,transcrib]'s note3 ,a few typographical errors h be5 correct$3 !y are li/$ at ! end ( ! text4 99 99 99 99 99 ,,! ,,e>l ,,( ,,pembroke ,,to ,,! ,,abbess ,,( ,,wilton4 ,g sp91 y jade6 g sp96 ,illu/ration3 ,,magnetism1 ,,light1 ,,& ,,molecul> ,,sp9n+ ,,tops4 ,page #abb4 ,,! ,,romance ,,( ,,sci5ce4 ,,sp9n+ ,,tops4 ,,! ,,op]atives' ,,lecture ,,( ,,! ,,briti% ,,association ,,meet+ ,,at ,,le$s1 #f? ,,septemb]1 #ahij4 ,,by ,,pr(essor ,,john ,,p]ry1 ,m4,e41 ,d4,sc1 ,,ll4,d41 ,f4,r4,s4 ,) ,num]\s ,illu/rations4 ,,repr9t ,,( ,,new ,,& ,,revis$ ,,edition1 ,) an ,illu/rat$ ,app5dix on ! ,use ( ,gyro/ats4 ,,london ,,society ,,= ,,promot+ ,,*ri/ian ,,k1 ,nor?umb]l& ,av5ue1 ,w4,c42 #dc1 ,que5 ,victoria ,/reet1 ,e4,c4 ,,brighton3 #abi1 ,nor? ,/reet4 ,,new ,,york3 ,e4 ,s4 ,,gorham4 #aiaj ,,publi%$ ,,"u ,,! ,,direction ,,( ,,! ,,g5]al ,,lit]ature ,,committee ,date ( la/ impression1 ,april #aijh ,?is ,report ( an ,exp]im5tal ,lecture ,,0 ,,inscrib$ ,,to ,,! ,,late ,,"l ,,kelv91 ,,by ,,8 ,,affectionate ,,pupil1 ,,! ,,lectur]1 ,,:o ,,h]eby ,,took ,a ,,conv5i5t ,,me?od ,,( ,,ackn[l$g+ ,,! ,,real ,,au?or ,,( ,,:atev] ,,is ,,wor? ,,publication ,,9 ,,! ,,foll[+ ,,pages4 99 99 99 99 99 ,,preface4 ,?is is n ! lecture z x 0 deliv]$4 ,in/ead ( two pages ( lett]press & a woodcut1 ! read] may imag9e t = half a m9ute ! lectur] play$ ) a sp9n+ top or gyro/at1 & occasionally ejaculat$ words ( w>n+1 admonition1 & explanation t[>ds 8 audi5ce4 ,a v]batim report w\ld make r un9t]e/+ read+1 & ,i h tak5 ! lib]ty ( try+1 by great] fullness ( explanation1 to make up to ! read] = 8 n hav+ se5 ! mov+ app>atus4 ,x has also be5 necess>y 9 a treatise int5d$ = g5]al read]s to simplify ! reason+1 ! lecture hav+ be5 deliv]$ to p]sons ^: life exp]i5ces peculi>ly fitt$ !m = und]/&+ sci5tific ?+s4 ,an argum5t has be5 add$ at ! end to make ! /eps ( ! reason+ cle>]4 ,,john ,,p]ry4 99 99 99 99 99 #i ,,sp9n+ ,,tops4 -------- ,at a ,le$s ,bo>d ,s*ool la/ week1 ! ma/] said to 8 class1 ,!re is to be a meet+ ( ! ,briti% ,association 9 ,le$s4 ,:at is x all ab\t8 ,:o are ! memb]s ( ! ,briti% ,association8 ,:at d !y d8 ,!re 0 a long pause4 ,at l5g? x 0 brok5 by an intellig5t %y boy3 ,please1 sir1 ,i "k--!y sp9 tops6#a ,n[ ,i am sorry to say t ?is answ] 0 wrong4 ,! memb]s ( ! ,briti% ,association & ! ,op]atives ( ,le$s h neglect$ top-sp9n+ s9ce !y 7 t5 ye>s ( age4 ,if m att5tion 7 paid to ! intellig5t exam9ation ( ! behavi\r ( tops1 !re w\ld be great] advances 9 me*anical eng9e]+ & a great _m indu/ries4 ,!re w\ld be a bett] g5]al k ( a/ronomy4 ,geologi/s w\ld n make mi/akes by millions ( ye>s1 & our k ( ,light1 & ,radiant ,heat1 & o!r #aj ,electro-magnetic ,ph5om5a w\ld ext5d mu* m rapidly ?an x does4 ,i %all try to %[ y t[>ds ! end ( ! lecture t ! fact ( our e>?'s be+ a sp9n+ body is "o :i* w\ld make itself kn[n to u ev5 if we liv$ 9 subt]ranean regions l ! com+ race ( an +5i\s noveli/4#b ,x is ! greate/ & mo/ p]si/5t cause ( _m ( ! ph5om5a :i* occur ar\nd u & b5ea? u1 & x is probable t ev5 ,t]re/rial ,magnetism is almo/ altoge!r due to x4 ,inde$ !re is only "o possible explanation ( ! ,vril-ya ignorance ab\t ! e>?'s rotation4 ,_! k ( me*anics & dynamics 0 imm5se2 no memb] att5d+ ! meet+ ( ! ,briti% ,association c approa* !m 9 _! k (1 ,i w n say1 ,vril1 b ev5 ( q vulg> electricity & magnetism2 & yet ?is great race :i* expresses s /rongly its contempt = ,anglo-,saxon ,koom-,po%]y 0 actually ignorant ( ! fact t x _h exi/$ = untold g5]ations inside an object t sp9s ab\t an axis4 ,c we imag9e = "o in/ant t ! *ildr5 ( t race _h nev] spun a top or trundl$ a hoop1 & s _h _h no *ance ( be+ l$ to ! greate/ /udy ( nature8 ,no2 ! only possible explanation lies 9 ! great noveli/'s nev] #aa hav+ done ^! ?+s himself4 ,he _h probably z a *ild a contempt = ! /udy ( nature1 he 0 a baby ,pelham1 & z a man he 0 condemn$ to rema9 9 ignorance ev5 ( ! p[]s ( ! new race t he _h creat$4 ,! ,vril-ya ignorance ( ! behavi\r ( sp9n+ bodies exi/+ z x does side by side ) _! deep k ( magnetism1 becomes ev5 m rem>kable :5 x comes home to u t ! ph5om5a ( magnetism & ( light are c]ta9ly closely connect$ ) ! behavi\r ( sp9n+ bodies1 & inde$ t a famili> k ( ! behavi\r ( su* bodies is absolutely necess>y = a prop] compreh5sion ( mo/ ( ! ph5om5a occurr+ 9 nature4 ,! in/9ctive crav+ to inve/igate ^! ph5om5a seems to manife/ itself soon aft] we are able to talk1 & :o kn[s h[ mu* ( ! intellectual inf]iority ( woman is due to h] neglect ( ! /udy ( sp9n+ tops2 b alas1 ev5 = boys 9 ! pursuit ( top-sp9n+1 ! y\?ful m9d & muscle are left ) no o!r guidance ?an t :i* is suppli$ by ! exp]i5ce ( "y & n v sci5tific companions4 ,i rememb] di/9ctly t !re 7 _m puzzl+ problems pres5t$ to me e day4 ,!re 7 tops :i* nobody seem$ able to sp91 & !re 7 o!rs1 well #ab priz$ objects1 (t5 /udi$ 9 _! behavi\r & covet$ z supremely valuable1 t behav$ well "u ! mo/ unsci5tific treatm5t4 ,& yet nobody1 ev5 ! mak]s1 seem$ to "k :y "o behav$ badly & ! o!r well4 ,i d n disguise f myself ! fact t x is r a difficult task to talk ( sp9n+ tops to m5 :o h long lo/ t skill :i* !y wond] at 9 _! *ildr52 t kn[+ness ( t\* & h&l+ :i* gave !m once s mu* p[] ov] :at ,i fe> to call inanimate nature4 ,a problem :i* ! *ild gives up z hopeless ( solution1 is seldom attack$ aga9 9 matur] ye>s2 he drives 8 desire = k into ! obscure lumb]-closets ( 8 m9d1 & !re x lies1 ) ! accumulat+ du/ ( 8 life1 a neglect$ & almo/ =gott5 in/9ct4 ,"s ( y may ?9k t ?is in/9ct only rema9s ) ^? m9ds s _m ( :i* are *ildi% ev5 to ! limit ( life's span2 & probably none ( y h _h ! opportunity ( see+ h[ ! old du/ rubs (f f ! life ( ! ord9>y man1 & ! old desire comes back to him to und]/& ! my/]ies t surr\nd him4 ,b ,i h n only felt ?is desire myself1 ,i h se5 x 9 ! excit$ eyes ( ! cr[d ( p :o /& by ! h\r "u ! dropp+ *]ry-blossoms beside ! r$-pill>$ temple ( #ac ,asakusa 9 ! ,ea/]n capital ( ,japan1 wat*+ ! t$zu-ma%i direct+ ! evolutions ( 8 heavily rimm$ ,koma4 ,fir/ he ?r[s away f him 8 great top obliquely into ! air & cat*es x sp9n+ on ! end ( a /ick1 or ! po9t ( a sword1 or any o!r conv5i5t implem5t2 he n[ s5ds x ab\t q c>elessly1 cat*+ x z x comes back to him f all sorts ( directions2 he makes x run up ! h&-rail ( a /aircase into a h\se by ! door & out aga9 by ! w9d[2 he makes x travel up a great corkscrew4 ,n[ he seizes x 9 8 h&s1 & ) a few dext]\s twi/s gives x a new /ock ( sp9n+ en]gy4 ,he makes x travel along a /ret*$ /r+ or ! edge ( a sword2 he does all sorts ( o!r curi\s ?+s ) 8 tops1 & sudd5ly s9ks f 8 ma/]ful position to beg = a few copp]s at ! end ( 8 p]=mance4 ,h[ tame all ?is mu/ seem to y :o m ?an half =get y\r *ildi% initiation into ! my/]ies ( nature2 b tru/ me1 if ,i c\ld only make t old top-sp9n] p]=m ^? magical op]ations ( 8 on ?is plat=m1 ! delight ( ! enjoym5t ( beautiful motion w\ld come back4 ,p]haps x is only 9 ,japan t su* an exhibition is possible2 ! l& :]e ! wav+ bamboo1 & ! circl+ hawk1 & ! undulat+ summ] sea1 & e beautiful motion ( nature #ad are look$ ^u ) t5d]ness2 & p]haps x is f ,japan t we %all le>n ! developm5t ( our *ildi% en?usiasm4 ,! devotees ( ! new emotional art ( beautiful motion & *ang+ col\r are /ill 9 ! ma9 begg>s l ,hom]1 & !y live 9 g>rets l ,johnson & ,savage2 b ! dawn ( a new era is h]ald$1 or r ! dawn has already come1 = ,sir ,william ,?omson's a*ievem5ts 9 ! /udy ( sp9n+ tops rank already z by no means ! meane/ ( 8 great c>e]4 ,if y w only ?9k ( x1 ! behavi\r ( ! commone/ sp9n+ top is v wond]ful4 ,:5 n sp9n+ y see t x falls d[n at once1 ,i f9d x impossible to balance x on its peg2 b :at a v diff]5t object x is :5 sp9n+2 y see t x n only does n fall d[n1 x (f]s a /range resi/ance :5 ,i /rike x1 & actually lifts itself m & m to an upright position4 ,once />t$ on sci5tific obs]vation1 nature gives u facts ( an analog\s k9d 9 great pl5ty4 ,^? ( y :o h obs]v$ a rapidly mov+ heavy belt or rope1 "k t rapid motion gives a peculi> quasi-rigidity to flexible & ev5 to fluid ?+s4 ,"h1 = example1 is a disc ( q ?9 pap] 7,fig4 #a71 & :5 ,i set x 9 rapid rotation y obs]ve t x resi/s ! =ce ex]t$ by my #ae h&1 ! bl[ ( my fi/1 z if x 7 a disc ( /eel4 ,he> h[ x res\nds :5 ,i /rike x ) a /ick4 ,:]e has its flexibility gone8 ,illu/ration3 ,,fig4 #a4 ,"h aga9 is a r+ ( *a9 :i* is q flexible4 ,x seems ridicul\s to imag9e t ?is #af c\ld be made to /& up l a /iff hoop1 & yet y obs]ve t :5 ,i give x a rapid rotation on ?is m&ril & let x slide (f ^u ! table1 x runs ov] ! table j z if x 7 a rigid r+1 & :5 x drops on ! floor x reb\nds l a boy's hoop 7,fig4 #b74 ,illu/ration3 ,,fig4 #b4 ,"h aga9 is a v s(t hat1 specially made = ?is sort ( exp]im5t4 ,y w note t x collapses to ! table 9 a %apeless mass :5 ,i lay x d[n1 & seems q incapable ( resi/+ =ces :i* t5d to alt] its %ape4 ,9 fact1 !re is almo/ a complete abs5ce ( rigidity2 b :5 ?is is spun on ! end ( a /ick1 fir/ note #ag h[ x has tak5 a v easily def9$ %ape2 secondly1 note h[ x runs along ! table z if x 7 made ( /eel2 ?irdly1 note h[ all at once x collapses aga9 into a %apeless heap ( s(t mat]ial :5 its rapid motion has ceas$4 ,ev5 s y w see t :5 a drunk5 man is n lean+ aga9/ a wall or lamp-po/1 he feels t 8 only *ance ( escape f ignom9i\s collapse is to get up a dec5t rate ( spe$1 to obta9 a quasi-sobriety ( demean\r by rapidity ( motion4 ,! wat] inside ?is glass vessel 7,fig4 #c7 is 9 a /ate ( rapid motion1 revolv+ ) ! vessel itself4 ,n[ obs]ve ! piece ( p>aff9 wax ,a imm]s$ 9 ! wat]1 & y w see :5 ,i pu% at x ) a rod t x vibrates j z if x 7 surr\nd$ ) a ?ick jelly4 ,let u n[ apply ,pr(4 ,fitzg]ald's improvem5t on ?is exp]im5t ( ,sir ,william ,?omson's4 ,"h is a disc ,b /uck on ! end ( ! rod2 obs]ve t :5 ,i introduce x1 al?\gh x does n t\* ,a1 ,a is repell$ f ! disc4 ,n[ obs]ve t :5 ,i twirl ! disc x seems to attract ,a4 ,illu/ration3 ,,fig4 #c4c ,at ! r\nd hole 9 front ( ?is box a rapid motion is giv5 to a small quantity ( air :i* is mix$ ) smoke t y may see x4 ,t smoke-r+ moves ?r\gh ! air almo/ l a solid body = a consid]able di/ance un*ang$1 & ,i am n sure t x may n be possible yet #ah to s5d z a projectile a huge poison$ smoke-r+1 s t x may de/roy or /upefy an army miles away4 ,rememb] t x is really ! same air all ! "t4 ,y w obs]ve t two smoke r+s s5t f two boxes h curi\s actions #ai ^u "o ano!r1 & ! /udy ( ^! actions has giv5 rise to ,?omson's smoke-r+ or vortex !ory ( ! con/itution ( matt] 7,fig4 #d74 ,illu/ration3 ,,fig4 #d4 ,x 0 ,rank9e1 ! great guide ( all eng9e]s1 :o fir/ sugge/$ ! idea ( molecul> vortices 9 8 explanations ( heat ph5om5a & ! ph5om5a ( ela/icity--! idea t e p>ticle ( matt] is l a little sp9n+ top2 b ,i am n[ speak+ ( ,?omson's !ory4 ,to imag9e t an atom ( matt] is m]ely a #bj curi\sly %ap$ smoke-r+ =m$ miracul\sly 9 a p]fect fluid1 & :i* c nev] und]go p]man5t alt]ation1 looks to be a v curi\s & f>-fet*$ hypo!sis4 ,b 9 spite ( c]ta9 difficulties1 x is ! f\ndation ( ! !ory :i* w be/ expla9 mo/ ( ! molecul> ph5om5a obs]v$ by philosoph]s4 ,:atev] be ! value ( ! !ory1 y see f ^! exp]im5ts t motion does give to small quantities ( fluid curi\s prop]ties ( ela/icity1 attraction & repulsion2 t ea* ( ^! entities refuses to be cut 9 two2 t y _c br+ a knife ev5 ne> ! smoke-r+2 & t :at may be call$ a collision betwe5 two ( !m is n v diff]5t 9 any way f ! collision betwe5 two r+s ( india-rubb]4 ,ano!r example ( ! rigidity giv5 to a fluid by rapid motion1 is ! feel+ ( utt] helplessness :i* ev5 ! /ronge/ swimm]s sometimes exp]i5ce :5 !y get caught 9 an eddy und]nea? ! wat]4 ,i c\ld1 if ,i lik$1 multiply ^! in/ances ( ! quasi-rigidity :i* m]e motion gives to flexible or fluid bodies4 ,9 ,nevada a jet ( wat] l ! jet f a fireman's hose1 except t x is mu* m rapid1 :i* is ne>ly z easily project$ 9 diff]5t directions1 is us$ 9 m9+1 & huge masses ( e>? & rock are rapidly dis9tegrat$ #ba by ! runn+ wat]1 :i* seems to be r l a b> ( /eel ?an a jet ( wat] 9 its rigidity4 ,x is1 h[ev]1 probable t y w take m int]e/ 9 ?is box ( brass :i* ,i hold 9 my h&s4 ,y see no?+ mov+1 b really1 inside ?is case !re is a fly-:eel revolv+ rapidly4 ,obs]ve t ,i re/ ?is case on ! table on its %>p edge1 a sort ( skate1 & x does n tumble d[n z an ord9>y box w\ld d1 or z ?is box w d aft] a :ile1 :5 its cont5ts come to re/4 ,obs]ve t ,i c /rike x viol5t bl[s1 & x does n seem to budge f its v]tical position2 x turns itself j a little r\nd1 b does n get tilt$1 h[ev] h>d ,i /rike x4 ,obs]ve t if ,i d get x tilt$ a little x does n fall d[n1 b sl[ly turns ) :at is call$ a precessional motion 7,fig4 #e74 ,y w1 ,i hope1 all[ me1 all ?r\gh ?is lecture1 to use ! t]m precessional = any motion ( ?is k9d4 ,probably y w object m /rongly to ! great lib]ty ,i %all take pres5tly1 ( say+ t ! case precesses :5 x has ?is k9d ( motion2 b ,i really h almo/ no option 9 ! matt]1 z ,i mu/ use "s v]b1 & ,i h no "t to inv5t a less b>b>\s "o4 ,illu/ration3 ,,fig4 #e4 ,:5 ,i hold ?is box 9 my h&s 7,fig4 #f71 ,i f9d t if ,i move x ) a motion ( m]e translation 9 any direction1 x feels j z x w\ld d #bb if its cont5ts 7 at re/1 b if ,i try to turn x 9 my h&s ,i f9d ! mo/ curi\s great resi/ance to su* a motion4 ,! result is t :5 y hold ?is 9 y\r h&s1 its read9ess to move s long z x is n turn$ r\nd1 & its great resi/ance to turn+ r\nd1 & its unexpect$ t5d5cy to turn 9 a diff]5t way f t 9 :i* y try to turn x1 give "o ! mo/ uncanny s5sations4 ,x seems almo/ z if an invisible be+ _h hold ( ! box & ex]cis$ =ces caprici\sly4 ,& #bc inde$ !re is a spiritual be+ inside1 :at ! algebraic p call an impossible quantity1 :at o!r ma!maticians call an op]ator4 ,illu/ration3 ,,fig4 #f4 ,ne>ly all ! exp]im5ts1 ev5 ! tops & o!r app>atus y h se5 or w see to-night1 h be5 arrang$ & made by my en?usia/ic assi/ant1 ,mr4 ,%eph]d4 ,! foll[+ exp]im5t is n only 8 9 arrangem5t2 ev5 ! idea ( x is 84 ,he said1 y may gr9 & contort y\r body ) t l>ge gyro/at 9 y\r h&s1 b _m ( y\r audi5ce w simply say to #bd !mselves t y only pret5d to f9d a difficulty 9 turn+ ! gyro/at4 ,s he arrang$ ?is pivot$ table = me to /& ^u1 & y w obs]ve t :5 ,i n[ try to turn ! gyro/at1 x w n turn2 h[ev] ,i may ex]t myself1 x keeps po9t+ to t p>ticul> corn] ( ! room1 & all my ef=ts only result 9 turn+ r\nd my own body & ! table1 b n ! gyro/at4 ,n[ y w f9d t 9 e case ?is box only resi/s hav+ ! axis ( revolution ( its hidd5 fly:eel turn$ r\nd1 & if y are int]e/$ 9 ! matt] & make a few obs]vations1 y w soon see t e sp9n+ body l ! fly-:eel inside ?is case resi/s m or less ! *ange ( direction ( its sp9n+ axis4 ,:5 ! fly-:eels ( /eam-eng9es & dynamo ma*9es & o!r quick spe$ ma*9es are rotat+ on bo>d %ip1 y may be q sure t !y (f] a great] resi/ance to ! pit*+ or roll+ or turn+ ( ! %ip1 or any o!r motion :i* t5ds to turn _! axes 9 direction1 ?an :5 !y are n rotat+4 ,"h is a top ly+ on a plate1 & ,i ?r[ x up into ! air2 y w obs]ve t its motion is v difficult to foll[1 & nobody c\ld pr$ict1 be=e x falls1 exactly h[ x w alight on ! plate2 x may come d[n peg-end =emo/1 or h9dmo/1 or sideways4 ,b :5 ,i sp9 x 7,fig4 #g71 & n[ ?r[ x up into ! air1 !re is no d\bt :atev] #be z to h[ x w come d[n4 ,! sp9n+ axis keeps p>allel to itself1 & ,i c ?r[ ! top up "t aft] "t1 )\t di/urb+ mu* ! sp9n+ motion4 ,illu/ration3 ,,fig4 #g4 ,illu/ration3 ,,fig4 #h4 ,if ,i pit* up ?is biscuit1 y w obs]ve t ,i c h no c]ta9ty z to h[ x w come d[n1 b if ,i give x a sp9 be=e x leaves my h& !re is no d\bt :atev] 7,fig4 #h74 ,"h is a hat4 ,i ?r[ x up1 & ,i _c be sure z to h[ x w move1 b if ,i give x a sp91 y see t1 z #bf ) ! top & ! biscuit1 ! axis ab\t :i* ! sp9n+ takes place keeps p>allel to itself1 & we h p]fect c]ta9ty z to ! hat's alight+ on ! gr\nd brim d[nw>ds 7,fig4 #i74 ,illu/ration3 ,,fig4 #i4 ,i ne$ n aga9 br+ be=e y ! v s(t hat to :i* we gave a quasi-rigidity a few m9utes ago2 b y w rememb] t my assi/ant s5t t (f l a projectile ?r\gh ! air :5 x 0 sp9n+1 & t x kept its sp9n+ axis p>allel to itself j l ?is m rigid hat & ! biscuit4 ,illu/ration3 ,,fig4 #aj4 ,illu/ration3 ,,fig4 #aa4 ,i once %[$ "s exp]im5ts on sp9n+ tops to a c(fee-dr9k+1 tobacco-smok+ audi5ce 9 t mo/ excell5t in/itution1 ! ,victoria ,music ,hall 9 ,london4 ,9 t music hall1 ?+s are n v diff]5t f :at !y are at any o!r #bg music hall except 9 be]1 w9e1 & spirits be+ unobta9able1 & 9 %ort sci5tific addresses be+ occasionally giv54 ,n[1 ,i impress$ my audi5ce z /rongly z ,i c\ld ) ! above fact1 t if "o wants to ?r[ a quoit ) c]ta9ty z to h[ x w alight1 "o gives x a sp92 if "o wants to ?r[ a hoop or a hat to somebody to cat* ^u a /ick1 "o gives ! hoop or hat a sp92 ! dis9cl9ation ( a sp9n+ body to let its axis get alt]$ 9 direction c always be dep5d$ ^u4 ,i told !m t ?is 0 :y smoo?-bore guns _c be dep5d$ ^u = accuracy2#d t ! sp9 :i* an ord9>y bullet took dep5d$ greatly on h[ x *anc$ to t\* ! muzzle z x j left ! gun1 :]eas b>rels are n[ rifl$1 t is1 spiral grooves are n[ cut inside ! b>rel ( a gun1 & excresc5ces f ! bullet or projectile fit into ^! grooves1 s t z x is =c$ along ! b>rel ( ! gun by ! explosive =ce ( ! p[d]1 x mu/ also sp9 ab\t its axis4 ,h5ce x leaves ! gun ) a p]fectly well-kn[n sp9n+ motion ab\t :i* !re c be no d\bt1 & we "k too t ,fig4 #aj %[s ! #bh k9d ( motion :i* x has aft]w>ds1 =1 j l ! hat or ! biscuit1 its sp9n+ axis keeps ne>ly p>allel to itself4 ,well1 ?is 0 all ,i c\ld d1 = ,i am n skilful 9 ?r[+ hats or quoits4 ,b aft] my address 0 f9i%$1 & aft] a "y lady 9 a spangl$ dress _h sung a comic song1 two juggl]s came ^u ! /age1 & ,i c\ld n h _h bett] illu/rations ( ! above pr9ciple ?an 7 giv5 9 almo/ e trick p]=m$ by ?is lady & g5tleman4 ,!y s5t hats1 & hoops1 & plates1 & umbrellas sp9n+ f "o to ! o!r4 ,"o ( !m ?rew a /ream ( knives into ! air1 cat*+ !m & ?r[+ !m up aga9 ) p]fect precision & my n[ educat$ audi5ce %\t$ ) delight1 & %[$ 9 o!r unmi/akable #bi ways t !y obs]v$ ! sp9 :i* t juggl] gave to e knife z x left 8 h&1 s t he might h a p]fect k z to h[ x w\ld come back to him aga9 7,fig4 #aa74 #cj ,x /ruck me ) a/oni%m5t at ! "t t1 almo/ )\t exception1 e juggl+ trick p]=m$ t ev5+ 0 an illu/ration ( ! above pr9ciple4 ,& n[1 if y d\bt my /atem5t1 j ask a *ild :e!r its hoop is m likely to tumble d[n :5 x is rapidly roll+ along1 or :5 x is go+ v sl[ly2 ask a man on a bicycle to g m & m sl[ly to see if he keeps 8 balance bett]2 ask a ballet-danc] h[ long %e c\ld /& on "o toe )\t balanc+ h]self ) h] arms or a pole1 if %e 7 n sp9n+2 ask a/ronom]s h[ _m mon?s w\ld elapse be=e ! e>? w\ld po9t ev] s f> away f ! pole /> if x 7 n sp9n+2 & above all1 ask a boy :e!r 8 top is z likely to /& upright ^u its peg :5 x is n sp9n+ z :5 x is sp9n+4 ,illu/ration3 ,,fig4 #ab4 ,we w n[ exam9e m c>efully ! behavi\r ( ?is common top 7,fig4 #ab74 ,x is n #ca sp9n+1 & y obs]ve t x tumbles d[n at once2 x is q un/able if ,i leave x re/+ upright on its peg4 ,b n[ note t :5 x is sp9n+1 x n only w rema9 upright re/+ on its peg1 b if ,i give x a bl[ & s di/urb its /ate1 x goes circl+ r\nd ) a precessional motion :i* gr[s gradually less & less z "t goes on1 & ! top lifts itself to ! upright position aga94 ,i hope y d n ?9k t "t sp5t 9 c>eful obs]vation ( a ph5om5on ( ?is k9d is wa/$4 ,educat$ obs]vation ( ! commone/ ph5om5a occurr+ 9 our ev]yday life is nev] wa/$1 & ,i (t5 feel t if workm51 :o are ! p]sons mo/ famili> ) inorganic nature1 c\ld only obs]ve & apply simple sci5tific laws to _! obs]vations1 in/ead ( a great discov]y e c5tury we %\ld h a great discov]y e ye>4 ,well1 to return to our top2 !re are two v curi\s obs]vations to make4 ,please neglect = a %ort "t ! slight wobbl+ motions t occur4 ,"o obs]vation we make is1 t ! top does n at fir/ b[ d[n 9 ! direction ( ! bl[4 ,if ,i /rike t[>ds ! s\?1 ! top b[s t[>ds ! we/2 if ,i /rike t[>ds ! we/1 ! top b[s d[n t[>ds ! nor?4 ,n[ ! reason ( ?is is kn[n to all sci5tific m51 & ! pr9ciple und]ly+ ! top's behavi\r is ( v great #cb importance 9 _m ways1 & ,i hope to make x cle> to y4 ,! second fact1 t ! top gradually rea*es its upright position aga91 is "o kn[n to ev]ybody1 b ! reason = x is n by any means well kn[n1 al?\gh ,i ?9k t y w h no great difficulty 9 und]/&+ x4 ,! fir/ ph5om5on w be obs]v$ 9 ?is case :i* ,i h already %[n y4 ,?is case 7,fig4 #e71 #cc ) ! fly-:eel inside x1 is call$ a gyro/at4 ,:5 ,i pu% ! case x does n b[ d[n1 b sl[ly turns r\nd4 ,?is gyro/at w n exhibit ! second ph5om5on2 x w n rise up aga9 if ,i manage to get x out ( its upright position1 b1 on ! contr>y1 w g precess+ 9 wid] & wid] circles1 gett+ fur!r & fur!r away f its upright position4 ,illu/ration3 ,,fig4 #ac4 ,illu/ration3 ,,fig4 #ad4 ,! fir/ ph5om5on is mo/ easily /udi$ 9 ?is balanc$ gyro/at 7,fig4 #ac74 ,y "h see ! fly-:eel ,g 9 a /rong brass frame ,f1 :i* is support$ s t x is free to move ab\t ! v]tical axis ,a ,b1 or ab\t ! horizontal axis ,c ,d4 ,! gyro/at is balanc$ by a weight ,w4 ,obs]ve t ,i c increase ! lev]age ( ,w or dim9i% x by %ift+ ! position ( ! sleeve at ,a s t x w t5d to ei!r lift or l[] ! gyro/at1 or exactly balance x z x does n[4 ,y mu/ obs]ve exactly :at x is t we wi% to /udy4 ,if ,i endeav\r to pu% ,f d[nw>ds1 ) ! end ( ?is /ick 7,fig4 #ad71 x really moves horizontally to ! "r2 n[ ,i pu% x to ! "r 7,fig4 #ae71 & x only rises2 n[ pu% x up1 & y see t x goes to ! left2 pu% x to ! left1 & x only goes d[nw>ds4 ,y w notice t if ,i clamp ! in/rum5t s t x _c move v]tically1 x moves at once horizontally2 if ,i prev5t m]e horizontal motion x readily moves v]tically :5 ,i pu% x4 ,leav+ x free z #cd be=e1 ,i w n[ %ift ! position ( ! weight ,w1 s t x t5ds cont9ually to lift ! gyro/at1 & ( c\rse ! in/rum5t does n lift1 x moves horizontally ) a sl[ precessional motion4 ,i n[ aga9 %ift ! weight ,w1 s t ! gyro/at w\ld fall if x 7 n sp9n+ 7,fig4 #af71 & x n[ moves horizontally ) a sl[ precessional motion :i* is 9 a direction oppos$ to ! la/4 ,^! ph5om5a are easily expla9$1 b1 #ce z ,i said be=e1 x is necess>y fir/ to obs]ve !m c>efully4 ,y all "k n[1 vaguely1 ! fundam5tal fact4 ,x is t if ,i try to make a v quickly sp9n+ body *ange ! direction ( its axis1 ! direction ( ! axis w *ange1 b n 9 ! way ,i int5d$4 ,x is ev5 m curi\s ?an my c\ntryman's pig1 = :5 he want$ ! pig to g to ,cork1 he _h to pret5d t he 0 driv+ ! pig home4 ,8 rule 0 a v #cf simple "o1 & we mu/ f9d a rule = our sp9n+ body1 :i* is r l a crab1 t w only g along ! road :5 y pu% x sidewise4 ,illu/ration3 ,,fig4 #ae4 ,illu/ration3 ,,fig4 #af4e ,illu/ration3 ,,fig4 #aj4 ,z an illu/ration ( ?is1 consid] ! sp9n+ projectile ( ,fig4 #aj4 ,! sp9 t5ds to keep its axis always 9 ! same direction4 ,b !re is a defect 9 ! arrangem5t1 :i* y are n[ 9 a #cg position to und]/&4 ,y see t at ,a ! air mu/ be press+ ^u ! und]surface ,a ,a1 & ,i h to expla9 t ?is pressure t5ds to make ! projectile turn itself broadside on to ! air4 ,a boat 9 a curr5t n all[$ to move z a :ole1 b ti$ at its middle1 sets itself broadside on to ! curr5t4 ,obs]ve ?is disc ( c>dbo>d :i* ,i drop ?r\gh ! air edgewise1 & note h[ quickly x sets itself broadside on & falls m sl[ly2 & "s ( y may h ?r[n ov] into ! wat] at ,ad5 small pieces ( silv] = ! div+ boys1 & y are aw>e t if x 7 n = ?is sl[ fall+ ( ! co9s ) a wobbl+ motion broadside on1 x w\ld be ne>ly impossible = any div+ boy to get possession ( !m4 ,n[ all ?is is a p>5!sis4 ,! #ch pressure ( ! air t5ds to make ! projectile turn broadside on1 b z ! projectile is sp9n+ x does n tilt up1 no m ?an ?is gyro/at does :5 ,i try to tilt x up1 x really tilts out ( ! plane ( ! diagram1 out ( ! plane ( its flight2 & only t artill]ym5 "k exactly :at x w d1 ?is k9d ( w9dage ( ! projectile w\ld give !m great tr\ble4 ,y w notice t an exp]i5c$ *ild :5 x wants to *ange ! direction ( a hoop1 j ex]ts a tilt+ pressure ) its hoop-/ick4 ,a man on a bicycle *anges 8 direction by lean+ ov] s z to be out ( balance4 ,x is well to rem9d y1 h[ev]1 t ! motion ( a bicycle & its rid] is n all rotational1 s t x is n altoge!r ! analogue ( a top or gyro/at4 ,! explanation ( ! sw]v+ f a /raight pa? :5 ! rid] tilts 8 body1 ultimately comes to ! same simple pr9ciple1 ,newton's second law ( motion1 b x is arriv$ at m readily4 ,x is = ! same reason--put briefly1 ! ex]cise ( a c5tripetal =ce--t :5 "o is rid+ he c mat]ially assi/ 8 horse to turn a corn] quickly1 if he does n m9d appe>ances1 by incl9+ 8 body t[>ds ! side to :i* he wants to turn2 & ! m sl[ly ! horse is go+ ! great] is ! t5d5cy to turn = a giv5 am\nt ( tilt+ ( "o's body4 ,circus-rid]s1 :5 gallop+ 9 a circle1 assi/ _! horses greatly by ! position ( _! bodies2 x is #ci n to save !mselves f fall+ by c5trifugal =ce t !y take a position on a horse's back :i* no rid+-ma/] w\ld all[ 8 pupil to imitate2 & ! respectable rid]s ( ?is c\ntry w\ld n scorn to help _! horses 9 ?is way to quick turn+ movem5ts1 if !y _h to *ase & collect cattle l ,am]ican c[boys4 ,v good illu/rations ( *ange ( direction are obta9$ 9 play+ b[ls4 ,y "k t a b[l1 if x _h no bias1 t is1 if x _h no little weight inside x t5d+ to tilt x1 w\ld roll along ! level b[l+-gre5 9 a /raight pa?1 its spe$ gett+ less & less till x /opp$4 ,z a matt] ( fact1 h[ev]1 y "k t at ! beg9n+1 :5 x is mov+ fa/1 its pa? is pretty /raight1 b because x always has bias ! pa? is nev] q /raight1 & x b5ds m & m rapidly z ! spe$ dim9i%es4 ,9 all our examples ! sl[] ! sp9 ! quick] is ! precession produc$ by giv5 tilt+ =ces4 ,n[ close obs]vation w give y a simple rule ab\t ! behavi\r ( a gyro/at4 ,z a matt] ( fact1 all t has be5 incompreh5sible or curi\s disappe>s at once1 if in/ead ( speak+ ( ?is gyro/at z mov+ up or d[n1 or to ! "r or left1 ,i speak ( its motions ab\t its v>i\s axes4 ,x (f]s no resi/ance to m]e motion ( translation4 ,b :5 ,i spoke ( its mov+ #dj horizontally1 ,i ought to h said t x mov$ ab\t ! v]tical axis ,a ,b 7,fig4 #ac74 ,aga91 :at ,i ref]r$ to z up & d[n motion ( ,f is really motion 9 a v]tical plane ab\t ! horizontal axis ,c ,d4 ,9 future1 :5 ,i speak ( try+ to give motion to ,f1 ?9k only ( ! axis ab\t :i* ,i try to turn x1 & !n a little obs]vation w cle> ! gr\nd4 ,illu/ration3 ,,fig4 #ag4 ,illu/ration3 ,,fig4 #ah4 ,"h is a gyro/at 7,fig4 #ag71 susp5d$ 9 gymbals s c>efully t nei!r gravity nor any frictional =ces at ! pivots con/ra9 x2 no?+ t ,i c d to ?is frame :i* ,i hold 9 my h& w affect ! direction ( ! axis ,e ,f ( ! gyro/at4 ,obs]ve t ,i :irl r\nd on my toes l a ballet-danc] :ile ?is is 9 my h&4 ,i move x ab\t 9 all sorts ( ways1 b if x 0 po9t+ to ! pole /> at ! beg9n+ x rema9s po9t+ to ! pole />2 if x po9t$ t[>ds ! moon at ! beg9n+ x /ill po9ts #da t[>ds ! moon4 ,! fact is1 t z !re is almo/ no frictional con/ra9t at ! pivots !re are almo/ no =ces t5d+ to turn ! axis ( rotation ( ! gyro/at1 & ,i c only give x motions ( translation4 ,b n[ ,i w clamp ?is v]tical sp9dle by means ( a screw & repeat my ballet-dance :irl2 y w note t ,i ne$ n :irl r\nd1 a v small portion ( a :irl is en\gh to cause ?is gyro/at 7,fig4 #ah7 to set its sp9n+ axis v]tical1 to set its axis p>allel to ! v]tical axis ( rotation :i* ,i give x4 ,n[ ,i :irl 9 ! opposite direction1 ! gyro/at at once turns a som]sault1 turns completely r\nd & rema9s aga9 ) its axis v]tical1 & if y 7 to c>efully note ! direction ( ! sp9n+ ( ! #db gyro/at1 y w\ld f9d ! foll[+ rule to be g5]ally true3--,pay no att5tion to m]e translational motion1 ?9k only ( rotation ab\t axes1 & j rememb] t :5 y con/ra9 ! axis ( a sp9n+ body to rotate1 x w endeav\r to set its own axis p>allel to ! new axis ab\t :i* y rotate x2 & n only is ?is ! case1 b x w endeav\r to h ! direction ( its own sp9 ! same z ! direction ( ! new rotation4 ,i aga9 twirl on my toes1 hold+ ?is frame1 & n[ ,i "k t to a p]son look+ d[n ^u ! gyro/at & me f ! ceil+1 z ,i revolv$ 9 ! direction ( ! h&s ( a clock1 ! gyro/at is sp9n+ 9 ! direction ( ! h&s ( a clock2 b if ,i revolve aga9/ ! clock direction 7,fig4 #ai7 ! gyro/at tumbles ov] s z aga9 to be revolv+ 9 ! same direction z t 9 :i* ,i revolve4 ,illu/ration3 ,,fig4 #ai4 ,?is !n is ! simple rule :i* w enable y to tell be=eh& h[ a gyro/at w move #dc :5 y try to turn x 9 any p>ticul> direction4 ,y h only to rememb] t if y cont9u$ y\r ef=t long en\gh1 ! sp9n+ axis w\ld become p>allel to y\r new axis ( motion1 & ! direction ( sp9n+ w\ld be ! same z ! direction ( y\r new turn+ motion4 ,n[ let me apply my rule to ?is balanc$ gyro/at4 ,i %ove x1 or give x an impulse d[nw>ds1 b obs]ve t ?is really means a rotation ab\t ! horizontal axis ,c ,d 7,fig4 #ac71 & h5ce ! gyro/at turns its axis z if x want$ to become p>allel to ,c ,d4 ,?us1 look+ d[n f above 7z %[n by ,fig4 #bj71 ,o ,e 0 ! direction ( ! sp9n+ axis1 ,o ,d 0 ! axis ab\t :i* ,i endeav\r$ to move x1 & ! in/antane\s effect 0 t ,o ,e alt]$ to ! position ,o ,g4 ,a great] impulse ( ! same k9d w\ld h caus$ ! sp9n+ axis in/antly to g to ,o ,h or ,o ,j1 :]eas an upw>d opposite impulse w\ld h in/antly made ! sp9n+ axis po9t 9 ! direction ,o ,k1 ,o ,l or ,o ,m1 dep5d+ on h[ great ! impulse 0 & ! rate ( sp9n+4 ,:5 "o obs]ves ^! ph5om5a = ! fir/ "t1 "o says1 ,i %ov$ x d[n1 & x mov$ to ! "r2 ,i %ov$ x up1 & x mov$ to ! left2 b if ! direction ( ! sp9 7 opposite to :at x is1 "o w\ld say1 ,i %ov$ x d[n1 & x mov$ to ! left2 ,i %ov$ x up1 & x mov$ to ! "r4 ,! simple #dd /atem5t 9 all cases ought to be1 ,i want$ to rotate x ab\t a new axis1 & ! effect 0 to s5d its sp9n+ axis t[>ds ! direction ( ! new axis4 ,& n[ if y play ) ?is balanc$ gyro/at z ,i am do+1 %ov+ x ab\t 9 all sorts ( ways1 y w f9d ! rule to be a correct "o1 & !re is no difficulty 9 pr$ict+ :at w happ54 ,illu/ration3 ,,fig4 #bj4 #de ,if ?is rule is "r1 we see at once :y precession takes place4 ,i put ?is gyro/at 7,fig4 #ac7 out ( balance1 & if x 7 n rotat+ x w\ld fall d[nw>ds2 b a =ce act+ d[nw>ds really causes ! gyro/at to move to ! "r1 & s y see t x is cont9ually mov+ 9 ?is way1 = ! =ce is always act+ d[nw>ds1 & ! sp9n+ axis is cont9ually *as+ ! new axes ab\t :i* gravity t5ds cont9ually to make x revolve4 ,we see also :y x is t if ! want ( balance is ! o!r way1 if gravity t5ds to lift ! gyro/at1 ! precession is 9 ! opposite direction4 ,& 9 play+ ) ?is gyro/at z ,i d n[1 giv+ x all sorts ( pu%es1 "o makes o!r obs]vations & sees t ! above rule simplifies !m all2 t is1 x enables u to rememb] !m4 ,= example1 if ,i use ?is /ick to hurry on ! precession1 ! gyro/at moves 9 opposition to ! =ce :i* causes ! precession4 ,i am p>ticul>ly anxi\s t y %\ld rememb] ?is4 ,at pres5t ! balance-weight is s plac$ t ! gyro/at w\ld fall if x 7 n sp9n+4 ,b x is sp9n+1 & s x precesses4 ,if gravity 7 great] x w\ld precess fa/]1 & x comes home to u t x is ?is precession :i* enables ! =ce ( gravity to be inop]ative 9 m]e d[nw>d motion4 ,y see t if ! precession is hurri$1 x is m ?an suffici5t to balance gravity1 #df & ! gyro/at rises4 ,if ,i ret>d ! precession1 x is unable to balance gravity1 & ! gyro/at falls4 ,if ,i clamp ?is v]tical axis s t precession is impossible1 y w notice t ! gyro/at falls j z if x 7 n sp9n+4 ,if ,i clamp ! in/rum5t s t x _c move v]tically1 y notice h[ readily ,i c make x move horizontally2 ,i c set x rotat+ horizontally l any ord9>y body4 ,9 apply+ our rule to ?is top1 obs]ve t ! axis ( sp9n+ is ! axis ,e ,f ( ! top 7,fig4 #ab74 ,z se5 9 ! figure1 gravity is t5d+ to make ! top rotate ab\t ! axis ,f ,d1 & ! sp9n+ axis 9 its *ase ( ! axis ,f ,d describes a cone 9 space z x precesses4 ,?is gyro/at1 :i* is top-heavy1 rotates & precesses 9 mu* ! same way z ! top2 t is1 if y apply our rule1 or use y\r obs]vation1 y w f9d t to an obs]v] above ! table ! sp9n+ & precession occur 9 ! same direction1 t is1 ei!r bo? ) ! h&s ( a wat*1 or bo? aga9/ ! h&s ( a wat*4 ,:]eas1 a top l ?is be=e y 7,fig4 #ba71 support$ above its c5tre ( gravity1 or ! gyro/at "h 7,fig4 #bb71 :i* is also support$ above its c5tre ( gravity1 or ! gyro/at %[n 9 ,fig4 #ef1 or any o!r gyro/at support$ 9 su* a way t x w\ld be 9 /able equilibrium if x 7 n sp9n+2 9 all ^! #dg cases1 to an obs]v] plac$ above ! table1 ! precession is 9 a direction opposite to t ( ! sp9n+4 ,illu/ration3 ,,fig4 #ba4 ,illu/ration3 ,,fig4 #bb4 #dh ,if an impulse be giv5 to a top or gyro/at 9 ! direction ( ! precession1 x w rise 9 opposition to ! =ce ( gravity1 & %\ld at any in/ant ! precessional velocity be great] ?an :at x ought to be = ! balance ( ! =ce ( gravity1 ! top or gyro/at w rise1 its precessional velocity dim9i%+4 ,if ! precessional velocity is too small1 ! top w fall1 & z x falls ! precessional velocity increases4 ,n[ ,i say t all ^! facts1 :i* are m]e facts ( obs]vation1 agree ) our rule4 ,i wi% ,i d>e ask y to rememb] !m all4 ,y w obs]ve t 9 ?is wall %eet ,i h made a li/ ( !m4 ,i speak ( gravity z caus+ ! precession1 b ! =ces may be any o!rs ?an su* z are due to gravity4 ,,wall ,,%eet4 ,i4 ,,rule4 ,:5 =ces act ^u a sp9n+ body1 t5d+ to cause rotation ab\t any o!r axis ?an ! sp9n+ axis1 ! sp9n+ axis sets itself 9 bett] agreem5t ) ! new axis ( rotation4 ,p]fect agreem5t w\ld mean p]fect p>allelism1 ! directions ( rotation be+ ! same4 ,,ii4 ,hurry on ! precession1 & ! body rises 9 opposition to gravity4 #di ,,iii4 ,delay ! precession & ! body falls1 z gravity w\ld make x d if x 7 n sp9n+4 ,,iv4 ,a common top precesses 9 ! same direction z t 9 :i* x sp9s4 ,v4 ,a top support$ above its c5tre ( gravity1 or a body :i* w\ld be 9 /able equilibrium if n sp9n+1 precesses 9 ! opposite direction to t ( its sp9n+4 ,,vi4 ,! la/ two /atem5ts come to ?is3--,:5 ! =ces act+ on a sp9n+ body t5d to make ! angle ( precession great]1 ! precession is 9 ! same direction z ! sp9n+1 & vice v]sa4 ,hav+ by obs]vation obta9$ a rule1 e natural philosoph] tries to make 8 rule a rational "o2 tries to expla9 x4 ,i hope y "k :at we mean :5 we say t we expla9 a ph5om5on2 we really mean t we %[ ! ph5om5on to be consi/5t ) o!r bett] kn[n ph5om5a4 ,?us :5 y unmask a spirituali/ & %[ t ! ph5om5a exhibit$ by him are due to m]e sleight-(-h& & trick]y1 y expla9 ! ph5om5a4 ,:5 y %[ t !y are all consi/5t ) well-obs]v$ & e/abli%$ mesm]ic influ5ces1 y are also said to expla9 ! ph5om5a4 ,:5 y %[ t !y c be effect$ by means ( telegraphic messages1 or by reflection ( light f mirrors1 y expla9 ! #ej ph5om5a1 al?\gh 9 all ^! cases y d n really "k ! nature ( mesm]ism1 electricity1 light1 or moral obliquity4 ,! meane/ k9d ( criticism is t ( ! man :o *eap5s a sci5tific explanation by say+ t ! v simple/ facts ( nature are unexpla9able4 ,su* a man pref]s ! *aotic & indiscrim9ate wond] ( ! savage to ! rev]5ce ( a ,sir ,isaac ,newton4 ,illu/ration3 ,,fig4 #bc4 ,! explanation ( our rule is easy4 ,"h is a gyro/at 7,fig4 #bc7 some?+ l ! e>? 9 %ape1 & x is at re/4 ,i am sorry to say t ,i am compell$ to support ?is globe 9 a v visible mann] by gymbal r+s4 ,if ?is globe 7 j float+ 9 ! air1 if x _h no t5d5cy to fall1 my explanation w\ld be easi] to und]/&1 & ,i c\ld illu/rate x bett] exp]im5tally4 ,obs]ve ! po9t ,p4 ,if ,i move ! globe slightly ab\t ! axis ,a1 ! po9t ,p moves to ,q4 ,b suppose in/ead ( ?is t ! globe & inn] gymbal #ea r+ _h be5 mov$ ab\t ! axis ,b2 ! po9t ,p w\ld h mov$ to ,r4 ,well1 suppose bo? ^? rotations took place simultane\sly4 ,y all "k t ! po9t ,p w\ld move nei!r to ,q nor to ,r1 b x w\ld move to ,s2 ,p ,s be+ ! diagonal ( ! little p>allelogram4 ,! resultant motion !n is nei!r ab\t ! axis ,o ,a 9 space1 nor ab\t ! axis ,o ,b1 b x is ab\t "s su* axis z ,o ,c4 ,to ?is globe ,i h giv5 two rotations simultane\sly4 ,suppose a little be+ to exi/ on ?is globe :i* c\ld n see ! gymbals1 b 0 able to obs]ve o!r objects 9 ! room4 ,x w\ld say t ! direction ( rotation is nei!r ab\t ,o ,a nor ab\t ,o ,b1 b t ! real axis ( its e>? is "s l9e int]m$iate1 ,o ,c 9 fact4 ,if !n a ball is sudd5ly /ruck 9 two diff]5t directions at ! same in/ant1 to und]/& h[ x w sp9 we mu/ fir/ f9d h[ mu* sp9 ea* bl[ w\ld produce if x act$ alone1 & ab\t :at axis4 ,a sp9 ( ?ree turns p] second ab\t ! axis ,o ,a 7,fig4 #bd71 & a sp9 ( two turns p] second ab\t ! axis ,o ,b1 really mean t ! ball w sp9 ab\t ! axis ,o ,c ) a sp9 ( ?ree & a half turns p] second4 ,to arrive at ?is result1 ,i made ,o ,a1 #c feet long 7any o!r scale ( repres5tation w\ld h be5 "r7 #eb & ,o ,b1 #b feet long1 & ,i f\nd ! diagonal ,o ,c ( ! p>allelogram %[n on ! figure to be #c-a_/b feet long4 ,obs]ve t if ! rotation ab\t ! axis ,o ,a is ) ! h&s ( a wat* look+ f ,o to ,a1 ! rotation ab\t ! axis ,o ,b look+ f ,o to ,b1 mu/ also be ) ! h&s ( a wat*1 & ! resultant rotation ab\t ! axis ,o ,c is also 9 a direction ) ! h&s ( a wat* look+ f ,o to ,c4 ,fig4 #be %[s 9 two diagrams h[ necess>y x is t on look+ f ,o along ei!r ,o ,a or ,o ,b1 ! rotation %\ld be 9 ! same direction z reg>ds ! h&s ( a wat*4 ,^! con/ructions are well kn[n to all :o h /udi$ elem5t>y me*anical pr9ciples4 ,obvi\sly if ! rotation ab\t ,o ,a is v mu* great] ?an ! rotation ab\t ,o ,b1 !n ! position ( ! new axis ,o ,c mu/ be mu* ne>] ,o ,a ?an ,o ,b4 ,illu/ration3 ,,fig4 #bd4 ,illu/ration3 ,,fig4 #be4 ,we see !n t if a body is sp9n+ ab\t an axis ,o ,a1 & we apply =ces to x :i* #ec w\ld1 if x 7 at re/1 turn x ab\t ! axis ,o ,b2 ! effect is to cause ! sp9n+ axis to be alt]$ to ,o ,c2 t is1 ! sp9n+ axis sets itself 9 bett] agreem5t ) ! new axis ( rotation4 ,?is is ! fir/ /atem5t on our wall %eet1 ! rule f :i* all our o!r /atem5ts are d]iv$1 assum+ t !y 7 n really d]iv$ f obs]vation4 ,n[ ,i d n say t ,i h "h giv5 a complete pro( = all cases1 = ! fly-:eels 9 ^! gyro/ats are runn+ 9 be>+s1 & ! be>+s con/ra9 ! axes to take ! new positions1 :]eas !re is no su* #ed con/ra9t 9 ?is top2 b 9 ! limit$ "t ( a popul> lecture l ?is x is n possible1 ev5 if x 7 desirable1 to give an exhau/ive pro( ( su* a univ]sal rule z ours is4 ,t ,i h n exhau/$ all t might be said on ?is subject w be evid5t f :at foll[s4 ,if we h a sp9n+ ball & we give to x a new k9d ( rotation1 :at w happ58 ,suppose1 = example1 t ! e>? 7 a homog5e\s sph]e1 & t !re 7 sudd5ly impress$ ^u x a new rotatory motion t5d+ to s5d ,africa s\?w>ds2 ! axis ( ?is new sp9 w\ld h its pole at ,java1 & ?is sp9 comb9$ ) ! old "o w\ld cause ! e>? to h its true pole some:]e betwe5 ! pres5t pole & ,java4 ,x w\ld no long] rotate ab\t its pres5t axis4 ,9 fact ! axis ( rotation w\ld be alt]$1 & !re w\ld be no t5d5cy = any?+ fur!r to occur1 because a homog5e\s sph]e w z readily rotate ab\t "o axis z ano!r4 ,b if su* a ?+ 7 to happ5 to ?is e>? ( ours1 :i* is n a sph]e b a flatt5$ sph]oid l an orange1 its pol> diamet] be+ ! "o-?ird ( "o p] c5t4 %ort] ?an ! equatorial diamet]2 !n z soon z ! new axis 0 e/abli%$1 ! axis ( symmetry w\ld res5t ! *ange & w\ld try to become aga9 ! axis ( rotation1 & a great wobbl+ motion w\ld ensue4 #ee ,i put ! matt] 9 popul> language :5 ,i speak ( ! res5tm5t ( an axis2 p]haps x is bett] to expla9 m exactly :at ,i mean4 ,i am go+ to use ! expression ,c5trifugal ,=ce4 ,n[ !re are capti\s critics :o object to ?is t]m1 b all eng9e]s use x1 & ,i l to use x1 & our capti\s critics submit to all sorts ( ignom9i\s involution ( language 9 evad+ ! use ( x4 ,x means ! =ce ) :i* any body acts ^u its con/ra9ts :5 x is con/ra9$ to move 9 a curv$ pa?4 ,! =ce is always direct$ away f ! c5tre ( ! curve4 ,:5 a ball is :irl$ r\nd 9 a curve at ! end ( a /r+ its c5trifugal =ce t5ds to break ! /r+4 ,:5 any body key$ to a %aft is revolv+ ) ! %aft1 x may be t ! c5trifugal =ces ( all ! p>ts j balance "o ano!r2 b sometimes !y d n1 & !n we say t ! %aft is out ( balance4 ,"h1 = example1 is a disc ( wood rotat+4 ,x is 9 balance4 ,b ,i /op its motion & fix ?is piece ( lead1 ,a1 to x1 & y obs]ve :5 x rotates t x is s mu* out ( balance t ! be>+s ( ! %aft & ! frame t holds !m1 & ev5 ! lecture-table1 are %ak+4 ,n[ ,i w put ?+s 9 balance aga9 by plac+ ano!r piece ( lead1 ,b1 on ! side ( ! sp9dle remote f ,a1 & :5 ,i aga9 rotate ! disc 7,fig4 #bf7 !re #ef is no long] any %ak+ ( ! framework4 ,:5 ! crank-%aft ( a locomotive has n be5 put 9 balance by means ( weights suitably plac$ on ! driv+-:eels1 !re is nobody 9 ! tra9 :o does n feel ! effects4 ,yes1 & ! coal-bill %[s ! effects1 = an unbalanc$ eng9e tugs ! tra9 spasmodically in/ead ( ex]t+ an effici5t /eady pull4 ,my fri5d ,pr(essor ,milne1 ( ,japan1 places e>?quake measur+ in/rum5ts on eng9es & 9 tra9s = measur+ ?is & o!r wants ( balance1 & he has %[n unmi/akably t two eng9es ( ne>ly ! same g5]al design1 "o balanc$ prop]ly & ! o!r n1 consume v diff]5t am\nts ( coal 9 mak+ ! same j\rney at ! same spe$4 ,illu/ration3 ,,fig4 #bf4 ,if a rotat+ body is 9 balance1 n only does ! axis ( rotation pass ?r\gh ! c5tre ( gravity 7or r c5tre ( mass7 ( ! body1 b #eg ! axis ( rotation mu/ be "o ( ! ?ree pr9cipal axes ?r\gh ! c5tre ( mass ( ! body4 ,"h1 = example1 is an ellipsoid ( wood2 ,a ,a1 ,b ,b1 & ,c ,c 7,fig4 #bg7 are its ?ree pr9cipal axes1 & x w\ld be 9 balance if x rotat$ ab\t any "o ( ^! ?ree axes1 & x w\ld n be 9 balance if x rotat$ ab\t any o!r axis1 unless1 inde$1 x 7 l a homog5e\s sph]e1 e diamet] ( :i* is a pr9cipal axis4 ,illu/ration3 ,,fig4 #bg4 ,e body has ?ree su* pr9cipal axes ?r\gh its c5tre ( mass1 & ?is body 7,fig4 #bg7 has !m2 b ,i h "h con/ra9$ x to rotate ab\t ! axis ,d ,d1 & y all obs]ve ! effect ( ! unbalanc$ c5trifugal =ces1 :i* is ne>ly great en\gh to te> ! framework 9 pieces4 ,! high] ! spe$ ! m important ?is want ( balance is4 ,if ! spe$ is d\bl$1 ! c5trifugal =ces become f\r times z great2 & mod]n me*anical eng9e]s ) _! quick spe$ eng9es1 "s ( :i* revolve1 l ! fan-eng9es ( torp$o-boats1 at #agjj revolutions p] m9ute1 require to pay great att5tion to ?is subject1 :i* ! old] eng9e]s nev] tr\bl$ _! #eh heads ab\t4 ,y mu/ rememb] t ev5 :5 want ( balance does n actually fracture ! framework ( an eng9e1 x w %ake ev]y?+1 s t nuts & keys & o!r fa/5+s are pretty sure to get loose4 ,i h se51 on a badly-balanc$ ma*9e1 a securely-fa/5$ pair ( nuts1 "o suppos$ to be lock+ ! o!r1 quietly revolv+ on _! bolt at ! same "t1 & g5tly lift+ !mselves at a regul> b fairly rapid rate1 until !y bo? tumbl$ f ! end ( ! bolt into my h&4 ,if my h& _h n be5 !re1 ! bolts w\ld h tumbl$ into a receptacle 9 :i* !y w\ld h produc$ int]e/+ b mo/ de/ructive ph5om5a4 ,y w\ld h somebody else lectur+ to y to-night if t ev5t _h come (f4 ,suppose1 !n1 t our e>? 7 sp9n+ ab\t any o!r axis ?an its pres5t axis1 ! axis ( figure4 ,if spun ab\t any diamet] ( ! equator = example1 c5trifugal =ces w\ld j keep ?+s 9 a /ate ( un/able equilibrium1 & no great *ange might be produc$ until "s accid5tal cause effect$ a slight alt]ation 9 ! sp9n+ axis1 & aft] t ! e>? w\ld wobble v greatly4 ,h[ long & h[ viol5tly x w\ld wobble1 w\ld dep5d on a numb] ( circum/ances ab\t :i* ,i w n n[ v5ture to guess4 ,if y #ei tell me t on ! :ole1 9 spite ( ! viol5ce ( ! wobbl+1 x w\ld n get %ak5 into a new =m altoge!r1 !n ,i "k t 9 consequ5ce ( tidal & o!r friction x w\ld ev5tually come to a quiet /ate ( sp9n+ ab\t its pres5t axis4 ,y see1 !n1 t al?\gh e body has ?ree axes ab\t :i* x w rotate 9 a balanc$ fa%ion )\t any t5d5cy to wobble1 ?is balance ( ! c5trifugal =ces is really an un/able balance 9 two out ( ! ?ree cases1 & !re is only "o axis ab\t :i* a p]fectly /able balanc$ k9d ( rotation w take place1 & a sp9n+ body g5]ally comes to rotate ab\t ?is axis 9 ! long run if left to itself1 & if !re is friction to /ill ! wobbl+4 ,to illu/rate ?is1 ,i h "h a me?od ( sp9n+ bodies :i* enables !m to *oose z _! sp9n+ axis t "o pr9cipal axis ab\t :i* _! rotation is mo/ /able4 ,! v>i\s bodies c be hung at ! end ( ?is /r+1 & ,i cause ! pulley f :i* ! /r+ hangs to rotate4 ,obs]ve t at fir/ ! disc 7,fig4 #bh a7 rotates sob]ly ab\t ! axis ,a ,a1 b y note ! small beg9n+ ( ! wobble2 n[ x gets q viol5t1 & n[ ! disc is /ably & smoo?ly rotat+ ab\t ! axis ,b ,b1 :i* is ! mo/ important ( its pr9cipal axes4 #fj ,illu/ration3 ,,fig4 #bh4 ,aga91 ?is cone 7,fig4 #bh b7 rotates smoo?ly at fir/ ab\t ! axis ,a ,a1 b ! wobble beg9s & gets v great1 & ev5tually ! cone rotates smoo?ly ab\t ! axis ,b ,b1 :i* is ! mo/ important ( its pr9cipal axes4 ,"h aga9 is a rod hung f "o end 7,fig4 #bh d74 ,see also ?is an*or r+4 ,b y may be m int]e/$ 9 ?is limp r+ ( *a9 7,fig4 #bh c74 ,see h[ at fir/ x hangs f ! cord v]tically1 & h[ ! wobbles & vibrations end 9 its becom+ a p]fectly circul> r+ ly+ all 9 a horizontal plane4 ,?is exp]im5t illu/rates also ! quasi-rigidity giv5 to a flexible body by rapid motion4 ,to return to ?is balanc$ gyro/at ( ours 7,fig4 #ac74 ,x is n precess+1 s y "k t ! weight ,w j balances ! gyro/at ,f4 ,n[ if ,i leave ! in/rum5t to itself aft] ,i give a d[nw>d impulse to ,f1 n ex]t+ m]ely a /eady pressure1 y w notice t ,f sw+s to ! "r = ! reason already giv52 b x sw+s too fa/ & too f>1 j l any o!r sw++ body1 & x is easy f :at ,i h already said1 to see t ?is wobbl+ motion 7,fig4 #bi7 %\ld be ! result1 & t x %\ld cont9ue until friction /ills x1 & ,f takes its p]man5t new position only aft] "s "t elapses4 ,y see t ,i c impose ?is wobble or nodd+ #fb motion ^u ! gyro/at :e!r x has a motion ( precession or n4 ,x is n[ nodd+ z x processes r\nd & r\nd--t is1 x is ris+ & fall+ z x precesses4 ,illu/ration3 ,,fig4 #bi4 ,p]haps ,i _h bett] put ! matt] a little m cle>ly4 ,y see ! same ph5om5on 9 ?is top4 ,if ! top is precess+ too fa/ = ! =ce ( gravity ! top rises1 & ! precession dim9i%es 9 consequ5ce2 ! precession be+ n[ too sl[ to balance gravity1 ! top falls a little & ! #fc precession increases aga91 & ?is sort ( vibration ab\t a mean position goes on j z ! vibration ( a p5dulum goes on till friction de/roys x1 & ! top precesses m regul>ly 9 ! mean position4 ,?is nodd+ is m evid5t 9 ! ne>ly horizontal balanc$ gyro/at ?an 9 a top1 because 9 a top ! turn+ effect ( gravity is less 9 ! high] positions4 ,:5 sci5tific m5 try to popul>ize _! discov]ies1 = ! sake ( mak+ "s fact v pla9 !y w (t5 tell slight untru?s1 mak+ /atem5ts :i* become r mislead+ :5 _! /ud5ts rea* ! high] levels4 ,?us a/ronom]s tell ! public t ! e>? goes r\nd ! sun 9 an elliptic pa?1 :]eas ! attractions ( ! planets cause ! pa? to be only approximately elliptic2 & electricians tell ! public t electric en]gy is convey$ ?r\gh wires1 :]eas x is really convey$ by all o!r space ?an t occupi$ by ! wires4 ,9 ?is lecture ,i h to "s small ext5t tak5 advantage ( y 9 ?is way2 = example1 at fir/ y w rememb]1 ,i neglect$ ! nodd+ or wobbl+ produc$ :5 an impulse is giv5 to a top or gyro/at1 &1 all ?r\gh1 ,i neglect ! fact t ! in/antane\s axis ( rotation is only ne>ly co9cid5t ) ! axis ( figure ( a precess+ gyro/at or top4 ,& inde$ y may g5]ally #fd take x t if all "o's /atem5ts 7 absolutely accurate1 x w\ld be necess>y to use hundr$s ( te*nical t]ms & involv$ s5t5ces ) explanatory1 police-l p>5!ses2 & to li/5 to _m su* /atem5ts w\ld be absolutely impossible1 ev5 = a sci5tific man4 ,y w\ld h>dly expect1 h[ev]1 t s great a sci5tific man z ! late ,pr(essor ,rank9e1 :5 he 0 seiz$ ) ! poetic f]v\r1 w\ld err ev5 m ?an ! popul> lectur] 9 mak+ 8 accuracy ( /atem5t subs]vi5t to ! exig5cies ( ! rhyme z well z to ! necessity = simplicity ( /atem5t4 ,he 9 8 poem1 ,! ,ma!matician 9 ,love1 has ! foll[+ l9es-- ,! lady lov$ danc+2--he !re=e appli$ ,to ! polka & waltz1 an equation2 ,b :5 to rotate on 8 axis he tri$1 ,8 c5tre ( gravity sway$ to "o side1 ,& he fell by ! e>?'s gravitation4 ,n[ ,i h no d\bt t ?is is z good dropp+ into poetry z c be expect$ 9 a sci5tific man1 & ----'s sci5ce is z good z c be expect$ 9 a man :o calls himself a poet2 b 9 bo? cases we h illu/rations ( ! incompatibility ( sci5ce & rhym+4 ,illu/ration3 ,,fig4 #ag4 ,! motion ( ?is gyro/at c be made ev5 m complicat$ ?an x 0 :5 we _h #fe nutation & precession1 b !re is really no?+ 9 x :i* is n readily expla9able by ! simple pr9ciples ,i h put be=e y4 ,look1 = example1 at ?is well-balanc$ gyro/at 7,fig4 #ag74 ,:5 ,i /rike ?is inn] gymbal r+ 9 any way y see t x wriggles quickly j z if x 7 a lump ( jelly1 its rapid vibrations dy+ away j l ! rapid vibrations ( any yield+ ela/ic body4 ,?is /range ela/icity is ( v great int]e/ :5 we consid] x 9 relation to ! molecul> prop]ties ( matt]4 ,"h aga9 7,fig4 #cj7 we h an example :i* is ev5 m int]e/+4 ,i h support$ ! cas$ #ff gyro/at ( ,figs4 #e & #f ^u a pair ( /ilts1 & y w obs]ve t x is mov+ ab\t a p]fectly /able position ) a v curi\s /agg]+ k9d ( vibratory motion2 b !re is no?+ 9 ^! motions1 h[ev] curi\s1 t y _c easily expla9 if y h foll[$ me s f>4 ,illu/ration3 ,,fig4 #cj4 ,"s ( y :o are m obs]vant ?an ! o!rs1 w h rem>k$ t all ^! precess+ gyro/ats gradually fall l[] & l[]1 j z !y w\ld d1 only m quickly1 if !y 7 n sp9n+4 ,& if y ca/ y\r eye ^u ! ?ird /atem5t ( our wall %eet 7p4 #di7 y w readily und]/& :y x is s4 ,delay ! precession & ! body falls1 z gravity w\ld make x d if x 7 n sp9n+4 #fg ,well1 ! precession ( e "o ( ^! is resi/$ by friction1 & s !y fall l[] & l[]4 ,i wond] if any ( y h foll[$ me s well z to "k already :y a sp9n+ top rises4 ,p]haps y h n yet _h "t to ?9k x out1 b ,i h acc5tuat$ sev]al times ! p>ticul> fact :i* expla9s ?is ph5om5on4 ,friction makes ! gyro/ats fall1 :at is x t causes a top to rise8 ,rapid ris+ to ! upright position is ! inv>iable sign ( rapid rotation 9 a top1 & ,i recollect t :5 q v]tical we us$ to say1 ,%e sleeps6 ,su* 0 ! ende>+ way 9 :i* ! y\?ful exp]im5t] ?\ght ( ! beautiful object ( 8 t5d] reg>d4 ,all s well kn[n z ?is ris+ t5d5cy ( a top has be5 ev] s9ce tops 7 fir/ spun1 ,i "q if any p]son 9 ?is hall kn[s ! explanation1 & ,i "q its be+ kn[n to m ?an a few p]sons any:]e4 ,any great ma!matician w tell y t ! explanation is surely to be f\nd publi%$ 9 ,r\?1 or t at all ev5ts he kn[s m5 at ,cambridge :o surely "k x1 & he ?9ks t he himself mu/ h kn[n x1 al?\gh he has n[ =gott5 ^? elaborate ma!matical demon/rations :i* he once ex]cis$ 8 m9d ^u4 ,i believe t all su* /atem5ts are made 9 error1 b ,i _c #fh be sure4#f ,a p>tial !ory ( ! ph5om5on 0 giv5 by ,mr4 ,ar*ibald ,smi? 9 ! ,cambridge ,ma!matical ,j\rnal _m ye>s ago1 b ! problem 0 solv$ by ,sir ,william ,?omson & ,pr(essor ,blackburn :5 !y /ay$ toge!r "o ye> at ! seaside1 read+ = ! great ,cambridge ma!matical exam9ation4 ,x mu/ h al>m$ a p]son int]e/$ 9 ,?omson's success to notice t ! seaside holiday 0 really sp5t by him & 8 fri5d 9 sp9n+ all sorts ( r\nd$ /ones :i* !y pick$ up on ! bea*4 ,& ,i w n[ %[ y ! curi\s ph5om5on t puzzl$ him t ye>4 ,?is ellipsoid 7,fig4 #ca7 w repres5t a wat]worn /one4 ,x is ly+ 9 its mo/ /able /ate on ! table1 & ,i give x a sp94 ,y see t = a second or two x 0 incl9$ to g on sp9n+ ab\t ! axis ,a ,a1 b x began to wobble viol5tly1 & aft] a :ile1 :5 ^! wobbles /ill$1 y saw t x 0 sp9n+ nicely ) its axis ,b ,b v]tical2 b !n a new s]ies ( wobbl+s began & became m viol5t1 & :5 !y ceas$ y saw t ! object _h at l5g? rea*$ a settl$ /ate ( #fi sp9n+1 /&+ upright ^u its longe/ axis4 ,?is is an extraord9>y ph5om5on to any p]son :o kn[s ab\t ! great incl9ation ( ?is body to sp9 9 ! v way 9 :i* ,i fir/ />t$ x sp9n+4 ,y w f9d t ne>ly any r\nd$ /one :5 spun w get up 9 ?is way ^u its longe/ axis1 if ! sp9 is only vigor\s en\gh1 & 9 ! v same way ?is sp9n+ top t5ds to get m & m upright4 ,illu/ration3 ,,fig4 #ca4 ,i believe t !re are v few ma!matical explanations ( ph5om5a :i* may n be giv5 9 q ord9>y language to p :o h an ord9>y am\nt ( exp]i5ce4 ,9 mo/ cases ! symbolical algebraic explanation mu/ be giv5 fir/ by somebody1 & !n comes ! "t = its translation into ord9>y language4 ,?is is ! f\ndation ( ! new ?+ call$ ,te*nical ,education1 :i* assumes t a #gj workman may be taught ! pr9ciples und]ly+ ! op]ations :i* g on 9 8 trade1 if we base our explanations on ! exp]i5ce :i* ! man has acquir$ already1 )\t tir+ him ) a f\r ye>s' c\rse ( /udy 9 elem5t>y ?+s su* z is mo/ suitable = inexp]i5c$ *ildr5 & y\?s at public s*ools & ! univ]sities4 ,illu/ration3 ,,fig4 #cb4 ,illu/ration3 ,,fig4 #cc4 ,) y\r pres5t exp]i5ce ! explanation ( ! ris+ ( ! top becomes ridicul\sly simple4 ,if y look at /atem5t two on ?is wall %eet 7p4 #dh7 & reflect a little1 "s ( y w be able1 )\t any elaborate ma!matics1 to give ! simple reason = ?is t ,?omson gave me sixte5 ye>s ago4 ,hurry on ! precession1 & ! body rises 9 opposition to gravity4 ,well1 z ,i am n t\*+ ! top1 & z ! body does rise1 we look at once = some?+ t is hurry+ on ! precession1 & we naturally look to ! way 9 :i* its peg is rubb+ on ! table1 =1 ) ! exception ( ! atmosph]e ?is top is t\*+ no?+ else ?an ! table4 ,obs]ve c>efully h[ any ( ^! objects precesses4 ,fig4 #cb %[s ! way 9 :i* a top sp9s4 ,look$ at f above1 if ! top is sp9n+ 9 ! direction ( ! h&s ( a wat*1 we "k f ! f\r? /atem5t ( our wall %eet1 or by m]e obs]vation1 t x also precesses 9 ! direction ( ! h&s #ga ( a wat*2 t is1 its precession is su* z to make ! peg roll at ,b into ! pap]4 ,= y w obs]ve t ! peg is roll+ r\nd a circul> pa? on ! table1 ,g be+ ne>ly motionless1 & ! axis ,a ,g ,a describ+ ne>ly a cone 9 space ^: v]tex is ,g1 above ! table4 ,fig4 #cc #gb %[s ! peg enl>g$1 & x is evid5t t ! po9t ,b t\*+ ! table is really l ! bottom ( a :eel ,b ,b'1 & z ?is :eel is rotat+1 ! rotation causes x to roll into ! pap]1 away f u4 ,b obs]ve t its m]e precession is mak+ x roll into ! pap]1 & t ! sp9 if great en\gh wants to roll ! top fa/] ?an ! precession lets x roll1 s t x hurries on ! precession1 & !re=e ! top rises4 ,t is ! simple explanation2 ! sp91 s long z x is #gc great en\gh1 is always hurry+ on ! precession1 & if y w ca/ y\r recollection back to ! days ( y\r y\?1 :5 a top 0 support$ on y\r h& z ?is is n[ on m9e 7,fig4 #cd71 & ! sp9 _h gr[n to be q small1 & 0 unable to keep ! top upright1 y w rememb] t y dext]\sly help$ ! precession by giv+ y\r h& a circl+ motion s z to get f y\r top ! advantages z to uprightness ( a slightly long] sp94 ,illu/ration3 ,,fig4 #cd4 ,i mu/ ask y n[ by obs]vation1 & ! application ( exactly ! same argum5t1 to expla9 ! /ruggle = uprightness on its long] axis ( any r\nd$ /one :5 x sp9s on a table4 ,i may tell y t "s ( ^! l>ge r\nd$-look+ objects :i* ,i n[ sp9 be=e y 9 illu/ration1 are made holl[1 & !y are ei!r ( wood or z9c1 because ,i h n ! skill necess>y to sp9 l>ge solid objects1 & yet ,i want$ to h objects :i* y w\ld be able to see4 ,?is small "o 7,fig4 #ca7 is ! l>ge/ solid "o to :i* my f+]s are able to give suffici5t sp94 ,"h is a v int]e/+ object 7,fig4 #ce71 sph]ical #gd 9 %ape1 b its c5tre ( gravity is n exactly at its c5tre ( figure1 s :5 ,i lay x on ! table x always gets to its position ( /able equilibrium1 ! :ite spot t\*+ ! table z at ,a4 ,"s ( y "k t if ?is sph]e is ?r[n into ! air x seems to h v curi\s motions1 because "o is s apt to =get t x is ! motion ( its c5tre ( gravity :i* foll[s a simple pa?1 & ! b\nd>y is ecc5tric to ! c5tre ( gravity4 ,its motions :5 set to roll ^u a c>pet are also extremely curi\s4 ,illu/ration3 ,,fig4 #ce4 ,n[ = ! v reasons t ,i h already giv51 :5 ?is sph]e is made to sp9 on ! table1 x always endeav\rs to get its :ite spot upp]mo/1 z 9 ,c1 ,fig4 #ce2 to get into ! position 9 :i* :5 n sp9n+ x w\ld be un/able4 ,illu/ration3 ,,fig4 #cf4 ,! precession ( a top or gyro/at leads u at once to ?9k ( ! precession ( ! great sp9n+ body on :i* we live4 ,y "k t ! e>? #ge sp9s on its axis a little m ?an once e tw5ty-f\r h\rs1 z ?is orange is revolv+1 & t x goes r\nd ! sun once 9 a ye>1 z ?is orange is n[ go+ r\nd a model sun1 or z is %[n 9 ! diagram 7,fig4 #cf74 ,its sp9n+ axis po9ts 9 ! direction %[n1 v ne>ly to ! /> :i* is call$ ! pole />1 almo/ inf9itely f> away4 ,9 ! figure & model ,i h greatly exagg]at$ ! elliptic nature ( ! e>?'s pa?1 z is q usual1 al?\gh x may be a little mislead+1 because ! e>?'s pa? is mu* m ne>ly circul> ?an _m p imag9e4 ,z a matt] ( fact ! e>? is ab\t ?ree million miles ne>] ! sun 9 w9t] ?an x is 9 summ]4 ,?is seems at fir/ p>adoxical1 b we get to und]/& x :5 we reflect t1 because ( ! slope ( ! e>?'s axis to ! ecliptic1 we p :o live 9 ! nor!rn hemisph]e h ! sun less v]tically above u1 & h a %ort] day 9 ! w9t]1 & h5ce ea* squ>e foot ( our "p ( ! e>?'s surface receives mu* less heat e day1 & s we feel cold]4 ,n[ 9 ab\t #ac1jjj ye>s ! e>? w h precess$ j half a revolution 7see ,fig4 #ch72 ! axis w !n be slop$ t[>ds ! sun :5 x is ne>e/1 in/ead ( away f x z x is n[2 consequ5tly we %all be mu* w>m] 9 summ] & cold] 9 w9t] ?an we are n[4 ,inde$ we %all !n be mu* worse (f ?an ! s\!rn #gg hemisph]e p are n[1 = !y h pl5ty ( oceanic wat] to temp] _! climate4 ,x is easy to see ! nature ( ! *ange f figures #cf1 #cg1 & #ch1 or f ! model z ,i c>ry ! orange & its symbolic knitt+-ne$le r\nd ! model sun4 ,let u imag9e an obs]v] plac$ above ?is model1 f> above ! nor? pole ( ! e>?4 ,he sees ! e>? rotat+ aga9/ ! direction ( ! h&s ( a wat*1 & he f9ds t x precesses ) ! h&s ( a wat*1 s t sp9 & precession are 9 opposite directions4 ,inde$ x is because ( ?is t we h ! ^w precession1 :i* we n[ apply to ! motion ( a top1 al?\gh ! precession ( a top is 9 ! same direction z t ( ! sp94 ,illu/ration3 ,,fig4 #cg4 ,illu/ration3 ,,fig4 #ch4 ,! practical a/ronom]1 9 expla9+ ! luni-sol> precession ( ! equ9oxes to y1 w n probably ref] to tops or gyro/ats4 ,he w tell y t ! longitude & "r asc5sion ( a /> seem to alt]2 9 fact t ! po9t on ! ecliptic f :i* he makes 8 measurem5ts1 namely1 ! spr+ equ9ox1 is sl[ly travell+ r\nd ! ecliptic 9 a direction opposite to t ( ! e>? 9 its orbit1 or to ! app>5t pa? ( ! sun4 ,! spr+ equ9ox is to him = heav5ly measurem5ts :at ! longitude ( ,gre5wi* is to ! navigator4 ,he w tell y t ab]ration ( light1 & p>allax ( ! />s1 #hj b m ?an bo?1 ?is precession ( ! equ9oxes1 are ! ?ree mo/ important ?+s :i* prev5t u f see+ 9 an obs]vatory by transit obs]vations ( ! />s1 t ! e>? is revolv+ ) p]fect uni=mity4 ,b 8 way ( describ+ ! precession mu/ n disguise = y ! physical fact t 8 ph5om5on & ours are id5tical1 & t to u :o are acqua9t$ ) sp9n+ tops1 ! sl[ conical motion ( a sp9n+ axis is m readily und]/ood ?an ^? details ( 8 measurem5ts 9 :i* an a/ronom]'s m9d is b\nd up1 & :i* s (t5 condemn a man ( great intellectual p[] to ! life ( drudg]y :i* we g5]ally associate ) ! idea ( ! p\nd-a-week *eap cl]k4 ,illu/ration3 ,,fig4 #bb4 ,! precession ( ! e>? is !n ( ! same nature z t ( a gyro/at susp5d$ above its c5tre ( gravity1 ( a body :i* w\ld be /able & n top-heavy if x 7 n sp9n+4 ,9 fact ! precession ( ! e>? is ( ! same nature z t ( ?is l>ge gyro/at 7,fig4 #bb71 :i* is susp5d$ 9 gymbals1 s t x has a vibration l a p5dulum :5 n sp9n+4 ,i w n[ sp9 x1 s t look$ at f above x goes aga9/ ! h&s ( a wat*1 & y obs]ve t x precesses ) ! h&s ( a wat*4 ,"h aga9 is a hemisph]ical wood5 %ip1 9 :i* !re is a gyro/at ) its axis v]tical4 ,x is 9 /able #ha equilibrium4 ,:5 ! gyro/at is n sp9n+1 ! %ip vibrates sl[ly :5 put out ( equilibrium2 :5 ! gyro/at is sp9n+ ! %ip gets a motion ( precession :i* is opposite 9 direction to t ( ! sp9n+4 ,a/ronom]s1 beg9n+ ) ,hipp>*us1 h made obs]vations ( ! e>?'s motion = u1 & we h obs]v$ ! motions ( gyro/ats1 & we naturally seek = an explanation ( ! precessional motion ( ! e>?4 ,! equator ( ! e>? makes an angle ( #bc-a_/b;deg ) ! ecliptic1 :i* is ! plane ( ! e>?'s orbit4 ,or ! sp9n+ axis ( ! e>? is always at angle ( #bc-a_/b;deg ) a p]p5dicul> to ! ecliptic1 & makes a complete revolution 9 #bf1jjj ye>s4 ,! surface ( ! wat] on :i* ?is wood5 %ip is float+ repres5ts ! ecliptic4 ,! axis #hb ( sp9n+ ( ! gyro/at is ab\t #bc-a_/b;deg to ! v]tical2 ! precession is 9 two m9utes in/ead ( #bf1jjj ye>s2 & only t ?is %ip does n revolve 9 a great circul> pa?1 we %\ld h 9 its precession a pretty exact illu/ration ( ! e>?'s precession4 ,! precessional motion ( ! %ip1 or ( ! gyro/at 7,fig4 #bb71 is expla9able1 & 9 ! same way ! e>?'s precession is at once expla9$ if we f9d t !re are =ces f ext]nal bodies t5d+ to put its sp9n+ axis at "r angles to ! ecliptic4 ,! e>? is a ne>ly sph]ical body4 ,if x 7 exactly sph]ical & homog5e\s1 ! resultant =ce ( attraction ^u x1 ( a di/ant body1 w\ld be 9 a l9e ?r\gh its c5tre4 ,& aga91 if x 7 sph]ical & non-homog5e\s1 b if its mass 7 arrang$ 9 uni=mly d5se1 sph]ical lay]s1 l ! coats ( an onion4 ,b ! e>? is n sph]ical1 & to f9d :at is ! nature ( ! attraction ( a di/ant body1 x has be5 necess>y to make p5dulum obs]vations all ov] ! e>?4 ,y "k t if a p5dulum does n alt] 9 l5g? z we take x ab\t to v>i\s places1 its "t ( vibration at ea* place enables ! =ce ( gravity at ea* place to be det]m9$2 & ,mr4 ,gre5 prov$ t if we "k ! =ce ( gravity at all places on ! surface ( ! e>?1 al?\gh we may "k no?+ ab\t ! #hc /ate ( ! inside ( ! e>?1 we c calculate ) absolute accuracy ! =ce ex]t$ by ! e>? on matt] plac$ any:]e outside ! e>?2 = in/ance1 at any "p ( ! moon's orbit1 or at ! sun4 ,& h5ce we "k ! equal & opposite =ce ) :i* su* matt] w act on ! e>?4 ,n[ p5dulum obs]vations h be5 made at a great _m places on ! e>?1 & we "k1 al?\gh ( c\rse n ) absolute accuracy1 ! attraction on ! e>?1 ( matt] outside ! e>?4 ,= in/ance1 we "k t ! resultant attraction ( ! sun on ! e>? is a =ce :i* does n pass ?r\gh ! c5tre ( ! e>?'s mass4 ,y may compreh5d ! result bett] if ,i ref] to ?is diagram ( ! e>? at midw9t] 7,fig4 #ci71 & use a popul> me?od ( description4 ,a & ,b may r\ghly be call$ ! protub]ant p>ts ( ! e>?--t protub]ant belt ( matt] :i* makes ! #hd e>? orange-%ap$ in/ead ( sph]ical4 ,on ! sph]ical portion inside1 assum$ r\ghly to be homog5e\s1 ! resultant attraction is a =ce ?r\gh ! c5tre4 ,illu/ration3 ,,fig4 #ci4 ,i w n[ consid] ! attraction on ! protub]ant equatorial belt indicat$ by ,a & ,b4 ,! sun attracts a p\nd ( matt] at ,b m ?an x attracts a p\nd ( matt] at ,a1 because ,b is ne>] ?an ,a1 & h5ce ! total resultant =ce is 9 ! direction ,m ,n r ?an ,o ,o1 ?r\gh ! c5tre ( ! e>?'s mass4 ,b we "k t a =ce 9 ! direction ,m ,n is equival5t to a =ce ,o ,o p>allel to ,m ,n1 toge!r ) a tilt+ c\ple ( =ces t5d+ to turn ! equator edge on to ! sun4 ,y w get ! true result z to ! tilt+ t5d5cy by imag9+ ! e>? to be motionless1 & ! sun's mass to be di/ribut$ z a circul> r+ ( matt] #ahd millions ( miles 9 diamet]1 incl9$ to ! equator at #bc-a_/b;deg4 ,"u ! influ5ce ( ! attraction ( ?is r+ ! e>? w\ld heave l a great %ip on a calm sea1 roll+ v sl[ly2 9 fact1 mak+ "o complete sw+ 9 ab\t ?ree ye>s4 ,b ! e>? is sp9n+1 & ! tilt+ c\ple or torque acts ^u x j l ! =ces :i* are always t5d+ to cause ?is %ip-model to /& upright1 & h5ce x has a precessional motion ^: complete p]iod is #bf1jjj ye>s4 ,:5 !re is no sp9 9 ! %ip1 its complete oscillation takes place 9 ?ree seconds1 & #he :5 ,i sp9 ! gyro/at on bo>d ! %ip1 ! complete p]iod ( its precession is two m9utes4 ,9 bo? cases ! effect ( ! sp9 is to conv]t :at w\ld be an oscillation into a v mu* sl[] precession4 ,!re is1 h[ev]1 a great diff]5ce betwe5 ! e>? & ! gyro/at4 ,! =ces act+ on ! top are always ! same1 b ! =ces act+ on ! e>? are cont9ually alt]+4 ,at midw9t] & midsumm] ! tilt+ =ces are greate/1 & at ! equ9oxes 9 spr+ & autumn !re are no su* =ces4 ,s t ! precessional motion *anges its rate e qu>t] ye> f a maximum to no?+1 or f no?+ to a maximum4 ,x is1 h[ev]1 always 9 ! same direction--! direction oppos$ to ! e>?'s sp94 ,:5 we speak !n ( ! precessional motion ( ! e>?1 we usually ?9k ( ! mean or av]age motion1 s9ce ! motion gets quick] & sl[] e qu>t] ye>4 ,fur!r1 ! moon is l ! sun 9 its action4 ,x tries to tilt ! equatorial "p ( ! e>? into ! plane ( ! moon's orbit4 ,! plane ( ! moon's orbit is ne>ly ! same z t ( ! ecliptic1 & h5ce ! av]age precession ( ! e>? is ( mu* ! same k9d z if only "o ( ! two1 ! moon or ! sun1 alone act$4 ,t is1 ! g5]al ph5om5on ( precession ( ! #hf e>?'s axis 9 a conical pa? 9 #bf1jjj ye>s is ! effect ( ! comb9$ tilt+ actions ( ! sun & moon4 ,y w obs]ve "h an in/ance ( ! sort ( untru? :i* x is almo/ imp]ative to tell 9 expla9+ natural ph5om5a4 ,hi!rto ,i _h spok5 only ( ! sun z produc+ precession ( ! e>?4 ,?is 0 conv5i5t1 because ! plane ( ! ecliptic makes always almo/ exactly #bc-a_/b;deg ) ! e>?'s equator1 & al?\gh on ! :ole ! moon's action is ne>ly id5tical ) t ( ! sun1 & ab\t twice z great1 yet x v>ies consid]ably4 ,! sup]ior tilt+ action ( ! moon1 j l its tide-produc+ action1 is due to its be+ s mu* ne>] u ?an ! sun1 & exi/s 9 spite ( ! v small mass ( ! moon z comp>$ ) t ( ! sun4 ,z ! ecliptic makes an angle ( #bc-a_/b;deg ) ! e>?'s equator1 & ! moon's orbit makes an angle #e-a_/b;deg ) ! ecliptic1 we see t ! moon's orbit sometimes makes an angle ( #bi;deg ) ! e>?'s equator1 & sometimes only #ah;deg1 *ang+ f #bi;deg to #ah;deg1 & back to #bi;deg aga9 9 ab\t n9ete5 ye>s4 ,?is causes :at is call$ ,nutation1 or ! nodd+ ( ! e>?1 = ! tilt+ action due to ! sun is greatly help$ & greatly modifi$ by x4 ,! result ( ! v>iable nature ( ! moon's action is !n t ! e>?'s axis #hg rotates 9 an elliptic conical pa? r\nd :at might be call$ its mean position4 ,we h also to rememb] t twice 9 e lun> mon? ! moon's tilt+ action on ! e>? is great]1 & twice x is z]o1 & t x cont9ually v>ies 9 value4 ,on ! :ole1 !n1 ! moon & sun1 & to a small ext5t ! planets1 produce ! g5]al effect ( a precession1 :i* repeats itself 9 a p]iod ( ab\t #be1fie ye>s4 ,x is n p]fectly uni=m1 be+ p]=m$ at a spe$ :i* is a maximum 9 summ] & w9t]2 t is1 !re is a *ange ( spe$ ^: p]iod is half a ye>2 & !re is a *ange ( spe$ ^: p]iod is half a lun> mon?1 ! precession be+ quick] to-night ?an x w be next ,saturday1 :5 x w increase = ab\t ano!r week1 & dim9i% ! next4 ,besides ?is1 because ( #e-a_/b;deg ( angul>ity ( ! orbits1 we h some?+ l ! nodd+ ( our precess+ gyro/at1 & ! incl9ation ( ! e>?'s axis to ! ecliptic is n con/ant at #bc-a_/b;deg1 b is *ang+1 its p]iodic "t be+ n9ete5 ye>s4 ,reg>d+ ! e>?'s c5tre z fix$ at ,o we see !n1 z illu/rat$ 9 ?is model & 9 ,fig4 #dj1 ! axis ( ! e>? describes almo/ a p]fect circle on ! cele/ial sph]e once 9 #be1hff ye>s1 its spe$ fluctuat+ e half ye> & e half mon?4 ,b x is n a p]fect circle1 x is really a wavy #hh l9e1 !re be+ a complete wave e n9ete5 ye>s1 & !re are small] ripples 9 x1 correspond+ to ! half-ye>ly & =tnightly p]iods4 ,b ! v cause ( ! nutation1 ! n9ete5-ye>ly p]iod ( retrogression ( ! moon's nodes1 z x is call$1 is itself really produc$ z ! precession ( a gyro/at is produc$1 t is1 by tilt+ =ces act+ on a sp9n+ body4 ,illu/ration3 ,,fig4 #dj4 ,imag9e ! e>? to be /ation>y1 & ! sun & moon revolv+ r\nd x4 ,x 0 ,gauss :o f\nd t ! pres5t action is ! same z if ! masses ( ! moon & sun 7 di/ribut$ all #hi r\nd _! orbits4 ,= in/ance1 imag9e ! moon's mass di/ribut$ ov] h] orbit 9 ! =m ( a rigid r+ ( #dhj1jjj miles diamet]1 & imag9e less ( x to exi/ :]e ! pres5t spe$ is great]1 s t ! r+ w\ld be ?ick] at ! moon's apogee1 & ?9n] at ! p]igee4 ,su* a r+ r\nd ! e>? w\ld be simil> to ,saturn's r+s1 :i* h also a precession ( nodes1 only ,saturn's r+s are n rigid1 else !re w\ld be no equilibrium4 ,n[ if we leave out ( acc\nt ! e>? & imag9e ?is r+ to exi/ by itself1 & t its c5tre simply _h a motion r\nd ! sun 9 a ye>1 s9ce x makes an angle ( #e-a_/b;deg ) ! ecliptic x w\ld vibrate into ! ecliptic till x made ! same angle on ! o!r side & back aga94 ,b x revolves once ab\t its c5tre 9 tw5ty-sev5 sol> days1 eight h\rs1 & x w no long] sw+ l a %ip 9 a gr\nd-swell1 b w get a motion ( precession oppos$ 9 direction to its own revolution4 ,z ! r+'s motion is aga9/ ! h&s ( a wat*1 look+ f ! nor? d[n on ! ecliptic1 ?is retrogression ( ! moon's nodes is 9 ! direction ( ! h&s ( a wat*4 ,x is exactly ! same sort ( ph5om5on z ! precession ( ! equ9oxes1 only ) a mu* %ort] p]iod ( #fgih days in/ead ( #be1hff ye>s4 ,i told y h[1 if we knew ! moon's mass or ! sun's1 we c\ld tell ! am\nt ( ! =ces1 or #ij ! torque z x is m prop]ly call$1 ) :i* x tries to tilt ! e>?4 ,we "k ! rate at :i* ! e>? is sp9n+1 & we h obs]v$ ! precessional motion4 ,n[ :5 we foll[ up ! me?od :i* ,i h sket*$ already1 we f9d t ! precessional velocity ( a sp9n+ body ought to be equal to ! torque divid$ by ! sp9n+ velocity & by ! mom5t ( in]tia#g ( ! body ab\t ! pol> axis4 ,h5ce ! great] ! tilt+ =ces1 & ! less ! sp9 & ! less ! mom5t ( in]tia1 ! great] is ! precessional spe$4 ,giv5 all ( ^! elem5ts except "o1 x is easy to calculate t unkn[n elem5t4 ,usually :at we aim at 9 su* a calculation is ! det]m9ation ( ! moon's mass1 z ?is ph5om5on ( precession & ! action ( ! tides are ! only two natural ph5om5a :i* h z yet enabl$ ! moon's mass to be calculat$4 ,i d n mean to apologize to y = ! introduction ( su* t]ms z ,mom5t ( ,in]tia1 nor d ,i mean to expla9 !m4 ,9 ?is lecture ,i h avoid$1 z mu* z ,i c\ld1 ! introduction ( ma!matical expressions & ! use ( te*nical t]ms4 ,b ,i want y to #ia und]/& t ,i am n afraid to introduce te*nical t]ms :5 giv+ a popul> lecture4 ,if !re is any (f5ce 9 su* a practice1 x mu/1 9 my op9ion1 be greatly aggravat$ by ! addition ( explanations ( ! precise mean+s ( su* t]ms4 ,! use ( a correct te*nical t]m s]ves sev]al useful purposes4 ,fir/1 x gives "s satisfaction to ! lectur]1 z x enables him to /ate1 v concisely1 some?+ :i* satisfies 8 own weak incl9ation to h 8 reason+ complete1 b :i* he luckily has n "t to tr\ble 8 audi5ce )4 ,second1 x corrects ! univ]sal belief ( all popul> audi5ces t !y "k ev]y?+ n[ t c be said on ! subject4 ,?ird1 x tea*es ev]ybody1 includ+ ! lectur]1 t !re is no?+ lo/ & (t5 a great deal ga9$ by ! adoption ( a casual me?od ( skipp+ :5 "o is work+ up a new subject4 ,"s ye>s ago x 0 argu$ t if ! e>? 7 a %ell fill$ ) liquid1 if ?is liquid 7 q frictionless1 !n ! mom5t ( in]tia ( ! %ell is all t we %\ld h to take into acc\nt 9 consid]+ precession1 & t if x 7 visc\s ! precession w\ld v soon disappe> altoge!r4 ,to illu/rate ! effect ( ! mom5t ( in]tia1 ,i h hung up "h a numb] ( glasses--"o a fill$ ) s&1 ano!r b ) treacle1 a ?ird c ) oil1 ! f\r? d ) wat]1 #ib ,illu/ration3 ,,fig4 #da4 #ic & ! fif? e is empty 7,fig4 #da74 ,y see t if ,i twi/ ^! susp5d+ wires & release !m1 a vibratory motion is set up1 j l t ( ! balance ( a wat*4 ,obs]ve t ! glass ) wat] vibrates quickly1 its effective mom5t ( in]tia be+ m]ely t ( ! glass itself1 & y see t ! "t ( sw+ is pretty mu* ! same z t ( ! empty glass2 t is1 ! wat] does n seem to move ) ! glass4 ,obs]ve t ! vibration goes on = a fairly long "t4 ,! glass ) s& vibrates sl[ly2 "h !re is great mom5t ( in]tia1 z ! s& & glass behave l "o rigid body1 & aga9 ! vibration goes on = a long "t4 ,9 ! oil & treacle1 h[ev]1 !re are long] p]iods ( vibration ?an 9 ! case ( ! wat] or empty glass1 & less ?an w\ld be ! case if ! vibrat+ bodies 7 all rigid1 b ! vibrations are /ill$ m rapidly because ( friction4 ,boil$ 7f7 & unboil$ 7g7 eggs susp5d$ f wires 9 ! same way w exhibit ! same diff]5ces 9 ! behavi\r ( bodies1 "o ( :i* is rigid & ! o!r liquid inside2 y see h[ mu* sl[] an oscillation ! boil$ has ?an ! unboil$4 ,ev5 on ! table "h x is easy to %[ ! diff]5ce betwe5 boil$ & unboil$ eggs4 #id ,roll !m bo?2 y see t "o ( !m /ops mu* soon] ?an ! o!r2 x is ! unboil$ "o t /ops soon]1 because ( its int]nal friction4 ,i mu/ ask y to obs]ve c>efully ! foll[+ v di/9ctive te/ ( :e!r an egg is boil$ or n4 ,i roll ! egg or sp9 x1 & !n place my f+] on x j = an in/ant2 long en\gh to /op ! motion ( ! %ell4 ,y see t ! boil$ egg _h q f9i%$ its motion1 b ! unboil$ egg's %ell alone 0 /opp$2 ! liquid inside goes on mov+1 & n[ r5ews ! motion ( ! %ell :5 ,i take my f+] away4 ,x 0 argu$ t if ! e>? 7 fluid inside1 ! effective mom5t ( in]tia ( ! %ell be+ comp>atively small1 & hav+1 z we see 9 ^! examples1 no?+ :atev] to d ) ! mom5t ( in]tia ( ! liquid1 ! precessional motion ( ! e>? ought to be enorm\sly quick] ?an x is4 ,?is 0 us$ z an argum5t aga9/ ! idea ( ! e>?'s be+ fluid inside4 ,we "k t ! obs]v$ half-ye>ly & half-mon?ly *anges ( ! precession ( ! e>? w\ld be mu* great] ?an !y are if ! e>? 7 a rigid %ell conta9+ mu* liquid1 & if ! %ell 7 n ne>ly inf9itely rigid ! ph5om5a ( ! tides w\ld n occur1 b 9 reg>d to ! g5]al precession ( ! e>? !re is n[ #ie no d\bt t ! old l9e ( argum5t 0 wrong4 ,ev5 if ! e>? 7 liquid inside1 x sp9s s rapidly t x w\ld behave l a rigid body 9 reg>d to su* a sl[ ph5om5on z precession ( ! equ9oxes4 ,9 fact1 9 ! old] l9e ( argum5t ! important fact 0 lo/ sight (1 t rapid rotation c give to ev5 liquids a quasi-rigidity4 ,n[ "h 7,fig4 #db a7 is a holl[ brass top fill$ ) wat]4 ,! frame is light1 & ! wat] inside has mu* m mass ?an ! outside frame1 & if y te/ ?is c>efully y w f9d t ! top sp9s 9 almo/ exactly ! same way z if ! wat] 7 q rigid2 9 fact1 z if ! :ole top 7 rigid4 ,"h y see x sp9n+ & precess+ j l any rigid top4 ,?is top1 ,i "k1 is n fill$ ) wat]1 x is only p>tially fill$2 b :e!r p>tially or :olly fill$ x sp9s v mu* l a rigid top4 ,illu/ration3 ,,fig4 #db4 #if ,?is is n ! case ) a long holl[ brass top ) wat] inside4 ,i told y t all bodies h "o axis ab\t :i* !y pref] to rotate4 ,! outside metal "p ( a top behaves 9 a way t is n[ well kn[n to y2 ! friction ( its peg on ! table compels x to get up on its long] axis4 ,b ! fluid inside a top is n con/ra9$ to sp9 on its long] axis ( figure1 & z x pref]s its %ort] axis l all ^! bodies ,i %[$ y1 x sp9s 9 its own way1 & by friction & pressure aga9/ ! case con/ra9s ! case to sp9 ab\t ! %ort] axis1 annull+ completely ! t5d5cy ( ! outside "p to rise or keep up on its long axis4 ,h5ce x is f\nd to be simply impossible to sp9 a long holl[ top :5 fill$ ) wat]4 ,illu/ration3 ,,fig4 #dc4 ,illu/ration3 ,,fig4 #dd4 ,"h1 = example1 is "o 7,fig4 #db b7 t only diff]s f ! la/ 9 be+ long]4 ,x is fill$1 or p>tially fill$1 ) wat]1 & y obs]ve t if #ig ,i sl[ly get up a great sp9 :5 x is m\nt$ 9 ?is frame1 & ,i let x out on ! table z ,i did ! o!r "o1 ?is "o lies d[n at once & refuses to sp9 on its peg4 ,?is diff]5ce ( behavi\r is mo/ rem>kable 9 ! two holl[ tops y see be=e y 7,fig4 #dc74 ,!y are bo? ne>ly sph]ical1 bo? fill$ ) wat]4 ,!y look s ne>ly alike t few p]sons among ! audi5ce are able to detect any diff]5ce 9 _! %ape4 ,b "o ( !m 7a7 is really slightly oblate l an orange1 & ! o!r 7b7 is slightly prolate l a lemon4 ,i w give !m bo? a gradually increas+ rotation 9 ?is frame #ih 7,fig4 #dd7 = a "t suffici5t to insure ! rotation ( ! wat] inside4 ,:5 j ab\t to be set free to move l ord9>y tops on ! table1 wat] & brass are mov+ l ! p>ts ( a rigid top4 ,y see t ! orange-%ap$ "o cont9ues to sp9 & precess1 & gets itself upright :5 di/urb$1 l an ord9>y rigid top2 inde$ ,i h seldom se5 a bett] behav$ top2 :]eas ! lemon-%ap$ "o lies d[n on its side at once1 & quickly ceases to move 9 any way4 ,illu/ration3 ,,fig4 #de4 ,& n[ y w be able to appreciate a f\r? te/ ( a boil$ egg1 :i* is mu* m easily se5 by a l>ge audi5ce ?an ! la/4 ,"h is ! unboil$ "o 7,fig4 #de b74 ,i try my be/ to sp9 x z x lies on ! table1 b y see t ,i _c give x mu* sp91 & s !re is no?+ ( any importance to look at4 ,b y obs]ve t x is q easy to sp9 ! boil$ #ii egg1 & t = reasons n[ well kn[n to y x behaves l ! /ones t ,?omson spun on ! sea-bea*2 x gets up on its long] axis1 a v pretty object = our educat$ eyes to look at 7,fig4 #de a74 ,y are all aw>e1 f ! behavi\r ( ! lemon-%ap$ top1 t ev5 if1 by ! use ( a :irl+ table sudd5ly /opp$1 or by any o!r contrivance1 ,i c\ld get up a sp9 9 ?is unboil$ egg1 x w\ld nev] make ! slighte/ ef=t to rise on its end & sp9 ab\t its long] axis4 ,i hope y don't ?9k t ,i h be5 speak+ too long ab\t a/ronomical matt]s1 = !re is "o o!r important ?+ connect$ ) a/ronomy t ,i mu/ speak (4 ,y see1 ,i h _h almo/ no?+ practically to d ) a/ronomy1 & h5ce ,i h a /rong int]e/ 9 ! subject4 ,x is v curi\s1 b q true1 t m5 practically engag$ 9 any pursuit are almo/ unable to see ! romance ( x4 ,?is is :at ! imag9ative outsid] sees4 ,b ! ov]work$ a/ronom] has a diff]5t po9t ( view4 ,z soon z x becomes "o's duty to d a ?+1 & x is "p ( "o's e-day "w1 ! ?+ loses a great deal ( its int]e/4 ,we h be5 told by a great ,am]ican philosoph] t ! only coa*m5 :o ev] saw ! romance ( coa*-driv+ are ^? titl$ individuals :o pay n[adays s l>gely = ! #ajj privilege4 ,9 almo/ any bran* ( eng9e]+ y w f9d t if any inv5tion is made x is made by an outsid]2 by "s "o :o comes to ! /udy ( ! subject ) a fre% m9d4 ,:o ev] he>d ( an old inhabitant ( ,japan or ,p]u writ+ an int]e/+ book ab\t ^? c\ntries8 ,at ! end ( two ye>s' resid5ce he sees only ! mo/ famili> ?+s :5 he takes 8 walks abroad1 & he feels unmitigat$ contempt = ! +5u\s globe-trott] :o writes a book ab\t ! c\ntry aft] a mon?'s travel ov] ! mo/ beat5 tracks 9 x4 ,n[ ! exp]i5c$ a/ronom] has =gott5 ! difficulties ( 8 pr$ecessors & ! d\bts ( outsid]s4 ,x is a long "t s9ce he felt t awe 9 gaz+ at a />ry sky t we outsid]s feel :5 we le>n ( ! sizes & di/ances ap>t ( ! ho/s ( heav54 ,he speaks q coolly ( millions ( ye>s1 & is ne>ly z call\s :5 he ref]s to ! anci5t hi/ory ( humanity on our planet z a wea!r-beat5 geologi/4 ,! reason is obvi\s4 ,mo/ ( y "k t ! ,nautical ,almanac is z a lit]>y production "o ( ! mo/ un9t]e/+ works ( ref]5ce 9 exi/5ce4 ,x is ev5 m disconnect$ ?an a diction>y1 & ,i %\ld ?9k t prep>+ c5sus-tables mu/ be ev] s mu* m romantic z an occupation ?an prep>+ ! tables ( ! ,nautical ,almanac4 ,& yet #aja a p>ticul> figure1 "o ( millions set d[n by an ov]work$ calculator1 may h all ! tragic importance ( life or dea? to ! crew & pass5g]s ( a %ip1 :5 x is head+ = safety or head+ = ! rocks "u ! m&ate ( t s+le pr9t$ "*4 ,b ?is may n be a fair sort ( criticism4 ,i s seldom deal ) a/ronomical matt]s1 ,i "k s little ( ! we> & te> & monotony ( ! e-day life ( ! a/ronom]1 t ,i d n ev5 "k t ! above facts are specially true ab\t a/ronom]s4 ,i only "k t !y are v likely to be true because !y are true ( o!r pr(essional m54 ,i am happy to say t ,i come 9 contact ) all sorts & conditions ( m51 & among o!rs1 ) "s m5 :o d5y _m ( ! ?+s taught 9 our e>lie/ s*ool-books4 ,= example1 t ! e>? is r\nd1 or t ! e>? revolves1 or t ,fr5*m5 speak a language diff]5t f ours4 ,n[ no man :o has be5 to sea w d5y ! r\ndness ( ! e>?1 h[ev] greatly he may wond] at x2 & no man :o has be5 to ,france w d5y t ! ,fr5* language is diff]5t f ours2 b _m m5 :o le>nt ab\t ! rotation ( ! e>? 9 _! s*ool-days1 & h _h a pl5tiful opportunity ( obs]v+ ! heav5ly bodies1 d5y ! rotation ( ! e>?4 #ajb ,!y tell y t ! />s & moon are revolv+ ab\t ! e>?1 = !y see !m revolv+ night aft] night1 & ! sun revolves ab\t ! e>?1 = !y see x d s e day4 ,& really if y ?9k ( x1 x is n s easy to prove ! revolution ( ! e>?4 ,by ! help ( good telescopes & ! electric telegraph or good *ronomet]s1 x is easy to %[ f ! want ( p>allax 9 />s t !y mu/ be v f> away2 b aft] all1 we only "k t ei!r ! e>? revolves or else ! sky revolves4#h ,( c\rse1 x seems inf9itely m likely t ! small e>? %\ld revolve ?an t ! :ole heav5ly ho/ %\ld turn ab\t ! e>? z a c5tre1 & inf9ite likelihood is really absolute pro(4 ,yet !re is nobody :o does n welcome an indep5d5t k9d ( pro(4 ,! ph5om5a ( ! tides1 & ne>ly e new a/ronomical fact1 may be said to be an addition to ! pro(4 ,/ill !re is ! abs5ce ( p]fect c]ta9ty1 & :5 we are told t ^! sp9n+-top ph5om5a give u a real pro( ( ! rotation ( ! e>? )\t our leav+ ! room1 we welcome #ajc x1 ev5 al?\gh we may sne] at x z unnecess>y aft] we h obta9$ x4 ,illu/ration3 ,,fig4 #ag4 ,y "k t a gyro/at susp5d$ ) p]fect fre$om ab\t axes1 :i* all pass ?r\gh its c5tre ( gravity1 ma9ta9s a con/ant direction 9 space h[ev] its support may be c>ri$4 ,its axis is n =c$ to alt] its direction 9 any way4 ,n[ ?is gyro/at 7,fig4 #ag7 has n ! p]fect abs5ce ( friction at its axes ( :i* ,i speak1 & ev5 ! slighte/ friction w produce "s con/ra9t :i* is injuri\s to ! exp]im5t ,i am ab\t to describe4 ,x mu/ be rememb]$1 t if !re 7 absolutely no con/ra9t1 !n1 ev5 if ! #ajd gyro/at 7 n sp9n+1 its axis w\ld keep a con/ant direction 9 space4 ,b ! sp9n+ gyro/at %[s its sup]iority 9 ?is1 t any con/ra9t due to friction is less p[]ful 9 alt]+ ! axis4 ,! great] ! sp91 !n1 ! bett] able are we to disreg>d effects due to friction4 ,y h se5 = y\rselves ! effect ( c>ry+ ?is gyro/at ab\t 9 all sorts ( ways--fir/1 :5 x is n sp9n+ & friction causes q a l>ge dep>ture f con/ancy ( direction ( ! axis2 second1 :5 x is sp9n+1 & y see t al?\gh !re is n[ ! same friction z be=e1 & ,i try to di/urb ! in/rum5t m ?an be=e1 ! axis rema9s s5sibly p>allel to itself all ! "t4 ,n[ :5 ?is in/rum5t is support$ by ! table x is really be+ c>ri$ r\nd by ! e>? 9 its daily rotation4 ,if ! axis kept its direction p]fectly1 & x 7 n[ po9t+ horizontally due ea/1 six h\rs aft] ?is x w po9t t[>ds ! nor?1 b incl9+ d[nw>ds1 six h\rs aft]w>ds x w po9t due we/ horizontally1 & aft] "o revolution ( ! e>? x w aga9 po9t z x does n[4 ,suppose ,i try ! exp]im5t1 & ,i see t x po9ts due ea/ n[ 9 ?is room1 & aft] a "t x po9ts due we/1 & yet ,i "k t ! gyro/at is con/antly po9t+ 9 ! same direction 9 space all ! "t1 surely x is obvi\s t ! room mu/ #aje be turn+ r\nd 9 space4 ,suppose x po9ts to ! pole /> n[1 9 six h\rs1 or twelve1 or eighte51 or tw5ty-f\r1 x w /ill po9t to ! pole />4 ,n[ x is n easy to obta9 s frictionless a gyro/at t x w ma9ta9 a good sp9 = su* a l5g? ( "t z w enable ! rotation ( ! room to be made visible to an audi5ce4 ,b ,i w describe to y h[ =ty ye>s ago x 0 prov$ 9 a laboratory t ! e>? turns on its axis4 ,?is exp]im5t is usually connect$ ) ! "n ( ,f\cault1 ! same philosoph] :o ) ,fizeau %[$ h[ 9 a laboratory we c measure ! velocity ( light1 & !re=e measure ! di/ance ( ! sun4 ,x 0 sugge/$ by ,mr4 ,lang ( ,ed9burgh 9 #ahcf1 al?\gh only c>ri$ out 9 #aheb by ,f\cault4 ,by ^! exp]im5ts1 if y 7 plac$ on a body f :i* y c\ld see no />s or o!r outside objects1 say t y 7 liv+ 9 und]gr\nd regions1 y c\ld discov]--fir/1 :e!r !re is a motion ( rotation1 & ! am\nt ( x2 second1 ! m]idian l9e or ! direction ( ! true nor?2 ?ird1 y\r latitude4 ,obta9 a gyro/at l ?is 7,fig4 #df7 b mu* l>g]1 & f> m frictionlessly susp5d$1 s t x is free to move v]tically or horizontally4 ,= ! v]tical motion y\r gymbal pivots ought to be h>d /eel knife-edges4 #ajf ,illu/ration3 ,,fig4 #df4 ,z = ! horizontal fre$om1 ,f\cault us$ a f9e /eel wire4 ,let !re be a f9e scale engrav$ crosswise on ! out] gymbal r+1 & try to discov] if x moves horizontally by means ( a microscope ) cross wires4 ,:5 ?is is c>efully done we f9d t !re is a motion1 #ajg b ?is is n ! motion ( ! gyro/at1 x is ! motion ( ! microscope4 ,9 fact1 ! microscope & all o!r objects 9 ! room are go+ r\nd ! gyro/at frame4 ,n[ let u consid] :at occurs4 ,! room is rotat+ ab\t ! e>?'s axis1 & we "k ! rate ( rotation2 b we only want to "k = our pres5t purpose h[ mu* ( ! total rotation is ab\t a v]tical l9e 9 ! room4 ,if ! room 7 at ! ,nor? ,pole1 ! :ole rotation w\ld be ab\t ! v]tical l9e4 ,if ! room 7 at ! equator1 none ( its rotation w\ld be ab\t a v]tical l9e4 ,9 our latitude n[1 ! horizontal rate ( rotation ab\t a v]tical axis is ab\t f\r-fif?s ( ! :ole rate ( rotation ( ! e>? on its axis1 & ?is is ! am\nt t w\ld be measur$ by our microscope4 ,?is exp]im5t w\ld give no result at a place on ! equator1 b 9 our latitude y w\ld h a laboratory pro( ( ! rotation ( ! e>?4 ,f\cault made ! measurem5ts ) great accuracy4 ,if y n[ clamp ! frame1 & all[ ! sp9n+ axis to h no motion except 9 a horizontal plane1 ! motion :i* ! e>? t5ds to give x ab\t a v]tical axis _c n[ affect ! gyro/at1 b ! e>? con/ra9s x to move ab\t an axis due nor? & s\?1 & consequ5tly ! sp9n+ axis tries to put itself p>allel #ajh to ! nor? & s\? direction 7,fig4 #dg74 ,h5ce ) su* an in/rum5t x is easy to f9d ! true nor?4 ,if !re 7 absolutely no friction ! in/rum5t w\ld vibrate ab\t ! true nor? position l ! compass ne$le 7,fig4 #ej71 al?\gh ) an exce$+ly sl[ sw+4 ,illu/ration3 ,,fig4 #dg4 ,x is ) a curi\s mixture ( feel+s t "o fir/ recognizes ! fact t all rotat+ bodies1 fly-:eels ( /eam-eng9es & ! l1 are always t5d+ to turn !mselves t[>ds ! pole />2 g5tly & va9ly tugg+ at _! f\ndations #aji to get r\nd t[>ds ! object ( _! adoration all ! "t !y are 9 motion4 ,illu/ration3 ,,fig4 #dh4 ,n[ we h f\nd ! m]idian z 9 ,fig4 #dg1 we c beg9 a ?ird exp]im5t4 ,prev5t motion horizontally1 t is1 ab\t a v]tical axis1 b give ! in/rum5t fre$om to move v]tically 9 ! m]idian1 l a transit in/rum5t 9 an obs]vatory #aaj ab\t its horizontal axis4 ,its revolution ) ! e>? w t5d to make x *ange its angul> position1 & !re=e x places itself p>allel to ! e>?'s axis2 :5 9 ?is position ! daily rotation no long] causes any *ange 9 its direction 9 space1 s x cont9ues to po9t to ! pole /> 7,fig4 #dh74 ,x w\ld be an int]e/+ exp]im5t to measure ) a delicate *emical balance ! =ce ) :i* ! axis raises itself1 & 9 ?is way weigh ! rotational motion ( ! e>?4#i ,n[ let u turn ! frame ( ! in/rum5t ,g ,b r\nd a "r angle1 s t ! sp9n+ axis c only move 9 a plane at "r angles to ! m]idian2 obvi\sly x is con/ra9$ by ! v]tical compon5t ( ! e>?'s rotation1 & po9ts v]tically d[nw>ds4 ,illu/ration3 ,,fig4 #di4 ,illu/ration3 ,,fig4 #ej4 ,?is la/ z well z ! o!r ph5om5a ( :i* ,i h spok5 is v sugge/ive4 ,"h is a magnetic ne$le 7,fig4 #di71 sometimes call$ a dipp+ ne$le f ! way 9 :i* x is susp5d$4 ,if ,i turn its #aaa frame s t x c only move at "r angles to ! m]idian1 y see t x po9ts v]tically4 ,y may reflect ^u ! analog\s prop]ties ( ?is magnetic ne$le 7,fig4 #ej7 & ( ! gyro/at 7,fig4 #dg72 !y bo?1 :5 only capable ( mov+ horizontally1 po9t to ! nor?2 & y see t a v frictionless gyro/at might be us$ z a compass1 or at all ev5ts z a corrector ( compasses4#aj ,i h j put be=e y ano!r analogy1 & ,i want y to und]/& t1 al?\gh ^! are only analogies1 !y are n m]e *ance analogies1 = !re is und\bt$ly a dynamical connection betwe5 ! magnetic & ! gyro/atic ph5om5a4 ,magnetism dep5ds on rotatory motion4 ,! molecules ( matt] are 9 actual rotation1 & a c]ta9 all9eation ( ! axes ( ! rotations produces :at we call magnetism4 ,9 a /eel b> n magnetiz$ ! little axes ( rotation are all 9 diff]5t directions4 ,! process #aab ( magnetization is simply br++ ^! rotations to be m or less r\nd p>allel axes1 an all9eation ( ! axes4 ,a honey-comb$ mass ) a sp9n+ gyro/at 9 e cell1 ) all ! sp9n+ axes p>allel1 & ! sp9s 9 ! same direction1 w\ld--,i 0 ab\t to say1 w\ld be a magnet1 b x w\ld n be a magnet 9 all its prop]ties1 & yet x w\ld resemble a magnet 9 _m ways4#aa ,illu/ration3 ,,fig4 #ea4 ,illu/ration3 ,,fig4 #eb4 ,"s ( y1 see+ electromotors & o!r electric contrivances ne> ?is table1 may ?9k t !y h to d ) our !ories & explanations ( magnetic ph5om5a4 ,b ,i mu/ expla9 t ?is electromotor :i* ,i hold 9 my h& 7,fig4 #ea7 is us$ by me m]ely z ! #aac mo/ conv5i5t means ,i c\ld f9d = ! sp9n+ ( my tops & gyro/ats4 ,on ! sp9dle ( ! motor is fa/5$ a circul> piece ( wood2 by t\*+ ?is key ,i c supply ! motor ) electric en]gy1 & ! wood5 disc is n[ rotat+ v rapidly4 ,i h only to br+ its rim 9 contact ) any ( ^! tops or gyro/ats to set !m sp9n+1 & y see t ,i c set half a doz5 gyro/ats a-sp9n+ 9 a few seconds2 ?is *a9 ( gyro/ats1 = in/ance4 ,aga91 ?is l>g] motor 7,fig4 #eb71 too l>ge to move ab\t 9 my h&1 is fa/5$ to ! table1 & ,i h us$ #aad x to drive my l>g] contrivances2 b y und]/& t ,i use ^! j z a b>b] might use !m to bru% y\r hair1 or ,s>ah ,jane to clean ! knives1 or j z ,i w\ld use a little /eam-eng9e if x 7 m conv5i5t = my purpose4 ,x 0 m conv5i5t = me to br+ f ,london ?is batt]y ( accumulators & ^! motors ?an to br+ sacks ( coals1 & boil]s1 & /eam-eng9es4 ,b1 inde$1 all ?is has ! deep] mean+ t we c give to x if we l4 ,love is z old z ! hills1 & e day ,love's messages are c>ri$ by ! late/ s]vant ( man1 ! telegraph4 ,^! sp9n+ tops 7 kn[n probably to primeval man1 & yet we h n le>nt f !m m ?an ! mo/ fractional portion ( ! lesson t !y are always s5d+ out to an unobs]vant _w4 ,toys l ^! 7 spun probably by ! build]s ( ! ,pyramids :5 !y 7 boys1 & "h y see !m side by side ) ! v late/ ( man's contrivances4 ,i feel almo/ z ,mr4 ,/anley might feel if1 ) ! help ( ! electric light & a magic-lant]n1 he describ$ 8 exp]i5ces 9 t dreadful ,african =e/ to ! usual company ( a ,london draw+-room4 ,! ph5om5a ,i h be5 describ+ to y play su* a v important "p 9 nature1 t if "t admitt$ ,i might g on exp\nd+ & #aae expla9+ )\t f9d+ any great reason to /op at "o place r ?an ano!r4 ,! "t at my disposal all[s me to ref] to only "o o!r matt]1 namely1 ! connection betwe5 light & magnetism & ! behavi\r ( sp9n+ tops4 ,y are all aw>e t s\nd takes "t to travel4 ,?is is a matt] ( common obs]vation1 z "o c see a di/ant wood*opp] lift 8 axe aga9 be=e "o he>s ! s\nd ( 8 la/ /roke4 ,a de/ructive sea wave is produc$ on ! coa/ ( ,japan _m h\rs aft] an e>?quake occurs (f ! coa/ ( ,am]ica1 ! wave motion hav+ tak5 "t to travel across ! ,pacific4 ,b al?\gh light travels m quickly ?an s\nd or wave motion 9 ! sea1 x does n travel ) inf9ite rapidity1 & ! appe>ance ( ! eclipse ( "o ( ,jupit]'s satellites is delay$ by an obs]vable numb] ( m9utes because light takes "t to travel4 ,! velocity has be5 measur$ by means ( su* obs]vations1 & we "k t light travels at ! rate ( ab\t #ahg1jjj miles p] second1 or ?irty ?\s& millions ( c5timetres p] second4 ,!re is no d\bt ab\t ?is figure be+ ne>ly correct1 = ! velocity ( light has be5 measur$ 9 ! laboratory by a p]fectly indep5d5t me?od4 ,n[ ! mo/ int]e/+ physical "w done s9ce ,newton's "t is ! outcome ( ! exp]im5ts ( ,f>aday & ! !oretical d$uctions ( #aaf ,?omson & ,maxwell4 ,x is ! !ory t light & radiant heat are simply electro-magnetic di/urbances propagat$ ?r\gh space4 ,i d>e n d m ?an j ref] to ?is matt]1 al?\gh x is ( enorm\s importance4 ,i c only say1 t ( all ! obs]v$ facts 9 ! sci5ces ( light1 electricity1 & magnetism1 we "k ( none t is 9 opposition to ,maxwell's !ory1 & we "k ( _m t support x4 ,! greate/ & e>lie/ support t x _h 0 ?is4 ,if ! !ory is correct1 !n a c]ta9 electro-magnetic measurem5t ought to result 9 exactly ! same quantity z ! velocity ( light4 ,n[ ,i want y to und]/& t ! electric measurem5t is "o ( quantities t seem to h no?+ :atev] to d ) light1 except t "o uses "o's eyes 9 mak+ ! measurem5t2 x requires ! use ( a two-foot rule & a magnetic ne$le1 & coils ( wire & curr5ts ( electricity4 ,x seem$ to be> a relation%ip to ! velocity ( light1 :i* 0 n v unlike ! fabl$ connection betwe5 ,t5t]d5 ,/eeple & ! ,goodw9 ,s&s4 ,x is a measurem5t :i* x is v difficult to make accurately4 ,a numb] ( skilful exp]im5t]s1 work+ indep5d5tly1 & us+ q diff]5t me?ods1 arriv$ at results only "o ( :i* is z mu* z five p] c5t4 diff]5t f ! obs]v$ velocity ( light1 & "s ( !m1 #aag on :i* ! be/ dep5d5ce may be plac$1 agree exactly ) ! av]age value ( ! measurem5ts ( ! velocity ( light4 ,!re is !n a wond]ful agreem5t ( ! two measurem5ts1 b )\t m explanation ?an ,i c give y n[1 y _c p]haps und]/& ! importance ( ?is agreem5t betwe5 two seem+ly unconnect$ magnitudes4 ,at all ev5ts we n[ "k1 f ! "w ( ,pr(essor ,h]tz 9 ! la/ two ye>s1 t ,maxwell's !ory is correct1 & t light is an electro-magnetic di/urbance2 & :at is m1 we "k t electro-magnetic di/urbances1 incomp>ably sl[] ?an r$-light or heat1 are pass+ n[ ?r\gh our bodies2 t ?is n[ recogniz$ k9d ( radiation may be reflect$ & refract$1 & yet w pass ?r\gh brick & /one walls & foggy atmosph]es :]e light _c pass1 & t possibly all milit>y & m>9e & ligh?\se signall+ may be conduct$ 9 ! future ?r\gh ! ag5cy ( ?is new & wond]ful k9d ( radiation1 ( :i* :at we call light is m]ely "o =m4 ,:y at ?is mom5t1 = all ,i "k1 two citiz5s ( ,le$s may be signall+ to ea* o!r 9 ?is way ?r\gh half a mile ( h\ses1 includ+ ?is hall 9 :i* we are pres5t4#ab #aah ,i m5tion ?is1 ! greate/ mod]n philosophical discov]y1 because ! g]m ( x1 :i* 0 publi%$ by ,?omson 9 #ahef1 makes direct ref]5ce to ! analogy betwe5 ! behavi\r ( our sp9n+-tops & magnetic & electrical ph5om5a4 ,x w be easi]1 h[ev]1 = u to consid] "h a me*anical illu/ration ( ! rotation ( ! plane ( pol>iz$ light by magnetism :i* ,?omson elaborat$ 9 #ahgd4 ,?is ph5om5on may1 ,i ?9k1 be reg>d$ z ! mo/ important ( all ,f>aday's discov]ies4 ,x 0 ( enorm\s sci5tific importance1 because x 0 made 9 a direction :]e a new ph5om5on 0 n ev5 suspect$4 ,( 8 discov]y ( induc$ curr5ts ( electricity1 to :i* all electric-light+ companies & transmission ( p[] companies ( ! pres5t day owe _! be+1 ,f>aday himself said t x 0 a natural consequ5ce ( ! discov]ies ( an e>li] exp]im5t]1 ,o]/$4 ,b ?is magneto-optic discov]y 0 q unexpect$4 ,i w n[ describe ! ph5om5on4 ,"s ( y are aw>e t :5 a beam ( light is s5t ?r\gh ?is implem5t1 call$ a ,ni*ol's ,prism1 x becomes pol>iz$1 or "o-sid$--t is1 all ! light t comes ?r\gh is kn[n to be propagat$ by vibrations :i* occur all 9 "o plane4 ,?is rope 7,fig4 #ec7 hang+ f ! ceil+ #aai illu/rates ! nature ( plane pol>iz$ light4 ,all po9ts 9 ! rope are vibrat+ 9 ! same plane4 ,well1 ?is prism ,a1 ,fig4 #ed1 only lets ?r\gh x light t is pol>iz$ 9 a v]tical plane4 ,& "h at ,b ,i h a simil> implem5t1 & ,i place x s t x also w only all[ light to pass ?r\gh x :i* is pol>iz$ 9 a v]tical plane4 ,h5ce mo/ ( ! light com+ ?r\gh ! pol>iz]1 z ! fir/ prism is call$1 w pass readily ?r\gh ! analyz]1 z ! second is call$1 & ,i am n[ lett+ ?is light ent] my eye4 ,b :5 ,i turn ! analyz] r\nd ?r\gh a "r angle1 ,i f9d t ,i see no light2 !re 0 a gradual d>k5+ z ,i rotat$ ! analyz]4 ,! analyz] w n[ only all[ light to pass ?r\gh :i* is pol>iz$ 9 a horizontal plane1 & x receives no su* light4 ,illu/ration3 ,,fig4 #ec4 ,illu/ration3 ,,fig4 #ed4 ,y w see 9 ?is model 7,fig4 #ee7 a good illu/ration ( pol>iz$ light4 ,! :ite1 brilliantly illum9at$ ?read ,m ,n is #abj pull$ by a weight beyond ! pulley ,m1 & its end ,n is fa/5$ to "o limb ( a tun+-=k4 ,"s ragg$-look+ pieces ( ?read r\nd ! portion ,n ,a prev5t its vibrat+ 9 any v det]m9ate way1 b f ,a to ,m ! ?read is free f all encumbrance4 ,a v]tical slot at ,a1 ?r\gh :i* ! ?read passes1 det]m9es ! nature ( ! vibration ( ! "p ,a ,b2 e "p ( ! ?read betwe5 ,a & ,b is vibrat+ 9 up & d[n directions only4 ,a v]tical slot 9 ,b all[s ! v]tical vibration to be communicat$ ?r\gh x1 & s we see ! "p ,b ,m vibrat+ 9 ! same way z ,a ,b4 ,i might po9t out q a lot ( ways 9 :i* ?is is n a p]fect illu/ration ( :at occurs ) light 9 ,fig4 #ed4 ,b x is q good en\gh = my pres5t purpose4 ,a is a pol>iz] ( vibration2 x only all[s up & d[n motion to pass ?r\gh x1 & ,b also all[s up & d[n motion to pass ?r\gh4 ,b n[1 z ,b is turn$ r\nd1 x lets less & less ( ! up & d[n motion pass ?r\gh x1 until :5 x is 9 ! second position %[n 9 ! l[] "p ( ! figure1 x all[s no up & d[n motion to pass ?r\gh1 & !re is no visible motion ( ! ?read betwe5 ,b & ,m4 ,y w obs]ve t if we did n "k 9 :at plane 79 ! pres5t case ! plane is v]tical7 ! vibrations ( ! ?read betwe5 ,a & ,b occurr$1 we %\ld only h to turn ,b r\nd until we f\nd no vibration #abb pass+ ?r\gh1 to obta9 ! in=mation4 ,h5ce1 z 9 ! light case1 we may call ,a a pol>iz] ( vibrations1 & ,b an analyz]4 ,illu/ration3 ,,fig4 #ee4 ,n[ if pol>iz$ light is pass+ f ,a to ,b 7,fig4 #ed7 ?r\gh ! air1 say1 & we h ! analyz] plac$ s t !re is d>kness1 we f9d t if we place 9 ! pa? ( ! ray "s solution ( sug> we %all no long] h d>kness at ,b2 we mu/ turn ,b r\nd to get ?+s d>k aga92 ?is is evid5ce ( ! sug> solution hav+ twi/$ r\nd ! plane ( pol>ization ( ! light4 ,i w n[ assume t y "k some?+ ab\t :at is meant by twi/+ ! plane ( pol>ization ( light4 ,y "k t sug> solution w d x1 & ! long] ! pa? ( ! ray ?r\gh ! sug>1 ! m twi/ x gets4 ,?is ph5om5on is tak5 advantage ( 9 ! sug> indu/ries1 to f9d ! /r5g?s ( sug> solutions4 ,= ! ?read illu/ration ,i am indebt$ to ,pr(essor ,silvanus ,?omson1 & ! next piece ( app>atus :i* ,i %all %[ also belongs to him4 ,i h "h 7see ,frontispiece7 a p[]ful arm\r-clad coil1 or electro-magnet4 ,!re is a c5tral hole ?r\gh x1 ?r\gh :i* a beam ( light may be pass$ f an electric lamp1 & ,i h a piece ( ,f>aday's heavy glass ne>ly fill+ ?is hole4 ,i h a pol>iz] at "o end1 & an analyz] at ! o!r4 ,y see n[ t ! #abc pol>iz$ light passes ?r\gh ! heavy glass & ! analyz]1 & ent]s ! eye ( an obs]v]4 ,i w n[ turn ,b until ! light no long] passes4 ,until n[ !re has be5 no magnetism1 b ,i h ! means "h ( produc+ a mo/ int5se magnetic field 9 ! direction 9 :i* ! ray passes1 & if y\r eye 7 "h y w\ld see t !re is light pass+ ?r\gh ! analyz]4 ,! magnetism has done some?+ to ! light1 x has made x capable ( pass+ :]e x c\ld n pass be=e4 ,:5 ,i turn ! analyz] a little ,i /op ! light aga91 & n[ ,i "k t :at ! magnetism did 0 to conv]t ! glass into a m$ium l ! sug>1 a m$ium :i* rotates ! plane ( pol>ization ( light4 ,9 ?is exp]im5t y h _h to rely ^u my p]sonal measurem5t ( ! actual rotation produc$4 ,b if ,i ins]t betwe5 ! pol>iz] & analyz] ?is disc ( ,pr(essor ,silvanus ,?omson's1 built up ( tw5ty-f\r radial pieces ( mica1 ,i %all h a means ( %[+ to ?is audi5ce ! actual rotation ( ! plane ( pol>ization ( light4 ,y see n[ on ! scre5 ! light :i* has pass$ ?r\gh ! analyz] 9 ! =m ( a cross1 & if ! cross rotates x is a sign ( ! rotation ( ! plane ( pol>ization ( ! light4 ,by means ( ?is electric key ,i c create1 de/roy1 & rev]se ! magnetic #abd field 9 ! glass4 ,z ,i create magnetism y see ! twi/+ ( ! cross2 ,i de/roy ! magnetism1 & x returns to its old position2 ,i create ! opposite k9d ( magnetism1 & y see t ! cross twi/s 9 ! opposite way4 ,i hope x is n[ kn[n to y t magnetism rotates ! plane ( pol>ization ( light z ! solution ( sug> did4 ,illu/ration3 ,,fig4 #ef4 ,illu/ration3 ,,fig4 #eg4 ,z an illu/ration ( :at occurs betwe5 pol>iz] & analyz]1 look aga9 at ?is rope 7,fig4 #ec7 fa/5$ to ! ceil+4 ,i move ! bottom end %>ply f ea/ to we/1 & y see t e "p ( ! rope moves f ea/ to we/4 ,c y imag9e a rope su* t :5 ! bottom end 0 mov$ f ea/ to we/1 a po9t "s y>ds up mov$ f ea/-nor?-ea/ to we/-s\'-we/1 t a high] po9t mov$ f nor?-ea/ to s\?-we/1 & s on1 ! direction gradually *ang+ = high] & high] po9ts8 ,"s ( y1 kn[+ :at ,i h done1 may be able to imag9e x4 ,we %\ld h :at we want if ?is rope 7 a *a9 ( gyro/ats su* z y see figur$ 9 ! diagram2 gyro/ats all sp9n+ 9 ! same way look$ at f bel[1 ) frictionless h+es betwe5 !m4 ,"h is su* a *a9 7,fig4 #ef71 "o ( _m t ,i h tri$ to use 9 ?is way = sev]al ye>s4 ,b al?\gh ,i h (t5 believ$ t ,i saw ! ph5om5on occur 9 #abf su* a *a91 ,i mu/ n[ confess to repeat$ failures4 ,! difficulties ,i h met ) are almo/ altoge!r me*anical ones4 ,y see t by t\*+ all ! gyro/ats 9 succession ) ?is rapidly revolv+ disc driv5 by ! little electromotor1 ,i c get !m all to sp9 at ! same "t2 b y w notice t :at ) bad me*anism & bad calculation on my "p1 & want ( skill1 ! ph5om5on is completely mask$ by wild movem5ts ( ! gyro/ats1 ! causes ( :i* are bett] kn[n ?an capable ( rectification4 ,! pr9ciple ( ! action is v visible 9 ?is gyro/at susp5d$ z ! bob ( a p5dulum 7,fig4 #eg74 ,y may imag9e ?is to repres5t a p>ticle ( ! #abg sub/ance :i* transmits light 9 ! magnetic field1 & y see by ! trickl+ ?9 /ream ( s& :i* falls f x on ! pap] t x is cont9ually *ang+ ! plane ( pol>ization4 ,b ,i am happy to say t ,i c %[ y to-night a really successful illu/ration ( ,?omson's pr9ciple2 x is ! v fir/ "t t ?is mo/ sugge/ive exp]im5t has be5 %[n to an audi5ce4 ,i h a numb] ( d\ble gyro/ats 7,fig4 #eh7 plac$ on ! same l9e1 jo9$ end to end by %ort pieces ( ela/ic4 ,ea* in/rum5t is support$ at its c5tre ( gravity1 & x c rotate bo? 9 horizontal & 9 v]tical planes4 ,illu/ration3 ,,fig4 #eh4 ,! end ( ! vibrat+ lev] ,a c only get a horizontal motion f my h&1 & ! motion is transmitt$ f "o gyro/at to ! next1 until x has travell$ to ! v end "o4 ,obs]ve t :5 ! gyro/ats are n sp9n+1 ! motion is #abh ev]y:]e horizontal4 ,n[ x is v important n to h any illu/ration "h ( a reflect$ ray ( light1 & s ,i h introduc$ a good deal ( friction at all ! supports4 ,i w n[ sp9 all ! gyro/ats1 & y w obs]ve t :5 ,a moves ne>ly /raight horizontally1 ! next gyro/at moves /raight b 9 a slightly diff]5t plane1 ! second gyro/at moves 9 ano!r plane1 & s on1 ea* gyro/at slightly twi/+ ! plane 9 :i* ! motion occurs2 & y see t ! end "o does n by any means receive ! horizontal motion ( ,a1 b a motion ne>ly v]tical4 ,?is is a me*anical illu/ration1 ! fir/ successful "o ,i h made aft] _m trials1 ( ! effect on light ( magnetism4 ,! reason = ! action t occurs 9 ?is model mu/ be kn[n to ev]ybody :o has tri$ to foll[ me f ! beg9n+ ( ! lecture4 ,& y c all see t we h only to imag9e t _m p>ticles ( ! glass are rotat+ l gyro/ats1 & t magnetism has p>tially caus$ an all9eation ( _! axes1 to h a dynamical !ory ( ,f>aday's discov]y4 ,! magnet twi/s ! plane ( pol>ization1 & s does ! solution ( sug>2 b x is f\nd by exp]im5t t ! magnet does x indiff]5tly = com+ & go+1 :]eas ! sug> does x 9 a way t corresponds ) a spiral /ructure ( molecules4 ,y see t 9 ?is important #abi p>ticul> ! gyro/at analogue mu/ foll[ ! magnetic me?od1 & n ! sug> me?od4 ,we mu/ reg>d ?is model1 !n1 ! analogue to ,f>aday's exp]im5t1 z giv+ great support to ! idea t magnetism consi/s ( rotation4 ,i h already exce$$ ! limits ( "t usually all[$ to a popul> lectur]1 b y see t ,i am v f> f hav+ exhau/$ our subject4 ,i am n q sure t ,i h accompli%$ ! object ) :i* ,i set out4 ,my object 01 />t+ f ! v diff]5t behavi\r ( a top :5 sp9n+ & :5 n sp9n+1 to %[ y t ! obs]vation ( t v common ph5om5on1 & a det]m9ation to und]/& x1 might lead u to und]/& v mu* m complex-look+ ?+s4 ,!re is no lesson :i* x is m important to le>n ?an ?is--,t x is 9 ! /udy ( e-day facts t all ! great discov]ies ( ! future lie4 ,?ree ?\s& ye>s ago sp9n+ tops 7 common1 b p nev] /udi$ !m4 ,?ree ?\s& ye>s ago p boil$ wat] & made /eam1 b ! /eam-eng9e 0 unkn[n to !m4 ,!y _h *>coal & saltpetre & sulphur1 b !y knew no?+ ( gunp[d]4 ,!y saw fossils 9 rocks1 b ! wond]s ( geology 7 un/udi$ by !m4 ,!y _h bits ( iron & copp]1 b n "o ( !m ?\ght ( any "o ( ! fifty simple #acj ways t are n[ kn[n to u ( comb9+ ^? kn[n ?+s into a telephone4 ,:y1 ev5 ! simple/ k9d ( signall+ by flags or lant]ns 0 unkn[n to !m1 & yet a k ( ?is might h *ang$ ! fate ( ! _w on "o ( ! great days ( battle t we read ab\t4 ,we look on ,nature n[ 9 an utt]ly diff]5t way1 ) a great deal m k1 ) a great deal m rev]5ce1 & ) mu* less unreason+ sup]/iti\s fe>4 ,& :at we are to ! p ( ?ree ?\s& ye>s ago1 s w be ! p ( "o hundr$ ye>s h5ce to u2 = inde$ ! accel]ation ( ! rate ( progress 9 sci5ce is itself accel]at+4 ,! army ( sci5tific work]s gets l>g] & l>g] e day1 & x is my belief t e unit ( ! population w be a sci5tific work] be=e long4 ,& s we are gradually mak+ "t & space yield to u & obey u4 ,b j ?9k ( x6 ,( all ! discov]ies ( ! next hundr$ ye>s2 ! ?+s t are unkn[n to u1 b :i* w be s well kn[n to our desc5dants t !y w sne] at u z utt]ly ignorant1 because ^! ?+s w seem to !m su* self-evid5t facts2 ,i say1 ( all ^! ?+s1 if "o ( u to-morr[ discov]$ "o ( !m1 he w\ld be reg>d$ z a great discov]]4 ,& yet ! *ildr5 ( a hundr$ ye>s h5ce w "k x3 x w be br\ght home to #aca !m p]haps at e footfall1 at ! flapp+ ( e coat-tail4 ,imag9e ! foll[+ "q set 9 a s*ool exam9ation pap] ( #bjij ,a4,d4--,c y acc\nt = ! crass ignorance ( our =efa!rs 9 n be+ able to see f ,engl& :at _! fri5ds 7 do+ 9 ,au/ralia8#ac ,or ?is--,messages are be+ receiv$ e m9ute f our fri5ds on ! planet ,m>s1 & are n[ be+ answ]$3 h[ d y acc\nt = our ance/ors be+ utt]ly ignorant t ^! messages 7 occasionally s5t to !m8 ,or ?is--,:at metal is z /rong comp>$ ) /eel z /eel is comp>$ ) lead8 & expla9 :y ! discov]y ( x 0 n made 9 ,%effield4 ,b !re is "o "q t our desc5dants w nev] ask 9 acc5ts ( jocul>ity1 = to _! bitt] sorr[ e man1 woman1 & *ild ( !m w "k ! answ]1 & t "q is ?is--,if our ance/ors 9 ! matt] ( coal economy 7 n q z ignorant z a baby :o takes a p5ny #acb z equival5t = a half-cr[n1 :y did !y wa/e our coal8 ,:y did !y de/roy :at nev] c be replac$8 ,my fri5ds1 let me conclude by impress+ ^u y ! value ( k1 & ! importance ( us+ e opportunity )9 y\r rea* to increase y\r own /ore ( x4 ,_m are ! glitt]+ ?+s t seem to compete successfully ) x1 & to ex]cise a /rong] fasc9ation ov] human he>ts4 ,weal? & rank1 fa%ion & luxury1 p[] & fame--^! fire ! ambitions ( m51 & attract myriads ( eag] wor%ipp]s2 b1 believe x1 !y are b poor ?+s 9 comp>ison ) k1 & h no su* pure satisfactions to give z ^? :i* x is able to be/[4 ,!re is no evil ?+ "u ! sun :i* k1 :5 wield$ by an e>ne/ & rightly direct$ w1 may n help to purge out & de/roy2 & !re is no man or woman born into ?is _w :o has n be5 giv5 ! capacity1 n m]ely to ga!r 9 k = 8 own improvem5t & delight1 b ev5 to add some?+1 h[ev] little1 to t g5]al /ock ( k :i* is ! _w's be/ weal?4 99 99 99 99 99 #acc ,,argum5t4 #a4 ,introduction1 pages #i-ad1 %[+ ! importance ( ! /udy ( sp9n+-top behavi\r4 #b4 ,quasi-rigidity induc$ ev5 9 flexible & fluid bodies by rapid motion1 #ad-ba4 ,illu/rations3 ,top1 #ad2 belt or rope1 #ad2 disc ( ?9 pap]1 #ad2 r+ ( *a91 #ae2 s(t hat1 #af2 drunk5 man1 #af2 rotat+ wat]1 #af2 smoke r+s1 #ag2 ,?omson's ,molecul> ,!ory1 #ai2 swimm] caught 9 an eddy1 #bj2 m9+ wat] jet1 #bj2 cas$ gyro/at1 #ba4 #c4 ,! nature ( ?is quasi-rigidity 9 sp9n+ bodies is a resi/ance to *ange ( direction ( ! axis ( sp9n+1 #ba-cj4 ,illu/rations3 ,cas$ gyro/at1 #ba-bd2 tops1 biscuits1 hats1 ?r[n into ! air1 #bd-bf2 quoits1 hoops1 projectiles f guns1 #bg2 juggl]s at ! ,victoria ,music ,hall1 #bf-cj2 *ild trundl+ hoop1 man on bicycle1 ballet-danc]1 ! e>? po9t+ to pole />1 boy's top1 #cj4 #d4 ,/udy ( ! crab-l behavi\r ( a sp9n+ body1 #cj-di4 ,illu/rations3 ,sp9n+ top1 #ca2 cas$ gyro/at1 #cb2 balanc$ gyro/at1 #cc-cf2 w9dage ( projectiles f #acd rifl$ guns1 #cf-ch2 tilt+ a hoop or bicycle1 turn+ quickly on horseback1 #ch2 b[ls1 #ci2 h[ to simplify "o's obs]vations1 #ci1 #dj2 ! illu/ration :i* gives u our simple univ]sal rule1 #dj-db2 te/+ ! rule1 #db-dd2 explanation ( precession ( gyro/at1 #dd1 #de2 precession ( common top1 #df2 precession ( ov]hung top1 #df2 li/ ( our results giv5 9 a wall %eet1 #dh1 #di4 #e4 ,pro( or explanation ( our simple univ]sal rule1 #ej-ed4 ,giv+ two indep5d5t rotations to a body1 #ej1 #ea2 composition ( rotations1 #eb1 #ec4 #f4 ,w>n+ t ! rule is n1 aft] all1 s simple1 #ed-ff4 ,two indep5d5t sp9s giv5 to ! e>?1 #ed2 c5trifugal =ce1 #ee2 balanc+ ( quick spe$ ma*9]y1 #ef1 #eg2 ! possible wobbl+ ( ! e>?1 #eh2 ! ?ree pr9cipal axes ( a body1 #ei2 ! free sp9n+ ( discs1 cones1 rods1 r+s ( *a91 #fj2 nodd+ motion ( a gyro/at1 #fb2 ( a top1 #fc2 p>5!sis ab\t inaccuracy ( /atem5t & ,rank9e's rhyme1 #fc1 #fd2 fur!r complications 9 gyro/atic behavi\r1 #fd2 /range ela/ic1 jelly-l behavi\r1 #fe2 gyro/at on /ilts1 #ff4 #g4 ,:y a gyro/at falls1 #ff1 #fg4 #h4 ,:y a top rises1 #fg-gd4 ,g5]al ignorance1 #fg2 ,?omson prep>+ = ! ma!matical tripos1 #fh2 behavi\r ( a wat]-worn /one :5 spun on a table1 #fh1 #fi2 p>5!sis on te*nical education1 #gj2 simple explanation ( :y a top rises1 #gj-gc2 behavi\r ( het]og5e\s sph]e :5 spun1 #gd4 #i4 ,precessional motion ( ! e>?1 #gd-ia4 ,its nature & effects on climate1 #ge-hj2 resemblance ( ! precess+ e>? to c]ta9 models1 #hj-hb2 tilt+ =ces ex]t$ by ! sun & moon on ! #ace e>?1 #hb-hd2 h[ ! e>?'s precessional motion is always alt]+1 #he-hh2 ! retrogression ( ! moon's nodes is itself ano!r example1 #hh1 #hi2 an exact /atem5t made & a sort ( apology = mak+ x1 #ij1 #ia4 #aj4 ,influ5ce ( possible int]nal fluidity ( ! e>? on its precessional motion1 #ia-ih4 ,effect ( fluids & s& 9 tumbl]s1 #ia-ic2 ?ree te/s ( ! int]nal rigidity ( an egg1 t is1 ( its be+ a boil$ egg1 #ic1 #id2 quasi-rigidity ( fluids due to rapid motion1 =gott5 9 orig9al argum5t1 #ie2 beautiful behavi\r ( holl[ top fill$ ) wat]1 #ie2 /rik+ contra/s 9 ! behavi\r ( two tops :i* are v mu* alike1 #ig1 #ih2 f\r? te/ ( a boil$ egg1 #ih4 #aa4 ,apology = dwell+ fur!r ^u a/ronomical matt]s1 & imp]t95t rem>ks ab\t a/ronom]s1 #ii-aja4 #ab4 ,h[ a gyro/at w\ld enable a p]son liv+ 9 subt]ranean regions to "k1 #a/1 t ! e>? rotates2 #bnd1 ! am\nt ( rotation2 #crd1 ! direction ( true nor?2 #d?1 ! latitude1 #aja-aaa4 ,"s m5's want ( fai?1 #aja2 disbelief 9 ! e>?'s rotation1 #ajb2 h[ a free gyro/at behaves1 #ajc1 #ajd2 ,f\cault's laboratory measurem5t ( ! e>?'s rotation1 #aje-ajg2 to f9d ! true nor?1 #ajh2 all rotat+ bodies va9ly endeav\r+ to po9t to ! pole />1 #ajh2 to f9d ! latitude1 #aaj2 analogies betwe5 ! gyro/at & ! m>9]'s compass & ! dipp+ ne$le1 #aaj1 #aaa2 dynamical connection betwe5 magnetism & gyro/atic ph5om5a1 #aaa4 #ac4 ,h[ ! lectur] spun 8 tops1 us+ electro-motors1 #aab-aad4 #ad4 ,light1 magnetism1 & molecul> sp9n+ tops1 #aae-abh4 ,light takes "t to travel1 #aae2 ! electro-magnetic #acf !ory ( light1 #aaf1 #aag2 signall+ ?r\gh fogs & build+s by means ( a new k9d ( radiation1 #aag2 ,f>aday's rotation ( ! plane ( pol>ization by magnetism1 ) illu/rations & models1 #aah-abd2 *a9 ( gyro/ats1 #abd2 gyro/at z a p5dulum bob1 #abf2 ,?omson's me*anical illu/ration ( ,f>aday's exp]im5t1 #abg1 #abh4 #ae4 ,conclusion1 #abi-acb4 ,! necessity = cultivat+ ! obs]vation1 #abi2 future discov]y1 #acj2 que/ions to be ask$ "o hundr$ ye>s h5ce1 #aca2 k ! ?+ mo/ to be wi%$ =1 #acb4 99 99 99 99 99 #acg ,,app5dix ,i4 ,,! ,,use ,,( ,,gyro/ats4 ,9 #ahgd two fam\s m5 made a great mi/ake 9 endeav\r+ to prev5t or dim9i% ! roll+ motion ( ! saloon ( a vessel by us+ a rapidly rotat+ :eel4 ,mr4 ,macf>lane ,gray po9t$ out _! mi/ake4 ,x is only :5 ! :eel is all[$ to precess t x c ex]cise a /eady+ effect2 ! mom5t :i* x !n ex]ts is equal to ! angul> spe$ ( ! precession multipli$ by ! mom5t ( mom5tum ( ! sp9n+ :eel4 ,x is a/oni%+ h[ _m eng9e]s :o "k ! laws ( motion ( m]e translation1 are ignorant ( angul> motion1 & yet ! analogies betwe5 ! two sets ( laws are p]fectly simple4 ,i h set out ^! analogies 9 my book on ,appli$ ,me*anics4 ,! la/ ( !m betwe5 c5tripetal =ce on a body mov+ 9 a curv$ pa?1 & torque or mom5t on a rotat+ body is ! simple key to all gyro/atic or top calculation4 ,:5 ! sp9 ( a top is greatly r$uc$ x is necess>y to rememb] t ! total mom5t ( mom5tum is n ab\t ! sp9n+ axis 7see my ,appli$ ,me*anics1 page #eid72 correction = ?is is1 ,i suppose1 :at introduces ! complexity :i* sc>es /ud5ts f /udy+ ! vag>ies ( tops2 b 9 all cases t are likely to come be=e an eng9e] x w\ld be absurd to /udy #ach su* a small correction1 & consequ5tly calculation is exce$+ly simple4 ,inv5tors us+ gyro/ats h succe$$ 9 do+ ! foll[+ ?+s-- 7#a7 ,keep+ ! plat=m ( a gun level on bo>d %ip1 h[ev] ! %ip may roll or pit*4 ,keep+ a subm>9e vessel or a fly+ ma*9e ) any plane exactly horizontal or incl9$ 9 any specifi$ way4#ad ,x is easy to effect su* objects )\t ! use ( a gyro/at1 z by means ( _s levels x is possible to comm& p[]ful electric or o!r motors to keep any?+ always level4 ,! actual me?ods employ$ by ,mr4 ,beau*amp ,t[] 7an hydraulic me?od71 & by myself 7an electric me?od71 dep5d ^u ! use ( a gyro/at1 :i* is really a p5dulum1 ! axis be+ v]tical4 7#b7 ,greatly r$uc+ ! roll+ 7or pit*+7 ( a %ip1 or ! saloon ( a %ip4 ,?is is ! problem :i* ,mr4 ,s*lick has solv$ ) great success1 at any rate 9 ! case ( torp$o boats4 7#c7 ,9 ,mr4 ,br5nan's ,mono-rail railway1 keep+ ! resultant =ce due to weight1 w9d pressure1 c5trifugal =ce1 etc41 exactly 9 l9e ) ! rail1 s t1 h[ev] ! load on a wagon may alt] 9 position1 & al?\gh ! wagon may be go+ r\nd a curve1 x is quickly br\ght to a position su* t !re are no =ces t5d+ to alt] its angul> position4 ,! wagon leans ov] t[>ds ! w9d or t[>ds ! c5tre ( ! curve ( ! rail s z to be 9 equilibrium4 7#d7 ,i ne$ n ref] to su* matt]s z ! use ( gyro/ats = ! correction ( compasses on bo>d %ip1 ref]r$ to 9 page #aaa4 #aci ,illu/ration3 ,,fig4 #a4 #adj ,problems 7#b7 & 7#c7 are ^? to :i* ,i wi% to ref]4 ,= a %ip ( #f1jjj tons ,mr4 ,s*lick w\ld use a l>ge :eel ( #aj to #bj tons1 revolv+ ab\t an axis ,e ,f 7fig4 #a7 ^: mean position is v]tical4 ,its be>+s are 9 a frame ,e ,c ,f ,d :i* c move ab\t a ?w>t-%ip axis ,c ,d ) a precessional motion4 ,its c5tre ( gravity is bel[ ?is axis1 s t l ! %ip itself ! frame is 9 /able equilibrium4 ,let ! %ip h roll$ ?r\gh an angle ,r f its upright position1 & suppose ! axis ,e ,f to h precess$ ?r\gh ! angle ,p f a v]tical position4 ,let ! angul> velocity ( roll+ be call$ 4,r1 & ! angul> velocity ( precession 4,p2 let ! mom5t ( mom5tum ( ! :eel be m4 ,= any vibrat+ body l a %ip x is easy to write out ! equation ( motion2 into ?is equation we h m]ely to introduce ! mom5t m 4,p dim9i%+ ,r2 into ! equation = ,p we m]ely introduce ! mom5t m 4,r increas+ ,p4 ,z usual we introduce frictional t]ms2 9 ! fir/ place ,f 4,r 7,f be+ a con/ant co-effici5t7 /ill+ ! roll ( ! %ip2 9 ! second case f 4,p a fluid friction introduc$ by a pair ( da% pots appli$ at ! p9s ,a & ,b to /ill ! precessional vibrations ( ! frame4 ,x w be f\nd t ! angul> motion ,p is v mu* great] ?an ! roll ,r4 ,inde$1 s great is ,p t !re are /ops to prev5t its exce$+ a c]ta9 am\nt4 ,( c\rse s long z a /op acts1 prev5t+ precession1 ! roll ( ! %ip proce$s z if ! gyro/at :eel 7 n rotat+4 ,mr4 ,s*lick drives 8 :eels by /eam2 he w probably 9 future d z ,mr4 ,br5nan does1 drive !m by electromotors1 & keep !m 9 air-tight cases 9 good vacuums1 because ! loss ( en]gy by friction aga9/ an atmosph]e is proportional to ! d5sity ( ! atmosph]e4 ,! solution ( ! equations to f9d ! nature ( ! ,r & ,p motions is sometimes t$i\s1 b requires no great am\nt ( ma!matical k4 ,9 a case consid]$ by me ( #ada a #f1jjj ton %ip1 ! p]iod ( a roll 0 increas$ f #ad to #bj seconds by ! use ( ! gyro/at1 & ! roll rapidly dim9i%$ 9 am\nt4 ,!re 0 accompany+ ?is sl[ p]iodic motion1 "o ( a two seconds' p]iod1 b if x did appe> x 0 damp$ out ) great rapidity4 ,( c\rse x is assum$ t1 by ! use ( bilge keels & roll+ *amb]s1 & z l[ a metac5tre z is all[able1 we h already l5g!n$ ! "t ( vibration1 & damp$ ! roll ,r z mu* z possible1 be=e apply+ ! gyro/at4 ,i take x t ev]ybody kn[s ! importance ( l5g!n+ ! p]iod ( ! natural roll ( a %ip1 al?\gh he may n "k ! reason4 ,! reason :y mod]n %ips ( great tonnage are s /eady is because _! natural p]iodic times ( roll+ vibration are s mu* great] ?an ! probable p]iods ( any waves ( ! sea1 = if a s]ies ( waves acts ^u a %ip t5d+ to make x roll1 if ! p]iodic "t ( ea* wave is n v diff]5t f ! natural p]iodic "t ( vibration ( ! %ip1 ! roll+ motion may become dang]\sly great4 ,if we try to apply ,mr4 ,s*lick's me?od to ,mr4 ,br5nan's c> x is easy to %[ t !re is in/ability ( motion1 :e!r !re is or is n friction4 ,if !re is no friction1 & we make ! gyro/at frame un/able by keep+ its c5tre ( gravity above ! axis ,c ,d1 !re w be vibrations1 b ! smalle/ am\nt ( friction w cause ^! vibrations to get great] & great]4 ,ev5 )\t friction !re w be in/ability if m1 ! mom5t ( mom5tum ( ! :eel1 is less ?an a c]ta9 am\nt4 ,we see1 !n1 t no =m ( ! ,s*lick me?od1 or modification ( x1 c be appli$ to solve ! ,br5nan problem4 #adb ,illu/ration3 ,,fig4 #b4 #adc ,mr4 ,br5nan's me?od ( work+ is q diff]5t f t ( ,mr4 ,s*lick4 ,fig4 #b %[s 8 model c> 7ab\t six feet long72 x is driv5 by electric accumulators c>ri$ by ! c>4 ,8 gyro/at :eels are driv5 by electromotors 7n %[n 9 fig4 #c72 z !y are revolv+ 9 ne>ly vacu\s spaces !y consume b little p[]1 & ev5 if ! curr5t 7 /opp$ !y w\ld cont9ue runn+ at suffici5tly high spe$s to be effective = a l5g? ( "t4 ,/ill x mu/ n be =gott5 t en]gy is wa/$ 9 friction1 & "w has to be done 9 br++ ! c> to a new position ( equilibrium1 & ?is en]gy is suppli$ by ! electromotors4 ,%\ld ! gyro/ats really /op1 or fall to a c]ta9 l[ spe$1 two supports are automatically dropp$1 "o on ei!r side ( ! c>2 ea* ( !m drops till x rea*es ! gr\nd2 "o ( !m dropp+1 p]haps1 mu* f>!r ?an ! o!r4 ,! real full-size c>1 :i* he is n[ con/ruct+1 may be pull$ ) o!r c>s by any k9d ( locomotive us+ electricity or petrol or /eam1 or ea* ( ! :eels may be a driv+ :eel4 ,he w\ld pref] to g5]ate electrop[] on 8 tra91 & to drive e :eel ) an electric motor4 ,8 :eels are s indep5d5t ( "o ano!r t !y c take v quick curves & v]tical inequalities ( ! rail4 ,! rail is fa/5$ to sleep]s ly+ on gr\nd t may h sidelong slope4 ,! model c> is support$ by a mono-rail bogie at ea* end2 ea* bogie has two :eels pivot$ bo? v]tically & horizontally2 x runs on a r\nd iron gas pipe1 & sometimes on /eel wire rope2 ! gr\nd is n[h]e levell$ or cut1 & at "o place ! rail is a /eel wire rope spann+ a gorge1 z %[n 9 fig4 #b4 ,x is int]e/+ to /op ! c> 9 ! middle ( ?is rope & to sw+ ! rope sideways to see ! automatic balanc+ ( ! c>4 ,! c> may be left "h or else:]e balanc+ itself ) nobody 9 *>ge ( x4 ,if ! load on ! c>--great lead weights--be dump$ ab\t into new positions1 ! c> adju/s itself to ! new conditions ) great #add quickness4 ,:5 ! c> is /opp$1 if a p]son /&+ on ! gr\nd pu%es ! c> sidewise1 ! c> ( c\rse pu%es 9 opposition1 l an indignant animal1 & by judici\s pu%+ & yield+ x is possible to cause a consid]able tilt4 ,left n[ to itself ! c> rights itself v quickly4 ,illu/ration3 ,,fig4 #c4 #ade ,illu/ration3 ,,fig4 #c;b 7%[+ ! gr\nd-plan ( ,fig4 #c74 #adf ,fig4 #c is a diagrammatic repres5tation ( ,mr4 ,br5nan's pair ( gyro/ats 9 sectional elevation & plan4 ,! cases ,g & ,g'1 inside :i* ! :eels ,f & ,f' are rotat+ 9 vacuo at ! same spe$ & 9 opposite directions 7driv5 by electromotors n %[n 9 ! figure71 are pivot$ ab\t v]tical axes ,e ,j & ,e' ,j'4 ,!y are connect$ by spur-too!d segm5ts ,j ,j & ,j' ,j'1 s t _! precessional motions are equal & opposite4 ,! :ole sy/em is pivot$ ab\t ,c1 a longitud9al axis4 ,?us :5 precess+ s t ,h comes out ( ! pap]1 s w ,h'1 & :5 ,h goes into ! pap]1 s does ,h'4 ,:5 ! c> is 9 equilibrium ! axes ,k ,h & ,k' ,h' are 9 l9e ,n ,o ,o' ,n' across ! c> 9 ! plane ( ! pap]4 ,!y are also 9 a l9e :i* is at "r angles to ! total resultant 7v]tical or ne>ly v]tical7 =ce on ! c>4 ,i w call ,n ,o ,o' ,n' ! mid position4 ,let #a_/bm be ! mom5t ( mom5tum ( ei!r :eel4 ,let u suppose t sudd5ly ! c> f9ds t x is n 9 equilibrium because ( a gu/ ( w9d1 or c5trifugal =ce1 or an alt]ation ( load+1 s t ! %elf ,d comes up aga9/ ,h1 ! sp9n+ axis 7or a roll] revolv+ ) ! sp9n+ axis7 ( ! gyro/at4 ,h beg9s to roll away f me1 & if no slipp+ occurr$ 7b !re always is slipp+1 &1 inde$1 slipp+ is a necess>y condition7 x w\ld roll1 t is1 ! gyro/ats w\ld precess ) a con/ant angul> velocity alpha1 & ex]t ! mom5t malpha ^u ! %elf ,d1 & !re=e on ! c>4 ,x is to be obs]v$ t ?is is great] z ! diamet] ( ! roll+ "p is great]4 ,?is precession cont9ues until ! roll] & ! %elf cease to t\*4 ,at fir/ ,h lifts ) ! %elf1 & aft]w>ds ! %elf mov+ d[nw>ds is foll[$ = "s di/ance by ! roll]4 ,if ! tilt _h be5 9 ! opposite direction ! %elf ,d' w\ld h act$ upw>ds ^u ! roll] ,h'1 & caus$ j ! opposite k9d ( precession1 & a mom5t ( ! opposite k9d4 ,we n[ h ! sp9dles out ( _! mid position2 h[ are !y br\ght back f ,o ,q & ,o' ,q' to ,o ,n & ,o' ,n'1 #adg b ) ,h p]man5tly l[]$ j ! "r am\nt8 ,x is ! ess5ce ( ,mr4 ,br5nan's inv5tion t aft] a re/or+ mom5t has be5 appli$ to ! c> ! sp9dles %all g back to ! position ,n ,o ,o' ,n' 7) ,h p]man5tly l[]$71 s z to be ready to act aga94 ,he effects ?is object 9 v>i\s ways4 ,"s ways describ$ 9 8 pat5ts are q diff]5t f :at is us$ on ! model1 & ! me?od to be us$ on ! full-size wagon w aga9 be q diff]5t4 ,i w describe "o ( ! me?ods4 ,mr4 ,br5nan tells me t he consid]s ?is old me?od to be crude1 b he is naturally unwill+ to all[ me to publi% 8 late/ me?od4 ,d' is a circul> %elf ext5d+ f ! mid position 9 my direction2 ,d is a simil> %elf ext5d+ f ! mid position into ! pap]1 or away f me4 ,x is on ^! %elves t ,h' & ,h roll1 caus+ precession away f ,n ,o ,o' ,n'1 z ,i h j describ$4 ,:5 ,h' is inside ! pap]1 or :5 ,h is outside ! pap]1 !y f9d no %elf to roll ^u4 ,!re are1 h[ev]1 two o!r %elves ,l & ,l'1 = two o!r roll]s ,m & ,m'1 :i* are atta*$ to ! frames conc5tric ) ! sp9dles2 !y are free to rotate1 b are n rotat$ by ! sp9dles4 ,:5 !y are press$ by _! %elves ,l or ,l' ?is causes negative precession1 & !y roll t[>ds ! ,n ,o ,o' ,n' position4 ,!re is1 ( c\rse1 friction at _! supports1 ret>d+ _! rotation1 & !re=e ! precession4 ,! important ?+ to rememb] is t ,h & ,h'1 :5 !y t\* _! %elves 7:5 "o is t\*+ ! o!r is n t\*+7 cause a precession away f ! mid position ,n ,o ,o' ,n' at a rate alpha1 :i* produces a re/or+ mom5t malpha ( ne>ly con/ant am\nt 7except = slipp+71 :]eas :]e ,m or ,m' t\*es its %elf ,l or ,l' 7:5 "o is t\*+ ! o!r is n t\*+7 ! pressure on ! %elf & friction det]m9e ! rate ( ! precession t[>ds ! mid position ,n ,o ,o' ,n'1 #adh z well z ! small v]tical motion4 ,! friction at ! supports ( ,m & ,m' is necess>y4 ,suppose t ! tilt f ! equilibrium position to be correct$ is ,r1 :5 ,d presses ,h upw>d4 ,! mom5t malpha1 & its "t ( action 7! total mom5tal impulse7 are too great1 & ,r is ov]-correct$2 ?is causes ! roll] ,m' to act on ,l'1 & ! sp9dles return to ! mid position2 !y g beyond ! mid position1 & n[ ! roll] ,h' acts on ,d'1 & !re is a return to ! mid position1 & beyond x a little1 & s x goes on1 ! sw+s ( ! gyro/ats out ( & into ! mid position1 & ! vibrations ( ! c> ab\t its position ( equilibrium gett+ rapidly less & less until aga9 nei!r ,h nor ,h'1 nor ,m nor ,m' is t\*+ a %elf4 ,x is inde$ m>vell\s to see h[ rapidly ! sw+s decay4 ,friction accel]ates ! precession away f ,n ,o ,o' ,n'4 ,friction ret>ds ! precession t[>ds ! middle position4 ,x w be se5 t by us+ ! two gyro/ats in/ead ( "o :5 !re is a curve on ! l9e1 al?\gh ! plane ,n ,o ,o' ,n' rotates1 & we may say t ! gyro/ats precess1 ! tilt+ c\ples :i* !y might ex]cise are equal & opposite4 ,i d n "k if ,mr4 ,br5nan has tri$ a s+le gyro/at1 ! mid position ( ! axis ( ! :eel be+ v]tical1 b ev5 9 ?is case a *ange ( slope1 or inequalities 9 ! l9e1 might make x necess>y to h a pair4 ,x is evid5t t ?is me?od ( ,mr4 ,br5nan is altoge!r diff]5t 9 "* f t ( ,mr4 ,s*lick4 ,"w is "h actually done :i* mu/ be suppli$ by ! electromotors4 ,"o ( ! mo/ important ?+s to "k is ?is3 ! ,br5nan model is wond]fully successful2 ! weight ( ! app>atus is n a l>ge fraction ( ! weight ( ! wagon2 w ?is also be ! case ) a c> weigh+ #a1jjj times z #adi mu*8 ,! calculation is n difficult1 b ,i may n give x "h4 ,if we assume t sudd5ly ! wagon f9ds itself at ! angle ,r f its position ( equilibrium1 x may be tak5 t if ! size ( ea* dim5sion ( ! wagon be multipli$ by n1 & ! size ( ea* dim5sion ( ! app>atus be multipli$ by p1 !n = a sudd5 gu/ ( w9d1 or sudd5ly com+ on a curve1 or a sudd5 %ift ( position ( "p ( ! c>go1 ,r may be tak5 z inv]sely proportional to n4 ,i ne$ n /ate ! reasonable assumption :i* und]lies ?is calculation1 b ! result is t if n is #aj1 p is #g4e4 ,t is1 if ! weight ( ! wagon is multipli$ by #a1jjj1 ! weight ( ! app>atus is only multipli$ by #dbj4 ,9 fact1 if1 9 ! model1 ! weight ( ! app>atus is #aj p] c5t4 ( t ( ! wagon1 9 ! l>ge wagon ! weight ( ! app>atus is only ab\t #d p] c5t4 ( t ( ! wagon4 ,?is is a v satisfactory result4#ae ,my calculations seem to %[ t ,mr4 ,s*lick's app>atus w =m a l>g] fraction ( ! :ole weight ( a %ip1 z ! %ip is l>g]1 b 9 ! pres5t exp]im5tal /age ( ! subject x is unfair to say m ?an t ?is seems probable4 ,my own op9ion is t l>ge %ips are suffici5tly /eady already4 ,9 bo? cases x has to be rememb]$ t if ! diamet] ( ! :eel c be increas$ 9 great] proportion ?an ! dim5sions ( %ip or wagon1 ! proportional weight ( ! app>atus may be dim9i%$4 ,a :eel ( twice ! diamet]1 b ( ! same weight1 may h twice ! mom5t ( mom5tum1 & may !re=e be twice z effective4 ,i assume ! /resses 9 ! mat]ial to be ! same4 99 99 99 99 99 #aej ,,app5dix ,,ii4 ,page #bc2 note at l9e #c4 ,pr(4 ,osborne ,reynolds made ! int]e/+ rem>k 7,collect$ ,pap]s1 ,vol4 ii41 p4 #aed71 ,t if solid matt] _h c]ta9 k9ds ( int]nal motions1 su* z ! box has1 pe>s diff]+1 say1 f apples1 ! laws ( motion w\ld n h be5 discov]$2 if discov]$ = pe>s !y w\ld n h appli$ to apples4 ,page #ch2 note at l9e #h4 ,! motion ( a rifle bullet is !re=e "o ( precession ab\t ! tang5t to ! pa?4 ,! ma!matical solution is difficult1 b ,pr(4 ,gre5hill has satisfi$ himself ma!matically t air friction damps ! precession1 & causes ! axis ( ! %ot to get ne>] ! tang5tial direction1 s t fig4 #aj illu/rates :at w\ld occur 9 a vacuum1 b n 9 air4 ,x is probable t ?is /atem5t applies only to c]ta9 proportions ( l5g? to diamet]4 ,page #abi2 note at l9e #e4 ,_m m5 wond] h[ ! e!r c h ! enorm\s rigidity necess>y = light transmission1 & yet behave l a frictionless fluid4 ,"o way ( see+ h[ ?is may occur is to imag9e t :5 ord9>y matt] moves 9 ! e!r x only t5ds to produce motion ( translation ( ! e!r p>ticles1 & !re=e no resi/ance4 ,b any?+ su* z light1 :i* mu/ op]ate 9 turn+ axes ( rotat+ p>ts1 may enc\nt] enorm\s ela/ic resi/ance4 ,ri*>d ,clay ,sons1 ,limit$1 ,london & ,bungay4 99 99 99 99 99 ,,publications ,,( ,,! ,,society ,,= ,,promot+ ,,*ri/ian ,,k4 ,,! ,,romance ,,( ,,sci5ce4 ,small po/ #hvo1 clo? bo>ds4 ,,coal1 ,,& ,,:at ,,we ,,get ,,f ,,x4 ,by ,pr(essor ,r4 ,,meldola1 ,f4,r4,s41 ,f4,i4,c4 ,) sev]al ,illu/rations4 #bs4 #f;d4 ,,col\r ,,measurem5t ,,& ,,mixture4 ,by ,sir ,w4 ,,de ,w4 ,,abney1 ,k4,c4,b41 ,r4,e41 ,f4,r4,s4 ,num]\s ,illu/rations4 #bs4 #f;d4 ,,diseases ,,( ,,plants4 ,by ,pr(essor ,,m>%all ,,w>d4 ,num]\s ,illu/rations4 #bs4 #f;d4 ,,our ,,secret ,,fri5ds ,,& ,,foes4 ,by ,,p]cy ,,f>aday ,,frankl&1 ,ph4,d41 ,b4,sc4 7,lond471 ,f4,r4,s4 ,illu/rat$4 #cs4 ,,soap-,,bubbles1 ,,& ,,! ,,=ces ,,:i* ,,m\ld ,,!m4 ,by ,c4 ,v4 ,,boys1 ,a4,r4,s4,m41 ,f4,r4,s4 ,illu/rat$4 #bs4 #f;d4 ,,s\nd+ ,,! ,,ocean ,,( ,,air4 ,by ,a4 ,,lawr5ce ,,rot*1 ,s4,b41 ,a4,m4 ,num]\s ,illu/rations4 #bs4 #f;d4 ,,sp9n+ ,,tops4 ,by ,pr(essor ,j4 ,,p]ry1 ,m4,e4 ,) sev]al ,illu/rations4 #bs4 #f;d4 ,,! ,,mak+ ,,( ,,fl[]s4 ,by ! ,rev4 ,pr(essor ,,george ,,h5sl[1 ,m4,a41 ,f4,l4,s41 ,f4,g4,s4 ,) ,illu/rations4 #bs4 #f;d4 ,,! ,,/ory ,,( ,a ,,t9d]-,,box4 ,by ! late ,,*>les ,,meymott ,,tidy1 ,m4,b41 ,m4,s41 ,f4,c4,s4 ,num]\s ,illu/rations4 #bs4 ,,"t ,,& ,,tide4 ,a ,romance ( ! ,moon4 ,by ,sir ,,rob]t ,s4 ,,ball1 ,,ll4,d4 ,) ,illu/rations4 #bs4 #f;d4 ,,! ,,bir? ,,& ,,gr[? ,,( ,,worlds4 ,by ! late ,pr(essor ,,gre51 ,f4,r4,s4 ,) ,illu/rations4 #as4 ,,! ,,spla% ,,( ,a ,,drop4 ,by ,pr(essor ,a4 ,m4 ,,wor?+ton1 ,f4,r4,s4 ,num]\s ,illu/rations4 #as4 #f;d4 ,,! ,,ma*9]y ,,( ,,! ,,univ]se4 ,by ,pr(essor ,a4 ,e4 ,,dolbe>1 ,a4,b41 ,a4,m41 ,m4,e41 ,ph4,d4 ,illu/rat$4 #bs4 ,,! ,,new ,,/ate ,,( ,,matt]4 ,an ,address by ,pr(essor ,h4 ,,pellat4 ,translat$ by ,,edmund ,,mcclure1 ,m4,a4 #as4 ,,turb9es4 ,by ,eng9e]-,comm&] ,a4 ,e4 ,,tompk9s1 ,r4,n4 ,illu/rat$4 #cs4 #f;d4 99 99 99 99 99 ,,works ,,by ,,mrs4 ,,rundle ,,*>les1 ,,au?or ,,( ,! ,*ronicles ( ! ,s*o5b]g-,cotta ,family4 ,,! ,,beatitudes4 ,?\ghts = ,all ,sa9ts' ,day4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,by ,,! ,,my/]y ,,( ,,?y ,,holy ,,inc>nation4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,by ,,?y ,,cross ,,& ,,passion4 ,?\ghts on ! words spok5 ar\nd & on ! ,cross4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,by ,,?y ,,glori\s ,,resurrection ,,& ,,asc5sion4 ,ea/] ,?\ghts4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,by ,,! ,,com+ ,,( ,,! ,,holy ,,gho/4 ,?\ghts = ,:itsuntide4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,! ,,true ,,v9e4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,! ,,great ,,pray] ,,( ,,*ri/5dom4 ,?\ghts on ! ,"l's ,pray]4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,an ,,old ,,/ory ,,( ,,be?lehem4 ,"o l9k 9 ! great ,p$igree4 ,fcap4 #dto1 ) six plates1 beautifully pr9t$ 9 col\rs4 ,clo? bo>ds4 #bs4 ,,joan ,,! ,,maid1 ,deliv]] ( ,engl& & ,france4 ,demy #hvo4 ,clo? bo>ds4 #bs4 #f;d4 ,,songs1 ,,old ,,& ,,new4 ,demy #afmo4 ,clo? bo>ds4 #bs4 #f;d4 ,,ecce ,,ancilla ,,dom9i4 ,m>y ! ,"m ( our ,"l4 ,/udies 9 ! ,ideal ( ,womanhood4 ,po/ #hvo4 ,clo? bo>ds4 #as4 #f;d4 ,,ecce ,,homo1 ,,ecce ,,rex4 ,pages f ! ,/ory ( ! ,moral ,conque/s ( ,*ri/ianity4 ,cr[n #hvo4 ,clo? bo>ds4 #bs4 #f;d4 ,,?ree ,,m>tyrs ,,( ,,! ,,n9ete5? ,,c5tury4 ,/udies f ! ,lives ( ,gordon1 ,liv+/one1 & ,patteson4 ,cr[n #hvo4 ,clo? bo>ds4 #bs4 #f;d4 ,,m>tyrs ,,& ,,sa9ts ,,( ,,! ,,fir/ ,,twelve ,,c5turies4 ,/udies f ! ,lives ( ! ,black-lett] ,sa9ts ( ! ,engli% ,cal5d>4 ,cr[n #hvo4 ,clo? bo>ds4 #bs4 #f;d4 ,,aga9/ ,,! ,,/ream4 ,! ,/ory ( an ,h]oic ,age 9 ,engl&4 ,) eight page woodcuts4 ,cr[n #hvo4 ,clo? bo>ds4 #bs4 #f;d4 ,,conqu]+ ,,& ,,to ,,conqu]4 ,a ,/ory ( ,rome 9 ! days ( ,/4 ,j]ome4 ,illu/rat$4 ,cr[n #hvo4 ,clo? bo>ds4 #bs4 ,,attila ,,& ,,8 ,,conqu]ors4 ,a ,/ory ( ! days ( ,/4 ,patrick & ,/4 ,leo ! ,great4 ,cr[n #hvo4 ,clo? bo>ds4 #bs4 ,,te ,,deum ,,laudamus4 ,*ri/ian ,life 9 ,song4 ,clo? #bs4 #f;d4 ,,e>ly ,,*ri/ian ,,missions ,,( ,,irel&1 ,,scotl&1 ,,& ,,engl&4 ,cr[n #hvo4 ,clo? bo>ds4 #bs4 #f;d4 ,,laps$1 ,,n ,,lo/4 ,a ,/ory ( ,roman ,c>?age4 ,cr[n #hvo4 ,clo? bo>ds4 #bs4 ,,)9 ,,! ,,veil4 ,/udies 9 ! ,epi/le to ! ,hebrews4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,! ,,book ,,( ,,! ,,unveil+4 ,/udies 9 ! ,revelation ( ,/4 ,john ! ,div9e4 ,po/ #hvo4 ,clo? bo>ds4 #as4 ,,lady ,,augu/a ,,/anley4 ,rem9isc5ces4 #ahmo4 ,limp clo?4 #f;d4 ,,sket*es ,,( ,,! ,,wom5 ,,( ,,*ri/5dom4 ,cr[n #hvo4 #bs4 #f;d4 99 99 99 99 99 ,,conv]sion ,,( ,,! ,,we/4 ,,fcap4 #h,,vo1 ,,) ,,map1 ,,clo? ,,bo>ds1 #b,s4 ,,ea*4 ,,! ,,cont95tal ,,teutons1 by ! late ,v ,rev4 ,c4 ,,m]ivale4 ,,! ,,engli%1 by ! late ,rev4 ,g4 ,f4 ,,macle>1 ,d4,d4 ,,! ,,nor?m51 by ! late ,rev4 ,g4 ,f4 ,,macle>1 ,d4,d4 ,,! ,,slavs1 by ! late ,rev4 ,g4 ,f4 ,,macle>1 ,d4,d4 99 99 99 99 99 ,,e>ly ,,brita94 ,?is ,s]ies has = its aim ! pres5tation ( ,e>ly ,brita9 at great hi/oric p]iods4 ,ea* volume is ! "w ( an accr$it$ speciali/1 & ! :ole gives ! result ( rec5t critical exam9ations ( our ,e>ly ,records4 ,,anglo-,,saxon ,,brita94 ,by ! late ,,grant ,,all54 ,) ,map4 #bs4 #f;d4 ,,celtic ,,brita94 ,by ,pr(essor ,,rhys4 ,) two ,maps4 #cs4 ,,norman ,,brita94 ,by ! ,rev4 ,w4 ,,hunt4 ,) ,map4 #bs4 ,,po/-,,norman ,,brita94 ,by ,,h5ry ,g4 ,,hewlett4 ,) ,map4 #cs4 ,,roman ,,brita94 ,by ! ,rev4 ,e4 ,,conybe>e4 ,) ,map4 #cs4 #f;d4 ,,roman ,,roads ,,9 ,,brita94 ,by ,,?omas ,,codr+ton1 ,m4 ,in/4 ,c4,e41 ,f4,g4,s4 ,) ,maps4 ,second ,edition1 revis$4 #es4 ,,sc&9avian ,,brita94 ,by ,w4 ,g4 ,,coll+wood1 ,m4,a41 ,f4,s4,a4 ,) ,*apt]s ,introductory to ! subject by ! late ,pr(essor ,f4 ,,york ,,p[ell1 ,m4,a4 #cs4 #f;d4 99 99 99 99 99 ,,! ,,dawn ,,( ,,european ,,lit]ature4 ,a set ( ,works design$ to pres5t ! *ief races ( ,europe z !y em]ge out ( pre-hi/oric d>kness into ! light furni%$ by _! e>lie/ record$ words4 ,,po/ #h,,vo1 ,,clo? ,,bo>ds1 #b,s4 #f;,d4 ,,ea*4 ,,anglo-,,saxon ,,lit]ature4 ,by ! ,rev4 ,pr(essor ,,e>le4 ,,fr5* ,,lit]ature4 ,by ! late ,,gu/ave ,,masson1 ,b4,a4 ,,slavonic ,,lit]ature4 ,by ,w4 ,r4 ,,morfill1 ,m4,a4 ,,! ,,greek ,,epic4 ,by ,,george ,c4 ,w4 ,,w>r1 ,m4,a4 #cs4 99 99 99 99 99 ,,! ,,fa!rs ,,= ,,engli% ,,read]s4 ,a ,s]ies ( ,monograms on ! ,*ief ,fa!rs ( ! ,*ur*1 ! ,fa!rs select$ be+ c5tres ( influ5ce at important p]iods ( ,*ur* ,hi/ory1 & 9 important sph]es ( action4 ,,fcap4 #h,,vo1 ,,clo? ,,bo>ds1 #b,s4 ,,ea*4 ,,boniface4 ,by ! ,rev4 ,canon ,,gregory ,,smi?4 #as4 #f;d4 ,,clem5t ,,( ,,alex&ria4 ,by ! ,rev4 ,f4 ,r4 ,,montgom]y ,,hit*cock1 ,b4,d4 #cs4 ,,leo ,,! ,,great4 ,by ! ,"r ,rev4 ,c4 ,,gore1 ,d4,d4 ,,gregory ,,! ,,great4 ,by ! late ,rev4 ,j4 ,,b>mby1 ,b4,d4 ,,sa9t ,,ambrose3 8 ,life1 ,times1 & ,tea*+4 ,by ! ,rev4 ,r4 ,,?ornton1 ,d4,d4 ,,sa9t ,,a?anasius3 8 ,life & ,times4 ,by ! ,rev4 ,r4 ,,:el] ,,bu%4 #bs4 #f;d4 ,,sa9t ,,augu/9e4 ,by ! late ,rev4 ,e4 ,l4 ,,cutts1 ,d4,d4 ,,sa9t ,,basil ,,! ,,great4 ,by ! ,rev4 ,r4 ,t4 ,,smi?1 ,b4,d4 ,,sa9t ,,b]n>d3 ,abbot ( ,clairvaux1 ,a4,d4 #ajia-aaec4 ,by ,rev4 ,s4 ,j4 ,,eales4 #bs4 #f;d4 ,,sa9t ,,j]ome4 ,by ! late ,rev4 ,,edw>d ,l4 ,,cutts1 ,d4,d4 ,,sa9t ,,hil>y ,,( ,,poiti]s1 ,,& ,,sa9t ,,m>t9 ,,( ,,t\rs4 ,by ! ,rev4 ,j4 ,,gibson ,,caz5ove1 ,d4,d4 ,,sa9t ,,john ,,( ,,damascus4 ,by ! ,rev4 ,j4 ,h4 ,,lupton4 ,,sa9t ,,patrick3 8 ,life & ,tea*+4 ,by ! ,rev4 ,e4 ,j4 ,,newell1 ,m4,a4 #bs4 #f;d4 ,,synesius ,,( ,,cyr5e1 ,philosoph] & ,bi%op4 ,by ,,alice ,,g>dn]4 ,,! ,,apo/olic ,,fa!rs4 ,by ! ,rev4 ,canon ,,scott ,,holl&4 ,,! ,,def5d]s ,,( ,,! ,,fai?2 or1 ,! ,*ri/ian ,apologi/s ( ! ,second & ,?ird ,c5turies4 ,by ! ,rev4 ,f4 ,,watson1 ,d4,d4 ,,! ,,v5]able ,,b$e4 ,by ! ,"r ,rev4 ,g4 ,f4 ,,br[ne4 99 99 99 99 99 ,,! ,,hi/ory ,,( ,,! ,,anci5t ,,peoples ,,( ,,! ,,classic ,,ea/4 ,by ,pr(essor ,,masp]o4 ,edit$ by ! ,rev4 ,pr(essor ,,sayce4 ,translat$ by ,m4 ,l4 ,,mcclure4 ,ea* volume conta9s ,maps1 col\r$ ,plates1 & num]\s o!r ,illu/rations4 ,,demy #d,,to1 ,,clo?1 ,,bevell$ ,,bo>ds4 ,volume ,i4 ,,! ,,dawn ,,( ,,civilization3 ,,egypt ,,& ,,*aldaea4 ,f\r? ,edition4 #bds42 half-morocco1 #dhs4 ,volume ,,ii4 ,,! ,,/ruggle ,,( ,,! ,,nations3 ,,egypt1 ,,syria1 ,,& ,,assyria4 #bes42 half-morocco1 #ejs4 ,volume ,,iii4 ,,! ,,pass+ ,,( ,,! ,,empires1 #hej ,b4,c4-#ccj ,b4,c4 #bes42 half-morocco1 #ejs4 99 99 99 99 99 ,,anci5t ,,hi/ory ,,f ,,! ,,monum5ts4 ,,fcap4 #h,,vo1 ,,clo? ,,bo>ds1 #b,s4 ,,ea*4 ,,assyria1 ,,f ,,! ,,e>lie/ ,,times ,,to ,,! ,,fall ,,( ,,n9eveh4 ,by ! late ,,george ,,smi?1 ( ! ,briti% ,museum4 ,a ,new & ,revis$ ,edition1 by ! ,rev4 ,pr(essor ,,sayce4 ,,s9ai1 ,,f ,,! ,,f\r? ,,egyptian ,,dyna/y ,,to ,,! ,,pres5t ,,day4 ,by ! late ,,h5ry ,s4 ,,palm]4 ,a ,new ,edition1 revis$ ?r\gh\t by ! ,rev4 ,pr(essor ,,sayce4 ,) ,map4 ,,babylonia 7,,! ,,hi/ory ,,(74 ,by ! late ,,george ,,smi?4 ,edit$ & br\ght up to date by ! ,rev4 ,pr(essor ,,sayce4 ,,p]sia1 ,,f ,,! ,,e>lie/ ,,p]iod ,,to ,,! ,,arab ,,conque/4 ,by ! late ,w4 ,s4 ,w4 ,,vaux1 ,m4,a4 ,a ,new & ,revis$ ,edition1 by ! ,rev4 ,pr(essor ,,sayce4 99 99 99 99 99 ,,! ,,high] ,,criticism ,,& ,,! ,,v]dict ,,( ,,! ,,monum5ts4 ,by ! ,rev4 ,pr(essor ,a4 ,h4 ,,sayce4 ,demy #hvo4 ,buckram1 bevell$ bo>ds1 #es4 99 99 99 99 99 ,,*ief ,,anci5t ,,philosophies4 ,?is ,s]ies deals ) ! *ief sy/ems ( ,anci5t ,?\ght1 n m]ely z dry matt]s ( ,hi/ory1 b z hav+ a be>+ on ,mod]n ,speculation4 ,,fcap4 #h,,vo1 ,,clo? ,,bo>ds1 #b,s4 #f;,d4 ,,ea*4 ,,neoplatonism4 ,by ! ,rev4 ,c4 ,,bigg1 ,d4,d4 #cs4 ,,platonism4 ,by ! ,rev4 ,,?omas ,b4 ,,/rong1 ,m4,a4 #cs4 ,,epicureanism4 ,by ! late ,pr(essor ,,william ,,wallace4 ,,/oicism4 ,by ,rev4 ,w4 ,w4 ,,capes1 ,fell[ ( ,h]t=d ,college4 ,,ari/otelianism4 ,,! ,,e?ics ,,( ,,ari/otle4 ,by ! ,rev4 ,i4 ,,gregory ,,smi?4 ,! ,logical ,treatises1 ! ,metaphysics1 ! ,psy*ology1 ! ,politics4 ,by ! ,rev4 ,w4 ,,grundy4 99 99 99 99 99 ,,diocesan ,,hi/ories4 ,?is ,s]ies furni%es a p]fect ,libr>y ( ,engli% ,ecclesia/ical ,hi/ory4 ,ea* volume is complete 9 itself1 & ! possibility ( repetition has be5 c>efully gu>d$ aga9/4 ,,fcap4 #h,,vo1 ,,) ,,map1 ,,clo? ,,bo>ds4 ,,ba? ,,& ,,wells4 ,by ! ,rev4 ,w4 ,,hunt4 #bs4 #f;d4 ,,cant]bury4 ,by ! late ,rev4 ,r4 ,c4 ,,j5k9s4 #cs4 #f;d4 ,,c>lisle4 ,by ! late ,,ri*>d ,s4 ,,f]guson4 #bs4 #f;d4 ,,*e/]4 ,by ! ,rev4 ,,rup]t ,h4 ,,morris4 ,) ,map4 #cs4 ,,*i*e/]4 ,by ! late ,v ,rev4 ,w4 ,r4 ,w4 ,,/eph5s4 ,) ,map & ,plan4 #bs4 #f;d4 ,,durham4 ,by ,rev4 ,j4 ,l4 ,,l[4 ,) ,map & ,plan4 #bs4 ,,h]e=d4 ,by ! late ,rev4 ,canon ,,phillpott4 #cs4 ,,li*field4 ,by ! ,rev4 ,w4 ,,b]es=d4 #bs4 #f;d4 ,,l9coln4 ,by ! late ,rev4 ,canon ,e4 ,,v5ables1 & ! late ,v54 ,,ar*deacon ,,p]ry4 ,) ,map4 #ds4 ,,ll&aff4 ,by ! ,rev4 ,e4 ,j4 ,,newell1 ,m4,a4 ,) ,map4 #cs4 #f;d4 ,,norwi*4 ,by ! ,rev4 ,a4 ,,jessopp1 ,d4,d4 #bs4 #f;d4 ,,ox=d4 ,by ! ,rev4 ,e4 ,,m>%all4 #bs4 #f;d4 ,,pet]bor\gh4 ,by ! ,rev4 ,g4 ,a4 ,,poole1 ,m4,a4 #bs4 #f;d4 ,,ro*e/]4 ,by ! ,rev4 ,a4 ,j4 ,,pe>man4 ,) ,map4 #ds4 ,,salisbury4 ,by ! ,rev4 ,w4 ,h4 ,,jones4 ,) ,map4 #bs4 #f;d4 ,,sodor ,,& ,,man4 ,by ,a4 ,w4 ,,moore1 ,m4,a4 #cs4 ,,/4 ,,asaph4 ,by ! ,v54 ,ar*deacon ,,?omas4 #bs4 ,,/4 ,,david',s4 ,by ! ,rev4 ,canon ,,bevan4 ,) ,map4 #bs4 #f;d4 ,,w9*e/]4 ,by ! ,rev4 ,w4 ,,b5ham1 ,b4,d4 #cs4 ,,worce/]4 ,by ! ,rev4 ,i4 ,,gregory ,,smi? & ,rev4 ,,phipps ,,onsl[4 #cs4 #f;d4 ,,york4 ,by ! ,rev4 ,canon ,,ornsby1 ,m4,a41 ,f4,s4,a4 #cs4 #f;d4 99 99 99 99 99 ,,e>ly ,,*ur* ,,classics4 ,,small ,,po/ #h,,vo1 ,,clo? ,,bo>ds4 ,a ,,homily ,,( ,,clem5t ,,( ,,alex&ria1 entitl$1 ,:o is ! ,ri* ,man t is ,be+ ,sav$8 ,by ,rev4 ,p4 ,,mordaunt ,,b>n>d4 #as4 ,,bi%op ,,s>apion',s ,,pray]-,,book3 ,an ,egyptian ,pontifical dat$ probably ab\t #cej-cef ,a4,d4 ,translat$ f ! ,edition ( ,dr4 ,g4 ,,wobb]m94 ,) ,introduction1 ,notes1 & ,indices1 by ! ,"r ,rev4 ,,john ,,wordswor?1 ,d4,d4 #as4 #f;d4 ,,orig5 ,,! ,,tea*]4 ,be+ ! ,address ( ,gregory ! ,wond]-,work] to ,orig51 toge!r ) ,orig5's ,lett] to ,gregory4 ,translat$1 ) an ,introduction & ,notes1 by ! ,rev4 ,w4 ,,metcalfe1 ,d4,d4 #as4 #f;d4 ,,/4 ,,cyprian ,,on ,,! ,,"l',s ,,pray]4 ,an ,engli% ,translation1 ) ,introduction by ! ,v54 ,ar*deacon ,t4 ,h4 ,,b9dley1 ,d4,d4 #as4 #f;d4 ,,/4 ,,polyc>p1 ,,bi%op ,,( ,,smyrna4 ,by ! late ,rev4 ,,blomfield ,,jackson1 ,m4,a4 #as4 ,,! ,,doctr9e ,,( ,,! ,,twelve ,,apo/les4 ,translat$ into ,engli%1 ) ,introduction & ,notes1 by ! ,rev4 ,,*>les ,,bigg1 ,d4,d4 #as4 ,,! ,,epi/le ,,( ,,/4 ,,clem5t1 ,,bi%op ,,( ,,rome4 ,by ! ,rev4 ,,john ,a4 ,f4 ,,gregg1 ,m4,a4 #as4 ,,/4 ,,augu/9e',s ,,treatise ,,on ,,! ,,city ,,( ,,god4 ,by ,rev4 ,f4 ,r4 ,m4 ,,hit*cock1 ,m4,a41 ,b4,d4 #as4 #f;d4 ,,/4 ,,*ryso/om ,,on ,,! ,,prie/hood4 ,by ! ,rev4 ,t4 ,,all5 ,,moxom1 ,m4,a4 #bs4 ,,! ,,apo/olical ,,con/itutions ,,& ,,cognate ,,docum5ts1 ) special ref]5ce to _! ,liturgical ,elem5ts4 ,by ! ,rev4 ,,de ,,lacy ,o',,le>y1 ,m4,a4 #as4 ,,! ,,epi/le ,,( ,,diognetus4 ,by ! ,rev4 ,l4 ,b4 ,,rad=d1 ,m4,a4 #as4 #f;d4 ,,! ,,epi/le ,,( ,,! ,,galilean ,,*ur*es3 ,lugdunum & ,vi5ne4 ,) an ,app5dix conta9+ ,t]tullian's ,address to ,m>tyrs & ! ,passion ( ,/4 ,p]petua4 ,translat$1 ) ,introduction & ,notes1 by ,v54 ,ar*deacon ,t4 ,h4 ,,b9dley1 ,d4,d4 #as4 ,,! ,,epi/les ,,( ,,/4 ,,ignatius1 ,,bi%op ,,( ,,antio*4 ,by ,rev4 ,j4 ,h4 ,,srawley1 ,m4,a4 ,9 two volumes4 #as4 ea*4 ,,! ,,liturgy ,,( ,,! ,,eigh? ,,book ,,( ,,! ,,apo/olic ,,con/itutions1 commonly call$ ! ,clem5t9e ,liturgy4 ,translat$ into ,engli%1 ) ,introduction & ,notes1 by ,rev4 ,r4 ,h4 ,,cresswell1 ,m4,a4 #as4 #f;d4 ,,! ,,%eph]d ,,( ,,h]mas4 ,by ! late ,rev4 ,c4 ,,taylor1 ,d4,d4 ,vols4 ,i4 & ,,ii4 #bs4 ea*4 99 99 99 99 99 ,,non-,,*ri/ian ,,religi\s ,,sy/ems4 ,fcap4 #hvo1 clo? bo>ds1 #bs4 #f;d4 ea*4 ,,buddhism3 be+ a sket* ( ! ,life & ,tea*+s ( ,gautama1 ! ,buddha4 ,by ,t4 ,w4 ,,rhys ,,davids1 ,m4,a4 ,) ,map4 ,,buddhism ,,9 ,,*9a4 ,by ! ,rev4 ,s4 ,,beal4 ,) ,map4 ,,confucianism ,,& ,,ta\ism4 ,by ,sir ,,rob]t ,k4 ,,d\glas1 ( ! ,briti% ,museum4 ,) ,map4 ,,h9duism4 ,by ! late ,sir ,m4 ,,moni]-,,williams1 ,m4,a41 ,d4,c4,l4 ,) ,map4 ,,islam ,,& ,,its ,,f\nd]4 ,by ,j4 ,w4 ,h4 ,,/ob>t4 ,) ,map4 ,,islam ,,z ,a ,,mission>y ,,religion4 ,by ,,*>les ,r4 ,,ha9es4 #bs4 ,,! ,,coran3 its ,composition & ,tea*+1 & ! ,te/imony x be>s to ! ,holy ,scriptures4 ,by ,,sir ,,william ,,muir1 ,k4,c4,s4,i4 ,,! ,,hi/orical ,,developm5t ,,( ,,! ,,quran4 ,by ! ,rev4 ,,edw>d ,,sell1 ,d4,d41 ,m4,r4,a4,s4 ,,! ,,religion ,,( ,,! ,,cresc5t1 ,,or ,,islam3 its ,/r5g?1 its ,weakness1 its ,orig91 its ,influ5ce4 ,by ! ,rev4 ,w4 ,,/4 ,,clair ,,tisdall1 ,m4,a4 #ds4 ,,/udies ,,( ,,non-,,*ri/ian ,,religions4 ,by ,,eliot ,,h[>d4 99 99 99 99 99 ,,colonial ,,*ur* ,,hi/ories4 ,fcap4 #hvo1 ) ,map1 clo? bo>ds4 ,,diocese ,,( ,,mack5zie ,,riv]1 by ! ,"r ,rev4 ,w4 ,c4 ,,bompas1 ,d4,d41 ,bi%op ( ! ,diocese4 #bs4 ,,new ,,zeal&1 by ! late ,v ,rev4 ,,h5ry ,,jacobs1 ,d4,d41 ,dean ( ,*ri/*ur*4 ,conta9+ ! ,dioceses ( ,auckl&1 ,*ri/*ur*1 ,dun$91 ,nelson1 ,waiapu1 ,well+ton & ,melanesia4 #es4 ,,hi/ory ,,( ,,! ,,*ur* ,,9 ,,ea/]n ,,canada ,,& ,,newf\ndl&1 by ! ,rev4 ,j4 ,,langtry4 #cs4 ,,! ,,*ur* ,,9 ,,! ,,we/ ,,indies1 by ! ,rev4 ,a4 ,,caldecott1 ,b4,d4 #cs4 #f;d4 ,,! ,,/ory ,,( ,,! ,,au/ralian ,,*ur*1 by ! ,rev4 ,e4 ,,symonds4 #bs4 #f;d4 99 99 99 99 99 ,,london3 ,,nor?umb]l& ,,av5ue1 ,w4,c4 #dc ,,que5 ,,victoria ,,/reet1 ,e4,c4 99 99 99 99 99 ,notes #a ,! ,op]atives' ,lecture is always well adv]tis$ 9 ! /reets be=eh& by l>ge po/]s4 #b ,bulw] ,lytton's ,com+ ,race4 #c ,! glass vessel ought to be broad] 9 comp>ison ) its height4 #d ,9 #agdf ,b5jam9 ,rob9s taught ! pr9ciples ( rifl+ z we "k !m n[4 ,he %[$ t ! sp9 ( ! r\nd bullet 0 ! mo/ important ?+ to consid]4 ,he %[$ t ev5 ! b5t b>rel ( a gun did n deflect ! bullet to any?+ l ! ext5t t ! sp9 ( ! bullet made x deflect 9 ! opposite direction4 #e ,,note4--,9 ,fig4 #af ! axis is %[n incl9$1 b1 only t x w\ld h be5 m tr\blesome to illu/rate1 ,i %\ld h pref]r$ to %[ ! precession occurr+ :5 ! axis keeps horizontal4 #f ,:5 ?is lecture conta9+ ! above /atem5t 0 9 ! h&s ( ! pr9t]s1 ,i 0 direct$ by ,pr(4 ,fitzg]ald to ! late ,pr(4 ,jellet's ,treatise on ! ,!ory ( ,friction1 publi%$ 9 #ahgb1 & !re at page #ah ,i f\nd ! ma!matical explanation ( ! ris+ ( a top4 #g ,r\ghly1 ! ,in]tia or ,mass ( a body expresses its resi/ance to *ange ( m]e translational velocity1 :]eas1 ! ,mom5t ( ,in]tia ( a body expresses its resi/ance to *ange ( rotational velocity4 #h ,x is a v unlikely1 & c]ta9ly absurd-look+1 hypo!sis1 b x seems t x is n contradict$ by any fact 9 spectrum analysis1 or ev5 by any probable !ory ( ! con/itution ( ! int]/ell> e!r1 t ! />s are m]ely images ( our own sun =m$ by reflection at ! b\nd>ies ( ! e!r4 #i ,sir ,william ,?omson has p]=m$ ?is4 #aj ,x mu/ be rememb]$ t 9 "o case ,i speak ( ! true nor?1 & 9 ! o!r ( ! magnetic nor?4 #aa ,rotat+ a l>ge mass ( iron rapidly 9 "o direction & !n 9 ! o!r 9 ! neighb\rhood ( a delicately-susp5d$ magnetic ne$le1 well protect$ f air curr5ts1 ought1 ,i ?9k1 to give rise to magnetic ph5om5a ( v great int]e/ 9 ! !ory ( magnetism4 ,i h hi!rto fail$ to obta9 any trace ( magnetic action1 b ,i attribute my failure to ! comp>atively sl[ spe$ ( rotation :i* ,i h employ$1 & to ! want ( delicacy ( my magnetomet]4 #ab ,i _h appli$ = a pat5t = ?is sy/em ( signall+ "s "t be=e ! above words 7 spok51 b al?\gh x 0 valid ,i all[$ x to lapse 9 pure %ame t ,i %\ld h s unblu%+ly pat5t$ ! use ( ! "w ( ,fitzg]ald1 ,h]tz1 & ,lodge4 #ac ,h[ to see by electricity is p]fectly well kn[n1 b no ri* man seems will+ to sacrifice ! few ?\s&s ( p\nds :i* are necess>y = mak+ ! app>atus4 ,if ,i c\ld sp>e ! money & "t ,i w\ld sp5d !m 9 do+ ?is ?+--t is1 ,i ?9k s--b x is j possible t if ,i c\ld af=d to ?r[ away ?ree ?\s& p\nds1 ,i might feel great] pleasure 9 ! gr[? ( a great =tune ?an 9 any o!r natural process4 #ad ,probably fir/ describ$ by ,mr4 ,br5nan4 #ae ,! weight ( ,mr4 ,br5nan's load$ wagon is #cac lb41 includ+ gyro/ats & /orage cells4 ,8 two :eels weigh #ac lb4 ,if made ( nickel /eel & run at _! highe/ safe spe$ !y w\ld weigh mu* less4 99 99 99 99 99 ,*anges made aga9/ pr9t$ orig9al4 ,page #ia4 all t we %\ld h to take into acc\nt3 duplicat$ 't' 9 orig9al4 ,page #aej4 appli$ to apples3 'appli$ to applies' 9 orig9al4 ,adv]tisem5ts4 ,p]sia 444 by ! ,rev4 ,pr(essor ,sayce3 ',pr(esssor' 9 orig9al4