darwin and modern science-第171节

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y　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。　6。）。　　The　dotted　curve　shows　a　form　of　equilibrium　of　rotating　liquid　as　computed　by　me　some　years　before；　and　it　was　added　for　the　sake　of　comparison。

On　turning　back　to　Fig。　5　the　reader　will　see　in　the　smooth　dotted　curve　the　light　variation　which　would　be　exhibited　by　such　a　binary　system　as　this。　　The　curve　is　the　result　of　computation　and　it　is　impossible　not　to　be　struck　by　the　closeness　of　the　coincidence　with　the　series　of　black　dots　which　denote　the　observations。

It　is　virtually　certain　that　RR　Centauri　is　a　case　of　an　eclipsing　binary　system；　and　that　the　two　stars　are　close　together。　　It　is　not　of　course　proved　that　the　figures　of　the　stars　are　ellipsoids；　but　gravitation　must　deform　them　into　a　pair　of　elongated　bodies；　and；　on　the　assumptions　that　they　are　not　enveloped　in　an　absorptive　atmosphere　and　that　they　are　ellipsoidal；　their　shapes　must　be　as　shown　in　the　figure。

This　light…curve　gives　an　excellent　illustration　of　what　we　have　reason　to　believe　to　be　a　stage　in　the　evolution　of　stars；　when　a　single　star　is　proceeding　to　separate　into　a　binary　one。

As　the　star　is　faint；　there　is　as　yet　no　direct　spectroscopic　evidence　of　orbital　motion。　　Let　us　turn　therefore　to　the　case　of　another　star；　namely　V　Puppis；　in　which　such　evidence　does　already　exist。　　I　give　an　account　of　it；　because　it　presents　a　peculiarly　interesting　confirmation　of　the　correctness　of　the　theory。

In　1895　Pickering　announced　in　the　〃Harvard　Circular〃　No。　14　that　the　spectroscopic　observations　at　Arequipa　proved　V　Puppis　to　be　a　double　star　with　a　period　of　3d　2h　46m。　　Now　when　Roberts　discussed　its　light…curve　he　found　that　the　period　was　1d　10h　54m　27s；　and　on　account　of　this　serious　discrepancy　he　effected　the　reduction　only　on　the　simple　assumption　that　the　two　stars　were　spherical；　and　thus　obtained　a　fairly　good　representation　of　the　light…curve。　　It　appeared　that　the　orbit　was　circular　and　that　the　two　spheres　were　not　quite　in　contact。　　Obviously　if　the　stars　had　been　assumed　to　be　ellipsoids　they　would　have　been　found　to　overlap；　as　was　the　case　for　RR　Centauri。　　（〃Astrophysical　Journ。〃　Vol。　XIII。　（1901）；　page　177。）　　The　matter　rested　thus　for　some　months　until　the　spectroscopic　evidence　was　re…examined　by　Miss　Cannon　on　behalf　of　Professor　Pickering；　and　we　find　in　the　notes　on　page　177　of　Vol。　XXVIII。　of　the　〃Annals　of　the　Harvard　Observatory〃　the　following：　　〃A。G。C。　10534。　　This　star；　which　is　the　Algol　variable　V　Puppis；　has　been　found　to　be　a　spectroscopic　binary。　　The　period　1d。454　（i。e。　1d　10h　54m）　satisfies　the　observations　of　the　changes　in　light；　and　of　the　varying　separation　of　the　lines　of　the　spectrum。　　The　spectrum　has　been　examined　on　61　plates；　on　23　of　which　the　lines　are　double。〃　　Thus　we　have　valuable　evidence　in　confirmation　of　the　correctness　of　the　conclusions　drawn　from　the　light…curve。　　In　the　circumstances；　however；　I　have　not　thought　it　worth　while　to　reproduce　Dr　Roberts's　provisional　figure。

I　now　turn　to　the　conclusions　drawn　a　few　years　previously　by　another　observer；　where