darwin and modern science-第170节

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figure　has　therefore　been　called　the　〃pear…shaped　figure　of　equilibrium。〃　　The　firm　line　shows　this　new　type　of　figure；　whilst；　as　already　explained；　the　dotted　line　shows　the　form　of　bifurcation　from　which　it　is　derived。　　The　specific　mark　of　this　new　family　is　the　protrusion　of　the　stalk　together　with　the　other　corresponding　smaller　differences。　　If　we　denote　this　difference　by　c；　while　A　＋　b　denotes　the　Jacobian　figure　of　bifurcation　from　which　it　is　derived；　the　new　family　may　be　called　A　＋　b　＋　c；　and　c　is　zero　initially。　　According　to　my　calculations　this　series　of　figures　is　stable　（M。　Liapounoff　contends　that　for　constant　density　the　new　series　of　figures；　which　M。　Poincare　discovered；　has　less　rotational　momentum　than　that　of　the　figure　of　bifurcation。　　If　he　is　correct；　the　figure　of　bifurcation　is　a　limit　of　stable　figures；　and　none　can　exist　with　stability　for　greater　rotational　momentum。　　My　own　work　seems　to　indicate　that　the　opposite　is　true；　and；　notwithstanding　M。　Liapounoff's　deservedly　great　authority；　I　venture　to　state　the　conclusions　in　accordance　with　my　own　work。）；　but　I　do　not　know　at　what　stage　of　its　development　it　becomes　unstable。

Professor　Jeans　has　solved　a　problem　which　is　of　interest　as　throwing　light　on　the　future　development　of　the　pear…shaped　figure；　although　it　is　of　a　still　more　ideal　character　than　the　one　which　has　been　discussed。　　He　imagines　an　INFINITELY　long　circular　cylinder　of　liquid　to　be　in　rotation　about　its　central　axis。　　The　existence　is　virtually　postulated　of　a　demon　who　is　always　occupied　in　keeping　the　axis　of　the　cylinder　straight；　so　that　Jeans　has　only　to　concern　himself　with　the　stability　of　the　form　of　the　section　of　the　cylinder；　which　as　I　have　said　is　a　circle　with　the　axis　of　rotation　at　the　centre。　　He　then　supposes　the　liquid　forming　the　cylinder　to　shrink　in　diameter；　just　as　we　have　done；　and　finds　that　the　speed　of　rotation　must　increase　so　as　to　keep　up　the　constancy　of　the　rotational　momentum。　　The　circularity　of　section　is　at　first　stable；　but　as　the　shrinkage　proceeds　the　stability　diminishes　and　at　length　vanishes。　　This　stage　in　the　process　is　a　form　of　bifurcation；　and　the　stability　passes　over　to　a　new　series　consisting　of　cylinders　which　are　elliptic　in　section。　　The　circular　cylinders　are　exactly　analogous　with　our　planetary　spheroids；　and　the　elliptic　ones　with　the　Jacobian　ellipsoids。

With　further　shrinkage　the　elliptic　cylinders　become　unstable；　a　new　form　of　bifurcation　is　reached；　and　the　stability　passes　over　to　a　series　of　cylinders　whose　section　is　pear…shaped。　　Thus　far　the　analogy　is　complete　between　our　problem　and　Jeans's；　and　in　consequence　of　the　greater　simplicity　of　the　conditions；　he　is　able　to　carry　his　investigation　further。　　He　finds　that　the　stalk　end　of　the　pear…like　section　continues　to　protrude　more　and　more；　and　the　flattening　between　it　and　the　axis　of　rotation　becomes　a　constriction。　　Finally　the　neck　breaks　and　a　satellite　cylinder　is　born。　　Jeans's　figure　for　an　advanced　stage　of　development　is　shown　in　a　figure　titled　〃Section　of　a　rotating　cylinder　of　liquid〃　（Fig。　4。）；　but　his　calculations　do　not　enable　him　actually　to　draw　the　state　of　affairs　after　the　rupture　of　the　neck。

There　are　certain　difficulties　in　admitting　the　exact　parallelism　between　this　problem　and　ours；　and　thus　the　final　development　of　our　pear…shaped　figure　and　the　end　of　its　stability　in　a　form　of　bifurcation　remain　hidden　from　our　view；　but　the　successive　changes　as　far　as　they　have　been　definitely　traced　are　very　suggestive　in　the　study　of　stellar　evolution。

Attempts　have　been　made　to　attack　this　problem　from　the　other　end。　　If　we　begin　with　a　liquid　satellite　revolving　about　a　liquid　planet　and　proceed　backwards　in　time；　we　must　make　the　two　masses　expand　so　that　their　density　will　be　diminished。　　Various　figures　have　been　drawn　exhibiting　the　shapes　of　two　masses　until　their　surfaces　approach　close　to　one　another　and　even　until　they　just　coalesce；　but　the　discussion　of　their　stability　is　not　easy。　　At　present　it　would　seem　to　be　impossible　to　reach　coalescence　by　any　series　of　stable　transformations；　and　if　this　is　so　Professor　Jeans's　investigation　has　ceased　to　be　truly　analogous　to　our　problem　at　some　undetermined　stage。　　However　this　may　be　this　line　of　research　throws　an　instructive　light　on　what　we　may　expect　to　find　in　the　evolution　of　real　stellar　systems。

In　the　second　part　of　this　paper　I　shall　point　out　the　bearing　which　this　investigation　of　the　evolution　of　an　ideal　liquid　star　may　have　on　the　genesis　of　double　stars。

II。

There　are　in　the　heavens　many　stars　which　shine　with　a　variable　brilliancy。　Amongst　these　there　is　a　class　which　exhibits　special　peculiarities；　the　members　of　this　class　are　generally　known　as　Algol　Variables；　because　the　variability　of　the　star　Beta　Persei　or　Algol　was　the　first　of　such　cases　to　attract　the　attention　of　astronomers；　and　because　it　is　perhaps　still　the　most　remarkable　of　the　whole　class。　　But　the　circumstances　which　led　to　this　discovery　were　so　extraordinary　that　it　seems　worth　while　to　pause　a　moment　before　entering　on　the　subject。

John　Goodricke；　a　deaf…mute；　was　born　in　1764；　he　was　grandson　and　heir　of　Sir　John　Goodricke　of　Ribston　Hall；　Yorkshire。　　In　November　1782；　he　noted　that　the　brilliancy　of　Algol　waxed　and　waned　（It　is　said　that　Georg　Palitzch；　a　farmer　of　Prohlis　near　Dresden；　had　about　1758　already　noted　the　variability　of　Algol　with　the　naked　eye。　　〃Journ。　Brit。　Astron。　Assoc。〃　Vol。　XV。　（1904…5）；　page　203。）；　and　devoted　himself　to　observing　it　on　every　fine　night　from　the　28th　December　1782　to　the　12th　May　1783。　　He　communicated　his　observations　to　the　Royal　Society；　and　suggested　that　the　variation　in　brilliancy　was　due　to　periodic　eclipses　by　a　dark　companion　star；　a　theory　now　universally　accepted　as　correct。　　The　Royal　Society　recognised　the　importance　of　the　discovery　by　awarding　to　Goodricke；　then　only　19　years　of　age；　their　highest　honour；　the　Copley　medal。　　His　later　observations　of　Beta　Lyrae　and　of　Delta　Cephei　were　almost　as　remarkable　as　those　of　Algol；　but　unfortunately　a　career　of　such　extraordinary　promise　was　cut　short　by　death；　only　a　fortnight　after　his　election　to　the　Royal　Society。　　（〃Dict。　of　National　Biography〃；　article　Goodricke　（John）。　　The　article　is　by　Miss　Agnes　Clerke。　　It　is　strange　that　she　did　not　then　seem　to　be　aware　that　he　was　a　deaf…mute；　but　she　notes　the　fact　in　her　〃Problems　of　Astrophysics〃；　page　337；　London；　1903。）

It　was　not　until　1889　that　Goodricke's　theory　was　verified；　when　it　was　proved　by　Vogel　that　the　star　was　moving　in　an　orbit；　and　in　such　a　manner　that　it　was　only　possible　to　explain　the　rise　and　fall　in　the　luminosity　by　the　partial　eclipse　of　a　bright　star　by　a　dark　companion。

The　whole　mass　of　the　system　of　Algol　is　found　to　be　half　as　great　again　as　that　of　our　sun；　yet　the　two　bodies　complete　their　orbit　in　the　short　period　of　2d　20h　48m　55s。　　The　light　remains　constant　during　each　period；　except　for　9h　20m　when　it　exhibits　a　considerable　fall　in　brightness　（Clerke；　〃Problems　of　Astrophysics〃　page　302　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