darwin and modern science-第138章

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his　subject　in　my　Presidential　address　to　the　British　Association　in　1905；　〃Report　of　the　75th　Meeting　of　the　British　Assoc。〃　（S。　Africa；　1905）；　London；　1906；　page　3。　　Some　reviewers　treated　my　speculations　as　fanciful；　but　as　I　believe　that　this　was　due　generally　to　misapprehension；　and　as　I　hold　that　homologous　considerations　as　to　stability　and　instability　are　really　applicable　to　evolution　of　all　sorts；　I　have　thought　it　well　to　return　to　the　subject　in　the　present　paper。）；　and　I　shall　pass　on　thence　to　illustrations　which　will　teach　us　something　of　the　evolution　of　stellar　systems。

States　or　governments　are　organised　schemes　of　action　amongst　groups　of　men；　and　they　belong　to　various　types　to　which　generic　names；　such　as　autocracy；　aristocracy　or　democracy；　are　somewhat　loosely　applied。　　A　definite　type　of　government　corresponds　to　one　of　our　types　of　motion；　and　while　retaining　its　type　it　undergoes　a　slow　change　as　the　civilisation　and　character　of　the　people　change；　and　as　the　relationship　of　the　nation　to　other　nations　changes。　　In　the　language　used　before；　the　government　belongs　to　a　family；　and　as　time　advances　we　proceed　through　the　successive　members　of　the　family。　　A　government　possesses　a　certain　degree　of　stability　hardly　measurable　in　numbers　howeverto　resist　disintegrating　influences　such　as　may　arise　from　wars；　famines；　and　internal　dissensions。　　This　stability　gradually　rises　to　a　maximum　and　gradually　declines。　　The　degree　of　stability　at　any　epoch　will　depend　on　the　fitness　of　some　leading　feature　of　the　government　to　suit　the　slowly　altering　circumstances；　and　that　feature　corresponds　to　the　characteristic　denoted　by　a　in　the　physical　problem。　　A　time　at　length　arrives　when　the　stability　vanishes；　and　the　slightest　shock　will　overturn　the　government。　　At　this　stage　we　have　reached　the　crisis　of　a　point　of　bifurcation；　and　there　will　then　be　some　circumstance；　apparently　quite　insignificant　and　almost　unnoticed；　which　is　such　as　to　prevent　the　occurrence　of　anarchy。　　This　circumstance　or　condition　is　what　we　typified　as　b。　　Insignificant　although　it　may　seem；　it　has　started　the　government　on　a　new　career　of　stability　by　imparting　to　it　a　new　type。　　It　grows　in　importance；　the　form　of　government　becomes　obviously　different；　and　its　stability　increases。　　Then　in　its　turn　this　newly　acquired　stability　declines；　and　we　pass　on　to　a　new　crisis　or　revolution。　　There　is　thus　a　series　of　〃points　of　bifurcation〃　in　history　at　which　the　continuity　of　political　history　is　maintained　by　means　of　changes　in　the　type　of　government。　　These　ideas　seem；　to　me　at　least；　to　give　a　true　account　of　the　history　of　states；　and　I　contend　that　it　is　no　mere　fanciful　analogy　but　a　true　homology；　when　in　both　realms　of　thought　the　physical　and　the　politicalwe　perceive　the　existence　of　forms　of　bifurcation　and　of　exchanges　of　stability。

Further　than　this；　I　would　ask　whether　the　same　train　of　ideas　does　not　also　apply　to　the　evolution　of　animals？　　A　species　is　well　adapted　to　its　environment　when　the　individual　can　withstand　the　shocks　of　famine　or　the　attacks　and　competition　of　other　animals；　it　then　possesses　a　high　degree　of　stability。　　Most　of　the　casual　variations　of　individuals　are　indifferent；　for　they　do　not　tell　much　either　for　or　against　success　in　life；　they　are　small　oscillations　which　leave　the　type　unchanged。　　As　circumstances　change；　the　stability　of　the　species　may　gradually　dwindle　through　the　insufficiency　of　some　definite　quality；　on　which　in　earlier　times　no　such　insistent　demands　were　made。　　The　individual　animals　will　then　tend　to　fail　in　the　struggle　for　life；　the　numbers　will　dwindle　and　extinction　may　ensue。　　But　it　may　be　that　some　new　variation；　at　first　of　insignificant　importance；　may　just　serve　to　turn　the　scale。　　A　new　type　may　be　formed　in　which　the　variation　in　question　is　preserved　and　augmented；　its　stability　may　increase　and　in　time　a　new　species　may　be　produced。

At　the　risk　of　condemnation　as　a　wanderer　beyond　my　province　into　the　region　of　biological　evolution；　I　would　say　that　this　view　accords　with　what　I　understand　to　be　the　views　of　some　naturalists；　who　recognise　the　existence　of　critical　periods　in　biological　history　at　which　extinction　occurs　or　which　form　the　starting…point　for　the　formation　of　new　species。　　Ought　we　not　then　to　expect　that　long　periods　will　elapse　during　which　a　type　of　animal　will　remain　almost　constant；　followed　by　other　periods；　enormously　long　no　doubt　as　measured　in　the　life　of　man；　of　acute　struggle　for　existence　when　the　type　will　change　more　rapidly？　　This　at　least　is　the　view　suggested　by　the　theory　of　stability　in　the　physical　universe。　　（I　make　no　claim　to　extensive　reading　on　this　subject；　but　refer　the　reader　for　example　to　a　paper　by　Professor　A。A。W。　Hubrecht　on　〃De　Vries's　theory　of　Mutations〃；　〃Popular　Science　Monthly〃；　July　1904；　especially　to　page　213。）

And　now　I　propose　to　apply　these　ideas　of　stability　to　the　theory　of　stellar　evolution；　and　finally　to　illustrate　them　by　certain　recent　observations　of　a　very　remarkable　character。

Stars　and　planets　are　formed　of　materials　which　yield　to　the　enormous　forces　called　into　play　by　gravity　and　rotation。　　This　is　obviously　true　if　they　are　gaseous　or　fluid；　and　even　solid　matter　becomes　plastic　under　sufficiently　great　stresses。　　Nothing　approaching　a　complete　study　of　the　equilibrium　of　a　heterogeneous　star　has　yet　been　found　possible；　and　we　are　driven　to　consider　only　bodies　of　simpler　construction。　　I　shall　begin　therefore　by　explaining　what　is　known　about　the　shapes　which　may　be　assumed　by　a　mass　of　incompressible　liquid　of　uniform　density　under　the　influences　of　gravity　and　of　rotation。　　Such　a　liquid　mass　may　be　regarded　as　an　ideal　star；　which　resembles　a　real　star　in　the　fact　that　it　is　formed　of　gravitating　and　rotating　matter；　and　because　its　shape　results　from　the　forces　to　which　it　is　subject。　　It　is　unlike　a　star　in　that　it　possesses　the　attributes　of　incompressibility　and　of　uniform　density。　　The　difference　between　the　real　and　the　ideal　is　doubtless　great；　yet　the　similarity　is　great　enough　to　allow　us　to　extend　many　of　the　conclusions　as　to　ideal　liquid　stars　to　the　conditions　which　must　hold　good　in　reality。　　Thus　with　the　object　of　obtaining　some　insight　into　actuality；　it　is　justifiable　to　discuss　an　avowedly　ideal　problem　at　some　length。

The　attraction　of　gravity　alone　tends　to　make　a　mass　of　liquid　assume　the　shape　of　a　sphere；　and　the　effects　of　rotation；　summarised　under　the　name　of　centrifugal　force；　are　such　that　the　liquid　seeks　to　spread　itself　outwards　from　the　axis　of　rotation。　　It　is　a　singular　fact　that　it　is　unnecessary　to　take　any　account　of　the　size　of　the　mass　of　liquid　under　consideration；　because　the　shape　assumed　is　exactly　the　same　whether　the　mass　be　small　or　large；　and　this　renders　the　statement　of　results　much　easier　than　would　otherwise　be　the　case。

A　mass　of　liquid　at　rest　will　obviously　assume　the　shape　of　a　sphere；　under　the　influence　of　gravitation；　and　it　is　a　stable　form；　because　any　oscillation　of　the　liquid　which　might　be　started　would　gradually　die　away　under　the　influence　of　friction；　however　small。　　If　now　we　impart　to　the　whole　mass　of　liquid　a　small　speed　of　rotation　about　some　axis；　which　may　be　called　the　polar　axis；　in　such　a　way　that　there　are　no　internal　currents　and　so　that　it　spins　in　the　same　way　as　if　it　were　solid；　the　shape　will　become　slightly　flattened　like　an　orange。　　Although　the　earth　and　the　other　planets　are　not　homogeneous　they　behave　in　the　same　way；　and　are　flattened　at　the　poles　and　protuberant　at　the　equator。　　This　shape　may　therefore　conveniently　be　described　as　planetary。

If　the　planetary　body　be　slightly　deformed　the　forces　of　restitution　are　slightly　less　than　they　were　for　the　sphere；　the　shape　is　stable　but　somewhat　less　so　than　the　sphere。　　We　have　then　a　planetary　spheroid；　rotating　slowly；　slightly　flattened　at　the　poles；　with　a　high　degree　of　stability；　and　possessing　a　certain　amount　of　rotational　momentum。　　Let　us　suppose　this　ideal　liquid　star　to　be　somewhere　in　stellar　space　far　removed　from　all　other　bodies；　then　it　is　subject　to　no　external　forces；　and　any　change　which　ensues　must　come　from　inside。　　Now　the　amount　of　rotational　momentum　existing　in　a　system　in　motion　can　neither　be　created　nor　destroyed　by　any　internal　causes；　and　therefore；　whatever　happens；　the　amount　of　rotational　momentum　possessed　by　the　star　must　remain　absolutely　constant。

A　real　star　radiates　heat；　and　as　it　cools　it　shrinks。　　Let　us　suppose　then　that　our　ideal　star　also　radiates　and　shrinks；　but　let　the　process　proceed　so　slowly　that　any　internal　currents　generated　in　the　liquid　by　the　cooling　are　annulled　so　quickly　by　fluid　friction　as　to　be　insignificant；　further　let　the　liquid　always　remain　at　any　instant　incompressible　and　homogeneous。　All　that　we　are　concerned　with　is　that；　as　time　passes；　the　liquid　star　shrinks；　rotates　in　one　piece　as　if　it　were　solid；　and　remains　incompressible　and　homogeneous。　　The　condition　is　of　course　artificial；　but　it　represents　the　actual　processes　of　nature　as　well　as　may　be；　consistently　with　the　postulated　incompressibility　and　homogeneity。　　（Mathematicians　are　accustomed　to　regard　the　density　as　constant　and　the　rotational　momentum　as　increasing。　　But　the　way　of　looking　at　the　matter；　which　I　have　adopted；　is　easier　of　comprehension；　and　it　comes　to　the　same　in　the　end。）

The　shrinkage　of　a　constant　mass　of　matter　involves　an　increase　of　its　density；　and　we　have　therefore　to　trace　the　changes　which　supervene　as　the　star　shrinks；　and　as　the　liquid　of　which　it　is　composed　increases　in　density。　　The　shrinkage　will；　in　ordinary　parlance；　bring　the　weights　nearer　to　the　axis　of　rotation。　　Hence　in　order　to　keep　up　the　rotational　momentum；　which　as　we　have　seen　must　remain　constant；　the　mass　must　rotate　quicker。　　The　greater　speed　of　rotation　augments　the　importance　of　centrifugal　force　compared　with　that　of　gravity；　and　as　the　flattening　of　the　planetary　spheroid　was　due　to　centrifugal　force；　that　flattening　is　increased；　in　other　words　the　ellipticity　of　the　planetary　spheroid　increases。

As　the　shrinkage　and　corresponding　increase　of　density　proceed；　the　planetary　spheroid　becomes　more　and　more　elliptic；　and　the　succession　of　forms　constitutes　a　family　classified　according　to　the　density　of　the　liquid。　　The　specific　mark　of　this　family　is　the　flattening　or　ellipticity。

Now　consider　the　stability　of　the　system；　we　have　seen　that　the　spheroid　with　a　slow　rotation；　which　forms　our　starting…point；　was　slightly　less　stable　than　the　sphere；　and　as　we　proceed　through　the　family　of　ever　flatter　ellipsoids　the　stability　continues　to　diminish。　　At　length　when　it　has　assumed　the　shape　shown　in　a　figure　titled　〃Planetary　spheroid　just　becoming　unstable〃　（Fig。　2。）　where　the　equatorial　and　polar　axes　are　proportional　to　the　numbers　1000　and　583；　the　stability　has　just　disappeared。　　According　to　the　general　principle　explained　above　this　is　a　form　of　bifurcation；　and　corresponds　to　the　form　denoted　A。　　The　specific　difference　a　of　this　family　must　be　regarded　as　the　excess　of　the　ellipticity　of　this　figure　above　that　of　all　the　earlier　ones；　beginning　with　the　slightly　flattened　planetary　spheroid。　　Accor