assert　and　we　may　consistently　admit；　inasmuch　as　we　construct　them　out　of　the　spherical　body；　and　since　the　spherical　body　has　two　movements　proper　to　itself；　namely　rolling　and　spinning；　it　follows　that　if　the　stars　have　a　movement　of　their　own；　it　will　be　one　of　these。　But　neither　is　observed。　（1）　Suppose　them　to　spin。　They　would　then　stay　where　they　were；　and　not　change　their　place；　as；　by　observation　and　general　consent；　they　do。　Further；　one　would　expect　them　all　to　exhibit　the　same　movement：　but　the　only　star　which　appears　to　possess　this　movement　is　the　sun；　at　sunrise　or　sunset；　and　this　appearance　is　due　not　to　the　sun　itself　but　to　the　distance　from　which　we　observe　it。　The　visual　ray　being　excessively　prolonged　becomes　weak　and　wavering。　The　same　reason　probably　accounts　for　the　apparent　twinkling　of　the　fixed　stars　and　the　absence　of　twinkling　in　the　planets。　The　planets　are　near；　so　that　the　visual　ray　reaches　them　in　its　full　vigour；　but　when　it　comes　to　the　fixed　stars　it　is　quivering　because　of　the　distance　and　its　excessive　extension；　and　its　tremor　produces　an　appearance　of　movement　in　the　star：　for　it　makes　no　difference　whether　movement　is　set　up　in　the　ray　or　in　the　object　of　vision。　　　（2）　On　the　other　hand；　it　is　also　clear　that　the　stars　do　not　roll。　For　rolling　involves　rotation：　but　the　'face'；　as　it　is　called；　of　the　moon　is　always　seen。　Therefore；　since　any　movement　of　their　own　which　the　stars　possessed　would　presumably　be　one　proper　to　themselves；　and　no　such　movement　is　observed　in　them；　clearly　they　have　no　movement　of　their　own。　　　There　is；　further；　the　absurdity　that　nature　has　bestowed　upon　them　no　organ　appropriate　to　such　movement。　For　nature　leaves　nothing　to　chance；　and　would　not；　while　caring　for　animals；　overlook　things　so　precious。　Indeed；　nature　seems　deliberately　to　have　stripped　them　of　everything　which　makes　selforiginated　progression　possible；　and　to　have　removed　them　as　far　as　possible　from　things　which　have　organs　of　movement。　This　is　just　why　it　seems　proper　that　the　whole　heaven　and　every　star　should　be　spherical。　For　while　of　all　shapes　the　sphere　is　the　most　convenient　for　movement　in　one　place；　making　possible；　as　it　does；　the　swiftest　and　most　selfcontained　motion；　for　forward　movement　it　is　the　most　unsuitable；　least　of　all　resembling　shapes　which　are　self…moved；　in　that　it　has　no　dependent　or　projecting　part；　as　a　rectilinear　figure　has；　and　is　in　fact　as　far　as　possible　removed　in　shape　from　ambulatory　bodies。　Since；　therefore；　the　heavens　have　to　move　in　one　lace；　and　the　stars　are　not　required　to　move　themselves　forward；　it　is　natural　that　both　should　be　spherical…a　shape　which　best　suits　the　movement　of　the　one　and　the　immobility　of　the　other。　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　9
  From　all　this　it　is　clear　that　the　theory　that　the　movement　of　the　stars　produces　a　harmony；　i。e。　that　the　sounds　they　make　are　concordant；　in　spite　of　the　grace　and　originality　with　which　it　has　been　stated；　is　nevertheless　untrue。　Some　thinkers　suppose　that　the　motion　of　bodies　of　that　size　must　produce　a　noise；　since　on　our　earth　the　motion　of　bodies　far　inferior　in　size　and　in　speed　of　movement　has　that　effect。　Also；　when　the　sun　and　the　moon；　they　say；　and　all　the　stars；　so　great　in　number　and　in　size；　are　moving　with　so　rapid　a　motion；　how　should　they　not　produce　a　sound　immensely　great？　Starting　from　this　argument　and　from　the　observation　that　their　speeds；　as　measured　by　their　distances；　are　in　the　same　ratios　as　musical　concordances；　they　assert　that　the　sound　given　forth　by　the　circular　movement　of　the　stars　is　a　harmony。　Since；　however；　it　appears　unaccountable　that　we　should　not　hear　this　music；　they　explain　this　by　saying　that　the　sound　is　in　our　ears　from　the　very　moment　of　birth　and　is　thus　indistinguishable　from　its　contrary　silence；　since　sound　and　silence　are　discriminated　by　mutual　contrast。　What　happens　to　men；　then；　is　just　what　happens　to　coppersmiths；　who　are　so　accustomed　to　the　noise　of　the　smithy　that　it　makes　no　difference　to　them。　But；　as　we　said　before；　melodious　and　poetical　as　the　theory　is；　it　cannot　be　a　true　account　of　the　facts。　There　is　not　only　the　absurdity　of　our　hearing　nothing；　the　ground　of　which　they　try　to　remove；　but　also　the　fact　that　no　effect　other　than　sensitive　is　produced　upon　us。　Excessive　noises；　we　know；　shatter　the　solid　bodies　even　of　inanimate　things：　the　noise　of　thunder；　for　instance；　splits　rocks　and　the　strongest　of　bodies。　But　if　the　moving　bodies　are　so　great；　and　the　sound　which　penetrates　to　us　is　proportionate　to　their　size；　that　sound　must　needs　reach　us　in　an　intensity　many　times　that　of　thunder；　and　the　force　of　its　action　must　be　immense。　Indeed　the　reason　why　we　do　not　hear；　and　show　in　our　bodies　none　of　the　effects　of　violent　force；　is　easily　given：　it　is　that　there　is　no　noise。　But　not　only　is　the　explanation　evident；　it　is　also　a　corroboration　of　the　truth　of　the　views　we　have　advanced。　For　the　very　difficulty　which　made　the　Pythagoreans　say　that　the　motion　of　the　stars　produces　a　concord　corroborates　our　view。　Bodies　which　are　themselves　in　motion；　produce　noise　and　friction：　but　those　which　are　attached　or　fixed　to　a　moving　body；　as　the　parts　to　a　ship；　can　no　more　create　noise；　than　a　ship　on　a　river　moving　with　the　stream。　Yet　by　the　same　argument　one　might　say　it　was　absurd　that　on　a　large　vessel　the　motion　of　mast　and　poop　should　not　make　a　great　noise；　and　the　like　might　be　said　of　the　movement　of　the　vessel　itself。　But　sound　is　caused　when　a　moving　body　is　enclosed　in　an　unmoved　body；　and　cannot　be　caused　by　one　enclosed　in；　and　continuous　with；　a　moving　body　which　creates　no　friction。　We　may　say；　then；　in　this　matter　that　if　the　heavenly　bodies　moved　in　a　generally　diffused　mass　of　air　or　fire；　as　every　one　supposes；　their　motion　would　necessarily　cause　a　noise　of　tremendous　strength　and　such　a　noise　would　necessarily　reach　and　shatter　us。　Since；　therefore；　this　effect　is　evidently　not　produced；　it　follows　that　none　of　them　can　move　with　the　motion　either　of　animate　nature　or　of　constraint。　It　is　as　though　nature　had　foreseen　the　result；　that　if　their　movement　were　other　than　it　is；　nothing　on　this　earth　could　maintain　its　character。　　　That　the　stars　are　spherical　and　are　not　selfmoved；　has　now　been　explained。
  10
  With　their　order…I　mean　the　position　of　each；　as　involving　the　priority　of　some　and　the　posteriority　of　others；　and　their　respective　distances　from　the　extremity…with　this　astronomy　may　be　left　to　deal；　since　the　astronomical　discussion　is　adequate。　This　discussion　shows　that　the　movements　of　the　several　stars　depend；　as　regards　the　varieties　of　speed　which　they　exhibit；　on　the　distance　of　each　from　the　extremity。　It　is　established　that　the　outermost　revolution　of　the　heavens　is　a　simple　movement　and　the　swiftest　of　all；　and　that　the　movement　of　all　other　bodies　is　composite　and　relatively　slow；　for　the　reason　that　each　is　moving　on　its　own　circle　with　the　reverse　motion　to　that　of　the　heavens。　This　at　once　leads　us　to　expect　that　the　body　which　is　nearest　to　that　first　simple　revolution　should　take　the　longest　time　to　complete　its　circle；　and　that　which　is　farthest　from　it　the　shortest；　the　others　taking　a　longer　time　the　nearer　they　are　and　a　shorter　time　the　farther　away　they　are。　For　it　is　the　nearest　body　which　is　most　strongly　influenced；　and　the　most　remote；　by　reason　of　its　distance；　which　is　least　affected；　the　influence　on　the　intermediate　bodies　varying；　as　the　mathematicians　show；　with　their　distance。
  11
  With　regard　to　the　shape　of　each　star；　the　most　reasonable　view　is　that　they　are　spherical。　It　has　been　shown　that　it　is　not　in　their　nature　to　move　themselves；　and；　since　nature　is　no　wanton　or　random　creator；　clearly　she　will　have　given　things　which　possess　no　movement　a　shape　particularly　unadapted　to　movement。　Such　a　shape　is　the　sphere；　since　it　possesses　no　instrument　of　movement。　Clearly　then　their　mass　will　have　the　form　of　a　sphere。　Again；　what　holds　of　one　holds　of　all；　and　the　evidence　of　our　eyes　shows　us　that　the　moon　is　spherical。　For　how　else　should　the　moon　as　it　waxes　and　wanes　show　for　the　most　part　a　crescent…shaped　or　gibbous　figure；　and　only　at　one　moment　a　half…moon？　And　astronomical　arguments　give　further　confirmation；　for　no　other　hypothesis　accounts　for　the　crescent　shape　of　the　sun's　eclipses。　One；　then；　of　the　heavenly　bodies　being　spherical；　clearly　the　rest　will　be　spherical　also。
  12
  There　are　two　difficulties；　which　may　very　reasonably　here　be　raised；　of　which　we　must　now　attempt　to　state　the　probable　solution：　for　we　regard　the　zeal　of　one　whose　thirst　after　philosophy　leads　him　to　accept　even　slight　indications　where　it　is　very　difficult　to　see　one's　way；　as　a　proof　rather　of　modesty　than　of　overconfidence。　　　Of　many　such　problems　one　of　the　strangest　is　the　problem　why　we　find　the　greatest　number　of　movements　in　the　intermediate　bodies；　and　not；　rather；　in　each　successive　body　a　variety　of　movement　proportionate　to　its　distance　from　the　primary　motion。　For　we　should　expect；　since　the　primary　body　shows　one　motion　only；　that　the　body　which　is　near