darwin and modern science-第167节

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19。　　I　have　dwelt　on　the　fundamental　ideas　of　Lamprecht；　because　they　are　not　yet　widely　known　in　England；　and　because　his　system　is　the　ablest　product　of　the　sociological　school　of　historians。　　It　carries　the　more　weight　as　its　author　himself　is　a　historical　specialist；　and　his　historical　syntheses　deserve　the　most　careful　consideration。　　But　there　is　much　in　the　process　of　development　which　on　such　assumptions　is　not　explained；　especially　the　initiative　of　individuals。　　Historical　development　does　not　proceed　in　a　right　line；　without　the　choice　of　diverging。　　Again　and　again；　several　roads　are　open　to　it；　of　which　it　chooses　onewhy？　　On　Lamprecht's　method；　we　may　be　able　to　assign　the　conditions　which　limit　the　psychical　activity　of　men　at　a　particular　stage　of　evolution；　but　within　those　limits　the　individual　has　so　many　options；　such　a　wide　room　for　moving；　that　the　definition　of　those　conditions；　the　〃psychical　diapasons；〃　is　only　part　of　the　explanation　of　the　particular　development。　　The　heel　of　Achilles　in　all　historical　speculations　of　this　class　has　been　the　role　of　the　individual。

The　increasing　prominence　of　economic　history　has　tended　to　encourage　the　view　that　history　can　be　explained　in　terms　of　general　concepts　or　types。　　Marx　and　his　school　based　their　theory　of　human　development　on　the　conditions　of　production；　by　which；　according　to　them；　all　social　movements　and　historical　changes　are　entirely　controlled。　　The　leading　part　which　economic　factors　play　in　Lamprecht's　system　is　significant；　illustrating　the　fact　that　economic　changes　admit　most　readily　this　kind　of　treatment；　because　they　have　been　less　subject　to　direction　or　interference　by　individual　pioneers。

Perhaps　it　may　be　thought　that　the　conception　of　SOCIAL　ENVIRONMENT　（essentially　psychical）；　on　which　Lamprecht's　〃psychical　diapasons〃　depend；　is　the　most　valuable　and　fertile　conception　that　the　historian　owes　to　the　suggestion　of　the　science　of　biologythe　conception　of　all　particular　historical　actions　and　movements　as　（1）　related　to　and　conditioned　by　the　social　environment；　and　（2）　gradually　bringing　about　a　transformation　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　dis