file :i* includes ! orig9al illu/rations4 ,see #bdbcf-;h4htm or #bdbcf-;h4zip3 7https3_/_/www4gut5b]g4org_/dirs_/#b_/d_ /b_/c_/bdbcf_/bdbcf-;h_/#bdbcf-;h4htm7 or 7https3_/_/www4gut5b]g4org_/dirs_/#b_/d_ /b_/c_/bdbcf_/bdbcf-;h4zip7 ,! ,romance ( ,sci5ce4 ,,"t ,,& ,,tide1 ,a ,romance ( ! ,moon4 ,be+ ,two ,lectures ,deliv]$ 9 ! ,!atre ( ! ,london ,in/itution1 on ! ,aft]noons ( ,novemb] #ai & #bf1 #ahhh4 by ,,sir ,,rob]t ,s4 ,,ball1 ,,ll4,d41 ,f4,r4,s41 ,royal ,a/ronom] ( ,irel&4 ,publi%$ "u ! ,direction ( ! ,committee ( ,g5]al ,lit]ature & ,education ,appo9t$ by ! ,society = ,promot+ ,*ri/ian ,k4 ,london3 ,society = ,promot+ ,*ri/ian ,k1 ,nor?umb]l& ,av5ue1 ,w4,c42 #dc1 ,que5 ,victoria ,/reet1 ,e4,c4 ,brighton3 #ace1 ,nor? ,/reet4 ,new ,york3 ,e4 ,j4 ,b4 ,"y ,co4 ,illu/ration3 ,,view ,,( ,,! ,,moon ,,two ,,days ,,aft] ,,fir/ ,,qu>t]4 ,f a photograph by ,mr4 ,,lewis ,m4 ,,ru!r=d4 ,frontispiece4 ,,to ,! ,memb]s ( ! ,london ,in/itution ,i ,,d$icate ,,?is ,,little ,,book4 ,,preface4 ,hav+ be5 hon\r$ once aga9 ) a reque/ t ,i %\ld lecture be=e ! ,london ,in/itution1 ,i *ose = my subject ! ,!ory ( ,tidal ,evolution4 ,! k9d reception :i* ^! lectures receiv$ has l$ to _! publication 9 ! pres5t volume4 ,i h tak5 ! opportunity to supplem5t ! lectures z actually deliv]$ by ! ins]tion ( "s additional matt]4 ,i am indebt$ to my fri5ds ,mr4 ,close & ,mr4 ,rambaut = _! k9dness 9 read+ ! pro(s4 ,,rob]t ,s4 ,,ball4 ,obs]vatory1 ,,co4 ,,dubl91 ,april #bf1 #ahhi4 ,,"t ,,& ,,tide4 ,,lecture ,i4 ,x is my privilege to address y ?is aft]noon on a subject 9 :i* sci5ce & poetry are bl5d$ 9 a happy conjunction4 ,if !re be a peculi> fasc9ation ab\t ! e>li] *apt]s ( any bran* ( hi/ory1 h[ great mu/ be ! int]e/ :i* atta*es to t mo/ primeval ( all t]re/rial hi/ories :i* relates to ! actual beg9n+s ( ?is globe on :i* we /&4 ,9 our ef=ts to grope into ! dim recesses ( ?is awful pa/1 we want ! aid ( "s /eadfa/ light :i* %all illum9e ! d>k places )\t ! trea*]y ( ! w-o'-!-wisp4 ,9 ! abs5ce ( t /eadfa/ light1 vague conjectures z to ! beg9n+ ( ?+s c\ld nev] be entitl$ to any m respect ?an 0 due to m]e matt]s ( speculation4 ,( late1 h[ev]1 ! requir$ light has be5 to "s consid]able ext5t =?com+1 & ! attempt has be5 made1 ) no little success1 to elucidate a mo/ int]e/+ & wond]ful *apt] ( an exce$+ly remote hi/ory4 ,to *ronicle ?is hi/ory is ! object ( ! pres5t lectures be=e ?is ,in/itution4 ,fir/1 let u be fully aw>e ( ! extraord9>y remot5ess ( t p]iod ( :i* our hi/ory treats4 ,to attempt to def9e t p]iod *ronologically w\ld be utt]ly futile4 ,:5 we h /at$ t x is m anci5t ?an almo/ any o!r p]iod :i* we c discuss1 we h express$ all t we are really entitl$ to say4 ,yet ?is conveys n a little4 ,x directs u to look back ?r\gh all ! ages ( mod]n human hi/ory1 ?r\gh ! great days ( anci5t ,greece & ,rome1 back ?r\gh ! times :5 ,egypt & ,assyria 7 names ( r5[n1 ?r\gh ! days :5 ,n9eveh & ,babylon 7 mighty & popul\s cities 9 ! z5i? ( _! glory4 ,back e>li] /ill to ^? m anci5t nations ( :i* we "k h>dly any?+1 & /ill e>li] to ! prehi/oric man1 ( :om we "k less2 back1 f9ally1 to ! days :5 man fir/ trod on ?is planet1 untold ages ago4 ,"h is inde$ a port5t\s retrospect f mo/ po9ts ( view1 b x is only ! comm5cem5t ( t :i* our subject sugge/s4 ,= man is b ! f9al product ( ! long ant]ior ages dur+ :i* ! developm5t ( life seems to h und]gone an exce$+ly gradual elevation4 ,our retrospect n[ takes its way along ! vi/as op5$ up by ! geologi/s4 ,we look ?r\gh ! protract$ t]ti>y ages1 :5 mighty animals1 n[ g5]ally ext9ct1 roam$ ov] ! cont95ts4 ,back /ill e>li] ?r\gh ^? wondr\s second>y p]iods1 :]e swamps or oceans (t5 cov]$ :at is n[ dry l&1 & :]e mighty reptiles ( unc\? =ms /alk$ & crawl$ & swam ?r\gh ! old _w & ! new4 ,back /ill e>li] ?r\gh ^? vitally significant ages :5 ! sunbeams 7 be+ g>n]$ & laid aside = man's use 9 ! great =e/s1 :i* 7 aft]w>ds pres]v$ by be+ trans=m$ into seams ( coal4 ,back /ill e>li] ?r\gh endless ?\s&s ( ye>s1 :5 lu/r\s fi%es ab\nd$ 9 ! oceans2 back aga9 to ^? p]iods *>act]iz$ by ! l[] types ( life2 & /ill e>li] to t incr$ibly remote epo* :5 life itself began to dawn on our awak5+ globe4 ,ev5 "h ! epo* ( our pres5t hi/ory c h>dly be said to h be5 rea*$4 ,we h to look ?r\gh a long succession ( ages /ill antec$5t4 ,! geologi/1 :o has hi!rto guid$ our view1 _c r5d] u mu* fur!r assi/ance2 b ! physici/ is at h&--he tea*es u t ! w>m globe on :i* life is beg9n+ has pass$ 9 its previ\s /ages ?r\gh e phase ( w>m?1 ( f]v\r1 ( gl[+ heat1 ( inc&esc5ce1 & ( actual fusion2 & ?us at la/ our retrospect rea*es to t p>ticul> p]iod ( our e>?'s pa/ hi/ory :i* is specially illu/rat$ by ! mod]n doctr9e ( ,"t & ,tide4 ,! pres5t is ! clue to ! pa/4 ,x is ! /eady application ( ?is pr9ciple :i* has l$ to su* epo*-mak+ lab\rs z ^? by :i* ,lyell disclos$ ! orig9 ( ! e>?'s cru/1 ,d>w9 ! orig9 ( species1 ,max ,mll] ! orig9 ( language4 ,9 our pres5t subject ! c\rse is equally cle>4 ,/udy exactly :at is go+ on at pres5t1 & !n h ! c\rage to apply consi/5tly & rigor\sly :at we h le>n$ f ! pres5t to ! int]pretation ( ! pa/4 ,?us we beg9 ) ! ripple ( ! tide on ! sea-bea* :i* we see to-day4 ,! ebb & ! fl[ ( ! tide are ! pres5t manife/ations ( an ag5t :i* has be5 con/antly at "w4 ,let t pres5t tea* u :at tides mu/ h done 9 ! indef9ite pa/4 ,x has be5 kn[n f ! v e>lie/ times t ! moon & ! tides 7 connect$ toge!r--connect$1 ,i say1 = a great advance _h to be made 9 human k be=e x w\ld h be5 possible to und]/& ! true relation betwe5 ! tides & ! moon4 ,inde$1 t relation is s f> f be+ ( an obvi\s "*1 t ,i ?9k ,i h read ( a race :o felt "s d\bt z to :e!r ! moon 0 ! cause ( ! tides1 or ! tides ! cause ( ! moon4 ,i %\ld1 h[ev]1 say t ! moon is n ! sole ag5t engag$ 9 produc+ ?is p]iodic movem5t ( our wat]s4 ,! sun also ar\ses a tide1 b ! sol> tide is s small 9 comp>ison ) t produc$ by ! moon1 t = our pres5t purpose we may leave x out ( consid]ation4 ,we mu/1 h[ev]1 ref] to ! sol> tide at a lat] p]iod ( our disc\rses1 = x w be f\nd to h play$ a v spl5did "p at ! initial /age ( ! ,e>?-,moon ,hi/ory1 :ile 9 ! remote future x w aga9 rise into prom95ce4 ,x w be well to set =? a few prelim9>y figures :i* %all expla9 h[ x comes to pass t ! effici5cy ( ! sun z a tide-produc+ ag5t is s greatly inf]ior to t ( ! moon4 ,inde$1 consid]+ t ! sun has a mass s /up5d\s1 t x controls ! entire planet>y sy/em1 h[ is x t a body s insignificant z ! moon c raise a bigg] tide on ! ocean ?an c ! sun1 ( :i* ! mass is #bf1jjj1jjj times z great z t ( our satellite8 ,?is app>5t p>adox w disappe> :5 we enunciate ! law accord+ to :i* ! effici5cy ( a tide-produc+ ag5t is to be e/imat$4 ,?is law is some:at diff]5t f ! famili> =m 9 :i* ! law ( gravitation is express$4 ,! gravitation betwe5 two di/ant masses is to be measur$ by multiply+ ^! masses toge!r1 & divid+ ! product by ! squ>e ( ! di/ance4 ,! law = express+ ! effici5cy ( a tide-produc+ ag5t v>ies n accord+ to ! inv]se squ>e1 b accord+ to ! inv]se cube ( ! di/ance4 ,?is diff]5ce 9 ! expression ( ! law w suffice to acc\nt = ! sup]iority ( ! moon z a tide-produc] ov] ! sun4 ,! moon's di/ance on an av]age is ab\t "o #chf? "p ( t ( ! sun1 & ?us x is easy to %[ t s f> z ! m]e attraction ( gravitation is conc]n$1 ! effici5cy ( ! sun's =ce on ! e>? is ab\t "o hundr$ & sev5ty-five times z great z ! =ce ) :i* ! moon attracts ! e>?4 ,t is ( c\rse calculat$ "u ! law ( ! inv]se squ>e4 ,to det]m9e ! tidal effici5cy we h to divide ?is by ?ree hundr$ & eighty-six1 & ?us we see t ! tidal effici5cy ( ! sun is less ?an half t ( ! moon4 ,:5 ! sol> tide & ! lun> tide are act+ 9 unison1 !y conspire to produce v high tides & v l[ tides1 or1 z we call !m1 spr+ tides4 ,on ! o!r h&1 :5 ! sun is s plac$ z to give u a l[ tide :ile ! moon is produc+ a high tide1 ! net result t we actually exp]i5ce is m]ely ! excess ( ! lun> tide ov] ! sol> tide2 ^! are :at we call neap tides4 ,9 fact1 by v c>eful & long-cont9u$ obs]vations ( ! rise & fall ( ! tides at a p>ticul> port1 x becomes possible to det]m9e ) accuracy ! relative ranges ( spr+ tides & neap tides2 & z ! spr+ tides are produc$ by moon plus sun1 :ile ! neap tides are produc$ by moon m9us sun1 we obta9 a means ( actually weigh+ ! relative masses ( ! sun & moon4 ,?is is "o ( ! rem>kable facts :i* c be d$uc$ f a prolong$ /udy ( ! tides4 ,! demon/ration ( ! law ( ! tide-produc+ =ce is ( a ma!matical "*1 & ,i d n int5d 9 ^! lectures to ent] into ma!matical calculations4 ,!re is1 h[ev]1 a simple l9e ( reason+ :i*1 ?\gh x falls f> %ort ( actual demon/ration1 may yet suffice to give a plausible reason = ! law4 ,! tides really owe _! orig9 to ! fact t ! tide-produc+ ag5t op]ates m p[]fully on ^? p>ts ( ! tide-exhibit+ body :i* are ne> to x1 ?an on ! m di/ant portions ( ! same4 ,! ne>] ! two bodies are toge!r1 ! l>g] proportionally w be ! diff]5ces 9 ! di/ances ( its v>i\s p>ts f ! tide-produc+ body2 & on ?is acc\nt ! lev]age1 s to speak1 ( ! action by :i* ! tides are produc$ is increas$4 ,= in/ance1 if ! two bodies 7 br\ght )9 half _! orig9al di/ance ( ea* o!r1 ! relative size ( ea* body1 z view$ f ! o!r1 w be d\bl$2 & :at we h call$ ! lev]age ( ! tide-produc+ ability w be increas$ tw(old4 ,! gravitation also betwe5 ! two bodies is increas$ f\rfold :5 ! di/ance is halv$1 & consequ5tly1 ! tide-produc+ ability is d\bl$ = "o reason1 & increas$ f\rfold aga9 by ano!r2 h5ce1 ! tides w be increas$ eightfold :5 ! di/ance is r$uc$ to "o half4 ,n[1 z eight is ! cube ( two1 ?is illu/ration may be tak5 z a v]ification ( ! law1 t ! effici5cy ( a body z a tide-produc] v>ies inv]sely z ! cube ( ! di/ance betwe5 x & ! body on :i* ! tides are be+ rais$4 ,= simplicity we may make ! assumption t ! :ole ( ! e>? is buri$ b5ea? ! ocean1 & t ! moon is plac$ 9 ! plane ( ! equator4 ,we may also entirely neglect = ! pres5t ! tides produc$ by ! sun1 & we %all also make ! fur!r assumption t friction is abs5t4 ,:at friction is capable ( do+ we %all1 h[ev]1 ref] to lat] on4 ,! moon w act on ! ocean & de=m x1 s t !re w be high tide along "o m]idian1 & high tide also on ! opposite m]idian4 ,?is is inde$ "o ( ! p>adoxes by :i* /ud5ts are frequ5tly puzzl$ :5 !y beg9 to le>n ab\t ! tides4 ,t ! moon %\ld pull ! wat] up 9 a heap on "o side seems plausible en\gh4 ,high tide w ( c\rse be !re2 & ! /ud5t might naturally ?9k t ! wat] be+ drawn 9 ?is way into a heap on "o side1 !re w ( c\rse be l[ tide on ! opposite side ( ! e>?4 ,a natural assumption1 p]haps1 b nev]!less a v wrong "o4 ,!re are at e mom5t two opposite p>ts ( ! e>? 9 a condition ( high wat]2 9 fact1 ?is w be obvi\s if we rememb] t e day1 or1 to speak a little m accurately1 9 e tw5ty-f\r h\rs & fifty "o m9utes1 we h on ! av]age two high tides at ea* locality4 ,( c\rse ?is c\ld n be if ! moon rais$ only "o heap ( high wat]1 because1 z ! moon only appe>s to revolve ar\nd ! e>? once a day1 or1 m accurately1 once 9 t same av]age p]iod ( tw5ty-f\r h\rs & fifty-"o m9utes1 x w\ld be impossible = u to h high tides succe$+ ea* o!r z !y d 9 p]iods a little long] ?an twelve h\rs1 if only "o heap 7 c>ri$ r\nd ! e>?4 ,! fir/ "q !n is1 z to h[ ^! two opposite heaps ( wat] are plac$ 9 respect to ! position ( ! moon4 ,! mo/ obvi\s explanation w\ld seem to be1 t ! moon %\ld pull ! wat]s up into a heap directly und]nea? x1 & t !re=e !re %\ld be high wat] und]nea? ! moon4 ,z to ! o!r side1 ! pres5ce ( a high tide !re 01 on ?is !ory1 to be acc\nt$ = by ! fact t ! moon pull$ ! e>? away f ! wat]s on ! m remote side1 j z x pull$ ! wat]s away f ! m remote e>? on ! side und]nea? ! moon4 ,x is1 h[ev]1 c]ta9ly n ! case t ! high tide is situat$ 9 ! simple position t ?is law w\ld indicate1 & :i* we h repres5t$ 9 ,fig4 #a1 :]e ! circul> body is ! e>?1 ! ocean surr\nd+ :i* is di/ort$ by ! action ( ! tides4 ,illu/ration3 ,,fig4 #a4 ,we h "h tak5 an oval to repres5t ! %ape into :i* ! wat] is suppos$ to be =c$ or drawn by ! tidal action ( ! tide-produc+ body4 ,?is may possibly be a correct repres5tation ( :at w\ld occur on an ideal globe entirely cov]$ ) a frictionless ocean4 ,b z our e>? is n cov]$ entirely by wat]1 & z ! ocean is v f> f be+ frictionless1 ! ideal tide is n ! tide t we actually "k2 nor is ! ideal tide repres5t$ by ?is oval ev5 an approximation to ! actual tides to :i* our oceans are subject4 ,inde$1 ! oval does n repres5t ! facts at all1 & ( ?is x is only necess>y to adduce a s+le fact 9 demon/ration4 ,i take ! fundam5tal issue s (t5 debat$1 z to :e!r 9 ! ocean vibrat+ ) ideal tides ! high wat] or ! l[ wat] %\ld be "u ! moon4 ,or to put ! matt] o!rwise2 :5 we repres5t ! displac$ wat] by an oval1 is ! long axis ( ! oval to be turn$ to ! moon1 z g5]ally suppos$1 or is x to be direct$ at "r angles !refrom8 ,if ! ideal tides 7 9 any degree repres5tative ( ! actual tides1 s fundam5tal a "q z ?is c\ld be at once answ]$ by an appeal to ! facts ( obs]vation4 ,ev5 if friction 9 "s degree mask$ ! ph5om5a1 surely "o w\ld ?9k t ! /ate ( ! actual tides %\ld /ill enable u to answ] ?is "q4 ,b a /udy ( ! tides at diff]5t ports fails to realize ?is expectation4 ,at "s ports1 no d\bt1 ! tide is high :5 ! moon is on ! m]idian4 ,9 t case1 ( c\rse1 ! high wat] is "u ! moon1 z app>5tly ought to be ! case inv>iably1 on a sup]ficial view4 ,b1 on ! o!r h&1 !re are ports :]e !re is (t5 l[ wat] :5 ! moon is cross+ ! m]idian4 ,yet o!r ports might be cit$ 9 :i* e int]m$iate phase c\ld be obs]v$4 ,if ! !ory ( ! tides 0 to be ! simple "o s (t5 describ$1 !n at e port noon %\ld be ! h\r ( high wat] on ! day ( ! new moon or ( ! full moon1 because !n bo? tide-excit+ bodies are on ! m]idian at ! same "t4 ,ev5 if ! friction ret>d$ ! great tidal wave uni=mly1 ! high tide on ! days ( full or *ange %\ld always occur at fix$ h\rs2 b1 un=tunately1 !re is no su* delightful !ory ( ! tides z ?is w\ld imply4 ,at ,gre5ock no d\bt !re is high wat] at or ab\t noon on ! day ( full or *ange2 & if x c\ld be simil>ly said t on ! day ( full or *ange !re 0 high wat] ev]y:]e at local noon1 !n ! equilibrium !ory ( ! tides1 z x is call$1 w\ld be beautifully simple4 ,b ?is is n ! case4 ,ev5 ar\nd our own coa/s ! discrepancies are su* z to utt]ly discr$it ! !ory z (f]+ any practical guide4 ,at ,ab]de5 ! high tide does n appe> till an h\r lat] ?an ! doctr9e w\ld sugge/4 ,x is two h\rs late at ,london1 ?ree at ,tynem\?1 f\r at ,tralee1 five at ,sligo1 & six at ,hull4 ,?is la/ port w\ld be inde$ ! hav5 ( refuge = ^? :o believe t ! l[ tide ought to be "u ! moon4 ,at ,hull ?is is no d\bt ! case2 & if at all o!r places ! wat] behav$ z x does at ,hull1 :y !n1 ( c\rse1 x w\ld foll[ t ! law ( l[ wat] "u ! moon 0 g5]ally true4 ,b !n ?is w\ld n tally ) ! condition ( affairs at ! o!r places ,i h nam$2 & to complete ! cycle ,i %all add a few m4 ,at ,bri/ol ! high wat] does n get up until sev5 h\rs aft] ! moon has pass$ ! m]idian1 at ,arkl[ ! delay is eight h\rs1 at ,y>m\? x is n9e1 at ! ,ne$les x is t5 h\rs1 :ile la/ly1 ! moon has ne>ly got back to ! m]idian aga9 ere x has succe$$ 9 dragg+ up ! tide on :i* ,liv]pool's great comm]ce s l>gely dep5ds4 ,nor does ! result ( /udy+ ! tides along o!r coa/s beside our own decide m conclusively on ! moot$ po9t4 ,ev5 ports 9 ! va/ ocean give a v unc]ta9 response4 ,k]guel5 ,isl& & ,santa ,cruz might seem to prove t ! high tide occurs "u ! moon1 b un=tunately bo? ,fiji & ,asc5sion seem to pres5t u ) an equally satisfactory demon/ration1 t b5ea? ! moon is ! inv>iable home ( l[ wat]4 ,i d n mean to say t ! /udy ( ! tides is 9 o!r respects su* a confus$ subject z ! facts ,i h /at$ w\ld seem to indicate4 ,x becomes r puzzl+1 no d\bt1 :5 we comp>e ! tides at "o port ) ! tides else:]e4 ,! law & ord] are1 !n1 by no means conspicu\s1 !y are (t5 h>dly disc]nible4 ,b :5 we conf9e our att5tion to ! tides at a s+le port1 ! problem becomes at once a v intelligible "o4 ,inde$1 ! inve/igation ( ! tides is an easy subject1 if we are cont5t$ ) a reasonably approximate solution2 %\ld1 h[ev]1 x be necess>y to discuss fully ! tides at any port1 ! !ory ( ! me?od necess>y = do+ s is available1 & a mo/ int]e/+ & beautiful !ory x c]ta9ly is4 ,let u !n speak = a few mom5ts ab\t ! me?ods by :i* we c /udy ! tides at a p>ticul> port4 ,! pr9ciple on :i* x is bas$ is a v simple "o4 ,x is ! mon? ( ,augu/1 ! #ah?1 we %all suppose1 & we are go+ to enjoy a delici\s swim 9 ! sea4 ,we desire1 ( c\rse1 to secure a high tide = ! purpose ( do+ s1 & we call an almanac to help u4 ,i ref] to ! ,?om's ,dubl9 ,directory1 :]e ,i f9d ! tide to be high at #aj;h4 #adm4 on ! morn+ ( ! #ah? ( ,augu/4 ,t w !n be ! "t to g d[n to ! ba?s at ,h[? or ,k+/[n4 ,b :at ,i am n[ go+ to disc\rse to y ab\t is n ! delights ( sea-ba?+1 x is r a diff]5t inquiry4 ,i want to ask1 ,h[ did ! p :o prep>$ t almanac "k ye>s be=eh&1 t on t p>ticul> day ! tide w\ld be high at t p>ticul> h\r8 ,h[ d !y pr$ict = e day ! h\r ( high wat]8 & h[ comes x to pass t ^! pr$ictions are inv>iably correct8 ,we fir/ ref] to t wond]ful book1 ! ,nautical ,almanac4 ,9 t volume ! movem5ts ( ! moon are set =? ) full detail2 & among o!r p>ticul>s we c le>n on page iv ( e mon? ! mean "t ( ! moon's m]idian passage4 ,x appe>s t on ! day 9 "q ! moon cross$ ! m]idian at #aa;h4 #bcm4 ,?us we see !re 0 high wat] at ,dubl9 at #aj;h4 #adm41 & #a;h4 #im4 lat]1 t is1 at #aa;h4 #bcm41 ! moon cross$ ! m]idian4 ,let u take ano!r in/ance4 ,!re is a high tide at #c4dj ,p4,m4 on ! #be? ,augu/1 & aga9 ! infallible ,nautical ,almanac tells u t ! moon cross$ ! m]idian at #e;h4 #ddm41 t is1 at #b;h4 #dm4 aft] ! high wat]4 ,9 ! fir/ case ! moon foll[$ ! tide 9 ab\t an h\r1 & 9 ! second case ! moon foll[$ 9 ab\t two h\rs4 ,n[ if we are to be satisfi$ ) a v r\gh tide rule = ,dubl91 we may say g5]ally t !re is always a high tide an h\r & a half be=e ! moon crosses ! m]idian4 ,?is w\ld n be a v accurate rule1 b ,i c assure y ( ?is1 t if y g by x y w nev] fail ( f9d+ a good tide to enable y to enjoy y\r swim4 ,i d n say ?is rule w\ld enable y to con/ruct a respectable tide-table4 ,a %ip-own] :o has to creep up ! riv]1 & to :om (t5 ! in*es ( wat] are mat]ial1 w require f> m accurate tables ?an ?is simple rule c\ld give4 ,b we ent] into r complicat$ matt]s :5 we attempt to give any really accurate me?ods ( computation4 ,on ^! we %all say a few words pres5tly4 ,:at ,i fir/ want to d1 is to impress ^u y 9 a simple way ! fact ( ! relation betwe5 ! tide & ! moon4 ,to give ano!r illu/ration1 let u see h[ ! tides at ,london ,bridge are relat$ to ! moon4 ,on ,jan4 #a/1 #ahhg1 x appe>$ t ! tide 0 high at #f;h4 #bfm4 ,p4,m41 & t ! moon _h cross$ ! m]idian #efm4 previ\sly2 on ! #h? ,jan4 ! tide 0 high at #j;h4 #dcm4 ,p4,m41 & ! moon _h cross$ ! m]idian #b;h4 #am4 previ\sly4 ,!re=e we w\ld h at ,london ,bridge high wat] foll[+ ! moon's transit 9 some:]e ab\t an h\r & a half4 ,i *oose a day at r&om1 = example--! #ab? ,april4 ,! moon crosses ! upp] m]idian at #c;h4 #cim4 ,a4,m41 & ! l[] m]idian at #d;h #fm4 ,p4,m4 ,add+ an h\r & a half to ea* w\ld give ! high tides at #e;h #im4 ,a4,m4 & #e;h4 #cfm4 ,p4,m42 z a matt] ( fact1 !y are #d;h4 #ehm4 ,a4,m4 & #e;h4 #bjm4 ,p4,m4 ,b ^! illu/rations are suffici5t4 ,we f9d t at ,london1 9 a g5]al way1 high wat] appe>s at ,london ,bridge ab\t an h\r & a half aft] ! moon has pass$ ! m]idian ( ,london4 ,x s happ5s t ! int]val at ,dubl9 is ab\t ! same1 i4e4 an h\r & a half2 only t 9 ! latt] case ! high wat] prec$es ! moon by t int]val in/ead ( foll[+ x4 ,we may employ ! same simple process at o!r places4 ,*oose two days ab\t a week di/ant2 f9d on ea* occasion ! int]val betwe5 ! transit ( ! moon & ! "t ( high wat]1 !n ! mean ( ^! two diff]5ces w always give "s notion ( ! int]val betwe5 high wat] & ! moon's transit4 ,if !n we take f ! ,nautical ,almanac ! "t ( ! moon's transit1 & apply to x ! correction prop] = ! port1 we %all always h a suffici5tly good tide-table to guide u 9 *oos+ a suitable "t = tak+ our swim or our walk by ! sea-side2 ?\gh if y be ! capta9 ( a vessel1 y w n be s imprud5t z to ent] port )\t tak+ c\nsel ( ! accurate tide-tables1 = :i* we are indebt$ to ! ,admiralty4 ,e "o :o visits ! sea-side1 or :o lives at a sea-port1 %\ld "k ?is con/ant = ! tides1 :i* affect him & 8 movem5ts s mat]ially4 ,if he w discov] x f 8 own exp]i5ce1 s mu* ! bett]4 ,! fir/ po9t to be asc]ta9$ is ! "t ( high wat]4 ,d n take ?is f any local table2 y ought to obs]ve x = y\rself4 ,y w g to ! pi] head1 or1 bett] /ill1 to "s place :]e ! rise & fall ( ! m]e waves ( ! sea w n emb>rass y 9 y\r "w4 ,y mu/ note by y\r wat* ! "t :5 ! tide is highe/4 ,an accurate way ( do+ ?is w be to h a scale on :i* y c measure ! height at int]vals ( five m9utes ab\t ! "t ( high wat]4 ,y w !n be able to conclude ! "t at :i* ! tide 0 actually at its highe/ po9t2 b ev5 if no great accuracy be obta9able1 y c /ill get mu* int]e/+ in=mation1 = y w )\t mu* difficulty be "r )9 t5 m9utes or a qu>t] ( an h\r4 ,! correction = ! port is prop]ly call$ ! e/abli%m5t1 ?is be+ ! av]age "t ( high wat] on ! days ( full & *ange ( ! moon at ! p>ticul> port 9 "q4 ,we c consid]ably am5d ! elem5t>y notion ( ! tides :i* ! =m] me?od has giv5 u1 if we adopt ! plan describ$ by ,dr4 ,:ewell 9 ! fir/ f\r editions ( ! ,admiralty ,manual ( ,sci5tific ,inquiry4 ,we speak ( ! int]val betwe5 ! transit ( ! moon & ! "t ( high wat] z ! luni-tidal int]val4 ,( c\rse at full & *ange ?is is ! same ?+ z ! e/abli%m5t1 b = o!r phases ( ! moon ! e/abli%m5t mu/ receive a correction be=e be+ us$ z ! luni-tidal int]val4 ,! correction is giv5 by ! foll[+ table-- ,h\r ( ,moon's transit aft] ,sun3 #j #a #b #c #d #e #f #g #h #i #aj #aa ---------------------------------------- ----- #j-bjm-#cjm-#ejm-#fjm-#fjm-#fjm-#djm-#aj m#ajm#bjm#ajm ,correction ( e/abli%m5t to f9d luni-tidal int]val3 ,?us at a port :]e ! e/abli%m5t 0 #c;h4 #bem41 let u suppose t ! transit ( ! moon took place at #f ,p4,m42 !n we correct ! e/abli%m5t by -#fjm41 & f9d ! luni-tidal int]val to be #b;h4 #bem41 & accord+ly ! high wat] takes place at #h;h4 #bem4 ,p4,m4 ,b ev5 ?is me?od is only an approximation4 ,! /udy ( ! tides is bas$ on accurate obs]vation ( _! rise & fall on diff]5t places r\nd ! e>?4 ,to %[ h[ ^! obs]vations are to be made1 & h[ !y are to be discuss$ & r$uc$ :5 !y h be5 made1 ,i may ref] to ! la/ edition ( ! ,admiralty ,manual ( ,sci5tific ,inquiry1 #ahhf4 ,= a complete /udy ( ! tides at any port a self-regi/]+ tide-gauge %\ld be erect$1 on :i* n alone ! heights & times ( high & l[ wat] %\ld be depict$1 b also ! cont9u\s curve :i* %[s at any "t ! height ( ! wat]4 ,9 fact1 ! :ole subject ( ! practical obs]vation & discussion & pr$iction ( tides is full ( valuable in/ruction1 & may be cit$ z "o ( ! mo/ complete examples ( ! mod]n sci5tific me?ods4 ,9 ! fir/ place1 ! tide-gauge itself is a delicate in/rum5t2 x is actuat$ by a float :i* rises & falls ) ! wat]1 due provision be+ made t ! m]e influ5ce ( waves %all n make x to oscillate inconv5i5tly4 ,! motion ( ! float :5 suitably r$uc$ by me*anism s]ves to guide a p5cil1 :i*1 act+ on ! pap] r\nd a revolv+ drum1 gives a fai?ful & un9t]mitt+ record ( ! height ( ! wat]4 ,?us :at ! tide-gauge does is to pres5t to u a long curv$ l9e ( :i* ! summits correspond to ! heights ( high wat]1 :ile ! depressions are ! correspond+ po9ts ( l[ wat]4 ,! long undulations ( ?is curve are1 h[ev]1 v irregul>4 ,at spr+ tides1 :5 ! sun & ! moon conspire1 ! elevations rise mu* high] & ! depressions s9k mu* l[] ?an !y d at neap tides1 :5 ! high wat] rais$ by ! moon is r$uc$ by ! action ( ! sun4 ,!re are also _m m9or irregul>ities :i* %[ ! tides to be n ne>ly su* simple ph5om5a z might be at fir/ suppos$4 ,b :at we might ha/ily ?9k ( z irregul>ities are1 9 tru?1 ! mo/ int]e/+ p>ts ( ! :ole ph5om5a4 ,j z 9 ! obs]vations ( ! planets ! /udy ( ! p]turbations has l$ u to results ( ! wide/ int]e/ & in/ruction1 s x is ^! m9or ph5om5a ( ! tides :i* seem mo/ pregnant ) sci5tific int]e/4 ,! tide-gauge gives u an elaborate curve4 ,h[ are we to int]pret t curve8 ,"h inde$ a mo/ beautiful ma!matical !orem comes to our aid4 ,j z ord9>y s\nds consi/ ( a numb] ( undulations bl5d$ toge!r1 s ! tidal wave consi/s ( a numb] ( di/9ct undulations sup]pos$4 ,( ^! ! ord9>y lun> tide & ! ord9>y sol> tide are ! two pr9cipal2 b !re are also m9or undulations1 h>monics1 s to speak1 "s orig9at+ f ! moon1 "s orig9at+ f ! sun1 & "s f bo? bodies act+ 9 conc]t4 ,9 ! /udy ( s\nd we c employ an ac\/ic app>atus = ! purpose ( decompos+ any propos$ note1 & f9d+ n only ! ma9 undulation itself1 b ! sev]al sup]pos$ h>monics :i* give to ! note its timbre4 ,s also we c analyze ! undulation ( ! tide1 & %[ ! compon5t p>ts4 ,! decomposition is effect$ by ! process kn[n z h>monic analysis4 ,! pr9ciple ( ! me?od may be v simply describ$4 ,let u fix our att5tion on any p>ticul> tide1 = s ! v>i\s elem5ts are d5ot$4 ,we c always det]m9e be=eh&1 ) z mu* accuracy z we may require1 :at ! p]iod ( t tide w be4 ,= in/ance1 ! p]iod ( ! lun> semi-diurnal tide w ( c\rse be half ! av]age "t occupi$ by ! moon to travel r\nd f ! m]idian ( any place until x rega9s ! same m]idian2 ! p]iod ( ! lun> diurnal tide w be d\ble z great2 & !re are =tnightly tides1 & o!rs ( p]iods /ill great]4 ,! ess5tial po9t to notice is1 t ! p]iods ( ^! tides are giv5 by purely a/ronomical consid]ations f ! p]iods ( ! motions !ory1 & d n dep5d ^u ! actual obs]vations4 ,we measure (f on ! curve ! height ( ! tide at int]vals ( an h\r4 ,! l>g] ! numb] ( su* measures t are available ! bett]2 b ev5 if !re be only ?ree hundr$ & sixty or sev5 hundr$ & tw5ty consecutive h\rs1 !n1 z %[n by ,pr(essor ,g4 ,h4 ,d>w9 9 ! ,admiralty ,manual already ref]r$ to1 x w /ill be possible to obta9 a v compet5t k ( ! tides 9 ! p>ticul> port :]e ! gauge has be5 plac$4 ,! art 7= su* inde$ x may be describ$7 ( h>monic analysis consi/s 9 d$uc+ f ! h\rly obs]vations ! facts ) reg>d to ea* ( ! con/itu5t tides4 ,?is art has be5 c>ri$ to su* p]fection1 t x has be5 r$uc$ to a v simple s]ies ( ari?metical op]ations4 ,inde$ x has n[ be5 f\nd possible to call 9 ! aid ( +5i\s me*anism1 by :i* ! lab\rs ( computation are entirely sup]s$$4 ,! po9t] ( ! h>monic analyz] has m]ely to be trac$ ov] ! curve :i* ! tide-gauge has drawn1 & x is ! function ( ! ma*9e to decompose ! composite undulation into its p>ts1 & to exhibit ! sev]al con/itu5t tides ^: conflu5ce gives ! total result4 ,z if no?+ %\ld be left to complete ! p]fection ( a process :i*1 bo? f its !oretical & its practical sides1 is ( su* importance1 a ma*9e = pr$ict+ tides has be5 design$1 con/ruct$1 & is n[ 9 ord9>y use4 ,:5 by ! aid ( ! h>monic analysis ! effectiv5ess ( ! sev]al con/itu5t tides affect+ a port h become fully det]m9$1 x is ( c\rse possible to pr$ict ! tides = t port4 ,ea* tide is a simple p]iodic rise & fall1 & we c compute = any future "t ! height ( ea* 7 x act+ alone4 ,^! heights c all be add$ toge!r1 & ?us ! height ( ! wat] is obta9$4 ,9 ?is way a tide-table is =m$1 & su* a table :5 complete w express n alone ! h\rs & heights ( high wat] on e day1 b ! height ( ! wat] at any int]v5+ h\r4 ,! computations necess>y = ?is purpose are no d\bt simple1 s f> z _! pr9ciple is conc]n$2 b !y are exce$+ly t$i\s1 & any process mu/ be welcom$ :i* af=ds mitigation ( a task s labori\s4 ,! entire !ory ( ! tides owes mu* to ,sir ,william ,?omson 9 ! me?ods ( obs]vation & 9 ! me?ods ( r$uction4 ,he has n[ complet$ ! practical p>ts ( ! subject by inv5t+ & con/ruct+ ! fam\s tide-pr$ict+ eng9e4 ,! pr9ciple ( ?is eng9e is comp>atively simple4 ,!re is a *a9 :i* at "o end is fix$1 & at ! o!r end c>ries ! p5cil :i* is press$ aga9/ ! revolv+ drum on :i* ! pr$iction is to be inscrib$4 ,betwe5 its two ends ! *a9 passes up & d[n ov] pulleys4 ,ea* pulley corresponds to "o ( ! tides1 & !re are ab\t a doz5 altoge!r1 "s ( :i* ex]cise b little effect4 ,( c\rse if ! c5tres ( ! pulleys 7 all fix$ ! p5 c\ld n move1 b ! c5tre ( ea* pulley describes a circle ) a radius proportional to ! amplitude ( ! correspond+ tide1 & 9 a "t proportional to ! p]iod ( t tide4 ,:5 ^! pulleys are all set s z to />t at ! prop] phases1 ! motion is produc$ by turn+ r\nd a h&le :i* makes ! drum rotate1 & sets all ! pulleys 9 motion4 ,! tide curve is ?us rapidly drawn out2 & s exp$iti\s is ! ma*9e1 t ! tides ( a port = an entire ye> c be completely work$ out 9 a c\ple ( h\rs4 ,:ile ! /ud5t or ! philosoph] :o seeks to r5d] any acc\nt ( ! tide on dynamical gr\nds is greatly emb>rass$ by ! difficulties introduc$ by friction1 we1 = our pres5t purpose 9 ! /udy ( ! great romance ( mod]n sci5ce op5$ up to u by ! !ory ( ! tides1 h to welcome friction z ! ag5t :i* gives to ! tides _! significance f our po9t ( view4 ,!re is ! greate/ diff]5ce betwe5 ! height ( ! rise & fall ( ! tide at diff]5t localities4 ,out 9 mid-ocean1 = in/ance1 an isl& l ,/4 ,hel5a is wa%$ by a tide only ab\t ?ree feet 9 range2 an enclos$ sea l ! ,caspian is subject to no appreciable tides :atev]1 :ile ! ,m$it]ranean1 not)/&+ its connection ) ! ,atlantic1 is /ill only subject to v inconsid]able tides1 v>y+ f "o foot to a few feet4 ,! /atem5t t wat] always f9ds its own level mu/ be receiv$1 l _m ano!r proposition 9 nature1 ) a consid]able degree ( qualification4 ,long ere "o tide c\ld h f\nd its way ?r\gh ! ,/raits ( ,gibralt> 9 suffici5t volume to h appreciably affect$ ! level ( ! great inl& sea1 its effects w\ld h be5 oblit]at$ by succe$+ tides4 ,on ! o!r h&1 !re are c]ta9 localities :i* expose a funnel-%ape op5+ to ! sea2 into ^! ! great tidal wave ru%es1 & z x passes onw>ds t[>ds ! n>r[ "p1 ! wat]s become pil$ up s z to produce tidal ph5om5a ( abnormal proportions4 ,?us1 9 our own isl&s1 we h 9 ! ,bri/ol ,*annel a wide m\? into :i* a great tide ent]s1 & z x hurries up ! ,sev]n x produces ! extraord9>y ph5om5on ( ! ,bore4 ,! ,bri/ol ,*annel also conc5trates ! great wave :i* gives ,*ep/[ & ,c>diff a tidal range ( ?irty-sev5 or ?irty-eight feet at spr+s1 & =ces ! sea up ! riv] ,avon s z to give ,bri/ol a wond]ful tide4 ,!re is h>dly any m int]e/+ spot 9 our isl&s = ! obs]vation ( tides ?an is f\nd on ,clifton ,susp5sion ,bridge4 ,f t beautiful /ructure y look d[n on a poor & n v attractive /ream1 :i* two h\rs lat] becomes trans=m$ into a riv] ( ample volume1 d[n :i* great %ips are navigat$4 ,b ( all places 9 ! _w1 ! mo/ colossal tidal ph5om5a are ^? 9 ! ,bay ( ,fundy4 ,"h ! ,atlantic passes into a long *annel ^: sides gradually conv]ge4 ,:5 ! great pulse ( ! tide ru%es up ?is *annel1 x is gradually accumulat$ into a mighty volume at ! upp] end1 ! ebb & fl[ ( :i* at spr+ tides ext5ds ?r\gh ! a/oni%+ range ( n less ?an fifty feet4 ,^! discrepancies betwe5 ! tides at diff]5t places are *iefly due to ! local =mations ( ! coa/s & ! sea-b$s4 ,inde$1 x seems t if ! :ole e>? 7 cov]$ ) an uni=m & deep ocean ( wat]1 ! tides w\ld be excessively feeble4 ,on no o!r supposition c we reasonably acc\nt = ! fact t our b>ometric records fail to af=d u any v di/9ct evid5ce z to ! exi/5ce ( tides 9 ! atmosph]e4 ,= y w1 ( c\rse1 rememb] t our atmosph]e may be reg>d$ z a deep & va/ ocean ( air1 :i* embraces ! :ole e>?1 ext5d+ f> above ! l(tie/ summits ( ! m\nta9s4 ,x is "o ( ! pr(\nde/ ( nature's laws t :]ev] friction takes place1 en]gy has to be consum$4 ,p]haps ,i ought r to say trans=m$1 = ( c\rse x is n[ well kn[n t consumption ( en]gy 9 ! s5se ( absolute loss is impossible4 ,?us1 :5 en]gy is exp5d$ 9 mov+ a body 9 opposition to ! =ce ( friction1 or 9 agitat+ a liquid1 ! en]gy :i* disappe>s 9 its me*anical =m reappe>s 9 ! =m ( heat4 ,! agitation ( wat] by paddles mov+ ?r\gh x w>ms ! wat]1 & ! accession ( heat ?us acquir$ measures ! en]gy :i* has be5 exp5d$ 9 mak+ ! paddles rotate4 ,! motion ( a liquid ( :i* ! p>ticles move among ea* o!r ) friction1 c only be su/a9$ by ! incessant degradation ( en]gy f ! me*anical =m into ! l[] =m ( diffus$ heat4 ,?us ! v fact t ! tides are ebb+ & fl[+1 & t !re is consequ5tly incessant friction go+ on among all ! p>ticles ( wat] 9 ! ocean1 %[s u t !re mu/ be "s great /ore ( en]gy con/antly available to supply ! incessant draughts made ^u x by ! daily oscillation ( ! tides4 ,9 addition to ! m]e friction betwe5 ! p>ticles ( wat]1 !re are also _m o!r ways 9 :i* ! tides proclaim to u t !re is "s great ho>d ( en]gy :i* is cont9ually accessible to _! wants4 ,/& on ! bank ( an e/u>y or riv] up & d[n :i* a great tidal curr5t ebbs & fl[s2 y w see ! wat] copi\sly *>g$ ) s$im5t :i* ! tide is be>+ along4 ,eng9e]s are well aw>e ( ! pot5cy ( ! tide z a vehicle = transport+ /up5d\s quantities ( s& or mud4 ,a s&-bank imp$es ! navigation ( a riv]2 ! removal ( t s&-bank w\ld be a task1 p]haps1 conceivably possible by ! use ( /eam dr$ges & o!r appliances1 :]eby va/ quantities ( s& c\ld be rais$ & transport$ to ano!r locality :]e !y w\ld be innocu\s4 ,x is sometimes possible to effect ! desir$ end by apply+ ! p[] ( ! tide4 ,a sea-wall judici\sly ?r[n out w sometimes conc5trate ! tide into a mu* n>r[] *annel4 ,its daily oscillations w be accompli%$ ) great] vehem5ce1 & z ! tide ru%es furi\sly backw>ds & =w>ds ov] ! ob/acle1 ! incessant action w gradually remove x1 & ! imp$im5t to navigation may be cle>$ away4 ,"h we actually see ! tides p]=m+ a piece ( def9ite & v labori\s "w1 to accompli% :i* by ! m ord9>y ag5ts w\ld be a /up5d\s task4 ,9 "s places ! tides are actually h>ness$ s z to accompli% useful "w4 ,i h read t und]nea? old ,london ,bridge !re us$ =m]ly to be great wat]-:eels1 :i* 7 turn$ by ! tide z x ru%$ up ! riv]1 & turn$ aga91 ?\gh 9 ! opposite way1 by ! ebb+ tide4 ,^! :eels 71 ,i believe1 employ$ to pump up wat]1 ?\gh x does n seem obvi\s = :at purposes ! wat] w\ld h be5 suitable4 ,inde$ 9 ! ebb & fl[ all r\nd our coa/s !re is a pot5tial s\rce ( en]gy :i* has hi!rto be5 all[$ to run to wa/e4 ,! tide c\ld be utiliz$ 9 v>i\s ways4 ,_m ( y w rememb] ! float+ mills on ! ,rh9e4 ,!y are vessels l paddle /eam]s an*or$ 9 ! rapid curr5t4 ,! fl[ ( ! riv] makes ! paddles rotate1 & ?us ! ma*9]y 9 ! int]ior is work$4 ,su* craft moor$ 9 a rapid tide-way c\ld also be made to convey ! p[] ( ! tides into ! me*anism ( ! mill4 ,or !re is /ill ano!r me?od :i* has be5 employ$1 & :i* w p]haps h a future be=e x 9 ^? approa*+ times :5 ! coal-cell>s ( ,engl& %all be exhau/$4 ,imag9e on ! sea-coa/ a l>ge flat ext5t :i* is inundat$ twice e day by ! tide4 ,let u build a /\t wall r\nd ?is area1 & provide x ) a sluice-gate4 ,op5 ! gate z ! tide rises1 & ! great pond w be fill$2 !n at ! mom5t ( high wat] close ! sluice1 & ! pond-full w be imp\nd$4 ,if at l[ tide ! sluice be op5$ ! wat] w ru% tumultu\sly out4 ,n[ suppose t a wat]-:eel be provid$1 s t ! rapid ru% ( wat] f ! exit %all fall ^u its blades2 !n a s\rce ( p[] is obvi\sly ! result4 ,at pres5t1 h[ev]1 su* a contrivance w\ld naturally f9d no advocates1 = ( c\rse ! comm]cial aspect ( ! "q is t :i* w decide :e!r ! s*eme is practicable & economical4 ,! issue inde$ c be v simply /at$4 ,suppose t a giv5 quantity ( p[] be requir$--let u say t ( "o hundr$ horse4 ,!n we h to consid] ! conditions "u :i* a contrivance ( ! k9d we h sket*$ %all yield a p[] ( ?is am\nt4 ,sir ,william ,?omson1 9 a v int]e/+ address to ! ,briti% ,association at ,york 9 #ahha1 discuss$ ?is "q1 & ,i %all "h make use ( ! facts he br\ght =w>d on t occasion4 ,he %[$ t to obta9 z mu* p[] z c\ld be produc$ by a /eam-eng9e ( "o hundr$ horse p[]1 a v l>ge res]voir w\ld be requir$4 ,x is d\btful inde$ :e!r !re w\ld be _m localities on ! e>? :i* w\ld be suitable = ! purpose4 ,suppose1 h[ev]1 an e/u>y c\ld be f\nd :i* _h an area ( =ty acres2 !n if a wall 7 ?r[n across ! m\? s t ! tide c\ld be imp\nd$1 ! total am\nt ( p[] t c\ld be yield$ by a wat]-:eel work$ by ! incessant influx & efflux ( ! tide w\ld be equal to t yield$ by ! "o hundr$ horse eng9e1 runn+ cont9u\sly f "o end ( ! ye> to ! o!r4 ,!re are _m drawbacks to a tide-mill ( ?is description4 ,9 ! fir/ place1 its situation w\ld naturally be f> remov$ f o!r conv5i5ces necess>y = manufactur+ purposes4 ,!n too !re is ! great irregul>ity 9 ! way 9 :i* ! p[] is r5d]$ available4 ,at c]ta9 p]iods dur+ ! tw5ty-f\r h\rs ! mill w\ld /op runn+1 & ! h\rs :5 ?is happ5$ w\ld be con/antly *ang+4 ,! inconv5i5ce f ! manufactur]'s po9t ( view ( a defici5cy ( p[] dur+ neap tides might n be comp5sat$ by ! fact t he _h an excessive supply ( p[] at spr+-tides4 ,be=e tide-mills c\ld be suitable = manufactur+ purposes1 "s means mu/ be f\nd = /or+ away ! en]gy :5 x is r$undant1 & apply+ x :5 its pres5ce is requir$4 ,we %\ld want 9 fact = great s\rces ( en]gy "s contrivance :i* %all fulfil ! same purpose z ! accumulators d 9 an electrical in/allation4 ,ev5 !n1 h[ev]1 ! f9ancial consid]ation rema9s1 z to :e!r ! co/ ( build+ ! dam & ma9ta9+ ! tide-mill 9 good ord] w n on ! :ole exce$ ! orig9al price & ! *>ges = ! ma9t5ance ( a hundr$ horse p[] /eam-eng9e4 ,!re _c be a d\bt t 9 ?is epo* ( ! e>?'s hi/ory1 s long z ! price ( coal is only a few %ill+s a ton1 ! tide-mill1 ev5 ?\gh we seem to get its p[] )\t curr5t exp5se1 is va/ly m exp5sive ?an a /eam-eng9e4 ,inde$1 ,sir ,william ,?omson rem>ks1 t :]ev] a suitable tidal bas9 c\ld be f\nd1 x w\ld be ne>ly z easy to reclaim ! l& altoge!r f ! sea4 ,& if ?is 7 9 any locality :]e manufactures 7 possible1 ! comm]cial value ( =ty acres ( reclaim$ l& w\ld greatly exce$ all ! exp5ses att5d+ ! /eam-eng9e4 ,b :5 ! "t comes1 z come x app>5tly w1 t ! price ( coal %all h ris5 to sev]al p\nds a ton1 ! economical aspect ( /eam z comp>$ ) o!r prime mov]s w be greatly alt]$2 x w !n no d\bt be f\nd advantage\s to utilize great s\rces ( en]gy1 su* z ,niag>a & ! tides1 :i* x is n[ m prud5t to let run to wa/e4 ,= my argum5t1 h[ev]1 x matt]s little t ! tides are n con/ra9$ to d mu* useful "w4 ,!y are always do+ "w ( "s k9d1 :e!r t be m]ely heat+ ! p>ticles ( wat] by friction1 or vaguely transport+ s& f "o "p ( ! ocean to ! o!r4 ,useful "w or useless "w are alike = ! purpose ( my argum5t4 ,we "k t "w c nev] be done unless by ! consumption or trans=mation ( en]gy4 ,= ea* unit ( "w t is done--:e!r by any ma*9e or contrivance1 by ! muscles ( man or any o!r animal1 by ! w9ds1 ! waves1 or ! tides1 or 9 any o!r way :atev]--a c]ta9 equival5t quantity ( en]gy mu/ h be5 exp5d$4 ,:51 !re=e1 we see any "w be+ p]=m$1 we may always look = ! s\rce ( en]gy to :i* ! ma*9e owes its effici5cy4 ,9 fact1 x is ! old /ory illu/rat$1 t p]petual motion is impossible4 ,a me*anical device1 h[ev] +5i\s may be ! con/ruction1 or h[ev] accurate ! workman%ip1 c nev] possess :at is call$ p]petual motion4 ,x is ne$less to ent] into details ( any propos$ contrivance ( :eels1 ( pumps1 ( pulleys2 x is suffici5t to say t no?+ 9 ! %ape ( me*anism c "w )\t friction1 t friction produces heat1 t heat is a =m ( en]gy1 & t to replace ! en]gy consum$ 9 produc+ ! heat !re mu/ be "s s\rce f :i* ! ma*9e is repl5i%$ if its motion is to be cont9u$ indef9itely4 ,h5ce1 z ! tides may be reg>d$ z a ma*9e do+ "w1 we h to asc]ta9 ! orig9 ( t en]gy :i* !y are cont9ually exp5d+4 ,x is at ?is po9t t we fir/ beg9 to feel ! difficulties inh]5t 9 ! !ory ( tidal evolution4 ,i d n mean difficulties 9 ! s5se ( d\bts1 = up to ! pres5t ,i h m5tion$ no d\btful po9t4 ,:5 ,i come to su* ,i %all give due w>n+4 ,by difficulties ,i n[ mean po9ts :i* x is n easy to und]/& )\t a little dynamical !ory2 b we mu/ face ^! difficulties1 & endeav\r to elucidate !m z well z we c4 ,let u fir/ see :at ! s\rces ( en]gy c possibly be on :i* ! tides are p]mitt$ to draw4 ,our c\rse is simplifi$ by ! fact t ! en]gy ( :i* we h to speak is ( a me*anical description1 t is to say1 n involv+ heat or o!r m obscure =ms ( en]gy4 ,a simple type ( en]gy is t possess$ by a clock-weight aft] ! clock has be5 w\nd4 ,a /ore ( p[] is ?us laid up :i* is gradually dol$ out dur+ ! week 9 small quantities1 second by second1 to su/a9 ! motion ( ! p5dulum4 ,! en]gy 9 ?is case is due to ! fact t ! weight is attract$ by ! e>?1 & is yield$ accord+ z ! weight s9ks d[nw>ds4 ,9 ! sep>ation betwe5 two mutually attract+ bodies1 a /ore ( en]gy is ?us impli$4 ,:at we le>n f an ord9>y clock may be ext5d$ to ! great bodies ( ! univ]se4 ,! moon is a gigantic globe sep>at$ f our e>? by a di/ance ( #bdj1jjj miles4 ,! attraction betwe5 ^! two bodies always t5ds to br+ !m toge!r4 ,no d\bt ! moon is n fall+ t[>ds ! e>? z ! desc5d+ clock-weight is do+4 ,we may1 9 fact1 consid] ! moon1 s f> z our pres5t object is conc]n$1 to be revolv+ almo/ 9 a circle1 ( :i* ! e>? is ! c5tre4 ,if ! moon1 h[ev]1 7 to be /opp$1 x w\ld at once comm5ce to ru% d[n t[>ds ! e>?1 :i!r x w\ld arrive ) an awful cra% 9 ! c\rse ( f\r or five days4 ,x is =tunately true t ! moon does n behave ?us2 b x has ! ability ( do+ s1 & ?us ! m]e sep>ation betwe5 ! e>? & ! moon involves ! exi/5ce ( a /up5d\s quantity ( en]gy1 capable "u c]ta9 conditions ( und]go+ trans=mation4 ,!re is also ano!r s\rce ( me*anical en]gy besides t we h j ref]r$ to4 ,a rapidly mov+ body possesses1 9 virtue ( its motion1 a /ore ( readily available en]gy1 & x is easy to %[ t en]gy ( ?is type is capable ( trans=mation into o!r types4 ,?9k ( a cannon-ball ru%+ ?r\gh ! air at a spe$ ( a ?\s& feet p] second2 x is capable ( wreak+ disa/] on any?+ :i* x meets1 simply because its rapid motion is ! vehicle by :i* ! en]gy ( ! gunp[d] is transf]r$ f ! gun to :]e ! bl[ is to be /ruck4 ,_h ! cannon be5 direct$ v]tically upw>ds1 !n ! projectile1 leav+ ! muzzle ) ! same initial velocity z be=e1 w\ld so> up & up1 ) gradually abat+ spe$1 until at la/ x rea*$ a turn+-po9t1 ! elevation ( :i* w\ld dep5d ^u ! initial velocity4 ,pois$ = a mom5t at ! summit1 ! cannon-ball may !n be lik5$ to ! clock-weight1 = ! entire en]gy :i* x possess$ by its motion has be5 trans=m$ into ! /atical en]gy ( a rais$ weight4 ,?us we see ^! two =ms ( en]gy are mutually int]*angeable4 ,! rais$ weight if all[$ to fall w acquire velocity1 or ! rapidly mov+ weight if direct$ upw>ds w acquire altitude4 ,! quantity ( en]gy :i* c be convey$ by a rapidly mov+ body increases greatly ) its spe$4 ,= in/ance1 if ! spe$ ( ! body be d\bl$1 ! en]gy w be increas$ f\rfold1 or1 9 g5]al1 ! en]gy :i* a mov+ body possesses may be said to be proportional to ! squ>e ( its spe$4 ,"h !n we h ano!r s\rce ( ! en]gy pres5t 9 our e>?-moon sy/em2 = ! moon is hurry+ along 9 its pa? ) a spe$ ( two-?irds ( a mile p] second1 or ab\t twice or ?ree times ! spe$ ( a cannon-%ot4 ,h5ce ! fact t ! moon is cont9u\sly revolv+ 9 a circle %[s u t x possesses a /ore ( en]gy :i* is n9e times z great z t :i* a cannon-ball z massive z ! moon1 & fir$ ) ! ord9>y velocity1 w\ld receive f ! p[d] :i* dis*>g$ x4 ,?us we see t ! moon is end[$ ) two s\rces ( en]gy1 "o ( :i* is due to its sep>ation f ! e>?1 & ! o!r to ! spe$ ( its motion4 ,?\gh ^! are di/9ct1 !y are connect$ toge!r by a l9k :i* x is important = u to compreh5d4 ,! spe$ ) :i* ! moon revolves ar\nd ! e>? is connect$ ) ! moon's di/ance f ! e>?4 ,! moon might1 = in/ance1 revolve 9 a l>g] circle ?an t :i* x actually pursues2 b if x did s1 ! spe$ ( its motion w\ld h to be appropriately less5$4 ,! orbit ( ! moon might h a mu* small] radius ?an x has at pres5t1 provid$ t ! spe$ 0 suffici5tly increas$ to comp5sate = ! increas$ attraction :i* ! e>? w\ld ex]cise at ! less5$ di/ance4 ,inde$1 ,i am "h only /at+ :at e "o is famili> ) "u ! =m ( ,kepl]'s ,law1 t ! squ>e ( ! p]iodic "t is 9 proportion to ! cube ( ! mean di/ance4 ,to ea* di/ance ( ! moon !re=e belongs an appropriate spe$4 ,! en]gy due to ! moon's position & ! en]gy due to its motion are !re=e connect$ toge!r4 ,"o ( ^! quantities _c be alt]$ )\t ! o!r und]go+ *ange4 ,if ! moon's orbit 7 increas$ !re w\ld be a ga9 ( en]gy due to ! enl>g$ di/ance1 & a loss ( en]gy due to ! dim9i%$ spe$4 ,^! w\ld n1 h[ev]1 exactly comp5sate4 ,on ! :ole1 we may repres5t ! total en]gy ( ! moon z a s+le quantity1 :i* increases :5 ! di/ance ( ! moon f ! e>? increases1 & less5s :5 ! di/ance f ! e>? to ! moon less5s4 ,= simplicity we may speak ( ?is z moon-en]gy4 ,b ! mo/ important con/itu5t ( ! /ore ( en]gy 9 ! e>?-moon sy/em is t contribut$ by ! e>? itself4 ,i d n n[ speak ( ! en]gy due to ! velocity ( ! e>? 9 its orbit r\nd ! sun4 ,! moon inde$ p>ticipates 9 ?is equally ) ! e>?1 b x does n affect ^? mutual actions betwe5 ! e>? & moon ) :i* we are at pres5t conc]n$4 ,we are1 9 fact1 discuss+ ! action ( t piece ( ma*9]y ! e>?-moon sy/em2 & its action is n affect$ by ! circum/ance t ! entire ma*9e is be+ bodily transport$ ar\nd ! sun 9 a great annual voyage4 ,?is has little m to d ) ! action ( our pres5t argum5t ?an has ! fact t a man is walk+ ab\t to d ) ! motions ( ! works ( ! wat* 9 8 pocket4 ,we %all1 h[ev]1 h to allude to ?is subject fur!r on4 ,! en]gy ( ! e>? :i* is significant 9 ! e>?-moon !ory is due to ! e>?'s rotation ^u its axis4 ,we may "h aga9 use z an illu/ration ! action ( ma*9]y2 & ! special contrivance t ,i n[ ref] to is ! pun*+-eng9e t is us$ 9 our %ip-build+ works4 ,9 prep>+ a plate ( iron to be rivet$ to ! side ( a %ip1 a numb] ( holes h to be made all r\nd ! m>g9 ( ! plate4 ,^! holes mu/ be half an in* or m 9 diamet]1 & ! plate is sometimes z mu* z1 or m ?an1 half an in* 9 ?ickness4 ,! holes are produc$ 9 ! metal by =c+ a /eel pun* ?r\gh x2 & ?is is accompli%$ )\t ev5 heat+ ! plate s z to s(t5 ! iron4 ,x is ne$less to say t an int5se =ce mu/ be appli$ to ! pun*4 ,on ! o!r h&1 ! di/ance ?r\gh :i* ! pun* has to be mov$ is comp>atively small4 ,! pun* is atta*$ to ! end ( a p[]ful lev]1 ! o!r end ( ! lev] is rais$ by a cam1 s z to depress ! pun* to d its "w4 ,an ess5tial "p ( ! ma*9e is a small b heavy fly-:eel connect$ by ge>+ ) ! cam4 ,?is fly-:eel :5 rapidly revolv+ conta9s )9 x1 9 virtue ( its motion1 a l>ge /ore ( en]gy :i* has gradually accumulat$ dur+ ! "t t ! pun* is n actually 9 action4 ,! en]gy is no d\bt orig9ally suppli$ f a /eam-eng9e4 ,:at we are especially conc]n$ ) is ! action ( ! rapidly rotat+ :eel z a res]voir 9 :i* a l>ge /ore ( en]gy c be conv5i5tly ma9ta9$ until su* "t z x is want$4 ,9 ! action ( pun*+1 :5 ! /eel die comes d[n ^u ! surface ( ! plate1 a l>ge quantity ( en]gy is sudd5ly dem&$ to =ce ! pun* aga9/ ! int5se resi/ance x exp]i5ces2 ! en]gy = ?is purpose is drawn f ! /ore 9 ! fly-:eel1 :i* exp]i5ces no d\bt a *eck 9 its velocity1 to be rega9$ aga9 f ! en]gy ( ! eng9e dur+ ! int]val :i* elapses be=e ! pun* is call$ on to make ! next hole4 ,ano!r illu/ration ( ! fly-:eel on a spl5did scale is se5 9 our mighty /eel works1 :]e pond]\s rails are be+ manufactur$4 ,a :ite-hot +ot ( /eel is pres5t$ to a pair ( p[]ful roll]s1 :i* grip ! /eel1 & s5d x ?r\gh at ! o!r side bo? compress$ & elongat$4 ,trem5d\s p[] is requir$ to meet ! sudd5 dem& on ! ma*9e at ! critical mom5t4 ,to obta9 ?is p[] an eng9e ( /up5d\s proportions is sometimes atta*$ directly to ! roll]s1 b m frequ5tly an eng9e ( r less horse-p[] w be us$1 ! might ( ?is eng9e be+ appli$ to giv+ rapid rotation to an imm5se fly-:eel1 :i* may ?us be reg>d$ z a res]voir full ( en]gy4 ,! roll+ mills !n obta9 f ?is /ore 9 ! fly-:eel :atev] en]gy is necess>y = _! gigantic task4 ,^! illu/rations w suffice to %[ h[ a rapidly rotat+ body may conta9 en]gy 9 virtue ( its rotation1 j z a cannon-ball conta9s en]gy 9 virtue ( its spe$ ( translation1 or z a clock-weight has en]gy 9 virtue ( ! fact t x has "s di/ance to fall be=e x rea*es ! e>?4 ,! rotat+ body ne$ n necess>ily h ! %ape ( a :eel--x may be globul> 9 =m2 nor ne$ ! axes ( rotation be fix$ 9 be>+s1 l ^? ( ! fly-:eel2 nor ( c\rse is !re any limit to ! dim5sions :i* ! rotat+ body may assume4 ,our e>? is1 9 fact1 a va/ rotat+ body #hjjj miles 9 diamet]1 & turn+ r\nd ^u its axis once e tw5ty-?ree h\rs & fifty-six m9utes4 ,view$ 9 ?is way1 ! e>? is to be reg>d$ z a gigantic fly-:eel conta9+ a quantity ( en]gy great 9 correspond5ce ) ! e>?'s mass4 ,! am\nt ( en]gy :i* c be /or$ by rotation also dep5ds ^u ! squ>e ( ! velocity ) :i* ! body turns r\nd2 ?us if our e>? turn$ r\nd 9 half ! "t :i* x does at pres5t1 t is1 if ! day 0 twelve h\rs in/ead ( tw5ty-f\r h\rs1 ! en]gy conta9$ 9 virtue ( t rotation w\ld be f\r times its pres5t am\nt4 ,rev]t+ n[ to ! e>?-moon sy/em1 ! en]gy :i* t sy/em conta9s consi/s ess5tially ( two p>ts--! moon-en]gy1 ^: composite "* ,i h already expla9$1 & ! e>?-en]gy1 :i* has its orig9 solely 9 ! rotation ( ! e>? on its axis4 ,x is necess>y to obs]ve t ^! are ess5tially di/9ct--!re is no necess>y relation betwe5 ! spe$ ( ! e>?'s rotation & ! di/ance ( ! moon1 su* z !re is betwe5 ! di/ance ( ! moon & ! spe$ ) :i* x revolves 9 its orbit4 ,= complet5ess1 x ought to be add$ t !re is also "s en]gy due to ! moon's rotation on its axis1 b ?is is v small = two reasons3 fir/1 because ! moon is small comp>$ ) ! e>?1 & second1 because ! angul> velocity ( ! moon is also v small comp>$ ) t ( ! e>?4 ,we may !re=e dismiss z insignificant ! contributions f ?is s\rce ( en]gy to ! sum total4 ,i h frequ5tly us$ illu/rations d]iv$ f ma*9]y1 b ,i want n[ to emphasize ! pr(\nd di/9ction t exi/s betwe5 ! rotation ( ! e>? & ! rotation ( a fly-:eel 9 a ma*9e %op4 ,!y are bo?1 no d\bt1 en]gy-hold]s1 b x mu/ be borne 9 m9d1 t z ! fly-:eel doles out its en]gy to supply ! wants ( ! ma*9es ) :i* x is connect$1 a re/itution ( its /ore is cont9ually go+ on by ! action ( ! eng9e1 s t on ! :ole ! spe$ ( ! fly-:eel does n slack54 ,! e>?1 h[ev]1 mu/ be lik5$ to a fly-:eel :i* has be5 disconnect$ ) ! eng9e4 ,if1 !re=e1 ! e>? h to supply c]ta9 dem&s on its accumulation ( en]gy1 x c only d s by a dim9ution ( its ho>d1 & ?is involves a sacrifice ( "s ( its spe$4 ,9 ! e>?-moon sy/em !re is no eng9e at h& to re/ore ! losses ( en]gy :i* are inevitable :5 "w has to be done4 ,b we h se5 t "w is done2 we h %[n1 9 fact1 t ! tides are at pres5t do+ "w1 & h be5 do+ "w = z long a p]iod 9 ! pa/ z our imag9ation c ext5d to4 ,! en]gy :i* ?is "w has necessitat$ c only h be5 drawn f ! exi/+ /ore 9 ! sy/em2 t en]gy consi/s ( two p>ts--! moon-en]gy & ! e>?'s rotation en]gy4 ,! problem !re=e = u to consid] is1 :i* ( ^! two banks ! tides h drawn on to meet _! con/ant exp5diture4 ,?is is n a "q t c be decid$ (fh&2 9 fact1 if we attempt to decide x 9 an (fh& mann] we %all c]ta9ly g wrong4 ,x seems s v plausible to say t z ! moon causes ! tides1 !re=e ! en]gy :i* ^! tides exp5d %\ld be contribut$ by ! moon4 ,b ?is is n ! case4 ,x actually happ5s t ?\gh ! moon does cause ! tides1 yet :5 ^? tides consume en]gy !y draw x n f ! di/ant moon1 b f ! va/ supply :i* !y f9d ready to _! h&1 /or$ up 9 ! rotation ( ! e>?4 ,! demon/ration ( ?is is n a v simple matt]2 9 fact1 x is s f> f be+ simple t _m philosoph]s1 includ+ "s em95t ones too1 :ile admitt+ t ( c\rse ! tides mu/ h drawn _! en]gy f "o or o!r or bo? ( ^! two s\rces1 yet f\nd !mselves unable to assign h[ ! dem& 0 di/ribut$ betwe5 ! two conceivable s\rces ( supply4 ,we are indebt$ to ,pr(essor ,purs] ( ,belfa/ = hav+ indicat$ ! true dynamical pr9ciple on :i* ! problem dep5ds4 ,x involves reason+ bas$ simply on ! laws ( motion & on elem5t>y ma!matics1 b n 9 ! lea/ involv+ que/ions ( a/ronomical obs]vation4 ,x w\ld be impossible = me 9 a lecture l ?is to give any explanation ( ! ma!matical pr9ciples ref]r$ to4 ,i %all1 h[ev]1 endeav\r by "s illu/rations to set be=e y :at ?is pr(\nd pr9ciple really is4 ,7 ,i to give x ! old "n ,i %\ld call x ! law ( ! cons]vation ( areas2 ! m mod]n writ]s1 h[ev]1 speak ( x z ! cons]vation ( mom5t ( mom5tum1 an expression :i* exhibits ! nature ( ! pr9ciple 9 a m def9ite mann]4 ,i d n see h[ to give any v accurate illu/ration ( :at ?is law means1 b ,i mu/ make ! attempt1 & if y ?9k ! illu/ration b5ea? ! dignity ( ! subject1 ,i c only plead ! difficulty ( ma!matics z an excuse4 ,let u suppose t a ball-room is fairly fill$ ) danc]s1 or ^? will+ to dance1 & t a m]ry waltz is be+ play$2 ! c\ples h =m$1 & ! floor is occupi$ ) pairs :o are :irl+ r\nd & r\nd 9 t delightful amusem5t4 ,"s c\ples drop out = a :ile & o!rs /rike 92 ! few] c\ples !re are ! wid] is ! range ar\nd :i* !y c waltz1 ! m num]\s ! c\ples ! less individual range w !y possess4 ,i want y to realize t 9 ! progress ( ! dance !re is a c]ta9 total quantity ( sp9 at any mom5t 9 progress2 ?is sp9 is p>tly made up ( ! rotation by :i* ea* danc] revolves r\nd 8 p>tn]1 & p>tly ( ! circul> orbit ab\t ! room :i* ea* c\ple endeav\rs to describe4 ,if !re are too _m c\ples on ! floor = ! g5]al enjoym5t ( ! dance1 !n bo? ! orbit & ! angul> velocity ( ea* c\ple w be re/rict$ by ! int]f]5ce ) _! neighb\rs4 ,we may1 h[ev]1 ass]t t s long z ! dance is 9 full sw+ ! total quantity ( sp91 p>tly rotational & p>tly orbital1 w rema9 con/ant4 ,:5 !re are b few c\ples ! unimp$$ rotation & ! l>ge orbits w produce z mu* sp9 z :5 !re is a mu* l>g] numb] ( c\ples1 = 9 ! latt] case ! dim9i%$ fre$om w less5 ! quantity ( sp9 produc$ by ea* individual pair4 ,x w sometimes happ5 too t collision w take place1 b ! slight div]sions ?us aris+ only increase ! g5]al m]rim5t1 s t ! total quantity ( sp9 may be su/a9$1 ev5 ?\gh "o or two c\ples are plac$ tempor>ily hors de combat4 ,i h invok$ a ball-room = ! purpose ( br++ out :at we may call ! law ( ! cons]vation ( sp94 ,no matt] h[ mu* ! individual p]=m]s may *ange1 or no matt] :at vicissitudes arise f _! collision & o!r mutual actions1 yet ! total quantity ( sp9 rema9s un*ang$4 ,let u look at ! e>?-moon sy/em4 ,! law ( ! cons]vation ( mom5t ( mom5tum may1 ) suffici5t accuracy = our pres5t purpose1 be int]pret$ to mean t ! total quantity ( sp9 9 ! sy/em rema9s unalt]$4 ,9 our sy/em ! sp9 is ?reefold2 !re is fir/ ! rotation ( ! e>? on its axis1 !re is ! rotation ( ! moon on its axis1 & !n !re is ! orbital revolution ( ! moon ar\nd ! e>?4 ,! law to :i* we ref] ass]ts t ! total quantity ( ^! ?ree sp9s1 ea* e/imat$ 9 ! prop] way1 w rema9 con/ant4 ,x matt]s n t tides may ebb & fl[1 or t ! di/ribution ( ! sp9 %all v>y1 b its total am\nt rema9s inflexibly con/ant4 ,"o con/itu5t ( ! total am\nt--t is1 ! rotation ( ! moon on its axis--is s insignificant1 t = our pres5t purposes x may be entirely disreg>d$4 ,we may !re=e ass]t t ! am\nt ( sp9 9 ! e>?1 due to its rotation r\nd its axis1 add$ to ! am\nt ( sp9 9 ! moon due to its revolution r\nd ! e>?1 rema9s unalt]able4 ,if "o ( ^! quantities *ange by increase or by decrease1 ! o!r mu/ correspond+ly *ange by decrease or by increase4 ,if1 !re=e1 f any cause1 ! e>? began to sp9 a little m quickly r\nd its axis1 ! moon mu/ d a little less sp92 & consequ5tly1 x mu/ %ort5 its di/ance f ! e>?4 ,or suppose t ! e>?'s velocity ( rotation is abat$1 !n its contribution to ! total am\nt ( sp9 is less5$2 ! defici5cy mu/ !re=e be made up by ! moon1 b ?is c only be done by an enl>gem5t ( ! moon's orbit4 ,i %\ld add1 z a caution1 t ^! results are true only on ! supposition t ! e>?-moon sy/em is isolat$ f all ext]nal int]f]5ce4 ,) ?is proviso1 h[ev]1 x matt]s n :at may happ5 to ! e>? or moon1 or :at influ5ce "o ( !m may ex]t ^u ! o!r1 no matt] :at tides may be rais$1 no matt] ev5 if ! e>? fly into fragm5ts1 ! :ole quantity ( sp9 ( all ^? fragm5ts w\ld1 if add$ to ! sp9 ( ! moon1 yield ! same unalt]able total4 ,we are "h 9 possession ( a mo/ valuable dynamical pr9ciple4 ,we are n conc]n$ ) any special !ory z to ! action ( ! tides2 x is suffici5t = u t 9 "s way or o!r ! tides h be5 caus$ by ! moon1 & t be+ s1 ! pr9ciple ( ! cons]vation ( sp9 w apply4 ,7 ! e>? & ! moon bo? rigid bodies1 !n !re c\ld be ( c\rse no tides on ! e>?1 x be+ rigid & devoid ( ocean4 ,! rotation ( ! e>? on its axis w\ld !re=e be absolutely )\t *ange1 & !re=e ! necess>y condition ( ! cons]vation ( sp9 w\ld be v simply atta9$ by ! fact t nei!r ( ! con/itu5t p>ts *ang$4 ,! e>?1 h[ev]1 n be+ entirely rigid1 & be+ subject to tides1 ?is simple /ate ( ?+s _c cont9ue2 !re mu/ be "s *ange 9 progress4 ,i h already %[n t ! fact ( ! ebb+ & ! fl[+ ( ! tide necessitates an exp5diture ( en]gy1 & we saw t ?is en]gy mu/ come ei!r f t /or$ up 9 ! e>? by its rotation1 or f t possess$ by ! moon 9 virtue ( its di/ance & revolution4 ,! law ( ! cons]vation ( sp9 w enable u to decide at once z to :5ce ! tides get _! en]gy4 ,suppose !y took x f ! moon1 ! moon w\ld !n lose 9 en]gy1 & consequ5tly come ne>] ! e>?4 ,! quantity ( sp9 contribut$ by ! moon w\ld !re=e be less5$1 & accord+ly ! sp9 to be made up by ! e>? w\ld be increas$4 ,t means1 ( c\rse1 t ! velocity ( ! e>? rotat+ on its axis mu/ be increas$1 & ?is aga9 w\ld necessitate an increase 9 ! e>?'s rotational en]gy4 ,x c be %[n1 too1 t to keep ! total sp9 "r1 ! en]gy ( ! e>? w\ld h to ga9 m ?an ! moon w\ld h lo/ by revolv+ 9 a small] orbit4 ,?us we f9d t ! total quantity ( en]gy 9 ! sy/em w\ld be increas$4 ,?is w\ld lead to ! absurd result t ! action ( ! tides manufactur$ en]gy 9 our sy/em4 ,( c\rse1 su* a doctr9e _c be true2 x w\ld am\nt to a p]petual motion6 ,we might z well try to get a /eam-eng9e :i* w\ld produce en\gh heat by friction n only to supply its own boil]s1 b to satisfy all ! !rmal wants ( ! :ole p>i%4 ,we mu/ !re=e adopt ! o!r alt]native4 ,! tides d n draw _! en]gy f ! moon2 !y draw x f ! /ore possess$ by ! e>? 9 virtue ( its rotation4 ,we c n[ /ate ! end ( ?is r long discussion 9 a v simple & brief mann]4 ,en]gy c only be yield$ by ! e>? at ! exp5se ( "s ( ! spe$ ( its rotation4 ,! tides mu/ !re=e cause ! e>? to revolve m sl[ly2 9 o!r words1 ! tides are increas+ ! l5g? ( ! day4 ,! e>? !re=e loses "s ( its velocity ( rotation2 consequ5tly x does less ?an its due %>e ( ! total quantity ( sp91 & an increas$ quantity ( sp9 mu/ !re=e be accompli%$ by ! moon2 b ?is c only be done by an enl>gem5t ( its orbit4 ,?us !re are two great consequ5ces ( ! tides 9 ! e>?-moon sy/em--! days are gett+ long]1 ! moon is rec$+ fur!r4 ,^! po9ts are s important t ,i %all try & illu/rate !m 9 ano!r way1 :i* w %[1 at all ev5ts1 t "o & bo? ( ^! tidal ph5om5a comm5d !mselves to our common s5se4 ,h we n %[n h[ ! tides 9 _! ebb & fl[ are incessantly produc+ friction1 & h we n also lik5$ ! e>? to a great :eel8 ,:5 ! driv] wants to /op a railway tra9 ! brakes are put on1 & ! brake is m]ely a contrivance = apply+ friction to ! circumf]5ce ( a :eel = ! purpose ( *eck+ its motion4 ,or :5 a great weight is be+ l[]$ by a crane1 ! motion is *eck$ by a b& :i* applies friction on ! circumf]5ce ( a :eel1 arrang$ = ! special purpose4 ,ne$ we !n be surpris$ t ! friction ( ! tides acts l a brake on ! e>?1 & gradually t5ds to *eck its mighty rotation8 ,! progress ( l5g!n+ ! day by ! tides is ?us readily intelligible4 ,x is n q s easy to see :y ! ebb+ & ! fl[+ ( ! tide on ! e>? %\ld actually h ! effect ( mak+ ! moon to retreat2 ?is ph5om5on is 9 def]5ce to a pr(\nd law ( nature1 :i* tells u t action & reaction are equal & opposite to ea* o!r4 ,if ,i might v5ture on a v homely illu/ration1 ,i may say t ! moon1 l a tr\blesome fell[1 is con/antly annoy+ ! e>? by dragg+ its wat]s backw>d & =w>d by means ( tides2 & ! e>?1 to free itself f ?is irritat+ int]f]5ce1 tries to pu% (f ! aggressor & to make him move fur!r away4 ,illu/ration3 ,,fig4 #b4 ,ano!r way 9 :i* we c illu/rate ! retreat ( ! moon z ! inevitable consequ5ce ( tidal friction is %[n 9 ! adjo9+ figure1 9 :i* ! l>ge body ,e repres5ts ! e>?1 & ! small body ,m ! moon4 ,we may = simplicity reg>d ! moon z a po9t1 & z ?is attracts ea* p>ticle ( ! e>?1 ! total effect ( ! moon on ! e>? may be repres5t$ by a s+le =ce4 ,by ! law ( equality ( action & reaction1 ! =ce ( ! e>? on ! moon is to be repres5t$ by an equal & opposite =ce4 ,if !re 7 no tides !n ! moon's =ce w\ld ( c\rse pass ?r\gh ! e>?'s c5tre2 b z ! effect ( ! moon is to slack5 ! e>?'s rotation1 x foll[s t ! total =ce does n exactly pass ?r\gh ! l9e ( ! e>?'s c5tre1 b a little to "o side1 9 ord] to pull ! opposite way to t 9 :i* ! e>? is turn+1 & ?us br+ d[n its spe$4 ,we may !re=e decompose ! e>?'s total =ce on ! moon into two p>ts1 "o ( :i* t5ds directly t[>ds ! e>?'s c5tre1 :ile ! o!r acts tang5tially to ! moon's orbit4 ,! c5tral =ce is ( c\rse ! ma9 guid+ p[] :i* keeps ! moon 9 its pa?2 b ! incessant tang5tial =ce con/antly t5ds to s5d ! moon out fur!r & fur!r1 & ?us ! gr[? ( its orbit c be acc\nt$ =4 ,we !re=e conclude f9ally1 t ! tides are mak+ ! day long] & s5d+ ! moon away fur!r4 ,x is ! developm5t ( ! consequ5ces ( ^! laws t specially dem&s our att5tion 9 ^! lectures4 ,we mu/ h ! c\rage to look at ! facts unfl9*+ly1 & d$uce f !m all ! wondr\s consequ5ces !y involve4 ,_! pot5cy arises f a *>act]i/ic feature--!y are un9t]mitt+4 ,mo/ ( ! great a/ronomical *anges ) :i* we are ord9>ily famili> are really p]iodic3 !y gradually increase 9 "o direction = ye>s1 = c5turies1 or = untold ages2 b !n a *ange comes1 & ! increase is *ang$ into a decrease1 s t aft] ! lapse ( becom+ p]iods ! orig9al /ate ( ?+s is re/or$4 ,su* p]iodic ph5om5a ab\nd 9 a/ronomy4 ,!re is ! annual fluctuation ( ! seasons2 !re is ! eighte5 or n9ete5 ye> p]iod ( ! moon2 !re is ! great p]iod ( ! precession ( ! equ9oxes1 am\nt+ to tw5ty-six ?\s& ye>s2 & !n !re is ! /up5d\s ,annus ,magnus ( hundr$s ( ?\s&s ( ye>s1 dur+ :i* ! e>?'s orbit itself brea!s 9 & out 9 response to ! attraction ( ! planets4 ,b ^! p]iodic ph5om5a1 h[ev] important !y may be to u m]e creatures ( a day1 are insignificant 9 _! effects on ! gr& evolution ?r\gh :i* ! cele/ial bodies are pass+4 ,! really pot5t ag5ts 9 fa%ion+ ! univ]se are ^? :i*1 h[ev] sl[ or feeble !y may seem to be1 are /ill incessant 9 _! action4 ,! effect :i* a cause %all be compet5t to produce dep5ds n alone ^u ! int5sity ( t cause1 b also ^u ! "t dur+ :i* x has be5 9 op]ation4 ,f ! ph5om5a ( geology1 z well z f ^? ( a/ronomy1 we "k t ?is e>? & ! sy/em to :i* x belongs has endur$ = ages1 n to be c\nt$ by scores ( ?\s&s ( ye>s1 or1 z ,pr(4 ,tyndall has s well rem>k$1 ,n = six ?\s& ye>s1 nor = sixty ?\s& ye>s1 nor six hundr$ ?\s& ye>s1 b = ons ( untold millions4 ,^? sl5d] ag5ts :i* h devot$ !mselves unceas+ly to ! accompli%m5t ( a s+le task may 9 ?is long lapse ( "t h accompli%$ results ( /up5d\s magnitude4 ,9 fam$ /alactite cav]ns we are %[n a colossal figure ( cry/al ext5d+ f floor to ro(1 & ! =mation ( t column is acc\nt$ = :5 we see a t9y drop fall+ f ! ro( above to ! floor b5ea?4 ,a lifetime may n suffice = t fall+ drop to add an appreciable increase to ! /alactite d[n :i* x trickles1 or to ! gr[+ /alagmite on :i* x falls2 b :5 ! op]ation has be5 9 progress = imm5se ages1 x is capable ( ! =mation ( ! /ately column4 ,"h we h an illu/ration ( an influ5ce :i*1 ?\gh app>5tly trivial1 acquires colossal significance :5 adequate "t is af=d$4 ,x is ph5om5a ( ?is k9d :i* ! /ud5t ( nature %\ld mo/ n>r[ly wat*1 = !y are ! real ar*itects ( ! univ]se4 ,! tidal consequ5ces :i* we h already demon/rat$ are emphatically ( ?is non-p]iodic class--! day is always l5g!n+1 ! moon is always retreat+4 ,to-day is long] ?an ye/]day2 to-morr[ w be long] ?an to-day4 ,x _c be said t ! *ange is a great "o2 x is inde$ too small to be appreciable ev5 by our mo/ delicate obs]vations4 ,9 "o ?\s& ye>s ! alt]ation 9 ! l5g? ( a day is only a small fraction ( a second2 b :at may be a v small matt] 9 "o ?\s& ye>s c become a v l>ge "o 9 _m millions ( ye>s4 ,?us x is t :5 we /ret* our view ?r\gh imm5se vi/as ( "t pa/1 or :5 we look =w>d ?r\gh immeasurable ages ( "t to come1 ! alt]ation 9 ! l5g? ( ! day w assume ! mo/ />tl+ proportions1 & involve ! mo/ mom5t\s consequ5ces4 ,let u fir/ look back4 ,!re 0 a "t :5 ! day1 in/ead ( be+ ! tw5ty-f\r h\rs we n[ h1 mu/ h be5 only tw5ty-?ree h\rs1 ,h[ _m millions ( ye>s ago t 0 ,i d n pret5d to say1 nor is ! po9t mat]ial = our argum5t2 suffice x to say1 t assum+1 z geology assures u we may assume1 ! exi/5ce ( ^! ons ( millions ( ye>s1 !re 0 once a "t :5 ! day 0 n only "o h\r %ort]1 b 0 ev5 sev]al h\rs less ?an x is at pres5t4 ,nor ne$ we /op our retrospect at a day ( ev5 tw5ty1 or fifte51 or t5 h\rs long2 we %all at once project our glance back to an immeasurably remote epo*1 at :i* ! e>? 0 sp9n+ r\nd 9 a "t only "o six? or ev5 less ( ! l5g? ( ! pres5t day4 ,!re is "h a reason = our retrospect to halt1 = at "s ev5tful p]iod1 :5 ! day 0 ab\t ?ree or f\r h\rs long1 ! e>? mu/ h be5 9 a condition ( a v critical k9d4 ,x is well kn[n t fe>ful accid5ts occasionally happ5 :]e l>ge gr9d/ones are be+ driv5 at a high spe$4 ,! velocity ( rotation becomes too great = ! t5acity ( ! /one to )/& ! /ress2 a rupture takes place1 ! /one flies 9 pieces1 & huge fragm5ts are hurl$ ar\nd4 ,= ea* p>ticul> gr9d/one !re is a c]ta9 special velocity dep5d+ ^u its actual mat]ials & "*1 at :i* x w\ld inevitably fly 9 pieces4 ,i h once be=e lik5$ our e>? to a :eel2 n[ let me lik5 x to a gr9d/one4 ,!re is !re=e a c]ta9 critical velocity ( rotation = ! e>? at :i* x w\ld be on ! br9k ( rupture4 ,we _c exactly say1 9 our ignorance ( ! int]nal con/itution ( ! e>?1 :at l5g? ( day w\ld be ! %orte/ possible = our e>? to h consi/5tly ) ! pres]vation ( its integrity2 we may1 h[ev]1 assume t x w be ab\t ?ree or f\r h\rs1 or p]haps a little less ?an ?ree4 ,! exact am\nt1 h[ev]1 is n really v mat]ial to u2 x w\ld be suffici5t = our argum5t to ass]t t !re is a c]ta9 m9imum l5g? ( day = :i* ! e>? c hold toge!r4 ,9 our retrospect1 !re=e1 ?r\gh ! abyss ( "t pa/ our view mu/ be b\nd$ by t /ate ( ! e>? :5 x is revolv+ 9 ?is critical p]iod4 ,) :at happ5$ be=e t we %all n at pres5t conc]n ourselves4 ,?us we look back to a "t at ! beg9n+ ( ! pres5t ord] ( ?+s1 :5 ! day 0 only "s ?ree or f\r h\rs long4 ,let u n[ look at ! moon1 & exam9e :]e x mu/ h be5 dur+ ^! pa/ ages4 ,z ! moon is gradually gett+ fur!r & fur!r f u at pres5t1 s1 look+ back into pa/ "t1 we f9d t ! moon 0 ne>] & ne>] to ! e>? ! fur!r back our view ext5ds2 9 fact1 conc5trat+ our att5tion solely on ess5tial features1 we may say t ! pa? ( ! moon is a sort ( spiral :i* w9ds r\nd & r\nd ! e>?1 gradually gett+ l>g]1 ?\gh ) extreme sl[ness4 ,look+ back we see ?is spiral gradually coil+ 9 & 91 until 9 a retrospect ( millions ( ye>s1 in/ead ( its di/ance f ! e>? be+ #bdj1jjj miles1 x mu/ h be5 mu* less4 ,!re 0 a "t :5 ! moon 0 only #bjj1jjj miles away2 !re 0 a "t _m millions ( ye>s ago1 :5 ! moon 0 only #ajj1jjj miles away4 ,nor c we "h /op our retrospect2 we mu/ look fur!r & fur!r back1 & foll[ ! moon's spiral pa? z x creeps 9 & 9 t[>ds ! e>?1 until at la/ x appe>s actually 9 contact ) t great globe ( ours1 f :i* x is n[ sep>at$ by a qu>t] ( a million ( miles4 ,surely ! tides h ?us l$ u to ! k ( an a/\nd+ epo* 9 our e>?'s pa/ hi/ory1 :5 ! e>? is sp9n+ r\nd 9 a few h\rs1 & :5 ! moon is1 practically speak+1 9 contact ) x4 ,p]haps ,i %\ld r say1 t ! mat]ials ( our pres5t moon 7 9 ?is situation1 = we w\ld h>dly be entitl$ to assume t ! moon !n possess$ ! same globul> =m 9 :i* we see x n[4 ,to =m a j appreh5sion ( ! true nature ( bo? bodies at ?is critical epo*1 we mu/ /udy _! concurr5t hi/ory z x is disclos$ to u by a totally diff]5t l9e ( reason+4 ,drop1 !n1 = a mom5t all ?\ght ( tides1 & let u br+ to our aid ! laws ( heat1 :i* w disclose c]ta9 facts 9 ! anci5t hi/ory ( ! e>?-moon sy/em p]haps z a/\nd+ z ^? to :i* ! tides h conduct$ u4 ,9 "o respect we may comp>e ^! laws ( heat ) ! laws ( ! tides2 !y are bo? alike non-p]iodic1 _! effects are cumulative f age to age1 & imag9ation c h>dly ev5 impose a limit to ! magnific5ce ( ! works !y c accompli%4 ,our argum5t f heat is f\nd$ on a v simple matt]4 ,x is q obvi\s t a heat$ body t5ds to gr[ cold4 ,i am n n[ speak+ ( fires or ( actual combu/ion :]eby heat is produc$2 ,i am speak+ m]ely ( su* heat z w\ld be possess$ by a r$-hot pok] aft] be+ tak5 f ! fire1 or by an iron ca/+ aft] ! metal has be5 run into ! m\ld4 ,9 su* cases z ?is ! g5]al law holds good1 t ! heat$ body t5ds to gr[ cold4 ,! cool+ may be ret>d$ no d\bt if ! passage ( heat f ! body is imp$$4 ,we c1 = in/ance1 ret>d ! cool+ ( a teapot by ! well-kn[n practice ( putt+ a cosy ^u x2 b ! law rema9s t1 sl[ly or quickly1 ! heat$ body w t5d to gr[ cold]4 ,x seems almo/ pu]ile to insi/ ) any emphasis on a po9t s obvi\s z ?is1 b yet ,i frequ5tly f9d t p d n readily appreh5d all ! gigantic consequ5ces t c fl[ f a pr9ciple s simple4 ,x is true t a pok] cools :5 tak5 f ! fire2 we also f9d t a gigantic ca/+ weigh+ _m tons w gr[ gradually cold1 ?\gh x may require days to d s4 ,! same pr9ciple w ext5d to any object1 no matt] h[ va/ x may happ5 to be4 ,7 t great ca/+ #bjjj miles 9 diamet]1 or 7 x #hjjj miles 9 diamet]1 x w /ill /eadily "p ) its heat1 ?\gh no d\bt ! process ( cool+ becomes greatly prolong$ ) an increase 9 ! dim5sions ( ! heat$ body4 ,! e>? & ! moon _c escape f ! application ( ^! simple pr9ciples4 ,let u fir/ speak ( ! e>?4 ,!re are multitudes ( volcanoes 9 action at ! pres5t mom5t 9 v>i\s c\ntries ^u ?is e>?4 ,n[ :atev] explanation may be giv5 ( ! approximate cause ( ! volcanic ph5om5a1 !re c be no d\bt t !y indicate ! exi/5ce ( heat 9 ! int]ior ( ! e>?4 ,x may possibly be1 z "s h urg$1 t ! volcanoes are m]ely v5ts = comp>atively small masses ( subt]ranean molt5 matt]2 x may be1 z o!rs m reasonably1 9 my op9ion1 believe1 t ! :ole int]ior ( ! e>? is at ! temp]ature ( inc&esc5ce1 & t ! eruptions ( volcanoes & ! %ocks ( e>?quakes are m]ely consequ5ces ( ! gradual %r9kage ( ! ext]nal cru/1 z x cont9ually /rives to accommodate itself to ! less5+ bulk ( ! fluid int]ior4 ,b :i*ev] view we may adopt1 x is at lea/ obvi\s t ! e>? is 9 "p1 at all ev5ts1 a heat$ body1 & t ! heat is n 9 ! nature ( a combu/ion1 g5]at$ & su/a9$ by ! progress ( *emical action4 ,no d\bt !re may be local ph5om5a ( ?is description1 b by f> ! l>g] proportion ( ! e>?'s int]nal heat seems m]ely ! f]v\r ( inc&esc5ce4 ,x is to be lik5$ to ! heat ( ! molt5 iron :i* has be5 run into ! s&1 r ?an to ! gl[+ coals 9 ! furnace 9 :i* t iron has be5 smelt$4 ,!re is "o volcanic outbreak ( su* exceptional int]e/ 9 ^! mod]n times t ,i _c refra9 f allud+ to x4 ,d\btless e "o has he>d ( t m>vell\s eruption ( ,krakatoa1 :i* occurr$ on ,augu/ #bf? & #bg?1 #ahhc1 & gives a unique *apt] 9 ! hi/ory ( volcanic ph5om5a4 ,n alone 0 ! eruption ( ,krakatoa al>m+ 9 its m ord9>y manife/ations1 b x 0 unp>allel$ bo? 9 ! vehem5ce ( ! %ock & 9 ! di/ance to :i* ! effects ( ! great eruption 7 propagat$4 ,i speak n n[ ( ! great waves ( ocean t inundat$ ! coa/s ( ,sumatra & ,java1 & swept away ?irty-six ?\s& p1 nor d ,i allude to ! int5se d>kness :i* spread = "o hundr$ & eighty miles or m all r\nd4 ,i %all j m5tion ! ?ree mo/ important ph5om5a1 :i* demon/rate ! en]gy :i* /ill resides 9 ! int]ior ( our e>?4 ,place a t]re/rial globe be=e y1 & fix y\r att5tion on ! ,/raits ( ,sunda2 ?9k also ( ! great atmosph]ic ocean "s two or ?ree hundr$ miles deep :i* envelopes our e>?4 ,:5 a pebble is toss$ into a pond a beautiful s]ies ( conc5tric ripples div]ge f x2 s :5 ,krakatoa bur/ up 9 t mighty cata/rophe1 a s]ies ( gigantic waves 7 propagat$ ?r\gh ! air2 !y embrac$ ! :ole globe1 conv]g$ to ! antipodes ( ,krakatoa1 !nce aga9 div]g$1 & return$ to ! seat ( ! volcano2 a second "t ! mighty s]ies ( atmosph]ic ripples spread to ! antipodes1 & a second "t return$4 ,sev5 times did t s]ies ( waves c\rse ov] our globe1 & leave _! traces on e self-record+ b>omet] t our e>? possesses4 ,?irty-six h\rs 7 occupi$ 9 ! j\rney ( ! great undulation f ,krakatoa to its antipodes4 ,p]haps ev5 m /rik+ 0 ! ext5t ( our e>?'s surface ov] :i* ! noise ( ! great explosion spread4 ,at ,batavia1 n9ety-f\r miles away1 ! concussions 7 simply deaf5+2 at ,macass>1 9 ,celebes1 two /eam]s 7 s5t out to inve/igate ! explosions :i* 7 he>d1 little ?9k+ t !y came f ,krakatoa1 n9e hundr$ & sixty-n9e miles away4 ,al>m+ s\nds 7 he>d ov] ! isl& ( ,timor1 "o ?\s& ?ree hundr$ & fifty-"o miles away f ,krakatoa4 ,diego ,g>cia 9 ! ,*ogos isl&s is two ?\s& two hundr$ & sixty-sev5 miles f ,krakatoa1 b ! ?und]s trav]s$ ev5 ?is di/ance1 & 7 attribut$ to "s %ip 9 di/ress1 = :i* a se>* 0 made4 ,mo/ a/\nd+ ( all1 !re is und\bt$ evid5ce t ! s\nd ( ! mighty explosion 0 propagat$ across ne>ly ! entire ,indian ocean1 & 0 he>d 9 ! isl& ( ,rodriguez1 almo/ ?ree ?\s& miles away4 ,! imm5se di/ance ov] :i* ?is s\nd j\rney$ w be appreciat$ by ! fact1 t ! noise did n rea* ,rodriguez until f\r h\rs aft] x _h left ,krakatoa4 ,9 fact1 x w\ld seem t if ,vesuvius 7 to explode ) ! same vehem5ce z ,krakatoa did1 ! ?und]s ( ! explosion might p5etrate s f> z to be he>d 9 ,london4 ,!re is ano!r & m beautiful manife/ation ( ! _w-wide significance ( ! ,krakatoa outbreak4 ,! va/ column ( smoke & a%es asc5d$ tw5ty miles high 9 ! air1 & comm5c$ a s]ies ( voyages ar\nd ! equatorial regions ( ! e>?4 ,9 ?ree days x cross$ ! ,indian ocean1 & 0 trav]s+ equatorial ,africa2 !n came an ,atlantic voyage2 & !n x c\rs$ ov] c5tral ,am]ica1 be=e a ,pacific voyage br\ght x back to its po9t ( dep>ture aft] ?irte5 days2 !n ! du/ />t$ aga91 & 0 trac$ ar\nd ano!r simil> circuit1 :ile x 0 ev5 track$ = a consid]able "t 9 plac+ ! ?ird girdle r\nd ! e>?4 ,/range blue suns & gre5 moons & o!r my/]i\s ph5om5a m>k$ ! progress ( ?is va/ volcanic cl\d4 ,at la/ ! cl\d began to lose its d5sity1 ! du/ spread m widely ov] ! tropics1 became diffus$ ?r\gh ! temp]ate regions1 & !n ! :ole e>? 0 able to p>ticipate 9 ! glories ( ,krakatoa4 ,! m>vell\s sunsets 9 ! autumn ( #ahhc are attributable to ?is cause2 & ?us once aga9 0 br\ght be=e u ! fact t ! e>? /ill conta9s l>ge /ores ( !rmal en]gy4 ,attempts are sometimes made to expla9 volcanic ph5om5a on ! supposition t !y are entirely ( a local "*1 & t we are n entitl$ to inf] ! inc&esc5t nature ( ! e>?'s int]ior f ! fact t volcanic outbreaks occasionally happ54 ,= our pres5t purpose ?is po9t is immat]ial1 ?\gh ,i mu/ say x appe>s to me unreasonable to d5y t ! int]ior ( ! e>? is 9 a mo/ highly heat$ /ate4 ,e te/ we c apply %[s u ! exi/5ce ( int]nal heat4 ,sett+ aside ! m colossal ph5om5a ( volcanic eruptions1 we h innum]able m9or manife/ations ( its pres5ce4 ,are !re n geys]s & hot spr+s 9 _m p>ts ( ! e>?8 & h we n all ov] our globe inv>iable te/imony confirm+ ! /atem5t1 t ! deep] we g d[n b5ea? its surface ! hott] does ! temp]ature become8 ,e m9] is famili> ) ^! facts2 he kn[s t ! deep] are 8 %afts ! w>m] x is d[n bel[1 & ! great] ! necessity = provid+ increas$ v5tilation to keep ! temp]ature )9 a limit t %all be suitable = ! workm54 ,all ^! v>i$ classes ( ph5om5a admit solely ( "o explanation1 & t is1 t ! int]ior ( ! e>? conta9s va/ /ores ( inc&esc5t heat4 ,we n[ apply to our e>? ! same reason+ :i* we %\ld employ on a pok] tak5 f ! fire1 or on a ca/+ drawn f ! f\ndry4 ,su* bodies w lose _! heat by radiation & conduction4 ,! e>? is !re=e los+ its heat4 ,no d\bt ! process is an extremely sl[ "o4 ,! mighty res]voirs ( int]nal heat are cov]$ by va/ lay]s ( rock1 :i* are su* excell5t non-conductors t !y (f] e possible imp$im5t to ! leakage ( heat f ! int]ior to ! surface4 ,we coat our /eam-pipes ov] ) non-conduct+ mat]ial1 & ?is c n[ be done s successfully1 t x is beg9n+ to be f\nd economical to transmit /eam = a v long di/ance ?r\gh prop]ly protect$ pipes4 ,b no non-conduct+ mat]ial t we c manufacture c be half s effective z ! %ell ( rock tw5ty miles or m 9 ?ickness1 :i* secures ! heat$ int]ior ( ! e>? f rapid loss by radiation into space4 ,ev5 7 ! e>?'s surface solid copp] or solid silv]1 bo? mo/ admirable conductors ( heat1 ! cool+ d[n ( ?is va/ globe w\ld be an extremely t>dy process2 h[ mu* m t>dy mu/ x !re=e be :5 su* exce$+ly bad conductors z rocks =m ! envelope8 ,h[ imp]fectly mat]ial ( ?is k9d w transmit heat is /rik+ly illu/rat$ by ! great bla/ iron furnaces :i* are s vitally important 9 "o ( ,engl&'s greate/ manufactur+ indu/ries4 ,a gl[+ mass ( coal & iron ore & lime/one is "h urg$ to vivid inc&esc5ce by a bla/ ( air itself heat$ to an int5se temp]ature4 ,! mighty heat ?us g5]at$--suffici5t z x is to deta* ! iron f its close alliance ) ! e>?y mat]ials & to r5d] ! metal out z a pure /ream ru%+ :ite-hot f ! v5t--is suffici5tly conf9$ by a few feet ( brick-"w1 "o side ( :i* is !re=e at ! temp]ature ( molt5 iron1 :ile ! o!r is at a temp]ature n mu* exce$+ t ( ! air4 ,we may lik5 ! brick-"w ( a bla/ furnace to ! rocky cov]+ ( ! e>?2 9 ea* case an exce$+ly high temp]ature on "o side is compatible ) a v mod]ate temp]ature on ! o!r4 ,al?\gh ! dra9age ( heat away f ! e>?'s int]ior to its surface1 & its loss !re by radiation into space1 is an extremely t>dy process1 yet x is incessantly go+ on4 ,we h "h aga9 to note ! ability = gigantic effect :i* a small b cont9ually op]at+ cause may h1 provid$ x always t5ds 9 ! same direction4 ,! e>? is incessantly los+ heat2 & ?\gh 9 a day1 a week1 or a ye> ! loss may n be v significant1 yet :5 we come to deal ) p]iods ( "t t h to be reckon$ by millions ( ye>s1 x may well be t ! effect ( a small loss ( heat p] annum c1 9 ! c\rse ( ^! ages1 rea* unimag9$ dim5sions4 ,suppose1 = in/ance1 t ! e>? exp]i5c$ a fall ( temp]ature 9 its int]ior :i* am\nt$ to only "o-?\s&? ( a degree 9 a ye>4 ,s m9ute a quantity z ?is is imp]ceptible4 ,ev5 9 a c5tury1 ! loss ( heat at ?is rate w\ld be only ! t5? ( a degree4 ,!re w\ld be no possible way ( detect+ x2 ! mo/ c>eful !rmomet] c\ld n be reli$ on to tell u = a c]ta9ty t ! temp]ature ( ! hot wat]s ( ,ba? _h decl9$ ! t5? ( a degree2 & ,i ne$ h>dly say1 t ! fall ( a t5? ( a degree w\ld signify no?+ 9 ! lavas ( ,vesuvius1 nor influ5ce ! ?und]s ( ,krakatoa by "o appreciable note4 ,s f> z a human life or ! life ( ! human race is conc]n$1 ! decl9e ( a t5? ( a degree p] c5tury 9 ! e>?'s int]nal heat is absolutely void ( significance4 ,i _c1 h[ev]1 impress ^u y too /rongly1 t ! m]e few ?\s&s ( ye>s ) :i* human hi/ory is cognizant are an inappreciable mom5t 9 comp>ison ) ^? unmeasur$ millions ( ye>s :i* geology op5s out to u1 or ) ^? f> m maje/ic p]iods :i* ! a/ronom] dem&s = ! ev5ts he has to describe4 ,an annual loss ( ev5 "o-?\s&? ( a degree w be capable ( /up5d\s a*ievem5ts :5 suppos$ to op]ate dur+ epo*s ( geological magnitude4 ,9 fact1 its effects w\ld be s va/1 t x seems h>dly cr$ible t ! pres5t loss ( heat f ! e>? %\ld be s great z to am\nt to an abatem5t ( "o-?\s&? ( a degree p] annum1 = t w\ld mean1 t 9 a ?\s& ye>s ! e>?'s temp]ature w\ld decl9e by "o degree1 & 9 a million ye>s ! decl9e w\ld am\nt to a ?\s& degrees4 ,at all ev5ts1 ! illu/ration may suffice to %[1 t ! fact t we are n able to prove by our in/rum5ts t ! e>? is cool+ is no argum5t :atev] aga9/ ! inevitable law1 t ! e>?1 l e o!r heat$ body1 mu/ be t5d+ t[>ds a l[] temp]ature4 ,)\t pret5d+ to any num]ical accuracy1 we c at all ev5ts give a qualitative if n a quantitative analysis ( ! pa/ hi/ory ( our e>?1 9 s f> z its *anges ( temp]ature are conc]n$4 ,a million ye>s ago our e>? d\btless conta9$ appreciably m heat ?an x does at pres5t4 ,i speak n n[1 ( c\rse1 ( m]e sol> heat--( ! heat :i* gives u ! vicissitudes ( seasons2 ,i am only ref]r+ to ! orig9al ho>d ( int]nal heat :i* is gradually wan+4 ,z !re=e our retrospect ext5ds ?r\gh millions & millions ( pa/ ages1 we see our e>? ev] gr[+ w>m] & w>m] ! fur!r & fur!r we look back4 ,!re 0 a "t :5 ^? heat$ /rata :i* we h n[ to g deep d[n 9 m9es to f9d 7 consid]ably ne>] ! surface4 ,at pres5t1 7 x n = ! sun1 ! heat ( ! e>? :]e we /& w\ld h>dly be appreciably above ! temp]ature ( inf9ite space--p]haps "s #bjj or #cjj degrees bel[ z]o4 ,b !re mu/ h be5 a "t :5 !re 0 suffici5t int]nal heat to ma9ta9 ! ext]ior at a w>m & inde$ at a v hot temp]ature4 ,nor is !re any b\nd to our retrospect aris+ f ! op]ation or int]v5tion ( any o!r ag5t1 s f> z we "k2 consequ5tly ! hott] & ! hott] gr[s ! surface ! fur!r & ! fur!r we look back4 ,nor c we /op until1 at an antiquity s great t ,i d n v5ture on any e/imate ( ! date1 we discov] t ?is e>? mu/ h consi/$ ( gl[+ hot mat]ial4 ,fur!r & fur!r we c look back1 & we see ! rocks--or :atev] o!r t]m we *oose to apply to ! !n +r$i5ts ( ! e>?'s cru/--9 a :ite-hot & ev5 9 a molt5 condition4 ,?us our argum5t has l$ u to ! belief t "t 0 :5 ?is n[ solid globe ( ours 0 a ball ( :ite-hot fluid4 ,on ! argum5t :i* ,i h "h us$ !re are j two rem>ks :i* ,i p>ticul>ly wi% to make4 ,note 9 ! fir/ place1 t our reason+ is f\nd$ on ! fact t ! e>? is at pres5t1 to "s ext5t1 heat$4 ,x matt]s n :e!r ?is heat be mu* or little2 our argum5t w\ld h be5 equally valid _h ! e>? only conta9$ a s+le p>ticle ( its mass at a some:at high] temp]ature ?an ! temp]ature ( space4 ,i am1 ( c\rse1 n allud+ 9 ?is to heat :i* c be g5]at$ by combu/ion4 ,! o!r po9t to :i* ,i ref] is to remove an objection :i* may possibly be urg$ aga9/ ?is l9e ( reason+4 ,i h argu$ t because ! temp]ature is cont9ually increas+ z we look backw>ds1 t !re=e a v great temp]ature mu/ once h prevail$4 ,)\t "s explanation ?is argum5t is n logically complete4 ,!re is1 x is well kn[n1 ! old p>adox ( ! geometric s]ies2 y may add a f>?+ to a halfp5ny1 & !n a half-f>?+1 & !n a qu>t]-f>?+1 & !n ! eigh? ( a f>?+1 foll[$ by ! sixte5?1 & ?irty-second1 & s on1 halv+ ! contribution ea* "t4 ,n[ no matt] h[ long y cont9ue ?is process1 ev5 if y w5t on ) x = ev]1 & ?us made an inf9ite numb] ( contributions1 y w\ld nev] accompli% ! task ( rais+ ! orig9al halfp5ny to ! dignity ( a p5ny4 ,an inf9ite numb] ( quantities may !re=e1 z ?is illu/ration %[s1 nev] succe$ 9 atta9+ any consid]able dim5sions4 ,our argum5t1 h[ev]1 ) reg>d to ! increase ( heat z we look back is ! v opposite ( ?is4 ,x is ! ess5ce ( a cool+ body to lose heat m rapidly 9 proportion z its temp]ature is great]4 ,?us ?\gh ! "o-?\s&? ( a degree may be all ! fall ( temp]ature t our e>? n[ exp]i5ces 9 a twelvemon?1 yet 9 ^? gl[+ days :5 ! surface 0 heat$ to inc&esc5ce1 ! loss ( heat p] annum mu/ h be5 imm5sely great] ?an x is n[4 ,x !re=e foll[s t ! rate ( ga9 ( ! e>?'s heat z we look back mu/ be ( a diff]5t "* to t ( ! geometric s]ies :i* ,i h j illu/rat$2 = ea* addition to ! e>?'s heat1 z we look back f ye> to ye>1 mu/ gr[ great] & great]1 & !re=e !re is "h no %elt] = a fallacy 9 ! argum5t on :i* ! exi/5ce ( high temp]ature ( primeval times is f\nd$4 ,! reason+ t ,i h appli$ to our e>? may be appli$ 9 almo/ simil> words to ! moon4 ,x is true t we h n any k ( ! int]nal nature ( ! moon at pres5t1 nor are we able to po9t to any active volcanic ph5om5a at pres5t 9 progress !re 9 support ( ! cont5tion t ! moon ei!r has n[ int]nal heat1 or did once possess x4 ,x is1 h[ev]1 impossible to d5y ! evid5ce :i* ! lun> crat]s af=d z to ! pa/ exi/5ce ( volcanic activity on our satellite4 ,heat1 !re=e1 !re 0 once 9 ! moon2 & accord+ly we are enabl$ to conclude t1 on a retrospect ?r\gh illimitable p]iods ( "t1 we mu/ f9d ! moon trans=m$ f t cold & in]t body %e n[ seems to a gl[+ & inc&esc5t mass ( molt5 mat]ial4 ,! e>? !re=e & ! moon 9 "s remote ages--n alone ant]ior to ! exi/5ce ( life1 b ant]ior ev5 to ! e>lie/ p]iods ( :i* geologi/s h cognizance--mu/ h be5 bo? globes ( molt5 mat]ials :i* h consolidat$ into ! rocks ( ! pres5t epo*4 ,we mu/ n[ rev]t to ! tidal hi/ory ( ! e>?-moon sy/em4 ,did we n %[ t !re 0 a "t :5 ! e>? & ! moon--or p]haps1 ,i %\ld say1 ! +r$i5ts ( ! e>? & moon--7 close toge!r1 7 inde$ 9 actual contact8 ,we h n[ le>n$1 f a :olly diff]5t l9e ( reason+1 t 9 v e>ly ages bo? bodies 7 highly heat$4 ,"h z else:]e 9 ?is !ory we c make little or no attempt to give any *ronology1 or to h>monize ! diff]5t l9es along :i* ! c\rse ( hi/ory has run4 ,no "o c =m ! slighte/ idea z to :at ! temp]ature ( ! e>? & ( ! moon mu/ h be5 9 ^? primeval ages :5 !y 7 9 contact4 ,x is impossible1 h[ev]1 to d5y t !y mu/ bo? h be5 9 a v highly heat$ /ate2 & ev]y?+ we "k ( ! matt] incl9es u to ! belief t ! temp]ature ( ! e>?-moon sy/em mu/ at ?is critical epo* h be5 "o ( gl[+ inc&esc5ce & fusion4 ,x is !re=e q possible t ^! bodies--! moon especially--may h !n be5 n at all ( ! =m we see !m n[4 ,x has be5 suppos$1 & !re are "s gr\nds = ! supposition1 t at ?is initial /age ( e>?-moon hi/ory ! moon mat]ials did n =m a globe1 b 7 dispos$ 9 a r+ :i* surr\nd$ ! e>?1 ! r+ be+ 9 a condition ( rapid rotation4 ,x 0 at a subsequ5t p]iod1 accord+ to ?is view1 t ! sub/ances 9 ! r+ gradually drew toge!r1 & !n by _! mutual attractions =m$ a globe :i* ultimately consolidat$ d[n into ! compact moon z we n[ see x4 ,i mu/1 h[ev]1 specially draw y\r att5tion to ! cle>ly-m>k$ l9e :i* divides ! facts :i* dynamics h taught u f ^? notions :i* are to be reg>d$ z m or less conjectural4 ,int]pret+ ! action ( ! tides by ! pr9ciples ( dynamics1 we are assur$ t ! moon 0 once--or r ! mat]ials ( ! moon--9 ! imm$iate vic9ity ( ! e>?4 ,!re1 h[ev]1 dynamics leaves u1 & un=tunately )holds its accurate illum9ation f ! ev5ts :i* imm$iately prec$$ t /ate ( ?+s4 ,! !ory ( tidal evolution :i* ,i am describ+ 9 ^! lectures is ma9ly ! "w ( ,pr(essor ,george ,h4 ,d>w9 ( ,cambridge4 ,mu* ( ! orig9al p>ts ( ! !ory ( ! tides 0 due to ,sir ,william ,?omson1 & ,i h also m5tion$ h[ ,pr(essor ,purs] contribut$ an important elem5t to ! dynamical !ory4 ,x is1 h[ev]1 ,d>w9 :o has p]si/5tly d$uc$ f ! !ory all ! v>i\s consequ5ces :i* c be legitimately drawn f x4 ,d>w91 = in/ance1 po9t$ out t z ! moon is rec$+ f u1 x mu/1 if we only look f> en\gh back1 h be5 once 9 practical contact ) ! e>?4 ,x is to ,d>w9 also t we owe _m ( ! o!r p>ts ( a fasc9at+ !ory1 ei!r 9 its ma!matical or a/ronomical aspect2 b ,i mu/ take ?is opportunity ( say+1 t ,i d n propose to make ,pr(essor ,d>w9 or any ( ! o!r ma!maticians ,i h nam$ responsible = all t ,i %all say 9 ^! lectures4 ,i mu/ be myself acc\ntable = ! way 9 :i* ! subject is be+ treat$1 z well z = _m ( ! illu/rations us$1 & "s ( ! d$uctions ,i h drawn f ! subject4 ,x is almo/ unavoidable = u to make a surmise z to ! cause by :i* ! moon _h come into ?is rem>kable position close to ! e>? at ! mo/ critical epo* ( e>?-moon hi/ory4 ,) ref]5ce to ?is ,pr(essor ,d>w9 has (f]$ an explanation1 :i* seems s exce$+ly plausible t x is impossible to resi/ ! notion t x mu/ be correct4 ,i w ask y to ?9k ( ! e>? n z a solid body cov]$ l>gely ) ocean1 b z a gl[+ globe ( molt5 mat]ial4 ,9 a globe ( ?is k9d x is possible = great undulations to be set up4 ,"h is a l>ge vase ( wat]1 & by displac+ x ,i c cause ! wat] to undulate ) a p]iod :i* dep5ds on ! size ( ! vessel2 undulations c be set up 9 a bucket ( wat]1 ! p]iod ( ^! undulations be+ dep5d5t ^u ! dim5sions ( ! bucket4 ,simil>ly 9 a va/ globe ( molt5 mat]ial c]ta9 undulations c\ld be set up1 & ^? undulations w\ld h a p]iod dep5d+ ^u ! dim5sions ( ?is vibrat+ mass4 ,we may conjecture a mode 9 :i* su* vibrations c\ld be orig9at$4 ,imag9e a ?9 %ell ( rigid mat]ial :i* j encases ! globe2 suppose ?is be divid$ into f\r qu>t]s1 l ! f\r qu>t]s ( an orange1 & t two ( ^! opposite qu>t]s be reject$1 leav+ two qu>t]s on ! liquid4 ,n[ suppose t ^! two qu>t]s be sudd5ly press$ 91 & !n be z sudd5ly remov$--!y w produce depressions1 ( c\rse1 on ! two opposite qu>t]s1 :ile ! uncompress$ qu>t]s w become protub]ant4 ,9 virtue ( ! mutual attractions betwe5 ! diff]5t p>ticles ( ! mass1 an ef=t w be made to re/ore ! globul> =m1 b ?is w ( c\rse r ov]%oot ! m>k2 & !re=e a s]ies ( undulations w be orig9at$ by :i* two opposite qu>t]s ( ! sph]e w alt]nately %r9k 9 & become protub]ant4 ,!re w be a p>ticul> p]iod to ?is oscillation4 ,= our globe x w\ld appe> to be some:]e ab\t an h\r & a half or two h\rs2 b !re is necess>ily a good deal ( unc]ta9ty ab\t ?is po9t4 ,we h se5 h[ 9 ^? primitive days ! e>? 0 sp9n+ ar\nd v rapidly2 & ,i h also /at$ t ! e>? might at ?is v critical epo* ( its hi/ory be comp>$ ) a gr9d/one :i* is be+ driv5 s rapidly t x is on ! v br9k ( rupture4 ,x is rem>kable to note1 t a cause t5d+ to precipitate a rupture ( ! e>? 0 at h&4 ,! sun !n rais$ tides 9 ! e>? z x does at pres5t4 ,:5 ! e>? revolv$ 9 a p]iod ( "s f\r h\rs or !reab\ts1 ! high tides caus$ by ! sun succe$$ ea* o!r at int]vals ( ab\t two h\rs4 ,:5 ,i speak ( tides 9 ?is respect1 ( c\rse ,i am n allud+ to oceanic tides2 ^! 7 ! days long be=e ocean exi/$1 at lea/ 9 ! liquid =m4 ,! tides ,i am speak+ ab\t 7 rais$ 9 ! fluids & mat]ials :i* !n con/itut$ ! :ole ( ! gl[+ e>?2 ^? tides rose & fell "u ! ?rob produc$ by ! sun1 j z truly z tides produc$ 9 an ord9>y ocean4 ,b n[ note ! significant co9cid5ce betwe5 ! p]iod ( ! ?rob produc$ by ! sun-rais$ tides1 & t natural p]iod ( vibration :i* belong$ to our e>? z a mass ( molt5 mat]ial4 ,x !re=e foll[s1 t ! impulse giv5 to ! e>? by ! sun h>moniz$ 9 "t ) t p]iod 9 :i* ! e>? itself 0 dispos$ to oscillate4 ,a well-kn[n dynamical pr9ciple "h comes into play4 ,y see a heavy weight hang+ by a /r+1 & 9 my h& ,i hold a little slip ( wood no heavi] ?an a common p5cil2 ord9>ily speak+1 ,i might /rike t heavy weight ) ?is slip ( wood1 & no effect is produc$2 b if ,i take c>e to "t ! little bl[s t ,i give s t !y %all h>monize ) ! vibrations :i* ! weight is naturally dispos$ to make1 !n ! effect ( _m small bl[s w be cumulative1 s mu* s1 t aft] a %ort "t ! weight beg9s to respond to my ef=ts1 & n[ y see x has acquir$ a sw+ ( v consid]able amplitude4 ,9 ,pr(essor ,fitzg]ald's address to ! ,briti% ,association at ,ba? la/ autumn1 he gives an acc\nt ( ^? a/\nd+ exp]im5ts ( ,h]tz1 9 :i* well-tim$ electrical impulses broke d[n an air resi/ance1 & reveal$ to u e!real vibrations :i* c\ld nev] h be5 made manife/ except by ! pr9ciple we are "h discuss+4 ,! +5i\s conjecture has be5 made1 t :5 ! e>? 0 ?r[n into tidal vibrations 9 ^? primeval days1 ^! slight vibrations1 h>moniz+ z !y did ) ! natural p]iod ( ! e>?1 gradually acquir$ amplitude2 ! result be+ t ! pulse ( ea* successive vibration increas$ at la/ to su* an ext5t t ! e>? sep>at$ "u ! /ress1 & ?rew (f a portion ( ^? semi-fluid mat]ials ( :i* x 0 compos$4 ,9 process ( "t ^! reject$ portions contract$ toge!r1 & ultimately =m$ t moon we n[ see4 ,su* is ! orig9 ( ! moon :i* ! mod]n !ory ( tidal evolution has pres5t$ to our notice4 ,!re are two great epo*s 9 ! evolution ( ! e>?-moon sy/em--two critical epo*s :i* possess a unique dynamical significance2 "o ( ^! p]iods 0 e>ly 9 ! beg9n+1 :ile ! o!r _c arrive = c\ntless ages yet to come4 ,i am aw>e t 9 discuss+ ?is matt] ,i am ent]+ some:at l>gely into ma!matical pr9ciples2 ,i mu/ only endeav\r to /ate ! matt] z succ9ctly z ! subject w admit4 ,9 an e>li] "p ( ?is lecture ,i h expla9$ h[1 dur+ all ! developm5t ( ! e>?-moon sy/em1 ! quantity ( mom5t ( mom5tum rema9s unalt]$4 ,! mom5t ( mom5tum ( ! e>?'s rotation add$ to ! mom5t ( mom5tum ( ! moon's revolution rema9s con/ant2 if "o ( ^! quantities increase ! o!r mu/ decrease1 & ! progress ( ! evolution w h ?is result1 t en]gy %all be gradually lo/ 9 consequ5ce ( ! friction produc$ by ! tides4 ,! inve/igation is "o appropriate = ma!matical =mul1 su* z ^? t c be f\nd 9 ,pr(essor ,d>w9's memoirs2 b nature has 9 ?is in/ance dealt k9dly ) u1 = %e has enabl$ an ab/ruse ma!matical pr9ciple to be dealt ) 9 a s+ul>ly cle> & concise mann]4 ,we want to obta9 a def9ite view ( ! alt]ation 9 ! en]gy ( ! sy/em :i* %all correspond to a small *ange 9 ! velocity ( ! e>?'s rotation1 ! moon ( c\rse accommodat+ itself s t ! mom5t ( mom5tum %all be pres]v$ unalt]$4 ,we c use = ?is purpose an angul> velocity :i* repres5ts ! excess ( ! e>?'s rotation ov] ! angul> revolution ( ! moon2 x is1 9 fact1 ! app>5t angul> velocity ) :i* ! moon appe>s to move r\nd ! heav5s4 ,if we repres5t by ,n ! angul> velocity ( ! e>?1 & by ,m ! angul> velocity ( ! moon 9 its orbit r\nd ! e>?1 ! quantity we desire to express is ,n--,m2 we %all call x ! relative rotation4 ,! ma!matical !orem :i* tells u :at we want c be enunciat$ 9 a concise mann] z foll[s4 ,! alt]ation ( ! en]gy ( ! sy/em may be express$ by multiply+ ! relative rotation by ! *ange 9 ! e>?'s angul> velocity4 ,?is result w expla9 _m po9ts to u 9 ! !ory1 b j at pres5t ,i am only go+ to make a s+le inf]5ce f x4 ,i mu/ adv]t = a mom5t to ! famili> conception ( a maximum or a m9imum4 ,if a magnitude be increas+1 t is1 gradually gr[+ great] & great]1 x has obvi\sly n atta9$ a maximum s long z ! gr[? is 9 progress4 ,nor if ! object be actually decreas+ c x be said to be at a maximum ei!r2 = !n x 0 great] a second ago ?an x is n[1 & !re=e x _c be at a maximum at pres5t4 ,we may illu/rate ?is by ! famili> example ( a /one ?r[n up into ! air2 at fir/ x gradually rises1 be+ high] at ea* in/ant ?an x 0 previ\sly1 until a culm9at+ po9t is rea*$1 :5 j = a mom5t ! /one is pois$ at ! summit ( its pa? ere x comm5ces its return to e>? aga94 ,9 ?is case ! maximum po9t is obta9$ :5 ! /one1 hav+ ceas$ to asc5d1 & n hav+ yet comm5c$ to desc5d1 is mom5t>ily at re/4 ,! same pr9ciples apply to ! det]m9ation ( a m9imum4 ,z long z ! magnitude is decl9+ ! m9imum has n be5 rea*$2 x is only :5 ! decl9e has ceas$1 & an increase is on ! po9t ( sett+ 91 t ! m9imum c be said to be t\*$4 ,! e>?-moon sy/em conta9s at any mom5t a c]ta9 /ore ( en]gy1 & to e conceivable condition ( ! e>?-moon sy/em a c]ta9 quantity ( en]gy is appropriate4 ,x is in/ructive = u to /udy ! diff]5t positions 9 :i* ! e>? & ! moon might lie1 & to exam9e ! diff]5t quantities ( en]gy :i* ! sy/em w conta9 9 ea* ( ^? v>i$ positions4 ,x is h[ev] to be und]/ood t ! diff]5t cases all presuppose ! same total mom5t ( mom5tum4 ,among ! diff]5t cases t c be imag9$1 ^? w be ( special int]e/ 9 :i* ! total quantity ( en]gy 9 ! sy/em is a maximum or a m9imum4 ,we mu/ = ?is purpose suppose ! sy/em gradually to run ?r\gh all conceivable *anges1 ) ! e>? & moon z ne> z possible1 & z f> z possible1 & 9 all int]m$iate positions2 we mu/ also attribute to ! e>? e v>iety 9 ! velocity ( its rotation :i* is compatible ) ! pres]vation ( ! mom5t ( mom5tum4 ,beg9n+ !n ) ! e>?'s velocity ( rotation at its l[e/1 we may suppose x gradually & cont9ually increas$1 &1 z we h already se51 ! *ange 9 ! en]gy ( ! sy/em is to be express$ by multiply+ ! relative rotation into ! *ange ( ! e>?'s angul> velocity4 ,x foll[s f ! pr9ciples we h already expla9$1 t ! maximum or m9imum en]gy is atta9$ at ! mom5t :5 ! alt]ation is z]o4 ,x !re=e foll[s1 t ! critical p]iods ( ! sy/em w arise :5 ! relative rotation is z]o1 t is1 :5 ! e>?'s rotation on its axis is p]=m$ ) a velocity equal to t ) :i* ! moon revolves ar\nd ! e>?4 ,?is is truly a s+ul> condition ( ! e>?-moon sy/em2 ! moon 9 su* a case w\ld revolve ar\nd ! e>? z if ! two bodies 7 b\nd toge!r by rigid bonds into :at 0 practically a s+le solid body4 ,at ! pres5t mom5t no d\bt to "s ext5t ?is condition is realiz$1 because ! moon always turns ! same face to ! e>? 7a po9t on :i* we %all h some?+ to say lat] on72 b 9 ! orig9al condition ( ! e>?-moon sy/em1 ! e>? w\ld also con/antly direct ! same face to ! moon1 a condition ( ?+s :i* is n[ v f> f be+ realiz$4 ,x c be %[n f ! ma!matical nature ( ! problem t !re are f\r /ates ( ! e>?-moon sy/em 9 :i* ?is condition may be realiz$1 & :i* are also compatible ) ! cons]vation ( ! mom5t ( mom5tum4 ,we c express :at ?is condition implies 9 a some:at m simple mann]4 ,let u und]/& by ! day ! p]iod ( ! e>?'s rotation on its axis1 :atev] t may be1 & let u und]/& by ! mon? ! p]iod ( revolution ( ! moon ar\nd ! e>?1 :atev] value x may h2 !n ! condition ( maximum or m9imum en]gy is atta9$ :5 ! day & ! mon? h become equal to ea* o!r4 ,( ! f\r occasions ma!matically possible 9 :i* ! day & ! mon? c be equal1 !re are only two :i* at pres5t ne$ engage our att5tion--"o ( ^! occurr$ ne> ! beg9n+ ( ! e>? & moon's hi/ory1 ! o!r rema9s to be approa*$ 9 ! immeasurably remote future4 ,! two rema9+ solutions are futile1 be+ :at ! ma!matician w\ld describe z imag9>y4 ,!re is a fundam5tal diff]5ce betwe5 ! dynamical conditions 9 ^! critical epo*s--9 "o ( !m ! en]gy ( ! sy/em has atta9$ a maximum value1 & 9 ! o!r ! en]gy ( ! sy/em is at a m9imum value4 ,x is impossible to ov]-e/imate ! significance ( ^! two /ates ( ! sy/em4 ,i may recall ! fundam5tal notion :i* e "o has le>n$ 9 me*anics1 z to ! diff]5ce betwe5 /able & un/able equilibrium4 ,! conceivable possibility ( mak+ an egg /& on its end is a practical impossibility1 because nature does n l un/able equilibrium1 & a body dep>ts !refrom on ! lea/ di/urbance2 on ! o!r h&1 /able equilibrium is ! position 9 :i* nature t5ds to place ev]y?+4 ,a log ( wood float+ on a riv] might conceivably float 9 a v]tical position ) its end up out ( ! wat]1 b y nev] c\ld succe$ 9 s balanc+ x1 because no matt] h[ c>efully y adju/$ ! log1 x w\ld almo/ in/antly turn ov] :5 y left x free2 on ! o!r h&1 :5 ! log floats naturally on ! wat] x assumes a horizontal position1 to :i*1 :5 mom5t>ily displac$ !refrom1 x w return if p]mitt$ to d s4 ,we h "h an illu/ration ( ! contra/ betwe5 /able & un/able equilibrium4 ,x w be f\nd g5]ally t a body is 9 equilibrium :5 its c5tre ( gravity is at its highe/ po9t or at its l[e/ po9t2 !re is1 h[ev]1 ?is important diff]5ce1 t :5 ! c5tre ( gravity is highe/ ! equilibrium is un/able1 & :5 ! c5tre ( gravity is l[e/ ! equilibrium is /able4 ,! pot5tial en]gy ( an egg pois$ on its end 9 un/able equilibrium is great] ?an :5 x lies on its side 9 /able equilibrium4 ,9 fact1 en]gy mu/ be exp5d$ to raise ! egg f ! horizontal position to ! v]tical2 :ile1 on ! o!r h&1 "w c\ld conceivably be done by ! egg :5 x passes f ! v]tical position to ! horizontal4 ,speak+ g5]ally1 we may say t ! /able position indicates l[ en]gy1 :ile a r$undancy ( t valuable ag5t is sugge/ive ( in/ability4 ,we may apply simil> pr9ciples to ! consid]ation ( ! e>?-moon sy/em4 ,x is true t we h "h a s]ies ( dynamical ph5om5a1 :ile ! illu/rations ,i h giv5 ( /able & un/able equilibrium relate only to /atical problems2 b we c h dynamical /ability & dynamical in/ability1 j z we c h /able & un/able equilibrium4 ,dynamical in/ability corresponds ) ! maximum ( en]gy1 & dynamical /ability to ! m9imum ( en]gy4 ,at t primitive epo*1 :5 ! en]gy ( ! e>?-moon sy/em 0 a maximum1 ! condition 0 "o ( dynamical in/ability2 x 0 impossible t x %\ld la/4 ,b n[ m>k h[ truly critical an occurr5ce ?is mu/ h be5 9 ! hi/ory ( ! e>?-moon sy/em1 = h ,i n already expla9$ t x is a necess>y condition ( ! progress ( tidal evolution t ! en]gy ( ! sy/em %\ld be always decl9+8 ,b "h our retrospect has conduct$ u back to a mo/ ev5tful crisis1 9 :i* ! en]gy 0 a maximum1 & !re=e _c h be5 imm$iately prec$$ by a /ate 9 :i* ! en]gy 0 great] /ill2 x is !re=e impossible = ! tidal evolution to h produc$ ?is /ate ( ?+s2 "s o!r influ5ce mu/ h be5 9 op]ation at ?is beg9n+ ( ! e>?-moon sy/em4 ,?us !re c be h>dly a d\bt t imm$iately prec$+ ! critical epo* ! moon orig9at$ f ! e>? 9 ! way we h describ$4 ,note also t ?is condition1 be+ "o ( maximum en]gy1 0 necess>ily ( dynamical in/ability1 x c\ld n la/2 ! moon mu/ adopt ei!r ( two c\rses--x mu/ tumble back on ! e>?1 or x mu/ />t outw>ds4 ,n[ :i* c\rse 0 ! moon to adopt8 ,! case is analog\s to t ( an egg /&+ on its end--x w inevitably tumble "o way or ! o!r4 ,"s inf9itesimal cause w produce a t5d5cy t[>ds "o side1 & to t side accord+ly ! egg w fall4 ,! e>?-moon sy/em 0 simil>ly 9 an un/able /ate1 an inf9itesimal cause might conceivably decide ! fate ( ! sy/em4 ,we are necess>ily 9 ignorance ( :at ! det]m9+ cause might h be51 b ! effect x produc$ is p]fectly cle>2 ! moon did n aga9 return to its "m e>?1 b set out on t mighty c>e] :i* is 9 progress to-day4 ,let x be not$ t ^! critical epo*s 9 ! e>?-moon hi/ory arise :5 & only :5 !re is an absolute id5tity betwe5 ! l5g? ( ! mon? & ! l5g? ( ! day4 ,x may be prop] !re=e t ,i %\ld provide a demon/ration ( ! fact1 t ! id5tity betwe5 ^! two p]iods mu/ necess>ily h occurr$ at a v e>ly p]iod 9 ! evolution4 ,! law ( ,kepl]1 :i* ass]ts t ! squ>e ( ! p]iodic "t is proportion$ to ! cube ( ! mean di/ance1 is 9 its ord9>y application conf9$ to a comp>ison betwe5 ! revolutions ( ! sev]al planets ab\t ! sun4 ,! p]iodic "t ( ea* planet is connect$ ) its av]age di/ance by ?is law2 b !re is ano!r application ( ,kepl]'s law :i* gives u in=mation ( ! di/ance & ! p]iod ( ! moon 9 =m] /ages ( ! e>?-moon hi/ory4 ,al?\gh ! actual pa? ( ! moon is ( c\rse an ellipse1 yet t ellipse is tr\bl$1 z is well kn[n1 by _m di/urb+ =ces1 & f ?is cause alone ! actual pa? ( ! moon is f> f be+ any ( ^? simple curves ) :i* we are s well acqua9t$4 ,ev5 7 ! e>? & ! moon absolutely rigid p>ticles1 p]turbations w\ld "w all sorts ( small *anges 9 ! pliant curve4 ,! ph5om5a ( tidal evolution imp>t an additional elem5t ( complexity into ! actual %ape ( ! moon's pa?4 ,we n[ see t ! ellipse is n m]ely subject to incessant deflections ( a p]iodic nature1 x also und]goes a gradual contraction z we look back ?r\gh "t pa/2 b we may1 ) all ne$ful accuracy = our pres5t purpose1 ?9k ( ! pa? ( ! moon z a circle1 only we mu/ attribute to t circle a cont9u\s contraction ( its radius ! fur!r & ! fur!r we look back4 ,! alt]ation 9 ! radius w be ev5 s sl[1 t ! moon w accompli% ?\s&s ( revolutions ar\nd ! e>? )\t any appreciable alt]ation 9 ! av]age di/ance ( ! two bodies4 ,we c !re=e ?9k ( ! moon z revolv+ at e epo* 9 a circle ( special radius1 & z accompli%+ t revolution 9 a special "t4 ,) ?is und]/&+ we c n[ apply ,kepl]'s law to ! sev]al /ages ( ! moon's pa/ hi/ory4 ,! p]iodic "t ( ea* revolution1 & ! mean di/ance at :i* t revolution 0 p]=m$1 w be always connect$ toge!r by ! =mula ( ,kepl]4 ,?us to take an in/ance 9 ! v remote pa/4 ,let u suppose t ! moon 0 at "o hundr$ & tw5ty ?\s& miles in/ead ( two hundr$ & =ty ?\s&1 t is1 at half its pres5t di/ance4 ,apply+ ! law ( ,kepl]1 we see t ! "t ( revolution mu/ !n h be5 only ab\t t5 days in/ead ( ! tw5ty-sev5 x is n[4 ,/ill fur!r1 let u suppose t ! moon revolves 9 an orbit ) "o-t5? ( ! diamet] x has at pres5t1 !n ! cube ( #aj be+ #ajjj1 & ! squ>e root ( #ajjj be+ #ca4f1 x foll[s t ! mon? mu/ h be5 less ?an ! ?irty-fir/ "p ( :at x is at pres5t1 t is1 x mu/ h be5 consid]ably less ?an "o ( our pres5t days4 ,?us y see ! mon? is gr[+ %ort] & %ort] ! fur!r we look back1 ! day is also gr[+ %ort] & %ort]2 b /ill ,i ?9k we c %[ t !re mu/ h be5 a "t :5 ! mon? w h be5 at lea/ z %ort z ! day4 ,= let u take ! mo/ extreme case 9 :i* ! moon %all h made ! close/ possible approximation to ! e>?4 ,two globes 9 contact w h a di/ance betwe5 _! c5tres :i* is equal to ! sum ( _! radii4 ,take ! e>? z hav+ a radius ( f\r ?\s& miles1 & ! moon a radius ( "o ?\s& miles1 ! two c5tres mu/ at _! %orte/ di/ance be five ?\s& miles ap>t1 t is1 ! moon mu/ !n be at ! =ty-eigh? "p ( its pres5t di/ance f ! e>?4 ,n[ ! cube ( #dh is #aaj1eib1 & ! squ>e root ( #aaj1eib is ne>ly #ccc1 !re=e ! l5g? ( ! mon? w be "o-?ree hundr$ & ?irty-?ird "p ( ! duration ( ! mon? at pres5t2 9 o!r words1 ! moon mu/ revolve ar\nd ! e>? 9 a p]iod ( some:at ab\t two h\rs4 ,x seems impossible t ! day c ev] h be5 z brief z ?is4 ,we h !re=e prov$ t1 9 ! c\rse ( its contract+ duration1 ! moon mu/ h ov]tak5 ! contract+ day1 & t !re=e !re mu/ h be5 a "t :5 ! moon 0 9 ! vic9ity ( ! e>?1 & hav+ a day & mon? ( equal p]iod4 ,?us we h %[n t ! critical condition ( dynamical in/ability mu/ h occurr$ 9 ! e>ly p]iod ( ! e>?-moon hi/ory1 if ! ag5ts !n 9 op]ation 7 ^? :i* we n[ "k4 ,! fur!r developm5t ( ! subject mu/ be po/pon$ until ! next lecture4 ,,lecture ,,ii4 ,/>t+ f t fitt+ comm5cem5t ( e>?-moon hi/ory :i* ! critical epo* af=ds1 we %all n[ describe ! dynamical ph5om5a z ! tidal evolution progress$4 ,! moon & ! e>? initially mov$ z a solid body1 ea* b5d+ ! same face t[>ds ! o!r2 b z ! moon retreat$1 & z tides began to be rais$ on ! e>?1 ! l5g? ( ! day began to increase1 z did also ! l5g? ( ! mon?4 ,we "k1 h[ev]1 t ! mon? increas$ m rapidly ?an ! day1 s t a "t 0 rea*$ :5 ! mon? 0 twice z long z ! day2 & /ill bo? p]iods kept on increas+1 b n at equal rates1 = 9 progress ( "t ! mon? grew s mu* m rapidly ?an ! day1 t _m days _h to elapse :ile ! moon accompli%$ a s+le revolution4 ,x is1 h[ev]1 only necess>y = u to note ^? /ages ( ! mighty progress :i* correspond to special ev5ts4 ,! fir/ ( su* /ages 0 atta9$ :5 ! mon? assum$ its maximum ratio to ! day4 ,at ?is "t1 ! mon? 0 ab\t tw5ty-n9e days1 & ! epo* appe>s to h occurr$ at a comp>atively rec5t date if we use su* /&>ds ( "t z tidal evolution requires2 ?\gh measur$ by hi/orical /&>ds1 ! epo* is ( incalculable antiquity4 ,i _c impress ^u y too (t5 ! enorm\s magnitude ( ! p]iod ( "t :i* ^! ph5om5a h requir$ = _! evolution4 ,pr(essor ,d>w9's !ory af=ds b little in=mation on ?is po9t1 & ! utmo/ we c d is to assign a m9or limit to ! p]iod ?r\gh :i* tidal evolution has be5 9 progress4 ,x is c]ta9 t ! bir? ( ! moon mu/ h occurr$ at lea/ fifty million ye>s ago1 b probably ! true p]iod is enorm\sly great] ?an ?is4 ,if inde$ we *oose to add a ciph] or two to ! figure j pr9t$1 ,i d n ?9k !re is any?+ :i* c\ld tell u t we h ov]-e/imat$ ! m>k4 ,!re=e1 :5 ,i speak ( ! epo* 9 :i* ! mon? possess$ ! greate/ numb] ( days z a rec5t "o1 x mu/ be und]/ood t ,i am m]ely speak+ ( ev5ts 9 relation to ! ord] ( tidal evolution4 ,view$ f ?is /&po9t1 we c %[ t ! epo* is a rec5t "o 9 ! foll[+ mann]4 ,at pres5t ! mon? consi/s ( a little m ?an tw5ty-sev5 days1 b at ?is maximum p]iod to :i* ,i h ref]r$ ! mon? 0 ab\t tw5ty-n9e days2 f t x began to decl9e1 & ! decl9e _c h proce$$ v f>1 = ev5 /ill !re are only two days less 9 ! mon? ?an at ! "t :5 ! mon? _h ! greate/ numb] ( days4 ,x ?us foll[s t ! pres5t epo*--! human epo*1 z we may call x--9 ! hi/ory ( ! e>? has fall5 at a "t :5 ! progress ( tidal evolution is ab\t half-way betwe5 ! initial & ! f9al /age4 ,i d n mean half-way 9 ! s5se ( actual measurem5t ( ye>s2 inde$1 f ?is po9t x w\ld seem t we _c yet be ne>ly half-way1 =1 va/ z are ! p]iods ( "t t h elaps$ s9ce ! moon fir/ took its dep>ture f ! e>?1 !y fall f> %ort ( t awful p]iod ( "t :i* w int]v5e betwe5 ! pres5t mom5t & ! h\r :5 ! next critical /ate ( e>?-moon hi/ory %all h be5 atta9$4 ,9 t /ate ! day is de/9$ once aga9 to be equal to ! mon?1 j z 0 ! case 9 ! initial /age4 ,! half-way /age w !re=e 9 "o s5se be t 9 :i* ! proportion ( ! mon? to ! day culm9ates4 ,?is is ! /age :i* we h b lately pass$2 & ?us x is t at pres5t we may be said to be almo/ half-way ?r\gh ! progress ( tidal evolution4 ,my n>rative ( ! e>?-moon evolution mu/ f ?is po9t =w>d cease to be retrospective4 ,hav+ begun at t critical mom5t :5 ! mon? & day 7 fir/ equal1 we h trac$ ! progress ( ev5ts to ! pres5t h\r4 ,:at we h n[ to say is !re=e a =eca/ ( ev5ts yet to come4 ,s f> z we c tell1 no ag5t is likely to int]f]e ) ! gradual evolution caus$ by ! tides1 :i* dynamical pr9ciples h disclos$ to u4 ,z ! ye>s roll on1 or p]haps1 ,i %\ld r say1 z ?\s&s ( ye>s & millions ( ye>s roll on1 ! day w cont9ue to elongate1 or ! e>? to rotate m sl[ly on its axis4 ,b c\ntless ages mu/ elapse be=e ano!r critical /age ( ! hi/ory %all be rea*$4 ,x is ne$less = me to pond] ov] ! t$i\s process by :i* ?is int]e/+ epo* is rea*$4 ,i %all r sket* :at ! actual condition ( our sy/em w be :5 t mom5t %all h arriv$4 ,! day w !n h exp&$ f ! pres5t famili> tw5ty-f\r h\rs up to a day m ?an twice1 m ?an five1 ev5 m ?an fifty times its pres5t duration4 ,9 r\nd numb]s1 we may say t ?is great day w occupy "o ?\s& f\r hundr$ ( our ord9>y h\rs4 ,to realize ! critical nature ( ! situation !n arriv$ at1 we mu/ foll[ ! correspond+ evolution ?r\gh :i* ! moon passes4 ,f its pres5t di/ance ( two hundr$ & =ty ?\s& miles1 ! moon w describe an ev]-enl>g+ orbit2 & z x does s ! duration ( ! mon? w also increase1 until at la/ a po9t w be rea*$ :5 ! mon? has become m ?an d\ble its pres5t l5g?1 & has atta9$ ! p>ticul> value ( "o ?\s& f\r hundr$ h\rs4 ,we are specially to obs]ve t ?is "o-?\s& f\r-hundr$-h\r mon? w be exactly rea*$ :5 ! day has also exp&$ to "o ?\s& f\r hundr$ h\rs2 & ! ess5ce ( ?is critical condition1 :i* may be reg>d$ z a significant po9t ( tidal evolution1 is t ! day & ! mon? h aga9 become equal4 ,! day & ! mon? 7 equal at ! beg9n+1 ! day & ! mon? w be equal at ! end4 ,yet h[ wide is ! diff]5ce betwe5 ! beg9n+ & ! end4 ,! day or ! mon? at ! end is "s hundr$s ( times z long z ! mon? or ! day at ! beg9n+4 ,i h already fully expla9$ h[1 9 any /age ( ! evolution>y progress 9 :i* ! day & ! mon? became equal1 ! en]gy ( ! sy/em atta9$ a maximum or a m9imum value4 ,at ! beg9n+ ! en]gy 0 a maximum2 at ! end ! en]gy w be a m9imum4 ,! mo/ important consequ5ces foll[ f ?is consid]ation4 ,i h already %[n t a condition ( maximum en]gy correspond$ to dynamic in/ability4 ,?us we saw t ! e>?-moon hi/ory c\ld n h comm5c$ )\t ! int]v5tion ( "s influ5ce o!r ?an tides at ! beg9n+4 ,n[ let u le>n :at ! simil> doctr9e has to tell u ) reg>d to ! end4 ,! condition !n arriv$ at is "o ( dynamical /ability2 = suppose t ! sy/em 7 to receive a slight alt]ation1 by :i* ! moon w5t out a little fur!r1 & ?us describ$ a l>g] orbit1 & s p]=m$ m ?an its %>e ( ! mom5t ( sp94 ,!n ! e>? w\ld h to d a little less sp9n+1 because1 "u all circum/ances1 ! total quantity ( sp9 mu/ be pres]v$ unalt]$4 ,b ! en]gy be+ at a m9imum1 su* a small displacem5t mu/ ( c\rse produce a /ate ( ?+s 9 :i* ! en]gy w\ld be increas$4 ,or if we conceiv$ ! moon to come 9 t[>ds ! e>?1 ! moon w\ld !n contribute less to ! total mom5t ( mom5tum4 ,x w\ld !re=e be incumb5t on ! e>? to d m2 & accord+ly ! velocity ( ! e>?'s rotation w\ld be augm5t$4 ,b ?is arrangem5t also c\ld only be produc$ by ! addition ( "s fre% en]gy to ! sy/em1 because ! position f :i* ! sy/em is suppos$ to h be5 di/urb$ is "o ( m9imum en]gy4 ,no di/urbance ( ! sy/em f ?is f9al position is !re=e conceivable1 unless "s en]gy c be communicat$ to x4 ,b ?is w demon/rate ! utt] incompet5cy ( ! tides to %ift ! sy/em by a hair's bread? f ?is position2 = x is ( ! ess5ce ( ! tides to wa/e en]gy by friction4 ,& ! trans=mations ( ! sy/em :i* ! tides h caus$ are inv>iably *>act]iz$ by a decl9e ( en]gy1 ! movem5ts be+ o!rwise arrang$ s t ! total mom5t ( mom5tum %all be pres]v$ intact4 ,note1 h[ f> we 7 ju/ifi$ 9 speak+ ( ?is condition z a f9al "o4 ,x is f9al s f> z ! lun> tides are conc]n$2 & 7 ! sy/em to be scre5$ f all out] int]f]5ce1 ?is accommodation betwe5 ! e>? & ! moon w\ld be et]nal4 ,!re is inde$ ano!r way ( demon/rat+ t a condition ( ! sy/em 9 :i* ! day has assum$ equality ) ! mon? mu/ necess>ily be "o ( dynamical equilibrium4 ,we h %[n t ! en]gy :i* ! tides dem& is d]iv$ n f ! m]e fact t !re are high tides & l[ tides1 b f ! circum/ance t ^! tides d rise & fall2 t 9 fall+ & ris+ !y d produce curr5ts2 & x is ^! curr5ts :i* g5]ate ! friction by :i* ! e>?'s velocity is sl[ly abat$1 its en]gy wa/$1 & no d\bt ultimately dissipat$ z heat4 ,if !re=e we c make ! ebb+ & ! fl[+ ( ! tides to cease1 !n our argum5t w disappe>4 ,?us suppose1 = ! sake ( illu/ration1 t at a mom5t :5 ! tides happ5$ to be at high wat] 9 ! ,?ames1 su* a *ange took place 9 ! behavi\r ( ! moon t ! wat] always rema9$ full 9 ! ,?ames1 & at e o!r spot on ! e>? rema9$ fix$ at ! exact height :i* x possess$ at ?is p>ticul> mom5t4 ,!re w\ld be no m tidal friction1 & !re=e ! sy/em w\ld cease to c\rse ?r\gh t s]ies ( *anges :i* ! exi/5ce ( tidal friction necessitates4 ,b if ! tide is always to be full 9 ! ,?ames1 !n ! moon mu/ be always 9 ! same position ) respect to ! m]idian1 t is1 ! moon mu/ always be fix$ 9 ! heav5s ov] ,london4 ,9 fact1 ! moon mu/ !n revolve ar\nd ! e>? j z fa/ z ,london does--! mon? mu/ h ! same l5g? z ! day4 ,! e>? mu/ !n %[ ! same face con/antly to ! moon1 j z ! moon always does %[ ! same face t[>ds ! e>?2 ! two globes w 9 fact revolve z if !y 7 connect$ ) invisible bonds1 :i* unit$ !m into a s+le rigid body4 ,we ne$ !re=e feel no surprise at ! cessation ( ! progress ( tidal evolution :5 ! mon? & ! day are equal1 = !n ! movem5t ( moon-rais$ tides has ceas$4 ,no d\bt ! same may be said ( ! /ate at ! beg9n+ ( ! hi/ory1 :5 ! day & ! mon? _h ! brief & equal duration ( a few h\rs4 ,:ile ! equality ( ! two p]iods la/$ !re c\ld be no tides1 & !re=e no progress 9 ! direction ( tidal evolution4 ,!re is1 h[ev]1 ! pr(\nd diff]5ce ( /ability & in/ability betwe5 ! two cases2 ! mo/ insignificant di/urbance ( ! sy/em at ! initial /age 0 suffici5t to precipitate ! revolv+ moon f its condition ( dynamical equilibrium1 & to />t ! c\rse ( tidal evolution 9 full vig\r4 ,if1 h[ev]1 any trifl+ d]angem5t %\ld take place 9 ! la/ condition ( ! sy/em1 s t ! mon? & ! day dep>t$ slightly f equality1 !re w\ld in/antly be an ebb+ & a fl[+ ( ! tides2 & ! friction g5]at$ by ^! tides w\ld op]ate to re/ore ! equality because ?is condition is "o ( dynamical /ability4 ,x w ?us be se5 ) :at ju/ice we c look =w>d to ! day & mon? ea* ( f\rte5 hundr$ h\rs z a f9ale to ! progress ( ! luni-tidal evolution4 ,?r\gh\t ! :ole ( ?is m>vell\s s]ies ( *anges x is always necess>y to rememb] ! "o con/ant & inv>iable elem5t--! mom5t ( mom5tum ( ! sy/em :i* tides _c alt]4 ,:atev] else ! friction c h done1 h[ev] fe>ful may h be5 ! loss ( en]gy by ! sy/em1 ! mom5t ( mom5tum :i* ! sy/em _h at ! beg9n+ x pres]ves unto ! end4 ,?is x is :i* *iefly gives u ! num]ical data on :i* we h to rely = ! quantitative features ( tidal evolution4 ,we h made s _m dem&s 9 ! c\rse ( ^! lectures on ! capacity ( tidal friction to accompli% />tl+ ph5om5a 9 ! evolution ( ! e>?-moon sy/em1 t x is well = u to seek = any evid5ce t may o!rwise be obta9able z to ! capacity ( tides = ! accompli%m5t ( gigantic op]ations4 ,i d n say t !re is any d\bt :i* requires to be dispell$ by su* evid5ce1 = z to ! g5]al outl9es ( ! doctr9e ( tidal evolution :i* has be5 "h sket*$ out !re c be no reasonable gr\nd = mi/ru/2 b nev]!less x is always desirable to wid5 our compreh5sion ( any natural ph5om5a by obs]v+ collat]al facts4 ,n[ !re is "o bran* ( tidal action to :i* ,i h z yet only 9 ! mo/ incid5tal way ref]r$4 ,we h be5 speak+ ( ! tides 9 ! e>? :i* are made to ebb & fl[ by ! action ( ! moon2 we h n[ to consid] ! tides 9 ! moon1 :i* are !re excit$ by ! action ( ! e>?4 ,= betwe5 ^! two bodies !re is a reciprocity ( tidal-mak+ en]gy--ea* ( !m is compet5t to raise tides 9 ! o!r4 ,z ! moon is s small 9 comp>ison ) ! e>?1 & z ! tides on ! moon are ( b little significance 9 ! progress ( tidal evolution1 x has be5 p]missible = u to omit !m f our =m] discussion4 ,b x is ^! tides on ! moon :i* w af=d u a /rik+ illu/ration ( ! compet5cy ( tides = /up5d\s tasks4 ,! moon pres5ts a monum5t to %[ :at tides are able to accompli%4 ,illu/ration3 ,fig4 #c4--,! ,moon4 ,i mu/ fir/1 h[ev]1 expla9 a difficulty :i* is almo/ sure to sugge/ itself :5 we speak ( tides on ! moon4 ,i %all be told t ! moon conta9s no wat] on its surface1 & h[ !n1 x w be said1 c tides ebb & fl[ :]e !re is no sea to be di/urb$8 ,!re are two answ]s to ?is difficulty2 x is no d\bt true t ! moon seems at pres5t entirely devoid ( wat] 9 s f> z its surface is expos$ to u1 b x is by no means c]ta9 t ! moon 0 always 9 ?is de/itute condition4 ,!re are v l>ge features m>k$ on its map z seas2 ^! regions are ( a d>k] hue ?an ! re/ ( ! moon's surface1 !y are l>ge objects (t5 _m hundr$s ( miles 9 diamet]1 & !y =m1 9 fact1 ^? d>k pat*es on ! brilliant surface :i* are conspicu\s to ! unaid$ eye1 & are repres5t$ 9 ,fig4 #c4 ,view$ 9 a telescope ^! s-call$ seas1 :ile cle>ly possess+ no wat] at ! pres5t "t1 are yet widely diff]5t f ! g5]al aspect ( ! moon's surface4 ,x has (t5 be5 suppos$ t great oceans once fill$ ^! bas9s1 & a plausible explanation has ev5 be5 (f]$ z to h[ ! wat]s !y once conta9$ c\ld h vani%$4 ,x has be5 ?\ght t z ! m9]al sub/ances deep 9 ! int]ior ( our satellite assum$ ! cry/all9e =m dur+ ! progress ( cool+1 ! dem& = wat] ( cry/allization requir$ = incorporation ) ! m9]als 0 s great t ! oceans ( ! moon became entirely absorb$4 ,x is1 h[ev]1 unnecess>y = our pres5t argum5t t ?is !ory %\ld be correct4 ,ev5 if !re nev] 0 a drop ( wat] f\nd on our satellite1 ! tides 9 its molt5 mat]ials w\ld be q suffici5t = our purpose2 any?+ t tides c\ld accompli% w\ld be done m spe$ily by va/ tides ( fl[+ lava ?an by m]ely oceanic tides4 ,!re c be no d\bt t tides rais$ on ! moon by ! e>? w\ld be great] ?an ! tides rais$ on ! e>? by ! moon4 ,! "q is1 h[ev]1 n a v simple "o1 = x dep5ds on ! masses ( bo? bodies z well z on _! relative dim5sions4 ,9 s f> z ! masses are conc]n$1 ! e>? be+ m ?an eighty times z heavy z ! moon1 ! tides w\ld on ?is acc\nt be va/ly l>g] on ! moon ?an on ! e>?4 ,on ! o!r h&1 ! moon's diamet] be+ mu* less ?an t ( ! e>?1 ! effici5cy ( a tide-produc+ body 9 its action on ! moon w\ld be less ?an t ( ! same body at ! same di/ance 9 its action on ! e>?2 b ! dim9ution ( ! tides f ?is cause w\ld be n s great z _! increase f ! =m] cause1 & !re=e ! net result w\ld be to exhibit mu* great] tides on ! moon ?an on ! e>?4 ,suppose t ! moon _h be5 orig9ally end[$ ) a rapid movem5t ( rotation ar\nd its axis1 ! effect ( ! tides on t rotation w\ld t5d to *eck its velocity j 9 ! same way z ! tides on ! e>? h effect$ a cont9ual elongation ( ! day4 ,only z ! tides on ! moon 7 s enorm\sly great1 _! capacity to *eck ! moon's spe$ w\ld h correspond+ efficacy4 ,9 addition to ?is1 ! mass ( ! moon be+ s small1 x c\ld only (f] feeble resi/ance to ! unceas+ action ( ! tide1 & !re=e our satellite mu/ succumb to :atev] ! tides desir$ ages be=e our e>? w\ld h be5 affect$ to a l ext5t4 ,x mu/ be notic$ t ! influ5ce ( ! tidal friction is n direct$ to ! total annihilation ( ! rotation ( ! two bodies affect$ by x2 ! velocity is only *eck$ d[n until x atta9s su* a po9t t ! spe$ 9 :i* ea* body rotates ^u its axis has become equal to t 9 :i* x revolves ar\nd ! tide-produc]4 ,! practical effect ( su* an adju/m5t is to make ! tide-agitat$ body turn a con/ant face t[>ds its torm5tor4 ,i may "h note a po9t ab\t :i* p sometimes f9d a little difficulty4 ,! moon con/antly turns ! same face t[>ds ! e>?1 & !re=e p are sometimes apt to ?9k t ! moon p]=ms no rotation :atev] ar\nd its own axis4 ,b ?is is inde$ n ! case4 ,! true inf]5ce to be drawn f ! con/ant face ( ! moon is1 t ! velocity ( rotation ab\t its own axis is equal to t ( its rotation ar\nd ! e>?2 9 fact1 ! moon revolves ar\nd ! e>? 9 tw5ty-sev5 days1 & its rotation ab\t its axis is p]=m$ 9 tw5ty-sev5 days also4 ,y may illu/rate ! movem5t ( ! moon ar\nd ! e>? by walk+ ar\nd a table 9 a room1 keep+ all ! "t y\r face turn$ t[>ds ! table2 9 su* a case z ?is y n only p]=m a motion ( revolution1 b y also p]=m a rotation 9 an equal p]iod4 ,! pro( t y d rotate is to be f\nd 9 ! fact t dur+ ! movem5t y\r face is be+ direct$ successively to all ! po9ts ( ! compass4 ,!re is no m s+ul> fact 9 ! sol> sy/em ?an ! con/ancy ( ! moon's face to ! e>?4 ,! p]iods ( rotation & revolution are bo? alike2 if "o ( ^! p]iods exce$$ ! o!r by an am\nt s small z ! hundr$? "p ( a second1 ! moon w\ld 9 ! lapse ( ages p]mit u to see t o!r side :i* is n[ s jeal\sly conceal$4 ,! m>vell\s co9cid5ce betwe5 ^! two p]iods w\ld be absolutely inexplicable1 unless we 7 able to assign x to "s physical cause4 ,x mu/ be rememb]$ t 9 ?is matt] ! moon occupies a unique position among ! heav5ly ho/4 ,! sun revolves ar\nd on its axis 9 a p]iod ( tw5ty-five or tw5ty-six days--?us we see "o side ( ! sun z frequ5tly z we see ! o!r4 ,! side ( ! sun :i* is turn$ t[>ds u to-day is almo/ entirely diff]5t f t we saw a =tnight ago4 ,nor is ! p]iod ( ! sun's rotation to be id5tifi$ ) any o!r rem>kable p]iod 9 our sy/em4 ,if x 7 equal to ! l5g? ( ! ye>1 = in/ance1 or if x 7 equal to ! p]iod ( any ( ! o!r planets1 !n x c\ld h>dly be cont5d$ t ! ph5om5on z pres5t$ by ! moon 0 unique2 b ! sun's p]iod is n simply relat$1 or inde$ relat$ at all1 to any ( ! o!r p]iodic times 9 ! sy/em4 ,nor d we f9d any?+ l ! moon's con/ancy ( face 9 ! behavi\r ( ! o!r planets4 ,jupit] turns n[ "o face to u & !n ano!r4 ,nor is 8 rotation relat$ to ! sun or relat$ to any o!r body1 z our moon's motion is relat$ to u4 ,x has inde$ be5 ?\ght t 9 ! movem5ts ( ! satellites ( ,jupit] a some:at simil> ph5om5on may be obs]v$ to t 9 ! motion ( our own satellite4 ,if ?is be s1 ! causes :]eby ?is ph5om5on is produc$ are d\btless id5tical 9 ! two cases4 ,s rem>kable a co9cid5ce z t :i* ! moon's motion %[s c\ld n reasonably be expla9$ z a m]e =tuit\s circum/ance2 nor ne$ we hesitate to admit t a physical explanation is requir$ :5 we f9d a mo/ satisfactory "o ready = our acceptance1 z 0 orig9ally po9t$ out by ,helmholtz4 ,!re c be no d\bt :atev] t ! con/ancy ( ! moon's face is ! "w ( anci5t tides1 :i* h long s9ce ceas$ to act4 ,we h %[n t if ! moon's rotation _h once be5 too rapid to p]mit ( ! same face be+ always direct$ t[>ds u1 ! tides w\ld op]ate z a *eck by :i* ! velocity ( t rotation w\ld be abat$4 ,on ! o!r h&1 if ! moon rotat$ s sl[ly t its o!r face w\ld be expos$ to u 9 ! c\rse ( ! revolution1 ! tides w\ld !n be dragg$ viol5tly ov] its surface 9 ! direction ( its rotation2 _! t5d5cy w\ld ?us be to accel]ate ! spe$ until ! angul> velocity ( rotation 0 equal to t ( revolution4 ,?us ! tides w\ld act z a controll+ ag5t ( ! utmo/ /r+5cy to hurry ! moon r\nd :5 x 0 n turn+ fa/ en\gh1 & to arre/ ! motion :5 go+ too fa/4 ,peace !re w\ld be none = ! moon until x yield$ absolute compliance to ! tyranny ( ! tides1 & adju/$ its p]iod ( rotation ) exact id5tity to its p]iod ( revolution4 ,d\btless ?is adju/m5t 0 made c\ntless ages ago1 & s9ce t p]iod ! tides h act$ s z to pres]ve ! adju/m5t1 z long z any "p ( ! moon 0 9 a /ate suffici5tly s(t or fluid to respond to tidal impression4 ,! pres5t /ate ( ! moon is a monum5t to :i* we may confid5tly appeal 9 support ( our cont5tion z to ! great p[] ( ! tides dur+ ! ages :i* h pass$2 x w s]ve z an illu/ration ( ! future :i* is res]v$ = our e>? 9 ages yet to come1 :5 our globe %all h also succumb$ to tidal influ5ce4 ,x is ow+ to ! smallness ( ! moon relatively to ! e>? t ! tidal process has rea*$ a mu* m advanc$ /age 9 ! moon ?an x has on ! e>?2 b ! moon is incessant 9 its ef=ts to br+ ! e>? into ! same condition :i* x has itself be5 =c$ to assume4 ,?us aga9 we look =w>d to an epo* 9 ! inconceivably remote future :5 tidal ?raldom %all be supreme1 & :5 ! e>? %all turn ! same face to ! moon1 z ! moon n[ turns ! same face to ! e>?4 ,9 ! critical /ate ( ?+s ?us loom+ 9 ! dim future1 ! e>? & ! moon w cont9ue to p]=m ?is adju/$ revolution 9 a p]iod ( ab\t f\rte5 hundr$ h\rs1 ! two bodies be+ held1 z x 71 by invisible b&s4 ,su* an arrangem5t might be et]nal if !re 7 no intrusion ( tidal influ5ce f any o!r body2 b ( c\rse 9 our sy/em z we actually f9d x ! sun produces tides z well z ! moon2 & ! sol> tides be+ at pres5t mu* less ?an ^? orig9at$ by ! moon1 we h neglect$ !m 9 ! g5]al outl9es ( ! !ory4 ,! sol> tides1 h[ev]1 mu/ necess>ily h an increas+ significance4 ,i d n mean t !y w intr9sically increase1 = !re seems no reason to appreh5d any gr[? 9 _! actual am\nt2 x is _! relative importance to ! lun> tides t is ! augm5t+ quantity4 ,z ! f9al /ate is be+ approa*$1 & z ! velocity ( ! e>?'s rotation is approximat+ to ! angul> velocity ) :i* ! moon revolves ar\nd x1 ! ebb+ & ! fl[+ ( ! lun> tides mu/ become ( evanesc5t importance2 & ?is inde$ = a d\ble reason1 p>tly on acc\nt ( ! moon's greatly augm5t$ di/ance1 & p>tly on acc\nt ( ! increas+ l5g? ( ! lun> day1 & ! extremely t>dy movem5ts ( ebb & fl[ t ! lun> tides w !n h4 ,?us ! lun> tides1 s f> z _! dynamical importance is conc]n$1 w ultimately become z]o1 :ile ! sol> tides reta9 all _! pri/9e effici5cy4 ,we h !re=e to exam9e ! dynamical effects ( sol> tides on ! e>? & moon 9 ! critical /age to :i* ! pres5t c\rse ( ?+s t5ds4 ,! e>? w !n rotate 9 a p]iod ( ab\t fifty-sev5 ( its pres5t days2 & consid]+ t ! l5g? ( ! day1 ?\gh s mu* great] ?an our pres5t day1 is /ill mu* less ?an ! ye>1 x foll[s t ! sol> tides mu/ /ill cont9ue s z to br+ ! e>?'s velocity ( rotation to a po9t ev5 l[] ?an x has yet atta9$4 ,9 fact1 if we c\ld v5ture to project our glance suffici5tly f> into ! future1 x w\ld seem t ! e>? mu/ ultimately h its velocity *eck$ by ! sun-rais$ tides1 until ! day itself _h become equal to ! ye>4 ,! dynamical consid]ations become1 h[ev]1 too complex = u to foll[ !m1 s t ,i %all be cont5t ) m]ely po9t+ out t ! influ5ce ( ! sol> tides w prev5t ! e>? & moon f et]nally pres]v+ ! relations ( b5d+ ! same face t[>ds ea* o!r2 ! e>?'s motion w1 9 fact1 be s f> *eck$1 t ! day w become long] ?an ! mon?4 ,?us ! doctr9e ( tidal evolution has conduct$ u to a prospect ( a condition ( ?+s :i* w "s "t be rea*$1 :5 ! moon w h rec$$ to a di/ance 9 :i* ! mon? %all h become ab\t fifty-sev5 days1 & :5 ! e>? ar\nd :i* ?is moon revolves %all actually require a /ill long] p]iod to accompli% its rotation on its axis4 ,"h is an odd condition = a planet ) its satellite2 inde$1 until a doz5 ye>s ago x w\ld h be5 pron\nc$ inconceivable t a moon %\ld :irl r\nd a planet s quickly t its j\rney 0 accompli%$ 9 less ?an "o ( ! planet's own days4 ,argum5ts might be f\nd to %[ t ?is 0 impossible1 or at lea/ unprec$5t$4 ,!re is our own moon1 :i* n[ takes tw5ty-sev5 days to g r\nd ! e>?2 !re is ,jupit]1 ) f\r moons1 & ! ne>e/ ( ^! to ! prim>y goes r\nd 9 =ty-two & a half h\rs4 ,no d\bt ?is is a v rapid motion2 b all ^? matt]s are mu* m lively ) ,jupit] ?an !y are "h4 ,! giant planet himself does n ne$ t5 h\rs = a s+le rotation1 s t y see 8 ne>e/ moon /ill takes betwe5 two & ?ree ,jovian days to accompli% a s+le revolution4 ,! example ( ,saturn might h be5 cit$ to %[ t ! quicke/ revolution t any satellite c\ld p]=m mu/ /ill require at lea/ twice z long z ! day 9 :i* ! planet p]=m$ its rotation4 ,nor c\ld ! rotation ( ! planets ar\nd ! sun af=d a case :i* c\ld be cit$4 ,= ev5 ,m]cury1 ! ne>e/ ( all ! planets to ! sun ( :i* ! exi/5ce is c]ta9ly kn[n1 & !re=e ! mo/ rapid 9 its revolution1 requires eighty-eight days to get r\nd once2 & 9 ! mean "t ! sun has _h "t to accompli% betwe5 ?ree & f\r rotations4 ,inde$1 ! analogies w\ld seem to h %[n s great an improbability 9 ! conclusion t[>ds :i* tidal evolution po9ts1 t !y w\ld h contribut$ a s]i\s ob/acle to ! g5]al acceptance ( t !ory4 ,b 9 #ahgg an ev5t took place s int]e/+ 9 a/ronomical hi/ory1 t we h to look back to ! memorable discov]y ( ,uranus 9 #agha be=e we c f9d a p>allel to x 9 importance4 ,m>s _h always be5 look$ ^u z "o ( ! moonless planets1 ?\gh gr\nds 7 n want+ = ! surmise t probably moons to ,m>s really exi/$4 ,x 0 "u ! influ5ce ( ?is belief t an attempt 0 made by ,pr(essor ,asaph ,hall at ,wa%+ton to make a det]m9$ se>*1 & see if ,m>s might n be att5d$ by satellites l>ge en\gh to be discov]able4 ,! circum/ances "u :i* ?is memorable inquiry 0 und]tak5 7 em95tly fav\rable = its success4 ,! orbit ( ,m>s is "o :i* possesses an exceptionally high ecc5tricity2 x consequ5tly happ5s t ! oppositions dur+ :i* ! planet is to be obs]v$ v>y v greatly 9 ! facilities !y af=d = a se>* l t contemplat$ by ,pr(essor ,hall4 ,x is obvi\sly advantage\s t ! planet %\ld be situat$ z ne> z possible to ! e>?1 & 9 ! opposition 9 #ahgg ! di/ance 0 almo/ at ! l[e/ po9t x is capable ( atta9+2 b ?is 0 n ! only po9t 9 :i* ,pr(essor ,hall 0 fav\r$2 he _h ! use ( a telescope ( magnific5t proportions & ( consummate optical p]fection4 ,8 obs]vatory 0 also plac$ 9 ,wa%+ton1 s t he _h ! advantage ( a pure sky & ( a mu* l[] latitude ?an any obs]vatory 9 ,great ,brita9 is plac$ at4 ,b ! mo/ conspicu\s advantage ( all 0 ! practis$ skill ( ! a/ronom] himself1 )\t :i* all ^! o!r advantages w\ld h be5 b ( little avail4 ,great success rew>d$ 8 well-design$ ef=ts2 n alone 0 "o satellite discov]$ :i* revolv$ ar\nd ! planet 9 a p]iod con=mable ) t ( o!r simil> cases1 b a second little satellite 0 f\nd1 :i* accompli%$ its revolution 9 a :olly unexpect$ & unprec$5t$ mann]4 ,! day ( ,m>s himself1 t is1 ! p]iod 9 :i* he c accompli% a rotation ar\nd 8 axis1 v closely approximates to our own day1 be+ 9 fact half an h\r long]4 ,?is little satellite1 ! inn] & m rapid ( ! pair1 requires = a s+le revolution a p]iod ( only sev5 h\rs ?irty-n9e m9utes1 t is to say1 ! little body scamp]s m ?an ?ree times r\nd its prim>y be=e ! prim>y itself has f9i%$ "o ( its leisurely rotations4 ,"h 0 inde$ a /rik+ fact1 a unique fact 9 our sy/em1 :i* rivet$ ! att5tion ( a/ronom]s on ?is mo/ beautiful discov]y4 ,y w n[ see ! be>+ :i* ! movem5t ( ! inn] satellite ( ,m>s has on ! doctr9e ( tidal evolution4 ,z a legitimate consequ5ce ( t doctr9e1 we came to ! conclusion t our e>?-moon sy/em mu/ ultimately atta9 a condition 9 :i* ! day is long] ?an ! mon?4 ,b ?is conclusion /ood unsupport$ by any analog\s facts 9 ! m anci5tly-kn[n tru?s ( a/ronomy4 ,! movem5t ( ! satellite ( ,m>s1 h[ev]1 af=ds ! precise illu/ration we want2 & ?is fact1 ,i ?9k1 adds an additional significance to ! int]e/ & ! beauty ( ,pr(essor ,hall's discov]y4 ,x is ( p>ticul> int]e/ to inve/igate ! possible connection :i* ! ph5om5a ( tidal evolution may h _h 9 connection ) ! geological ph5om5a ( ! e>?4 ,we h already po9t$ out ! great] clos5ess ( ! moon to u 9 times pa/4 ,! tides rais$ by ! moon on ! e>? mu/ !re=e h be5 great] 9 pa/ ages ?an !y are n[1 = ( c\rse ! ne>] ! moon ! bigg] ! tide4 ,z soon z ! e>? & ! moon _h sep>at$ to a consid]able di/ance we may say t ! height ( ! tide w v>y inv]sely z ! cube ( ! moon's di/ance2 x w !re=e happ51 t :5 ! moon 0 at half its pres5t di/ance f u1 8 tide-produc+ capacity 0 n alone twice z mu* or f\r times z mu*1 b ev5 eight times z mu* z x is at pres5t2 & a mu* great] rate ( tidal rise & fall indicates1 ( c\rse1 a prepond]ance 9 e o!r manife/ation ( tidal activity4 ,! tidal curr5ts1 = in/ance1 mu/ h be5 mu* great] 9 volume & 9 spe$2 ev5 n[ !re are places 9 :i* ! tidal curr5ts fl[ at f\r or m miles p] h\r4 ,we c imag9e1 !re=e1 ! vehem5ce ( ! tidal curr5ts :i* mu/ h fl[$ 9 ^? days :5 ! moon 0 a mu* small] di/ance f u4 ,x is int]e/+ to view ^! consid]ations 9 _! possible be>+s on geological ph5om5a4 ,x is true t we h "h _m elem5ts ( unc]ta9ty1 b !re is1 h[ev]1 a c]ta9 g5]al outl9e ( facts :i* may be laid d[n1 & :i* appe>s to be in/ructive1 ) ref]5ce to ! pa/ hi/ory ( our e>?4 ,i h all ?r\gh ^! lectures indicat$ a mighty sy/em ( *ronology = ! e>?-moon sy/em4 ,x is true t we _c give our *ronology any accurate expression 9 ye>s4 ,! v>i\s /ages ( ?is hi/ory are to be repres5t$ by ! successive di/ances betwe5 ! e>? & ! moon4 ,ea* successive epo*1 = in/ance1 may be m>k$ by ! numb] ( ?\s&s ( miles :i* sep>ate ! moon f ! e>?4 ,b we h ano!r sy/em ( *ronology d]iv$ f a :olly diff]5t sy/em ( ideas2 x too relates to p]iods ( va/ duration1 &1 l our great tidal p]iods1 ext5ds to times ant]ior to human hi/ory1 or ev5 to ! duration ( human life on ?is globe4 ,! facts ( geology op5 up to u a maje/ic *ronology1 ! epo*s ( :i* are famili> to u by ! succession ( /rata =m+ ! cru/ ( ! e>?1 & by ! succession ( liv+ be+s ^: rema9s ^! /rata h pres]v$4 ,f ! pres5t or rec5t age our retrospect ov] geological *ronology leads u to look ?r\gh a vi/a embrac+ p]iods ( "t ov]:elm+ 9 _! duration1 until at la/ our view becomes lo/1 & our imag9ation is baffl$ 9 ! ef=t to compreh5d ! =mation ( ^? va/ /ratifi$ rocks1 a doz5 miles or m 9 ?ickness1 :i* seem to lie at ! v base ( ! /ratifi$ sy/em on ! e>?1 & 9 :i* x w\ld appe> t ! dawn+s ( life on ?is globe may be almo/ disc]n$4 ,we h ?us ! two sy/ems ( *ronology to comp>e--"o1 ! a/ronomical *ronology measur$ by ! successive /ages 9 ! gradual retreat ( ! moon2 ! o!r1 ! geological *ronology measur$ by ! successive /rata con/itut+ ! e>?'s cru/4 ,nev] 0 a m noble problem propos$ 9 ! physical hi/ory ( our e>? ?an t :i* is impli$ 9 ! attempt to correlate ^! two sy/ems ( *ronology4 ,:at we w\ld especially desire to "k is ! moon's di/ance :i* corresponds to ea* ( ! successive /rata on ! e>?4 ,h[ f> (f1 = in/ance1 0 t moon :i* look$ d[n on ! coal =e/s 9 ! "t ( _! greate/ luxuriance8 or :at 0 ! app>5t size ( ! full moon at :i* ! i*?yosaurus c\ld h peep$ :5 he turn$ t wond]ful eye ( 8 to ! sky on a f9e ev5+8 ,b int]e/+ z ?is great problem is1 x lies1 alas6 outside ! possibility ( exact solution4 ,inde$ we %all n make any attempt :i* mu/ necess>ily be futile to correlate ^! *ronologies2 all we c d is to /ate ! "o fact :i* is absolutely und5iable 9 ! matt]4 ,let u fix our att5tion on t specially int]e/+ epo* at ! dawn ( geological "t1 :5 ^? mighty ,laur5tian rocks 7 deposit$ ( :i* ! ?ickness is s a/\nd+1 & let u consid] :at ! di/ance ( ! moon mu/ h be5 at ?is initial epo* ( ! e>?'s hi/ory4 ,all we "k = c]ta9 is1 t ! moon mu/ h be5 ne>]1 b :at proportion t di/ance bore to ! pres5t di/ance is necess>ily q unc]ta94 ,"s ye>s ago ,i deliv]$ a lecture at ,birm+ham1 entitl$ ,a ,glimpse ?r\gh ! ,corridors ( ,"t1 & 9 t lecture ,i ?rew out ! sugge/ion t ! moon at ?is primeval epo* may h only be5 at a small fraction ( its pres5t di/ance f u1 & t consequ5tly t]rific tides may 9 ^! days h ravag$ ! coa/4 ,!re 0 a good deal ( discussion on ! subject1 & :ile x 0 univ]sally admitt$ t ! tides mu/ h be5 l>g] 9 palozoic times ?an !y are at pres5t1 yet !re 0 a consid]able body ( op9ion to ! effect t ! tides ev5 !n may h be5 only ab\t twice1 or possibly n s mu*1 great] ?an ^? tides we h at ! pres5t4 ,:at ! actual fact may be we h no way ( kn[+2 b x is int]e/+ to note t ev5 ! smalle/ accession to ! tides w\ld be a valuable factor 9 ! p]=mance ( geological "w4 ,= let me recall to y\r m9ds a few ( ! fundam5tal ph5om5a ( geology4 ,^? /ratifi$ rocks ) :i* we are n[ conc]n$ h be5 *iefly manufactur$ by deposition ( s$im5t 9 ! ocean4 ,riv]s1 swoll51 x may be1 by floods1 & turbid ) a quantity ( mat]ial held 9 susp5sion1 dis*>ge _! wat]s into ! sea4 ,grant+ "t & quiet1 ?is s$im5t falls to ! bottom2 successive additions are made to its ?ickness dur+ c5turies & ?\s&s ( ye>s1 & ?us b$s are =m$ :i* 9 ! c\rse ( ages consolidate into actual rock4 ,9 ! =mation ( su* b$s ! tides w play a "p4 ,into ! e/u>ies at ! m\?s ( riv]s ! tides hurry 9 & hurry out1 & especially dur+ spr+ tides !re are curr5ts :i* fl[ ) trem5d\s p[]2 !n too1 z ! waves batt] aga9/ ! coa/ !y gradually we> away & crumble d[n ! mightie/ cliffs1 & waft ! s& & mud ?us produc$ to augm5t t :i* has be5 br\ght d[n by ! riv]s4 ,9 ?is op]ation also ! tides play a "p ( conspicu\s importance1 & :]e ! ebb & fl[ is greate/ x is obvi\s t an additional impetus w be giv5 to ! manufacture ( /ratifi$ rocks4 ,9 fact1 we may reg>d ! wat]s ( ! globe z a mighty mill1 incessantly occupi$ 9 gr9d+ up mat]ials = future /rata4 ,! ma9 op]at+ p[] ( ?is mill is ( c\rse d]iv$ f ! sun1 = x is ! sun :i* br+s up ! ra9s to n\ri% ! riv]s1 x is ! sun :i* raises ! w9d :i* la%es ! waves aga9/ ! %ore4 ,b !re is an auxili>y p[] to keep ! mill 9 motion1 & t auxili>y p[] is af=d$ by ! tides4 ,if !n we f9d t by any cause ! effici5cy ( ! tides is increas$ we %all f9d t ! mill = ! manufacture ( /rata obta9s a correspond+ accession to its capacity4 ,assum+ ! e/imate ( ,pr(essor ,d>w91 t ! tide may h _h twice z great a v]tical range ( ebb & fl[ )9 geological times z x has at pres5t1 we f9d a consid]able addition to ! effici5cy ( ! ocean 9 ! manufacture ( ! anci5t /ratifi$ rocks4 ,x mu/ be rememb]$ t ! ext5t ( ! area ?r\gh :i* ! tides w subm]ge & lay b>e ! c\ntry1 w (t5 be increas$ m ?an tw(old by a tw(old increase ( height4 ,a little illu/ration may %[ :at ,i mean4 ,suppose a cone to be fill$ ) wat] up to a c]ta9 height1 & t ! quantity ( wat] 9 x be measur$2 n[ let ! cone be fill$ until ! wat] is at d\ble ! dep?2 !n ! surfaces ( ! wat] 9 ! two cases w be 9 ! ratio ( ! circles1 "o ( :i* has d\ble ! diamet] ( ! o!r4 ,! areas ( ! two surfaces are ?us z f\r to "o2 ! volumes ( ! wat]s 9 ! two cases w be 9 ! proportion ( two simil> solids1 ! ratios ( _! dim5sions be+ z two to "o4 ,( c\rse ?is means t ! wat] 9 ! "o case w\ld be eight times z mu* z 9 ! o!r4 ,?is p>ticul> illu/ration w n (t5 apply exactly to tidal ph5om5a1 b ,i may m5tion "o place t ,i happ5 to "k (1 9 ! vic9ity ( ,dubl91 9 :i* ! effect ( ! rise & fall ( ! tide w\ld be some:at ( ?is description4 ,at ,malahide !re is a wide %all[ e/u>y cut (f f ! sea by a railway embankm5t1 & !re is a viaduct 9 ! embankm5t ?r\gh :i* a great tidal curr5t fl[s 9 & out alt]nately4 ,at l[ tide !re is b little wat] 9 ?is e/u>y1 b at high tide x ext5ds = miles inl&4 ,we may reg>d ?is inlet ) suffici5t approximation to ! tru? z half ( a cone ) a v l>ge angle1 ! railway embankm5t ( c\rse =m+ ! diamet]2 h5ce x foll[s t if ! tide 0 to be rais$ to d\ble its height1 s l>ge an area ( additional l& w\ld be subm]g$1 & s va/ an increase ( wat] w\ld be necess>y = ! purpose1 t ! fl[ "u ! railway bridge w\ld h to be mu* m consid]able ?an x is at pres5t4 ,9 "s degree ! same ph5om5a w be repeat$ else:]e ar\nd ! coa/4 ,simply multiply+ ! height ( ! tide by two w\ld (t5 mean t ! bord] ( l& betwe5 high & l[ wat] w\ld be increas$ m ?an tw(old1 & t ! volume ( wat] alt]nately p\r$ on ! l& & drawn (f x w\ld be increas$ 9 a /ill l>g] proportion4 ,! velocity ( all tidal curr5ts w\ld also be great] ?an at pres5t1 & z ! p[] ( a curr5t ( wat] = transport+ solid mat]ial held 9 susp5sion increases rapidly ) ! velocity1 s we may inf] t ! effici5cy ( tidal curr5ts z a vehicle = ! transport ( comm9ut$ rocks w\ld be greatly increas$4 ,x is ?us obvi\s t tides ) a rise & fall d\ble 9 v]tical height ( ^? :i* we "k at pres5t w\ld add a l>ge increase to _! effici5cy z geological ag5ts4 ,inde$1 ev5 7 ! tides only half or "o-?ird great] ?an ^? we "k n[1 we might reasonably expect t ! manufacture ( /ratifi$ rocks mu/ h proce$$ m rapidly ?an at pres5t4 ,! "q !n w assume ?is =m4 ,we "k t ! tides mu/ h be5 great] 9 ,cambrian or ,laur5tian days ?an !y are at pres5t2 s t !y 7 available z a means ( assi/+ o!r ag5ts 9 ! /up5d\s op]ations ( /rata manufacture :i* 7 !n conduct$4 ,?is c]ta9ly helps u to und]/& h[ ^! trem5d\s b$s ( /rata1 a doz5 miles or m 9 solid ?ickness1 7 deposit$4 ,x seems imp]ative t = ! accompli%m5t ( a task s mighty1 "s ag5ts m pot5t ?an ^? ) :i* we are famili> %\ld be requir$4 ,! doctr9e ( tidal evolution has %[n u :at ^? ag5ts 74 ,x only leaves u un9=m$ z to ! degree 9 :i* _! mighty capabilities 7 drawn ^u4 ,x is ! prop]ty ( sci5ce z x gr[s to f9d its bran*es m & m int]wov51 & ?is seems especially true ( ! two greate/ ( all natural sci5ces--geology & a/ronomy4 ,) ! beg9n+s ( our e>? z a globe 9 ! %ape 9 :i* we f9d x bo? ^! sci5ces are directly conc]n$4 ,i h "h t\*$ ^u ano!r bran* 9 :i* !y illu/rate & confirm ea* o!r4 ,z ! !ory ( tidal evolution has %$ su* a flood ( light into ! previ\sly d>k hi/ory ( our e>?-moon sy/em1 x becomes ( int]e/ to see :e!r ! tidal ph5om5a may n h a wid] scope2 :e!r !y may n1 = in/ance1 h det]m9$ ! =mation ( ! planets by bir? f ! sun1 j z ! moon seems to h orig9at$ by bir? f ! e>?4 ,our fir/ presumption1 t ! cases are analog\s1 is n h[ev] ju/ifi$ :5 ! facts are c>efully inquir$ into4 ,a pr9ciple :i* ,i h n hi!rto discuss$ "h assumes prom95ce1 & !re=e we %all devote our att5tion to x = a few m9utes4 ,let u und]/& :at we mean by ! sol> sy/em4 ,!re is fir/ ! sun at ! c5tre1 :i* prepond]ates ov] all ! o!r bodies s enorm\sly1 z %[n 9 ,fig4 #d1 9 :i* ! e>? & ! sun are plac$ side by side = comp>ison4 ,!re is !n ! ret9ue ( planets1 among ! small] ( :i* our e>? takes its place1 a view ( ! comp>ative sizes ( ! planets be+ %[n 9 ,fig4 #e4 ,illu/ration3 ,fig4 #d4--;,comp>ative sizes ( ,e>? & ,sun4 ,n to emb>rass ourselves ) ! p]plexities ( a problem s complicat$ z our sol> sy/em is 9 its entirety1 we %all = ! sake ( cle> reason+ assume an ideal sy/em1 consi/+ ( a sun & a l>ge planet--9 fact1 su* z our own sy/em w\ld be if we c\ld )draw f x all o!r bodies1 leav+ ! sun & ,jupit] only rema9+4 ,we %all suppose1 ( c\rse1 t ! sun is mu* l>g] ?an ! planet1 9 fact1 x w be conv5i5t to keep 9 m9d ! relative masses ( ! sun & ,jupit]1 ! weight ( ! planet be+ less ?an "o-?\s&? "p ( ! sun4 ,we "k1 ( c\rse1 t bo? ( ^? bodies are rotat+ ^u _! axes1 & ! "o is revolv+ ar\nd ! o!r2 & = simplicity we may fur!r suppose t ! axes ( rotation are p]p5dicul> to ! plane ( revolution4 ,9 bodies s con/itut$ tides w be manife/$4 ,jupit] w raise tides 9 ! sun1 ! sun w raise tides 9 ,jupit]4 ,if ! rotation ( ea* body be p]=m$ 9 a less p]iod ?an t ( ! revolution 7! case :i* alone conc]ns u71 !n ! tides w imm$iately op]ate 9 _! habitual mann] z a brake = ! *eck+ ( rotation4 ,! tides rais$ by ! sun on ,jupit] w t5d !re=e to l5g!n ,jupit]'s day2 ! tides rais$ on ! sun by ,jupit] w t5d to augm5t ! sun's p]iod ( rotation4 ,bo? ,jupit] & ! sun w !re=e lose "s mom5t ( mom5tum4 ,we _c1 h[ev]1 repeat too (t5 ! dynamical tru? t ! total mom5t ( mom5tum mu/ rema9 con/ant1 !re=e :at is lo/ by ! rotation mu/ be made up 9 ! revolution2 ! orbit ( ,jupit] ar\nd ! sun mu/ accord+ly be swell+4 ,s f> ! reason+ appe>s simil> to t :i* l$ to su* />tl+ consequ5ces 9 reg>d to ! moon4 ,illu/ration3 ,fig4 #e4--;,comp>ative sizes ( ,planets4 ,b n[ = ! fundam5tal diff]5ce betwe5 ! two cases4 ,! moon1 x w be rememb]$1 always revolves ) ! same face t[>ds ! e>?4 ,! tides h ceas$ to op]ate !re1 & consequ5tly ! moon is n able to contribute any mom5t ( mom5tum1 to be appli$ to ! enl>gem5t ( its di/ance f ! e>?2 all ! mom5t ( mom5tum necess>y = ?is purpose is ( c\rse drawn f ! s+le supply 9 ! rotation ( ! e>? on its axis4 ,b 9 ! case ( ! sy/em consi/+ ( ! sun & ,jupit] ! circum/ances are q diff]5t--,jupit] does n always b5d ! same face to ! sun2 s f>1 inde$1 is ?is f be+ true1 t ,jupit] is em95tly rem>kable = ! rapidity ( 8 rotation1 & = ! incessantly v>y+ aspect 9 :i* he w\ld be se5 f ! sun4 ,jupit] has !re=e a /ore ( available mom5t ( mom5tum1 z has also ( c\rse ! sun4 ,?us 9 ! sun & planet sy/em we h 9 ! rotations two available /ores ( mom5t ( mom5tum on :i* ! tides c make draughts = application to ! enl>gem5t ( ! revolution4 ,! proportions 9 :i* ^! two available s\rces c be drawn ^u = contributions is n left arbitr>y4 ,! laws ( dynamics provide ! %>es 9 :i* ea* ( ! bodies is to contribute = ! jo9t purpose ( driv+ !m fur!r ap>t4 ,let u see if we _c =m an e/imate by elem5t>y consid]ations z to ! division ( ! lab\r4 ,! tides rais$ on ,jupit] by ! sun w be practically proportional to ! sun's mass & to ! radius ( ,jupit]4 ,ow+ to ! enorm\s size ( ! sun1 ! effici5cy ( ^! tides & ! mom5t ( ! friction-brake !y produce w be f> great] on ! planet ?an w ! conv]se op]ation ( ! planet be on ! sun4 ,h5ce x foll[s t ! effici5cy ( ! tides 9 depriv+ ,jupit] ( mom5t ( mom5tum w be greatly sup]ior to ! effici5cy ( ! tides 9 depriv+ ! sun ( mom5t ( mom5tum4 ,)\t foll[+ ! matt] into any close num]ical calculation1 we may ass]t t = e "o "p ! sun contributes to ! common object1 ,jupit] w contribute at lea/ a ?\s& p>ts2 & ?is inequality appe>s all ! m /rik+1 n to say unju/1 :5 x is rememb]$ t ! sun is m abundantly provid$ ) mom5t ( mom5tum ?an is ,jupit]--! sun has1 9 fact1 ab\t tw5ty ?\s& times z mu*4 ,! case may be illu/rat$ by suppos+ t a ri* man & a poor man comb9e toge!r to a*ieve "s common purpose to :i* bo? are to contribute4 ,! e?ical notion t ,dives %all contribute l>gely1 accord+ to 8 l>ge means1 & ,laz>us accord+ to 8 sl5d] means1 is q antagoni/ic to ! scale :i* dynamics has impos$4 ,dynamics decl>es t ! ri* man ne$ only give a p5ny to e p\nd t has to be extort$ f ! poor man4 ,n[ ?is is precisely ! case ) reg>d to ! sun & ,jupit]1 & x involves a some:at curi\s consequ5ce4 ,z long z ,jupit] possesses available mom5t ( mom5tum1 we may be c]ta9 t no l>ge contribution ( mom5t ( mom5tum has be5 obta9$ f ! sun4 ,=1 return+ to our illu/ration1 if we f9d t ,laz>us /ill has some?+ left 9 8 pocket1 we are ( c\rse assur$ t ,dives _c h exp5d$ mu*1 because1 z ,laz>us _h b little to beg9 )1 & z ,dives only puts 9 a p5ny = e p\nd t ,laz>us sp5ds1 x is obvi\s t no l>ge am\nt c h be5 devot$ to ! common object4 ,h5ce x foll[s t :atev] transf] ( mom5t ( mom5tum has tak5 place 9 ! sun-,jupit] sy/em has be5 almo/ entirely obta9$ at ! exp5se ( ,jupit]4 ,n[ 9 ! sol> sy/em at pres5t1 ! orbital mom5t ( mom5tum ( ,jupit] is ne>ly fifty ?\s& times z great z 8 pres5t /ore ( rotational mom5t ( mom5tum4 ,if1 !re=e1 ! dep>ture ( ,jupit] f ! sun _h be5 ! consequ5ce ( tidal evolution1 x w\ld foll[ t ,jupit] mu/ once h conta9$ _m ?\s&s ( times ! mom5t ( mom5tum t he has at pres5t4 ,?is seems utt]ly incr$ible1 = ev5 7 ,jupit] dilat$ into an enorm\sly l>ge mass ( vapor\s matt]1 sp9n+ r\nd ) ! utmo/ conceivable spe$1 x is impossible t he %\ld ev] h possess$ en\gh mom5t ( mom5tum4 ,we are !re=e =c$ to ! conclusion t ! tides alone d n provide suffici5t explanation = ! retreat ( ,jupit] f ! sun4 ,!re is r a subtle po9t 9 ! consid]ations n[ br\ght =w>d1 on :i* x w be necess>y = u to pond]4 ,9 ! illu/ration ( ,dives & ,laz>us1 ! contributions ( ,laz>us ( c\rse ceas$ :5 8 pockets 7 exhau/$1 b ^? ( ,dives w cont9ue1 & 9 ! lapse ( "t may atta9 any am\nt )9 ! utmo/ limits ( ,dives' res\rces4 ,! ess5tial po9t to notice is1 t s long z ,laz>us reta9s any?+ 9 8 pocket1 we "k = c]ta9 t ,dives has n giv5 mu*2 if ,laz>us1 h[ev]1 has 8 pocket absolutely empty1 & if we d n "k h[ long !y may h be5 9 t condition1 we h no means ( kn[+ h[ l>ge a portion ( weal? ,dives may n h actually exp5d$4 ,! turn+-po9t ( ! !ory ?us involves ! fact t ,jupit] /ill reta9s available mom5t ( mom5tum 9 8 rotation2 & ?is 0 our sole me?od ( prov+ t ! sun1 :i* 9 ?is case 0 ,dives1 _h nev] giv5 mu*4 ,b our argum5t mu/ h tak5 an entirely diff]5t l9e _h x s happ5$ t ,jupit] con/antly turn$ ! same face to ! sun1 & t !re=e 8 pockets 7 entirely empty 9 s f> z available mom5t ( mom5tum is conc]n$4 ,x w\ld be app>5tly impossible = u to say to :at ext5t ! res\rces ( ! sun may n h be5 drawn ^u2 we c1 h[ev]1 calculate :e!r 9 any case ! sun c\ld possibly h suppli$ en\gh mom5t ( mom5tum to acc\nt = ! recession ( ,jupit]4 ,speak+ 9 r\nd numb]s1 ! revolutional mom5t ( mom5tum ( ,jupit] is ab\t ?irty times z great z ! rotational mom5t ( mom5tum at pres5t possess$ by ! sun4 ,i d n "k t !re is any?+ impossible 9 ! supposition t ! sun might1 by an augm5t$ volume & an augm5t$ velocity ( rotation1 conta9 _m times ! mom5t ( mom5tum t x has at ?is mom5t4 ,x !re=e foll[s t if x _h happ5$ t ,jupit] con/antly b5t ! same face to ! sun1 !re w\ld app>5tly be no?+ impossible 9 ! fact t ,jupit] _h be5 born ( ! sun1 j z ! moon 0 born ( ! e>?4 ,^! same consid]ations %\ld also lead u to obs]ve ) /ill m special att5tion ! developm5t ( ! e>?-moon sy/em4 ,let u re/ate ! matt] ( ! e>? & moon 9 ! light :i* ! argum5t ) respect to ,jupit] has giv5 u4 ,at pres5t ! rotational mom5t ( mom5tum ( ! e>? is ab\t a fif? "p ( ! revolutional mom5t ( mom5tum ( ! moon4 ,ow+ to ! fact t ! moon keeps ! same face to u1 %e has n[ no available mom5t ( mom5tum1 & all ! mom5t ( mom5tum requir$ to acc\nt = h] retreat has ( late come f ! rotation ( ! e>?2 b suppose t ! moon /ill _h "s liquid on its surface :i* c\ld be agitat$ by tides1 suppose fur!r t x did n always b5d ! same face t[>ds u1 t x !re=e _h "s available mom5t ( mom5tum due to its rotation on :i* ! tides c\ld op]ate1 !n see h[ ! argum5t w\ld h be5 alt]$4 ,! gradual increase ( ! moon's di/ance c\ld be provid$ = by a transf] ( mom5t ( mom5tum f two s\rces1 due ( c\rse to ! rotational velocities ( ! two bodies4 ,"h aga9 ! moon & ! e>? w contribute accord+ to t dynamical b v iniquit\s pr9ciple :i* regulat$ ! appropriations f ! purses ( ,dives & ,laz>us4 ,! moon mu/ give n accord+ to h] abundance1 b 9 ! inv]se ratio !re(--because %e has little %e mu/ give l>gely4 ,nor %all we make an errone\s e/imate if we say t n9e-t5?s ( ! :ole mom5t ( mom5tum necess>y = ! enl>gem5t ( ! orbit w\ld h be5 exact$ f ! moon2 t means t ! moon mu/ once h _h ab\t five or six times z mu* mom5t ( mom5tum z ! e>? possesses at ?is mom5t4 ,consid]+ ! small size ( ! moon1 ?is c\ld only h aris5 by t]rific velocity ( rotation1 :i* x is inconceivable t its mat]ials c\ld ev] h possess$4 ,?is pres5ts ! demon/ration ( tidal evolution 9 a fre% light4 ,if ! moon n[ dep>t$ to any consid]able ext5t f %[+ ! con/ant face to ! e>?1 x w\ld seem t its retreat c\ld n h be5 caus$ by tides4 ,"s o!r ag5t = produc+ ! pres5t configuration w\ld be necess>y1 j z we f\nd t "s o!r ag5t ?an ! tides has be5 necess>y 9 ! case ( ,jupit]4 ,b ,i mu/ say a few words z to ! attitude ( ?is "q ) reg>d to ! entire sol> sy/em4 ,?is sy/em consi/s ( ! sun presid+ at ! c5tre1 & ( ! planets & _! satellites 9 revolution ar\nd _! respective prim>ies1 & ea* also animat$ by a rotation on its axis4 ,i %all 9 s f> dep>t f ! actual configuration ( ! sy/em z to trans=m x into an ideal sy/em1 :]e( ! masses1 ! dim5sions1 & ! velocities %all all be pres]v$2 b t ! sev]al planes ( revolution %all be all flatt5$ into "o plane1 in/ead ( be+ incl9$ at small angles z !y are at pres5t2 nor w x be unreasonable = u at ! same "t to br+ into p>allelism all ! axes ( rotation1 & to arrange t _! common directions %all be p]p5dicul> to ! plane ( _! common orbits4 ,= ! purpose ( our pres5t rese>* ?is ideal sy/em may pass = ! real sy/em4 ,9 its orig9al /ate1 :atev] t /ate may h be51 a magnific5t end[m5t 0 conf]r$ ^u ! sy/em4 ,p]haps ,i may1 )\t d]ogation f ! dignity ( my subject1 speak ( ! end[m5t z p>tly p]sonal & p>tly entail$4 ,! sy/em _h ( c\rse diff]5t p[]s ) reg>d to ! disposal ( ! two portions2 ! p]sonal e/ate c\ld be squ&]$4 ,x consi/$ entirely ( :at we call en]gy2 & consid]+ h[ frequ5tly we use ! expression cons]vation ( en]gy1 x may seem /range to say n[ t ?is portion ( ! end[m5t has be5 f\nd capable ( ali5ation1 nay1 fur!r1 t our sy/em has be5 squ&]+ x p]si/5tly f ! fir/ mom5t until n[4 ,al?\gh ! doctr9e ( ! cons]vation ( en]gy is1 we h e reason to believe1 a fundam5tal law affect+ ! :ole univ]se1 yet x w\ld be :olly inaccurate to say t any p>ticul> sy/em su* z our sol> sy/em %all inv>iably pres]ve precisely ! same quantity ( en]gy )\t alt]ation4 ,! circum/ance t heat is a =m ( en]gy inde$ negatives ?is supposition4 ,= our sy/em possesses en]gy ( all ! diff]5t k9ds3 !re is en]gy due to ! motions bo? ( rotation & ( revolution2 !re is en]gy due to ! fact t ! mutually attract+ bodies ( our sy/em are sep>at$ by di/ances ( enorm\s magnitude2 & !re is also en]gy 9 ! =m ( heat2 & ! laws ( heat p]mit t ?is =m ( en]gy %all be radiat$ (f into space1 & ?us disappe> entirely1 9 s f> z our sy/em is conc]n$4 ,on ! o!r h&1 !re may no d\bt be "s small am\nt ( en]gy accru+ to our sy/em f ! o!r sy/ems 9 space1 :i* l ours are radiat+ =? en]gy4 ,any ga9 f ?is s\rce1 h[ev]1 is necess>ily s v small 9 comp>ison to ! loss to :i* we h ref]r$1 t x is q impossible t ! "o %\ld balance ! o!r4 ,?\gh x is und\bt$ly true t ! total quantity ( en]gy 9 ! univ]se is con/ant1 yet ! %>e ( t en]gy belong+ to any p>ticul> sy/em su* z ours decl9es /eadily f age to age4 ,i may inde$ rem>k1 t ! "q z to :at becomes ( all ! radiant en]gy :i* ! millions ( suns 9 ! univ]se are daily dis*>g+ (f]s a problem app>5tly n easy to solve2 b we ne$ n discuss ! matt] at pres5t1 we are only go+ to trace out ! vicissitudes ( our own sy/em2 & :atev] o!r *anges t sy/em may exhibit1 ! fact is c]ta9 t ! total quantity ( en]gy x conta9s is decl9+4 ,( ! two end[m5ts ( en]gy & ( mom5t ( mom5tum orig9ally conf]r$ on our sy/em ! mom5t ( mom5tum is ! entail$ e/ate4 ,no matt] h[ ! bodies may move1 no matt] h[ _! actions may int]f]e ) "o ano!r1 no matt] h[ ?is body is pull$ "o way & ! o!r body t way1 ! cons]vation ( mom5t ( mom5tum is n imp]ill$1 nor1 no matt] :at losses ( heat may be exp]i5c$ by radiation1 c\ld ! /ore ( mom5t ( mom5tum be affect$4 ,! only conceivable way 9 :i* ! quantity ( mom5t ( mom5tum 9 ! sol> sy/em c\ld be tamp]$ ) is by ! int]f]5ce ( "s ext]nal attract+ body4 ,we "k1 h[ev]1 t ! />s are all situat$ at su* enorm\s di/ances1 t ! influ5ces !y c ex]t 9 ! p]turbation ( ! sol> sy/em are absolutely ins5sible2 !y are beyond ! rea* ( ! mo/ delicate a/ronomical measurem5ts4 ,h5ce we see h[ ! end[m5t ( ! sy/em ) mom5t ( mom5tum has conf]r$ ^u t sy/em a some?+ :i* is absolutely inali5able1 ev5 to ! smalle/ portion4 ,be=e go+ any fur!r x w\ld be necess>y = me to expla9 m fully ?an ,i h hi!rto done ! true nature ( ! me?od ( e/imat+ mom5t ( mom5tum4 ,! mom5t ( mom5tum consi/s ( two p>ts3 !re is fir/ t due to ! revolution ( ! bodies ar\nd ! sun2 !re is secondly ! rotation ( ^! bodies on _! axes4 ,let u fir/ ?9k simply ( a s+le planet revolv+ 9 a circul> orbit ar\nd ! sun4 ,! mom5tum ( t planet at any mom5t may be reg>d$ z ! product ( its mass & its velocity2 !n ! mom5t ( mom5tum ( ! planet 9 ! case m5tion$ is f\nd by multiply+ ! mom5tum by ! radius ( ! pa? pursu$4 ,9 a m g5]al case1 :]e ! planet does n revolve 9 a circle1 b pursu$ an elliptic pa?1 ! mom5t ( mom5tum is to be f\nd by multiply+ ! planet's velocity & its mass into ! p]p5dicul> f ! sun on ! direction 9 :i* ! planet is mov+4 ,^! rules provide ! me?ods = e/imat+ all ! mom5ts ( mom5tum1 s f> z ! revolutions 9 our sy/em are conc]n$4 ,= ! rotations some:at m elaborate processes are requir$4 ,let u ?9k ( a sph]e rotat+ r\nd a fix$ axis4 ,e p>ticle ( t sph]e w ( c\rse describe a circle ar\nd ! axis1 & all ^! circles w lie 9 p>allel planes4 ,we may = our pres5t purpose reg>d ea* atom ( ! body z a little planet revolv+ 9 a circul> orbit1 & !re=e ! mom5t ( mom5tum ( ! entire sph]e w be f\nd by simply add+ toge!r ! mom5ts ( mom5tum ( all ! diff]5t atoms ( :i* ! sph]e is compos$4 ,to p]=m ?is addition ! use ( an elaborate ma!matical me?od is requir$4 ,i d n propose to ent] into ! matt] any fur!r1 except to say t ! total mom5t ( mom5tum is ! product ( two factors--"o ! angul> velocity ) :i* ! sph]e is turn+ r\nd1 :ile ! o!r involves ! sph]e's mass & dim5sions4 ,to illu/rate ! pr9ciples ( ! computation we %all take "o or two examples4 ,suppose t two circles be drawn1 "o ( :i* is d\ble ! diamet] ( ! o!r4 ,let two planets be tak5 ( equal mass1 & "o ( ^! be put to revolve 9 "o circle1 & ! o!r to revolve 9 ! o!r circle1 9 su* a way t ! p]iods ( bo? revolutions %all be equal4 ,x is requir$ to f9d ! mom5ts ( mom5tum 9 ! two cases4 ,9 ! l>g] ( ! two circles x is pla9 t ! planet mu/ be mov+ twice z rapidly z 9 ! small]1 !re=e its mom5tum is twice z great2 & z ! radius is also d\ble1 x foll[s t ! mom5t ( mom5tum 9 ! l>ge orbit w be f\r times t 9 ! small orbit4 ,we ?us see t ! mom5t ( mom5tum increases 9 ! proportion ( ! squ>es ( ! radii4 ,if1 h[ev]1 ! two planets 7 revolv+ ab\t ! same sun1 "o ( ^! orbits be+ d\ble ! o!r1 ! p]iodic times c\ld n be equal1 = ,kepl]'s law tells u t ! squ>e ( ! p]iodic "t is proportional to ! cube ( ! mean di/ance4 ,suppose1 !n1 t ! di/ance ( ! fir/ planet is #a1 & t ( ! second planet is #b1 ! cubes ( ^? numb]s are #a & #h1 & !re=e ! p]iodic times ( ! two bodies w be z #a to ! squ>e root ( #h4 ,we c ?us see t ! velocity ( ! out] body mu/ be less ?an t ( ! inn] "o1 = :ile ! l5g? ( ! pa? is only d\ble z l>ge1 ! "t tak5 to describe t pa? is ! squ>e root ( eight times z great2 9 fact1 ! velocity ( ! out] body w be only ! squ>e root ( twice t ( ! inn] "o4 ,z1 h[ev]1 its di/ance f ! sun is twice z great1 x foll[s t ! mom5t ( mom5tum ( ! out] body w be ! squ>e root ( twice t ( ! inn] body4 ,we may /ate ?is result a little m g5]ally z foll[s-- ,9 comp>+ ! mom5ts ( mom5tum ( ! sev]al planets :i* revolve ar\nd ! sun1 t ( ea* planet is proportional to ! product ( its mass ) ! squ>e root ( its di/ance f ! sun4 ,let u n[ comp>e two sph]es toge!r1 ! diamet] ( "o sph]e be+ d\ble t ( ! o!r1 :ile ! times ( rotation ( ! two are id5tical4 ,& let u n[ comp>e toge!r ! mom5ts ( mom5tum 9 ^! two cases4 ,x c be %[n by reason+1 into :i* ,i ne$ n n[ ent]1 t ! mom5t ( mom5tum ( ! l>ge sph]e w be ?irty-two times t ( ! small "o4 ,9 g5]al we may /ate t if a sph]e ( homog5e\s mat]ial be rotat+ ab\t an axis1 its mom5t ( mom5tum is to be express$ by ! product ( its angul> velocity by ! fif? p[] ( its radius4 ,we c n[ take /ock1 z x 71 ( ! con/itu5ts ( mom5ts ( mom5tum 9 our sy/em4 ,we may omit ! satellites = ! pres5t1 :ile su* unsub/antial bodies z comets & su* small bodies z meteors ne$ n conc]n u4 ,! pres5t inve/m5t ( ! mom5t ( mom5tum ( our sy/em is to be f\nd by multiply+ ! mass ( ea* planet by ! squ>e root ( its di/ance f ! sun2 ^! products = all ! sev]al planets =m ! total revolutional mom5t ( mom5tum4 ,! rema9d] ( ! inve/m5t is 9 rotational mom5t ( mom5tum1 ! collective am\nt ( :i* is to be e/imat$ by multiply+ ! angul> velocity ( ea* planet into its d5sity1 & ! fif? p[] ( its radius if ! planet be reg>d$ z homog5e\s1 or into su* o!r p[] z may be necess>y :5 ! planet is n homog5e\s4 ,inde$1 z ! d5s] p>ts ( ! planet necess>ily lie 9 its int]ior1 & h !re=e nei!r ! velocity nor ! radius ( ! m sup]ficial portions1 x seems necess>y to admit t ! mom5ts ( mom5tum ( ! planets w be proportional to "s l[] p[] ( ! radius ?an ! fif?4 ,! total mom5t ( mom5tum ( ! planets by rotation1 :5 multipli$ by a con/ant factor1 & add$ to ! revolutional mom5t ( mom5tum1 w rema9 absolutely con/ant4 ,x may be int]e/+ to note ! pres5t disposition ( ?is va/ inh]itance among ! diff]5t bodies ( our sy/em4 ,! bigge/ item ( all is ! mom5t ( mom5tum ( ,jupit]1 due to its revolution ar\nd ! sun2 9 fact1 9 ?is s+le inve/m5t ne>ly sixty p] c5t4 ( ! total mom5t ( mom5tum ( ! sol> sy/em is f\nd4 ,! next heavie/ item is ! mom5t ( mom5tum ( ,saturn's revolution1 :i* is tw5ty-f\r p] c5t4 ,!n come ! simil> contributions ( ,uranus & ,neptune1 :i* are six & eight p] c5t4 respectively4 ,only "o m item is wor? m5tion+1 z f> z magnitude is conc]n$1 & t is ! ne>ly two p] c5t4 t ! sun conta9s 9 virtue ( its rotation4 ,9 fact1 all ! o!r mom5ts ( mom5tum are comp>atively insignificant 9 ?is me?od ( view+ ! subject4 ,jupit] f 8 rotation has n ! fifty ?\s&? "p ( 8 revolutional mom5t ( mom5tum1 :ile ! e>?'s rotational %>e is n "o t5 ?\s&? "p ( t ( ,jupit]1 & !re=e is )\t importance 9 ! g5]al aspect ( ! sy/em4 ,! revolution ( ! e>? contributes ab\t "o eight hundr$? "p ( t ( ,jupit]4 ,^! facts z "h /at$ w suffice = u to make a =eca/ ( ! utmo/ ! tides c effect 9 ! future trans=mation ( our sy/em4 ,we h already expla9$ t ! g5]al t5d5cy ( tidal friction is to augm5t revolutional mom5t ( mom5tum at ! exp5se ( rotational4 ,! total1 h[ev]1 ( ! rotational mom5t ( mom5tum ( ! sy/em b>ely rea*es two p] c5t4 ( ! :ole am\nt2 ?is is ( c\rse almo/ entirely contribut$ by ! sun1 = all ! planets toge!r h n a ?\s&? "p ( ! sun's rotational mom5t4 ,! utmo/ !re=e t tidal evolution c effect 9 ! sy/em is to di/ribute ! two p] c5t4 9 augm5t+ ! revolution>y mom5t ( mom5tum4 ,x does n seem t ?is c produce mu* appreciable d]angem5t 9 ! configuration ( ! sy/em4 ,no d\bt if x 7 all appli$ to "o ( ! small] planets x w\ld produce v consid]able effect4 ,our e>?1 = in/ance1 w\ld h to be driv5 out to a di/ance _m hundr$s ( times fur!r ?an x is at pres5t 7 ! sun's disposable mom5t ( mom5tum ultimately to be transf]r$ to ! e>? alone4 ,on ! o!r h&1 ,jupit] c\ld absorb ! :ole ( ! sun's %>e by q an insignificant enl>gem5t ( its pres5t pa?4 ,x does n seem likely t ! di/ribution t mu/ ultimately take place c mu* affect ! pres5t configuration ( ! sy/em4 ,we ?us see t ! tides d n appe> to h ex]cis$ any?+ l ! same influ5ce 9 ! affairs ( our sol> sy/em g5]ally :i* !y h done 9 t v small "p ( ! sol> sy/em :i* consi/s ( ! e>? & moon4 ,?is is1 z ,i h endeav\r$ to %[ 9 ^! lectures1 ! sc5e ( supremely int]e/+ tidal ph5om5a2 b h[ small x is 9 comp>ison ) ! :ole magnitude ( our sy/em may be inf]r$ f ! foll[+ illu/ration4 ,i repres5t ! :ole mom5t ( mom5tum ( our sy/em by #a1jjj1jjj1jjj1 ! bulk ( :i* is compos$ ( ! revolutional mom5ts ( mom5tum ( ! great planets1 & ! rotational mom5t ( mom5tum ( ! sun4 ,on ?is scale ! rotational %>e :i* has fall5 to our e>? & moon does n ev5 rise to ! dignity ( a s+le p\nd1 x c only be repres5t$ by ! v mode/ figure ( #ais4 #e;d4 ,?is is divid$ into two p>ts--! e>? by its rotation acc\nts = #cs4 #d;d41 leav+ #afs4 #a;d4 z ! equival5t ( ! revolution ( ! moon4 ,! o!r inf]ior planets h /ill less to %[ ?an ! e>?4 ,v5us c b>ely h m ?an #bs4 #f;d42 ev5 ,m>s' two satellites _c br+ 8 figure up beyond ! sl5d] value ( #a;d42 :ile ,m]cury w be amply repres5t$ by ! smalle/ co9 kn[n at h] ,maje/y's m9t4 ,! same illu/ration w br+ out ! contra/ betwe5 ! ,jovian sy/em & our e>? sy/em4 ,! rotational %>e ( ! =m] w\ld be totally repres5t$ by a sum ( ne>ly #ab1jjj2 ( ?is1 h[ev]1 ,jupit]'s satellites only contribute ab\t #hi1 not)/&+ t !re are f\r ( !m4 ,?us ,jupit]'s satellites h n "o hundr$? "p ( ! mom5t ( mom5tum :i* ! rotation ( ,jupit] exhibits4 ,h[ wide is ! contra/ betwe5 ?is /ate ( ?+s & ! e>?-moon sy/em1 = ! e>? does n conta9 9 its rotation "o-fif? ( ! mom5t ( mom5tum t ! moon has 9 its revolution2 9 fact1 ! moon has gradually robb$ ! e>?1 :i* orig9ally possess$ #ais4 #e;d41 ( :i* ! moon has c>ri$ (f all b #cs4 #d;d4 ,& ?is process is /ill go+ on1 s t ultimately ! e>? w be left v poor1 ?\gh n absolutely p5niless1 at lea/ if ! ret5tion ( a halfp5ny c be reg>d$ z ju/ify+ t ass]tion4 ,saturn1 revolv+ z x does ) great rapidity1 & hav+ a v l>ge mass1 possesses ab\t #bgjj1 :ile ,uranus & ,neptune tak5 toge!r w\ld figure = ab\t ! same am\nt4 ,9 conclusion1 let u rev]t aga9 to ! two critical conditions ( ! e>?-moon sy/em4 ,z to :at happ5$ be=e ! fir/ critical p]iod1 ! tides tell u no?+1 & e o!r l9e ( reason+ v little2 we c to "s ext5t =esee :at may happ5 aft] ! second critical epo* is rea*$1 at a "t s remote t ,i d n v5ture ev5 to express ! numb] ( ciph]s :i* ought to foll[ ! significant digit 9 ! expression = ! numb] ( ye>s4 ,i m5tion$1 h[ev]1 t at ?is "t ! sun tides w produce ! effect ( apply+ a /ill fur!r brake to ! rotation ( ! e>?1 s t ultimately ! mon? w h become a %ort] p]iod ?an ! day4 ,x is !re=e int]e/+ = u to trace out ! tidal hi/ory ( a sy/em 9 :i* ! satellite revolves ar\nd ! prim>y 9 less "t ?an ! prim>y takes to g r\nd on its own axis--su* a sy/em1 9 fact1 z ,m>s w\ld pres5t at ?is mom5t 7 ! out] satellite to be ab/ract$4 ,! effect ( ! tides on ! planet rais$ by its satellite w\ld !n be to accel]ate its rotation2 = z ! planet1 s to speak1 lags beh9d ! tides1 friction w\ld n[ manife/ itself by ! cont9u\s endeav\r to drag ! prim>y r\nd fa/]4 ,! ga9 ( spe$1 h[ev]1 ?us atta9$ w\ld involve ! prim>y 9 p]=m+ m ?an its orig9al %>e ( ! mom5t ( mom5tum2 less mom5t ( mom5tum w\ld !re=e rema9 to be done by ! satellite1 & ! only way to accompli% ?is w\ld be = ! satellite to come inw>ds & revolve 9 a small] orbit4 ,we might inde$ h inf]r$ ?is f ! consid]ations ( en]gy alone1 = :atev] happ5s 9 ! de=mation ( ! orbit1 heat is produc$ by ! friction1 & ?is heat is lo/1 & ! total en]gy ( ! sy/em mu/ consequ5tly decl9e4 ,n[ if x be a consequ5ce ( ! tides t ! velocity ( ! prim>y is accel]at$1 ! en]gy correspond+ to t velocity is also increas$4 ,h5ce ! prim>y has m en]gy ?an x _h be=e2 ?is en]gy mu/ h be5 obta9$ at ! exp5se ( ! satellite2 ! satellite mu/ !re=e draw inw>ds until x has yield$ up en\gh ( en]gy n alone to acc\nt = ! increas$ en]gy ( ! prim>y1 b also = ! absolute loss ( en]gy by :i* ! :ole op]ation is *>act]iz$4 ,x !re=e appe>s t 9 ! excessively remote future ! retreat ( ! moon w n only be *eck$1 b t ! moon may actually return to a po9t to be det]m9$ by ! *anges 9 ! e>?'s rotation4 ,x is1 h[ev]1 extremely difficult to foll[ up ! /udy ( a case :]e ! problem ( ?ree bodies has become ev5 m complicat$ ?an usual4 ,! importance ( tidal evolution 9 our sol> sy/em has also to be view$ 9 connection ) ! celebrat$ nebul> hypo!sis ( ! orig9 ( ! sol> sy/em4 ,( c\rse x w\ld be und]/ood t tidal evolution is 9 no s5se a rival doctr9e to t ( ! nebul> !ory4 ,! nebul> orig9 ( ! sun & ! planets sculptur$ out ! ma9 features ( our sy/em2 tidal evolution has m]ely come into play z a subsidi>y ag5t1 by :i* a detail "h or a feature !re has be5 *isell$ into p]fect =m4 ,9 ! nebul> !ory x is believ$ t ! planets & ! sun h all orig9at$ f ! cool+ & ! contraction ( a mighty heat$ mass ( vap\rs4 ,( late ye>s ?is !ory1 9 its ma9 outl9es at all ev5ts1 has /r5g!n$ its hold on ! belief ( ^? :o try to int]pret nature 9 ! pa/ by :at we see 9 ! pres5t4 ,! fact t our sy/em at pres5t conta9s "s heat 9 o!r bodies z well z 9 ! sun1 & ! fact t ! laws ( heat require cont9ual loss by radiation1 demon/rate t our sy/em1 if we look back f> en\gh1 & if ! pres5t laws h act$1 mu/ h _h 9 "p1 at all ev5ts1 an orig9 l t :i* ! nebul> !ory w\ld suppose4 ,i feel t ,i h 9 ! progress ( ^! two lectures be5 only able to give ! m]e/ outl9e ( ! !ory ( tidal evolution 9 its application to ! e>?-moon sy/em4 ,inde$ ,i h be5 oblig$1 by ! nature ( ! subject1 to omit almo/ entirely any ref]5ce to a l>ge body ( ! p>ts ( ! !ory4 ,i _c br+ myself to close ^! lectures )\t j allud+ to ?is omission1 & )\t giv+ expression to ! fact1 t ,i feel x is impossible = me to h r5d]$ adequate ju/ice to ! /r5g? ( ! argum5t on :i* we claim t tidal evolution is ! mo/ rational mode ( acc\nt+ = ! pres5t condition 9 :i* we f9d ! e>?-moon sy/em4 ,( c\rse x w be und]/ood t we h nev] cont5d$ t ! tides (f] ! only conceivable !ory z to ! pres5t condition ( ?+s4 ,! argum5t lies 9 ?is wise4 ,a c]ta9 body ( facts are pat5t to our obs]vation4 ,! tides (f] an explanation z to ! orig9 ( ^! facts4 ,! tides are a v]a causa1 & 9 ! abs5ce ( o!r sugge/$ causes1 ! tidal !ory holds ! field4 ,b mu* w dep5d on ! volume & ! significance ( ! gr\p ( associat$ facts ( :i* ! doctr9e (f]s a solution4 ,! facts t x has be5 9 my p[] to discuss )9 ! compass ( disc\rses l ! pres5t1 only give a v meagre & inadequate notion ( ! entire ph5om5a connect$ ) ! moon :i* ! tides w expla94 ,we h n unfrequ5tly1 = ! sake ( simplicity1 spok5 ( ! moon's orbit z circul>1 & we h n ev5 allud$ to ! fact t ! plane ( t orbit is incl9$ to ! ecliptic4 ,a compreh5sive !ory ( ! moon's orig9 %\ld r5d] an acc\nt ( ! ecc5tricity ( ! moon's orbit2 x mu/ also involve ! obliquity ( ! ecliptic1 ! incl9ation ( ! moon's orbit1 & ! direction ( ! moon's axis4 ,i h be5 p]=ce compell$ to omit ! discussion ( ^! attributes ( ! e>?-moon sy/em1 & 9 do+ s ,i h inflict$ :at is really an inju/ice on ! tidal !ory4 ,= x is ! *ief claim ( ! !ory ( tidal evolution1 z exp\nd$ by ,pr(essor ,d>w91 t x l9ks toge!r all ^! v>i\s features ( ! e>?-moon sy/em4 ,x af=ds a connect$ explanation1 n only ( ! fact t ! moon always turns ! same face to ! e>?1 b also ( ! ecc5tricity ( ! moon's pa? ar\nd ! e>?1 & ! /ill m difficult po9ts ab\t ! incl9ations ( ! v>i\s axes & orbits ( ! planets4 ,x is ! consid]ation ( ^! po9ts t =ms ! /ronghold ( ! doctr9e ( tidal evolution4 ,= :5 we f9d t a !ory dep5d+ ^u influ5ces t und\bt$ly exi/1 & are 9 ceaseless action ar\nd u1 c at ! same "t br+ into connection & (f] a common explanation ( a numb] ( ph5om5a :i* w\ld o!rwise h no common bond ( union1 x is impossible to refuse to believe t su* a !ory does actually correspond to nature4 ,! greate/ ( ma!maticians h ev] f\nd 9 a/ronomy problems :i* tax1 & problems :i* greatly surpass1 ! utmo/ ef=ts ( :i* !y are capable4 ,! usual way 9 :i* ! p[]s ( ! ma!matician h be5 awak5$ into action is by ! ef=t to remove "s gl>+ discrepancy betwe5 an imp]fect !ory & ! facts ( obs]vation4 ,! g5ius ( a ,laplace or a ,lagrange 0 exp5d$1 & wor?ily exp5d$1 9 ef=ts to %[ h[ "o planet act$ on ano!r planet1 & produc$ irregul>ities 9 its orbit2 ! g5ius ( an ,adams & a ,lev]ri] 0 nobly appli$ to expla9 ! irregul>ities 9 ! motion ( ,uranus1 & to discov] a cause ( ^? irregul>ities 9 ! unse5 ,neptune4 ,9 all ^! cases1 & 9 _m o!rs :i* might be m5tion$1 ! ma!matician has be5 /imulat$ by ! laudable anxiety to cle> away "s blemi% f ! !ory ( gravitation ?r\gh\t ! sy/em4 ,! blemi% 0 se5 to exi/ be=e its removal 0 sugge/$4 ,9 t application ( ma!matics ) :i* we h be5 conc]n$ 9 ^! lectures ! call = ! ma!matician has be5 ( q a diff]5t k9d4 ,a c]ta9 famili> ph5om5on on our sea-coa/s has invit$ att5tion4 ,! tidal ripples murmur a secret1 b n = e e>4 ,to int]pret t secret fully1 ! he>] mu/ be a ma!matician4 ,ev5 !n ! int]pretation c only be won aft] ! pr(\nde/ ef=ts ( ?\ght & att5tion1 b at la/ ! language has be5 made intelligible4 ,! lab\r has be5 glori\sly rew>d$1 & an int]e/+ *apt] ( our e>?'s hi/ory has = ! fir/ "t be5 writt54 ,9 ! progress ( ^! lectures ,i h s\ght to int]e/ y 9 ^? pr(\nd inve/igations :i* ! mod]n ma!matician has made 9 8 ef=ts to explore ! secrets ( nature4 ,he has felt t ! laws ( motion1 z we und]/& !m1 are b\nd$ by no consid]ations ( space1 are limit$ by no duration ( "t1 & he has comm5c$ to speculate on ! logical consequ5ces ( ^? laws :5 "t ( indef9ite duration is assum$ to be at 8 disposal4 ,f ! v nature ( ! case1 obs]vations = confirmation 7 impossible4 ,ph5om5a t requir$ millions ( ye>s = _! developm5t _c be submitt$ to ! in/rum5ts 9 our obs]vatories4 ,b ?is is p]haps "o ( ! special reasons :i* make su* inve/igations ( peculi> int]e/1 & entitle u to speak ( ! revelations ( ,"t & ,tide z a romance ( mod]n sci5ce4 ,,index4 ,ab]de51 tides at1 #bc ,action & reaction1 #fi ,adams1 discov]] ( ,neptune1 #ahf ,admiralty ,manual ( ,sci5tific ,inquiry1 #cj1 #ca1 #cd ,admiralty tide tables1 #bi ,africa1 ,krakatoa du/ ov]1 #hd ,analysis1 h>monic1 ( tides1 #cd ,analysis ( tide into its con/itu5ts1 #cc ,anci5t tides on moon1 #acf ,annus ,magnus ( sol> sy/em1 #gb ,areas1 cons]vation (1 #fa ,arkl[1 tides at1 #bc ,asc5sion1 tides at1 #bd ,a/ronomical *ronology1 #adg ,atlantic1 ,krakatoa du/ ov]1 #hd ,atlantic1 tides 91 #ch ,atmosph]e1 tides 91 #dj ,avon1 tides 91 at ,bri/ol1 #ci ,ball-room1 illu/ration1 #fb ,b>ometric records ( ,krakatoa airwave1 #hb ,batavia1 ,krakatoa he>d at1 #hc ,ba?1 hot wat]s at1 #hi ,bay ( ,fundy1 #ci ,b$s ( rock1 h[ =m$1 #adi ,birm+ham1 lecture at1 #adh ,bir? ( moon1 #aah ,bla/ iron furnace1 #hg ,blue sun produc$ by ,krakatoa1 #hd ,bodily tides ( moon1 #aca ,brake illu/rat+ friction1 #fh ,brickwork z a non-conductor1 #hg ,bri/ol ,*annel1 #ci ,bucket ( wat]1 oscillations 91 #ih ,cambrian rocks1 #aec ,cannon-ball1 en]gy (1 #ea ,c>diff1 tides at1 #ci ,caspian ,sea1 tides 91 #ch ,ca/+1 cool+ (1 #gi ,celebes1 ,krakatoa he>d at1 #hc ,c5tral ,am]ica1 #hf ,*ange & full1 tides at1 #bb ,*emical action 9 e>?1 #ha ,*ep/[1 tides at1 #ci ,*ronology1 ! two sy/ems (1 #adg ,clifton1 tides 9 ,avon at1 #ci ,clock1 illu/ration (1 #di ,coal1 #aa ,co9cid5ce ( moon's rotation & revolution1 #acd ,combu/ion1 heat (1 #ib ,cones1 volume (1 #aea ,cons]vation ( sp9 or areas1 #fd ,con/itu5t tides1 #ce ,consumption ( en]gy by tides1 #dh ,cool+1 laws (1 #gi ,cool+ ( e>? f primitive heat1 #hg ,crane1 brakes on1 #fi ,crat]s ( moon1 #id ,critical epo* 9 e>?'s hi/ory1 #ge ,d>w91 #ab ,d>w91 ,g4 ,h41 9 ,admiralty ,manual1 #cd ,d>w91 ,g4 ,h41 on tidal evolution1 #ig1 #aah1 #abb1 #aea1 #ahe ,day & mon? equal1 #ajg ,day at pres5t increas+1 #fh ,day ( #adjj h\rs1 #aba ,day ( #c or #d h\rs1 #ge ,decl9e ( e>?'s heat1 #ij ,diagram %[+ :y moon rec$es1 #gj ,diego ,g>cia1 ,krakatoa he>d at1 #hc ,difficulties ( tidal evolution1 #dh ,dives & ,laz>us1 #afa ,du/ cl\ds1 #hd ,dynamical pr9ciple1 #fe ,dynamical /ability1 #aaj ,e>? & moon z rigid body1 #ajg ,e>? a fly-:eel1 #eg ,e>?1 fusion (1 #ab ,e>?1 heat (1 #hj ,e>? 9 highly heat$ e>ly /ate1 #ib ,e>?'s cru/1 ,lyell on1 #ab ,e>?'s hi/ory1 #ab ,e>?-moon sy/em orig9ally1 #ajg ,e>?quakes1 #hj ,ecc5tricity ( moon's pa? expla9$1 #ahd ,ecliptic1 obliquity (1 expla9$1 #ahd ,economic aspects ( tides1 #de ,egg on end1 #ajh ,elliptic orbit ( moon1 #aac ,end[m5t ( mom5t ( mom5tum1 #afg ,en]gy = tides1 :5ce1 #fg ,en]gy lo/ by tides1 #fj ,en]gy ( moon's position1 #ej ,en]gy ( motion1 #ea ,en]gy ( sep>ation1 #ej ,en]gy1 s\rces (1 #di ,equality ( day & mon?1 #abb ,equilibrium1 /able & un/able1 #ajh ,equ9oxes1 precession (1 #gb ,eruption ( volcanoes1 #hj ,e/abli%m5t1 #cj ,e/u>y1 tides 91 #aeb ,explosion ( ,krakatoa1 #hc ,ext9ct season1 moon1 #abi ,fiji1 #bd ,fi%es1 p]iods ( fossil1 #ab ,fitzg]ald1 ,pr(41 on ,h]tz' exp]im5ts1 #aja ,float+ log1 #aji ,=tnightly tide1 #cd ,friction brake1 #fi ,friction1 tidal1 #dj1 #dg ,full & *ange1 tides dur+1 #bb ,fundy1 ,bay (1 tides 91 #ci ,gauge = tides1 #ca ,geological *ronology1 #adf ,geology & tides1 #add ,geometric s]ies1 #ib ,geys]s1 #he ,gibralt>1 ,/raits (1 tides 91 #ch ,glimpse ?r\gh ! corridors ( "t1 #adh ,glori\s sunsets f ,krakatoa1 #he ,greate/ l5g? ( day1 #aba ,greate/ l5g? ( mon?1 #abb ,greate/ tides1 #ci ,gre5 moons f ,krakatoa du/1 #hd ,gre5ock1 tides at1 #bb ,gr9d/one1 rupture (1 #gf ,gunp[d]1 en]gy f1 #ea ,hall1 ,pr(4 ,a41 discov]s satellites ( ,m>s1 #adb ,h>monic analyz]1 #ce ,heat$ body1 cool+ (1 #gi ,height ( tide1 h[ to measure1 #bi ,helmholtz expla9s ! con/ant face ( ! moon1 #acf ,h]tz1 undulations ( e!r1 #aja ,high wat]1 is x "u ! moon8 #ba ,high wat]1 simple rules =1 #bf ,high wat] twice a day1 #ah ,hot spr+s1 #he ,hot wat]s ( ,ba?1 #hi ,h\r ( high wat]1 h[ f\nd1 #bf ,h[?1 #be ,hull1 tides at1 #bc ,i*?yosaurus1 #adh ,impulse1 effect ( tim$1 #aja ,inc&esc5ce ( e>?'s int]ior1 #he ,inc&esc5ce ( moon1 #id ,indian ocean1 #hd ,initial condition ( e>? & moon1 #gf ,in/ability1 dynamical1 #aaj ,int]val1 luni-tidal1 #cj ,iron1 ma*9e = pun*+1 #ee ,iron smelt+1 #hg ,java1 #hb ,jupit]1 #ada1 #aef ,kepl]'s ,law1 #ec1 #aad ,k]guel5 ,isl&1 #bd ,k+/[n1 #ba ,krakatoa1 #eh ,lagrange1 #ahf ,language1 orig9 (1 #ab ,laplace1 #ahf ,laur5tian rocks1 #adh ,law ( tides1 #ae ,laz>us & ,dives1 #afa ,leakage ( heat1 #hf ,l5g? ( day increas+1 #fh ,lev]ri] discov]s ,neptune1 #ahf ,london1 tides at1 #bc1 #bg ,lun> & sol> tides comp>$1 #ae ,lun> diurnal tide1 #cd ,luni-tidal int]val1 #cj ,lyell1 #ab ,macass>1 explosion ( ,krakatoa he>d at1 #hc ,ma*9e = analyz+ tides1 #ce ,ma*9e = pr$ict+ tides1 #ce ,ma*9e = obs]v+ tides1 #cb ,malahide e/u>y1 #aeb ,m>s1 moons (1 #adb ,mass ( moon f\nd f tides1 #af ,max ,mll]1 #ab ,maximum & m9imum1 #ajd ,m$it]ranean1 tides 91 #ch ,m]idian position ( moon at high wat]1 #bf ,mills1 tidal1 #dc ,m9es1 heat 91 #hf ,mom5t ( mom5tum1 h[ e/imat$1 #agj ,mon? equals day1 #abb ,mon? ( #adjj h\rs1 #abb ,mon? ) greate/ numb] ( days1 #aah ,moon & tides connect$1 #ac ,moon1 con/ant face (1 #acf ,moon-en]gy1 #ed ,moon1 volcanic activity on1 #id ,moons ( ,m>s1 #adb ,motion1 p]petual1 #dh ,nautical almanac1 #bf ,neap tides1 #af ,ne$les1 tides at1 #bc ,niag>a1 utilization (1 #dg ,noise f ,krakatoa1 #hc ,num]ical data ( tidal evolution1 #abg ,obliquity ( ecliptic & tides1 #ahd ,obs]vations ( tides1 #bi ,ocean tides1 #ch ,orbit ( e>?1 *anges 91 #gb ,orbit ( moon expla9$ by tides1 #ahd ,orig9 ( moon1 #ajj ,oscillations ( wat]1 #ih ,pacific1 #hd ,p>adox ( geometric s]ies1 #ib ,p5dulum1 motion (1 #di ,p]iodic ph5om5a1 #ga ,p]iods ( rotation & revolution ( moon equal1 #dc ,p]iods ( tides1 #cd ,p]petual motion1 #dh ,planets & tides1 #aee ,precession ( equ9oxes1 #gb ,pr$iction ( tides1 #ce ,pr9cipal tides1 #cc ,pun*+-eng9e1 #ee ,purs]1 ,pr(essor1 #fa ,railway brakes1 #fh ,reaction & action1 #fi ,relative rotation1 #ajd ,relative tides on e>? & moon1 #aca ,reptiles1 fossil1 #aa ,retreat ( moon expla9$1 #fi ,retrospect ( moon's hi/ory1 #gg ,rh9e1 mills on1 #dc ,r+ !ory ( moon's orig91 #if ,riv]s1 #adi ,rocks1 =mation (1 #aej ,rodriguez1 ,krakatoa he>d at1 #hc ,roll+ mills1 #ef ,rotation ( moon on its axis1 #acc ,rupture ( e>?1 #gf ,rupture ( gr9d/one1 #ge ,/4 ,hel5a1 tides at1 #ch ,santa ,cruz1 #bd ,satellites ( ,jupit]1 #ace ,saturn1 #ada ,seasons1 #gb ,seas1 s call$1 on moon1 #abi ,second>y ages1 #aa ,sligo1 tides at1 #bc ,small tides1 #ch ,smelt+ ( iron1 #hg ,sol> & lun> tides comp>$1 #ae ,sol> sy/em1 #aee ,sol> tides1 #ad ,sol> tides1 ultimate importance (1 #aci ,s\nds f ,krakatoa1 #hc ,s\rce ( tidal en]gy1 #fg ,spr+ tides1 #af ,/ability1 dynamical1 #aaj ,/able equilibrium1 #ajh ,/ages ( special importance1 #aag ,/alactites1 #gc ,/eam eng9e & tides comp>$1 #de ,/rata1 =mation (1 aid$ by tides1 #aed ,sumatra1 #hb ,sun1 rotation (1 #acd ,sunbeams /or$1 #aa ,sunda1 #hb ,sunsets1 ,krakatoa1 #he ,table ( luni-tidal corrections1 #cj ,telescope at ,wa%+ton1 #adc ,temp]ature ( space1 #ia ,t]ti>y ages1 #aa ,?ames1 tides 91 #abe ,?omson1 ,sir ,w41 #cf1 #dd ,tidal curr5ts us$ 9 mak+ rocks1 #aec ,tidal effici5cy1 h[ e/imat$1 #ad ,tidal evolution1 to :om due1 #ig ,tide gauge1 #ca ,tide mills1 #dd ,tide pr$ict+ eng9e1 #cf ,tides & geology1 #add ,tides at ,london bridge1 #bh ,tides1 *ange & full1 #bb ,tides1 comm]cial value (1 #dg ,tides1 due to moon1 #ac ,tides1 h[ to obs]ve1 #bi ,tides 9 ,jupit]1 #ach ,tides 9 moon1 #abh ,tides1 small1 #ch ,tides1 sol> & lun> comp>$1 #ae ,tides v>y+ inv]sely z cube ( di/ance1 #ae ,"t & tide1 #ab ,timor1 ,krakatoa he>d at1 #hc ,tralee1 tides at1 #bc ,tyndall1 #gc ,tynem\?1 #bc ,undulations ( a fluid globe1 #ii ,undulations ( air f ,krakatoa1 #hb ,un9t]mitt+ ph5om5a1 #ga ,un/able equilibrium1 #ajh ,uranus1 #adb ,va/ tides1 #ci ,volcanoes1 #hj ,voyage ( ,krakatoa du/1 #hd ,wa%+ton reflector1 #adb ,wat] abs5t f moon1 #abi ,wat]-:eels "u ,london bridge1 #dc ,waves ( air f ,krakatoa1 #hb ,:ewell on tides1 #cj ,"w done by tides1 #db1 #dg ,"w ( tides1 #db ,y>m\?1 tides at1 #bc ,,! ,,end4 ,ri*>d ,clay ,sons1 ,limit$1 ,london ,bungay4