darwin and modern science-第192章

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　and　chapter　XVIII。）；　the　curve　which　represents　the　variation　in　the　light　is　shown　in　a　figure　titled　〃The　light…curve　and　system　of　Beta　Lyrae〃　（Fig。　7。）。

The　spectroscope　has　enabled　astronomers　to　prove　that　many　stars；　although　apparently　single；　really　consist　of　two　stars　circling　around　one　another　（If　a　source　of　light　is　approaching　with　a　great　velocity　the　waves　of　light　are　crowded　together；　and　conversely　they　are　spaced　out　when　the　source　is　receding。　　Thus　motion　in　the　line　of　sight　virtually　produces　an　infinitesimal　change　of　colour。　　The　position　of　certain　dark　lines　in　the　spectrum　affords　an　exceedingly　accurate　measurement　of　colour。　　Thus　displacements　of　these　spectral　lines　enables　us　to　measure　the　velocity　of　the　source　of　light　towards　or　away　from　the　observer。）；　they　are　known　as　spectroscopic　binaries。　　Campbell　of　the　Lick　Observatory　believes　that　about　one　star　in　six　is　a　binary　（〃Astrophysical　Journ。〃　Vol。　XIII。　page　89；　1901。　　See　also　A。　Roberts；　〃Nature〃；　Sept。　12；　1901；　page　468。）；　thus　there　must　be　many　thousand　such　stars　within　the　reach　of　our　spectroscopes。

The　orientation　of　the　planes　of　the　orbits　of　binary　stars　appears　to　be　quite　arbitrary；　and　in　general　the　star　does　not　vary　in　brightness。　　Amongst　all　such　orbits　there　must　be　some　whose　planes　pass　nearly　through　the　sun；　and　in　these　cases　the　eclipse　of　one　of　the　stars　by　the　other　becomes　inevitable；　and　in　each　circuit　there　will　occur　two　eclipses　of　unequal　intensities。

It　is　easy　to　see　that　in　the　majority　of　such　cases　the　two　components　must　move　very　close　to　one　another。

The　coincidence　between　the　spectroscopic　and　the　photometric　evidence　permits　us　to　feel　complete　confidence　in　the　theory　of　eclipses。　　When　then　we　find　a　star　with　a　light…curve　of　perfect　regularity　and　with　a　characteristics　of　that　of　Algol；　we　are　justified　in　extending　the　theory　of　eclipses　to　it；　although　it　may　be　too　faint　to　permit　of　adequate　spectroscopic　examination。　　This　extension　of　the　theory　secures　a　considerable　multiplication　of　the　examples　available　for　observation；　and　some　30　have　already　been　discovered。

Dr　Alexander　Roberts；　of　Lovedale　in　Cape　Colony；　truly　remarks　that　the　study　of　Algol　variables　〃brings　us　to　the　very　threshold　of　the　question　of　stellar　evolution。〃　　（〃Proc。　Roy。　Soc。　Edinburgh〃；　XXIV。　Part　II。　（1902）；　page　73。）　　It　is　on　this　account　that　I　propose　to　explain　in　some　detail　the　conclusion　to　which　he　and　some　other　observers　have　been　led。

Although　these　variable　stars　are　mere　points　of　light；　it　has　been　proved　by　means　of　the　spectroscope　that　the　law　of　gravitation　holds　good　in　the　remotest　regions　of　stellar　space；　and　further　it　seems　now　to　have　become　possible　even　to　examine　the　shapes　of　stars　by　indirect　methods；　and　thus　to　begin　the　study　of　their　evolution。　　The　chain　of　reasoning　which　I　shall　explain　must　of　necessity　be　open　to　criticism；　yet　the　explanation　of　the　facts　by　the　theory　is　so　perfect　that　it　is　not　easy　to　resist　the　conviction　that　we　are　travelling　along　the　path　of　truth。

The　brightness　of　a　star　is　specified　by　what　is　called　its　〃magnitude。〃　　The　average　brightness　of　all　the　stars　which　can　just　be　seen　with　the　naked　eye　defines　the　sixth　magnitude。　　A　star　which　only　gives　two…fifths　as　much　light　is　said　to　be　of　the　seventh　magnitude；　while　one　which　gives　2　1/2　times　as　much　light　is　of　the　fifth　magnitude；　and　successive　multiplications　or　divisions　by　2　1/2　define　the　lower　or　higher　magnitudes。　　Negative　magnitudes　have　clearly　to　be　contemplated；　thus　Sirius　is　of　magnitude　minus　1。4；　and　the　sun　is　of　magnitude　minus　26。

The　definition　of　magnitude　is　also　extended　to　fractions；　for　example；　the　lights　given　by　two　candles　which　are　placed　at　100　feet　and　100　feet　6　inches　from　the　observer　differ　in　brightness　by　one…hundredth　of　a　magnitude。

A　great　deal　of　thought　has　been　devoted　to　the　measurement　of　the　brightness　of　stars；　but　I　will　only　describe　one　of　the　methods　used；　that　of　the　great　astronomer　Argelander。　　In　the　neighbourhood　of　the　star　under　observation　some　half　dozen　standard　stars　are　selected　of　known　invariable　magnitudes；　some　being　brighter　and　some　fainter　than　the　star　to　be　measured；　so　that　these　stars　afford　a　visible　scale　of　brightness。　　Suppose　we　number　them　in　order　of　increasing　brightness　from　1　to　6；　then　the　observer　estimates　that　on　a　given　night　his　star　falls　between　stars　2　and　3；　on　the　next　night；　say　between　3　and　4；　and　then　again　perhaps　it　may　return　to　between　2　and　3；　and　so　forth。　　With　practice　he　learns　to　evaluate　the　brightness　down　to　small　fractions　of　a　magnitude；　even　a　hundredth　part　of　a　magnitude　is　not　quite　negligible。

For　example；　in　observing　the　star　RR　Centauri　five　stars　were　in　general　used　for　comparison　by　Dr　Roberts；　and　in　course　of　three　months　he　secured　thereby　300　complete　observations。　　When　the　period　of　the　cycle　had　been　ascertained　exactly；　these　300　values　were　reduced　to　mean　values　which　appertained　to　certain　mean　places　in　the　cycle；　and　a　mean　light…curve　was　obtained　in　this　way。　　Figures　titled　〃Light　curve　of　RR　Centauri〃　（Fig。　5）　and　〃The　light…curve　and　system　of　Beta　Lyrae〃　（Fig。　7）　show　examples　of　light　curves。

I　shall　now　follow　out　the　results　of　the　observation　of　RR　Centauri　not　only　because　it　affords　the　easiest　way　of　explaining　these　investigations；　but　also　because　it　is　one　of　the　stars　which　furnishes　the　most　striking　results　in　connection　with　the　object　of　this　essay。　　（See　〃Monthly　notices　R。A。S。〃　Vol。　63；　1903；　page　527。）　　This　star　has　a　mean　magnitude　of　about　7　1/2；　and　it　is　therefore　invisible　to　the　naked　eye。　　Its　period　of　variability　is　14h　32m　10s。76；　the　last　refinement　of　precision　being　of　course　only　attained　in　the　final　stages　of　reduction。　　Twenty…nine　mean　values　of　the　magnitude　were　determined；　and　they　were　nearly　equally　spaced　over　the　whole　cycle　of　changes。　　The　black　dots　in　Fig。　5　exhibit　the　mean　values　determined　by　Dr　Roberts。　　The　last　three　dots　on　the　extreme　right　are　merely　the　same　as　the　first　three　on　the　extreme　left；　and　are　repeated　to　show　how　the　next　cycle　would　begin。　　The　smooth　dotted　curve　will　be　explained　hereafter；　but；　by　reference　to　the　scale　of　magnitudes　on　the　margins　of　the　figure；　it　may　be　used　to　note　that　the　dots　might　be　brought　into　a　perfectly　smooth　curve　by　shifting　some　few　of　the　dots　by　about　a　hundredth　of　a　magnitude。

This　light…curve　presents　those　characteristics　which　are　due　to　successive　eclipses；　but　the　exact　form　of　the　curve　must　depend　on　the　nature　of　the　two　mutually　eclipsing　stars。　　If　we　are　to　interpret　the　curve　with　all　possible　completeness；　it　is　necessary　to　make　certain　assumptions　as　to　the　stars。　　It　is　assumed　then　that　the　stars　are　equally　bright　all　over　their　disks；　and　secondly　that　they　are　not　surrounded　by　an　extensive　absorptive　atmosphere。　　This　last　appears　to　me　to　be　the　most　dangerous　assumption　involved　in　the　whole　theory。

Making　these　assumptions；　however；　it　is　found　that　if　each　of　the　eclipsing　stars　were　spherical　it　would　not　be　possible　to　generate　such　a　curve　with　the　closest　accuracy。　　The　two　stars　are　certainly　close　together；　and　it　is　obvious　that　in　such　a　case　the　tidal　forces　exercised　by　each　on　the　other　must　be　such　as　to　elongate　the　figure　of　each　towards　the　other。　　Accordingly　it　is　reasonable　to　adopt　the　hypothesis　that　the　system　consists　of　a　pair　of　elongated　ellipsoids；　with　their　longest　axes　pointed　towards　one　another。　　No　supposition　is　adopted　a　priori　as　to　the　ratio　of　the　two　masses；　or　as　to　their　relative　size　or　brightness；　and　the　orbit　may　have　any　degree　of　eccentricity。　　These　last　are　all　to　be　determined　from　the　nature　of　the　light…curve。

In　the　case　of　RR　Centauri；　however；　Dr　Roberts　finds　the　conditions　are　best　satisfied　by　supposing　the　orbit　to　be　circular；　and　the　sizes　and　masses　of　the　components　to　be　equal；　while　their　luminosities　are　to　one　another　in　the　ratio　of　4　to　3。　　As　to　their　shapes　he　finds　them　to　be　so　much　elongated　that　they　overlap；　as　exhibited　in　his　figure　titled　〃The　shape　of　the　star　RR　Centauri〃　（Fig