darwin and modern science-第137章

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ansformation　of　that　environment。　　But　no　given　transformation　can　be　proved　to　be　necessary　（pre…determined）。　　And　types　of　development　do　not　represent　laws；　their　meaning　and　value　lie　in　the　help　they　may　give　to　the　historian；　in　investigating　a　certain　period　of　civilisation；　to　enable　him　to　discover　the　interrelations　among　the　diverse　features　which　it　presents。　　They　are；　as　some　one　has　said；　an　instrument　of　heuretic　method。

20。　　The　men　engaged　in　special　historical　researcheswhich　have　been　pursued　unremittingly　for　a　century　past；　according　to　scientific　methods　of　investigating　evidence　（initiated　by　Wolf；　Niebuhr；　Ranke）have　for　the　most　part　worked　on　the　assumptions　of　genetic　history　or　at　least　followed　in　the　footsteps　of　those　who　fully　grasped　the　genetic　point　of　view。　　But　their　aim　has　been　to　collect　and　sift　evidence；　and　determine　particular　facts；　comparatively　few　have　given　serious　thought　to　the　lines　of　research　and　the　speculations　which　have　been　considered　in　this　paper。　　They　have　been　reasonably　shy　of　compromising　their　work　by　applying　theories　which　are　still　much　debated　and　immature。　　But　historiography　cannot　permanently　evade　the　questions　raised　by　these　theories。　　One　may　venture　to　say　that　no　historical　change　or　transformation　will　be　fully　understood　until　it　is　explained　how　social　environment　acted　on　the　individual　components　of　the　society　（both　immediately　and　by　heredity）；　and　how　the　individuals　reacted　upon　their　environment。　　The　problem　is　psychical；　but　it　is　analogous　to　the　main　problem　of　the　biologist。


XXVIII。　　THE　GENESIS　OF　DOUBLE　STARS。

By　SIR　GEORGE　DARWIN；　K。C。B。；　F。R。S。　Plumian　Professor　of　Astronomy　and　Experimental　Philosophy　in　the　University　of　Cambridge。

In　ordinary　speech　a　system　of　any　sort　is　said　to　be　stable　when　it　cannot　be　upset　easily；　but　the　meaning　attached　to　the　word　is　usually　somewhat　vague。　　It　is　hardly　surprising　that　this　should　be　the　case；　when　it　is　only　within　the　last　thirty　years；　and　principally　through　the　investigations　of　M。　Poincare；　that　the　conception　of　stability　has；　even　for　physicists；　assumed　a　definiteness　and　clearness　in　which　it　was　previously　lacking。　　The　laws　which　govern　stability　hold　good　in　regions　of　the　greatest　diversity；　they　apply　to　the　motion　of　planets　round　the　sun；　to　the　internal　arrangement　of　those　minute　corpuscles　of　which　each　chemical　atom　is　constructed；　and　to　the　forms　of　celestial　bodies。　　In　the　present　essay　I　shall　attempt　to　consider　the　laws　of　stability　as　relating　to　the　last　case；　and　shall　discuss　the　succession　of　shapes　which　may　be　assumed　by　celestial　bodies　in　the　course　of　their　evolution。　　I　believe　further　that　homologous　conceptions　are　applicable　in　the　consideration　of　the　transmutations　of　the　various　forms　of　animal　and　of　vegetable　life　and　in　other　regions　of　thought。　　Even　if　some　of　my　readers　should　think　that　what　I　shall　say　on　this　head　is　fanciful；　yet　at　least　the　exposition　will　serve　to　illustrate　the　meaning　to　be　attached　to　the　laws　of　stability　in　the　physical　universe。

I　propose；　therefore；　to　begin　this　essay　by　a　sketch　of　the　principles　of　stability　as　they　are　now　formulated　by　physicists。

I。

If　a　slight　impulse　be　imparted　to　a　system　in　equilibrium　one　of　two　consequences　must　ensue；　either　small　oscillations　of　the　system　will　be　started；　or　the　disturbance　will　increase　without　limit　and　the　arrangement　of　the　system　will　be　completely　changed。　　Thus　a　stick　may　be　in　equilibrium　either　when　it　hangs　from　a　peg　or　when　it　is　balanced　on　its　point。　　If　in　the　first　case　the　stick　is　touched　it　will　swing　to　and　fro；　but　in　the　second　case　it　will　topple　over。　　The　first　position　is　a　stable　one；　the　second　is　unstable。　　But　this　case　is　too　simple　to　illustrate　all　that　is　implied　by　stability；　and　we　must　consider　cases　of　stable　and　of　unstable　motion。　　Imagine　a　satellite　and　its　planet；　and　consider　each　of　them　to　be　of　indefinitely　small　size；　in　fact　particles；　then　the　satellite　revolves　round　its　planet　in　an　ellipse。　　A　small　disturbance　imparted　to　the　satellite　will　only　change　the　ellipse　to　a　small　amount；　and　so　the　motion　is　said　to　be　stable。　　If；　on　the　other　hand；　the　disturbance　were　to　make　the　satellite　depart　from　its　initial　elliptic　orbit　in　ever　widening　circuits；　the　motion　would　be　unstable。　　This　case　affords　an　example　of　stable　motion；　but　I　have　adduced　it　principally　with　the　object　of　illustrating　another　point　not　immediately　connected　with　stability；　but　important　to　a　proper　comprehension　of　the　theory　of　stability。

The　motion　of　a　satellite　about　its　planet　is　one　of　revolution　or　rotation。　　When　the　satellite　moves　in　an　ellipse　of　any　given　degree　of　eccentricity；　there　is　a　certain　amount　of　rotation　in　the　system；　technically　called　rotational　momentum；　and　it　is　always　the　same　at　every　part　of　the　orbit。　　（Moment　of　momentum　or　rotational　momentum　is　measured　by　the　momentum　of　the　satellite　multiplied　by　the　perpendicular　from　the　planet　on　to　the　direction　of　the　path　of　the　satellite　at　any　instant。）

Now　if　we　consider　all　the　possible　elliptic　orbits　of　a　satellite　about　its　planet　which　have　the　same　amount　of　〃rotational　momentum；〃　we　find　that　the　major　axis　of　the　ellipse　described　will　be　different　according　to　the　amount　of　flattening　（or　the　eccentricity）　of　the　ellipse　described。　　A　figure　titled　〃A　'family'　of　elliptic　orbits　with　constant　rotational　momentum〃　（Fig。　1）　illustrates　for　a　given　planet　and　satellite　all　such　orbits　with　constant　rotational　momentum；　and　with　all　the　major　axes　in　the　same　direction。　　It　will　be　observed　that　there　is　a　continuous　transformation　from　one　orbit　to　the　next；　and　that　the　whole　forms　a　consecutive　group；　called　by　mathematicians　〃a　family〃　of　orbits。　　In　this　case　the　rotational　momentum　is　constant　and　the　position　of　any　orbit　in　the　family　is　determined　by　the　length　of　the　major　axis　of　the　ellipse；　the　classification　is　according　to　the　major　axis；　but　it　might　have　been　made　according　to　anything　else　which　would　cause　the　orbit　to　be　exactly　determinate。

I　shall　come　later　to　the　classification　of　all　possible　forms　of　ideal　liquid　stars；　which　have　the　same　amount　of　rotational　momentum；　and　the　classification　will　then　be　made　according　to　their　densities；　but　the　idea　of　orderly　arrangement　in　a　〃family〃　is　just　the　same。

We　thus　arrive　at　the　conception　of　a　definite　type　of　motion；　with　a　constant　amount　of　rotational　momentum；　and　a　classification　of　all　members　of　the　family；　formed　by　all　possible　motions　of　that　type；　according　to　the　value　of　some　measurable　quantity　（this　will　hereafter　be　density）　which　determines　the　motion　exactly。　　In　the　particular　case　of　the　elliptic　motion　used　for　illustration　the　motion　was　stable；　but　other　cases　of　motion　might　be　adduced　in　which　the　motion　would　be　unstable；　and　it　would　be　found　that　classification　in　a　family　and　specification　by　some　measurable　quantity　would　be　equally　applicable。

A　complex　mechanical　system　may　be　capable　of　motion　in　several　distinct　modes　or　types；　and　the　motions　corresponding　to　each　such　type　may　be　arranged　as　before　in　families。　　For　the　sake　of　simplicity　I　will　suppose　that　only　two　types　are　possible；　so　that　there　will　only　be　two　families；　and　the　rotational　momentum　is　to　be　constant。　　The　two　types　of　motion　will　have　certain　features　in　common　which　we　denote　in　a　sort　of　shorthand　by　the　letter　A。　　Similarly　the　two　types　may　be　described　as　A　＋　a　and　A　＋　b；　so　that　a　and　b　denote　the　specific　differences　which　discriminate　the　families　from　one　another。　　Now　following　in　imagination　the　family　of　the　type　A　＋　a；　let　us　begin　with　the　case　where　the　specific　difference　a　is　well　marked。　　As　we　cast　our　eyes　along　the　series　forming　the　family；　we　find　the　difference　a　becoming　less　conspicuous。　　It　gradually　dwindles　until　it　disappears；　beyond　this　point　it　either　becomes　reversed；　or　else　the　type　has　ceased　to　be　a　possible　one。　　In　our　shorthand　we　have　started　with　A　＋　a；　and　have　watched　the　characteristic　a　dwindling　to　zero。　　When　it　vanishes　we　have　reached　a　type　which　may　be　specified　as　A；　beyond　this　point　the　type　would　be　A　…　a　or　would　be　impossible。

Following　the　A　＋　b　type　in　the　same　way；　b　is　at　first　well　marked；　it　dwindles　to　zero；　and　finally　may　become　negative。　　Hence　in　shorthand　this　second　family　may　be　described　as　A　＋　b；。。。A；。。。A　…　b。

In　each　family　there　is　one　single　member　which　is　indistinguishable　from　a　member　of　the　other　family；　it　is　called　by　Poincare　a　form　of　bifurcation。　　It　is　this　conception　of　a　form　of　bifurcation　which　forms　the　important　consideration　in　problems　dealing　with　the　forms　of　liquid　or　gaseous　bodies　in　rotation。

But　to　return　to　the　general　question；thus　far　the　stability　of　these　families　has　not　been　considered；　and　it　is　the　stability　which　renders　this　way　of　looking　at　the　matter　so　valuable。　　It　may　be　proved　that　if　before　the　point　of　bifurcation　the　type　A　＋　a　was　stable；　then　A　＋　b　must　have　been　unstable。　　Further　as　a　and　b　each　diminish　A　＋　a　becomes　less　pronouncedly　stable；　and　A　＋　b　less　unstable。　　On　reaching　the　point　of　bifurcation　A　＋　a　has　just　ceased　to　be　stable；　or　what　amounts　to　the　same　thing　is　just　becoming　unstable；　and　the　converse　is　true　of　the　A　＋　b　family。　　After　passing　the　point　of　bifurcation　A　＋　a　has　become　definitely　unstable　and　A　＋　b　has　become　stable。　　Hence　the　point　of　bifurcation　is　also　a　point　of　〃exchange　of　stabilities　between　the　two　types。〃　　（In　order　not　to　complicate　unnecessarily　this　explanation　of　a　general　principle　I　have　not　stated　fully　all　the　cases　that　may　occur。　　Thus：　　firstly；　after　bifurcation　A　＋　a　may　be　an　impossible　type　and　A　＋　a　will　then　stop　at　this　point；　or　secondly；　A　＋　b　may　have　been　an　impossible　type　before　bifurcation；　and　will　only　begin　to　be　a　real　one　after　it；　or　thirdly；　both　A　＋　a　and　A　＋　b　may　be　impossible　after　the　point　of　bifurcation；　in　which　case　they　coalesce　and　disappear。　　This　last　case　shows　that　types　arise　and　disappear　in　pairs；　and　that　on　appearance　or　before　disappearance　one　must　be　stable　and　the　other　unstable。）

In　nature　it　is　of　course　only　the　stable　types　of　motion　which　can　persist　for　more　than　a　short　time。　　Thus　the　task　of　the　physical　evolutionist　is　to　determine　the　forms　of　bifurcation；　at　which　he　must；　as　it　were；　change　carriages　in　the　evolutionary　journey　so　as　always　to　follow　the　stable　route。　　He　must　besides　be　able　to　indicate　some　natural　process　which　shall　correspond　in　effect　to　the　ideal　arrangement　of　the　several　types　of　motion　in　families　with　gradually　changing　specific　differences。　　Although；　as　we　shall　see　hereafter；　it　may　frequently　or　even　generally　be　impossible　to　specify　with　exactness　the　forms　of　bifurcation　in　the　process　of　evolution；　yet　the　conception　is　one　of　fundamental　importance。

The　ideas　involved　in　this　sketch　are　no　doubt　somewhat　recondite；　but　I　hope　to　render　them　clearer　to　the　non…mathematical　reader　by　homologous　considerations　in　other　fields　of　thought　（I　considered　this　subject　in　my　Presidential　address　to　the　British　Association　in　1905；　〃Report　of　the　75th　Meeti