+ helium atoms 9 a vacuum tube suffici5tly to give ?is k9d ( light1 already well kn[n 9 ! />s4 ,two o!r r+s are due to hydrog54 ,) ^! ?ree exceptions none ( ! r+s h yet be5 imitat$ 9 ! laboratory4 ,= in/ance1 we d n "k :at elem5ts are produc+ ! two brighte/ r+s on ! extreme "r & left respectively4 ,we are sometimes ask$ :e!r any new elem5ts %[ !mselves 9 ! />s :i* are n pres5t or are n yet discov]$ on ! e>?4 ,we c give fairly confid5tly ! answ] ,no4 ,t1 h[ev]1 is n because ev]y?+ se5 9 ! />s has be5 id5tifi$ ) kn[n t]re/rial elem5ts4 ,! answ] is 9 fact giv5 n by ! a/ronom] b by ! physici/4 ,! latt] has be5 able to make out ! ord]ly s*eme ( ! elem5ts2 & x transpires t !re are no gaps left = fre% elem5ts until we come to elem5ts ( v high atomic weight1 :i* w\ld n be likely to rise into ! atmosph]e ( a /> & %[ !mselves 9 a/ronomical obs]vation4 ,e elem5t c>ries a numb]1 />t+ ) hydrog5 :i* is ,no4 #a1 & go+ up to uranium :i* is ,no4 #ib4 ,illu/ration3 ,fig4 #h4 ,,! ,,r+ ,,nebula ,,9 ,,lyra ,illu/ration3 ,fig4 #i4 ,,hydrog5--,,! ,,balm] ,,s]ies ,& :at is m1 ! elem5t c>ries its numb]-plate s conspicu\sly t a physici/ is able to read x4 ,he c1 = in/ance1 see t iron is ,no4 #bf )\t hav+ to c\nt up h[ _m kn[n elem5ts prec$e x4 ,! elem5ts h be5 call$ ov] by _! numb]s1 & up to ,no4 #hd !y h all answ]$ #8,pres5t'4#ae ,! elem5t helium 7,no4 #b7 0 fir/ discov]$ by ,locky] 9 ! sun1 & n until _m ye>s lat] 0 x f\nd on ! e>?4 ,a/rophysici/s are n likely to repeat ?is a*ievem5t2 !y _c discov] new elem5ts if !re ar5't any4 ,! unkn[n s\rce ( ! two r+s close toge!r on ! "r ( ! photograph 7a bright r+ & a fa9t] r+7 has be5 call$ nebulium4 ,b nebulium is n a new elem5t4 ,x is "s q famili> elem5t :i* we _c id5tify because x has lo/ sev]al ( its electrons4 ,an atom :i* has lo/ an electron is l a fri5d :o has %av$ (f 8 m\/a*e2 8 old acqua9tances d n recognize him4 ,we %all recognize nebulium "s day4 ,! !oretical physici/s are at "w try+ to f9d laws :i* w det]m9e exactly ! k9d ( light giv5 (f by atoms 9 v>i\s /ages ( mutilation--s t x w be purely a matt] ( calculation to inf] ! atom f ! light x emits4 ,! exp]im5tal physici/s are at "w try+ m & m p[]ful means ( batt]+ atoms1 s t "o day a t]re/rial atom w be /imulat$ to give nebulium light4 ,x is a great race2 & ,i d n "k :i* side to back4 ,! a/ronom] _c d mu* to help ! solution ( ! problem he has set4 ,i believe t if he w\ld measure ) ! greate/ c>e ! ratio ( int5sity ( ! two nebulium l9es he w\ld give ! physici/s a useful h9t4 ,he also provides ano!r clue--?\gh x is difficult to make any?+ ( x--namely1 ! diff]5t sizes ( ! r+s 9 ! photograph1 %[+ a diff]5ce 9 ! di/ribution ( ! emitt+ atoms4 ,evid5tly nebulium has a fondness = ! out] p>ts ( ! nebula & helium = ! c5tre2 b x is n cle> :at inf]5ce %\ld be drawn f ?is diff]5ce 9 _! habits4 ,! atoms ( diff]5t elem5ts1 & atoms ( ! same elem5t 9 diff]5t /ates ( ionization1 all h di/9ctive sets ( l9es :i* are %[n :5 ! light is exam9$ ?r\gh a spectroscope4 ,"u c]ta9 conditions 7z 9 ! nebulae7 ^! appe> z bright l9es2 b m (t5 !y are impr9t$ z d>k l9es on a cont9u\s backgr\nd4 ,9 ei!r case ! l9es enable u to id5tify ! elem5t1 unless !y happ5 to belong to an atom 9 a /ate ( :i* we h _h no t]re/rial exp]i5ce4 ,! ra% prophecy t k ( ! composition ( ! heav5ly bodies mu/ be = ev] beyond our rea* has long be5 disprov$2 & ! famili> elem5ts1 hydrog51 c>bon1 calcium1 titanium1 iron1 & _m o!rs1 c be recogniz$ 9 ! mo/ di/ant p>ts ( ! univ]se4 ,! ?rill ( ?is e>ly discov]y has n[ pass$4 ,b mean:ile /ell> spectroscopy has greatly ext5d$ its scope2 x is no long] *emical analysis1 b physical analysis4 ,:5 we meet an old acqua9tance !re is fir/ ! /age ( recognition2 ! next "q is #8,h[ are y8' ,aft] recogniz+ ! /ell> atom we put ?is "q1 & ! atom answ]s1 #8,q s\nd' or #8,badly sma%$'1 z ! case may be4 ,its answ] conveys in=mation z to its environm5t--! sev]ity ( ! treatm5t to :i* x is be+ subject$--& h5ce leads to a k ( ! conditions ( temp]ature & pressure 9 ! object obs]v$4 ,survey+ ! s]ies ( />s f ! coole/ to ! hotte/1 we c trace h[ ! calcium atoms are at fir/ :ole1 !n s+ly ioniz$1 !n d\bly ioniz$--a sign t ! batt]+ becomes m sev]e z ! heat becomes m int5se4 7,! la/ /age is indicat$ by ! disappe>ance ( all visible signs ( calcium1 because ! ion ) two electrons miss+ has no l9es 9 ! obs]vable "p ( ! spectrum47 ,! progressive *ange ( o!r elem5ts is %[n 9 a simil> way4 ,a great advance 9 ?is /udy 0 made 9 #aibj by ,pr(essor ,m4 ,n4 ,saha1 :o fir/ appli$ ! quantitative physical laws :i* det]m9e ! degree ( ionization at any giv5 temp]ature & pressure4 ,he !reby /ruck out a new l9e 9 a/rophysical rese>* :i* has be5 widely develop$4 ,?us1 if we note ! place 9 ! /ell> sequ5ce :]e complete calcium atoms give place to atoms ) "o electron miss+1 ! physical !ory is able to /ate ! correspond+ temp]ature or pressure4#af ,saha's me?ods h be5 improv$ by ,r4 ,h4 ,f[l] & ,e4 ,a4 ,milne4 ,"o important application 0 to det]m9e ! surface temp]atures ( ! hotte/ types ( />s 7#ab1jjj--be1jjj71 s9ce alt]native me?ods available = cool] />s are n satisfactory at ^! high temp]atures4 ,ano!r r /rik+ result 0 ! discov]y t ! pressure 9 ! /> 7at ! level survey$ by ! spectroscope7 is only ? ( an atmosph]e2 previ\sly x _h be5 assum$ on no v def9ite evid5ce to be ab\t ! same z t ( our own atmosph]e4 ,we commonly use ! me?od ( spectrum analysis :5 we wi% to det]m9e :i* elem5ts are pres5t 9 a giv5 m9]al on ! e>?4 ,x is equally tru/wor?y 9 exam9+ ! />s s9ce x c make no diff]5ce :e!r ! light we are /udy+ comes f a body close at h& or has travell$ to u = hundr$s ( ye>s across space4 ,b "o limitation 9 /ell> "w mu/ always be rememb]$4 ,:5 ! *emi/ is look+1 say1 = nitrog5 9 8 m9]al1 he takes c>e to provide ! conditions :i* accord+ to 8 exp]i5ce are necess>y = ! nitrog5 spectrum to %[ itself4 ,b 9 ! />s we h to take ! conditions z we f9d !m4 ,if nitrog5 does n appe>1 t is no pro( t nitrog5 is abs5t2 x is mu* m likely t ! /ell> atmosph]e does n hit (f ! "r conditions = ! te/4 ,9 ! spectrum ( ,sirius ! l9es ( hydrog5 are exce$+ly prom95t & ov]:elm ev]y?+ else4 ,we d n inf] t ,sirius is compos$ ma9ly ( hydrog52 we inf] in/ead t its surface is at a temp]ature ne> #aj1jjj1 because x c be calculat$ t t is a temp]ature mo/ fav\rable = a great developm5t ( ^! hydrog5 l9es4 ,9 ! sun ! mo/ prom95t spectrum is iron4 ,we d n inf] t ! sun is unusually ri* 9 iron2 we inf] t x is at a comp>atively l[ temp]ature ne> #f1jjj fav\rable = ! production ( ! iron spectrum4 ,at "o "t x 0 ?\ght t ! prom95ce ( hydrog5 9 ,sirius & ( metallic elem5ts 9 ! sun indicat$ an evolution ( ! elem5ts1 hydrog5 turn+ into heavi] elem5ts z ! /> cools f ! ,sirian to ! sol> /age4 ,!re is no gr\nd = int]pret+ ! obs]vations 9 t way2 ! fad+ ( ! hydrog5 spectrum & ! increase ( ! iron spectrum w\ld occur 9 any case z ! result ( ! fall ( temp]ature2 & simil> spuri\s appe>ances ( evolution ( elem5ts c be arrang$ 9 ! laboratory4 ,x is r probable t ! *emical elem5ts h mu* ! same relative abundance 9 ! />s t !y h on ! e>?4 ,all ! evid5ce is consi/5t ) ?is view2 & = a few ( ! common] elem5ts !re is "s positive confirmation4 ,b we are limit$ to ! outside ( ! /> z we are limit$ to ! outside ( ! e>? 9 comput+ ! abundance ( ! elem5ts1 s t ?is v provisional conclusion %\ld n be press$ unduly4 ,spectral ,s]ies ,to illu/rate fur!r ?is k9d ( d$uction1 let u consid] ! spectrum %[n 9 ,fig4 #i & see :at may be le>nt f x4 ,) a little tr\ble we c dis5tangle a beautifully regul> s]ies ( bright l9es4 ,! m>ks above w assi/ y to pick out ! fir/ few l9es ( ! s]ies f ! num]\s o!r spectra mix$ up ) x4 ,notic+ ! dim9i%+ spac+ f "r to left1 y w be able to see t ! s]ies cont9ues to ! left = at lea/ fifte5 l9es beyond ! la/ "o m>k$1 ! l9es ultimately draw+ close toge!r & =m+ a #8head' to ! s]ies4 ,?is is ! fam\s ,balm] ,s]ies ( hydrog51 & hav+ recogniz$ x we id5tify hydrog5 z "o ( ! elem5ts pres5t 9 ! s\rce ( ! light4 ,b t is only ! fir/ /ep1 & we c proce$ to fur!r inf]5ces4 ,pr(essor ,bohr's !ory ( ! hydrog5 atom tea*es u t ea* l9e ( ! s]ies is emitt$ by an atom 9 a diff]5t /ate4 ,^! #8/ates ( excitation' c be numb]$ consecutively1 />t+ f ! normal /ate ( ! hydrog5 atom z ,no4 #a4 ,! light emitt$ 9 ! fir/ few /ates comes into ! "p ( ! spectrum n reproduc$ "h1 & ! fir/ l9e 9 our picture corresponds to /ate ,no4 #h4 ,c\nt+ to ! left f ?is y w recognize ! successive l9es )\t mu* difficulty up to /ate ,no4 #cj4 ,n[ ! successive /ates correspond to m & m swoll5 atoms1 t is to say1 ! planet electron#ag makes a wid] & wid] circuit4 ,! radius 7or m /rictly ! semi-axis7 ( its orbit is proportional to ! squ>e ( ! numb] ( ! /ate1 s t ! orbit = /ate ,no4 #cj is #ijj times l>g] ?an ! orbit = ! normal atom ,no4 #a4 ,! diamet] ( ! orbit 9 ,no4 #cj is approximately a t5-?\s&? ( a millimetre4 ,"o inf]5ce c be drawn imm$iately--! spectrum %[n 9 ,fig4 #i 0 n produc$ 9 any t]re/rial laboratory4 ,9 ! highe/ vacuum t c be us$ 9 t]re/rial spectroscopy ! atoms are /ill too cr[d$ to leave room = an orbit s l>ge z ?is4 ,! s\rce mu/ be matt] s t5u\s t !re is vacant space = ! electron to make ?is wide circuit )\t collid+ ) or suff]+ int]f]5ce f o!r atoms4 ,)\t ent]+ into fur!r detail we c conclude t ,fig4 #i is a spectrum ( matt] m r>efi$ ?an ! highe/ vacuum kn[n on ! e>?4#ah ,x is int]e/+ to notice t1 :]eas ?r\gh\t mo/ ( ! picture ! l9es are %[n on a d>k backgr\nd1 at ! extreme left ! backgr\nd is bright2 ! *ange occurs j at ! po9t :]e ! ,balm] ,s]ies comes to an end4 ,?is backgr\nd ( light is also due to hydrog5 & x is caus$ 9 ! foll[+ way4 ,! swoll5 atoms 9 /ate ,no4 #cj or !reab\ts are p]il\sly ne> ! bur/+-po9t1 s x is natural t along ) !m !re %\ld be atoms :i* h ov]/epp$ ! limit & bur/4 ,!y h lo/ _! planet electrons & are occupi$ 9 cat*+ new ones4 ,j z en]gy is requir$ 9 ord] to wr5* away an electron f an atom1 s !re w be sup]flu\s en]gy to be got rid ( :5 ! atom tames a wild electron4 ,?is sup]flu\s en]gy is radiat$ & =ms ! bright backgr\nd ref]r$ to4 ,)\t ent]+ into te*nicalities ( ! !ory1 we c see t x is appropriate t ?is light f ! bur/ atoms %\ld appe> 9 ! spectrum imm$iately beyond ! l9es f ! mo/ swoll5 atoms1 s9ce bur/+ is a sequel to ov]swell+4 ,:il/ y h ?is photograph ( ! ,balm] ,s]ies be=e y ,i may take ! opportunity ( rec\nt+ ! hi/ory ( ano!r fam\s s]ies4 ,9 "s ( ! hotte/ />s a relat$ s]ies ( l9es kn[n z ! ,pick]+ ,s]ies 0 discov]$ 9 #ahif4 ,?is is spac$ on precisely ! same regul> plan1 b ! l9es fall half way betwe5 ! l9es ( ! ,balm] ,s]ies--n exactly half way because ( ! gradually dim9i%+ int]vals f "r to left1 b j :]e "o w\ld naturally int]polate l9es 9 ord] to d\ble _! numb] :il/ keep+ ! spac+ regul>4 ,unlike ! ,balm] ,s]ies1 ! ,pick]+ ,s]ies _h nev] be5 produc$ 9 any laboratory4 ,:at elem5t 0 caus+ x8 ,! answ] seem$ obvi\s2 surely ^! two relat$ s]ies1 "o fitt+ half way betwe5 ! o!r1 mu/ belong to diff]5t modes ( vibration ( ! same atom1 hydrog54 ,t seem$ to be ! only possible answ] at ! "t2 b we h le>n$ m ab\t atoms s9ce !n4 ,we may fairly argue t ! ideal simplicity ( ^! two s]ies indicates t !y are produc$ by an atomic sy/em ( ! simple/ possible type1 viz4 an atom ) "o planet electron2 b x mu/ be rememb]$ t ?is condition only tells u h[ ! atom is clo!d1 n :at ! atom is4 ,! helium atom 7or1 = t matt]1 ! uranium atom7 c on occasion masqu]ade 9 ! scanty attire ( ! hydrog5 atom4 ,normal helium has two planet electrons2 b if "o ( ^! is lo/1 x becomes hydrog5-l & copies ! simple hydrog5 sy/em on a diff]5t scale4 ,x is significant t ! ,pick]+ ,s]ies appe>s only 9 ! v hotte/ />s--9 conditions likely to cause loss ( an electron4 ,! diff]5ce betwe5 hydrog5 & hydrog5-l helium is fir/ly ! diff]5ce ( atomic weight2 ! helium nucleus is f\r times z massive4 ,b ?is sc>cely affects ! spectrum because bo? nuclei are s massive t !y rema9 almo/ un%ak5 by ! danc+ electron4 ,secondly1 ! helium nucleus has a d\ble electric *>ge2 ?is is equival5t to sub/itut+ 9 ! vibrat+ sy/em a controll+ spr+ ( twice ! /r5g?4 ,:at c be m natural ?an t ! d\bl$ =ce ( ! spr+ %\ld d\ble ! numb] ( l9es 9 ! s]ies )\t o!rwise alt]+ its plan8 ,9 ?is way ,pr(essor ,bohr discov]$ ! real orig9 ( ! ,pick]+ ,s]ies2 x is due to ioniz$ helium1 n to hydrog54#ai ,! heavy nucleus1 :e!r ( hydrog5 or helium1 rema9s almo/ un%ak5 by ! atomic vibration--almo/1 b n q4 ,at a lat] date ,pr(essor ,a4 ,f[l] succe$$ 9 reproduc+ ! ,pick]+ ,s]ies 9 ! laboratory & 0 able to measure ! l9es ) mu* great] accuracy ?an c\ld be a*iev$ 9 /ell> spectroscopy2 he 0 !n able to %[ f 8 measures t ! nucleus is n q irresponsive4 ,x 0 a delicate d\ble-/> problem transf]r$ to ! int]ior ( ! atom2 or p]haps a clos] analogy w\ld be ! mutual influ5ce ( ! sun & ,jupit]1 because ,jupit]1 hav+ a ?\s&? ( ! mass ( ! sun1 di/urbs x to ab\t ! same ext5t t ! light electron di/urbs ! hydrog5 nucleus4 ,ioniz$ helium is a fai?ful copy ( ! hydrog5 atom 7on ! alt]$ scale7 9 ev]y?+ except ! #8%ake'2 ! %ake is less ?an 9 hydrog5 because ! helium nucleus is /ill m massive & rock-l4 ,! diff]5ce ( %ake ?r[s ! ,pick]+ ,s]ies ( helium & ! ,balm] ,s]ies ( hydrog5 slightly out ( /ep ) respect to "o ano!r2 & by measur+ ?is misfit ,pr(essor ,f[l] 0 able to make a v accurate det]m9ation ( ! %ake & !re=e ( ! mass ( ! electron4 ,9 ?is way ! mass ( ! electron is f\nd to be ? ( ! mass ( ! hydrog5 nucleus2 ?is agrees well ) ! mass f\nd by o!r me?ods1 & ! det]m9ation is probably n inf]ior 9 accuracy to any ( !m4 ,& s ! clue fir/ pick$ up 9 />s #cjj light ye>s away1 foll[$ 9 turn by ! !oretical & ! exp]im5tal physici/1 leads 9 ! end to ! smalle/ ( all ?+s kn[n4 ,! ,cl\d 9 ,space ,hav+ already consid]$ ! d5se/ matt] 9 ! univ]se1 we n[ turn to consid] ! r>e/4 ,9 spite ( great improvem5ts 9 ! art ( exhau/+ vessels we are /ill a long way f produc+ a real vacuum4 ,! atoms 9 a vacuum tube be=e x is exhau/$ mu/] a =midable numb] conta9+ ab\t tw5ty digits4 ,high exhau/ion means knock+ (f five or six n\ghts at ! end ( t numb]2 & ! mo/ /r5u\s ef=ts to knock (f "o m n\ght seem ludicr\sly ineffective--a m]e nibbl+ at ! huge numb] t mu/ rema94 ,"s ( ! />s are extremely r>efi$4 ,betelgeuse1 = example1 has a d5sity ab\t a ?\s&? t ( air4 ,we %\ld call x a vacuum 7 x n contra/$ ) ! mu* great] vacuosity ( surr\nd+ space4 ,n[adays physici/s h no difficulty 9 produc+ a bett] vacuum ?an ,betelgeuse2 b 9 e>li] times ?is /> w\ld h be5 reg>d$ z a v cr$itable attempt at a vacuum4 ,! out] p>ts ( a />1 & especially ! light app5dages su* z ! sol> *romosph]e & corona1 rea* mu* l[] d5sities4 ,also ! gase\s nebulae are1 z _! appe>ance sugge/s1 extremely t5u\s4 ,:5 !re is space en\gh to put a p9's head betwe5 adjac5t atoms we c beg9 to talk ab\t a #8real vacuum4' ,at ! c5tre ( ! ,orion nebula t degree ( r>efaction is probably rea*$ & surpass$4 ,a nebula has no def9ite b\nd>y & ! d5sity gradually fades (f4 ,!re is reason to ?9k t ! fad+ (f becomes sl[ at great di/ances4 ,be=e we pass entirely out ( ! sph]e ( "o nebula we ent] ! sph]e ( ano!r1 s t !re is always "s residual d5sity 9 int]/ell> space4 ,i believe t1 reason+ f ! tail+ (f ( ! nebulae1 we are 9 a position to make an e/imate ( ! am\nt ( matt] rema9+ unaggregat$ 9 space4 ,an ord9>y region :]e !re is no obs]vable nebulosity is ! highe/ vacuum exi/+--)9 ! limits ( ! /ell> sy/em at lea/--b !re /ill rema9s ab\t "o atom 9 e cubic in*4 ,x dep5ds on our po9t ( view :e!r we reg>d ?is z an amaz+ fullness or an amaz+ empt9ess ( space4 ,p]haps x is ! fullness t impresses u mo/4 ,! atom c f9d no place ( real solitude )9 ! sy/em ( ! />s2 :]ev] x goes x c nod to a colleague n m ?an an in* away4 ,let u approa* ! same subject f a diff]5t angle4 ,9 ! #8,/ory ( ,algol' ,i ref]r$ to ! way 9 :i* we measure ! velocity ( rotation ( ! sun4 ,we po9t ! spectroscope fir/ on "o limb ( ! sun & !n on ! o!r4 ,tak+ any "o ( ! d>k l9es ( ! spectrum1 we f9d t x has %ift$ a little betwe5 ! two obs]vations4 ,?is tells u t ! mat]ial :i* impr9t$ ! l9e 0 mov+ t[>ds or away f u ) diff]5t velocities 9 ! two obs]vations4 ,t is :at we expect$ to f9d2 ! rotation ( ! sun makes sol> mat]ial move t[>ds u on "o side ( ! disk & away f u on ! o!r side4 ,b !re are a few d>k l9es :i* d n %[ ?is *ange4 ,!y are 9 j ! same position :e!r we obs]ve !m on ! ea/ or on ! we/ ( ! sun4 ,cle>ly ^! _c orig9ate on ! sun4 ,!y h be5 impr9t$ on ! light aft] x left ! sun & be=e x rea*$ our telescope4 ,we h ?us discov]$ a m$ium occurr+ some:]e betwe5 ! sun & our telescope2 & z "s ( ! l9es are recogniz$ z belong+ to oxyg51 we c inf] t x is a m$ium conta9+ oxyg54 ,?is seems to be ! beg9n+ ( a great discov]y1 b x ends 9 a ba?os4 ,x happ5s t we 7 already aw>e ( a m$ium conta9+ oxyg5 ly+ some:]e betwe5 our telescope & ! sun4 ,x is a m$ium ess5tial to our exi/5ce4 ,! t]re/rial atmosph]e is responsible = ! #8fix$' l9es se5 9 ! sun's spectrum4 ,j z ! spectroscope c tell u t ! sun is turn+ r\nd 7a fact already famili> to u f wat*+ ! surface m>k+s71 s x c tell u t c]ta9 />s are w&]+ r\nd an orbit1 & !re=e are "u ! influ5ce ( a second /> :i* may or may n be visible itself4 ,b "h aga9 we sometimes f9d #8fix$' l9es :i* d n *ange ) ! o!rs4 ,!re=e some:]e betwe5 ! /> & ! telescope !re exi/s a /ation>y m$ium :i* impr9ts ^! l9es on ! light4 ,?is "t x is n ! e>?'s atmosph]e4 ,! l9es belong to two elem5ts1 calcium & sodium1 nei!r ( :i* occur 9 ! atmosph]e4 ,moreov]1 ! calcium is 9 a sma%$ /ate1 hav+ lo/ "o ( its electrons1 & ! conditions 9 our atmosph]e are n su* z w\ld cause ?is loss4 ,!re seems to be no d\bt t ! m$ium conta9+ ! sodium & ioniz$ calcium--& no d\bt _m o!r elem5ts :i* d n %[ !mselves--is sep>ate f ! e>? & ! />4 ,x is ! #8fullness' ( int]/ell> space already m5tion$4 ,light has to pass "o atom p] cubic in* all ! way f ! /> to ! e>?1 & x w pass q en\gh atoms dur+ its j\rney ( _m hundr$ billion miles to impr9t ^! d>k l9es on its spectrum4 ,at fir/ !re 0 a rival int]pretation4 ,x 0 ?\ght t ! l9es 7 produc$ 9 a cl\d atta*$ to ! />--=m+ a k9d ( aureole r\nd x4 ,! two compon5ts travel 9 orbits r\nd ea* o!r1 b _! orbital motion ne$ n di/urb a diffuse m$ium fill+ & surr\nd+ ! comb9$ sy/em4 ,?is 0 a v reasonable sugge/ion1 b x c\ld be put to ! te/4 ,! te/ 0 aga9 velocity4 ,al?\gh ei!r compon5t c move p]iodically to & fro )9 ! surr\nd+ cl\d ( calcium & sodium1 x is cle> t its av]age approa* to u or recession f u tak5 ov] a long "t mu/ agree ) t ( ! calcium & sodium if ! /> is n to leave its halo beh9d4 ,pr(essor ,plaskett ) ! #gb-;in* reflector at ! ,dom9ion ,obs]vatory 9 ,briti% ,columbia c>ri$ out ?is te/4 ,he f\nd t ! secul> or av]age rate ( approa* ( ! />#bj 0 9 g5]al q diff]5t f ! rate %[n by ! fix$ calcium or sodium l9es4 ,cle>ly ! mat]ial responsible = ! fix$ l9es c\ld n be an app5dage ( ! /> s9ce x 0 n keep+ pace ) x4 ,plaskett w5t f>!r & %[$ t :]eas ! />s !mselves _h all sorts ( individual velocities1 ! mat]ial ( ! fix$ l9es _h ! same or ne>ly ! same velocity 9 all p>ts ( ! sky1 z ?\gh x 7 "o cont9u\s m$ium ?r\gh\t int]/ell> space4 ,i ?9k !re c be no d\bt t ?is rese>* demon/rates ! exi/5ce ( a cosmic cl\d p]vad+ ! /ell> sy/em4 ,! fullness ( int]/ell> space becomes a fact ( obs]vation & no long] a !oretical conjecture4 ,! sy/em ( ! />s is float+ 9 an ocean--n m]ely an ocean ( space1 n m]ely an ocean ( e!r1 b an ocean t is s f> mat]ial t "o atom or !reab\ts occurs 9 ea* cubic in*4 ,x is a placid ocean )\t mu* relative motion2 curr5ts probably exi/1 b !y are ( a m9or "* & d n atta9 ! high spe$s commonly possess$ by ! />s4 ,_m po9ts ( int]e/ arise1 b ,i w only t\* on "o or two4 ,:y are ! calcium atoms ioniz$8 ,9 ! calm ( int]/ell> space we seem to h pass$ away f ! turmoil :i* sma%$ ! calcium atoms 9 ! int]ior ( a />2 s at fir/ x seems difficult to und]/& :y ! atoms 9 ! cl\d %\ld n be complete4 ,h[ev]1 ev5 9 ! dep?s ( space ! break+-up ( ! atom cont9ues2 because !re is always />light pass+ across space1 & "s ( ! light-waves are q p[]ful en\gh to wr5* a fir/ or second electron away f ! calcium atom4 ,x is "o ( ! mo/ curi\s discov]ies ( mod]n physics t :5 a light-wave is att5uat$ by spread+1 :at x really suff]s f is laz9ess r ?an actual loss ( p[]4 ,:at is weak5$ is n ! p[] b ! probability t x w display ! p[]4 ,a light-wave capable ( bur/+ an atom /ill reta9s ! p[] :5 x is att5uat$ a million-fold by spread+2 only x is a million times m sp>+ 9 ! ex]cise ( ! p[]4 ,to put x ano!r way1 an atom expos$ to ! att5uat$ waves w on ! av]age h to wait a million times long] be=e a wave *ooses to explode x2 b ! explosion :5 x does occur w be ( precisely ! same /r5g? h[ev] great ! att5uation4 ,?is is entirely unlike ! behavi\r ( wat]-waves2 a wave :i* is at fir/ /rong en\gh to capsize a boat w1 aft] spread+1 become too weak4 ,x is m l ma*9e-gun fire :i* is m likely to miss a giv5 object at great] di/ance b is equally de/ructive if x hits4 ,! prop]ty "h ref]r$ to 7! quantum prop]ty7 is ! deepe/ my/]y ( light4 ,?us 9 int]/ell> space electrons are /ill be+ torn f calcium atoms1 only v infrequ5tly4 ,! o!r side ( ! "q is ! rate ( repair1 & 9 ?is connexion ! l[ d5sity ( ! cosmic cl\d is ! decid+ factor4 ,! atom has s few opportunities = repair4 ,rov+ ?r\gh space ! atom meets an electron only ab\t once a mon?1 & x by no means foll[s t x w capture ! fir/ "o x meets4 ,consequ5tly v infrequ5t sma%+ w suffice to keep ! majority ( ! atoms ioniz$4 ,! sma%$ /ate ( ! atoms inside a /> c be comp>$ to ! dilapidation ( a h\se visit$ by a tornado2 ! sma%$ /ate 9 int]/ell> space is a dilapidation due to ord9>y we> & te> c\pl$ ) excessive slackness 9 mak+ repairs4 ,a calculation indicates t mo/ ( ! calcium atoms 9 int]/ell> space h lo/ two electrons2 ^! atoms d n int]f]e ) ! light & give no visible spectrum4 ,! #8fix$ l9es' are produc$ by atoms tempor>ily 9 a bett] /ate ( repair ) only "o electron miss+2 !y _c am\nt at any mom5t to m ?an "o-?\s&? ( ! :ole numb]1 b ev5 s !y w be suffici5tly num]\s to produce ! obs]v$ absorption4 ,we g5]ally ?9k ( int]/ell> space z excessively cold4 ,x is q true t any !rmomet] plac$ !re w\ld %[ a temp]ature only ab\t #c above ! absolute z]o--if x 7 capable ( regi/]+ s l[ a read+4 ,compact matt] su* z a !rmomet]1 or ev5 matt] :i* f ! ord9>y /&po9t is reg>d$ z highly diffuse1 falls to ?is l[ temp]ature4 ,b ! rule does n apply to matt] z r>efi$ z ! int]/ell> cl\d4 ,its temp]ature is gov]n$ by o!r consid]ations1 & x w probably be n mu* bel[ ! surface-temp]ature ( ! hotte/ />s1 say #ae1jjj4 ,int]/ell> space is at ! same "t excessively cold & decid$ly hot4#ba ,! ,sun's ,*romosph]e ,once aga9 we %ift ! sc5e1 & n[ we are back 9 ! out] p>ts ( ! sun4 ,fig4 #ajbb %[s "o ( ! huge prom95ce flames :i* f "t to "t %oot out ( ! sun4 ,! flame 9 ?is picture 0 ab\t #abj1jjj miles high4 ,x w5t ?r\gh great *anges ( =m & disappe>$ 9 n mu* m ?an tw5ty-f\r h\rs4 ,?is 0 r an exceptional specim54 ,small] flames occur commonly en\gh2 x seems t ! curi\s black m>ks 9 ,fig4 #a1 (t5 look+ l rifts1 are really prom95ces se5 9 projection aga9/ ! /ill bright] backgr\nd ( ! sun4 ,! flames consi/ ( calcium1 hydrog51 & sev]al o!r elem5ts4 ,we are conc]n$ n s mu* ) ! prom95ces z ) ! lay] f :i* !y spr+4 ,! ord9>y atmosph]e ( ! sun t]m9ates r abruptly1 b above x !re is a deep ?\gh v r>efi$ lay] call$ ! *romosph]e consi/+ ( a few select$ elem5ts :i* are able to float--float1 n on ! top ( ! sun's atmosph]e1 b on ! sunbeams4 ,! art ( rid+ a sunbeam is evid5tly r difficult1 because only a few ( ! elem5ts h ! necess>y skill4 ,! mo/ exp]t is calcium4 ,! light & nimble hydrog5 atom is fairly good at x1 b ! pond]\s calcium atom does x be/4 ,! lay] ( calcium susp5d$ on ! sunlight is at lea/ #e1jjj miles ?ick4 ,we c obs]ve x be/ :5 ! ma9 "p ( ! sun is hidd5 by ! moon 9 an eclipse2 b ! spectroheliograph enables u to /udy x to "s ext5t )\t an eclipse4 ,illu/ration3 ,fig4 #aj4 ,,sol> ,,prom95ce ,illu/ration3 ,fig4 #aa4 ,,/> ,,clu/] ,,c5tauri ,on ! :ole x is /eady & quiesc5t1 al?\gh1 z ! prom95ce flames %[1 x is liable to be bl[n sky-high by viol5t outbur/s4 ,! conclusions ab\t ! calcium *romosph]e t ,i am go+ to describe re/ on a s]ies ( rem>kable rese>*es by ,pr(essor ,milne4 ,h[ does an atom float on a sunbeam8 ,! possibility dep5ds on ! pressure ( light to :i* we h already ref]r$ 7p4 #bf74 ,! sunlight travell+ outw>ds c>ries a c]ta9 outw>d mom5tum2 if ! atom absorbs ! light x absorbs also ! mom5tum & s receives a t9y impulse outw>ds4 ,?is impulse enables x to recov] ! gr\nd x 0 los+ 9 fall+ t[>ds ! sun4 ,! atoms 9 ! *romosph]e are kept float+ above ! sun l t9y %uttlecocks1 dropp+ a little & !n asc5d+ aga9 f ! impulse ( ! light4 ,only ^? atoms :i* c absorb l>ge quantities ( sunlight 9 proportion to _! weight w be able to float successfully4 ,we mu/ look r closely into ! me*anism ( absorption ( ! calcium atom if we are to see :y x excels ! o!r elem5ts4 ,! ord9>y calcium atom has two r loose electrons 9 its att5dant sy/em2 ! *emi/s express ?is by say+ t x is a dival5t elem5t1 ! two loose electrons be+ especially important 9 det]m9+ ! *emical behavi\r4 ,ea* ( ^! electrons possesses a me*anism = absorb+ light4 ,b "u ! conditions prevail+ 9 ! *romosph]e "o ( ! electrons is brok5 away1 & ! calcium atoms are 9 ! same sma%$ /ate t gives rise to ! #8fix$ l9es' 9 ! int]/ell> cl\d4 ,! *romosph]ic calcium ?us supports itself on :at sunlight x c ga!r 9 ) ! "o loose electron rema9+4 ,to "p ) ?is w\ld be fatal2 ! atom w\ld no long] be able to absorb sunlight1 & w\ld drop l a /one4 ,x is true t aft] two electrons are lo/ !re are /ill eighte5 rema9+2 b ^! are held s tightly t sunlight has no effect on !m & !y c only absorb %ort] waves :i* ! sun does n radiate 9 any quantity4 ,! atom !re=e c\ld only save itself if x re/or$ its ma9 absorb+ me*anism by pick+ up a pass+ electron2 x has little *ance ( cat*+ "o 9 ! r>efi$ *romosph]e1 s x w\ld probably fall all ! way to ! sun's surface4 ,!re are two ways 9 :i* light c be absorb$4 ,9 "o ! atom absorbs s gre$ily t x bur/s1 & ! electron scurries (f ) ! surplus en]gy4 ,t is ! process ( ionization :i* 0 %[n 9 ,fig4 #e4 ,cle>ly ?is _c be ! process ( absorption 9 ! *romosph]e because1 z we h se51 ! atom _c af=d to lose ! electron4 ,9 ! o!r me?od ( absorption ! atom is n q s gre$y4 ,x does n bur/1 b x swells visibly4 ,to accommodate ! extra en]gy ! electron is toss$ up into a high] orbit4 ,?is me?od is call$ excitation 7cf4 p4 #ei74 ,aft] rema9+ 9 ! excit$ orbit = a little :ile ! electron comes d[n aga9 spontane\sly4 ,! process has to be repeat$ #bj1jjj times a second 9 ord] to keep ! atom balanc$ 9 ! *romosph]e4 ,! po9t we are lead+ up to is1 ,:y %\ld calcium be able to float bett] ?an o!r elem5ts8 ,x has always seem$ odd t a r heavy elem5t 7,no4 #bj 9 ord] ( atomic weight7 %\ld be f\nd 9 ^! upp]mo/ regions :]e "o w\ld expect only ! lighte/ atoms4 ,we see n[ t ! special skill dem&$ is to be able to toss up an electron #bj1jjj times a second )\t ev] mak+ ! fatal blund] ( dropp+ x4 ,t is n easy ev5 = an atom4 ,calcium#bc scores because x possesses a possible orbit ( excitation only a little way above ! normal orbit s t x c juggle ! electron betwe5 ^! two orbits )\t s]i\s risk4 ,) mo/ o!r elem5ts ! fir/ available orbit is relatively mu* high]2 ! en]gy requir$ to rea* ?is orbit is n s v mu* less ?an ! en]gy requir$ to deta* ! electron altoge!r2 s t we _c v well h a cont9u\s s\rce ( light capable ( caus+ ! orbit-jumps )\t sometimes ov]do+ x & caus+ loss ( ! electron4 ,x is ! wide diff]5ce betwe5 ! en]gy ( excitation & ! en]gy ( ionization ( calcium :i* is s fav\rable2 ! sun is v ri* 9 e!r-waves capable ( caus+ ! fir/1 & is almo/ lack+ 9 e!r-waves capable ( caus+ ! second4 ,! av]age "t occupi$ by ea* p]=mance is ? ( a second4 ,?is is divid$ into two p]iods4 ,!re is a p]iod dur+ :i* ! atom is pati5tly wait+ = a light-wave to run into x & ?r[ up ! electron4 ,!re is ano!r p]iod dur+ :i* ! electron revolves /eadily 9 ! high] orbit be=e decid+ to come d[n aga94 ,pr(essor ,milne has %[n h[ to calculate f obs]vations ( ! *romosph]e ! durations ( bo? ^! p]iods4 ,! fir/ p]iod ( wait+ dep5ds on ! /r5g? ( ! sun's radiation4 ,b we focus att5tion especially on ! second p]iod1 :i* is m int]e/+ because x is a def9ite prop]ty ( ! calcium atom1 hav+ no?+ to d ) local circum/ances4 ,al?\gh we measure x = ions 9 ! sun's *romosph]e1 ! same result mu/ apply to calcium ions any:]e4 ,milne's result is t an electron toss$ into ! high] orbit rema9s !re = an av]age "t ( a hundr$-million? ( a second be=e x spontane\sly drops back aga94 ,i may add t dur+ ?is brief "t x makes some?+ l a million revolutions 9 ! upp] orbit4 ,p]haps ?is is a piece ( in=mation t y 7 n p>ticul>ly burn+ to "k4 ,i d n ?9k x c be call$ int]e/+ except to ^? :o make a hobby ( atoms4 ,b x does seem to me int]e/+ t we %\ld h to turn a telescope & spectroscope on ! sun to f9d out ?is homely prop]ty ( a sub/ance :i* we h&le daily4 ,x is a k9d ( measurem5t ( imm5se importance 9 physics4 ,! !ory ( ^! atomic jumps comes "u ! quantum !ory :i* is /ill ! greate/ puzzle ( physical sci5ce2 & x is greatly 9 ne$ ( guidance f obs]vation on j su* a matt] z ?is4 ,we c imag9e :at a s5sation w\ld be caus$ if1 aft] a million revolutions r\nd ! sun1 a planet made a jump ( ?is k9d4 ,h[ eag]ly we %\ld try to det]m9e ! av]age int]val at :i* su* jumps occurr$6 ,! atom is r l a sol> sy/em1 & x is n ! less int]e/+ because x is on a small] scale4 ,!re is no prospect at pres5t ( measur+ ! "t ( relaxation ( ! excit$ calcium atom 9 a diff]5t way4 ,x has1 h[ev]1 be5 f\nd possible to det]m9e ! correspond+ "t = "o or two o!r k9ds ( atoms by laboratory exp]im5ts4 ,x is n necess>y t ! "t %\ld be at all closely ! same = diff]5t elem5ts2 b laboratory measurem5ts = hydrog5 also give ! p]iod z a hundr$-million? ( a second1 s !re is no fault to f9d ) ! a/ronomical det]m9ation = calcium4 ,! excitation ( ! calcium atom is p]=m$ by light ( two p>ticul> wave-l5g?s1 & ! atoms 9 ! *romosph]e support !mselves by robb+ sunlight ( ^! two con/itu5ts4 ,x is true t aft] a hundr$-million? ( a second a relapse comes & ! atom has to disgorge :at x has appropriat$2 b 9 re-emitt+ ! light x is z likely to s5d x inw>ds z outw>ds1 s t ! outfl[+ sunlight suff]s m loss ?an x recov]s4 ,consequ5tly1 :5 we view ! sun ?r\gh ?is mantle ( calcium ! spectrum %[s gaps or d>k l9es at ! two wave-l5g?s conc]n$4 ,^! l9es are d5ot$ by ! lett]s ,h & ,k4 ,!y are n entirely black1 & x is important to measure ! residual light at ! c5tre ( ! l9es1 because we "k t x mu/ h an int5sity j /rong en\gh to keep calcium atoms float+ "u sol> gravity2 z soon z ! outfl[+ light is s weak5$ t x c support no m atoms x c suff] no fur!r depr$ations1 & s x em]ges into out] space ) ?is limit+ int5sity4 ,! measurem5t gives num]ical data = work+ out ! con/ants ( ! calcium atom includ+ ! "t ( relaxation m5tion$ above4 ,! atoms at ! top ( ! *romosph]e re/ on ! weak5$ light :i* has pass$ ?r\gh ! scre5 bel[2 ! full sunlight w\ld bl[ !m away4 ,milne has d$uc$ a consequ5ce :i* may p]haps h a practical application 9 ! ph5om5a ( explosion ( #8new />s' or novae1 & 9 any case is curi\sly int]e/+4 ,ow+ to ! ,doppl] effect a mov+ atom absorbs a r diff]5t wave-l5g? f a /ation>y atom2 s t if = any cause an atom moves away f ! sun x w support itself on light :i* is a little to "o side ( ! deepe/ absorption4 ,?is light1 be+ m int5se ?an t :i* provid$ a balance1 w make ! atom rec$e fa/]4 ,! atom's own absorption w ?us gradually draw cle> ( ! absorption ( ! scre5 bel[4 ,speak+ r metaphorically1 ! atom is balanc$ prec>i\sly on ! summit ( ! absorption l9e & x is liable to topple (f into ! full sunlight on "o side4 ,app>5tly ! spe$ ( ! atom %\ld g on increas+ until x has to climb an adjac5t absorption l9e 7due p]haps to "s o!r elem5t72 if ! l9e is too int5se to be surm\nt$ ! atom w /ick "p-way up1 ! velocity rema9+ fix$ at a p>ticul> value4 ,^! lat] inf]5ces may be r f>-fet*$1 b at any rate ! argum5t indicates t !re is likely to be an escape ( calcium into out] space4 ,by ,milne's !ory we c calculate ! :ole weight ( ! sun's calcium *romosph]e4 ,its mass is ab\t #cjj million tons4 ,"o sc>cely expects to meet ) su* a trifl+ figure 9 a/ronomy4 ,x is less ?an ! tonnage h&l$ by our ,engli% railways ea* ye>4 ,i ?9k t sol> obs]v]s mu/ feel r hoax$ :5 !y consid] ! lab\r t !y h be5 induc$ to sp5d on ?is airy no?+4 ,b sci5ce does n despise trifles4 ,& a/ronomy c /ill be in/ructive ev5 :51 = once 9 a way1 x desc5ds to commonplace numb]s4 ,! ,/ory ( ,betelgeuse ,?is /ory has n mu* to d ) atoms1 & sc>cely comes "u ! title ( ^! lectures2 b we h _h occasion to allude to ,betelgeuse z ! fam\s example ( a /> ( great size & l[ d5sity1 & its hi/ory is closely associat$ ) "s ( ! developm5ts t we are /udy+4 ,no /> has a disk l>ge en\gh to be se5 ) our pres5t telescopes4 ,we c calculate t a l5s or mirror ( ab\t #bj feet ap]ture w\ld be ne$$ to %[ traces ev5 ( ! l>ge/ /> disk4 ,imag9e = a mom5t t we h con/ruct$ an in/rum5t ( ?is ord] ( size4 ,:i* w\ld be ! mo/ hopeful /> to try x on8 ,p]haps ,sirius sugge/s itself fir/1 s9ce x is ! brighte/ /> 9 ! sky4 ,b ,sirius has a :ite-hot surface radiat+ v int5sely1 s t x is n necess>y t x %\ld h a wide expanse4 ,evid5tly we %\ld pref] a /> :i*1 al?\gh bright1 has its surface 9 a feebly gl[+ condition2 !n ! app>5t brightness mu/ be due to l>ge area4 ,we ne$1 !n1 a /> :i* is bo? r$ & bright4 ,betelgeuse seems be/ to satisfy ?is condition4 ,x is ! bright] ( ! two %\ld]-/>s ( ,orion--! only conspicu\s r$ /> 9 ! con/ellation4 ,!re are "o or two rivals1 includ+ ,ant>es1 :i* might possibly be pref]r$2 b we _c g f> wrong 9 turn+ our new in/rum5t on ,betelgeuse 9 ! hope ( f9d+ ! l>ge/ or ne>ly ! l>ge/ /> disk4 ,y may notice t ,i h paid no att5tion to ! di/ances ( ^! />s4 ,x happ5s t di/ance is n relevant4 ,x w\ld be relevant if we 7 try+ to f9d ! /> ( greate/ actual dim5sions2 b "h we are consid]+ ! /> :i* pres5ts ! l>ge/ app>5t disk1#bd i4e4 cov]s ! l>ge/ area ( ! sky4 ,if we 7 at twice our pres5t di/ance f ! sun1 we %\ld receive only "o-qu>t] z mu* light2 b ! sun w\ld look half its pres5t size l9e>ly1 & its app>5t area w\ld be "o-qu>t]4 ,?us ! light p] unit area ( disk is unalt]$ by di/ance4 ,remov+ ! sun to great] & great] di/ance its disk w appe> small] b gl[+ n less int5sely1 until x is s f> away t ! disk _c be discrim9at$4 ,by spectroscopic exam9ation we "k t ,betelgeuse has a surface temp]ature ab\t #c1jjj4 ,a temp]ature ( #c1jjj is n unatta9able 9 ! laboratory1 & we "k p>tly by exp]im5t & p>tly by !ory :at is ! radiat+ p[] ( a surface 9 ?is /ate4 ,?us x is n difficult to compute h[ l>ge an area ( ! sky ,betelgeuse mu/ cov] 9 ord] t ! area multipli$ by ! radiat+ p[] may give ! obs]v$ brightness ( ,betelgeuse4 ,! area turns out to be v small4 ,! app>5t size ( ,betelgeuse is t ( a half-p5ny fifty miles away4 ,us+ a m sci5tific measure1 ! diamet] ( ,betelgeuse pr$ict$ by ?is calculation is #jjea ( a second ( arc4 ,no exi/+ telescope c %[ s small a disk4 ,let u consid] briefly h[ a telescope =ms an image--9 p>ticul> h[ x reproduces t detail & contra/ ( light & d>kness :i* betrays t we are look+ at a disk or a d\ble /> & n a blur emanat+ f a s+le po9t4 ,?is optical p]=mance is call$ resolv+ p[]2 x is n prim>ily a matt] ( magnification b ( ap]ture1 & ! limit ( resolution is det]m9$ by ! size ( ap]ture ( ! telescope4 ,to create a %>ply def9$ image ! telescope mu/ n only br+ light :]e !re ought to be light1 b x mu/ also br+ d>kness :]e !re ought to be d>kness4 ,! latt] task is ! m difficult4 ,light-waves t5d to spread 9 all directions1 & ! telescope _c prev5t individual wavelets f /ray+ on to p>ts ( ! picture :]e !y h no bus9ess4 ,b x has ?is "o rem$y--= e trespass+ wavelet x mu/ s5d a second wavelet by a slightly long] or %ort] r\te s z to arrive 9 a phase opposite to ! fir/ wavelet & cancel its effect4 ,?is is :]e ! utility ( a wide ap]ture arises--by af=d+ a wid] diff]5ce ( r\te ( ! individual wavelets1 s t ^? f "o "p ( ! ap]ture may be ret>d$ relatively to & int]f]e ) ^? f ano!r "p4 ,a small object-glass c furni% light2 x takes a big object-glass to furni% d>kness 9 ! picture4 ,n[ we may ask ourselves :e!r ! ord9>y circul> ap]ture is necess>ily ! mo/ effici5t = giv+ ! wavelets ! requir$ pa?-diff]5ces4 ,any deviation f a symmetrical %ape is likely to spoil ! def9ition ( ! image--to produce w+s & fr+es4 ,! image w n s closely resemble ! object view$4 ,b on ! o!r h& we may be able to %>p5 up ! tell-tale features4 ,x does n matt] h[ widely ! image-patt]n may diff] f ! object1 provid$ t we c read ! significance ( ! patt]n4 ,if we _c reproduce a />-disk1 let u try :e!r we c reproduce some?+ di/9ctive ( a />-disk4 ,a little reflection %[s t we ought to improve matt]s by block+ out ! middle ( ! object-glass1 & us+ only ! extreme regions on "o side or ! o!r4 ,= ^! regions ! diff]5ce ( light-pa? ( ! waves is greate/1 & !y are ! mo/ effici5t 9 furni%+ ! d>k contra/ ne$$ to outl9e ! image prop]ly4 ,b if ! middle ( ! object-glass is n go+ to be us$1 :y g to ! exp5se ( manufactur+ x8 ,we are l$ to ! idea ( us+ two widely sep>at$ ap]tures1 ea* involv+ a comp>atively small l5s or mirror4 ,we ?us arrive at an in/rum5t aft] ! patt]n ( a rangef9d]4 ,?is in/rum5t w n %[ u ! disk ( a />4 ,if we look ?r\gh x ! ma9 impression ( ! /> image is v l :at we %\ld h se5 ) ei!r ap]ture s+ly--a #8spuri\s disk' surr\nd$ by diffraction r+s4 ,b look+ att5tively we see t ?is image is cross$ by d>k & bright b&s :i* are produc$ by int]f]5ce betwe5 ! light-waves com+ f ! two ap]tures4 ,at ! c5tre ( ! image ! waves f ! two ap]tures arrive cre/ on cre/ s9ce !y h travell$ symmetrically along equal pa?s2 accord+ly !re is a bright b&4 ,a v little to "o side ! asymmetry causes ! waves to arrive cre/ on tr\gh1 s t !y cancel "o ano!r2 "h !re is a d>k b&4 ,! wid? ( ! b&s decreases z ! sep>ation ( ! two ap]tures increases1 & = any giv5 sep>ation ! actual wid? is easily calculat$4 ,ea* po9t ( ! />'s disk is giv+ rise to a diffraction image ) a sy/em ( b&s ( ?is k9d1 b s long z ! disk is small comp>$ ) ! f9e/ detail ( ! diffraction image !re is no appreciable blurr+4 ,if we cont9ually increase ! sep>ation ( ! two ap]tures & s make ! b&s n>r[]1 !re comes a "t :5 ! bright b&s = "o "p ( ! disk are fall+ on ! d>k b&s = ano!r "p ( ! disk4 ,! b& sy/em !n becomes indi/9ct4 ,x is a matt] ( ma!matical calculation to det]m9e ! resultant effect ( summ+ ! b& sy/ems = ea* po9t ( ! disk4 ,x c be %[n t = a c]ta9 sep>ation ( ! ap]tures ! b&s w disappe> altoge!r2 & beyond ?is sep>ation ! sy/em %\ld reappe> ?\gh n atta9+ its orig9al %>pness4 ,! complete disappe>ance occurs :5 ! diamet] ( ! />-disk is equal to #a times ! wid? ( ! b&s 7f ! c5tre ( "o bright b& to ! next74 ,z already /at$1 ! b&wid? c be calculat$ f ! kn[n sep>ation ( ! ap]tures4 ,! obs]vation consi/s 9 slid+ ap>t ! two ap]tures until ! b&s disappe>4 ,! diamet] ( ! disk is inf]r$ at once f _! sep>ation :5 ! disappe>ance occurr$4 ,al?\gh we measure ! size ( ! disk 9 ?is way we nev] see ! disk4 ,we c summ>ize ! pr9ciple ( ! me?od 9 ! foll[+ way4 ,! image ( a po9t ( light se5 ?r\gh a telescope is n a po9t b a small diffraction patt]n4 ,h5ce1 if we look at an ext5d$ object1 say ,m>s1 ! diffraction patt]n w blur ! f9e detail ( ! m>k+ on ! planet4 ,if1 h[ev]1 we are look+ at a /> :i* is almo/ a po9t1 x is simpl] to inv]t ! idea2 ! object1 n be+ an ideal po9t1 w slightly blur ! detail ( ! diffraction patt]n4 ,we %all only p]ceive ! blurr+ if ! diffraction patt]n conta9s detail f9e en\gh to suff] f x4 ,betelgeuse on acc\nt ( its f9ite size mu/ !oretically blur a diffraction patt]n2 b ! ord9>y diffraction disk & r+s produc$ ) ! l>ge/ telescope are too co>se to %[ ?is4 ,we create a diffraction image ) f9] detail by us+ two ap]tures4 ,!oretically we c make ! detail z f9e z we please by increas+ ! sep>ation ( ! two ap]tures4 ,! me?od accord+ly consi/s 9 wid5+ ! sep>ation until ! patt]n becomes f9e en\gh to be p]ceptibly blurr$ by ,betelgeuse4 ,= a small] />-disk ! same effect ( blurr+ w\ld n be app>5t until ! detail _h be5 made /ill f9] by fur!r sep>ation ( ! ap]tures4 ,?is me?od 0 devis$ long ago by ,pr(essor ,mi*elson1 b x 0 only 9 #aibj t he tri$ x on a l>ge scale ) a great #bj-;foot beam across ! #ajj-;in* reflector at ,m\nt ,wilson ,obs]vatory4 ,aft] _m attempts ,pease & ,&]son 7 able to %[ t ! bright & d>k b&s = ,betelgeuse disappe>$ :5 ! ap]tures 7 sep>at$ #aj feet4 ,! d$uc$ diamet] is #jjde a second ( arc 9 good en\gh agreem5t ) ! pr$ict$ value 7p4 #gh74 ,only five or six />s h disks l>ge en\gh to be measur$ ) ?is in/rum5t4 ,x is und]/ood t ! con/ruction ( a #ej-;foot int]f]omet] is contemplat$2 b ev5 ?is w be insuffici5t = ! great majority ( ! />s4 ,we are fairly confid5t t ! me?od ( calculation fir/ describ$ gives ! correct diamet]s ( ! />s1 b confirmation by ,mi*elson's m direct me?od ( measurem5t is always desirable4 ,to inf] ! actual size ( ! /> f its app>5t diamet]1 we mu/ "k ! di/ance4 ,betelgeuse is r a remote /> & its di/ance _c be measur$ v accurately1 b ! unc]ta9ty w n *ange ! g5]al ord] ( magnitude ( ! results4 ,! diamet] is ab\t #cjj million miles4 ,betelgeuse is l>ge en\gh to conta9 ! :ole orbit ( ! e>? inside x1 p]haps ev5 ! orbit ( ,m>s4 ,its volume is ab\t fifty million times ! volume ( ! sun4 ,!re is no direct way ( le>n+ ! mass ( ,betelgeuse because x has no companion ne> x ^: motion x might influ5ce4 ,we c1 h[ev]1 d$uce a mass f ! mass-brightness relation 9 ,fig4 #g4 ,?is gives ! mass equal to #ce x sun4 ,if ! result is "r1 ,betelgeuse is "o ( ! mo/ massive />s--b1 ( c\rse1 n massive 9 proportion to its bulk4 ,! mean d5sity is ab\t "o-million? ( ! d5sity ( wat]1 or n mu* m ?an "o-?\s&? ( ! d5sity ( air4#be ,!re is "o way 9 :i* we might h inf]r$ t ,betelgeuse is less d5se ?an ! sun1 ev5 if we _h _h no gr\nds ( !ory or analogy = e/imat+ its mass4 ,accord+ to ! mod]n !ory ( gravitation1 a globe ( ! size ( ,betelgeuse & ( ! same mean d5sity z ! sun w\ld h "s rem>kable prop]ties3 ,fir/ly1 ow+ to ! great int5sity ( its gravitation1 light w\ld be unable to escape2 & any rays %ot out w\ld fall back aga9 to ! /> by _! own weight4 ,secondly1 ! ,e9/e9 %ift 7us$ to te/ ! d5sity ( ! ,companion ( ,sirius7 w\ld be s great t ! spectrum w\ld be %ift$ out ( exi/5ce4 ,?irdly1 mass produces a curvature ( space1 & 9 ?is case ! curvature w\ld be s great t space w\ld close up r\nd ! />1 leav+ u outside--t is to say1 n[h]e4 ,except = ! la/ consid]ation1 x seems r a pity t ! d5sity ( ,betelgeuse is s l[4 99 99 99 99 99 ,x is n[ well realiz$ t ! />s are a v important adjunct to ! physical laboratory--a sort ( high-temp]ature annex :]e ! behavi\r ( matt] c be /udi$ "u greatly ext5d$ conditions4 ,be+ an a/ronom]1 ,i naturally put ! connexion some:at diff]5tly & reg>d ! physical laboratory z a l[-temp]ature /ation atta*$ to ! />s4 ,x is ! laboratory conditions :i* %\ld be c\nt$ abnormal4 ,ap>t f ! int]/ell> cl\d :i* is at ! mod]ate temp]ature ( ab\t #ae1jjj1 ,i suppose t n9e-t5?s ( ! matt] ( ! univ]se is above #a1jjj1jjj4 ,"u ord9>y conditions--y w und]/& my use ( ! ^w--matt] has r simple prop]ties4 ,b !re are 9 ! univ]se exceptional regions ) temp]ature n f> remov$ f ! absolute z]o1 :]e ! physical prop]ties ( matt] acquire great complexity2 ! ions surr\nd !mselves ) complete electron sy/ems & become ! atoms ( t]re/rial exp]i5ce4 ,our e>? is "o ( ^! *illy places & "h ! /range/ complications c arise4 ,p]haps /range/ ( all1 "s ( ^! complications c meet toge!r & speculate on ! significance ( ! :ole s*eme4 ,,lecture ,,iii ,,! ,,age ,,( ,,! ,,/>s ,,we h se5 t spatially ! scale ( man is ab\t midway betwe5 ! atom & ! />4 ,i am tempt$ to make a simil> comp>ison z reg>ds "t4 ,! span ( ! life ( a man comes p]haps midway 9 scale betwe5 ! life ( an excit$ atom 7p4 #gd7 & ! life ( a />4 ,= ^? :o insi/ on great] accuracy--?\gh ,i w\ld n l to claim accuracy = pres5t e/imates ( ! life ( a />--,i w modify ?is a little4 ,z reg>ds mass1 man is r too ne> to ! atom & a /rong] claimant = ! midway position w\ld be ! hippopotamus4 ,z reg>ds "t1 man's ?ree score ye>s & t5 is a little too ne> to ! />s & x w\ld be bett] to sub/itute a butt]fly4 ,!re is "o s]i\s moral 9 ?is fantasy4 ,we %all h to consid] p]iods ( "t :i* appall our imag9ation4 ,we fe> to make su* drafts on et]nity4 ,& yet ! va/ness ( ! "t-scale ( /ell> evolution is less remote f ! scale ( human exp]i5ce ?an is ! m9ut5ess ( ! "t-scale ( ! processes /udi$ 9 ! atom4 ,our approa* to ! #8age ( ! />s' w be devi\s1 & c]ta9 incid5tal problems w deta9 u on ! way4 ,pulsat+ ,/>s ,! /> ,cephei is "o ( ! v>iable />s4 ,l ,algol1 its fluctuat+ light s5ds u a message4 ,b ! message :5 x is decod$ is n 9 ! lea/ l ! message f ,algol4 ,let me say at once t exp]ts diff] z to ! int]pretation ( ! message ( ,cephei4 ,?is is n ! place to argue ! matt]1 or to expla9 :y ,i ?9k t rival int]pretations _c be accept$4 ,i c only tell y :at is to ! be/ ( my belief ! correct /ory4 ,! int]pretation :i* ,i foll[ 0 sugge/$ by ,plumm] & ,%apley4 ,! latt] 9 p>ticul> made x v conv9c+1 & subsequ5t developm5ts h1 ,i ?9k1 t5d$ to /r5g!n x4 ,i w\ld n1 h[ev]1 claim t all d\bt is bani%$4 ,algol turn$ out to be a pair ( />s v close toge!r :i* f "t to "t eclipse "o ano!r2 ,cephei is a s+le /> :i* pulsates4 ,x is a globe :i* swells & contracts symmetrically ) a regul> p]iod ( #e days4 ,& z ! globe swells & contracts caus+ great *anges ( pressure & temp]ature 9 ! int]ior1 s ! issu+ /ream ( light rises & falls 9 int5sity & v>ies also 9 quality or col\r4 ,!re is no "q ( eclipses2 ! light signals are n 9 ! =m ( #8dots' & #8da%es'2 & 9 any case ! *ange ( col\r %[s t !re is a real *ange 9 ! physical condition ( ! s\rce ( ! light4 ,b at fir/ explanations always assum$ t two />s 7 conc]n$1 & aim$ at connect+ ! physical *anges ) an orbital motion4 ,= in/ance1 x 0 sugge/$ t ! pr9cipal /> 9 go+ r\nd its orbit bru%$ ?r\gh a resi/+ m$ium :i* heat$ its front surface2 ?us ! light ( ! /> v>i$ accord+ z ! heat$ front surface or cool] re> surface 0 pres5t$ t[>ds u4 ,! orbital explanation has n[ collaps$ because x is f\nd t !re is lit]ally no room = two />s4 ,! suppos$ orbit _h be5 work$ out 9 ! usual way f spectroscopic measurem5ts ( velocity ( approa* & recession2 lat] we began to le>n m ab\t ! true size ( />s1 fir/ by calculation1 & aft]w>ds 7= a few />s7 by direct measurem5t4 ,x turn$ out t ! /> 0 big & ! orbit small2 & ! second /> if x exi/$ w\ld h to be plac$ inside ! pr9cipal />4 ,?is ov]lapp+ ( ! />s is a r$uctio ad absurdum ( ! b9>y hypo!sis1 & "s o!r explanation mu/ be f\nd4 ,:at _h be5 tak5 to be ! approa* & recession ( ! /> z a :ole 0 really ! approa* & recession ( ! surface z x heav$ up & d[n ) ! pulsation4 ,! />s :i* v>y l ,cephei are diffuse />s enorm\sly l>g] ?an ! sun1 & ! total displacem5t measur$ am\nts to only a fraction ( ! />'s radius4 ,!re is !re=e no ne$ to assume a bodily displacem5t ( ! /> 7orbital motion72 ! measures foll[ ! oscillation ( t "p ( ! />'s surface pres5t$ t[>ds u4 ,! decision t ,cephei is a s+le /> & n d\ble has "o imm$iate consequ5ce4 ,x means t ! p]iod ( #e days is intr9sic 9 ! /> & is !re=e "o ( ! clues to its physical condition4 ,x is a free p]iod1 n a =c$ p]iod4 ,x is important to appreciate ! significance ( ?is4 ,! numb] ( sunspots fluctuates f a maximum to m9imum & back to maximum 9 a p]iod ( ab\t #aa ye>s2 al?\gh we d n yet und]/& ! reason = ?is fluctuation1 we realize t ?is p]iod is some?+ *>act]i/ic ( ! sun 9 its pres5t /ate & w\ld *ange if any notable *ange happ5$ to ! sun4 ,at "o "t1 h[ev]1 !re 0 "s speculation z to :e!r ! fluctuation ( ! sunspots might n be caus$ by ! revolution ( ! planet ,jupit]1 :i* has a p]iod n s v diff]5t2 if t explanation _h be5 t5able ! #aa-ye> p]iod w\ld h be5 some?+ =c$ on ! sun f )\t & w\ld tea* u no?+ z to ! prop]ties ( ! sun itself4 ,hav+ conv9c$ ourselves t ! light-p]iod ( ,cephei is a free p]iod ( a s+le />1 belong+ to x 9 ! same way t a p>ticul> note belongs to a tun+-=k1 we c accept x z a valuable indicator ( ! con/ancy 7or o!rwise7 ( ! />'s physical condition4 ,9 /ell> a/ronomy we usually feel v happy if we c det]m9e our data--p>allax1 radius1 mass1 absolute brightness1 c4--to )9 #e p] c5t42 b ! measurem5t ( a p]iod (f]s *ances ( f> sup]ior accuracy4 ,i believe t ! mo/ accurately kn[n quantity 9 ! :ole ( sci5ce 7exclud+ pure ma!matics7 is ! moon's mean p]iod1 :i* is commonly giv5 to twelve significant figures4 ,! p]iod ( ,cephei c be f\nd to six significant figures at lea/4 ,by fa/5+ an obs]vable p]iod to ! intr9sic conditions ( a /> we h secur$ an indicator s5sitive en\gh to %[ extremely small *anges4 ,y w n[ guess :y ,i am approa*+ #8! age ( ! />s' ?r\gh ! ,cepheid v>iables4 ,up to ! pres5t !y are ! only />s kn[n to c>ry a s5sitive indicator1 by :i* we might hope to te/ ! rate ( evolution>y *ange4 ,we believe t ,cephei l o!r />s has cond5s$ out ( a nebula1 & t ! cond5sation & contraction are /ill cont9u+4 ,no "o w\ld expect to detect ! contraction by our r\gh det]m9ations ( ! radius ev5 if cont9u$ = a hundr$ ye>s2 b ! evolution mu/ inde$ be sl[ if an intr9sic p]iod measurable to #a "p 9 #aj1jjj1jjj %[s no *ange 9 a c5tury4 ,x does n greatly matt] :e!r or n we und]/& ! nature ( ?is intr9sic p]iod4 ,if a /> contracts1 ! p]iod ( pulsation1 ! p]iod ( rotation1 or any o!r free p]iod associat$ ) x1 w alt]4 ,if y pref] to foll[ any ( ! rival int]pretations ( ! message ( ,cephei1 y c make ! necess>y alt]ations 9 ! word+ ( my argum5t1 b ! g5]al v]dict z to ! rate ( progress ( evolution w be un*ang$4 ,only if y deta* ! p]iod f ! /> itself by go+ back to ! old d\ble /> int]pretation w ! argum5t collapse2 b ,i d n ?9k any ( ! rival int]pret]s propose to d t4 ,x is n surpris+ t ^! pulsat+ />s %\ld be reg>d$ ) special int]e/4 ,ord9>y />s mu/ be view$ respectfully l ! objects 9 glass cases 9 museums2 our f+]s are it*+ to p9* !m & te/ _! resili5ce4 ,pulsat+ />s are l ^? fasc9at+ models 9 ! ,sci5ce ,museum provid$ ) a button :i* c be press$ to set ! ma*9]y 9 motion4 ,to be able to see ! ma*9]y ( a /> ?robb+ ) activity is mo/ in/ructive = ! developm5t ( our k4 ,! !ory ( a /eady />1 :i* 0 describ$ 9 ! fir/ lecture1 c be ext5d$ to pulsat+ />s2 & we c calculate ! free p]iod ( pulsation = a /> ( assign$ mass & d5sity4 ,y w rememb] t we h already calculat$ ! heat emission or brightness & comp>$ x ) obs]vation1 obta9+ "o satisfactory te/ ( ! tru? ( ! !ory2 n[ we c calculate ! p]iod ( pulsation & by comp>+ x ) obs]vation obta9 ano!r te/4 ,ow+ to lack ( in=mation z to a c]ta9 con/ant ( /ell> mat]ial !re is an unc]ta9ty 9 ! calculation repres5t$ by a factor ( ab\t #b2 t is to say1 we calculate two p]iods1 "o d\ble ! o!r1 betwe5 :i* ) any reasonable luck ! true p]iod ought to lie4 ,! obs]vational confirmation is v good4 ,!re are sixte5 ,cepheid v>iables on :i* ! te/ c be made2 _! p]iods range f #ac h\rs to #ce days1 & !y all agree ) ! calculat$ values to )9 ! limits ( accuracy expect$4 ,9 a m indirect way ! same confirmation is %[n 9 ,fig4 #g by ! close agreem5t ( ! squ>es1 repres5t+ ,cepheid v>iables1 ) ! !oretical curve4 ,! ,cepheid z a #8,/&>d ,c&le' ,cepheid v>iables ( ! same p]iod are closely simil> to "o ano!r4 ,a ,cepheid ( p]iod #e days f\nd 9 any "p ( ! univ]se w be practically a replica ( ,cephei2 9 p>ticul> x w be a /> ( ! same absolute brightness4 ,?is is a fact discov]$ by obs]vation1 & is n pr$ict$ by any "p ( ! !ory yet explor$4 ,! brightness1 z we h se51 dep5ds ma9ly on ! mass2 ! p]iod1 on ! o!r h&1 dep5ds ma9ly on ! d5sity2 s t ! obs]v$ relation betwe5 brightness & p]iod involves a relation betwe5 mass & d5sity4 ,presumably ?is relation signifies t = a giv5 mass !re is j "o special d5sity--"o /age 9 ! c\rse ( cond5sation ( ! />--at :i* pulsations are liable to occur2 at o!r d5sities ! /> c only burn /eadily4 ,?is prop]ty r5d]s ! ,cepheid extremely useful to a/ronom]s4 ,x s]ves z a /&>d c&le--a s\rce ( kn[n light-p[]4 ,9 an ord9>y way y _c tell ! real brightness ( a light m]ely by look+ at x4 ,if x appe>s dim1 t may mean ei!r real fa9tness or great di/ance4 ,at night "t on ! sea y obs]ve _m lights ^: di/ance & real brightness y _c e/imate2 y\r judgem5t ( ! real brightness may be wrong by a factor ( a qu9tillion if y happ5 to mi/ake ,arcturus = a %ip's light4 ,b among !m y may notice a light :i* goes ?r\gh a regul> s]ies ( *anges 9 a c]ta9 numb] ( seconds2 t tells y t x is su*-&-su* a ligh?\se1 kn[n to project a light ( s _m ?\s& c&lep[]4 ,y may n[ e/imate ) c]ta9ty h[ f> (f x is--provid$1 ( c\rse1 t !re is no fog int]v5+4 ,s1 too1 :5 we look up at ! sky1 mo/ ( ! lights t we see might be at any di/ance & h any real brightness4 ,ev5 ! mo/ ref9$ measurem5ts ( p>allax only succe$ 9 locat+ a few ( ! ne>] lights4 ,b if we see a light w9k+ 9 ! ,cepheid mann] ) a p]iod ( #e days1 we "k t x is a replica ( ,cephei & is a light ( #gjj sun-p[]4 ,or if ! p]iod is any o!r numb] ( days we c assign ! prop] sun-p[] = t p]iod4 ,f ?is we c judge ! di/ance4 ,! app>5t brightness1 :i* is a comb9ation ( di/ance & true brightness1 is measur$2 !n x is a simple calculation to answ] ! "q1 ,at :at di/ance mu/ a light ( #gjj sun-p[] be plac$ 9 ord] to give ! app>5t brightness obs]v$8 ,h[ ab\t int]f]5ce by fog8 ,c>eful discussions h be5 made1 & x appe>s t not)/&+ ! cosmical cl\d 9 int]/ell> space !re is ord9>ily no appreciable absorption or scatt]+ ( ! />light on its way to u4 ,) ! ,cepheids s]v+ z /&>d c&les di/ances 9 ! /ell> univ]se h be5 survey$ f> exce$+ ^? rea*$ by previ\s me?ods4 ,if ! di/ances 7 m]ely ^? ( ! ,cepheid v>iables !mselves t w\ld n be s important1 b mu* m in=mation is yield$4 ,fig4 #aabf %[s a fam\s />-clu/] call$ ,c5tauri4 ,among/ ! ?\s&s ( />s 9 ! clu/] no less ?an #gf ,cepheid v>iables h be5 discov]$4 ,ea* is a /&>d c&le s]v+ to measure ! di/ance prim>ily ( itself b also incid5tally ( ! great clu/] 9 :i* x lies4 ,! #gf gauges agree wond]fully among !mselves1 ! av]age deviation be+ less ?an #e p] c5t4 ,by ?is means ,%apley f\nd ! di/ance ( ! clu/] to be #bj1jjj light ye>s4 ,! light messages :i* we receive to-day 7 s5t f ! clu/] #bj1jjj ye>s ago4#bg ,! a/ronom]1 m ?an o!r devotees ( sci5ce1 le>ns to appreciate ! advantage ( n be+ too ne> ! objects he is /udy+4 ,! ne>] />s are all "r 9 _! way1 b x is a great nuisance be+ 9 ! v mid/ ( !m4 ,= ea* /> has to be treat$ s+ly & locat$ at its prop] di/ance by elaborate measurem5ts2 progress is v labori\s4 ,b :5 we det]m9e ! di/ance ( ?is remote clu/]1 we secure at "o scoop ! di/ances ( _m ?\s&s ( />s4 ,! di/ance be+ kn[n1 ! app>5t magnitudes c be turn$ into true magnitudes1 & /ati/ics & correlations ( absolute brightness & col\r c be asc]ta9$4 ,ev5 be=e ! di/ance is discov]$ we c le>n a great deal f ! />s 9 clu/]s :i* x is impracticable to f9d out f less remote />s4 ,we c see t ! ,cepheids are mu* above ! av]age brightness & are surpass$ by relatively few />s4 ,we c asc]ta9 t ! bright] ! ,cepheid ! long] is its p]iod4 ,we discov] t ! brighte/ />s ( all are r$4#bh ,& s on4 ,!re is a rev]se side to ! picture2 ! t9y po9ts ( light 9 ! di/ant clu/] are n ! mo/ satisfactory objects to measure & analyse1 & we c\ld ill sp>e ! ne>] />s2 b ! fact rema9s t !re are c]ta9 l9es ( /ell> inve/igation 9 :i* remot5ess proves to be an actual advantage1 & we turn f ! ne>] />s to objects fifty ?\s& light ye>s away4 ,ab\t #hj globul> clu/]s are kn[n ) di/ances rang+ f #bj1jjj to #bjj1jjj light ye>s4 ,is !re any?+ yet m remote8 ,x has long be5 suspect$ t ! spiral nebulae1#bi :i* seem to be exce$+ly num]\s1 are outside our /ell> sy/em & =m #8isl& univ]ses'4 ,! evid5ce = ?is has become gradually /rong]1 & n[ is believ$ to be decisively confirm$4 ,9 #aibd ,hubble discov]$ a numb] ( ,cepheid v>iables 9 ! great ,&rom$a nebula :i* is ! l>ge/ & presumably "o ( ! ne>e/ ( ! spirals4 ,z soon z _! p]iods _h be5 det]m9$ !y 7 available z /&>d c&les to gauge ! di/ance ( ! nebula4 ,_! app>5t magnitude 0 mu* fa9t] ?an t ( ! correspond+ ,cepheids 9 globul> clu/]s1 %[+ t !y mu/ be ev5 m remote4 ,hubble has s9ce f\nd ! di/ance ( "o or two o!r spirals 9 ! same way4 ,) ! nak$ eye y c see ! ,&rom$a nebula z a fa9t pat* ( light4 ,:5 y look at x y are look+ back #ijj1jjj ye>s into ! pa/4 ,! ,contraction ,hypo!sis ,! problem ( provid+ suffici5t supplies ( en]gy to ma9ta9 ! sun's output ( light & heat has (t5 be5 debat$ by a/ronom]s & o!rs4 ,9 ! la/ c5tury x 0 %[n by ,helmholtz & ,kelv9 t ! sun c\ld ma9ta9 its heat = a v long "t by cont9ually %r9k+4 ,contraction involves an approa* or fall ( ! matt] t[>ds ! c5tre2 gravitational pot5tial en]gy is ?us conv]t$ & made available z heat4 ,x 0 assum$ t ?is 0 ! sole res\rce s9ce no o!r supply capable ( yield+ any?+ l s l>ge an am\nt 0 kn[n4 ,b ! supply is n unlimit$1 & on ?is hypo!sis ! bir? ( ! sun mu/ be dat$ n m ?an #bj1jjj1jjj ye>s ago4 ,ev5 at ! "t ( :i* ,i am speak+ ! "t-limit 0 f\nd to be cramp+2 b ,kelv9 assur$ ! geologi/s & biologi/s t !y mu/ conf9e _! outl9es ( t]re/rial hi/ory )9 ?is p]iod4 ,ab\t ! beg9n+ ( ! pres5t c5tury ! contraction !ory 0 9 ! curi\s position ( be+ g5]ally accept$ & g5]ally ignor$4 ,:il/ few v5tur$ to dispute ! hypo!sis1 no "o seems to h _h any hesitation1 if x suit$ him1 9 c>ry+ back ! hi/ory ( ! e>? or moon to a "t long be=e ! suppos$ era ( ! =mation ( ! sol> sy/em4 ,"l ,kelv9's date ( ! creation 0 treat$ ) no m respect ?an ,ar*bi%op ,us%]'s4 ,! s]i\s consequ5ces ( ! hypo!sis become p>ticul>ly prom95t :5 we consid] ! diffuse />s ( high lum9osity2 ^! are prodigal ( _! en]gy & squ&] x a hundr$ or a ?\s& times fa/] ?an ! sun4 ,! economical sun c\ld h subsi/$ on its contraction en]gy = #bj1jjj1jjj ye>s1 b = ! high lum9osity />s ! limit is cut d[n to #ajj1jjj ye>s4 ,?is includes mo/ ( ! nak$-eye />s4 ,d>e we believe t !y 7 =m$ )9 ! la/ #ajj1jjj ye>s8 ,is ! antiquity ( man great] ?an t ( ! />s n[ %9+8 ,d />s 9 ! ,&rom$a nebula run _! c\rse 9 less "t ?an _! light takes to rea* u8 ,x is "o ?+ to feel a limitation ( "t-scale irksome1 rul+ out ideas & explanations :i* are o!rwise plausible & attractive2 x is ano!r ?+ to produce def9ite evid5ce aga9/ ! "t-scale4 ,i d n ?9k t a/ronom]s _h 9 _! own t]ritory any weapon = a direct attack on ! ,helmholtz-,kelv9 hypo!sis until ! ,cepheid v>iables suppli$ "o4 ,to come to figures3 ,cephei emits m ?an #gjj times z mu* heat z ! sun4 ,we "k its mass & radius1 & we c calculate )\t difficulty h[ fa/ ! radius mu/ contract 9 ord] to provide ?is heat4 ,! requir$ rate is "o "p 9 #dj1jjj p] annum4 ,n[ ,cephei 0 fir/ obs]v$ c>efully 9 #aghe1 s t 9 ! "t x has be5 "u obs]vation ! radius mu/ h *ang$ by "o "p 9 #cjj if ! contraction hypo!sis is "r4 ,y rememb] t we h 9 ,cephei a v s5sitive indicator ( any *anges occurr+ 9 x1 viz4 ! p]iod ( pulsation2 cle>ly *anges ( ! above magnitude c\ld n occur )\t di/urb+ ?is indicator4 ,does ! p]iod %[ any *ange8 ,x is d\btful2 !re is p]haps suffici5t evid5ce = a slight *ange1 b x is n m ?an ? ( ! *ange dem&$ by ! contraction hypo!sis4 ,accept+ ! pulsation !ory1 ! p]iod %\ld dim9i% #ag seconds e ye>--a quantity easily detectable4 ,! actual *ange is n m ?an "o-t5? ( a second p] ye>4 ,at lea/ dur+ ! ,cepheid /age ! />s are draw+ on "s s\rce ( en]gy o!r ?an t provid$ by contraction4 ,on su* an important "q we %\ld n l to put implicit tru/ 9 "o argum5t alone1 & we turn to ! si/] sci5ces = o!r & p]haps m conclusive evid5ce4 ,physical & geological inve/igations seem to decide def9itely t ! age ( ! e>?--reckon$ f an epo* :i* by no means goes back to its beg9n+s z a planet--is f> great] ?an ! ,helmholtz-,kelv9 e/imate ( ! age ( ! sol> sy/em4 ,x is usual to lay mo/ /ress on a det]m9ation ( ! age ( ! rocks f ! uranium-lead ratio ( _! cont5ts4 ,uranium dis9tegrates into lead & helium at a kn[n rate4 ,s9ce lead is unlike uranium 9 *emical prop]ties ! two elem5ts w\ld n naturally be deposit$ toge!r2 s t ! lead f\nd ) uranium has presumably be5 =m$ by its decomposition4#cj ,by measur+ h[ mu* lead occurs ) ! uranium we c det]m9e h[ long ago ! uranium 0 deposit$4 ,! age ( ! old] rocks is f\nd to be ab\t #a1bjj million ye>s2 l[] e/imates h be5 urg$ by "s au?orities1 b none l[ en\gh to save ! contraction hypo!sis4 ,! sun1 ( c\rse1 mu/ be v mu* old] ?an ! e>? & its rocks4 ,we seem to require a "t-scale :i* w all[ at lea/ #aj1jjj1jjj1jjj ye>s = ! age ( ! sun2 c]ta9ly we _c abate our dem&s bel[ #a1jjj1jjj1jjj ye>s4 ,x is necess>y to look = a m prolific s\rce ( en]gy to ma9ta9 ! heat ( ! sun & />s ?r\gh ?is ext5d$ p]iod4 ,we c at once n>r[ d[n ! field ( se>*4 ,no s\rce ( en]gy is ( any avail unless x lib]ates heat 9 ! deep int]ior ( ! />4 ,! crux ( ! problem is n m]ely ! provision = radiation b ! ma9t5ance ( ! int]nal heat :i* keeps ! gravitat+ mass f collaps+4 ,y w rememb] h[ 9 ! fir/ lecture we _h to assign a c]ta9 am\nt ( heat at ea* po9t 9 ! /ell> int]ior 9 ord] to keep ! /> 9 balance4 ,b ! int]nal heat is cont9ually runn+ away t[>ds ! cool] outside & !n escap+ into space z ! />'s radiation4 ,?is1 or its equival5t1 mu/ be put back if ! /> is to be kept /eady--if x is n to contract & evolve at ! rate ( ! ,kelv9 "t-scale4 ,& x is no use to put x back at ! surface ( ! />--by bomb>d+ ! /> ) meteors1 = example4 ,x c\ld n fl[ up ! temp]ature-gradi5t1 & s x w\ld simply take ! fir/ opportunity ( escap+ z additional radiation4 ,y _c ma9ta9 a temp]ature-gradi5t by supply+ heat at ! bottom end4 ,heat mu/ be p\r$ 9 at ! top end1 i4 e4 9 ! deep int]ior ( ! />4 ,s9ce we _c well imag9e an extrane\s s\rce ( heat able to release itself at ! c5tre ( a />1 ! idea ( a /> pick+ up en]gy z x goes along seems to be def9itely rul$ out4 ,x foll[s t ! /> conta9s hidd5 )9 x ! en]gy :i* has to la/ ! re/ ( its life4 ,en]gy has mass4 ,_m p w\ld pref] to say--en]gy is mass2 b x is n necess>y = u to discuss t4 ,! ess5tial fact is t an erg ( en]gy 9 any =m has a mass ( #aa4 #aj-ba grammes4 ,! erg is ! usual sci5tific unit ( en]gy2 b we c measure en]gy also by ! gramme or ! ton z we measure any?+ else :i* possesses mass4 ,!re is no real reason :y y %\ld n buy a p\nd ( light f an electric light company--except t x is a l>g] quantity ?an y are likely to ne$ & at curr5t rates w\ld co/ y some?+ ov] #ajj1jjj1jjj4 ,if y c\ld keep all ?is light 7e!r-waves7 travell+ to & fro betwe5 mirrors =m+ a clos$ vessel1 & !n weigh ! vessel1 ! obs]v$ weight w\ld be ! ord9>y weight ( ! vessel plus #a lb4 repres5t+ ! weight ( ! light4 ,x is evid5t t an object weigh+ a ton _c conta9 m ?an a ton ( en]gy2 & ! sun ) a mass ( #b4jjj quadrillion tons 7p4 #bd7 _c conta9 m ?an #b4jjj quadrillion tons ( en]gy at ! mo/4 ,en]gy ( #ah4 #ajed ergs has a mass #b4 #ajcc grammes :i* is ! mass ( ! sun2 consequ5tly t is ! sum total ( ! en]gy :i* ! sun conta9s--! en]gy :i* has to la/ x all ! re/ ( its life4#ca ,we d n "k h[ mu* ( ?is is capable ( be+ conv]t$ into heat & radiation2 if x is all conv]tible !re is en\gh to ma9ta9 ! sun's radiation at ! pres5t rate = #ae billion ye>s4 ,to put ! argum5t 9 ano!r =m1 ! heat emitt$ by ! sun ea* ye> has a mass ( #abj billion tons2 & if ?is loss ( mass cont9u$ !re w\ld be no mass left at ! end ( #ae billion ye>s4 ,subatomic ,en]gy ,?is /ore ( en]gy is1 ) insignificant exception1 en]gy ( con/itution ( atoms & electrons2 t is to say1 subatomic en]gy4 ,mo/ ( x is inh]5t 9 ! con/itution ( ! electrons & protons--! elem5t>y negative & positive electric *>ges--out ( :i* matt] is built2 s t x _c be set free unless ^! are de/roy$4 ,! ma9 /ore ( en]gy 9 a /> _c be us$ = radiation unless ! matt] compos+ ! /> is be+ annihilat$4 ,x is possible t ! /> may h a long en\gh life )\t raid+ ! ma9 en]gy /ore4 ,a small "p ( ! /ore c be releas$ by a process less dra/ic ?an annihilation ( matt]1 & ?is might be suffici5t to keep ! sun burn+ = #aj1jjj1jjj1jjj ye>s or s1 :i* is p]haps z long z we c reasonably require4 ,! less dra/ic process is transmutation ( ! elem5ts4 ,?us we h rea*$ a po9t :]e a *oice lies op5 be=e u2 we c ei!r p9 our fai? to transmutation ( ! elem5ts1 cont5t+ ourselves ) a r cramp$ "t-scale1 or we c assume ! annihilation ( matt]1 :i* gives a v ample "t-scale4 ,b at pres5t ,i c see no possibility ( a ?ird *oice4 ,let me run ov] ! argum5t aga94 ,fir/ we f\nd t en]gy ( contraction 0 hopelessly inadequate2 !n we f\nd t ! en]gy mu/ be releas$ 9 ! int]ior ( ! />1 s t x comes f an int]nal1 n an ext]nal1 s\rce2 n[ we take /ock ( ! :ole int]nal /ore ( en]gy4 ,no supply ( any importance is f\nd until we come to consid] ! electrons & atomic nuclei2 "h a reasonable am\nt c be releas$ by regr\p+ ! protons & electrons 9 ! atomic nuclei 7transmutation ( elem5ts71 & a mu* great] am\nt by annihilat+ !m4 ,transmutation ( ! elem5ts--s long ! dream ( ! al*emi/--is realiz$ 9 ! trans=mation ( radio-active sub/ances4 ,uranium turns sl[ly into a mixture ( lead & helium4 ,b none ( ! kn[n radio-active processes lib]ate any?+ l en\gh en]gy to ma9ta9 ! sun's heat4 ,! only important release ( en]gy by transmutation occurs at ! v beg9n+ ( ! evolution ( ! elem5ts4 ,we mu/ />t ) hydrog54 ,! hydrog5 atom consi/s simply ( a positive & negative *>ge1 a proton = ! nucleus plus a planet electron4 ,let u call its mass #a4 ,f\r hydrog5 atoms w make a helium atom4 ,if ! mass ( ! helium atom 7 exactly #d1 t w\ld %[ t all ! en]gy ( ! hydrog5 atoms rema9$ 9 ! helium atom4 ,b actually ! mass is #cig2 s t en]gy ( mass a #jjc mu/ h escap$ dur+ ! =mation ( helium f hydrog54 ,by annihilat+ #d grammes ( hydrog5 we %\ld h releas$ #d grammes ( en]gy1 b by transmut+ x into helium we release #jjc grammes ( en]gy4 ,ei!r process might be us$ to furni% ! sun's heat ?\gh1 z we h already /at$1 ! second gives a mu* small] supply4 ,! release ( en]gy occurs because 9 ! helium atom only two ( ! f\r electrons rema9 z planet electrons1 ! o!r two be+ cem5t$ ) ! f\r protons close toge!r 9 ! helium nucleus4 ,9 br++ positive & negative *>ges close toge!r y cause a *ange ( ! en]gy ( ! electric field1 & release electrical en]gy :i* spreads away z e!r-waves4 ,t is :]e ! #jjc grammes ( en]gy has gone4 ,! /> c absorb ^! e!r-waves & utilize !m z heat4 ,we c g on f helium to high] elem5ts1 b we d n obta9 mu* m release ( en]gy4 ,= example1 an oxyg5 atom c be made f #af hydrog5 atoms or #d helium atoms2 b z ne>ly z we c tell x has j ! weight ( ! #d helium atoms1 s t ! release ( en]gy is n appreciably great] :5 ! hydrog5 is transmut$ into oxyg5 ?an :5 x is transmut$ into helium4#cb ,?is becomes cle>] if we take ! mass ( a hydrog5 atom to be #ajjh1 s t ! mass ( helium is exactly #d & ( oxyg5 #af2 !n x is kn[n f ,dr4 ,a/on's rese>*es ) ! mass-spectrograph t ! atoms ( o!r elem5ts h masses :i* are v closely :ole numb]s4 ,! loss ( #jjjh p] hydrog5 atom applies approximately :atev] ! elem5t t is =m$4 ,! view t ! en]gy ( a /> is d]iv$ by ! build+ up ( o!r elem5ts f hydrog5 has ! great advantage t !re is no d\bt ab\t ! possibility ( ! process2 :]eas we h no evid5ce t ! annihilation ( matt] c occur 9 ,nature4 ,i am n ref]r+ to ! alleg$ transmutation ( hydrog5 into helium 9 ! laboratory2 ^? ^: au?ority ,i accept are n conv9c$ by ^! exp]im5ts4 ,to my m9d ! exi/5ce ( helium is ! be/ evid5ce we c\ld desire ( ! possibility ( ! =mation ( helium4 ,! f\r protons & two electrons con/itut+ its nucleus mu/ h be5 assembl$ at "s "t & place2 & :y n 9 ! />s8 ,:5 !y 7 assembl$ ! surplus en]gy mu/ h be5 releas$1 provid+ a prolific supply ( heat4 ,prima facie ?is sugge/s ! int]ior ( a /> z a likely locality1 s9ce und\bt$ly a prolific s\rce ( heat is !re 9 op]ation4 ,i am aw>e t _m critics consid] ! conditions 9 ! />s n suffici5tly extreme to br+ ab\t ! transmutation--! />s are n hot en\gh4 ,! critics lay !mselves op5 to an obvi\s retort2 we tell !m to g & f9d a hott] place4 ,b "h ! advantage seems to end4 ,!re are _m a/ronomical indications t ! hypo!sis attribut+ ! en]gy ( ! />s to ! transmutation ( hydrog5 is unsatisfactory4 ,x may p]haps be responsible = ! rapid lib]ation ( en]gy 9 ! e>lie/ 7giant7 /ages :5 ! /> is a l>ge diffuse body radiat+ heat abundantly2 b ! en]gy 9 lat] life seems to come f a s\rce subject to diff]5t laws ( emission4 ,!re is consid]able evid5ce t z a /> gr[s old] x gets rid ( a l>ge fraction ( ! matt] :i* orig9ally con/itut$ x1 & app>5tly ?is c only be contriv$ by ! annihilation ( ! matt]4 ,! evid5ce1 h[ev]1 is n v coh]5t1 & ,i d n ?9k we are 9 a position to come to a def9ite decision4 ,on ! :ole ! hypo!sis ( annihilation ( matt] seems ! m promis+2 & ,i %all pref] x 9 ! brief discussion ( /ell> evolution :i* ,i propose to give4 ,! phrase #8annihilation ( matt]' s\nds l some?+ sup]natural4 ,we d n yet "k :e!r x c occur naturally or n1 b !re is no obvi\s ob/acle4 ,! ultimate con/itu5ts ( matt] are m9ute positive *>ges & negative *>ges :i* we may picture z c5tres ( opposite k9ds ( /ra9 9 ! e!r4 ,if ^! c\ld be p]suad$ to run toge!r !y w\ld cancel out1 leav+ no?+ except a spla% 9 ! e!r :i* spreads out z an electromagnetic wave c>ry+ (f ! en]gy releas$ by ! undo+ ( ! /ra94 ,! am\nt ( ?is en]gy is amaz+ly l>ge2 by annihilat+ a s+le drop ( wat] we %\ld be suppli$ ) #bjj horsep[] = a ye>4 ,we turn covet\s eyes on ?is /ore )\t1 h[ev]1 ent]ta9+ mu* hope ( ev] discov]+ ! secret ( releas+ x4 ,if x %\ld prove t ! />s h discov]$ ! secret & are us+ ?is /ore to ma9ta9 _! heat1 our prospect ( ultimate success w\ld seem di/9ctly ne>]4 ,i suppose t _m physici/s w reg>d ! subject ( subatomic en]gy z a field ( airy speculation4 ,t is n ! way 9 :i* x pres5ts itself to an a/ronom]4 ,if x is grant$ t ! />s evolve mu* m sl[ly ?an on ! contraction-hypo!sis1 ! measurem5t ( ! output ( subatomic en]gy is "o ( ! commone/ a/ronomical measurem5ts--! measurem5t ( ! heat or light ( ! />s4#cc ,! collection ( obs]vational data z to ! activity ( lib]ation ( subatomic en]gy is "p ( ! r\t9e ( practical a/ronomy2 & we h to pursue ! usual c\rse ( arrang+ ! measurem5ts into "s k9d ( coh]5ce1 s z to f9d out h[ ! output is relat$ to ! temp]ature1 d5sity1 or age ( ! mat]ial supply+ x--9 %ort1 to discov] ! laws ( emission4 ,f ?is po9t onw>ds ! discussion may be m or less hypo!tical accord+ to ! temp]am5t ( ! inve/igator2 & inde$ x is likely t 9 ?is z 9 o!r bran*es ( k advances may come by a prop] use ( ! sci5tific imag9ation4 ,va9 speculation is to be condemn$ 9 ?is z 9 any o!r subject1 & !re is no ne$ = x2 ! problem is "o ( induction f obs]vation ) due reg>d to our !oretical k ( ! possibilities inh]5t 9 atomic /ructure4 ,i _c pass f ?is subject )\t m5tion+ ! p5etrat+ radiation long kn[n to exi/ 9 our atmosph]e1 :i* accord+ to ! rese>*es ( ,kohlhr/] & ,millikan comes f out] space4 ,p5etrat+ p[] is a sign ( %ort wave-l5g? & int5se conc5tration ( en]gy4 ,hi!rto ! greate/ p5etrat+ p[] has be5 display$ by ,gamma rays orig9at$ by subatomic processes occurr+ 9 radio-active sub/ances4 ,! cosmic radiation is /ill m p5etrat+1 & x seems reasonable to ref] x to m en]getic processes 9 ! atom su* z ^? sugge/$ = ! s\rce ( /ell> en]gy4 ,c>eful measurem5ts h be5 made by ,millikan1 & he concludes t ! prop]ties accord ) ^? :i* %\ld be possess$ by radiation lib]at$ 9 ! transmutation ( hydrog52 x is n p5etrat+ en\gh to be attribut$ to a process s en]getic z ! annihilation ( protons & electrons4 ,!re seems to be no d\bt t ?is radiation is travell+ d[nw>ds f ! sky4 ,?is is %[n by measurem5ts ( its /r5g? at diff]5t heights 9 ! atmosph]e & at diff]5t dep?s bel[ ! surface ( m\nta9 lakes2 x is weak5$ accord+ to ! am\nt ( air or wat] t x has _h to trav]se4 ,presumably its s\rce mu/ be extra-t]re/rial4 ,its /r5g? does n v>y ) ! sun's altitude1 s x is n com+ f ! sun4 ,!re is "s evid5ce t x v>ies accord+ to ! position ( ! ,milky ,way1 mo/ radiation be+ receiv$ :5 ! greate/ ext5sion ( ! /ell> sy/em is ov]head4 ,x _c come f ! int]ior ( ! />s1 ! p5etrat+ p[] be+ too limit$2 all ! hotte/ & d5se/ matt] 9 ! univ]se is %ut (f f u by imp5etrable walls4 ,at ! mo/ x c\ld come only f ! out] r9d ( ! />s :]e ! temp]ature is mod]ate & ! d5sity is l[2 b x is m likely t its ma9 s\rce is 9 ! diffuse nebulae or possibly 9 ! matt] =m+ ! g5]al cl\d 9 space4#cd ,we mu/ await fur!r developm5ts be=e we c reg>d ! suppos$ subatomic orig9 ( ?is radiation z o!r ?an speculative2 we m5tion x "h only z a possible op5+ = progress4 ,x w be ( great int]e/ if we c rea* by ?is means a m direct acqua9tance ) ! processes :i* we assume to be ! s\rce ( /ell> en]gy2 & ! messages borne to u by ! cosmic rays :i* purport to relate to ^! processes des]ve ! close/ att5tion4 ,our views ( /ell> en]gy are likely to be affect$ on "o crucial po9t4 ,hi!rto we h usually suppos$ t ! v high temp]ature 9 ! int]ior ( a /> is "o ( ! ess5tial conditions = lib]ation ( subatomic en]gy1 & t a reasonably high d5sity is also important4 ,!oretically x w\ld seem almo/ incr$ible t ! build+ up ( high] elem5ts or ! annihilation ( protons & electrons c\ld proce$ ) any degree ( vig\r 9 regions :]e enc\nt]s are r>e & !re is no high temp]ature or int5se radiation to wake ! atoms f apa?y2 b ! m we face ! difficulties ( all !ories ( ! release ( subatomic en]gy ! less incl9$ we are to condemn any evid5ce z incr$ible4 ,! pres5ce ( sodium & calcium 9 ! cosmical cl\d1 ( helium & nebulium 9 ! diffuse nebulae1 ( titanium & zirconium 9 l>ge quantities 9 ! atmosph]es ( ! y\nge/ />s1 be>s witness t ! evolution ( ! elem5ts is already f> advanc$ dur+ ! diffuse pre/ell> /age--unless inde$ our univ]se is built f ! debris ( a =m] creation4 ,f ?is po9t ( view x is fitt+ t we %\ld disc]n symptoms ( subatomic activity 9 op5 space4 ,b ! physici/ may well %ake 8 head ov] ! problem4 ,h[ are f\r protons & two electrons to ga!r toge!r to =m a helium nucleus 9 a m$ium s r>e t ! free pa? la/s = days8 ,! only com=t is t ! mode ( ?is occurr5ce is 7accord+ to pres5t k7 s inconceivable "u any conditions ( d5sity & temp]ature t we may po/ulate x 9 ! nebulae--on ! pr9ciple t we may z well be hung = a %eep z = a lamb4 ,evolution ( ! ,/>s ,tw5ty ye>s ago /ell> evolution seem$ to be v simple4 ,! />s beg9 by be+ v hot & gradually cool d[n until !y g out4 ,on ?is view ! temp]ature ( a /> indicat$ ! /age ( evolution t x _h rea*$4 ,! outl9e ( ! sequ5ce 0 suffici5tly indicat$ by ! crude obs]vation ( col\r--:ite-hot1 yell[-hot1 r$-hot2 a m detail$ ord] ( temp]ature 0 asc]ta9$ by exam9+ ! light ) a spectroscope4 ,! r$ />s naturally came la/ 9 ! sequ5ce2 !y 7 ! olde/ />s on ! v]ge ( ext9ction4 ,sir ,norman ,locky] /rongly oppos$ ?is s*eme & to a consid]able ext5t anticipat$ ! m mod]n view2 b mo/ a/ronom]s p9n$ _! fai? to x up to ab\t #aiac4 ,t5 ye>s ago m k _h be5 ga9$ ( ! d5sities ( />s4 ,x seem$ likely t d5sity w\ld be a m direct crit]ion ( evolution>y developm5t ?an temp]ature4 ,grant$ t a /> cond5ses out ( nebul\s mat]ial1 x mu/ 9 ! y\nge/ /age be v diffuse2 f t /age x w contract & /eadily increase 9 d5sity4 ,b ?is necessitates an entire re>rangem5t ( ! s*eme ( evolution1 because ! ord] accord+ to d5sity is by no means ! same z ! ord] accord+ to surface temp]ature4 ,on ! =m] view all ! cool r$ />s 7 old & dy+4 ,b a l>ge numb] ( !m are n[ f\nd to be extremely diffuse--/>s l ,betelgeuse1 = in/ance4 ,^! mu/ be set d[n z ! v y\nge/ ( ! />s2 aft] all x is n unnatural t a /> j beg9n+ to cond5se out ( nebul\s mat]ial %\ld />t at ! l[e/ /age ( temp]ature4 ,n all ! r$ />s are diffuse2 !re are _m l ,krueg] #fj :i* h high d5sity1 & ^! we leave undi/urb$ z repres5t+ ! la/ /age ( evolution4 ,bo? ! fir/ & la/ p]iods ( a />'s life are *>act]iz$ by l[ temp]ature2 9 betwe5 :iles ! temp]ature mu/ h ris5 to a maximum & fall5 aga94 ,! #8giant & dw>f !ory' propos$ by ,h]tzsprung & ,russell br\ght ^! conclusions into excell5t ord]4 ,x recogniz$ a s]ies ( giant />s1 comp>atively diffuse />s ) temp]ature ris+1 & a s]ies ( dw>f or d5se />s ) temp]ature fall+4 ,! two s]ies m]g$ at ! highe/ temp]atures4 ,an individual /> dur+ its lifetime w5t up ! giant s]ies to its highe/ temp]ature & !n d[n ! dw>f s]ies4 ,! brightness rema9$ fairly /eady ?r\gh\t ! giant /age because ! cont9ually increas+ temp]ature c\nt]balanc$ ! r$uction ( ! surface area ( ! />2 9 ! dw>f /age ! decreas+ temp]ature & ! contraction ( ! surface caus$ a rapid decrease ( brightness z ! /> progress$ d[n ! s]ies4 ,?is 0 9 accordance ) obs]vation4 ,! !ory has dom9at$ mo/ rec5t a/rophysical rese>* & has be5 in/rum5tal 9 br++ to light _m important facts4 ,"o example mu/ suffice4 ,al?\gh we may h a giant & a dw>f /> ) ! same surface temp]ature1 & !re=e %[+ v simil> spectra1 nev]!less a close exam9ation ( ! spectrum reveals tell-tale diff]5ces2 & x is n[ q easy to asc]ta9 f ! spectrum :e!r ! /> is a diffuse giant or a d5se dw>f4 ,! attractive feature ( ! giant & dw>f !ory 0 ! simple explanation giv5 = ! up-&-d[n progress ( ! temp]ature4 ,! pass+ ov] f ! giant to ! dw>f s]ies 0 suppos$ to occur :5 ! d5sity _h rea*$ su* a value 7ab\t "o-qu>t] ! d5sity ( wat]7 t ! deviation ( ! mat]ial f a p]fect gas began to be s]i\s4 ,x 0 %[n by ,lane fifty ye>s ago t a globe ( p]fect gas mu/ rise 9 temp]ature z x contracts1 8 me?od ( f9d+ ! int]nal temp]ature be+ t consid]$ on p4 #ab2 ?us ! ris+ temp]ature 9 ! giant /age is pr$ict$4 ,b ! rise dep5ds ess5tially on ! easy compressibility ( ! gas2 & :5 ! compressibility is lo/ at high d5sity ! ris+ temp]ature may be expect$ to give place to fall+ temp]ature s t ! /> cools z a solid or liquid w\ld d4 ,t 0 believ$ to acc\nt = ! dw>f /age4 ,i h be5 try+ to recall ideas ( tw5ty & t5 ye>s ago1 & y mu/ n suppose t f ! /&po9t ( pres5t-day k ,i c endorse ev]y?+ "h /at$4 ,i h int5tionally be5 vague z to :e!r by ! hotness ( a /> ,i mean ! int]nal or ! surface temp]ature s9ce ideas 7 =m]ly v loose on ?is po9t2 ,i h made no ref]5ce to :ite dw>fs1 :i* are n[ ?\ght to be ! d5se/ & presumably ! olde/ />s ( all4 ,b x is ! la/ p>agraph especially :i* conflicts ) our late/ conclusions1 = we no long] admit t /ell> mat]ial w cease to behave z a p]fect gas at "o-qu>t] ! d5sity ( wat]4 ,our result t ! mat]ial 9 ! d5se dw>f />s is /ill p]fect gas 7p4 #ch7 /rikes a fatal bl[ at ?is "p ( ! giant & dw>f !ory4 ,x w\ld be difficult to say :at is ! accept$ !ory ( /ell> evolution to-day4 ,! !ory is 9 ! melt+-pot & we are /ill wait+ = some?+ satisfactory to em]ge4 ,! :ole subject is 9 d\bt & we are prep>$ to reconsid] almo/ any?+4 ,provisionally1 h[ev]1 ,i %all assume t ! =m] !ory 0 "r 9 assum+ t ! sequ5ce ( evolution is f ! mo/ diffuse to ! d5se/ />s4 ,al?\gh ,i make ?is assumption ,i d n feel sure t x is all[able4 ,! =m] !ory _h /rong reasons = mak+ x :i* no long] apply4 ,s long z contraction 0 suppos$ to be ! s\rce ( a />'s heat1 contraction & increas+ d5sity 7 ess5tial ?r\gh\t its :ole c>e]2 ) ! acceptance ( subatomic en]gy contraction ceases to play ?is fundam5tal role4 ,i propose to conf9e att5tion to ! dw>f />s#ce because x is among !m t ! upset has occurr$4 ,!y =m a well-def9$ s]ies /ret*+ f high surface-temp]ature to l[ surface-temp]ature1 high lum9osity to l[ lum9osity1 & ! d5sity increases /eadily along ! s]ies4 ,we n[ call ?is ! ,ma9 ,s]ies4 ,x comprises ! great majority ( ! />s4 ,to fix ideas let u take ?ree typical />s along ! s]ies--,algol ne> ! top1 ! ,sun ne> ! middle1 & ,krueg] #fj ne> ! bottom4 ,! relevant in=mation ab\t !m is summ>iz$ bel[3 ,mean ,c5tral d5sity temp]ature ,surface ,mass 7,wat] 7million temp]ature ,lum9osity ,/>4 7,sun #a74 #a74 deg474 7deg47 ,col\r4 7,sun #a74 ,algol #dc #jae #dj #ab1jjj :ite #aej ,sun #a #ad #dj #f1jjj yell[ #a ,krueg] #fj #jbg #ia #ce #c1jjj r$ #jja ,! idea ( evolution is t ^! repres5t ! /ages pass$ ?r\gh 9 ! life-hi/ory ( an individual />4#cf ,! increas+ d5sity 9 ! ?ird column %\ld be notic$2 accord+ to our accept$ crit]ion x indicates t ! ord] ( developm5t is ,algol,sun,krueg] #fj4 ,a confusion betwe5 int]nal temp]ature & surface temp]ature is responsible = "s ( ! mi/akes ( ! old] !ories4 ,to outw>d view ! /> cools f #ab1jjj to #c1jjj 9 pass+ d[n ! s]ies1 b !re is no su* *ange 9 its int]nal heat4 ,! c5tral temp]ature rema9s surpris+ly /eady4 7,no special reliance c be plac$ on ! slight fall+ (f app>5tly %[n by ,krueg] #fj47 ,x is v rem>kable t all />s ( ! ma9 s]ies h a c5tral temp]ature ( ab\t #dj million degrees z ne>ly z we c calculate4 ,x is difficult to resi/ ! impression t !re is "s unusual prop]ty associat$ ) ?is temp]ature1 al?\gh all our physical in/9cts w>n u t ! idea is absurd4 ,b ! vital po9t is ! decrease ( mass %[n 9 ! second column4 ,if an individual /> is to progress any "p ( ! way d[n ! ma9 s]ies x mu/ lose mass4 ,we c put ! same inf]5ce 9 a m g5]al way4 ,n[ t x has be5 f\nd t lum9osity dep5ds ma9ly on mass1 !re c be no important evolution ( fa9t />s f bright />s unless ! />s lose a consid]able "p ( _! mass4 ,x is ?is result :i* has caus$ ! hypo!sis ( annihilation ( matt] to be s]i\sly discuss$4 ,all progress 9 ! !ory ( /ell> evolution is held up p5d+ a decision on ?is hypo!sis4 ,if x is accept$ x provides an easy key to ^! *anges4 ,! /> may 7aft] pass+ ?r\gh ! giant /age7 rea* ! /age ( ,algol1 & !n by ! gradual annihilation ( ! matt] 9 x pass d[n ! ma9 s]ies until :5 only "o-sixte5? ( ! orig9al mass rema9s x w be a fa9t r$ /> l ,krueg] #fj4 ,b if !re is no annihilation ( matt]1 ! /> :5 once x has rea*$ ! dw>f /age seems to be immovable2 x has to /ay at ! po9t ( ! s]ies correspond+ to its con/ant mass4 ,let x be cle>ly und]/ood :at is ! po9t at issue4 ,! />s lose mass by _! radiation2 !re is no "q ab\t t4 ,! sun is los+ #abj billion tons annually :e!r its radiation comes f annihilation ( matt] or any o!r int]nal s\rce4 ,! "q is1 ,h[ long c ?is loss cont9ue8 ,unless !re is annihilation ( matt]1 all ! mass t c escape z radiation w h escap$ 9 a comp>atively %ort "t2 ! sun w !n be ext9ct & !re is an end to ! loss & to ! evolution4 ,b if !re is annihilation ( matt] ! life ( ! sun & ! loss ( mass cont9ue f> long]1 & an ext5d$ track ( evolution lies op5 be=e ! sun2 :5 x has got rid ( ?ree-qu>t]s ( its pres5t mass x w h become a fa9t /> l ,krueg] #fj4 ,our *oice betwe5 ! possible !ories ( subatomic en]gy only affects /ell> evolution 9 "o po9t--b x is ! vital po9t4 ,unless we *oose annihilation ( matt]1 we cut ! life ( a /> s %ort t !re is no "t = any significant evolution at all4 ,i feel ! same objection t e "o mu/ feel to build+ ext5sively on a hypo!tical process )\t any direct evid5ce t ! laws ( ,nature p]mit ( its occurr5ce4 ,b ! alt]native is to leave ! />s 9 sleepy uni=mity ) no prospect ( developm5t or *ange until _! lives come to an end4 ,some?+ is ne$$ to galvanize ! sc5e into t activity1 :e!r ( progress or decay1 9 :i* we h s long believ$4 ,r desp]ately we seize on ! "o visible *ance4 ,! petrifi$ sy/em wakes4 ,! ultimate p>ticles "o by "o yield up _! en]gy & pass out ( exi/5ce4 ,_! sacrifice is ! life-=ce ( ! />s :i* n[ progress on _! high adv5ture3 ,atoms or sy/ems into ru9 hurl'd1 ,& n[ a bubble bur/1 & n[ a _w4 ,radiation ( ,mass ,our fir/ evid5ce ( ! ext5t ( ! "t-scale ( /ell> evolution 0 af=d$ by ! /ead9ess ( condition ( ,cephei4 ,?is 0 supplem5t$ by evid5ce ( ! great ext5sion ( geological "t on ! e>?4 ,we c\ld n d m ?an set an upp] limit to ! rate ( progress ( evolution & a l[] limit to ! age ( ! />s4 ,b ?is limit 0 suffici5t to rule out ! contraction hypo!sis & drive u to consid] ! /ore ( subatomic en]gy4 ,we n[ make a new attack1 :i* dep5ds on ! belief t ! rate ( evolution is det]m9$ by ! rate at :i* a /> c get rid ( its mass4 ,we are "h consid]+ only ! evolution ( fa9t />s f bright />s1 & !re w rema9 scope = a c]ta9 am\nt ( developm5t 9 ! giant /age to :i* our argum5ts w n directly apply4 ,b to ab&on all l9es ( evolution betwe5 bright />s & fa9t />s w\ld mean admitt+ t "o /> diff]s f ano!r /> 9 brightness because x 0 diff]5t orig9ally4 ,?is may be true2 b we ought n to surr5d] ! ma9 field ( /ell> evolution )\t mak+ a fight = x4 ,by ! new l9e ( attack we rea* a def9ite det]m9ation ( ! "t-scale & n m]ely a l[] limit4 ,we "k ! rate at :i* />s 9 ea* /age are los+ mass by radiation2 !re=e we c f9d ! "t tak5 to lose a giv5 mass & !reby pass on to a /age ( small] mass4 ,evolution f ,algol to ! ,sun requires five billion ye>s2 evolution f ! ,sun to ,krueg] #fj requires #ejj billion ye>s4 ,x is int]e/+ to note t />s 9 ! /age betwe5 ! ,sun & ,krueg] #fj are mu* m abundant ?an ^? betwe5 ,algol & ! ,sun--a fact some:at confirmatory ( ! calculat$ duration ( ! two /ages4 ,! abundance ( fa9t />s does n1 h[ev]1 increase s rapidly z ! calculat$ duration2 p]haps ! /ell> univ]se has n exi/$ long en\gh = ! old />s to be fully repres5t$4 ,a /> ( great] mass ?an ,algol squ&]s its mass v rapidly1 s t we d n increase ! age ( ! ,sun appreciably by suppos+ x to h />t$ ) great] mass ?an ,algol4 ,! upp] limit to ! pres5t age ( ! ,sun is #eb billion ye>s h[ev] great its initial mass4 ,b1 x may be ask$1 _c a /> accel]ate its progress by gett+ rid ( matt] 9 "s o!r way ?an by radiation8 ,_c atoms escape f its surface8 ,if s ! loss ( mass & consequ5t evolution w be spe$$ up1 & ! "t requir$ may p]haps ev5 be br\ght )9 range ( ! alt]native !ory ( transmutation ( ! elem5ts4 ,b x is fairly c]ta9 t ! mass escap+ 9 ! =m ( mat]ial atoms is negligible comp>$ ) t :i* imp]ceptibly glides away 9 ! =m ( radiation4 ,y w p]haps be 9 d\bt z to :e!r ! #abj billion tons p] annum lo/ by ! sun 9 radiation is 7a/ronomically reg>d$7 a l>ge quantity or a small quantity4 ,f c]ta9 aspects x is a l>ge quantity4 ,x is m ?an #ajj1jjj times ! mass ( ! calcium *romosph]e4 ,! sun w\ld h to bl[ (f its *romosph]e & =m an entirely fre% "o e five m9utes 9 ord] to get rid ( z mu* mass 9 ?is way z x loses by radiation4 ,x is obvi\s f sol> obs]vation t !re is no su* outru% ( mat]ial4 ,to put x ano!r way--9 ord] to halve ! "t-scale ( evolution /at$ above x w\ld be necess>y t a billion atoms %\ld escape ea* second ?r\gh ea* squ>e c5timetre ( ! sun's surface4 ,i ?9k we may conclude t !re is no %ort cut to small] mass & t radiation is responsible = practically ! :ole loss4 ,we notic$ e>li] 7p4 #be7 t ,nature builds />s :i* are mu* alike 9 mass1 b all[s h]self "s deviation f h] patt]n am\nt+ sometimes to a mi/ake ( "o #j4 ,i ?9k we may h done h] an inju/ice1 & t %e is m c>eful ov] h] "w ?an we suppos$4 ,we ought to h exam9$ co9s fre% f h] m9t2 x 0 n fair to take co9s promiscu\sly1 includ+ _m t _h be5 9 circulation = "s hundr$s ( billions ( ye>s & _h worn r ?94 ,tak+ ! newly =m$ />s1 i4 e4 ! diffuse />s1 we f9d t #ij p] c5t4 ( !m are betwe5 #b & #e times ! mass ( ! sun--%[+ t initially ! />s are made ne>ly z closely to patt]n z human be+s are4 ,9 ?is range radiation pressure increases f #ag to #ce p] c5t1 ( ! :ole pressure2 ,i ?9k ?is w\ld be expect$ to be ! crucial /age 9 its rise to importance4 ,our idea is t ! /ell> masses initially h ?is r close uni=mity 7:i* does n exclude a small proportion ( exceptional />s outside ! above limits72 ! small] masses are evolv$ f ^! 9 c\rse ( "t by ! radiation ( mass4 ,= ! "t be+ ! sun is com=tably settl$ 9 its pres5t /ate1 ! am\nt ( en]gy radiat$ be+ j balanc$ by ! subatomic en]gy lib]at$ inside x4 ,ultimately1 h[ev]1 x mu/ move on4 ,! mov+ on1 or evolution1 is cont9u\s1 b = conv5i5ce ( explanation we %all speak ( x z ?\gh x occurr$ 9 /eps4 ,two possible motives = *ange c be imag9$1 7#a7 ! supply ( subatomic en]gy might fall (f by exhau/ion & no long] balance ! radiation1 & 7#b7 ! sun is sl[ly becom+ a /> ( small] mass4 ,9 =m] !ories ! fir/ motive has g5]ally be5 assum$1 & we may /ill reg>d x z effective dur+ ! giant /age ( ! />s2 b x is cle> t ! motive to move d[n ! ma9 s]ies mu/ be loss ( mass4#cg ,app>5tly ! di/9ction betwe5 giant & dw>f />s1 replac+ ! old di/9ction ( p]fect & imp]fect gas1 is t ! prolific & soon exhau/$ supplies ( subatomic en]gy 9 ! giant /age disappe> & leave a mu* /eadi] supply 9 ! dw>f /age4 ,:5 ! sun has become a /> ( small] mass x w ne$ to resettle its int]nal conditions4 ,suppose t at fir/ x tries to reta9 its pres5t d5sity4 ,z expla9$ on p4 #ab1 we c calculate ! int]nal temp]ature1 & we f9d t ! r$uc$ mass c\pl$ ) con/ant d5sity involves l[] temp]ature4 ,?is w slightly turn (f ! tap ( subatomic en]gy1 because !re c be little d\bt t ! release ( subatomic en]gy is m rapid at high] temp]ature4 ,! r$uc$ supply w no long] be suffici5t to balance ! radiation2 accord+ly ! /> w contract j z x 0 suppos$ to d on ! old contraction hypo!sis :i* corresponds to ! tap ( subatomic en]gy be+ turn$ (f altoge!r4 ,! motive is loss ( mass2 ! fir/ consequ5ce is an increase ( d5sity :i* is ano!r *>act]i/ic ( progress d[n ! ma9 s]ies4 ,trac+ ! consequ5ces a little f>!r1 ! increas+ d5sity causes a ris+ temp]ature :i* 9 turn reop5s ! tap ( subatomic en]gy4 ,z soon z ! tap is op5$ en\gh to balance ! rate ( radiation ( ! />1 ! contraction /ops & ! /> rema9s settl$ 9 equilibrium at ! small] mass & high] d5sity4 ,y w see t ! laws ( release ( subatomic en]gy mu/ be invok$ if we are to expla9 quantitatively :y a p>ticul> d5sity corresponds to a p>ticul> mass 9 ! progress d[n ! ma9 s]ies4 ,! contraction has to proce$ s f> z to br+ ! int]nal conditions to a /ate 9 :i* ! release ( en]gy is at ! exact rate requir$ to balance ! radiation4 ,i am afraid ?is all s\nds v complicat$1 b my purpose is to %[ t ! adju/m5t ( ! /> aft] an alt]ation ( mass is automatic4 ,aft] a *ange ( mass ! /> has to re-solve ! problem ( ! int]nal conditions necess>y = its equilibrium4 ,s f> z me*anical conditions are conc]n$ 7support+ ! weight ( ! upp] lay]s7 x c *oose any "o ( a s]ies ( /ates ( diff]5t d5sity provid$ x has ! int]nal temp]ature appropriate to t d5sity4 ,b su* equilibrium is only tempor>y1 & ! /> w n really settle d[n until ! tap ( subatomic en]gy is op5$ to ! "r ext5t to balance ! rate ( radiation :i*1 z we h already se51 is practically fix$ by ! mass4 ,! /> fiddles ab\t ) ! tap until x secures ?is balance4 ,"o important conclusion has be5 po9t$ out by ,pr(essor ,russell4 ,:5 ! /> is adju/+ ! tap x does n d s intellig5tly2 "o trial mu/ automatically lead to ! next trial1 & x is all-important t ! next trial %\ld automatically be ne>] to & n f>!r f ! "r rate4 ,! condition t x %all be ne>] to ! "r rate is t ! lib]ation ( subatomic en]gy %all increase ) temp]ature or d5sity4#ch ,if x decreases1 or ev5 if x is unalt]$1 ! trials w be successively f>!r & f>!r f ! requir$ rate1 s t al?\gh a /eady balance is possible ! /> w nev] be able to f9d x4 ,x is !re=e ess5tial to admit z "o ( ! laws ( lib]ation ( subatomic en]gy t ! rate increases ) temp]ature or ) d5sity or ) bo?2 o!rwise subatomic en]gy w n fulfil ! purpose = :i* x 0 introduc$1 viz4 to keep ! /> /eady = a v long "t4 ,! /range ?+ is t ! condition ( balance is rea*$ :5 ! c5tral temp]ature is ne> #dj million degrees--! same :e!r ! /> is at ! top1 middle1 or bottom ( ! ma9 s]ies4 ,/>s at ! top release f ea* gramme ( mat]ial #gjj ergs ( en]gy p] second2 ! sun releases #a ergs p] second2 ,krueg] #fj releases #jjh ergs p] second4 ,x seems extraord9>y t />s requir+ su* diff]5t supplies %\ld all h to asc5d to ! same temp]ature to procure !m4 ,x looks z ?\gh at temp]atures bel[ ?is /&>d n ev5 #jjh ergs p] second is available1 b on rea*+ ! /&>d ! supply is practically unlimit$4 ,we c sc>cely believe t !re is a k9d ( boil+-po9t 7indep5d5t ( pressure7 at :i* matt] boils (f into en]gy4 ,! :ole ph5om5on is mo/ p]plex+4 ,i may add t ! giant />s h temp]atures consid]ably bel[ #dj million degrees4 ,x w\ld appe> t !y are tapp+ special supplies ( subatomic en]gy releas$ at l[] temp]atures4 ,aft] us+ up ^! supplies ! /> passes on to ! ma9 s]ies1 & proce$s to tap ! ma9 supply4 ,x seems necess>y to suppose fur!r t ! ma9 supply does n la/ indef9itely1 s t ultimately ! /> 7or :at is left ( x7 leaves ! ma9 s]ies & passes on to ! :ite dw>f /age4 ,we are n[ 9 a position to deal ) a "q :i* y may h wi%$ to ask e>li]4 ,:y does ,cephei pulsate8 ,"o possible answ] is t ! oscillation 0 />t$ (f by "s accid5t4 ,s f> z we c calculate an oscillation1 if once />t$1 w\ld cont9ue = some?+ l #aj1jjj ye>s be=e becom+ damp$ d[n4 ,b #aj1jjj ye>s is n[ deem$ to be an insignificant p]iod 9 ! life ( a />1 &1 hav+ reg>d to ! abundance ( ,cepheids1 ! explanation seems inadequate ev5 if we c\ld envisage ! k9d ( accid5t suppos$4 ,x is mu* m likely t ! pulsation arises spontane\sly4 ,enorm\s supplies ( heat en]gy are be+ releas$ 9 ! />--f> m ?an en\gh to />t & ma9ta9 ! pulsation--& !re are at lea/ two alt]native ways 9 :i* ?is heat c be suppos$ to op]ate a me*anism ( pulsation4 ,"h is "o alt]native4 ,suppose fir/ t !re is a v small pulsation4 ,:5 compress$ ! /> has high] temp]ature & d5sity ?an usual & ! tap ( subatomic en]gy is op5$ m fully4 ,! /> ga9s heat1 & ! expansive =ce ( ! extra heat assi/s ! reb\nd f compression4 ,at greate/ expansion ! tap is turn$ (f a little & ! loss ( heat dim9i%es ! resi/ance to ! ensu+ compression4 ,?us ! successive expansions & compressions become m & m vigor\s & a l>ge pulsation gr[s out ( an inf9itesimal beg9n+4 ,x w be se5 t ! /> works ! tap ( subatomic en]gy j z an eng9e works ! valve admitt+ heat into its cyl9d]2 s t ! pulsations ( a /> are />t$ up l ! pulsations ( an eng9e4 ,! only objection t ,i c f9d to ?is explanation is t x is too successful4 ,x %[s :y a /> may be expect$ to pulsate2 b ! tr\ble is t />s 9 g5]al d n pulsate--x is only ! r>e exceptions t behave 9 ?is way4 ,x is n[ s easy to acc\nt = ! ,cepheids t we h to turn back & face ! m difficult problem ( acc\nt+ = ! normal /eady />s4 ,:e!r ! pulsation w />t up or n dep5ds on :e!r ! eng9e ( pulsation is suffici5tly p[]ful to ov]come ! =ces t5d+ to damp out & dissipate pulsations4 ,we _c pr$ict ! occurr5ce or non-occurr5ce f any settl$ !ory2 we h r to seek to frame ! laws ( release ( subatomic en]gy s z to con=m to our k t ! majority ( ! />s rema9 /eady1 b c]ta9 conditions ( mass & d5sity give ! pulsatory =ces ! upp] h&4 ,cepheid pulsation is a k9d ( di/emp] :i* happ5s to />s at a c]ta9 y\?ful p]iod2 aft] pass+ ?r\gh x !y burn /eadily4 ,!re may be ano!r attack ( disease lat] 9 life :5 ! /> is subject to ^? cata/rophic outbur/s :i* occasion ! appe>ance ( #8new />s' or novae4 ,b v little is kn[n z to ! conditions = ?is1 & x is n c]ta9 :e!r ! outbreak is spontane\s or provok$ f outside4 ,s long z we /ick to g5]alities ! !ory ( subatomic en]gy & especially ! !ory ( annihilation ( matt] makes a fairly promis+ op5+4 ,x is :5 we come to te*nical details t d\bts & p]plexities arise4 ,difficulties appe> 9 ! simultane\s pres5ce ( giant & dw>f />s 9 coeval clu/]s1 not)/&+ _! widely diff]5t rates ( evolution4 ,!re are difficulties 9 devis+ laws ( release ( subatomic en]gy :i* w safegu>d ! /ability ( ! />s )\t sett+ e /> into pulsation4 ,difficulties arise f ! fact t z a rule 9 ! giant /age ! l[] ! temp]ature & d5sity ! m rapid ! release ( en]gy2 & al?\gh we acc\nt = ?is 9 a g5]al way by consid]+ ! exhau/ibility ( ! m prolific s\rces ( en]gy1 ! facts are n all /raight5$ out by su* a s*eme4 ,f9ally grave difficulties arise 9 reconcil+ ! laws ( release inf]r$ f a/ronomical obs]vation ) any !oretical picture we c =m ( ! process ( annihilation ( matt] by ! int]play ( atoms1 electrons1 & radiation4 ,! subject is highly important1 b we _c v well pursue x fur!r 9 ?is lecture4 ,:5 ! guidance ( !ory is cle> int]e/ c5tres r\nd ! broad pr9ciples2 :5 ! !ory is rudim5t>y1 int]e/ c5tres r\nd te*nical details :i* are anxi\sly scrut9iz$ z !y appe> to fav\r n[ "o view n[ ano!r4 ,i h dealt ma9ly ) two sali5t po9ts--! problem ( ! s\rce ( a />'s en]gy & ! *ange ( mass :i* mu/ occur if !re is any evolution ( fa9t />s f bright />s4 ,i h %[n h[ ^! appe> to meet 9 ! hypo!sis ( annihilation ( matt]4 ,i d n hold ?is z a secure conclusion4 ,i hesitate ev5 to advocate x z probable1 because !re are _m details :i* seem to me to ?r[ consid]able d\bt on x1 & ,i h =m$ a /rong impression t !re mu/ be "s ess5tial po9t :i* has n yet be5 grasp$4 ,i simply tell x y z ! clue :i* at ! mom5t we are try+ to foll[ up--n kn[+ :e!r x is false sc5t or true4 ,i %\ld h lik$ to h clos$ ^! lectures by lead+ up to "s great climax4 ,b p]haps x is m 9 accordance ) ! true conditions ( sci5tific progress t !y %\ld fizzle out ) a glimpse ( ! obscurity :i* m>ks ! fronti]s ( pres5t k4 ,i d n apologize = ! lam5ess ( ! conclusion1 = x is n a conclusion4 ,i wi% ,i c\ld feel confid5t t x is ev5 a beg9n+4 ,,footnotes3 ,footnote #a3 ,fig4 #a is f a photograph tak5 by ,mr4 ,ev]%$ at ,kodaikanal ,obs]vatory1 ,madras4 ,fig4 #b is f ! ,m\nt ,wilson ,obs]vatory1 ,cali=nia4 ,footnote #b3 ,i am indebt$ to ,pr(essor ,c4 ,t4 ,r4 ,wilson = ,figs4 #c-f4 ,footnote #c3 ,prim>ily x is ! electric *>ge & n ! high spe$ ( p>ticles :i* det]m9es _! appe>ance 9 ^! photographs4 ,b a high-spe$ p>ticle leaves beh9d x a trail ( electrically *>g$ p>ticles--! victims ( its furi\s driv+--s t x is %[n indirectly by its l9e ( victims4 ,footnote #d3 ,o!r sub/itutions = silv] d n z a rule cause great] *ange1 & ! diff]5ces are likely to be ton$ d[n by mixture ( _m elem5ts4 ,exclud+ hydrog51 ! mo/ extreme *ange is f #dh p>ticles = silv] to #ha p>ticles = an equal mass ( helium4 ,b = hydrog5 ! *ange is f #dh to #baf1 s t hydrog5 gives widely diff]5t results f o!r elem5ts4 ,footnote #e3 ,! mean d5sity ( ,capella is ne>ly ! same z ! d5sity ( ! air4 ,footnote #f3 ,unless o!rwise indicat$ #8gase\s' is int5d$ to mean #8compos$ ( p]fect gas'4 ,footnote #g3 ,= ?is pr$iction x is unnecess>y to "k ! *emical composition ( ! />s1 provid$ t extreme cases 7e4 g4 an excessive proportion ( hydrog57 are exclud$4 ,= example1 consid] ! hypo!ses t ,capella is made respectively ( 7a7 iron1 7b7 gold4 ,accord+ to !ory ! opacity ( a /> made ( ! heavi] elem5t w\ld be #b times ! opacity ( a /> made ( iron4 ,?is by itself w\ld make ! gold5 /> a magnitude 7 #b times7 fa9t]4 ,b ! temp]ature is rais$ by ! sub/itution2 & al?\gh1 z expla9$ on p4 #bc1 ! *ange is n v great1 x increases ! outfl[ ( heat approximately #b times4 ,! resultant effect on ! brightness is practically no *ange4 ,:il/ ?is indep5d5ce ( *emical con/itution is satisfactory 9 reg>d to def9it5ess ( ! results1 x makes ! discrepant factor #aj p>ticul>ly difficult to expla94 ,footnote #h3 ,obs]vation %[s t ! sun is ab\t #d magnitudes fa9t] ?an ! av]age diffuse /> ( ! same spectral class1 & ,krueg] #fj is #aj magnitudes fa9t] ?an diffuse />s ( its class4 ,! :ole drop 0 g5]ally assum$ to be due to deviation f a p]fect gas2 b ?is made no all[ance = a possible diff]5ce ( mass4 ,! comp>ison ) ! curve enables ! d5se /> to be comp>$ ) a gase\s /> ( its own mass1 & we see t ! diff]5ce !n disappe>s4 ,s t 7if !re has be5 no mi/ake7 ! d5se /> is a gase\s />1 & ! diff]5ces above m5tion$ 7 due :olly to diff]5ces ( mass4 ,footnote #i3 ,r\gh] e/imates 7 made mu* e>li]4 ,footnote #aj3 ,! obs]v$ p]iod ( ,algol is ! p]iod ( revolution1 n ( rotation4 ,b ! two compon5ts are v close toge!r1 & !re c be no d\bt t ow+ to ! l>ge tidal =ces !y keep ! same faces turn$ t[>ds ea* o!r2 t is to say1 ! p]iods ( rotation & ( revolution are equal4 ,footnote #aa3 ,x may be ( int]e/ to add t al?\gh ! prop] light ( ,algol ,b is inappreciable1 we c obs]ve a reflection 7or re-radiation7 ( ! light ( ,algol ,a by x4 ,?is reflect$ light *anges l moonlight accord+ z ,algol ,b is #8new' or #8full'4 ,footnote #aa3 ,! mass-lum9osity relation 0 n suspect$ at ! "t ( :i* ,i am speak+4 ,footnote #ac3 ,my ref]5ces to #8p]fect gas ( ! d5sity ( plat9um' & #8mat]ial #b1jjj times d5s] ?an plat9um' h (t5 be5 run toge!r by report]s into #8p]fect gas #b1jjj times d5s] ?an plat9um'4 ,x is sc>cely possible to calculate :at is ! condition ( ! mat]ial 9 ! ,companion ( ,sirius1 b ,i d n expect x to be a p]fect gas4 ,footnote #ad3 ,photograph$ by ,dr4 ,w4 ,h4 ,wright at ! ,lick ,obs]vatory1 ,cali=nia4 ,footnote #ae3 ,nos4 #dc1 #fa1 #ge are rec5t discov]ies & may require confirmation4 ,!re n[ rema9 only two gaps 7#he & #hg7 ap>t f possible elem5ts beyond uranium4 ,footnote #af3 ,x does n give bo? temp]ature & pressure1 b x gives "o if ! o!r is kn[n4 ,?is is valuable in=mation :i* may be piec$ toge!r ) o!r k ( ! conditions at ! surface ( ! />s4 ,footnote #ag3 ,hydrog5 7be+ elem5t ,no4 #a7 has only "o planet electron4 ,footnote #ah3 ,fig4 #i is a photograph ( ! #8fla% spectrum' ( ! sun's *romosph]e tak5 by ,mr4 ,davidson 9 ,sumatra at ! eclipse ( #ad ,janu>y #aibf4 ,footnote #ai3 ,! helium l9e 9 ! ,r+ ,nebula on :i* we h already comm5t$ is n a memb] ( ! ,pick]+ ,s]ies1 b x has _h ! same hi/ory4 ,x 0 fir/ suppos$ to be due to hydrog51 lat] 79 #aiab7 reproduc$ by ,f[l] t]re/rially 9 a mixture ( helium & hydrog51 & f9ally discov]$ by ,bohr to belong to helium4 ,footnote #bj3 ,?is1 ( c\rse1 is f\nd f ! o!r l9es ( ! spectrum :i* g5u9ely belong to ! /> & %ift to & fro z x describes its orbit4 ,footnote #ba3 ,z ! ^w temp]ature is sometimes us$ ) new-fangl$ mean+s1 ,i may add t #ae1jjj is ! temp]ature correspond+ to ! individual spe$s ( ! atoms & electrons--! old-fa%ion$ gas-temp]ature4 ,footnote #bb3 ,photograph tak5 by ,e4 ,t4 ,cott+ham & ! au?or 9 ,pr9cipe at ! total eclipse ( #bi ,may #aiai4 ,footnote #bc3 ,we ref] to calcium z x occurs 9 ! *romosph]e1 i4 e4 ) "o electron miss+4 ,footnote #bd3 ,!re is an awkw>dness 9 apply+ ! t]m #8app>5t' to some?+ too small to be se52 b1 rememb]+ t we h arm$ ourselves ) an imag9>y telescope capable ( %[+ ! disk1 ! mean+ w be cle>4 ,footnote #be3 ,d5sities bel[ t ( air h be5 f\nd = "s ( ! ,algol v>iables by an entirely diff]5t k9d ( inve/igation1 & also = "s ( ! ,cepheid v>iables by /ill ano!r me?od4 ,!re are also _m o!r examples ( />s ( bulk comp>able ) t ( ,betelgeuse4 ,footnote #bf3 ,f a photograph tak5 at ! ,royal ,obs]vatory1 ,cape ( ,good ,hope4 ,footnote #bg3 ,= comp>ison1 ! ne>e/ fix$ /> is di/ant #d light ye>s4 ,ap>t f clu/]s we r>ely deal ) di/ances above #b1jjj light ye>s4 ,footnote #bh3 ,"o _c always be sure t :at is true ( ! clu/] />s w be true ( />s 9 g5]al2 & our k ( ! ne>] />s1 ?\gh lagg+ beh9d t ( ! />s 9 clu/]s1 does n entirely agree ) ?is association ( col\r & brightness4 ,footnote #bi3 ,! t]m nebula cov]s a v>iety ( objects1 & x is only ! nebulae class$ z spirals t are likely to be outside our /ell> sy/em4 ,footnote #cj3 ,?is c be *eck$ because uranium lead has a diff]5t atomic weight f lead n s d]iv$4 ,ord9>y lead is a mixture ( sev]al k9ds ( atoms 7isotopes74 ,footnote #ca3 ,y may wond] :y1 hav+ said t ! sun conta9s #b1jjj quadrillion tons ( en]gy at ! mo/1 ,i n[ assume t x conta9s j ?is am\nt4 ,x is really only a v]bal po9t dep5d+ on ! sci5tific def9ition ( en]gy4 ,all mass is mass ( some?+1 & we n[ call t some?+ #8en]gy' :e!r x is "o ( ! famili> =ms ( en]gy or n4 ,y w see 9 ! next s5t5ce t we d n assume t ! en]gy is conv]tible into kn[n =ms1 s t x is a t]m9ology :i* commits u to no?+4 ,footnote #cb3 ,a/on 9 8 late/ rese>*es has be5 able to detect t ! oxyg5 atom is j appreciably light] ?an ! f\r helium atoms4 ,footnote #cc3 ,a measurem5t ( ! heat obs]v$ to fl[ f a cont9u\s f\nta9 ( heat is a measurem5t ( ! output ( ! f\nta91 unless !re is a /or+ ( en]gy betwe5 ! output & ! outfl[4 ,! breakd[n ( ! ,kelv9 "t-scale indicates t ! /or+ 9 ! />s 7positive or negative7 & consequ5t expansion or contraction is negligible comp>$ to ! output or outfl[4 ,footnote #cd3 ,! />s all put toge!r cov] an area ( ! sky mu* less ?an ! app>5t disk ( ! sun1 s t unless _! surface-lay]s are g5]at+ ?is radiation v mu* m abundantly ?an ! sun does1 !y _c be responsible = x4 ,footnote #ce3 ,! t]m #8dw>f />s' is n meant to include :ite dw>fs4 ,footnote #cf3 ,we c sc>cely suppose t all />s aft] rea*+ ! ma9 s]ies pass ?r\gh precisely ! same /ages4 ,= example1 ,algol1 :5 x has become r$uc$ to ! mass ( ! ,sun1 may h slightly diff]5t d5sity & temp]ature4 ,b ! obs]vational evid5ce indicates t ^! individual diff]5ces are small4 ,! ma9 s]ies is ne>ly a l9e> sequ5ce2 x mu/ h "s #8bread?' z well z #8l5g?'1 b at pres5t ! scatt] ( ! individual />s away f ! c5tral l9e ( ! sequ5ce seems to be due *iefly to ! probable errors ( ! obs]vational data & ! true bread? has n be5 det]m9$4 ,footnote #cg3 ,exhau/ion ( supply )\t *ange ( mass w\ld cause ! /> to contract to high] d5sity2 x w\ld ?us h a comb9ation ( d5sity & mass :i* 7accord+ to obs]vation7 is n f\nd 9 any actual />s4 ,footnote #ch3 ,?is increase 0 assum$ 9 our detail$ description ( ! automatic adju/m5t ( ! />1 & x w be se5 t x 0 ess5tial to assume x4 ,,app5dix ,fur!r ,rem>ks on ! ,companion ( ,sirius ,i ,,h pref]r$ n to complicate ! ,/ory ( ! ,companion ( ,sirius ) details ( a te*nical k9d2 "s fur!r in=mation may1 !re=e1 be welcome to ^? read]s :o are curi\s to le>n z mu* z possible ab\t ?is rem>kable />4 ,i am also able to add a fur!r in/alm5t ( ! #8detective /ory' :i* has j come to h&1 ! sleu? ?is "t be+ ,mr4 ,r4 ,h4 ,f[l]4 ,! /> is betwe5 ! eigh? & n9? magnitude1 s t x is n an excessively fa9t object4 ,! difficulty 9 detect+ x arises entirely f ! ov]p[]+ light ( its neighb\r4 ,at fav\rable epo*s x has be5 se5 easily ) an #h-;in* telescope4 ,! p]iod ( revolution is #di ye>s4 ,! ,companion is sep>at$ f ,sirius by a di/ance ne>ly equal to ! di/ance ( ,uranus f ! ,sun--or tw5ty times ! e>?'s di/ance f ! sun4 ,x has be5 sugge/$ t ! light might be reflect$ light f ,sirius4 ,?is w\ld acc\nt = its :it5ess1 b w\ld n directly acc\nt = its spectrum1 :i* diff]s appreciably f t ( ,sirius4 ,to reflect ? ( ! light ( ,sirius 7its actual brightness7 ! ,companion w\ld h to be #gd million miles 9 diamet]4 ,! app>5t diamet] ( its disk w\ld be #jc1 :i*1 "o w\ld ?9k1 c\ld sc>cely escape notice 9 spite ( unfav\rable conditions ( obs]vation4 ,b ! /ronge/ objection to ?is hypo!sis ( reflect$ light is t x applies only to ?is "o />4 ,! o!r two recogniz$ :ite dw>fs h no brilliant /> 9 _! neighb\rhood1 s t !y _c be %9+ by reflect$ light4 ,x is sc>cely wor? :ile to inv5t an elaborate explanation = "o ( ^! /range objects :i* does n cov] ! o!r two4 ,! ,e9/e9 effect1 :i* is appeal$ to = confirmation ( ! high d5sity1 is a l5g!n+ ( ! wave-l5g? & correspond+ decrease ( ! frequ5cy ( ! light due to ! int5se gravitational field ?r\gh :i* ! rays h to pass4 ,consequ5tly ! d>k l9es 9 ! spectrum appe> at long] wave-l5g?s1 i4e4 displac$ t[>ds ! r$ z comp>$ ) ! correspond+ t]re/rial l9es4 ,! effect c be d$uc$ ei!r f ! relativity !ory ( gravitation or f ! quantum !ory2 = ^? :o h "s acqua9tance ) ! quantum !ory ! foll[+ reason+ is probably ! simple/4 ,! /ell> atom emits ! same quantum ( en]gy h z a t]re/rial atom1 b ?is quantum has to use up "s ( its en]gy 9 ord] to escape f ! attraction ( ! />2 ! en]gy ( escape is equal to ! mass h_/c#b multipli$ by ! gravitational pot5tial at ! surface ( ! />4 ,accord+ly ! r$uc$ en]gy aft] escape is h7#a - _/c#b72 & s9ce ?is mu/ /ill =m a quantum h'1 ! frequ5cy has to *ange to a value ' 7#a - _/c#b74 ,?us ! displacem5t ' - is proportional to 1 i4e4 to ! mass divid$ by ! radius ( ! />4 ,! effect on ! spectrum resembles ! ,doppl] effect ( a velocity ( recession1 & c !re=e only be discrim9at$ if we "k already ! l9e-(-sight velocity4 ,9 ! case ( a d\ble /> ! velocity is kn[n f obs]vation ( ! o!r compon5t ( ! sy/em1 s t ! "p ( ! displacem5t attributable to ,doppl] effect is kn[n4 ,ow+ to orbital motion !re is a diff]5ce ( velocity betwe5 ,sirius & its ,companion am\nt+ at pres5t to #dc km4 p] sec4 & ?is has be5 duly tak5 into acc\nt2 ! obs]v$ diff]5ce 9 position ( ! spectral l9es ( ,sirius & its ,companion corresponds to a velocity ( #bc km4 p] sec4 ( :i* #d km4 p] sec4 is attributable to orbital motion1 & ! rema9+ #ai km4 p] sec4 mu/ be int]pret$ z ,e9/e9 effect4 ,! result re/s ma9ly on measurem5ts ( "o spectral l9e ,h4 ,! o!r fav\rable l9es are 9 ! blu] "p ( ! spectrum1 & s9ce atmosph]ic scatt]+ increases ) blu5ess1 ! scatt]$ light ( ,sirius int]f]es4 ,h[ev]1 !y af=d "s useful confirmatory evid5ce4 ,( ! o!r :ite dw>fs #b ,eridani is a d\ble />1 its companion be+ a r$ dw>f fa9t] ?an itself4 ,! r$ %ift ( ! spectrum w be small] ?an 9 ! ,companion ( ,sirius & x w n be s easy to sep>ate x f v>i\s possible s\rces ( error4 ,nev]!less ! prospect is n hopeless4 ,! o!r recogniz$ :ite dw>f is an unnam$ /> discov]$ by ,van ,maan52 x is a solit>y />1 & consequ5tly !re is no means ( di/+ui%+ betwe5 ,e9/e9 %ift & ,doppl] %ift4 ,v>i\s o!r />s h be5 suspect$ ( be+ 9 ?is condition1 includ+ ! ,companions ( ,procyon1 #he ,pegasi1 & ,mira ,ceti4 ,if ! ,companion ( ,sirius 7 a p]fect gas its c5tral temp]ature w\ld be ab\t #a1jjj1jjj1jjj1 & ! c5tral "p ( ! /> w\ld be a million times z d5se z wat]4 ,x is1 h[ev]1 unlikely t ! condition ( a p]fect gas cont9ues to hold4 ,x %\ld be und]/ood t 9 any case ! d5sity w fall (f t[>ds ! outside ( ! />1 & ! regions :i* we obs]ve are entirely normal4 ,! d5se mat]ial is tuck$ away "u high pressure 9 ! int]ior4 ,p]haps ! mo/ puzzl+ feature t rema9s is ! extraord9>y diff]5ce ( developm5t betwe5 ,sirius & its ,companion1 :i* mu/ bo? h orig9at$ at ! same "t4 ,ow+ to ! radiation ( mass ! age ( ,sirius mu/ be less ?an a billion ye>s2 an initial mass1 h[ev] l>ge1 w\ld radiate itself d[n to less ?an ! pres5t mass ( ,sirius )9 a billion ye>s4 ,b su* a p]iod is insignificant 9 ! evolution ( a small /> :i* radiates m sl[ly1 & x is difficult to see :y ! ,companion %\ld h already left ! ma9 s]ies & gone on to ?is 7presumably7 lat] /age4 ,?is is ak9 to o!r difficulties 9 ! problem ( /ell> evolution1 & ,i feel conv9c$ t !re is some?+ ( fundam5tal importance t rema9s undiscov]$4 ,until rec5tly ,i h felt t !re 0 a s]i\s 7or1 if y l1 a comic7 difficulty ab\t ! ultimate fate ( ! :ite dw>fs4 ,_! high d5sity is only possible because ( ! sma%+ ( ! atoms1 :i* 9 turn dep5ds on ! high temp]ature4 ,x does n seem p]missible to suppose t ! matt] c rema9 9 ?is compress$ /ate if ! temp]ature falls4 ,we may look =w>d to a "t :5 ! supply ( subatomic en]gy fails & !re is no?+ to ma9ta9 ! high temp]ature2 !n on cool+ d[n1 ! mat]ial w return to ! normal d5sity ( t]re/rial solids4 ,! /> mu/1 !re=e1 exp&1 & 9 ord] to rega9 a d5sity a ?\s&fold less ! radius mu/ exp& t5fold4 ,en]gy w be requir$ 9 ord] to =ce out ! mat]ial aga9/ gravity4 ,:]e is ?is en]gy to come f8 ,an ord9>y /> has n en\gh heat en]gy inside x to be able to exp& aga9/ gravitation to ?is ext5t2 & ! :ite dw>f c sc>cely be suppos$ to h _h suffici5t =esight to make special provision = ?is remote dem&4 ,?us ! /> may be 9 an awkw>d pr$icam5t--x w be los+ heat cont9ually b w n h en\gh en]gy to cool d[n4 ,"o sugge/ion = avoid+ ?is dilemma is l ! device ( a noveli/ :o br+s 8 *>act]s into su* a mess t ! only solution is to kill !m (f4 ,we might assume t subatomic en]gy w nev] cease to be lib]at$ until x has remov$ ! :ole mass--or at lea/ conduct$ ! /> out ( ! :ite dw>f condition4 ,b ?is sc>cely meets ! difficulty2 ! !ory ought 9 "s way to gu>d automatically aga9/ an impossible pr$icam5t1 & n to rely on disconnect$ prop]ties ( matt] to protect ! actual />s f tr\ble4 ,! :ole difficulty seems1 h[ev]1 to h be5 remov$ 9 a rec5t inve/igation by ,r4 ,h4 ,f[l]4 ,he concludes unexpect$ly t ! d5se matt] ( ! ,companion ( ,sirius has an ample /ore ( en]gy to provide = ! expansion4 ,! int]e/+ po9t is t 8 solution invokes "s ( ! mo/ rec5t developm5ts ( ! quantum !ory--! #8new /ati/ics' ( ,e9/e9 & ,bose & ! wave-!ory ( ,s*rd+]4 ,x is a curi\s co9cid5ce t ab\t ! "t t ?is matt] ( transc5d5tly high d5sity 0 engag+ ! att5tion ( a/ronom]s1 ! physici/s 7 develop+ a new !ory ( matt] :i* specially conc]ns high d5sity4 ,accord+ to ?is !ory matt] has c]ta9 wave prop]ties :i* b>ely come into play at t]re/rial d5sities2 b !y are ( s]i\s importance at d5sities su* z t ( ! ,companion ( ,sirius4 ,x 0 9 consid]+ ^! prop]ties t ,f[l] came ^u ! /ore ( en]gy t solves our difficulty2 ! classical !ory ( matt] gives no indication ( x4 ,! :ite dw>f appe>s to be a happy hunt+ gr\nd = ! mo/ revolution>y developm5ts ( !oretical physics4 ,to ga9 "s idea ( ! new !ory ( d5se matt] we c beg9 by ref]r+ to ! photograph ( ! ,balm] ,s]ies 9 ,fig4 #i4 ,?is %[s ! light radiat$ by a l>ge numb] ( hydrog5 atoms 9 all possible /ates up to ,no4 #cj 9 ! proportions 9 :i* !y occur naturally 9 ! sun's *romosph]e4 ,! old-/yle electromagnetic !ory pr$ict$ t electrons mov+ 9 curv$ pa?s w\ld radiate cont9u\s light2 & ! old-/yle /ati/ical !ory pr$ict$ ! relative abundance ( orbits ( diff]5t sizes1 s t ! di/ribution ( light along ?is cont9u\s spectrum c\ld be calculat$4 ,^! pr$ictions are wrong & d n give ! di/ribution ( light %[n 9 ! photograph2 b !y become less gl>+ly wrong z we draw ne> to ! head ( ! s]ies4 ,! lat] l9es ( ! s]ies cr[d toge!r & pres5tly become s close z to be practically indi/+ui%able f cont9u\s light4 ,?us ! classical pr$iction ( cont9u\s spectrum is becom+ approximately true2 simultane\sly ! classical pr$iction ( its int5sity approa*es ! tru?4 ,!re is a fam\s ,correspond5ce ,pr9ciple enunciat$ by ,bohr :i* ass]ts t = /ates ( v high numb] ! new quantum laws m]ge into ! old classical laws4 ,if we nev] h to consid] /ates ( l[ numb] x is indiff]5t :e!r we calculate ! radiation or /ati/ics accord+ to ! old laws or ! new4 ,9 high-numb]$ /ates ! electron is = mo/ ( ! "t f> di/ant f ! nucleus4 ,cont9u\s proximity to ! nucleus indicates a l[-numb]$ /ate4 ,mu/ we n expect1 !n1 t 9 extremely d5se matt] ! cont9u\s proximity ( ! p>ticles w give rise to ph5om5a *>act]i/ic ( l[-numb]$ /ates8 ,!re is no real discont9uity betwe5 ! organization ( ! atom & ! organization ( ! />2 ! ties :i* b9d ! p>ticles 9 ! atom1 b9d also m ext5d$ gr\ps ( p>ticles & ev5tually ! :ole />4 ,s long z ^! ties are ( high quantum numb]1 ! alt]native conception is suffici5tly ne>ly valid :i* repres5ts ! int]actions by =ces aft] ! classical fa%ion & takes no cognizance ( #8/ates'4 ,= v high d5sity !re is no alt]native conception1 & we mu/ ?9k n 9 t]ms ( =ce1 velocity1 & di/ribution ( indep5d5t p>ticles1 b 9 t]ms ( /ates4 ,! effect ( ?is breakd[n ( ! classical conception c be/ be se5 by pass+ at once to ! f9al limit :5 ! /> becomes a s+le sy/em or molecule 9 /ate ,no4 #a4 ,l an excit$ atom collaps+ ) discont9u\s jumps su* z ^? :i* give ! ,balm] ,s]ies1 ! /> ) a few la/ gasps ( radiation w rea* ! limit+ /ate :i* has no /ate beyond4 ,?is does n mean t fur!r contraction is b>r$ by ! ultimate p>ticles jamm+ 9 contact1 any m ?an collapse ( ! hydrog5 atom is b>r$ by ! electron jamm+ aga9/ ! proton2 progress is /opp$ because ! /> has got back to ! fir/ ( an integral s]ies ( possible conditions ( a mat]ial sy/em4 ,a hydrog5 atom 9 /ate ,no4 #a _c radiate2 nev]!less its electron is mov+ ) high k9etic en]gy4 ,simil>ly a /> :5 x has rea*$ /ate ,no4 #a no long] radiates2 nev]!less its p>ticles are mov+ ) extremely great en]gy4 ,:at is its temp]ature8 ,if y measure temp]ature by radiat+ p[] its temp]ature is absolute z]o1 s9ce ! radiation is nil2 if y measure temp]ature by ! av]age spe$ ( molecules its temp]ature is ! highe/ atta9able by matt]4 ,! f9al fate ( ! :ite dw>f is to become at ! same "t ! hotte/ & ! colde/ matt] 9 ! univ]se4 ,our difficulty is d\bly solv$4 ,because ! /> is int5sely hot x has en\gh en]gy to cool d[n if x wants to2 because x is s int5sely cold x has /opp$ radiat+ & no long] wants to gr[ any cold]4 ,we h describ$ :at is believ$ to be ! f9al /ate ( ! :ite dw>f & p]haps !re=e ( e />4 ,! ,companion ( ,sirius has n yet rea*$ ?is /ate1 b x is s f> on ! way t ! classical treatm5t is already inadmissible4 ,if any />s h rea*$ /ate ,no4 #a !y are invisible2 l atoms 9 ! normal 7l[e/7 /ate !y give no light4 ,! b9d+ ( ! atom :i* defies ! classical conception ( =ces has ext5d$ to cov] ! />4 ,i little imag9$ :5 ?is survey ( ,/>s & ,atoms 0 begun t x w\ld end ) a glimpse ( a ,/>-,atom4 ,pr9t$ 9 ,engl& at ! ,,ox=d ,,univ]sity ,,press by ,john ,johnson ,pr9t] to ! ,univ]sity